BR 45(1)

Admiralty
Manual of Navigation

Volume I
Revised 1987
Reprinted in CD / loose leaf format 2003 |
Superseding the edition of 1964

March 1987 By Command of the Defence Council

MINISTRY OF DEFENCE
Directorate of Naval Warfare
D/DNW/102/3/14/2

© Crown copyright 1987 and 2003 |

First published 1956
New edition 1987
Reprinted in CD / A4 Loose Leaf Format 2003 |
| Alterations Made During 2003 Reprint
| The 2003 reprint is a faithful representation of the original 1987 version and retains the same
| pagination / page numbering, although it is now published as a CD and available in A4 loose-leaf
| format instead of in hard bound Imperial size. The following minor alterations have also been
| made:
| • Where later volumes of the BR 45 series have superseded original information
| in this volume, the appropriate pages are watermarked “See BR 45 Vol ..” .
| • Graphic images have been updated to modern versions, while retaining the
| same purpose and information as the original.
| • Preface pages have been updated to reflect current information about this book
| and about other books in the BR 45 series. Such alterations are identified by
| sidelining.
| • Certain terms and abbreviations have been updated to the current usage. Such
| alterations are identified by sidelining.
| • Where appropriate, diagrams have been corrected to show the standard
| conventions for arrowheads in chartwork. Such alterations are identified by
| sidelining.
|
 iii

Preface |
|
The Admiralty Manual of Navigation (BR 45) consists of seven volumes: |
Volume 1 is a hard bound book (also supplied in A4 loose leaf from 2003), covering General |
Navigation and Pilotage (Position and Direction, Geodesy, Projections, Charts and Publications, |
Chartwork, Fixing, Tides and Tidal Streams, Coastal Navigation, Visual and Blind Pilotage, |
Navigational Errors, Relative Velocity, Elementary Surveys and Bridge Organisation). This |
book is available to the public from The Stationary Office. |
Volume 2 is a loose-leaf A4 book covering Astro Navigation (including Time). Chapters 1 to |
3 cover the syllabus for officers studying for the Royal Navy ‘Navigational Watch Certificate’ |
(NWC) and for the Royal Navy ‘n’ Course. (The NWC is equivalent to the certificate awarded |
by the Maritime & Coastguard Agency (MCA) to OOWs in the Merchant Service under the |
international Standardisation of Training, Certification and Watchkeeping (STCW) agreements.) |
The remainder of the book covers the detailed theory of astro-navigation for officers studying |
for the Royal Navy Specialist ‘N’ Course, but may also be of interest to ‘n’ level officers who |
wish to research the subject in greater detail. Volume 2 is not available to the general public, |
although it may be released for sale in the future. |
Volume 3 is a protectively marked loose-leaf A4 book, covering navigation equipment and |
systems (Radio Aids, Satellite Navigation, Direction Finding, Navigational Instruments, Logs |
and Echo Sounders, Gyros and Magnetic Compasses, Inertial Navigation Systems, Magnetic |
Compasses and De-Gausing, Automated Navigation and Radar Plotting Systems, Electronic |
Chart equipment). Volume 3 is not available to the general public. |
Volume 4 is a protectively marked loose-leaf A4 book covering conduct and operational methods |
at sea (Navigational Command and Conduct of RN ships, passage planning and routeing, and |
operational navigation techniques that are of particular concern to the RN). Assistance |
(Lifesaving) and Salvage are also included. Volume 4 is not available to the general public. |
Volume 5 is a loose-leaf A4 book containing exercises in navigational calculations (Tides and |
Tidal Streams, Astro-Navigation, Great Circles and Rhumb Lines, Time Zones, and Relative |
Velocity). It also provides extracts from most of the tables necessary to undertake the exercise |
calculations. Volume 5 (Supplement) provides worked answers. Volumes 5 and 5 (Supplement) |
are not available to the general public, although they may be released for sale in the future. |
Volume 6 is supplied in three, loose-leaf A4 binders: the non-protectively marked Binder 1 |
covering generic principles of shiphandling (Propulsion of RN ships, Handling Ships in Narrow |
Waters Manoeuvring and Handling Ships in Company, Replenishment, Towing, Shiphandling |
in Heavy Weather and Ice), and the protectively marked Binders 2 and 3 covering all aspects of |
class-specific Shiphandling Characteristics of RN Ships / Submarines and RFAs). Turning data |
quoted in Volume 6 is approximate and intended only for overview purposes. Volume 6 is |
not available to the general public, although Binder 1 may be released for sale in the future. |
Volume 7 is a protectively marked loose-leaf A4 book covering the management of a chart outfit |
(Upkeep, Navigational Warnings, Chronometers and Watches, Portable and Fixed Navigational |
Equipment, and Guidance for the Commanding Officer / Navigating Officer). Volume 7 is not |
available to the general public. |
|
Note. Terms appearing in italics in newer books are defined in the ‘Glossary’ of each book. |
 iv

Acknowledgements
Thanks are due to the following, who have provided advice and assistance in the production of
Volume 1:

The Navigation Section, School of Maritime Operations, HMS Mercury.

Britannia Royal Naval College, Dartmouth.
The Hydrographic Department, Ministry of Defence.
The Admiralty Compass Observatory, Slough.
The Naval Operational Command Systems Group, ARE Portsdown.
The RN Hydrographic School, HMS Drake.
The Directorate of Naval Analysis, Ministry of Defence.
The Marine Division of the Department of Transport.
The Royal Institute of Navigation.
The Nautical Institute.
The Honourable Company of Master Mariners.
The General Council of British Shipping (GCBS) and, through the GCBS, the Deep Sea
Cargo Division of The Peninsular and Oriental Steam Navigation Company and Furness
Withy (Shipping) Ltd.
The College of Maritime Studies, Warsash, Southampton.
The Department of Maritime Studies, City of London Polytechnic.
The Department of Maritime Studies, Liverpool Polytechnic.
The Department of Maritime Science, Plymouth Polytechnic.
The Department of Nautical Science, South Tyneside College.

Acknowledgements are also due to the Department of Transport, Marine Division, for
permission to use the extracts from Merchant Shipping Notices M854 and M1102, and from
Statutory Instrument 1982 No. 1699, Merchant Shipping (Certification and Watchkeeping)
Regulations 1982; and to the International Chamber of Shipping, for permission to use the
extracts from the ICS Bridge Procedures Guide (1977).

| Thanks are due to the UK Hydrographic Office (UKHO) for their permission and assistance
| in reproducing data contained in this volume. This data has been derived from material
| published by the UK Hydrographic Office and further reproduction is not permitted without the
| express prior written permission of CINCFLEET / PFSA and UKHO. Applications for
| permission should be addressed to CINCFLEET / PFSA, at the Fleet Staff Author’s Group, Pepys
| Building, HMS COLLINGWOOD, Fareham, Hants PO14 1AS and also to the Copyright
| Manager at the UKHO, Admiralty Way, Taunton, TA1 2DN, United Kingdom.
 v

Contents

Page

Preface v

Chapter
1 Position and Direction on the Earth’s Surface 1

POSITION ON THE EARTH’S SURFACE. The Earth ) latitude and longitude ) 1

difference of latitude, longitude ) calculation of d.lat and d.long ) the sea mile ) the
length of the sea mile ) the geographical mile ) the international nautical mile ) the
statute mile ) the knot ) linear measurement of latitude and longitude ) the Earth as
a sphere
DIRECTION ON THE EARTH’S SURFACE. True direction ) true north ) true 10
bearing ) position of close objects ) true course
The compass. The gyro-compass ) the magnetic compass ) the magnetic meridian ) 12
magnetic north ) variation ) deviation, compass north ) magnetic and compass
courses and bearings ) graduation of older magnetic compass cards
Practical application of compass errors. Conversion of magnetic and compass 17
courses and bearings to true ) to find the compass course from the true course )
checking the deviation
Relative bearings 21
2 The Sailings (1) 23
The rhumb line ) departure 23
PARALLEL SAILING 24
PLANE SAILING Proof of the plane sailing formulae 25
MEAN AND CORRECTED MEAN LATITUDE SAILING 27
TRAVERSE SAILING 30
MERCATOR SAILING 33
SPHERICAL GREAT-CIRCLE AND COMPOSITE SAILING The great circle ) 33
great-circle distance and bearing ) great-circle sailing ) the vertex ) the composite
track
Solution of spherical great-circle problems. The cosine method ) a great-circle 37
distance ) the initial course
vi

Chapter Page

3 An Introduction to Geodesy 41
DEFINITIONS AND FORMULAE The oblate spheroid ) the flattening of the 41
Earth ) the eccentricity ) geodetic and geocentric latitudes ) the parametric latitude )
the length of one minute of latitude ) the length of one minute of longitude ) the
geodesic ) geodetic datum
THE DETERMINATION OF POSITION ON THE SPHEROID The geoid ) 45
calculation of the position ) geodetic latitude and longitude ) reference datums and
spheroids ) satellite geodesy ) world geodetic systems

4 Projections and Grids 51

GENERAL The ‘Flat Earth’ ) orthomorphism or conformality ) derivation of 51
projections of a sphere ) projections of the spheroid ) Lambert’s conical
orthomorphic projection ) Mercator’s projection ) transverse Mercator projection )
skew orthomorphic projection ) gnomonic projection ) stereographic projection )
polyconic projection
MERCATOR PROJECTION/CHART Principle of the Mercator projection ) 61
longitude scale on a Mercator chart ) graduation of charts and the measurement of
distance ) meridional parts ) to find the meridional parts of any latitude ) difference
of meridional parts ) property of orthomorphism ) to construct a Mercator chart of
the world ) to construct a Mercator chart on a larger scale ) great-circle tracks on a
Mercator chart
TRANSVERSE MERCATOR PROJECTION/CHART 71
GNOMONIC PROJECTION/CHART To transfer a great-circle track to a Mercator 73
chart ) practical use of gnomonic charts
GRIDS Grid convergence ) grids constructed on the transverse Mercator projection 77
- transferring grid positions

5 The Sailings (2) 85

MERCATOR SAILING ON THE SPHERE To find the course and distance from 85
the meridional parts
THE VERTEX AND THE COMPOSITE TRACK IN SPHERICAL GREAT- 88
CIRCLE SAILING To find the position of the vertex of a great circle ) to plot a
great-circle track on a Mercator chart ) calculating the composite track
SPHEROIDAL RHUMB-LINE SAILING 93
To find the rhumb-line course and distance. The length of the meridional arc ) 94
meridional parts for the spheroid ) calculation of the rhumb-line course and distance
SPHEROIDAL GREAT-CIRCLE SAILING Calculation of the initial course and 97
distance ) a comparison of distances
 vii

Chapter Page
6 Charts and Chart Outfits 101
GENERAL REMARKS ON CHARTS Charting policy ) description and coverage 102
) metrication ) geographical datum ) International charts ) latticed charts ) IALA
Maritime Buoyage System
NAVIGATIONAL CHARTS Charts drawn on the Mercator projection ) charts 106
drawn on the gnomonic projection ) charts drawn on the transverse Mercator
projection ) harbour plans ) the plotting chart ) distortion of the printed chart )
information shown on charts ) colours used on charts ) to describe a particular copy
of a chart ) distinguishing a well surveyed chart ) the reliability of charts ) hints on
using charts
THE ARRANGEMENT OF CHARTS The chart folio ) the Hydrographic 121
Supplies Handbook ) the Chart Correction Log and Folio Index ) the Catalogue of
Admiralty Charts and Other Hydrographic Publications ) classified charts
OTHER TYPES OF CHARTS AND DIAGRAMS Astronomical charts and 123
diagrams ) co-tidal charts ) gnomonic charts ) magnetic charts ) Routeing charts )
passage planning charts ) ships’ boats’ charts ) instructional charts and diagrams )
ocean sounding charts ) practice and exercise area (PEXA) charts ) meteorological
working charts ) miscellaneous folios
UPKEEP OF CHART OUTFITS First supply ) state of correction upon supply ) 126
action on receipt of the chart outfit action on receipt of a newly published chart or a
New Edition ) action on transfer of chart folios ) subsequent upkeep of chart outfits
) disposal of chart outfits ) chronometers and watches

NAVIGATIONAL WARNINGS 130

Admiralty Notices to Mariners. Weekly Editions ) Cumulative List of Admiralty 130
Notices to Mariners ) Annual Summary of Admiralty Notices to Mariners ) Fleet
Notices to Mariners ) Small Craft Editions of Notices to Mariners ) distribution of
Notices to HM Ships
Radio navigational warnings. Coastal radio warnings ) local radio warnings ) long- 133
range radio warnings
Local Notices to Mariners 135

CORRECTION OF CHARTS AND PUBLICATIONS Correction and warning 135

system ) tracings for chart correction ) hints on correcting charts ) hints on
correcting publications
HYDROGRAPHIC REPORTS Forms ) general remarks 139

Information for charts and Admiralty Sailing Directions. Newly discovered dangers 141
) soundings ) shoals ) discoloured water ) port information ) lights ) buoys )
beacons and marks ) conspicuous objects ) wrecks ) channels and passages )
positions ) tidal streams ) ocean currents ) magnetic variation ) information
concerning radio services ) zone time ) sketches and photographs
NAVIGATIONAL FORMS Contents of the Small Envelope 146

THE PRODUCTION OF THE ADMIRALTY CHART Reproduction methods ) 146

plate correction
viii

Chapter Page
7 Publications 151
PUBLICATIONS SUPPLIED BY THE HYDROGRAPHER Sets of navigational 151
publications ) meteorological publications ) aviation publications
Navigational publications. Admiralty Sailing Directions ) Views for Sailing 152
Directions ) The Mariner’s Handbook ) Ocean Passages for the World ) Admiralty
Distance Tables ) Admiralty List of Lights and Fog Signals ) Admiralty List of
Radio Signals ) tide and tidal stream publications ) astronomical publications )
miscellaneous publications
OTHER BOOKS OF INTEREST TO THE NAVIGATING OFFICER The Queen’s 161
Regulations for the Royal Navy ) Admiralty Manual of Seamanship ) Rules for the
Arrangement of Structures and Fittings in the Vicinity of Magnetic Compasses and
Chronometers ) Collisions and Groundings (and Other Accidents) ) A Seaman’s
Guide to the Rule of the Road ) tactical publications ) classified books ) technical
publications
‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER 163
8 Chartwork 173
SYMBOLS USED IN CHARTWORK Positions and position lines 173
DEFINING AND PLOTTING A POSITION Plotting a position ) transferring a 175
position ) position by observation
CALCULATING THE POSITION Dead Reckoning ) Estimated Position ) plotting 176
the track ) Position Probability Area ) allowing for wind, tidal stream, current and
surface drift ) allowing for the turning circle ) correction for change of speed
CHARTWORK PLANNING 190
CHARTWORK ON PASSAGE Fixing ) plotting the ship’s position ) frequency of 192
fixing ) speed ) time taken to fix ) keeping the record ) establishing the track ) time
of arrival ) general points on chartwork
SUMMARY 196
9 Fixing the Ship 197
Taking bearings 198
METHODS OF OBTAINING A POSITION LINE Compass bearing ) relative 198
bearing ) transit ) horizontal angle ) vertical sextant angle of an object of known
height ) range by distance meter when the height of the object is known ) range by
rangefinder ) rising or dipping range ) soundings ) radio fixing aids ) radar range )
astronomical observation ) sonar range
THE TRANSFERRED POSITION LINE The use of a single transferred position 204
line
FIXING THE SHIP Fixing by cross bearings ) fixing by a bearing and a 206
range ) fixing by a bearing and a sounding ) fixing by a bearing and a
horizontal angle from which a range may be calculated ) fixing by a
 ix

Chapter Page
transit and an angle ) fixing by two bearings of a single object, with a time interval
between observations (running fix) ) fixing by a line of soundings ) fixing by two or
more ranges ) radio fixing aids
ERROR IN THE COMPASS AND ELIMINATING THE COCKED HAT 219
HORIZONTAL SEXTANT ANGLES AND VISUAL BEARING LATTICES 224
Fixing by horizontal sextant angles. Horizontal sextant angles ) strength of the HSA 224
fix ) choosing objects ) when not to fix using horizontal angles ) rapid plotting
without instruments
Bearing lattices 230
THE SELECTION OF MARKS FOR FIXING Choosing objects ) fixing procedure 232
) short cuts to fixing ) ‘shooting up’

10 Visual and Audible Aids to Navigation 237

LIGHTS Characteristics of lights ) classes of lights ) Admiralty List of Lights and 237
Fog Signals ) range of lights ) range displayed in the List of Lights ) determining
the maximum range of a light
Light-vessels, lanbys, light-floats. Remarks on light-vessels, etc. ) lights on oil and 250
gas platforms, drilling rigs and single point moorings ) other types of light ) notes
on using lights
BUOYS AND BEACONS Buoys ) beacons ) sources of information 254
The International Association of Lighthouse Authorities (IALA) System 254
Application of the IALA System in Region A. Fixed marks ) types of mark ) lateral 256
marks ) cardinal marks ) isolated danger marks ) safe water marks ) special marks )
new dangers ) buoyage around the British Isles ) chartered buoy and beacon
symbols
USING FLOATING STRUCTURES FOR NAVIGATION Buoys 264
FOG SIGNALS Types of fog signals ) Morse Code fog signals ) using fog signals 266
for navigation

11 Tides and Tidal Streams 269

TIDAL THEORY 269
The Earth-Moon system. The gravitational force ) the tide-raising force ) effect of 269
Earth’s rotation ) change of Moon’s declination ) the distance of the Moon
The Earth-Sun system 277
Springs and neaps. Spring tides ) neap tides ) frequency of springs and neaps ) 278
equinoctial and solstitial tides ) priming and lagging
Summary of tidal theory 281
THE TIDES IN PRACTICE Shallow water and other special effects ) 281
meteorological effects on tides ) seismic waves (tsunamis)
x

Chapter Page
TIDAL PREDICTION Harmonic constituents ) principles of harmonic tidal 286
analysis ) tidal prediction ) Simplified Harmonic Method of Tidal Prediction ) co-
tidal charts
TIDAL STREAMS AND CURRENTS Types of tidal streams ) tidal stream data ) 290
tidal stream atlases ) tidal stream observations ) tidal streams at depth ) eddies,
races and overfalls
ADMIRALTY TIDE TABLES Standard ports ) secondary ports ) using the Tide 293
Tables ) supplementary information in the Tide Tables
LEVELS AND DATUMS Datum of tidal prediction ) chart datum and land survey 295
datum ) tide levels and heights

12 Coastal Navigation 299

PREPARATORY WORK Charts and publications ) information required ) 299
appraisal
PLANNING THE PASSAGE Choosing the route ) clearance from the coast and 301
off-lying dangers ) ships’ routeing and traffic separation schemes ) conduct of ships
in traffic separation schemes ) under-keel clearances
The passage plan. Times of arrival and departure ) the passage chart ) the passage 310
graph ) large-scale charts
EXECUTION OF THE PASSAGE PLAN Method of fixing ) selecting marks for 316
fixing ) fixing using radar, radio fixing aids and beacons ) navigational equipment )
keeping clear of dangers
PRACTICAL HINTS Calculating the distance that an object will pass abeam ) the 327
time of arrival ) buoys and light-vessels ) when not to fix ) tidal stream and current
) the record ) flat and featureless coastlines ) fixing by night ) altering course )
entering shallow water
PASSAGES IN FOX AND THICK WEATHER Before entering fog ) practical 333
considerations for passages in fog
NAVIGATION IN CORAL REGIONS Growth of coral reefs ) navigating by eye ) 337
cross currents and weather ) edges of coral reefs ) passing unsurveyed reefs
13 Pilotage 341
REGULATIONS FOR PILOTAGE HM Ships ) merchant ships 342
PLANNING AND EXECUTION OF PILOTAGE 343
PREPARATORY WORK Charts and publications ) times of arrival and departure 343
) limiting danger lines ) appraisal of the passage

THE PILOTAGE PLAN 347

Selection of the track. Dangers ) tidal streams and wind ) distance to run ) night 347
entry/departure ) blind pilotage ) constrictions ) the Sun
Headmarks. Transits ) line of bearing ) edge of land ) distance of the headmark ) no 349
headmark available
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Chapter Page
Altering course. Advance and transfer ) distance to new course ) turning on to a 352
predetermined line ) to allow for a current or tidal stream when altering course ) use
of a single position line
Keeping clear of dangers. Clearing bearings ) vertical and horizontal danger angles 358
) echo sounder

Miscellaneous considerations. Gyro checks ) ‘shooting up’ ) using radar to support 361
the visual plan ) point of no return ) alternative anchor berth ) Navigating Officer’s
Note Book ) conning ) tugs ) final stages of the plan ) check-off lists
The plan 366
EXECUTION OF PILOTAGE Organisation and records ) maintaining the track ) 369
assessment of danger ) identification of marks ) shipping ) use of the echo sounder )
altering course and speed ) buoys ) tides, tidal streams and wind ) service to the
Command ) action on making a mistake ) checks before departure or arrival
Miscellaneous considerations in pilotage execution. Taking over the navigation ) 377
using one’s eyes ) making use of communications ) personal equipment
The shiphandling phase 378
Pilotage mistakes. Do’s ) Don’ts 378
NAVIGATION IN CANALS AND NARROW CHANNELS 379
Annex A to Chapter 13 Pilotage Check-off List 381

14 Anchoring and Mooring 383

Choosing a position in which to anchor. The depth of water ) swinging room when 383
at anchor ) proximity of dangers ) amount of cable to be used ) distance from other
ships ) reduced swinging radius
Anchoring a ship in a chosen position. Planning the approach ) approach to an 390
anchor berth: reduction of speed
Executing the anchorage plan 394
Anchoring in deep water, in a wind or in a tidal stream. Anchoring in deep water ) 397
anchoring in a tidal stream
Heavy weather in harbour. Letting go second anchor ) dragging 398
Anchoring at a definite time without altering speed 398
Ensuring that the anchor berth is clear 400
Anchoring in a poorly charted area 400
Anchoring in company 400
Mooring ship. Swinging room when moored ) planning the approach ) executing 402
the mooring plan
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Chapter Page

15 Radar, Blind Pilotage 405

RADAR WAVES: TRANSMISSION, RECEPTION, PROPAGATION AND 405
REFLECTION Radar detection ) range discrimination and minimum range ) beam
width and bearing discrimination ) video signals ) improvements to video signals )
atmospheric refraction ) attenuation of radar waves ) appearance of weather echoes )
reflection from objects ) unwanted echoes ) radar shadow
RADAR FOR NAVIGATION Suppression controls ) radar and the Rule of the 417
Road ) other ships’ radar
Range errors. Index errors ) other design factors ) using the display ) other causes of 418
range error
Finding the radar index error. Radar calibration chart ) use of the normal chart ) 419
two-mark method ) three-mark method ) horizontal sextant angle method ) two-ship
method ) three-ship method ) standard set comparison method ) allowing for range
index error
Bearing errors. Causes of bearing errors ) bearing alignment accuracy check 424
Comparison of 10 cm and 3 cm radars 425
LANDFALLS AND LONG-RANGE FIXING Radar range/height nomograph ) 426
long-range radar fixes ) plotting the long-range fix ) the Radar Station Pointer
RADAR IN COASTAL WATERS Fixing by radar range and visual bearing ) fixing 431
by radar ranges ) fixing by radar range and bearing ) use of a radar clearing range
BLIND PILOTAGE Assessment of the risk involved in a blind pilotage passage ) 434
parallel index technique ) radar clearing ranges ) course alterations
Blind pilotage in HM Ships. Responsibilities ) the conduct of blind pilotage ) blind 435
pilotage team and duties
Planning and execution of blind pilotage. General principles ) blind pilotage 439
planning ) blind pilotage execution ) blind anchorages ) navigational records )
horizontal displays
TRUE MOTION RADAR Advantages of true motion radar ) disadvantages of true 445
motion radar
RADAR BEACONS (RACONS AND RAMARKS) Racons ) ramarks ) interference 447
from radar beacons
SHORE-BASED RADAR 449
Port radar systems. Positional information ) reporting points within port radar 449
systems
Traffic surveillance and management systems. Position fixing assistance ) basis of 450
operation ) reporting points within traffic surveillance systems
USE OF RADAR IN OR NEAR ICE 454
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Chapter Page
16 Navigational Errors 455
INTRODUCTION 455
NAVIGATIONAL ACCURACIES Definitions 457
TYPES OF ERROR 458
Faults. Blunders 458
Systematic errors 459
Random errors 459
Composite errors 461
Random errors in one dimension. Bias 461
Random errors in two dimensions. Radial error ) orthogonal position lines ) the 464
error ellipse and the equivalent probability circle ) circular error probable
THE PRACTICAL APPLICATION OF NAVIGATIONAL ERRORS 468
Allowing for faults and systematic errors ) allowing for random errors ) limits
of random errors ) Most Probable Position
Annex A to Chapter 16 Navigational Errors 477
ONE-DIMENSIONAL RANDOM ERRORS Variance and linear standard deviation 477
) combining one-dimensional random errors
Rectangular errors. Rounding-off errors ) effect of rectangular errors 482
TWO-DIMENSIONAL RANDOM ERRORS Probability heap ) the circle of 484
error ) the error ellipse ) equivalent probability circles ) circular error probable
Derivation of the Most Probable Position from three or more position lines 494
17 Relative Velocity and Collision Avoidance 497
Definitions 497
PRINCIPLES OF RELATIVE VELOCITY Relative speed ) relative track and 498
relative speed ) comparison between relative and true tracks ) the velocity triangle )
initial positions of ships ) relative movement
USE OF RADAR Radar displays ) using the relative motion stabilised radar display 504
to solve relative velocity problems ) radar plotting on relative and true motion
displays
Radar limitations 508
Relative or true motion plotting. Aspect ) effect of leeway ) effect of drift and set 509
Automated radar plotting aids 514
SOME RELATIVE VELOCITY PROBLEMS 516
18 Surveying 523
Types of surveying work 524
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Chapter Page
PASSAGE SOUNDING 524
FIXING NEW NAVIGATIONAL MARKS AND DANGERS 524
DISASTER RELIEF SURVEYS Reporting new dangers 525
INFORMATION ON NEW PORT INSTALLATIONS Sounding out a berth 526
alongside a jetty
RUNNING SURVEYS 527
SEARCHES FOR REPORTED DANGERS 529
TIDAL STREAM OBSERVATIONS Pole current log ) observing procedure ) 530
recording
A COMPLETE MINOR SURVEY 532
Principles of surveying. Control ) horizontal control ) triangulation ) scale ) the 532
base line ) orientation ) geographical position ) vertical control
The practical survey. Survey equipment ) reconnaissance and planning ) marking ) 538
observing ) use of the sine formula ) calculation of the longest side ) plotting and
graduation ) tracing and field boards ) sounding ) methods of fixing the boat )
accurate positioning of soundings ) recording boat soundings ) reduction of
soundings ) inking in of soundings ) the ship’s echo sounder ) tides ) coastline )
fixing navigational marks and dangers ) topography ) aerial photography ) tidal
stream observations ) Admiralty Sailing Directions ) preparing the fair sheet ) report
of survey ) Shadwell Testimonial

19 Bridge Organisation and Procedures 559

BRIDGE ORGANISATION AND PROCEDURES WITHIN THE ROYAL NAVY 559
Definitions
The Captain. Command responsibilities ) charge of the ship ) calling the Captain ) 560
Captain’s Night Order Book ) shiphandling ) importance of a shiphandling plan )
supervision of the Navigating Officer ) training of seaman officers ) bridge
watchkeeping non-seaman officers
The Officer of the Watch. Looking out ) calls by the Officer of the Watch ) 562
emergencies ) equipment failures ) conning orders ) action information organisation
The Navigating Officer. Method of navigation ) in doubt ) instructions for the 565
Officer of the Watch
The Principal Warfare Officer. Essential information from the operations room 567
Special sea dutymen 567
Standing orders and instructions. Captain’s Standing Orders ) Bridge Emergency 568
Orders ) Bridge File ) books and publications ) Navigational Departmental Orders )
orders for Quartermasters ) orders for Navigator’s Yeoman
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Chapter Page
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE MERCHANT 570
NAVY Navigation safety (quoting Merchant Shipping Notice M.854) ) bridge
organisation (quoting ICS Bridge Procedures Guide) ) principles of watchkeeping
arrangements for navigational watch (quoting Statutory Instrument 1982 No. 1699) )
operational guidance for officers in charge of a navigational watch (quoting
Merchant Shipping Notice M.1102) ) routine bridge check lists (quoting ICS Bridge
Procedures Guide) ) action in an emergency (quoting ICS Bridge Procedures
Guide)
Appendix

1 Basic Trigonometry 581

The degree ) the radian 581
The definitions of trigonometric functions. The right-angled triangle ) 582
complementary angles ) trigonometric functions of certain angles ) The signs and
values of the trigonometric functions between 000° and 360° ) the sine, cosine and
tangent curves ) inverse trigonometric functions ) Pythagorean relationships
between trigonometrical functions
Acute and obtuse triangles. The sine formula ) the cosine formula ) the area of a 590
triangle ) functions of the sum and difference of two angles ) double and half-angle
formulae ) sum and difference of functions ) the sine of a small angle ) the cosine of
a small angle
2 A Summary of Spherical Trigonometry 596
DEFINITIONS The sphere ) great circle ) small circle ) spherical triangle ) 596
spherical angles ) properties of the spherical triangle
THE SOLUTION OF THE SPHERICAL TRIANGLE The cosine and sine formulae 597
) polar triangles ) the four-part formula ) right-angled triangles ) Napier’s mnemonic
for right-angled triangles ) quadrantal triangles ) the haversine ) the haversine
formula ) the half log haversine formula

3 The Spherical Earth 609

MERIDIONAL PARTS FOR THE SPHERE Construction of the mer. part formula 609
for the sphere ) evaluation of the mer. part formula
CORRECTED MEAN LATITUDE FOR THE SPHERE 611
4 Projections 615
THE CONICAL ORTHOMORPHIC PROJECTION ON THE SPHERE The scale ) 615
the constant of the cone ) conical orthomorphic projection with two standard
parallels
DEDUCTION OF THE MER. PART FORMULA FOR THE SPHERE 618
THE POSITION CIRCLE ON THE MERCATOR CHART 620
THE MODIFIED POLYCONIC PROJECTION 622
THE POLAR STEREOGRAPHIC PROJECTION 624
xvi

Appendix Page
GNOMONIC PROJECTION Principal or central meridian ) angle between two 624
meridians on the chart ) parallels of latitude ) to construct a gnomonic graticule )
equatorial gnomonic graticule
THE TRANSVERSE MERCATOR PROJECTION 632
Conversion from geographical to grid co-ordinates and vice versa. Symbols ) to 632
find the length of the meridional arc given the latitude ) to find the ‘footpoint’
latitude, given the true grid co-ordinates ) to convert from geographical to grid co-
ordinates ) to convert from grid to geographical co-ordinates

5 The Spheroidal Earth 636

THE EQUATION OF THE ELLIPSE 636
GEODETIC, GEOCENTRIC AND PARAMETRIC LATITUDES Geodetic and 638
geocentric latitudes - the parametric latitude
THE LENGTH OF ONE MINUTE OF LATITUDE 640
THE LENGTH OF THE MERIDIONAL ARC 643
MERIDIONAL PARTS FOR THE SPHEROIDAL EARTH 646
THE LENGTH OF THE EARTH’S RADIUS IN VARIOUS LATITUDES 648
6 Vertical and Horizontal Sextant Angles 649
VERTICAL SEXTANT ANGLES Base of the object below the observer’s horizon 649
HORIZONTAL SEXTANT ANGLES Rapid plotting without instruments ) 652
preparing a lattice for plotting HSA fixes ) fixing objects within the boundaries of
the chart ) fixing objects outside the boundaries of the chart

7 Errors in Terrestrial Position Lines 657

SEXTANT ERRORS Personal error 657
ERRORS IN TAKING AND LAYING OFF BEARINGS Displacement of fix when 657
the same error occurs in two lines of bearing ) the cocked hat ) the cocked hat
arising from the same error in three lines of bearing ) the cocked hat in general
ERRORS IN HSA FIXES Maximum errors in the HSA fix ) reliability of HSA 663
fixes ) the angle of cut
Examples of satisfactory HSA fixes 669
Example of an unsatisfactory fix 670
DOUBLING THE ANGLE OF THE BOW AND THE EFFECT OF CURRENT OR 670
TIDAL STREAM Effect of the tidal stream when N has particular values
Bibliography 675

Index 697
 1

CHAPTER 1
Position and Direction
on the Earth’s Surface

Navigation is the process of planning and carrying out the movement of

transport of all kinds from one place to another ) at sea, in the air, on land or
in space. The navigation of ships and all waterborne craft is called marine
navigation to distinguish it from navigation in other surroundings, and it is
marine navigation that is dealt with in this book and its companion volumes,
which together comprise a new edition of the Admiralty Manual of
Navigation.
The last thirty years have seen great advances in navigational techniques.
Man has landed on the moon. Spacecraft are exploring the outer regions of
the solar system. The new techniques developed for space navigation have
benefited marine navigation: detailed study of the first satellites in orbit
around the Earth has led to the development of a world-wide navigation
satellite system which can tell a ship’s navigator his position with an accuracy
of a few hundred metres. Automated computer-assisted navigational systems
enable the navigator to maintain a continuous and accurate track and to avoid
collisions. Hand-held calculators and desk-top computers, enable him to
reckon courses and distances around the globe with great precision, taking
into account the true shape of the Earth.
The principles of marine navigation remain unchanged by new
techniques; therefore the treatment of the subject in this manual has been
designed to re-state the principles while reflecting the latest methods.
Volume I deals with the essentials of marine navigation ) position and
direction on the Earth’s surface, map projections, charts and publications,
chartwork, tides, coastal navigation and pilotage. Summaries of plane and
spherical trigonometry, proofs of formulae, etc. may be found in the
appendices at the back of the book.
This opening chapter introduces the basic terms dealing with position and
direction on the Earth’s surface.

POSITION ON THE EARTH’S SURFACE

The Earth
The Earth is not a perfect sphere; it is slightly flattened, the smaller diameter
being about 24 miles less than the larger. The Earth’s shape is known as an
oblate spheroid (Fig. 1-1) with greatest (a) and least (b) radii of approximately
3444 and 3432* international nautical miles. The Earth turns about its shortest

* These figures are taken for the International (1924) Spheroid, which is explained in Chapter 3.
2 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

diameter PP1, called the axis, the extremities of which are called the poles.
An oblate spheroid is a figure traced out by the revolution of a semi-
ellipse such as PWP1, in Fig. 1-1, about its minor axis PP1. The successive
positions of PWP1 are called meridians. The meridian passing through
Greenwich is called the prime meridian. The circle traced out by W is called
the equator.
The Earth revolves about its axis PP1 in the direction shown by the arrow.
The direction of revolution is called east, the opposite direction west. The
North Pole is on the left and the South Pole on the right of the observer
facing east.

Fig. 1-1. The Earth, an oblate spheroid

Latitude and longitude

A position on the Earth’s surface is expressed by reference to the lane of the
equator and the plane of the prime meridian. The latitude of a place (also
called the geodetic, geographical or true latitude) is the angle which the
perpendicular to the Earth’s surface at the place makes with the plane of the
equator. It is measured from 0° to 90° north or south of the equator. Fig. 1-2
shows a meridional section of the spheroid. The latitude of point M is the
angle MLE (N), where L is the point of intersection of the perpendicular to the
Earth’s surface at M and the plane of the equator OE.
Planes parallel to the plane of the equator joining all places of the same
latitude are known as parallels of latitude. They are also known as small
circles (see page 9).
POSITION ON THE EARTH’S SURFACE 3

Fig. 1-2. Latitude of a place

The longitude of a place is the angle between the plane of the prime
(Greenwich) meridian and the meridian of the place measured from 0° to 180°
east or west of Greenwich (Fig. 1-3).

Fig. 1-3. Longitude of a place

4 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

In Fig. 1-3 the longitude of F is the arc AB = angle AOB (east).

The position of a place may therefore be expressed in latitude and
longitude. For example, the Central Signal Station Flagstaff, Portsmouth
Dockyard, is in latitude 50 degrees 47minutes 57 seconds north of the equator
and in longitude 1 degree 6 minutes 32 seconds west of Greenwich.
The position may be recorded as follows:

50°47'57"N 50°47'.95N + 50°.79917

or or
1°06'32"W 1°06'.53W - 1°.10889

The third method of recording shown above is for use in a calculator, +ve
signs being used for N latitudes and E longitudes, -ve signs for S latitudes
and W longitudes.

Difference of latitude, longitude

The difference of latitude (d.lat) between two places is the arc of the meridian
between the two parallels of latitude. When a ship is proceeding from one
place to another, d.lat is named north or south according to whether the
parallel of the destination is north or south of the parallel of the place of
departure. In Fig. 1-4 the d.lat between F and T is the same as the d.lat
between G and T, where GF is the parallel of latitude through F.

d.lat from F to T = angle GDT (south) = lat F ) lat T

Fig. 1-4. d.lat

The difference of longitude (d.long) between two places is the smaller arc
of the equator between their meridians. When a ship is proceeding from one
place to another, d.long is named east or west according to whether the
meridian of the destination is east or west of the meridian of the place of
departure. In Fig. 1-5 the d.long from F to T = arc BA = angle BOA (west) =
angle FPT (the angle at the pole between the meridians of the two places).
POSITION ON THE EARTH’S SURFACE 5

Fig. 1-5. d.long

Calculation of d.lat and d.long

The rule for finding the d.lat and the d.long is as follows:

Same names: Subtract Opposite names: Add

If, when using this rule, the sum of the longitudes exceeds 180°, this sum
is subtracted from 360° to find the smaller angle and the name is reversed.

EXAMPLES
Find the d.lat and d.long between:
1. Portsmouth (F): (50°48'N, 1°07'W) and New York (T): (40°40'N,
74°00'W).
2. Malta (F): (35°53'N, 14°31'E) and Gibraltar (T): (36°07'N, 5°21'W).
3. Sydney (F): (33°52'S, 151°13'E) and Honolulu (T): (21°18'N, 157°52'W).

1. lat F 50°48'N long F 1°07'W

lat T 40°40'N long T 74°00'W
d.lat 10°08'S d.long 72°53'W
2. lat F 35°53'N long F 14°31'E
lat T 36°07'N long T 5°21'W
d.lat 0°14'N d.long 19°52'W
3. lat F 33°52'S long F 151°13'E
lat T 21°18'N long T 157°52'W
d.lat 55°10'N d.long 309°05'W
subtract from 360°
d.long 50°55'E
6 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

The sea mile

The sea mile is the length of one minute of arc (1') measured along the
meridian in the latitude of the position. This is illustrated in Fig. 1-6.
If M is the place on the Earth’s surface and C the centre of curvature at
M, and AMB is an arc of the meridian subtending an angle of 1' at C, then
AMB is the length of the sea mile at M.

Fig. 1-6. The sea mile

On Admiralty charts on the Mercator projection (see Chapter 4), the

latitude graduations form a scale of sea miles.*
Except on charts, where the symbol M is used, the sea mile is denoted by
', which is the symbol for a minute of arc. Thus, 10'.8 means 10.8 sea miles.
The symbol is always placed before the decimal point.

The length of the sea mile

The radius of curvature in the meridian increases as M moves from the
equator to the pole; thus, the distance subtended by 1' of arc also increases.
The length of the sea mile † is shortest at the equator (1842.9 m) and longest
at the poles (1861.7 m), with a mean value of 1852.3 m at 45° latitude. Its
length is tabulated in Spheroidal Tables (NP 240), published by the
Hydrographer of the Navy.
The formula for the length of 1' of arc is given in Chapter 3 and its
derivation in Appendix 5.

* It is a common but mistaken practice for mariners to refer to a sea mile as a nautical mile. The British
Standard Nautical Mile was discarded in 1970.
† For the International (1924) Spheroid, see Chapter 3.
POSITION ON THE EARTH’S SURFACE 7

One-tenth of a sea mile is known as a cable, which varies between

184.3 m and 186.2 m according to latitude. A cable approximates to 200
yards, a convenient measure frequently used at sea for navigational purposes.

The geographical mile

The geographical mile is the length of 1' of arc measured along the equator
(i.e. 1' of longitude). As the equator is a circle the length of the geographical
mile is the same at all parts of the equator and is equal to (a sin 1' of arc),
where a is the radius of the equator. For the International (1924) Spheroid,
its value is 1855.4 m.

The international nautical mile

This is a standard fixed length of 1852 m. Its correct abbreviation is the term
n mile. Distances given in the Admiralty Distance Tables and in Ocean
Passages of the World are in international nautical miles.

The statute mile

The statue or land mile is the unit of distance of 1760 yards or 5280 feet
(1609.3 m).

The knot
In navigation, it is convenient to have a fixed or standard unit for measuring
speed. This unit is one international nautical mile (1852 m) per hour and is
called a knot, abbreviated to kn.
In normal practice, the errors arising from using international nautical
miles instead of sea miles are very small (less than 0.5%). Sometimes,
however, it is necessary to determine the error and this is set out in Appendix
5.

Linear measurement of latitude and longitude

The linear latitude of a place is the length of the arc of the meridian between
the equator and that place. It is measured in sea miles north or south of the
equator. This is illustrated in Fig. 1-7.

If point M is in latitude 60°N, then:

angle MLW = 60°

= 60 x 60 minutes of arc = 3600'

The linear latitude of M is 3600 sea miles north of the equator.

If a place M1 is situated 1800 sea miles south of the equator, its latitude
is
1800'
or 30° S.
60
The linear longitude of a place is the smaller arc of the equator between
the prime meridian and the meridian of the place. Along the equator it is
measured in geographical miles (see above) east or west of the prime
meridian. This is illustrated in Fig. 1-8.
8 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

Fig. 1-7. Linear measurement of latitude

Fig. 1-8. Linear measurement of longitude

If point B is 40°E of the prime meridian PAP1, the angle AOB is 40°, the
arc AB of the equator is 40° = 40 x 60 = 2400 minutes of arc along the
equator, i.e. 2400 geographical miles.
It will be seen from Fig. 1-8 that the distance on the Earth’s surface
between any two meridians is greatest at the equator and diminishes until it
POSITION ON THE EARTH’S SURFACE 9

is zero at the poles, where all the meridians meet. The linear distance of a
degree of longitude on the surface of the Earth varies approximately with the
cosine of the latitude. (The error in assuming that the length of a degree of
longitude varies directly with the cosine of the latitude lies between zero at
the equator and 0.34% at latitude 89° for the International (1924) Spheroid.)
The precise formulae for the length of 1' of latitude and 1' of longitude are
given in Chapter 3.

The Earth as a sphere

Although the shape of the Earth is that of an oblate spheroid, for most
purposes of navigation it may be assumed to be a sphere, with radius equal
to the mean of the greatest and least radii and measuring approximately 3440
international nautical miles.* A sphere is the figure formed by rotating a
semi-circle about its diameter.
Any plane through the centre of the sphere cuts the surface in what is
known as a great circle. Any plane which cuts the surface of the sphere, but
does not pass through the centre, is called a small circle (Fig. 1-9). Thus,
when the Earth is regarded as a sphere, meridians of longitude become semi-
great circles joining (but not passing through) the poles cutting the equator
at right angles. The equator is a great circle but all other parallels of latitude
are small circles.

Fig. 1-9. The Earth as a sphere

2a + b
* This figure is taken from the International (1924) Spheroid, which has mean radius = 6,371,229.3 m
3
10 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

The great circle is important in navigation because it gives the shortest

distance between two points. It is also the path taken by an electro-magnetic
radiation near the Earth’s surface (radio, radar, light, etc.).
Using the mean radius for the sphere derived from the International
(1924) Spheroid, the length of 1' of arc on the meridian or on the equator
equals 1853.3 m. This distance approximates very closely to the length of the
international nautical mile of 1852 m. The Earth may therefore be treated,
without appreciable error, as a sphere where 1' of latitude is considered equal
to 1 n mile anywhere on the surface. (The errors introduced by assuming a
spherical Earth based on the international nautical mile are not more than
0.5% for latitude, 0.2% for longitude.) On the equator 1' of arc of longitude
also equals one n mile. This means that linear latitude and linear longitude
may now be measured in the same units, n miles.

DIRECTION ON THE EARTH’S SURFACE

True direction
The true direction between two points on the Earth’s surface is given by the
great circle between them; it is expressed in terms of the angle between the
meridian and the great circle (angle PFT in Fig. 1-10(a)).

True north
True north is the northerly direction of the meridian and is the reference from
which true bearings and courses are measured.

True bearing
The true bearing of an object is the angle between the meridian and the
direction of the object.
In Figs 1-10 and 1-11 the true bearing of T from F is given by the angle
PFT, where PF is the meridian through F and FT is the great circle joining F
to T.
PFT is measured clockwise from 000° to 360°. In Fig. 1-10 T bears 030°
from F: in Fig. 1-11 T bears 330° from F.
Over short distances the great circle may be drawn as a straight line
without appreciable error, as in Figs 1-10(b) and 1-11(b). The error varies
with the latitude and the bearing.

Position of close objects

It is often convenient to indicate the position of an object by its bearing and
distance from a known or key position, rather than by latitude and longitude.
A shoal, for example, might be described as being 239°, 7 miles from a
certain lighthouse.

True course
True course is the direction along the Earth’s surface in which the ship is
being steered (or intended to be steered). It is measured by the angle between
the meridian through the ship’s position and the fore-and-aft line, clockwise
from 000° to 360°.
DIRECTION ON THE EARTH’S SURFACE 11

Fig. 1-10(a) True bearing )small Fig. 1-10(b) True bearing )small
bearing )great circle bearing )straight line

Fig. 1-11(a) True bearing )large Fig. 1-11(b) True bearing )large
bearing )great circle bearing )straight line

True course is not to be confused with heading (or ship’s head), which
is the instantaneous direction of the ship and is thus a constantly changing
value if the ship yaws across the course due to the effect of wind, sea and
steering errors.
12 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

The compass
The navigational compass is an instrument which provides the datum from
which courses and bearings may be measured. There are two principal types
of compass )the gyro-compass and the magnetic compass. (These
instruments are described in detail in Volume III.) The general principles of
the two types of compass are set out below with an explanation as to how true
courses and bearings may be obtained from them.

The gyro-compass
This instrument is a rapidly spinning wheel or gyroscope, the axis of which
is made to point along the meridian towards true north. Courses and bearings
which are measured using a gyro-compass are true provided there is no error
in the compass, and are measured clockwise from 000° to 360°.

Error of the gyro-compass

For a number of reasons the gyro-compass will not always point exactly
towards true north. Any error must be known before the compass may be
used as an accurate reference. Details of how the error may be found are
given in Chapter 9.
The degree of accuracy of gyro-compasses used in the Royal Navy is such
that the maximum error is of the order of ½° at the equator and 1° at latitude
60°. However, in a number of commercial compasses the error may exceed
this by one or two degrees.

Fig.1-12(a) Gyro error high Fig. 1-12(b) Gyro error low

If the gyro bearing of an object is 077°, while its true bearing is known
to be 075°, then it can be seen from Fig. 1-12(a) that the gyro is reading 2°
high; similarly, if the gyro bearing is 073°, as in Fig. 1-12(b), the gyro is
reading 2° low. In order to obtain the true bearing, a gyro error high must be
subtracted from the gyro bearing, and a gyro error low must be added to the
DIRECTION ON THE EARTH’S SURFACE 13

gyro bearing. The suffixes G or T may be used to denote Gyro or True

courses and bearings respectively.

The magnetic compass

This instrument may be considered as a bar magnet freely suspended in the
horizontal plane and acted upon by the Earth’s magnetic field and the
magnetic properties of the ship.
The Earth may be considered as a gigantic magnet. Magnetic lines of
force emanate from a position near King George V Land in Antarctica known
as the South Magnetic Pole. These lines of force follow approximate semi-
great circle paths to the North Magnetic Pole, north of Bathurst Island in the
Canadian Arctic. These magnetic poles are not stationary but are continually
moving over a largely unknown path in a cycle of some hundreds of years.

The magnetic meridian

A freely suspended magnetic compass needle acted upon by the Earth’s
magnetic field alone will lie in the vertical plane containing the line of total
force of the Earth’s magnetic field. This vertical plane is known as the
magnetic meridian. Magnetic meridians, however, do not necessarily point
towards the magnetic poles because the Earth’s magnetic field is irregular.
In addition, the magnetic poles are not 180° apart; thus, it is rare for the
magnetic needle to point towards the magnetic pole.

Magnetic north
Magnetic north is the name given to the direction in which the ‘north’ end of
a magnetic needle, suspended so as to remain horizontal, would point when
subject only to the influence of the Earth’s magnetism. It is the northerly
direction of the magnetic meridian.

Variation
Variation is the angle between the geographic (true) and magnetic meridians
at any place. It is measured east or west from true north; in Fig. 1-13 the
variation at F is 20° west.
Variation has different values at different places and is gradually
changing. Its value at any place may be found from the chart which gives the
variation for a certain year together with a note of the annual change. The
navigator must always allow for this annual change.
Variation may also be obtained from special isogonic charts on which all
places of equal variation are joined by isogonic lines and known as isogonals
(not to be confused with magnetic meridians, which are lines of force).

Deviation, compass north

If a magnetic compass is put in a ship, the presence of iron, steel or electrical
equipment will cause the magnetic compass to deviate from the magnetic
meridian. The angle between the magnetic meridian (magnetic north) and the
direction in which the needle points (compass north) is called the deviation.
It is measured east or west from magnetic north.
The magnetic field of the ship changes direction and amount, in part, as
14 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

the ship alters course.

Consequently the deviation
is different for different
compass courses.
In practice, the deviation
in a ship’s magnetic compass
is reduced to a minimum by
the use of permanent
magnets and soft-iron
correctors. The residual
deviation is found by
swinging the ship through
360° and tabulating that
residual deviation for the
various compass headings.
(Both these procedures are
explained in detail in
Fig. 1-13. Variation Volume III.)
The residual deviation
may be tabulated as in Table
1-1.
Table 1-1. Deviation table*

BEARING OF DISTANT
COMPASS HEADING OBJECT DEVIATION

MAGNETIC COMPASS
(FROM CHART) (OBSERVED)

N (000°) 236°M 237½ °C 1½ °W

NNE (022½°) 236°M 237¾ °C 1¾ °W
NE (045°) 236°M 237¾ °C 1¾ °W
ENE (067½°) 236°M 237½ °C 1½ °W
E (090°) 236°M 237 °C 1 °W
ESE (112½°) 236°M 236½ °C ½ °W
SE (135°) 236°M 235½ °C ½ °E
SSE (157½°) 236°M 235 °C 1 °E
S (180°) 236°M 234½ °C 1½ °E
SSW (202½°) 236°M 234 °C 2 °E
SW (225°) 236°M 234 °C 2 °E
WSW (247½°) 236°M 234¼ °C 1¾ °E
W (270°) 236°M 234¾ °C 1¼ °E
WNW (292½°) 236°M 235¼ °C ¾ °E
NW (315°) 236°M 236 °C NIL
NNW (337½°) 236°M 237 °C 1 °W

* The standard forms used in the Royal Navy to record deviation (S374A, Record of Observations for Deviation,
and S387, Table of Deviation) are tabulated every 22½° to facilitate the calculation of the various compass
coefficients (see Volume III). Intervals of 10° or 20° may be used if so desired.
DIRECTION ON THE EARTH’S SURFACE 15

It may also be shown in the form of a curve where deviation is plotted against
the compass heading. This is shown in Fig. 1-14.

Fig. 1-14 Deviation curve

16 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

Intermediate values for deviation may be found by interpolation from the

tables or inspection of the curve. For example, the deviation for 260°
compass heading may be found to be 1½°E.

Magnetic and compass courses and bearings

Magnetic courses and bearings are measured clockwise from 000° to 360°
from magnetic north (the magnetic meridian) and are given the suffix M, e.g.
075°M. They differ from true courses and bearings by the variation. This is
illustrated in Fig. 1-15.

Fig. 1-15. Magnetic courses and bearings

The magnetic bearing of T from F (angle MFT) is 085°M, while the true
bearing of T from F (angle PFT) is 065°. The difference is the variation,
20°W.
Compass courses and bearings are measured clockwise from 000° to 360°
from compass north, and are given the suffix C, e.g. 195°C. They differ from
true courses and bearings by the amount of variation for the place and the
deviation for the compass heading. This is illustrated in Fig. 1-16.
The compass bearing of T from F (angle CFT) is 055°C, whereas the
magnetic bearing (angle MFT) is 065°M and the true bearing (angle PFT) is
045°. Angle MFC is the deviation, 10°E, angle PFM is the variation, 20°W.

Graduation of older magnetic compass cards

There may still be some older magnetic compass cards* at sea which are
divided into four quadrants of 90°, the angles being measured from north and
south to east and west. For example, the bearing 137°M would be shown as
S43°E.

* Even older cards may still be found which are divided into four quadrants by the cardinal points, north, east, south,
west. Each quadrant is divided into eight equal parts, the division marks being called points: each point has a
distinctive name)north, north by east, north north east and so on. There are 32 points in the whole card.
DIRECTION ON THE EARTH’S SURFACE 17

Fig. 1-16. Magnetic and compass bearings

Practical application of compass errors

All charts have what are known as compass roses printed on them. When
there are two concentric rings, the outer ring represents the true compass and
the inner the magnetic compass, as shown in Fig. 1-17. Some small-scale
charts have only the true compass rose; others also have an indication of the
amount of magnetic variation.
On the north ) south line of the magnetic rose is written the variation, the
year for which it is correct, and its rate of change.
Before he can use this magnetic rose for laying off the compass bearing
or the compass course, the navigator must apply both the deviation and the
change in variation.

Conversion of magnetic and compass courses and bearings to true

The following rule should be applied for the conversion of magnetic or
compass courses and bearings to true:

Easterly variation and deviation are added or applied clockwise.

Westerly variation and deviation are subtracted or applied anti-clockwise.

This rule may be memorised by the mnemonic CADET:

C AD E T
Compass Add East True

i.e. when converting from compass to true, add east, subtract west and vice
versa.
An alternative mnemonic which may be used is:

Error West, Compass Best.

Error East, Compass Least.
18 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

Fig. 1-17. Compass rose printed on Admiralty charts

Remember that, as explained earlier, variation is the difference between

true and magnetic, while deviation is the difference between magnetic and
compass, i.e.

True ± Variation = Magnetic

Magnetic ± Deviation = Compass

There are two methods available for laying off the compass course or
bearing.

Method 1
Deviation (for the compass course steered) and variation (corrected to date)
are applied to the compass course or bearing in accordance with the above
DIRECTION ON THE EARTH’S SURFACE 19

rule to obtain the true course or bearing. The parallel ruler is then placed at
the true reading on the true rose.

Method 2
The parallel ruler is placed on the given compass bearing or course on the
magnetic rose. It is then slewed through a small angle in accordance with the
above rule to allow for:

1. The change in variation to bring it up to date.

2. The deviation for the compass course being steered.

The algebraic sum (+ve for east, -ve for west) of the deviation and the change
in variation is called the rose correction.
These two methods are illustrated by the following example.

EXAMPLE
A ship is steering 260°C. Variation from the chart was 12°W in 1982,
decreasing 10' annually. The compass bearing of an object is 043°C. Using
the deviation from Fig. 1-14, what is the true course and how would the
bearing be plotted using the above two methods? The year is 1985.
Variation in 1982 12 °W
Change in variation 1982-1985: 3 x 10'E ½ °E
Variation in 1985 11½ °W
Deviation for 260°C heading 1½ °E
Compass heading 260 °C
Deviation + 1½ °E
Magnetic heading 261½ °M
Variation -11½ °W
True course 250 °
Plotting the bearing
Method 1
Compass bearing 043 °C
Deviation + 1½ °E
Magnetic bearing 044½ °M
Variation -11½ °W
True bearing to be plotted 033 °

For any particular compass heading, it will be evident that the combined
effect of deviation and variation may be applied as a total error correction.
In this case, total error correction =+1½°E - 11½°W = -10°W. To convert
to true while on heading 260°C, all compass bearings should be reduced by
10°.
The application of compass error in one step avoids a very common
mistake, that of taking out the deviation for the compass bearing of the object
instead of the compass course of the ship.
20 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

Method 2
Place the parallel rule on the magnetic rose in the direction 043°M. Slew
through a total rose correction of +2° clockwise (½° clockwise to allow for
the easterly change of variation and 1½° clockwise to allow for the easterly
deviation). Plot the bearing on the magnetic rose, 045°M. As magnetic north
on the compass rose is offset 12° to the west (see Fig. 1-17), it will be
immediately apparent that 045°M is the same as 033°T, the true bearing.

To find the compass course from the true course

The mnemonic CADET is used in the reverse direction, i.e.

True to compass, add west, subtract east

There is, however, a small complication. Before the navigator can find his
compass course he must know the deviation, but he cannot find his deviation
until he knows his compass course. He therefore enters the deviation table
with the magnetic course in lieu of compass course and, particularly if the
deviation is large, makes a second calculation to get the exact deviation.
For example:

True course 260 °

Variation +10 °W
Magnetic course 270 °M
Deviation (for 270°M) - 1¼ °E
Approx. compass course 268¾ °C

If the navigator enters the deviation table with this approximate course
of 268¾°C, he will see that the correct deviation to use is nearer 1½°E than
1¼°E, giving a revised compass course of 268½°C.

Checking the deviation

If a compass bearing is taken of an object which has a known true bearing and
if the variation is also known, then the deviation may be found and compared
with that obtained from the deviation table. The various methods of checking
the deviation are given in Chapter 9.
In practice within the Royal Navy, the deviation of a magnetic compass
providing the primary means of navigation should remain within 2° of the
residual deviation obtained at the time of the swing over a period of several
months, whilst that for a magnetic compass providing a secondary means of
navigating (or a primary means of steering) should remain within 5° over a
similar period.
DIRECTION ON THE EARTH’S SURFACE 21

EXAMPLE
By calculation, the sun’s true bearing is 230°, the compass bearing is 235°C,
variation 12°W. What is the deviation?

True bearing 230 °

Variation +12 °W
Magnetic bearing 242 °M
Deviation ± ?
Compass bearing 235 °C

Clearly deviation is -7° and since, true to compass, east is subtracted, the
deviation is 7°E.

Relative bearings
The line of reference is the fore-and-aft line of the ship, i.e. the ship’s course.
Bearings are relative to this line and are measured from the bow from 0° to
180° on each side. Starboard bearings are Green, port bearings are Red.

Fig. 1-18. Relative bearings

Relative bearings may also be measured clockwise from 000° to 360°

from the fore-and-aft line of the ship and are given the suffix Rel, e.g. 135°
Rel.
In Fig. 1-18 the bearing of X is Green 30 (030° Rel), that of Y Red 140
(220° Rel). If the ship is steering 045°, the true bearing of X is 075°, and of
Y 265°. Alternatively, X could be said to be 30° on the starboard bow, Y 40°
on the port quarter.
22 CHAPTER 1 - POSITION AND DIRECTION ON THE EARTH’S SURFACE

The expressions on the bow, on the beam, and on the quarter without any
specified number of degrees or points mean respectively 45° (4 points), 90°
(8 points), 135° (12 points) from ship’s head.
 23

CHAPTER 2
The Sailings (1)

The sailings are terms used to describe the various mathematical methods of
finding course and distance from one place on the Earth’s surface to another.
The various sailings are:

1. Parallel sailing.
2. Plane sailing.
3. Mean and corrected mean latitude sailing.
4. Traverse sailing.
5. Mercator sailing.
6. Great-circle sailing.
7. Composite sailing.

All these sailings are described in this chapter. Mercator sailing is, however,
covered in detail in Chapters 4 and 5, while the finding of the vertex and the
composite track in great-circle sailing are set out in Chapter 5.

The rhumb line

The first five sailings all use the rhumb line, a curve drawn on the Earth’s
surface cutting all the meridians at the same angle (Fig. 2-1). A ship steering
a constant course is moving along a rhumb line.

Fig. 2-1. The rhumb line

24 CHAPTER 2 - THE SAILINGS (1)

The equator, parallels of latitude and meridians of longitude are special cases
of rhumb line. Along the equator and parallel of latitude, the rhumb line of
constant course is 090° or 270°, whilst along the meridian it is 000° or 180°.
Other rhumb lines, crossing the meridian at a constant angle, spiral towards
the pole and are often referred to as loxodromes.

Departure
Departure is the distance made good in an east-west direction in sailing from
one place to another along a rhumb line.

PARALLEL SAILING

If (Fig. 2-2) a ship is travelling along the equator from A to B, the departure
and d.long are equal.

Fig. 2-2(a) The arc of a parallel of Fig. 2-2(b) Alteration of the arc
latitude with a change of latitude

When the ship is travelling along any other parallel of latitude φ , FT, the
d.long 8, is still AB, but the distance FT is numerically less than the d.long.
The nearer the parallel is to the pole ) in other words, the higher the
latitude ) the shorter FT becomes. But the d.long does not alter. The
relationship between distance and d.long may be found as follows.
The radius r of the circle of latitude φ is R cos φ , where R is the radius
of the sphere.
PLANE SAILING 25

The distance FT along the parallel of latitude

= r8, where 8 is in radians

= R 8 cos φ
= AB cos φ
= 8 cos φ , where 8 is in minutes
= d.long (in minutes) cos latitude
i.e. departure = d.long cos latitude . . . 2.1

For the perfect sphere, the distance along a parallel of latitude in

minutes of latitude is equal to the d.long, expressed in minutes of arc,
multiplied by the cosine of the latitude.
Parallel sailing is thus a method of converting the departure along a
parallel of latitude into longitude, assuming the Earth is a sphere.
If, for example, the latitude of the parallel is 40°N and the longitudes of
F and T are 15°E and 60°E respectively, the d.long is 45° or, in minutes of arc
along the equator, 2700'.

FT = 2700' cos 40° = 2068'.3

Had the latitude been 60°N instead of 40°N, the distance along this new
parallel would have been 2700' cos 60°, i.e. 1350'.

PLANE SAILING

When a ship travels along any rhumb line other than a parallel of latitude or
a meridian of longitude, her d.lat, departure, distance and course may be
considered as forming a plane right-angled triangle (Fig. 2-3).

Fig. 2-3. d.lat/departure/distance

26 CHAPTER 2 - THE SAILINGS (1)

Various formulae may be deduced from this triangle:

departure = distance sin course . . . 2.2

d.lat = distance cos course* . . . 2.3
By dividing (2.2) by (2.3):
departure
= tan course . . . 2.4
d.lat

Plane sailing is thus a method of solving the relationship between d.lat,

departure, distance and course. It does not involve d.long except indirectly
(see page 28).

Proof of the plane sailing formulae

Fig. 2-4. The division of the rhumb line

In Fig. 2-4, let the rhumb line FT be divided into a large number n of
equidistant parallels of latitude cutting the rhumb line in F, A, B, C, etc. Let
the meridians through the points cut the parallels of latitude in X, Y, Z, etc.
In the small triangles FAX, ABY, BCZ, etc. the angles FXA, AYB, BZC are
right angles. The angles FAX, ABY, BCZ are all equal, being equal to the
course. The sides AX, BY, CZ are all equal.
The triangles are therefore equal in all respects and, as they are very
small, may be considered as plane right-angled triangles.

* When using formula (2.3) to find the distance, there is a fundamental weakness in the formula as the course
approaches 90° because small errors in the course introduce large errors in the distance. Formula (2.2) should be
used instead.
MEAN AND CORRECTED MEAN LATITUDE SAILING 27

In the triangle FAX:

AX = FA cos course
∴ nAX = nFA cos course
∴ d.lat = distance cos course . . . (2.3)
FX = FA sin course
nFX = nFA sin course
∴ departure = distance sin course . . . (2.2)

Dividing (2.2) by (2.3):

departure
tan course = . . . (2.4)
d.lat

MEAN AND CORRECTED MEAN LATITUDE SAILING

There are two methods by which a ship may determine her latitude and
longitude after travelling along a rhumb line other than in a north-south or
east-west direction. One of these methods uses the mean or corrected mean
latitude, the other uses Mercator sailing (described later).
Consider the rhumb line FT in Fig. 2-5. The departure is greater than HT,
the departure along the parallel through T, and less than FG, the departure
along the parallel through F.
The departure from F to T must therefore equal the departure along a
parallel lying somewhere between FG and HT. Let this parallel by UV.

Fig. 2-5. The mean and corrected mean latitude

Provided that the d.lat between F and T is fairly small and, the latitudes
of F and T are not too high, this departure is approximately equal to the arc
of the parallel MN, which has as its latitude the mathematical mean between
F and T.
28 CHAPTER 2 - THE SAILINGS (1)

This latitude is referred to as the mean latitude. In these particular

circumstances MN and UV are almost identical.
If QR is the d.long between F and T:

since MN = QR cos QM (formula 2.1)

then, for the sphere:
departure = d.long cos (mean latitude) . . . 2.5

This formula is not accurate mathematically except when F and T are on

the same parallel of latitude. In practice, its accuracy depends on how close
T is to F. Such a formula should not be used for distances exceeding 600'.
If the latitudes of F and T are on each side of the equator and also within
10° of latitude of the equator, the departure may be taken as the d.long
without appreciable error. (The maximum error in departure cannot exceed
0.4%.)
The true or corrected mean latitude between F and T is given by UV. It
is frequently referred to in nautical tables and navigational publications as the
middle latitude.*
For the sphere, it may be shown (see Appendix 3) that the latitude L of
UV, may be found from the following formulae:

7915.7045 é æ T° ö æ F° ö ù
sec L = log tan ç 45°+ ÷ − log tan ç 45°+ ÷
d.lat (min s of arc) êë 10 è 2ø 10
è 2 ø úû

. . . 2.6
or:
DMP
sec L = (see Chapter 4) . . . 2.7
d.lat(minutes of arc)
EXAMPLE 1
A ship steams from position F in latitude 30°N, longitude 40°W to a point T
in latitude 34°N, longitude 36°W. Determine the departure, course and
distance.

d.lat = 4°N = 240'N

d.long = 4°E = 240'E
mean lat = ½ (30° + 34°)N = 32°N

From formula (2.5):

dep = 240' cos 32°E = 203'.53E

From formula (2.4):

dep
tan course =
d.lat
course = 040° .3
From formula (2.3):
distance = d.lat sec course = 240' sec 040°.3 = 314'.68
* Throughout the Admiralty Manual of Navigation, the term corrected mean latitude is used in preference to middle
latitude.
MEAN AND CORRECTED MEAN LATITUDE SAILING 29

The corrected mean latitude may be found from formula (2.6):

7915.7045 é æ 34° ö æ 30° ö ù

sec L = log
ê 10 tan ç 45°+ ÷ − log tan ç 45°+ ÷
240' ë è 2 ø 10
è 2 ø úû

L = 32°.033158 (32°02')
dep = 203'.46
course = 040°.3
distance = 314'.64

The difference in distance (0.013%) is so small that the mean latitude may
be used without appreciable error.

EXAMPLE 2
A ship in position F, 70°N, 20°W, steers a course of 020° for a distance of
600 miles. What is her latitude and longitude at the end of the run?

From formula (2.3):

d.lat = 600' cos 20°N
= 563'.81557N
= 9°.3969262 = 9° 23'.8N
lat T = 79° 23'.8N

From formula (2.2):

dep = 600' sin 20°E = 205'.21209E
mean lat = 74°.6984631N (74° 41'.9N)

From formula (2.5):

d.long = 205'.21209 sec 74°.6984631E
= 777'.61623E = 12° 57'.6E
long T = 7° 02'.4W

From formula (2.6):

7915.7045
sec L =
563'.81557
(log10 tan 84° .698463 − log10 tan 80° )
L = 75° .197922 ( 75°11'.9N )

From formula (2.5):

d.long = 205'.21209 sec 75°.197922
= 803'.23871E
= 13°.387312E = 13° 23'.2E
long T = 6° 36'.8W

The discrepancy in longitude is 25'.6E, i.e. 4.7 miles.

The discrepancy in position (0.8% of the distance) at the end of the run
illustrates the danger of using the mean latitude in high latitudes, even though
the distance is only 600 miles.
30 CHAPTER 2 - THE SAILINGS (1)

Although the computation of the longitude using the corrected mean

latitude is an accurate one, it is for the sphere. If one wishes to compute
accurately the rhumb-line position taking into account the spheroidal shape
of the Earth, another method should be used. This is described in Chapter 5.

TRAVERSE SAILING

Traverse sailing is the term given to the combination of plane sailing

solutions when there are more than two courses. The various legs of the
ship’s track are the hypotenuses of a series of plane sailing triangles (see Fig.
2-4). The individual d.lats and departures may be found using formulae (2.2)
to (2.4) and the d.long using formula (2.5).
The traverse table in Norie’s Nautical Tables solves the d.lat/departure/
distance/course plane triangles for any distance up to 600'. Instructions for
the use of these tables are given in the explanation. The tables may also be
used to solve the d.long by means of formula (2.5) by treating the course as
mean latitude, d.lat as departure and distance as d.long.
A pocket calculator with the normal trigonometric ratios is quicker and
more accurate to use than the traverse table and, if a calculator with a co-
ordinate conversion is available, it should be possible to read off d.lat and
departure directly using Cartesian (x, y) co-ordinates. Using a calculator
avoids the need to interpolate between sets of figures as when using the
traverse table.

Fig. 2-6. Polar, Cartesian, co-ordinates of a position

TRAVERSE SAILING 31

In Fig.2-6 the position of T may be defined in polar (r, θ) or Cartesian

(x, y) co-ordinates where:
r = distance
θ = course
x = departure
y = d.lat*
EXAMPLE
A ship in position 45°25'N, 15°05'W at 0900 steers the following courses
and speeds. What is her position at 1315?

TIME COURSE SPEED

0900-0946 045° 15 knots
0946-1015 312° 16½ knots
1015-1122 217° 14¾ knots
1122-1247 103° 17 knots
1247-1315 190° 15 knots

Fig. 2-7. Traverse sailing

* When carrying out polar to Cartesian conversion using a calculator, d.lat appears as x and departure as y because
of the difference between mathematical and navigational conventions on the initial line from which angles are
measured. In navigational notation, course is measured clockwise from the north-south line, while in mathematical
notation, angle is measured anti-clockwise from the east-west line.
 32

Table 2-1 Traverse sailing

TRAVERSE TABLE CALCULATOR

TIME COURSE SPEED DISTANCE
COURSE DEP D.LAT DEP D.LAT
θ r
x ORD y ORD

0900-0946 045° 15 kn 11'.5 N45°E 8'.13E 8'.13N 8'.132 8'.132

0946-1015 312° 16½

kn 7'.975 N48°W 5'.96W 5'.33N -5'.927 5'.336

1015-1122 217° 14¾

kn 16'.471 S37°W 9'.91W 13'.16S -9'.912 -13'.154

1122-1247 103° 17kn 24'.083 S77°E 23'.46E 5'.42S 23'.466 - 5'.417

1247-1315 190° 15kn 7'.0 S10°W 1'.22W 6'.89S -1'.216 - 6'.894

14'.5E 12'.01S +14'.543 -11'.997

(E) (S)

mean lat 0900-1315: 45°19'.0N

d.long (formula 2.5): 20'.7E
position at 1315: 45°13'.0N
14°44'.3W
CHAPTER 2 - THE SAILINGS (1)
MERCATOR SAILING 33

MERCATOR SAILING

As mentioned on page 27, Mercator sailing provides a method of determining

position after travelling along a rhumb line other than in a north-south or
east-west direction. It is similar to plane sailing but uses difference of
meridional parts (DMP) instead of d.lat and d.long instead of departure.
Meridional parts are a feature of the Mercator projection on which the
great majority of small-scale Admiralty navigational charts are based and are
discussed at length in Chapter 4. The calculations involved in Mercator
sailing are set out in Chapter 5.

SPHERICAL GREAT-CIRCLE AND COMPOSITE SAILING

The great circle

A straight line is the shortest distance between two points and, when the two
points lie on the surface of a sphere, the arc of the great circle joining them
is the curve that most nearly approaches the straight line, because it has the
greatest radius and therefore the least curvature. The shorter arc of the great
circle joining two places on the Earth’s surface is thus the shortest route
between them. In Fig. 2-8 FT is such an arc and its length is the shortest
distance between the two points F and T on the Earth’s surface. PF and PT
are arcs of the meridians passing through F and T and are also arcs of great
circles. The triangle PFT is therefore a spherical triangle, and the problem of
finding the shortest distance between two points is the problem of finding the
length of the side opposite the pole in this triangle.

Fig. 2-8. The great circle

34 CHAPTER 2 - THE SAILINGS (1)

The navigator very often requires to know the true bearing of one point
from another. The true bearing of T from F is the angle between the meridian
through F and the great circle joining F and T, measured clockwise from the
meridian ) that is, the angle PFT. This angle represents the initial course to
be steered by a ship sailing on a great circle from F to T. Radio waves also
travel along great circles near the Earth’s surface, and the angle PFT is thus
the bearing of T from F as it would be given by MFDF (Figs 2-9(a) and 2-9(b)).
In Fig. 2-9(a) at any intermediate point G, between F and T, the true
bearing of T is the angle PGT, and this is not equal to the angle PFT. To an
observer moving along the great circle from F to T, the true bearing of T
changes continuously. Only when T is close to F may this change be
neglected. The area of the Earth’s surface traversed by FT is then sufficiently
small to be considered as a plane or flat surface, on which great circles appear
as straight lines.

Fig. 2-9(a) Great-circle bearings Fig. 2-9(b) Initial and final

great-circle courses
Great-circle distance and bearing
The length of the side FT (Fig. 2-8) and the true bearing PFT are found by
solving the spherical triangle FPT. In this triangle the angle FPT is clearly
the d.long between F and T. The lengths of the sides PF and PT depend upon
the latitudes of F and T. When these latitudes have the same name ) both F
and T are north in Fig. 2-8 ) PF is (90° - latitude F) and PT is (90° - latitude
T). The distance (90° - latitude) is known as the co-latitude of the place
concerned.
When the destination is in the opposite hemisphere ) T1 has south latitude
in Fig. 2-8 ) the length of the side PT1 is (90° + latitude T1). Therefore:

For latitudes of the same name:

PF = 90° - latitude F = co-latitude F

PT = 90° - latitude T = co-latitude T
angle FPT = d.long
SPHERICAL GREAT-CIRCLE AND COMPOSITE SAILING 35

For latitudes of the opposite name:

PF = 90° - latitude F = co-latitude F

PT1 = 90° + latitude T1
angle FPT1 = d.long

When F is also in southern latitudes, as in Fig. 2-10, the same relations

hold if P1 is substituted for P, so that for either hemisphere:

PF = 90° ± lat F
PT = 90° ± lat T

the sign being determined by the name of the pole and by the latitude of the
place (same names, subtract; opposite names, add).

Fig. 2-10. The solution of the spherical triangle and the vertex

Great-circle sailing
If a ship followed the great-circle track she would have to change course
continually. In practice, the great-circle track is divided into suitable lengths,
successive points on the great circle being joined to form a succession of
rhumb lines. This is known as approximate great-circle sailing, or simply
great-circle sailing.
Fig. 2-11 illustrates any such approximate great circle. The navigator
would alter course at A, B and C and he would choose the lengths FA, AB, etc.
to suit his convenience. FA for example, might be a twelve-hour run or when
a suitable meridian is crossed, e.g. 10°W, 20°W, 30°W, 40°W and so on.
36 CHAPTER 2 - THE SAILINGS (1)

Fig. 2-11. Great-circle and rhumb-line tracks

The vertex
The point at which a great circle most nearly approaches the pole is called the
vertex (of that great circle) ) V in Fig. 2-10. At this point, the great circle
ceases to approach the pole and begins to curve away. It must therefore cut
the meridian through the vertex at right angles. The method of finding this
position involves the use of right-angled spherical triangles, and is described
in Chapter 5.

The composite track

Since the great-circle track between two places not on the equator passes
nearer to the pole than does the rhumb-line track, the ship may be carried into
the ice region. When ice is likely to be encountered, the great-circle track
must therefore be modified to avoid such high latitudes, while remaining the
shortest possible safe track. This modified track is known as the composite
track, and is formed by two great-circle arcs joined by an arc of the limiting
or ‘safe’ parallel of latitude.

Fig. 2-12. The composite track

In Fig. 2-12 FLVMT is the great circle joining F and T. Latitudes higher
than the parallel of LM are assumed to be dangerous. The ship cannot,
therefore, follow the great-circle arc LVM. Nor would she go from F to L,
along to M and then down to T. The shortest route she can take is FABT,
where FA and BT are great-circle arcs tangential to the safe parallel at A
and B.
SPHERICAL GREAT-CIRCLE AND COMPOSITE SAILING 37

FABT is thus the composite track in this example. It is the shortest route
because, if L and M are taken as any points on the parallel outside the part
AB, (FL + LA) is greater than FA and (BM + MT) is greater than BT.
Moreover, since A is the point nearest the pole on the great circle of which FA
is an arc, any other great circle from F to a point between A and B would cut
the parallel between L and A and so carry the ship into danger.
The calculation of the composite track is set out in Chapter 5.

Solution of spherical great-circle problems

Six methods are considered altogether for solving spherical great-circle
problems. Table 2-2 lists the methods and their applicability to finding the
distance and the course/bearing.
Table 2-2. Solving great-circle problems
METHOD DISTANCE COURSE/
BEARING

Cosine x x
Sine x
Haversine x
Sight reduction x x
tables (NP 401)
Half log haversine x
ABC tables x
(Norie’s)

The cosine method is very suitable for use with a pocket calculator and
is described below. The sine method may be used to cross-check the cosine
solution and may also be used to determine the course or bearing. Both the
cosine and the sine formulae are set out in Appendix 2. Although the sine
formula is ambiguous, this ambiguity is easily resolved in most cases, and the
calculation is simpler than the cosine method. An example is given below.
The haversine and half log haversine methods are set out in Appendix 2.
The sight reduction and ABC methods are set out in Volume II.
The calculation of great-circle courses and distances taking into account
the spheroidal shape of the Earth is set out in Chapter 5.

The cosine method

Great-circle distance

cos FT = cos FP cos PT + sin FP sin PT cos FPT

cos distance = cos (90° ± lat F) cos (90° ± lat T)
+ sin (90° ± lat F) sin (90° ± lat 7) cos d. long . . . 2.8
38 CHAPTER 2 - THE SAILINGS (1)

Fig. 2-13. Solution of spherical great-circle problems

The sign is determined by the name of the pole and the latitude of the
place (same names, subtract; opposite names, add).
In Fig. 2-13 F and T are on opposite sides of the equator; thus, the
latitude of F would be added and that of T subtracted.
When F and T are both on the same side of the equator, formula (2.8)
resolves into:

cos distance = sin lat F sin lat T + cos lat F cos lat T cos d.long . . . 2.9

This basic formula (2.9) may also be used to cover the contrary case by
making any opposite (to the elevated pole) latitude negative. In Fig. 2-13 sin
lat (-F) and cos lat (-F) would be used.
Formula (2.9) may be modified as follows:

cos distance = (tan lat F tan lat T + cos d.long) cos lat F cos lat T
. . . 2.10
Great-circle course/bearing

cos PT = cos FP cos FT + sin FP sin FT cos PFT

cos PT − cos FP cos FT

cos PFT =
sin FP sin FT

cos (90°± lat T ) − cos (90°± lat F ) cos FT

= . . . 2.11
sin (90°± lat F ) sin FT
SPHERICAL GREAT-CIRCLE AND COMPOSITE SAILING 39

In Fig. 2-13 the latitude of T would be subtracted and that of F added.

When F and T are both on the same side of the equator, formula (2.11)
resolves into:

sin lat T − sin lat F cos distance

cos initial course = . . . 2.12
cos lat F sin distance

EXAMPLE
A ship steams from position F (45°N, 140°E) to T (65°N, 110°W). Find the
great-circle distance and the initial course by the cosine method, and also the
initial course by the sine method.

Fig. 2-14. A great-circle problem

A great-circle distance

The cosine method

cos distance = sin lat F sin lat T

+ cos lat F cos lat T cos d.long . . . (2.9)
= sin lat 45° sin lat 65°
+ cos lat 45° cos lat 65° cos 110°
= 0.53864837 (by pocket calculator)*
G.C. distance = 57°.408325 = 3444'.5

* In this and subsequent examples using the sailings, the final answer is usually rounded off to the nearest degree
for course and 0.1 mile for distance. This is the degree of precision to which the practical navigator usually works
these problems at sea, as governed by the accuracy of the equipment available. However, so that the student may
follow the examples given using his own electronic calculator, the workings are normally shown to six or more
decimal places.
40 CHAPTER 2 - THE SAILINGS (1)

The initial course

The cosine method

sin lat T − sin lat F cos distance

cos initial course = . . . (2.12)
cos lat F sin distance

sin lat 65°− sin lat 45° cos 57° .408325

=
cos lat 45° sin 57° .408325

0.52542587
= = 0.88194343
0.59575915

initial course = N28°.122305E = 028°

sine rule check:

sin 57° .408325 sin 25°

= = 0.8966024
sin 110° sin 28° .122305

The sine method

sin FT sin PT
=
sin FPT sin PFT

sin PT sin FPT

sin PFT =
sin FT
sin (90°± lat T ) sin d.long
sin initial course = . . . 2.13
sin distance

cos lat T sin d.long

=
sin distance

cos 65° sin 110°

= = 0.47135526
sin 57° .408325

PFT = N28°.122305E or N151°.87769E

In this case the ambiguity is easily resolvable, as the great-circle course

from F to T must lie to the north of east. Thus:
initial course = 028°
 41

CHAPTER 3
An Introduction to Geodesy

Goedesy is that branch of mathematics concerned with large areas in which

allowance must be made for the curvature of the Earth’s surface. As the
accuracy to which a ship may now be navigated world-wide is governed by
this irregular shape, a general understanding of geodesy is necessary. This
chapter introduces the navigator to this subject.

DEFINITIONS AND FORMULAE

The oblate spheroid

As already mentioned in Chapter 1, the Earth is an oblate spheroid rotating
about its shortest diameter which is the polar axis, PP1 in Fig. 3-1.

Fig. 3-1. The oblate spheroid

The flattening of the Earth

The polar radius b is somewhat less than the equatorial radius a; thus, the
Earth may be considered as being ‘flattened’ in the polar regions.
42 CHAPTER 3 - AN INTRODUCTION TO GEODESY

The flattening or ellipticity of the Earth may be defined by a quantity f

where:

. . . 3.1

The eccentricity
When a point M (Fig. 3-2) moves so that its distance from a fixed point S (the
focus) is always in a constant ratio e (less than unity) to its perpendicular
distance from a fixed straight line AB (the directrix), the locus of M is called
an ellipse of eccentricity e.

Fig. 3-2. The eccentricity of the ellipse

In Fig. 3-2:
MS = eMC
e may be defined in terms of a and b by the formula:
1/2
æ a 2 − b2 ö
e= ç 2
÷ . . . 3.2
è a ø
From formula (3.1):

(
e= 2f − f 2 )1/2 . . . 3.3
DEFINITIONS AND FORMULAE 43

Geodetic and geocentric latitudes

Fig. 3-3 shows a meridional section of the spheroid. M is a point on the
meridian PAP1, and MK is the tangent to the meridian at M. If the normal to
this tangent LM cuts OA in L, the angle MLA is called the geodetic latitude of
M, and denoted by φ .

The angle MOA is called the geocentric latitude of M and is denoted by θ.

Fig. 3-3. Geodetic and geocentric latitudes

φ and θ are connected by the formula (see Appendix 5):

b2
tan θ = tan φ . . . 3.4
a2
2
= (1 − f ) tan φ . . . 3.5

= (1 − e 2 )tan φ . . . 3.6

The difference between the geodetic and geocentric latitudes is zero at the
equator and the poles and has a greatest value when φ = 45°. For the
International (1924) Spheroid the greatest value is about 11.6 minutes of arc.

The parametric latitude

Fig. 3-4 shows a meridional section of a spheroid WPE; its polar axis is OP
and its shape and size are defined by the radii OE = a, and OP = b. WBE is
the meridional section of a sphere with centre O, polar axis OB and radii OE
= OB = a. M is a point on the spheroid with geodetic latitude φ . HM is
parallel to OP and produced to cut the circle WBE at U. The radius OU
makes an angle β with the X axis.
44 CHAPTER 3 - AN INTRODUCTION TO GEODESY

Fig. 3-4. Parametric latitude

It may be shown (Appendix 5) that:
b
tan β = tan φ . . . 3.7
a
The angle β is known as the parametric or reduced latitude of the point
M. This parametric latitude is frequently used in long distance calculations
on the spheroid (see Chapter 5).
The length of one minute of latitude
As indicated on page 6, the length of the sea mile varies between the
equator and the poles because of the changing radius of curvature.
The length of 1 minute of latitude may be found from the formula ρ dφ ,
where ρ is the radius of curvature in the meridian and dφ is a small
increase (measured in radians) in the geodetic latitude φ (Fig. 3-5). It may
be shown (Appendix 5) that:

ρ=
( )
a 1 − e2
. . . 3.8
(1 − e2sin2φ )3/2
When dφ is equal to 1 minute of arc:

l' of latitude =
( )
a 1 − e2
sin l'
. . . 3.9

(1 − e2sin2φ )3/2
when φ = zero

(
l' of latitude at the equator = a 1 − e2 sin 1' ) . . . 3.10
THE DETERMINATION OF POSITION ON THE SPHEROID 45

Fig. 3-5. The length of one minute of latitude

The length of one minute of longitude

As indicated on page 7:
l' of longitude at the equator = a sin 1' . . . 3.11

At latitude φ : a cos φ
l' longitude = sin 1' . . . 3.12
(1 − e 2
sin 2 φ )
1/ 2

The geodesic
In the same way that a great-circle gives the shortest distance between two
points on a sphere, a geodesic is the shortest line between two points on the
spheroidal Earth.

Geodetic datum
In geodesy there are two kinds of datum: a horizontal datum, e.g. the
Ordnance Survey of Great Britain (1936) Datum, from which basis the
latitude and longitude of a place may be determined taking into account the
spheroidal shape of the Earth; a vertical datum, e.g. Ordnance Datum
(Newlyn), to which heights are referred.

THE DETERMINATION OF POSITION ON THE SPHEROID

Anyone at the Central Signal Station Flagstaff in Portsmouth Dockyard

knows where he is in relation to his geographical surroundings. However, to
inform someone else in another place, for example the Falkland Islands, of
46 CHAPTER 3 - AN INTRODUCTION TO GEODESY

that position, details need to be sent using a recognisable method, e.g. latitude
(50°47'.95N) and longitude (1°06'.53W).
Provided that the same horizontal datum is used for the determination of
latitude and longitude in both places, it is possible to calculate with accuracy
the position of one place relative to the other. However, when places are a
long way apart, the same horizontal datum is frequently not used. Thus,
although the latitude and longitude of both locations may be ‘known’, as
exact calculation of the bearing and distance between them cannot be made.

Fig. 3-6. The spheroidal shape of the Earth

The geoid
The basis for the determination of latitude and longitude depends upon the
spheroidal shape of the Earth. However, the shape cannot be measured
directly although it is possible to measure a section of its surface, e.g. AB in
Fig. 3-6. This measurement is usually taken along a meridian of longitude.
THE DETERMINATION OF POSITION ON THE SPHEROID 47

The positions of A and B may be determined using instruments such as

the theodolite to measure horizontal and vertical angles on the Earth, and the
theodolite or the astrolabe to obtain the astronomical position. These
instruments must however be levelled before use, and thus require the use of
gravity to determine the vertical. But the vertical itself is deflected by the
mass of the Earth and this means that the ‘horizontal’ with reference to which
the observation has been made is irregular. In Fig. 3-6, this ‘horizontal’ is
shown by the pecked line GLG1. This pecked line is known as the geoid and
may be defined as that surface which corresponds to the Mean Sea Level of
the oceans, assuming that it would be possible to take a mean sea level
through the Earth’s continents. It tends to rise under mountains and dip
above ocean basins. The direction of gravity (or local vertical) is always
perpendicular to the geoid.
Since the geoid is not of a regular shape, its surface cannot be defined by
a single, simple, algebraic formula. It is not, therefore, used for the
mathematical calculations required to determine latitude and longitude
because of the complexity involved.
This difficulty is overcome by using a regular but fictional surface, PLQ
in Fig. 3-6, called the spheroid for the calculation. This spheroid is chosen
as the closest fit to the geoidal section GLG1.

Calculation of the position

The observer at A measures his position by observation of heavenly bodies
and adjusts it to mean sea level to fit the geoid at A1. He then very carefully
measures the position of B on the spheroid by use of his instruments, using
chosen values of OP and OQ. The position of B on the geoid, B1, may now
be calculated. Astronomical observations at B will show the difference
between the two positions, and this difference is a measure of the way the
chosen spheroid PLQ ‘fits’ the geoid GLG1. Usually at least two more places
C and D, etc. are also observed, to check that the chosen spheroid is
satisfactory.

Geodetic latitude and longitude

Before these calculations can be used for the determination of latitude and
longitude using the selected values of the spheroid, there is one further
problem to resolve.
The astronomical observation at A (reduced to Mean Sea Level to give
the position at A1) is determined by the direction of the local vertical at A1,
A1V. Thus, the astronomical (observed) latitude of A1 is the angle A1VQ. But
as it is intended to use the spheroid PLQ for calculating latitude and
longitude, the observed latitude must be corrected for the fact that the normal
to the spheroid is not A1V but A2M and the geodetic (spheroidal) latitude
which is the one actually charted is the angle A2MQ.*
Geodetic (charted) longitude may be determined in the same way, being
the angle between the plane of the geodetic meridian at Greenwich and the
geodetic meridian of the place. The astronomical (observed) longitude is

* The deviation of the vertical, i.e. the difference between the angle A1VQ and A2MQ is very small (only a few
seconds of arc) in flat countries, and larger in mountainous regions. In extreme cases (e.g. Colombia in South
America) it may be as much as 1 minute of arc.
48 CHAPTER 3 - AN INTRODUCTION TO GEODESY

adjusted for any difference between the local vertical at Greenwich and the
local vertical at the place, to arrive at the geodetic (charted) longitude.
Once the observed latitude and longitude have been adjusted in this way,
the chart may be drawn up for geodetic latitude and longitude using the
assumed values of the spheroid.
Very often, to make the calculation simpler, the spheroid and the geoid
are assumed to be coincident and parallel at the chosen point known as the
origin. There is then no difference between the two verticals. This is not a
necessary requirement, however, and geodetic values may be chosen which
given the ‘best fit’ over the largest area, or use the same spheroidal shape as
adjacent systems.
A horizontal datum is thus a connected series of survey stations whose
positions are defined by a spheroid and by the relationship between the
spheroid and a point established as the origin, e.g. the Ordnance Survey of
Great Britain (1936) Datum is based on the Airy Spheroid and has its origin
at Herstmonceux.

Reference datums and spheroids

Throughout the world, a number of these datums and associated spheroids
have been used for charting. In consequence, there are differences to
geodetic latitudes and longitudes, albeit small, between different charting
systems. Table 3-1 gives some examples of the datums and spheroids used.

Satellite geodesy
Since the 1960s the limitations of the classical methods have been overcome
by the use of extremely accurate satellite techniques. Accurate co-ordinates
of ground stations and the Earth’s gravity field have been determined from
Doppler and laser observations to satellites, and the height of the geoid has
been measured over sea areas by satellite altimetry.
By combining these data with surface measurements, a worldwide 3-D
reference system and a spheroid which best fits the geoid have been defined.
It has also been possible to establish the relationships between previously
unconnected datums and to convert them to the world datum.

World geodetic systems (WGS)

In the past the differences in the various datums used for charting had
very little effect on the day to day navigation of ships, particularly as the
errors inherent in astronomical observation were larger than any discrepancy
in charted latitude and longitude. However, it became clear in the late 1950s
that the increasing range of weapon systems (thousands of miles in some
cases) and the requirements for manned space flight necessitated the
establishment of an agreed worldwide spheroid which fitted the actual shape
of the whole Earth as closely as possible and whose centre coincided with its
centre of mass. This came about with the development of the World Geodetic
System 1972 (WGS 72) spheroid, details of which are given in Table 3-1. A
few metric charts throughout the world are now compiled on this basis.
The US Navy Navigation Satellite System (TRANSIT), which came into
being in 1964, is now based on WGS. The increasing world-wide use of this
system, accurate to the order of 100 metres, shows up the discrepancies in the
Table 3-1. Comparison of datums and spheroids

CHARTED DATUM SPHEROID EQUATORIAL POLAR FLATTENING ECCENTRICITY ECCENTRICITY2

AREAS RADIUS a RADIUS b
METRES METRES f=a!b e = (2f ! f2)1/2 e2 = 2f ! f2
(N MILES) (N MILES) a

British Ordnance Airy 6 377 563 6 356 257

Isles Survey of 1/299.325 0.081673374 0.006670540
Great Britain (3443.609) (3432.104)
(1936) Datum
North-West European Inter- 6 378 388 6 356 912
Europe Datum national* 1/297 0.08199189 0.006722670
(1950) (1924) (3444.054) (3432.458)
North The North Clarke 6 378 206 6 356 584
America American 1866 1/294.98 0.08227185 0.006768658
(1927) Datum (3443.956) (3432.281)
Southern Arc Datum Clarke† 6 378 249 6 356 515
Africa 1880 1/293.465 0.0824834 0.006803511
(3443.98) (3432.245)
THE DETERMINATION OF POSITION ON THE SPHEROID

Worldwide World WGS 72 6 378 135 6 356 751

Geodetic 1/298.26 0.0818188 0.006694318
System 1972 (3443.917) (3432.371)

* The International (1924) Spheroid is used for the calculations of distances in the Admiralty Distance Tables and Ocean Passages for the World.
† Meridional parts (see Chapter 4) for the Clarke (1880) Spheroid are tabulated in Norie’s Tables.
49
50 CHAPTER 3 - AN INTRODUCTION TO GEODESY

various datums used for charting. It has thus become necessary to tabulate
this discrepancy on any chart not based on WGS in the form of a correction
to the latitude and longitude of the position obtained from TRANSIT. This
correction is known as the datum shift and may be as large as several hundred
metres in well surveyed areas. For example, in Southampton Water the datum
shift amounts to about 130 metres (145 yards). A further error, amounting to
a mile or more in poorly surveyed areas such as parts of the Pacific Ocean,
may also arise from errors in the charted geographical position.
A similar problem exists with the Royal Navy’s automated Navigational
Plotting System, which is also based on WGS.
NAVSTAR GPS is based on the WGS 84 Datum, which uses the GRS
(Geodetic Reference System) 80 Spheroid. As far as the navigator is
concerned, the differences between WGS 72 and WGS 84 are negligible.
These three systems are described in detail in Volume III of this manual.
 51

CHAPTER 4
Projections and Grids

GENERAL

For the purposes of navigation it is necessary to project the features of the

Earth’s surface on to a chart. A projection is a means of representing a
spheroidal surface on the plane. It is usually expressed as a mathematical
formula for converting geographical co-ordinates on the spheroid to plane co-
ordinates on the chart or map. Provided it is suitable a projection may be
used to represent any portion of the Earth’s surface.
Since it is impossible to fit exactly a plane surface on to a spheroidal one,
projections of anything but very small areas will contain some distortion. For
example, in Fig. 4-1 it can be seen that three identical circular areas on the
Earth’s surface are each represented by a quite different size and shape when
the outline is projected from a point of origin at the centre of the Earth on to
a plane chart.
The distortion of a projection must involve some or all of the following
properties:

1. Shape. 2. Bearing. 3. Scale. 4. Area.

It is possible to devise a good projection which will eliminate or reduce

to negligible proportions some of these distortions while keeping the others
within reasonable and thus usable limits. The choice of projection for a chart
of map is governed by the requirements of the user. The mariner requires a
chart which will not only show the correct shape of the land he is looking at,
but also give him his correct position, course and speed when he plots
bearings and distances on it. Unfortunately all these requirements cannot be
met in one single projection, and a compromise must be made by accepting
a very close approximation to all three (shape, bearing, distance), or
satisfaction of two (usually shape and bearing) at the expense of the third
(distance or scale).
The network of lines representing the meridians of longitude and parallels
of latitude which derive from any projection is known as a graticule.
A grid is a reference system of rectangular (Cartesian) co-ordinates
obtained when a projection is applied to a particular part, or the whole of the
world. Grids are described in detail at the end of this chapter.
Further information on projections, including their mathematical
derivations, is given in Appendix 4.
52 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-1. Distortion on a chart of the Earth’s features

 GENERAL

Fig. 4-2. Mercator chart of the world

53
54 CHAPTER 4 - PROJECTIONS AND GRIDS

The ‘flat Earth’

Over a limited area (12 mile radius from a point) the Earth may be assumed
to be flat for all practical purposes, as the errors introduced by this
assumption are less than those resulting from the measurement of angles and
distances. At a distance of 50 miles from a point, the errors introduced by
assuming the Earth is flat are about 1:12,000 for distance (i.e. approximately
8 metres in 50 miles) and 8" for angles, and increase fairly rapidly beyond
this distance. A plan may be constructed on the principle of the assumed
flatness of the Earth by transferring measurements made on the spherical
surface directly to a sheet of squared paper.

Orthomorphism or conformality
An orthomorphic or conformal projection is a type of chart or map projection
on which the shape of the land truly pictures that on the Earth. At any point
on that chart or map the scale, whatever it may be, is the same in all
directions, and also the parallel of latitude and meridian of longitude at that
point are at right angles to each other. Thus, angles around any point on that
chart or map are correctly represented.
Correctness of shape applies only to small areas. On the same chart the
scale in one latitude may not be the same as the scale in another latitude, but
so long as the scale along the meridian is equal to the scale along the parallel,
the immediate neighbourhood of that point is just as correctly shown as the
immediate neighbourhood of a point some distance removed. Mercator charts
are orthomorphic. On a Mercator chart of the world, for example (Fig. 4-2),
the area around Cape Farewell in Greenland is just as correctly shown for
shape as is the estuary of the Amazon in South America, although Greenland
as a whole ‘appears’ about the same size as South America whereas it is
actually about one-tenth the size. This is because the scale of distance in the
Greenland area is quite different from the scale being used to depict South
America on the same chart.
The real significance for navigation of this orthomorphic property of
charts is as follows. If distortion of shape occurs, then distortion of the
bearing scale or compass rose must also occur. A compass rose on a chart
which is not orthomorphic will not be circular, nor will its graduation be
uniform, and it would be very difficult if not impossible to lay off courses and
bearings correctly.

Derivation of projections of a sphere

Consider an imaginary sphere shown in Fig. 4-3. It would be possible to fit
plane surfaces around it in a variety of ways, six of which are shown. In (1), (3)
and (5) the surfaces touch the sphere along a circle or at a point; in (2), (4) and (6)
they have been sunk into the sphere, in (2) and (4) cutting it along two circles and
in (6) cutting it along a single circle.
If the detail on the sphere is now projected on to the plane surface from
a point on the axis of the cone, cylinder or plane circle, there will be no
distortion of scale along the tangential circles or points which are shown in
stipple. Elsewhere there is distortion of some sort or another, which will
persist when the planes are unwrapped and laid flat.
GENERAL 55

Fig. 4-3. Projections of a sphere

56 CHAPTER 4 - PROJECTIONS AND GRIDS

In (1), (2), (3) and (4) the point from which the projection takes place is
usually the centre of the sphere, while with (5) and (6) it may take place form
anywhere on the axis at right angles to the plane but usually either from B, the
centre of the sphere, or A, the opposite ‘pole’. The projections are usually
referred to as follows:

1 Conical with one standard parallel.

2 Conical with two standard parallels.
3 Cylindrical with one standard parallel.
4 þ Cylindrical with two standard parallels.
5 and 6
ý Zenithal projected from A ) stereographic.
ü
Zenithal projected from B ) gnomonic.

There is no reason except convenience why the cones should occupy the
upright position as in Fig. 4-3; they could equally well be inclined at any
angle to the vertical.
Projections of the spheroid
None of the projections shown in Fig. 4-3 (except 5 and 6 when projected
from A) is orthomorphic for the sphere, and none of them is orthomorphic for
the spheroid (the shape of the Earth). To overcome this, a whole family of
projections has been devised, analogous to the graphical ones in Fig. 4-3 but
all completely mathematical, with their formulae adjusted in such a way as to
ensure that some are orthomorphic, some are equal area and so on, as
required.
Types of projection in current use both for charts and grids are
summarised in Table 4-1 pp. 58-9.
Lambert’s conical orthomorphic projection
This projection (Table 4-1, A) is a modification of the conical projection with
one or two standard parallels (Fig. 4-3(1) and (2)). The parallels other than
the standard parallels appear as circular arcs concentric with the standard
parallels, but the distances between them are chosen so that the projection is
orthomorphic. To achieve this, the scale along the meridian at any place must
be equal to the scale along the parallel at that place. Clearly, the scale along
the meridians cannot now be uniform but must be adjusted to the scale along
the parallels. The scale is correct only along the standard parallels; if there
are two of these, the scale is smaller between them and it becomes
increasingly large outside. The extent of latitude covered by the projection
is limited so that the scale error does not become unacceptable. Great circles
are very nearly represented by straight lines on this projection.
Lambert’s projection is suitable for countries with a large extent in
longitude but not much in latitude; however, it cannot be used at all in very
high latitudes. It has been used a great deal in the past but is being
superseded by the Universal Transverse Mercator (UTM) projection.
Mercator’s projection
This projection (Table 4-1, B) is described in detail later. It is a special case
of the Lambert’s conical orthomorphic projection in which the equator is used
as the latitude of the origin. It is also special in that the units employed are
GENERAL 57

generally minutes of longitude measured along the equator. Owing to its

unique properties the projection is widely used for navigational charts. In this
form the actual grid is not shown, although accurate calculations are generally
carried out in terms of meridional parts which form the unit of the grid.

Transverse Mercator projection

This projection (Table 4-1, C) is described in detail later. It is made by
turning the Mercator projection through 90° so that the equator becomes in
effect a central meridian and a chosen geographical meridian becomes the
transverse equator. The scale error and distortion in shape away from this
central meridian or transverse equator are the same as those of the standard
Mercator away from the equator. If wide bands of longitude have to be
covered, new central meridians must be chosen for new zones. The
projection is orthomorphic while the geographical meridians and parallels are
curved lines (except the meridian where the cylinder touches the sphere, Fig.
4-3(3) turned through a right angle).
This projection may be used for polar charts and maps although RN polar
charts are based on the polar stereographic projection (see below).
The transverse Mercator projection has been used for new Admiralty
large-scale charts and harbour plans since the mid 1970s instead of the
modified polyconic (see page 61).

Skew orthomorphic projection

The skew orthomorphic projection (Table 4-1, D) is the general case, of
which both the Mercator and transverse Mercator projections are special
cases. It is used mainly for land surveys, particularly those of narrow extent,
e.g. Malaysia and Malagasy. Instead of a central meridian, a central great
circle passing through the axis of the country is used as the transverse
equator.

Gnomonic projection
The gnomonic projection (Table 4-1, G) is described in detail later. It is only
applied to a sphere which represents the Earth and on it great circles project
as straight lines. It is not orthomorphic. It is used for very small scale charts,
which enable the navigator easily to obtain great-circle tracks.

Stereographic projection
The point of origin of a stereographic projection (Table 4-1, F) may be
anywhere; however, as this projection is only used in polar areas, only a brief
description of the Universal Polar Stereographic projection is given.
The meridians and parallels of latitude are projected on to a plane
tangential to the pole, the centre of projection being the opposite pole (Fig.
4-3(5)). Meridians appear as straight lines originating from the pole, parallels
of latitude as circles radiating outwards from and centred on the pole. The
projection is orthomorphic and has less distortion than the polar gnomonic
projection previously used for polar charts. Great circles (except meridians)
are not projected as straight lines (although in practical terms little accuracy
is lost by plotting them as such).
58 CHAPTER 4 - PROJECTIONS AND GRIDS

Table 4-1. Types of projection in use

GENERAL 59

INTENTIONALLY BLANK |
60 CHAPTER 4 - PROJECTIONS AND GRIDS

This projection is used for polar charts and orthomorphic maps of polar
regions. It should be noted that there are now no Admiralty charts on the
polar gnomonic projection.

Polyconic projection
The polyconic projection (Table 4-1, H and Fig. 4-4) is another modification
of the simple conical projection. The chosen central meridian of the area to
be shown is divided correctly for intervals of latitude, but each parallel is
constructed as if it were the standard parallel of a simple conical projection.
The parallels are arcs of circles, the radii of which steadily increase as the
latitude decreases. The meridians, other than the central one, are curved. The
central meridian is of course a straight line.

Fig. 4-4. Polyconic projection

The projection is neither orthomorphic nor equal area, so it is unsuitable

for large areas. Its main advantage is that, if small areas are shown on this
projection, each area covering the same amount of longitude, the sheets on
which the geographical graticules are drawn fit exactly along their northern
and southern edges and, for ordinary purposes, along their eastern and
western edges, although the join here is a ‘rolling fit’ as the meridians are
curved. It is therefore suitable for topographical maps which, individually
covering a small area, combine to cover a large one.
MERCATOR PROJECTION/CHART 61

In slightly modified form (in which the meridians project as straight lines) the
polyconic projection is used for the 1:1 Million International maps, and for
most large-scale Admiralty charts. In this latter form it has often wrongly
been referred to as the gnomonic projection, and is indeed so referred to on
the large-scale chart itself. As mentioned on page 57, this projection has now
been superseded by the transverse Mercator for large-scale charts since the
mid-1970s.

MERCATOR PROJECTION/CHART

To the navigator, the most useful chart is one on which he can show the track
of his ship by drawing a straight line between his starting point and his
destination, and thus measure the steady course he must steer in order to
arrive there. The Mercator chart permits him to do this because it is
constructed so that:

1. Rhumb lines on the Earth appear as straight lines on the chart.

2. The angles between these rhumb lines are unaltered, as between Earth
and chart.

It therefore follows that:

1. The equator, which is a rhumb line as well as a great circle, appears on

the chart as a straight line.
2. The parallels of latitude appear as straight lines parallel to the equator.
3. The meridians appear as straight lines perpendicular to the equator.*

The idea of the projection belongs to Gerhard Kremer, a Fleming who

adopted the name Mercator. Kremer used the graticule derived from the
projection in the world map which he published in 1569. The graticule,
however, was inaccurately drawn above the parallels of 40°, and there was no
mathematical explanation of it. That was not forthcoming until Wright
calculated the positions of the parallels and published the results in his Errors
of Navigation Corrected thirty years later. The chart came into general use
among navigators in about 1630, but the first complete description of it did
not arrive until 1645, when Bond published the logarithmic formula.

Principle of the Mercator projection

Earlier in this chapter (page 56) the Mercator projection is referred to as a
special case of the Lambert conical orthomorphic projection in which the
equator is used as the latitude of the origin φ0 . Fig 4-5 shows what happens
when the latitude of the origin is 0°.
RO is a central meridian and is equal in length to Vo cot φ , where Vo is the
radius of curvature at right angles to the meridian at O for the figure of the
Earth in use, and φ is the latitude of O. As the cotangent of 0° is infinity, R
recedes northwards (or southwards) to infinity.

* For all practical purposes, a meridian may be considered as a rhumb line on a Mercator projection. The argument
that it cannot be one since there is a change of direction of 180° at the pole is academic as the Mercator projection
cannot extend as far as the pole.
62 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-5. Mercator projection

The angle between true north and grid north becomes zero for this
projection, thus there is no convergence.
OPo coincides with grid east, all the parallels become straight lines
parallel to OPo and, since there is no convergence, all the meridians are
parallel to grid north.
The choice of a minute of longitude measured along the equator (or
standard parallel) as the unit of the grid makes this projection very suitable
for navigational work.
The characteristics of this protection are governed by two considerations:
it is orthomorphic and the constant of the cone is zero.* For this reason it is
always known among cartographers as a cylindrical orthomorphic projection,
and it is a mathematical, not a perspective, projection.

* The quantity sin φ0 , is known as the Constant of the Cone, and it is of course a constant for any given latitude
of the point of origin. When the equator is the point of origin:
sin φ0 = sin 0° = 0
MERCATOR PROJECTION/CHART 63

The orthomorphic property is achieved by spacing the parallels at

increasing intervals as they approach the poles; this arrangement coupled
with the fact that the meridians and the parallels on any cylindrical projection
where the standard parallel is the equator must be straight lines at right
angles, the meridians furthermore being equally spaced, leads to the other
property so important to the navigator, namely that rhumb lines also are
straight lines. The meridians on a Mercator chart being thus parallel straight
lines running north and south, any straight transversal makes a constant angle
with them, and there is no distortion of this angle because the orthomorphic
property ensures that the correct shape is preserved at all points along the
transversal. It is thus the true angle and, since it is constant, the transversal
is a rhumb line.
The problem of the Mercator chart is thus the problem of finding the chart
length of any parallel from the equator when the orthomorphic property is to
be achieved.

Longitude scale on a Mercator chart

Since the meridians of the Mercator graticule are straight lines at right angles
to the equator, the longitude scale is the same everywhere and provides the
means of comparing chart lengths. Let the scale of any Mercator chart be x
millimetres to 1' of d.long. Then, since departure • d.long cos lat,* the
departure on the chart represented by x millimetres approximates to 1' cos lat:
i.e. one mile in that particular latitude is represented by x sec lat millimetres
on the chart, approximately.
The latitude scale cannot be used because it is continually being stretched
as the latitude increases, and the distance of any parallel from the equator
must be expressed in units of the longitude scale in order that the parallel may
be drawn in its correct position on the graticule. The scale of latitude and
distance at any part of a Mercator chart is proportional to the secant of the
latitude of that part. For this reason, the amount of distortion in any latitude
is governed by the secant of that latitude. Greenland, in 70°N, for example,
appears as broad as Africa is drawn at the equator, although Africa is three
times as broad as Greenland (sec 70°• 3). For a similar reason Borneo, an
island on the equator, appears about the same size as Iceland in 65°N,
although in area Borneo is about five and a half times as large as Iceland.

Graduation of charts and the measurement of distance

Graduation of charts
Mercator charts are graduated along the left-hand and right-hand edges for
latitude and distance, and along the top and bottom for longitude. The
longitude scale is used only for laying down or taking off the longitude of a
place, never for measuring a distance.

Measurement of distance on the chart

The length of the rhumb line between two places is referred to as the distance
between them.

* This formula is only correct for the sphere. For the spheroid, the precise length of one minute of longitude is
given by formula (3.12) (see page 45).
64 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-6. Measurement of distance

In Fig. 4-6 FABCT is a rhumb line as it appears on the chart; FF1, AA1,
BB1 etc. are parallels of latitude.
The distance FA must be measured on the latitude scale between F1 and
A1, the distance AB on the scale between A1 and B1, and so on. If FT is not
large ) less than 100' ) no appreciable error is made by measuring it on the
scale roughly either side of its middle point.

Meridional parts
Since the latitude and distance scale at any part of a Mercator chart is
proportional to the secant of the latitude of that part, this scale continually
increases as it recedes from the equator, until at the pole it becomes infinite.
(For this reason, the complete polar regions cannot be shown on a Mercator
chart.) The latitude scale thus affords no ready means of comparison with the
fixed longitude scale. The tangent of the course-angle PFT, for example, is
not PT divided by FP, where PT is measured on the longitude scale and FP
on the latitude scale. For that ratio to be valid, PT and FP must be measured
in the same fixed units. The fixed longitude scale provides this unit, which
is the length of 1 minute of arc on that scale. This length is called a
meridional part, and gives rise to the definition:

The meridional parts of any latitude are the number of longitude units
in the length of a meridian between the parallel of that latitude and the
equator.

The number of meridional parts for any latitude may be found from
formulae (4.1) for the sphere (page 65), and (5.21) for the spheroid (page 95).
They are also tabulated in:

Norie’s Nautical Tables (NP 320) (compression ratio 1/293.465)

Burton’s Nautical Tables
Table of Meridional Parts based on the International (1924) Spheroid
(NP 239) (compression ratio 1/297)
MERCATOR PROJECTION/CHART 65

If the longitude scale on the Mercator chart is 1 degree or 60 meridional

parts to 10 mm, the length of the meridian between the parallel of 45°N and
the equator, when measured on the chart, is not 450 mm but 502.3 mm, the
length of 3013.58 meridional parts (NP 239). Meridional parts thus involve
chart lengths. They are not in any way connected with distance on the Earth’s
surface, which is expressed in sea or n miles.

To find the meridional parts of any latitude

In Fig. 4-7, the upper half of which represents a part of the Earth’s surface,
F is a point on the equator, and FT the rhumb line joining it to T. The lower
half of the figure shows this same rhumb line as the straight line ft on a
Mercator chart.
If TQ is now divided into n small lengths α, so that (nα) is equal to the
latitude of T, the arcs of parallels drawn through the points of division are
equally spaced and, with the meridians, form a series of small triangles FAX,
ABY, ... If, furthermore, α is so small that these triangles may be considered
plane, they are equal in all respects, since:

FX = AY = ... = α
FXA = AYB = ... = one right angle
XFA = YAB = ... = the course
∴ AX = BY = ...

and, since these small arcs recede in succession from the equator, the
meridians which bound them are spaced successively farther apart. Hence:

FQ1 < Q1Q2 < . . .

A comparison of the two halves of the figure should make clear the
relation between the small triangles when they are drawn on the Earth and
their appearance on the chart. On the Earth they are all equal, but on the chart
they are only similar. They increase progressively as they recede from the
equator. This increase can be found by considering two similar and
corresponding triangles. Thus:
fx ax FQ1
= = = sec lat A
FX AX AX
fx = FX sec lat A
= α sec α
Similarly, by considering the triangles ABY and aby:
ay = α sec 2 α
But qt, the length of the meridian between the parallel through t and the
equator, is the sum of all the elements fx, ay . . . kz. That is:

qt = α (sec α + sec 2α + sec 3α + . . . + sec nα)

æ T° ö
= 7915.7045log10 tanç 45°+ ÷ . . . 4.1
è 2ø
66 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-7. Meridional parts

MERCATOR PROJECTION/CHART 67

This formula (see Appendix 3) gives the number of meridional parts in

the latitude of T for a perfect sphere. In the Table of Meridional Parts (NP
239), as previously mentioned (page 64), the meridional parts are given
allowing for the spheroidal shape of the Earth; the accurate formula is given
in Chapter 5, formula (5.21) (page 95) and its proof given in Appendix 5. For
example, the number of meridional parts between the parallel of 20° and the
equator is 1217.23.

Difference of meridional parts

Where the two positions are both remote from the equator, for example A and
K in Fig. 4-7, their relative position may be determined by the difference
between the meridional parts for K and the meridional parts for A, which
gives the number of longitude units in the length of a meridian between the
two parallels of latitude through A and K. This length mk is usually referred
to as the difference of meridional parts and written as DMP. (See the
examples given on pages 87 and 95 of this volume for the sphere and the
spheroid respectively.)

Property of orthomorphism
Since the scale along a meridian in the neighbourhood of a point in latitude φ
is stretched by the same amount (sec φ ) as the scale along the parallel through
that point, and the meridians and parallels on the Mercator projection are at
right angles, the projection must be orthomorphic. (See pages 54 and 62 of
this chapter.)

To construct a Mercator chart of the world

Since there is no distortion at the equator, the base on which the chart is built
must be the line representing the equator, and convenience governs the length
of this line. Suppose it is 720 mm (about 28 in). Then the longitude scale
must be:
length of equator in degrees 360
=
length of base in millimetres 720
that is, ½° of longitude or 30 meridional parts to 1 mm; more conveniently,
5° of longitude or 300 meridional parts to 10 mm. Vertically the scale will
be the same, 300 meridional parts to 10 mm.
If it is required to draw the meridians for every 20°, for example, the
equatorial line must be divided into eighteen equal parts, 40 mm long. The
perpendiculars drawn through the points of division will be the meridians.
The one through the left-hand extremity will be the meridian of 180°W, the
one through the right-hand extremity the meridian of 180°E.
The Table of Meridional Parts (NP 239) gives all the information
necessary for deciding the positions of the parallels of latitude. The number
of meridional parts between the parallel of 20° and the equator is 1217.23
and, since these are drawn on a scale of 300 meridional parts to 10 mm, the
parallels of 20° must be drawn 1217.23 ÷30, or 40.57 mm either side of the
equatorial line on the chart.
68 CHAPTER 4 - PROJECTIONS AND GRIDS

The number of meridional parts between the parallel of 40° and the
equator if 2607.82. The parallel of 40° is therefore drawn 2607.82÷ 30, or
86.93 mm from the equatorial line.
In the same way the other parallels are drawn, and on the graticule thus
formed it is possible to insert the position of any place the latitude and
longitude of which are known.

To construct a Mercator chart on a larger scale

In order that small portions of the Earth may be shown in detail, it is
necessary to employ a larger scale and construct only the relevant portion of
the chart. If it so happens that the equator is not included, the chart lengths
between successive parallels of latitude on the chart are found by reducing to
millimetres, according to the scale employed, the difference between the
corresponding meridional parts.
Suppose, for example, it is required to construct a chart from 142°E to
146°E, and 45°N to 49°N, the scale of the chart being 1° of longitude to
30
30 mm, or 1' of longitude to = 0.5 mm
60

The difference of longitude between limiting meridians is 4° and, since

the scale of the chart is 1° of longitude to 30 mm, the line at the bottom of the
chart representing the parallel of 45°N is 120 mm long, as shown in Fig. 4-8.
The meridians of 142°, 143°, 144°, 145° and 146° will be perpendiculars
erected on this line at its two ends and at the points dividing it into four equal parts.
The length in millimetres between the parallels of 45° to 49° can be
deduced from the difference of meridional parts as shown in Table 4-2.

Table 4-2. Chart lengths between parallels

LATITUDE MERIDIONAL PARTS DMP CHART LENGTH

(INTERNATIONAL SPHEROID) BETWEEN
PARALLELS (DMP X 0.5)

mm
49° 3364.62
90.29 45.14
48° 3274.33
88.54 44.27
47° 3185.79
86.89 43.45
46° 3098.90
85.32 42.66
45° 3013.58

In order to increase the accuracy with which positions can be plotted, the
chart lengths between meridians and between parallels are divided, if
necessary, into convenient units: 10' of longitude between meridians, and 10'
of latitude between parallels. this division is easily effected on the longitude
scale because that is fixed. On the latitude scale, however, it can be carried
out only with the further aid of the relevant table of meridional parts (see page
64), which is now entered for every 10' between 45° and 49° instead of every
degree.
MERCATOR PROJECTION/CHART 69

Fig. 4-8. Constructing a Mercator chart

70 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-8 shows the complete graticule. Each rectangle, whatever its
dimensions in millimetres, represents a part of the Earth’s surface bounded
by meridians 1° apart in longitude and parallels 1° apart in latitude; and,
although the chart lengths between these parallels vary from 42.66 mm to
45.14 mm as shown, each length represents a distance of 60 miles on the
Earth’s surface. The actual distance in miles between the meridians depends
on the latitude in which it is measured on the chart, and may be obtained from
Spheroidal Tables (NP 240), published by the Hydrographer of the Navy,
Norie’s Tables, or formulae (3.12) and (3.9).
As already explained, distances between places must be measured on the
latitude scale on either side of the places. The distance between F and T, for
example, is measured on the latitude scale between 46° and 48°, and is found
to be 135 miles.

Great-circle tracks on a Mercator chart

Since only rhumb lines appear as straight lines on a Mercator chart, great
circles will in general appear as curves.

Fig. 4-9. Great-circle tracks on a Mercator chart

TRANSVERSE MERCATOR PROJECTION/CHART 71

Moreover, since the limiting great circles are the equator, which appears
as a horizontal line, and any double meridian, which appears as two separate
lines 180° apart and perpendicular to the equator, any other great circle
passing through their points of intersection must appear as two curves with
vertices towards the poles, as shown in Fig. 4-9. The great circle joining F
and T will, therefore, always lie on the polar side of the rhumb line joining
them and, when the difference of latitude between F and T is small and the
difference of longitude large, it is seen that the difference between the two
tracks is considerable. If, however, the two points lie on opposite sides of the
equator, as at A and B, then the rhumb line almost coincides with the great
circle.

TRANSVERSE MERCATOR PROJECTION/CHART

Fig. 4-10. Transverse Mercator projection (1)

This very important projection, also known as the Gauss conformal

projection, is essentially a Mercator projection turned through 90°.
In the transverse Mercator projection a cylinder is chosen touching the
Earth along a chosen geographical meridian. This central meridian is then the
transverse equator of the chart ) NOS in Fig. 4-10. If a system of great
circles is drawn through the places where the axis of the cylinder cuts the
surface of the Earth, E and W in Fig. 4-10, then these may be regarded as
transverse meridians. A system of small circles parallel to NOS corresponds
to transverse parallels.
These systems are transferred to the cylinder in the same way as the
meridians and parallels are transferred in the normal Mercator projection; the
expansion of the distance between successive small circles is proportional to
the secant of their angular distance from the central meridian NOS. The small
circle QR is projected at Q1R1 and the transverse meridian PQM is projected
at PQ1M1.
72 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-11. Transverse Mercator projection (2)

Fig. 4-11 shows part of a transverse Mercator grid, which has been made
by turning the Mercator projection through 90°, where the central meridian
is represented by SOQFR and is similar to the equator on the Mercator
projection. The lines SS1, OO1 and FP are all great circles (or geodesics)
cutting the central meridian at right angles. They are therefore analogous to
the meridians on the Mercator projection, and will plot on the transverse
Mercator projection as parallel straight lines at right angles to the central
meridian.
Grid north on the projection is defined as the direction SOQFR; it is
coincident with true north on the central meridian only. Grid east is defined
as the directions SS1, OO1 or FP, all of which are parallel on the projection.
GNOMONIC PROJECTION/CHART 73

It follows that the meridians and parallels (with the exception of the central
meridian and the equator) will plot as curves on the projection. PN is the
meridian through P, and PQ is the parallel through P; the angle NPQ is of
course 90°. Geodesics on the projection will all plot as curves unless they
coincide with the central meridian, or grid east lines. (The grid east lines are
not quite geodesics, due to the fact that scale factor changes very slowly with
grid northing, but the difference is very small indeed.)
In order to make the projection orthomorphic, the scale in an east-west
direction has to be increased, away from the central meridian, to make it
everywhere equal to the slowly increasing scale in a north-south direction.
Put another way, this means that the east-west distance on the Earth, from the
central meridian to a point P, has to be increased slightly before plotting the
point by its co-ordinates on the projection, whilst the north-south distance is
plotted direct. The analogy with the Mercator projection is exact.
In Fig. 4-11 the point of origin of this particular grid is on the central
meridian at O; it might equally well be anywhere else along the central
meridian. The true point of origin of the projection is always on the central
meridian and the equator.
The scale error and distortion in shape away from the central meridian are
exactly those of the standard Mercator away from the equator so that, for
topographical large-scale map use, when the maximum permissible scale
errors are limited to amounts of less than 0.1%, this projection can be used
only for a limited extent in longitude. If wide bands of longitude have to be
covered, new central meridians must be chosen for new zones.
This projection has now been used since the mid-1970s for new
Admiralty large-scale charts instead of the modified polyconic or gnomonic
projection (see page 61).

GNOMONIC PROJECTION/CHART

In order to assist the navigator in finding the great-circle track between two
places, charts are constructed so that any straight line drawn on them shall
represent a great circle. These are known as gnomonic charts, and they are
formed by projecting the Earth’s surface from the Earth’s centre on to the
tangent plane at any convenient point. They are thus a zenithal projection
from position B (see Fig. 4-3(5) on page 55). The angle at the apex of the
cone is 180°, whereby the cone becomes a plane, touching the surface of the
sphere at the one tangent point. The gnomonic projection is a perspective
projection, the meridians and parallels being projected on to the tangent plane
from the centre of the sphere. The tangent point is chosen at the centre of the
area to be shown on the chart, to minimise distortion.
Since a great circle is formed by the intersection of a plane through the
Earth’s centre with the Earth’s surface, and as one plane will always cut
another in a straight line, all great circles will appear on the chart as straight
lines. However, the meridians will not be parallel unless the tangent point is
on the equator, nor will rhumb lines be straight. Angles are also distorted,
except at the tangent point. It is therefore impossible to take courses and
distances from a gnomonic chart. The mathematical theory of this chart is
explained in Appendix 4.
74 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-12 shows the graticule of a gnomonic chart in which the tangent
point is on the equator, and it will be noticed that the graticule is symmetrical
about the meridian through this tangent point, which is independent of the
longitude. The longitude scale can therefore be adjusted to suit the
navigator’s convenience. In the figure the tangent point is in longitude 0°.
Chart 5029, the Great-circle Diagram, is a graticule of this type.

Fig. 4-12. Gnomonic chart

To transfer a great-circle track to a Mercator chart

The transference of a great-circle track, such as FT in Fig. 4-12, from a
gnomonic to a Mercator chart, which is the normal navigational chart, is
effected by noting the latitude and longitude of convenient points A, B, C ...
on the line FT, marking these points on the Mercator chart, and joining them
by a smooth curve.
GNOMONIC PROJECTION/CHART 75

When F and T lie on opposite sides of the equator, F being north and T
south, the same chart can be used because a gnomonic chart of both
hemispheres when the tangent point is on the equator must be symmetrical
about the equator. The following geometrical construction therefore suffices:

1. Mark the position of T as if it were in the northern hemisphere.

2. Join F to K, the point on the equator which has T’s longitude.
3. Joint T to H, the point on the equator which has F’s longitude.
4. Drop a perpendicular RQ on the equator from R, the point where FK cuts
TH.
5. Draw FQ and QT. Then FQ is the great-circle track in the northern
hemisphere, and QT is the reflection of its continuation south of the
equator. Points on QT may therefore be treated as if they were in the
southern hemisphere.

Fig. 4-13. Gnomonic graticule

In Fig. 4-13, FT is the great-circle track between the points 40°S, 90°W,
and 35°S, 150°W. As it appears on the gnomonic chart, it tells the navigator
little about the course he must steer in order to follow it because angles, other
than bearings from the tangent point, are distorted. The track must therefore
be transferred to a Mercator chart, a transference that is easily made by noting
the latitudes of the points where the great-circle track cuts the meridians. The
result is the smooth curve FT in Fig. 4-14. The dotted line FT shows the
rhumb line.
Fig. 4-15 shows three tracks ) rhumb-line, great-circle and composite )
between two places, for comparison, all on a Mercator chart.
76 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-14. Great-circle track transferred to a Mercator chart

Fig. 4-15. Rhumb-line, great-circle and composite tracks

GRIDS 77

Practical use of gnomonic charts

The distortion of the gnomonic graticule, which is a perspective distortion
that gives neither the orthormorphic nor the equal area property, makes the
graticule quite unsuitable for civil purposes. Its purpose is limited entirely
to the use that can be made of the fact that, on it, great circles are represented
by straight lines.

GRIDS

A grid is a reference system of rectangular (Cartesian) co-ordinates obtained

when a projection is applied to a particular part, or the whole, of the world.
It will have all the properties of a projection and may have some special ones
peculiar to itself. Several grids, all different, may be based on the same
projection.
Fig. 4-16 shows a grid on which has been superimposed a geographical
graticule. It is simply a large piece of graph paper, specially constructed, and
graduated in suitable units north, south, east and west from the point of
origin.

Fig. 4-16. A grid

78 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-17. The National Grid of Great Britain

GRIDS 79

The intersections of the meridians and parallels are converted into quantities
known as grid eastings and northings. Eastings refer to the linear distance
eastwards from the north-south grid line which passes through the origin.
Northings refer to the linear distance northward from the east-west grid line
which passes through the origin. Distances west and south of the point or
origin are given negative values of eastings and northings respectively.
The northings and eastings are then plotted as individual points on the
grid and the points joined by smooth curves to form the geographical
graticule. To make this conversion simple, a set of tables will have been
constructed, depending on the projection in use.
At the point of origin of the grid, in this case (0,0) or 50°N, 20°W, the
scale factor of any projection in all directions is such that there is no
distortion at this point. Distortion elsewhere on the grid will depend upon the
type of projection in use.
The point of origin does not necessarily have to be numbered (0,0). For
example, the point of origin of the Ordnance Survey National Grid of Great
Britain is 49°N, 2°W (Fig. 4-17). To ensure that all positions in Great Britain
are covered by positive co-ordinates (i.e. above and to the right of the point
of origin) this position is given a false easting of +400 000 metres. It is also
given a false northing of -100 000 metres to ensure that all points on the
mainland of Scotland will have northings less than 1 000 000 metres. This
then produces a false origin 100 kilometres north and 400 kilometres west of
the true origin. It is from this false origin that all positions on the National
Grid are referenced.

Grid convergence
All the north-south grid lines do not point due north, as may be seen from
Fig. 4-18, and this has a significance for navigation when using grids (see
page 81). At any point, the angle between the meridian, as represented on the
plane of the projection and grid in use, and the grid north line is known as the
grid convergence C.* It will vary from place to place, depending on the
projection, and can be as much as 180° on certain projections (e.g. polar
stereographic). On the Mercator projection, on which most small-scale charts
are constructed, the convergence is zero everywhere but grid convergence
still exists if the grid is a different projection.
In Fig. 4-18 that part of the grid in Fig. 4-16 containing the points A and
B is shown enlarged. AP1 and BP are the meridians through A and B
respectively. It will be noticed that they are both curved. AN1 and BN both
define the direction of grid north.

C, the convergence at B = angle PBN

C1, the convergence at A = angle P1AN1

* The quantity used by mariners to correct a great-circle bearing (or true azimuth) to a Mercatorial or grid bearing
which is a straight line on the chart is usually referred to as half-convergency and must not be confused with grid
convergence. The correction for half-convergency is described in Volume III of this revised edition.
80 CHAPTER 4 - PROJECTIONS AND GRIDS

Fig. 4-18. Grid convergence

Grids constructed on the transverse Mercator projection

There are many grids constructed on the transverse Mercator projection, such
as the National grid of Great Britain (Fig. 4-17), the Universal Transverse
Mercator Grid and the Jamaica Grid. Scale on the central meridian of this
projection is correct over the entire distance from the North to the South Pole
so that it is suitable for world-wide cover using several zones of similar
limited longitude extent, and as such is used for US military surveys.
GRIDS 81

Universal Transverse Mercator (UTM) Grid

If, in Fig. 4-11, O is made to coincide with S, the figure represents the UTM
Grid. P is then a point north and east of the point of origin; by inverting the
diagram, overturning it, or both, the figure can be made to represent the
situation in either hemisphere or on either side of the central meridian.
The UTM Grid covers the whole world from latitude 84°N to 80°S, in
zones of longitude 6° wide. These zones are numbered from 1, which covers
180°W to 174°W in an easterly direction, to 60, which covers 174°E to
180°E. Each zone is therefore about 360 miles wide at the equator, 180 miles
wide in latitude 60°, and 62 miles wide in latitude 80°. The central meridian
of each zone bisects it.
Latitude and longitude may be converted into grid terms and vice versa,
using the appropriate formulae and a suitable programmed calculator or mini-
computer (see Appendix 4).

Transferring grid positions

Sometimes it will be found necessary to transfer a grid (e.g. for bombardment
purposes) from a map to a chart. There is a theoretical difficulty in doing
this, because the chart and map projections will almost certainly be different.
Thus, the lines of the grid may not be parallel to the parallels of latitude nor
to the meridians of longitude, and may indeed be curved (see Fig. 4-16).
Also, the degree of distortion from the central meridian or standard parallel
may not be the same for both projections. Moreover, there may be a
difference in the geodetic datums (see Chapter 3) used for chart and grid.
On a small-scale chart drawn on the Mercator projection, a grid
transferred from any of the topographical map projections would be formed
by curved lines but, in practice, when a larger scale chart (such as the
standard coastal chart) is used and the area covered small, the grid may be
drawn with straight lines without appreciable loss of accuracy. If, however,
the whole of the coastal chart is gridded up, grid positions on the eastern and
western edges being joined together by a straight line, appreciable errors can
occur. These can be as much as 200 yards in the centre of a 1:75,000 chart
and 800 yards in the centre of a 1:150,000 chart. Grid positions of suitable
intermediate points across the chart must be identified and the curved east-
west grid lines drawn accordingly.
Ideally, the transfer of the grid position to the chart and vice versa should
be carried out using the appropriate mathematical formulae on a computer,
provided the appropriate programs are available and the computer itself is
suitable. If such facilities are not available, grid positions may be transferred
using rough graphical methods as described below.
A gridded map usually gives the geographical positions of the corners of
the map and, if these are plotted on the chart, the grid may be inserted
according to scale. this assumes, however, that the determinations of latitude
and longitude for map and chart are in agreement. If they are not and this can
be seen by inspection, an adjustment must be made before the grid is
transferred. On a small-scale Mercator chart, where rapid change of scale
occurs away from the equator, the transferred grid will appear as a series of
trapeziums of curved sides, but on a larger scale coastal chart, where the scale
over the small area to be covered is approximately the same in all directions,
the transferred grid will be in the form of squares, (Fig. 4-19).
 82

Fig. 4-19. A grid transferred to a chart

CHAPTER 4 - PROJECTIONS AND GRIDS
GRIDS 83

Another method, and probably the most satisfactory graphical method for
all practical purposes, is to identify at least two and preferably four (one
towards each corner of the area to be gridded) marks common to both chart
and map. From these the grid may be constructed taking into account:

1. The difference between true and grid north.

2. The scales of the chart and map.

When the geographical positions of the corners of a gridded map are not
given, the geographical position of the origin is normally shown, and from
this the grid corners of the map may be calculated.
A map may sometimes have to be used as a chart, as happened for
example during the Korean War. Maps, however, do not usually show
enough navigational information and may have insufficient sea area.
Provided that the map is orthomorphic, it may be used with the following
modifications:
1. A compass rose is cut from a chart and pasted on the map. More than one
rose may be needed, as the grid convergence (see page 79) may be
different on different parts of the map.
2. Distance scales, which must take account of any change in scale away
from the central meridian or standard parallel over the area to be used,
should be pasted in a convenient position.
3. The sea may have to be extended to seaward with blank chart paper
pasted along the edge and navigational information, marks, soundings,
etc. transferred.

The most likely projections used for the map are the Lambert conical
orthomorphic (see page 56) or some form of the transverse Mercator (see
page 57). The former is steadily being superseded by the latter. In both cases
the map is orthomorphic. The other projection still used for topographical
maps is the polyconic (see page 60) and the mariner may come across this
from time to time. Although not orthomorphic, provided the map is of a
reasonably large scale (i.e. similar to that for the standard coastal chart or
larger), the mariner may treat it as such for all practical purposes without any
measurable loss of accuracy.
 84 CHAPTER 4 - PROJECTIONS AND GRIDS

| INTENTIONALLY BLANK
 85

CHAPTER 5
The Sailings (2)

The sailings were introduced in Chapter 2, which dealt with the parallel,
plane, mean and corrected mean latitude, traverse and great-circle sailings.
This chapter now deals with the somewhat more complex sailings, which are
as follows:

1. Mercator sailing on the sphere.

2. The vertex and the composite track in spherical great-circle sailing.
3. Spheroidal rhumb-line sailing.
4. Spheroidal great-circle sailing.

MERCATOR SAILING ON THE SPHERE

This was introduced in Chapter 2 (page 33). It uses meridional parts, which
were described in Chapter 4 (page 64). Meridional parts for the sphere are
given by formula (4.1), φ being the latitude:
æ φ° ö
meridional parts = 7915.7045log10 tanç 45°+ ÷ . . .(4.1)
è 2ø

To find the course and distance from the meridional parts

Where any point does not lie on the equator, its latitude has its meridional
parts. The number of meridional parts in the length of a meridian on a
Mercator chart between the parallels of latitude through two points F and T
(Fig. 5-1) will therefore be;

1. F and T on the same side of the equator (Fig. 5-1(a))

mer. parts T minus mer. parts F . . . 5.1

2. F and T on opposite sides of the equator (Fig. 5-1(b))

mer. parts T plus mer. parts F . . . 5.2

This length MT is always called the difference of meridional parts and

written DMP.
From the triangle FTM in Fig. 5-1, it is apparent that:

FM d.long(E / W)
tan course = = . . . 5.3
MT DMP(N / S)
86 CHAPTER 5 -THE SAILINGS (2)

Fig. 5-1. Difference of meridional parts (DMP)

The angle thus obtained is exact, irrespective of the length of FT. That
length, as in plane sailing, is obtained from formula (2.3), slightly modified:

distance = d.lat sec course . . . 5.4

Formula (5.4) is quite satisfactory in use for courses approaching 90°,

when using a calculator which will register the course to at least 6 decimal
places. There is, however, a fundamental weakness in this formula at course
angles between 60° and 90° because, as mentioned in Chapter 2, small errors
in the course introduce increasingly large errors in the distance. When using
tables in these circumstances it is preferable to use the formula:

d.long
distance = d.lat cosec course . . . 5.5
DMP

or distance = dep cosec course . . . 5.6

Fig. 5-2 shows the relation between the two methods of finding the
course. In the meridional parts method the d.lat is stretched into DMP and
the d.long remains unchanged; in the departure method, the d.lat remains
unchanged and the d.long is compressed into departure. Hence:
d.long dep . . . 5.7
= tan course =
DMP d.lat

The use of the departure formula, however, involves finding a corrected

mean latitude (page 28) if an error in the course is to be avoided. For this
reason, the DMP formula is preferred.
MERCATOR SAILING ON THE SPHERE 87

Fig. 5-2. DMP/d.long/departure/d.lat

EXAMPLE
What is the rhumb-line course and distance by Mercator sailing from
F(45°N, 140°E) to T(65°N, 110°W) (the positions given in the example in
Chapter 2, page 39)?
d.long 110°E, 6600'E
d.lat 20°N, 1200'N
From formula (4.1):
æ 65° ö
mer. parts T: 7915.7045 log10 tan ç 45°+ ÷ = 5178.81
è 2 ø
æ 45° ö
mer. parts F: 7915.7045 log10 tan ç 45°+ ÷ = 3029.94
è 2 ø
DMP(F to T) = 2148.87N
From formula (5.3):
d.long(E)
tan course =
DMP(N)
6600
=
2148.87
= 3.0713817
course = N71°.97E (calculator reading 71°.965457)
= 072°

From formula (5.4):

distance = d.lat sec course
= 1200' sec 71°.965457 = 3876'.09
88 CHAPTER 5 -THE SAILINGS (2)

Using the alternative formula (5.5), the distance is also 3876'.09.

The rhumb-line distance may also be found from formula (2.7) using the
corrected mean latitude (56°.052499 in this example) but this is always bound
to give the same result as using meridional parts directly, as the formula:
DMP
sec L =
d.lat
may be manipulated into
d.long
tan course =
DMP
using formulae (2.5) and (2.4).

THE VERTEX AND THE COMPOSITE TRACK

IN SPHERICAL GREAT-CIRCLE SAILING

The vertex and the composite track were introduced in Chapter 2 (page 36).
The calculations of the vertex and the composite track are given below.

To find the position of the vertex of a great circle

If a series of parallels is drawn, it is clear that one parallel will touch the great
circle FT at a point V, the vertex of the great circle, and it is the point on the
great circle nearest the pole in the appropriate hemisphere (Fig. 5-3). (See
also page 36.)

Since the great circle and the parallel touch at V and the meridian PV cuts
the parallel at right angles, it also cuts the great circle at right angles, and the
spherical triangles PFV and PTV are right-angled at V.

Fig. 5-3. The vertex

THE VERTEX AND THE COMPOSITE TRACK IN SPHERICAL 89
GREAT-CIRCLE SAILING

The longitude of the vertex can be found at once from the formula:
tan d.long VT = tan lat F cot lat T cosec d.long FT-cot d.long FT . . . 5.8
The latitude may be found from:
cot lat V = cot lat F cos d.long FV . . . 5.9
Otherwise, if the initial course has been found, the position of V can be
obtained from Napier’s rules (Appendix 2, page 603). Thus:
cos lat V = cos lat F sin initial course . . . 5.10
tan d.long FV = cosec lat F cot initial course . . . 5.11
EXAMPLE
Find the position of the vertex in the example given on page 39, F (45°N,
140°E) to T (65°N, 110°W), using the information from the cosine method
(page 39).
cos lat vertex = cos lat F sin initial course
= cos lat 45° sin 28°.122305
lat vertex = 70°.530896N = 70°31'.85N
tan d.long FV = cosec lat F cot initial course
= cosec 45° cot 28°.122305
d.long FV = 69°.297735E = 69°17'.86E
long vertex = 150°.70227W =
150°42'.14W
Note: The vertex may not be situated between F and T. There is only one
great-circle between F and T, and the point at which it most nearly
approaches the pole may be beyond F or T. For example, if the final course
angle is less than 90° the vertex lies beyond T.
To plot a great-circle track on a Mercator chart
The simplest method of plotting a great-circle track on a Mercator chart is
that by which points are transferred from a gnomonic chart (see Chapter 4)
but, if a gnomonic chart is not available, the track can be plotted with
reference to the vertex.
Consider the position of any point G on the great circle joining F and T,
G being fixed by its difference of longitude from V (Fig. 5-4, page 90).
Having found the position of V (formulae 5.10, 5.11), intermediate
positions are obtained from the following formula, where G is any position
on the great circle:
cos d.long VG = cot lat V tan lat G . . . 5.12
or tan lat G = tan lat V cos d.long VG . . . 5.13
A table of latitudes may now be prepared using suitable intervals of
longitude.
90 CHAPTER 5 -THE SAILINGS (2)

Fig. 5-4. Plotting a great-circle track on a chart

EXAMPLE
Find the latitudes where the great-circle track in the example given on page
89 cuts the meridians of 150°E, 160°E, 170°E, 180°, 170°W, 160°W, 150°W,
140°W, 130°W, 120°W. (F (45°N, 140°E), T (65°N, 110°W).)

Using formula (5.13), Table 5-1 may be prepared.

Table 5-1
LONGITUDE

LONG 150°E 160°E 170°E 180° 170°W

VG (D.LONG) 59°.298 49°.298 39°.298 29°.298 19°.298
LAT G 55°18'.1 61°32'.3 65°26'.9 67°56'.1 69°28'.0
LONG 160°W 150°W 140°W 130°W 120°W
VG (D.LONG) 9°.298 0°.702 10°.702 20°.702 30°.702
LAT G 70°17'.5 70°31'.8 70°12'.8 69°17'.9 67°39'.0

The latitudes and longitudes of G may now be plotted on the Mercator

chart and joined by means of a series of rhumb lines, which the navigator may
now steer.
Alternatively, the following formula may be used to find where a track
cuts intermediate meridians. This method avoids the need to find the position
of the vertex.
tan lat F sin d.long GT + tan lat T sin d.long FG
tan lat G =
sin d.long FT
. . . 5.14
THE VERTEX AND THE COMPOSITE TRACK IN SPHERICAL 91
GREAT-CIRCLE SAILING

If, however, a number of intersections are required, it is simpler to find

the vertex first, then apply (5.12) or (5.13).
There is no simple formula for finding where a track cuts parallels of
latitude without knowing the position of the vertex.

Calculating the composite track

The reasons for adopting composite sailing were described in Chapter 2.

Fig. 5-5. The composite track

In Fig. 5-5 LABM is the limiting parallel; the great circle joining F and T
is FLVMT. The composite track is FABT, in which FA and BT are great-circle
arcs touching the parallel at A and B, and AB is part of the limiting parallel
itself.
The positions of A and B are quickly found because the course angles at
A and B are right angles. Also, along AB the ship is steering a course of
090°/270° and, if the latitude of this limiting parallel is φ :

AB = d.long cos φ

The formulae to be used are those for the spherical right-angled triangle:

cos PF = cos PA cos FA

cos PF . . . 5.15
i.e. cos FA =
cos PA
sin FA . . . 5.16
sin FPA =
sin PF

Formula (5.15) gives the length of the great-circle arc FA and formula
(5.16) the d.long between F and A by which the position of A may be found.
BT may also be found in a similar manner.
92 CHAPTER 5 -THE SAILINGS (2)

EXAMPLE
Find the distance in the example on page 89, when a limiting latitude of 67°N
is applied. (F (45°N, 140°E), T (65°N, 110°W).)

Fig. 5-6. The great-circle example. F and T in the Northern Hemisphere

The total distance = FA + AB + BT

cos PF cos 45°
cos FA = =
cos PA cos 23°
FA = 39°.809911
= 39°48'.6 = 2388.6 miles
cos PT cos 25°
cos BT = =
cos PB cos 23°
BT = 10°.075896
= 10°04'.6 = 604.6 miles
sin FA sin 39° .809911
sin FPA = =
sin PF sin 45°
FPA = 64°.882575 = 64°53'E

Thus position of A is 67°N, 155°07'W.

sin TB sin 10° .075896
sin TPB = =
sin PT sin 25°
TPB = 24°.454656 = 24°27'.3

Thus position of B is 67°N, 134°27'.3W.

SPHEROIDAL RHUMB-LINE SAILING 93

AB = APB cos 67°

= [FPT - (FPA + TPB)] cos 67°
= 20°.662769 cos 67°
= 8°.0735870 = 484.4 miles

Thus composite distance = 2388.6 + 604.6 + 484.4 miles

= 3477.6 miles
The course from F to A and B to T may be found by the usual methods
described earlier.

SPHEROIDAL RHUMB-LINE SAILING

The formulae for plane sailing, corrected mean latitude (Chapter 2) and
Mercator sailing (Chapter 5) are accurate for the sphere. If these formulae are
used for the spheroid without suitable adjustment, the rhumb-line solution will
be inaccurate to some extent, dependent on course, distance and latitude. In
the days before computers and accurate navigational aids such as SATNAV,
these small inaccuracies (less than about 0.5% at worst) were swept up in
those larger errors incidental to the practice of navigation and thus did not
matter to the practical navigator. Nowadays, however, they have to be
considered.
Various efforts have been made from time to time to resolve this problem,
Meridional parts have been used for the spheroid instead of the sphere, but this
method is still inaccurate if the eccentricity of the Earth is not also allowed for
in formula (5.4), distance = d.lat sec course. Other methods use the corrected

Fig. 5-7. Length of the meridional arc

94 CHAPTER 5 -THE SAILINGS (2)

mean (middle) latitude derived from meridional parts for the spheroid, but
some of these mid.lat correction tables are wrong, erroneous in principle and
only valid for small latitude differences.
Provided that the meridional parts and the length of the meridional arc
between the latitudes of the two places concerned, e.g. EM in Fig. 5-7, are
computed for the spheroid, an accurate rhumb-line course and distance on any
spheroid may be determined.

To find the rhumb-line course and distance

The length of the meridional arc
The length R of the meridional arc EM may be found from the formula:
φ . . . 5.17
l = òo ρdφ
where φ is the geodetic latitude of the place and ρ the radius of curvature in
the meridian. The value of ρ is given in formula (3.8) in Chapter 3 (page 44)
and thus the precise formula to be integrated becomes:

( )
φ
l = a 1 − e 2 òo
1
3/ 2 dφ
( 2 2
1 − e sin φ ) . . . 5.18

R may be determined for any spheroid of known major semi-axis α and

eccentricity e (see Chapter 3), and expressed, dependent on what unit is used
for α, in metres, international nautical miles, etc.
Such a formula is expanded in the form:
φ
(
òo ρdφ = a Aoφ − A2 sin 2φ + A4 sin 4φ − A6 sin 6φ + ... ) . . . 5.19

where φ is measured in radians and:

1 3 4 5 6
Ao = 1 − e2 − e − e − ...
4 64 256
3 æ 2 1 4 15 6 ö
A2 = çe + e + e + ...÷
8è 4 128 ø
15 æ 4 3 6 ö
A4 = ç e + e + ...÷
256 è 4 ø
35 6
A6 = e + ...
3072
A computer is ideal for this calculation; a program may be devised to carry
out the computation to as many terms as the user wishes.

Meridional parts for the spheroid

Meridional parts for the spheroid are tabulated in the following publications:

Table of Meridional Parts based on the International (1924) Spheroid

(NP 239), published by the Hydrographer.
SPHEROIDAL RHUMB-LINE SAILING 95

Norie’s Nautical Tables (NP 320), based on the Clarke (1880)

Spheroid.
Burton’s Nautical Tables, also based on the Clarke (1880)
Spheroid.
Meridional parts m may be evaluated for any spheroid from the formula:
sec φ
m=
10800
π
(1 − e2 )òoφ 2 2 dφ
1 − e sin φ
. . . 5.20

10800 é æ π φö 1 4 3 1 6 5
=
π ë è 4 2ø
2
ê ln tan ç + ÷ − e sinφ − e sin φ − e sin φ − ...
3 5
]
. . . 5.21
where φ is measured in radians.
Once again a computer is ideal for this calculation.
Calculation of the rhumb-line course and distance
The rhumb-line course and distance may now be calculated as follows:
d.long . . . 5.22
tan course =
m1 ± m2
where m1 and m2 are the meridional parts evaluated from formula (5.21), or
extracted from the appropriate tables.
distance = (R1 ± R2)sec course . . . 5.23
where R1 and R2 are the lengths of the meridional arcs evaluated from formula
(5.19).
EXAMPLE
What is the rhumb-line course and distance from F (40°43'N, 74°00'W) to T
(55°45'S, 37°37'E) on the International (1924) Spheroid?
d.long = 111°37'E = 6697'E
Using formula (5.21) or NP 239:
m1 (F) = 2664.031
m2 (T) = -4028.034
DMP = -6692.065 (i.e. 6692.065S)
Using formula (5.22):
course = S45°.021E(-45°.021118) = 134°.98
Using formulae (5.19) and (5.23):
distance = 8166.09 n miles
Such a calculation may also be determined reasonably quickly and to a
high degree of accuracy using an ordinary pocket calculator and disregarding
terms of e6 (10-7 x 3.1) and higher powers.
96 CHAPTER 5 -THE SAILINGS (2)

a = 3444.0540 n mile
e2 = 0.00672267
lat F = 0.71063989 radians
T = 0.97302106 radians
Meridional parts (5.21) F T
æ π φö 0.77932467 1.1772729
Log tan ç + ÷
e è 4 2ø
-e2 sin φ -0.00438532 -0.00555689
1 4 3 -0.00000418 -0.00000851
− e sin φ 0.77493517 1.1717075
3
m 2664.031 4028.034
m1 ± m2 6692.065S
Meridional arc (5.19)

æ e 2φ 3e 2 3e 4 3e 4 15e 4 ö
l = aç φ - − sin 2φ − φ− sin 2φ + sin 4φ ÷
è 4 8 64 32 256 ø
. . . 5.24
F T
φ 0.71063989 0.97302106
e2φ -0.00119435 -0.00163532
−
4
3 2 -0.00249287 -0.00234558
− e sin 2φ
8
3 4 -0.00000151 -0.00000206
− e φ
64
3 4 -0.00000419 -0.00000394
− e sin 2φ
32
15 4 +0.00000078 -0.00000181
+ e sin 4φ 0.70694775 0.96903235
256

R 2434.7662 n mile 3337.3997 n mile

R1 " R 2 5772.1659 n mile
Using formulae (5.22) and (5.23):
course = 134°.978882 (135°)
distance = 8166.09 n mile*
* If the DMP for the spheroid were to be used with d.lat only, the rhumb-line distance would be 8188'.49 measured
in units of minutes of latitude.
SPHEROIDAL GREAT-CIRCLE SAILING 97

SPHEROIDAL GREAT-CIRCLE SAILING*

There are a variety of solutions for computing the shortest distance (the
geodesic) and course on the spheroid. Some of these use the geodetic and
some the parametric latitude, terms described in Chapter 3. Some of the
formulae required are much too complex for general use.
One of the most suitable formulae is the Andoyer-Lambert method using
parametric latitude; this is described below. This method has been adopted by
the US Naval Oceanographic Office for navigational applications and is also
used in the Royal Navy’s automated plotting system. The method has a
maximum error of 1 metre at 500 miles and 7 metres at 6000 miles, the
azimuth (bearing) being correct to within 1 second of arc.
In this method distance and bearing are pre-computed on a sphere of
radius equal to the semi-major axis of the spheroid on which the positions are
located (see Fig. 3-4 on page 44). Corrections are then made to obtain the
corresponding spheroidal values.

Calculation of the initial course and distance

In this calculation latitude N, longitude E, and d.long E are given a positive
(+) value, while latitude S, longitude W, and d.long W are given a negative (-)
value.
The latitudes are reduced to parametric form to compensate for the
flattening of the Earth using formula (3.7):

b
tan β = tan φ
a
where β is the parametric and φ the geodetic latitude, and a and b are the
equatorial and polar radii.
The azimuth from the departure point F to the arrival point T may be
found from the formula:
sin d.long . . . 5.25
tan az =
cos β1 tan β2 − sin β1cos d.long

where β1 and β2 are the parametric latitudes of F and T.

The spherical distance σ is now computed using formula (2.9):

cos σ = sin β1 sin β2 + cos β1 cos β2 cos d.long

and converted into radians.

The spheroidal corrections M, N, U, V are now calculated as follows:

M = (sin β1 + sin β2)2

N = (sin β1 ! sin β2)2
σ − sin σ
U=
1 + cos σ
* Strictly speaking, the title should be spheroidal geodesic sailing but the term ‘great-circle’ has been used in
preference as it is more familiar.
98 CHAPTER 5 -THE SAILINGS (2)

σ + sins σ
V=
1 − cos σ
f
geodesic distance = σ − ( MU + NV ) in radians
4
é f ù
= a ê σ − ( MU + NV ) ú n miles
ë 4 û
. . . 5.26
where a is the equatorial radius measured in international nautical miles and
f the flattening coefficient for the spheroid in use (see Chapter 3).

EXAMPLE
What is the geodesic course and distance from F (40°43'N, 74°00'W) to T
(55°45'S, 37°37'E) on the International (1924) Spheroid?

Fig. 5-8. Geodesic course and distance

On the International Spheroid:

a = 3444.0540 n mile
b = 3432.4579 n mile
f = 1/297
d.long = +111°.61667
φ1 = +40°.71667 φ2 = -55°.75
b b
tan β1 = tan φ1 tan β 2 = tan φ 2
a a
β1 = +40°.621149 β2 = -55°.660048
SPHEROIDAL GREAT-CIRCLE SAILING 99

From formula (5.25):

sin 111° .61667
tan az =
(cos 40° .621149 tan -55° .660048) - (sin 40° .621149 cos 111° .61667)
az = 133°.140011 or 313°.140011
which by inspection must be the former.
Initial course = 133°.14
From formula (2.9):
cos σ = (sin 40°.621149 sin -55°.660048)
+ (cos 40°.621149 cos -55°.660048 cos 111°.61667)
σ = 134°.05233 = 2.3396545 radians
M = (sin 40°.621149 + sin -55°.660048)2 = 0.03050287
N = (sin 40°.621149 - sin -55°.660048)2 = 2.1808189
2.3396545 − sin 134° .05233 = 5.3200842
U=
1 + cos 134° .05233
2.3396545 + sin 134° .05233 = 1.8040066
V=
1 − cos 134° .05233
f
geodesic distance = σ - ( MU + NV) radians
4
=2.3396545 - 0.00344822 = 2.3362063 radians
= 3444.0540 x 2.3362063 n miles = 8046.02 n miles
A comparison of distances
Table 5-2 gives a comparison of distances when evaluated by different methods,
using the positions in the example on page 95, also when T is in the Northern
Hemisphere.
Table 5-2. Comparison of distances

POSITION SPHERE INTERNATIONAL (1924) SPHEROID

(WGS 72 IN BRACKETS)

MERIDIONAL RHUMB-LINE GREAT-CIRCLE MERIDIONAL COMPUTED COMPUTED

PARTS DISTANCE DISTANCE PARTS RHUMB-LINE GREAT-CIRCLE
DISTANCE DISTANCE

F40°43'N 2679.12 2644.031

74°00'W (2644.094)

T55°45'S -4047.17 8167'.67 8048'.08 -4028.034 8166.09 8046.03

37°37'E (-4028.114) (8165.83) (8045.78)

T55°45'N 4047.17 4506'.74 4052'.35 4028.034 4522.75 4066.54

37°37'E (4028.114) (4522.54) (4066.35)

Note: Distances on the spheroid are in international nautical miles.

Distances on the sphere are in units of minutes of latitude.
 100 CHAPTER 5 -THE SAILINGS (2)

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 101

CHAPTER 6
Charts and Chart Outfits

This chapter includes: general remarks on charts; navigational charts; the

arrangement of charts; other types of charts and diagrams; upkeep of chart
outfits; navigational warnings; correction of charts and publications;
hydrographic reports; and production of the Admiralty chart. Reference is
also made to some associated navigational publications including the
Admiralty Sailing Directions, Admiralty List of Lights and Fog Signals and
Admiralty List of Radio Signals.
British Admiralty charts are produced by the Hydrographic Department
of the Ministry of Defence (Navy). This department was formed in 1795
because, it was said, more HM Ships were being lost on uncharted or badly
charted shoals than were being sunk by enemy action.
Lead and line was the only means of obtaining soundings until the echo
sounder came into general use in about 1935, although the hand lead
continued for inshore work into the 1950s. A sounding with lead and line
covered only the few centimetres actually struck by the lead and objects less
than a metre away from each cast remains undetected. Echo sounders only
examine a narrow strip immediately under the hull of the ship, and even on
a large-scale harbour chart these strips can be as much as 60 metres apart. It
only became possible to detect shoals and wrecks lying between sounding
lines in about 1973, with the advent of sidescan sonar ) a form of towed sonar
equipment which enables the survey ship to ‘look sideways’ and thus search,
and record, depths of bottom features between the sounding lines.
Although this equipment is now employed extensively by the
Hydrographer, the large majority of charts in use are still based on older
surveying data. Ships can still find that in every part of the world there are
areas which were surveyed using the hand lead only.
Up to the early 1960s, the survey service did not examine in detail any
object likely to be deeper than 66 feet (20 metres). Deep-draught ships need
to exercise care within the 200 metre depth contour, even in well recognised
shipping lanes, because of this problem.
It is still quite possible to find uncharted rocks, shoals and wrecks
anywhere in the world. Within recent years, rocky pinnacles rising to within
30 feet of the surface have been found in well used waters such as the
approaches to Holyhead in Wales and Auckland in New Zealand. Walter
Shoals, with 18 metres over them and surrounded by great ocean depths,
lying on the route from the Cape of Good Hope to the Sunda Strait, were not
discovered until 1962. It is estimated that there are some 20,000 wrecks or
102 CHAPTER 6 -CHARTS AND CHART OUTFITS

underwater obstructions in British coastal waters alone, but the exact position
or the depth of water over many of them is unknown.
It follows, therefore, that no chart is infallible. Every chart is liable to be
incomplete, either through imperfections in the surveys on which it is based,
or through subsequent alterations to the topography and sea-bed.
Ideally, all charts should include information concerning the origin, date,
scale and limits of the various surveys. Around the British Isles, a special
chart (Q6090) shows the dates of the surveyed areas on the Continental Shelf.
GENERAL REMARKS ON CHARTS
Charting policy
British charting policy is to chart all waters, ports and harbours in UK home
waters and certain Commonwealth and other areas on a scale sufficient for
safe navigation. Elsewhere overseas, Admiralty charts are schemed to enable
ships to cross the oceans and proceed along the coasts of the world to reach
the approaches to major ports using the most appropriate scale. In general,
smaller foreign ports are only charted on a scale adequate for ships under
pilotage although a number of major ports (e.g. New York) are charted on
larger scales.
In some overseas areas, charts (particularly the large-scale ones) of other
national Hydrographic Offices, whose addresses are given in the Catalogue
of Admiralty Charts and Other Hydrographic Publications, may be required.
British merchant ships are legally required to carry an adequate outfit of
charts and in certain places, for particular purposes, this may require that
charts produced by other nations should be held on board.
Description and coverage
There are about 3400 British Admiralty navigational charts covering the
whole world. In addition, over 600 of these charts are available with
overprinted lattices for use with electronic navigation systems (see page 104).
In areas where the United Kingdom is, or until recently has been, the
responsible hydrographic authority ) i.e. home waters, some Commonwealth
countries, British colonies, and certain areas like the Persian Gulf, Red Sea
and parts of the eastern Mediterranean ) the Admiralty charts, afford detailed
cover of all waters, ports and harbours. In other areas, charts are compiled
mainly from information given on published foreign charts, and the
Admiralty versions are designed to provide charts for ocean passage and
landfall, and approach and entry to the major ports, usually under pilotage.
The Admiralty chart series contains charts on many different scales
ranging from route planning charts on the smaller scales through medium
scale coasting charts to very large scale harbour plans.
In recent years, a new-style chart has been designed to meet the needs of
modern navigation, to take advantage of present-day cartographic techniques
including automation, and to facilitate updating procedures. At the same
time, the units of charted depths are being converted from fathoms and feet
to metres.
Metrication
The first Admiralty chart showing the depth of water in metres instead of
fathoms and feet was published in 1968 and, if the present rate is maintained,
the conversion of all Admiralty charts should be completed by the year 2000.
GENERAL REMARKS ON CHARTS 103

Metric charts are added to the series of navigational charts in three ways.
First, there is the traditional way, a new chart being published to meet a fresh
requirement or because the extent of newly acquired information is such as
to make replacement preferable to correction. Secondly, metric charts are
acquired through bilateral or international arrangements, for example
adoption into the British Admiralty series of Australian and New Zealand
charts. The third way is ‘active metrication’ through following a policy of
block metrication region by region. Resources are devoted exclusively to the
chosen area irrespective of the degree of outdatedness of the existing charts.
The first such area to be covered in this way was home waters between 1972
and 1980 and it has been followed by, for example, Europe and the Far East.
A criticism made of the earlier metric charts was that the process of
reducing the amount of detail shown, not only for clarity but also to speed up
the change-over process, had gone too far, and so the amount of detail in
inshore waters and in the topography has been increased. Other changes
since 1979 have been:

1. The introduction of the transverse Mercator projection for large-scale

charts instead of the modified polyconic (‘gnomonic’) projection.
2. The graduation for latitude and longitude of most harbour plans, however
small their size or inextensive their cover; this should facilitate chart
correction.
3. The introduction of a graduated central meridian on certain Mercator
charts of NW Europe including the British Isles. This is particularly
welcome in small craft where lack of space necessitates the folding of the
chart in use, thereby denying the chart user the linear scales in the east
and west borders.

Geographical datum
The completely recompiled metric chart permits the adoption of a generally
accepted basis for the determination of latitude and longitude, either a
regional one such as the European Datum or an international one such as that
based on the World Geodetic System 1972 (WGS 72) (see page 48).
The increased use of satellite navigation systems (the US Navy
Navigation Satellite System (TRANSIT) is based on WGS) has shown the
wide discrepancies in horizontal datums in use on charts. These
discrepancies have arisen from astronomical fixes used for early surveys, the
accuracy of which may have been affected by local gravitational anomalies.
There are two main reasons for this. First, the geographical position in which
a given point on the earth is charted will usually have been computed on a local
geographical datum. The reference spheroid of this local datum will have been
chosen to given the ‘best fit’ to the Earth’s surface in the limited area concerned,
whereas the reference spheroid of WGS is chosen to given the ‘best fit’ to the
whole surface of the Earth. This causes a discrepancy known as the datum shift,
which is usually of the order of a few hundred metres. Secondly, the survey
from which the chart was compiled may itself have contained errors in
geographical positions. Such errors, though negligible for modern
104 CHAPTER 6 -CHARTS AND CHART OUTFITS

surveys, may amount to 1 mile or more in poorly charted areas such as parts
of the Pacific Ocean. the systematic acquisition and publication of datum
shift information on Admiralty charts is now being undertaken by the
Hydrographic Department.

International charts
The 1967 conference of the International Hydrographic Organisation (IHO)
set up a six-nation Commission to determine an agreed set of specifications
for a series of small-scale International (INT) charts with a view to sharing
the production of these charts among a number of member states. The
intention was that any member state of the IHO could reprint any or all of
these International charts, making modifications as necessary to conform with
its own national chart series. Two separate world-wide schemes have been
agreed for use in route planning and ocean navigation: a 1:10 million series
comprising 19 sheets and a 1:3.5 million series comprising 60 sheets. Sixteen
member states participate in their production. It is expected that all the charts
in these two series will have been completed and incorporated into the
Admiralty series by the mid-1980s.
International charts are now also being published on larger scales
including medium and large-scale charts, priority being given to large-scale
INT charts for ports. A regional charting group has already devised a scheme
of INT charts for the North Sea and the north-east Atlantic between
Greenland, North Cape and Ushant. Further regional charting groups are
being established to extend schemes of medium and large-scale INT charts
across the world, for example in the Mediterranean and in the Straits of
Malacca and Singapore.
INT charts follow the new internationally agreed chart specification of
the IHO. This specification differs little from that used for the standard
Admiralty chart.
INT charts are treated as part of the national series of charts, having a
national chart number as well as an INT number. They should be ordered,
corrected, etc. in exactly the same way as any other national chart, using the
appropriate national chart number.

Latticed charts
Many nautical charts are available with coloured overprints showing the
position-fixing lines of various radio navigation systems. By far the most
commonly used of these is the Racal-Decca Navigator, and latticed versions
of appropriate medium and small-scale charts in the area of system coverage
are available. Omega Navigation System lattices for the 10.2 kHz basic
frequency are available on many small-scale ocean charts throughout the
world. Charts with Loran-C overprints are available for the coasts of USA
and Canada and for those areas of the North Atlantic within the ground wave
coverage of the system. The lattices for these systems are overprinted on the
standard navigational charts. They can therefore always be corrected for
ordinary navigational changes. The colours are carefully controlled in
printing so that the charts may be used in a dual role, for navigation both with
and without electronic aids.
 GENERAL REMARKS ON CHARTS

Fig. 6-1. The IALA Maritime Buoyage System regions

105
106 CHAPTER 6 -CHARTS AND CHART OUTFITS

IALA Maritime Buoyage System

Details of the IALA system of buoyage are given in Chapter 10; but the
system is introduced here because of the implications for charts and charting
policy. Two systems were originally envisaged, System A (Red to Port) and
System B (Red to Starboard). These two systems have been merged into one
single IALA Maritime Buoyage System which, when applied to Region A and
Region B (Fig. 6-1), differs only in the use of red and green in lateral marks.
In Region A, lateral marks are red on the port hand, and in Region B, red on
the starboard hand, related to the conventional direction of buoyage. Full
harmonisation to eliminate this difference was not attainable due to long-
standing differences in practice. Shapes of lateral marks are the same in the
two regions; can to port, conical to starboard.
Within both regions, use is made of the full range of cardinal and other
marks established for System A. Some minor features, appropriate in both
regions, have been added to the existing System A range, the most significant
being the provision of a modified lateral mark for indicating the preferred
route where a channel divides.
The standardisation of the buoyage system in Region A should have been
largely completed by about 1985 and in Region B some time after 1987.

NAVIGATIONAL CHARTS

Charts drawn on the Mercator projection

As discussed in Chapter 2, a line on the Earth’s surface which cuts all the
meridians and parallels at the same angle is called a rhumb line. If two places
on the Earth’s surface are joined by a rhumb line and the ship steers along
that line, the direction of the ship’s head will remain the same throughout the
passage. This direction is determined by the angle from the meridian to the
rhumb line, measured clockwise from 0° to 360°, and is called the course.
The rhumb line itself is often spoken of as the course. On the Earth’s surface,
a continuous rhumb line will in general spiral towards the pole. To the
navigator, the most useful chart is one on which he can show the track of his
ship by drawing a straight line between his starting-point and his destination,
and then measure the steady course he must steer in order to arrive there. The
Mercator chart permits him to do this (see page 61) and the main properties
are set out here for ease of reference.

1. Rhumb lines on the Earth appear as straight lines on the chart.

2. The angles between these rhumb lines are unaltered, as between Earth
and chart.
3. The equator, which is a rhumb line as well as a great circle, appears on
the chart as a straight line.
4. The parallels of latitude (which are both small circles and rhumb lines)
appear as straight lines parallel to the equator.
5. The meridians (which are rhumb lines as well as great circles) appear as
straight lines at right angles to the equator.
6. A straight line joining two points does not represent the shortest distance
between them, unless it happens to be a great circle as well. A great
NAVIGATIONAL CHARTS 107

circle which is not a meridian or the equator will appear as a curve (Fig.
6-2).
7. The chart is orthomorphic, that is, at any point on it the scale is the same
in all directions and angles are preserved; hence, the chart correctly
represents the shape of charted features in any small area.

Fig. 6-2. Mercator projection of the North Atlantic Ocean

Scale on a Mercator chart

Since the equator is shown on a Mercator chart as a straight line of definite
length, and the meridians appear as straight lines perpendicular to it, the
108 CHAPTER 6 -CHARTS AND CHART OUTFITS

longitude scale throughout the chart is determined by the horizontal distance

between the meridians. This distance remains constant in all latitudes
represented on Mercator’s projection. On the Earth, however, the meridians
converge (Fig. 6-3(a)) and therefore land masses on a Mercator chart (Fig. 6-
2) will be increasingly distorted in an east-west direction proportional to their
distance from the equator, until at the poles their sizes would be infinite.

Fig. 6-3(a) Converging of Fig. 6-3(b) Spacing of the

the meridians parallels of latitude

In order to preserve the correct shape or orthomorphic property, therefore,

the parallels of latitude, which are equally spaced on the Earth’s surface (Fig.
6-3(b)), must be increasingly spaced towards the poles on the Mercator chart
(Fig. 6-2) until at the poles the latitude scale is infinite.
This distortion, explained in Chapter 4, is governed by the secant of the
latitude. Thus, on a Mercator chart of the world (Fig. 6-1) Greenland appears
as broad as Africa at the equator, although the latter is three times wider.
This becomes apparent once the distance is measured at the latitude scale in
the vicinity of the two areas.
The Mercator projection is used for all Admiralty charts having a natural
scale* smaller than 1:50,000 ) a scale, that is, of less than 1½ inches to 1
mile. The latitude scale is displayed down both sides of the chart margin and,
on some charts, along a central meridian as well.
Because the parallels of latitude have to be increasingly spaced towards
the poles, the representation of distance on the Mercator chart varies with
latitude. As explained in Chapter 4, distances should always be measured,
using the latitude scale, at the latitude of the place concerned. The longitude
scale must not be used for measuring distances on the Mercator chart.

Charts drawn on the gnomonic projection

A full description of this projection is given in Chapter 4.
The chart drawn on a flat surface is conceived as touching the Earth at
one point, usually the central point of the chart, known as the tangent point.

* The natural scale is the ratio of a length measured on the chart to the corresponding length measured on the
Earth’s surface.
NAVIGATIONAL CHARTS 109

Lines are drawn from the centre of the Earth, through points on the
Earth’s surface, until they reach the flat surface of the chart. Hence:
1. Great circles appear as straight lines on the chart, and rhumb lines appear
curved.
2. Meridians are straight lines converging to the poles.
3. Parallels of latitude are curves.
4. The farther a point on the chart is away from the tangent point, the greater
will be the distortion.
This projection is used for great-circle sailing charts (see page 123). On
many Admiralty charts of scale 1:50,000 and larger, the term ‘gnomonic’ has
been quoted to describe the projection on which they are constructed although
in fact a modified form of polyconic projection has been used. The use of the
term gnomonic (though strictly incorrect) indicates that, on the chart, lines of
sight and other great circles are represented by straight lines. Thus, for all
practical purposes, straight lines can be used to plot all bearing and direction
lines. Modern charts of this scale are drawn on the transverse Mercator
projection.
Charts drawn on the transverse Mercator projection
This projection is essentially a Mercator projection turned through 90°; it is
described in detail in Chapter 4. Since the late 1970s it has been used for new
Admiralty charts of natural scale 1:50,000 and larger.
The projection is orthomorphic but the geographical meridians and
parallels are curved lines, except the meridian at which the cylinder touches
the sphere. Because of the large scale, these lines will appear as straight lines
to the user and, for all practical purposes, straight lines can be used to plot all
bearings and direction lines on the chart.
Harbour plans
Most harbour plans are graduated for latitude and longitude, which facilitates
chart correcting. Linear scales of feet, metres and cables (1 cable = 0.1 sea
mile, see page 7) are given on all plans.
An example of a modern harbour plan is given in Fig. 6-4.
Constructing a scale of longitude on a plan
On older plans, the scale of longitude may not be given. This may be found
from the following construction.
From the zero on the scale of latitude draw a line making an angle with
it equal to the latitude of the plan ) for example 45°, as shown in Fig. 6-5.
From each division on the scale of latitude draw a perpendicular to this
line. The intersections of these perpendiculars with the line mark the scale
of longitude.
The plotting chart
The navigator wishing to work out his position, after manoeuvring in a
limited area out of sight of land, normally determines his position by reference
to the automatic plotting table, transferring his ‘run’ at regular intervals to the
chart. If such a table is not available to him, he has to work out his position by
laying off courses and distances on a plan of his own making, called a
110 CHAPTER 6 -CHARTS AND CHART OUTFITS

Fig. 6-4. A harbour plan ) Brixham ) depths and heights in metres

NAVIGATIONAL CHARTS 111

Fig. 6-5. Constructing a scale of longitude

plotting chart. On this, a convenient meridian and parallel of latitude are

taken as axes, and the scale for latitude and distance assumed to be constant
anywhere on the plotting chart. He may drawn up a scale of longitude if he
so desires, as set out above, or he may use formula (2.5) slightly modified:

d.long = departure sec (mean latitude)

Fig. 6-6 shows the track of a ship as it would appear on a plotting chart
(turning circles being disregarded) if the ship steams 6' on a course 075°, a
distance and course indicated by OA; 4' on a course 340° (AB); and 3½' on a
course 210° (BC). The position of C is then fixed in relation to O by its d.lat
and departure.

d.lat (CX) = 2'.3N

dep (CY) = 2'.7E

If the position of O is 43°N, 15°W, the latitude of C is:

lat O 43°00'.0N
d.lat 2'.3N
lat C 43°02'.3N
112 CHAPTER 6 -CHARTS AND CHART OUTFITS

By calculation (2'.7 sec 43°) d.long is seen to be 3'.7E. The longitude of C

is:

long O 15°00'.0W
d.long 3'.7E
long C 14°56'.3W

Fig. 6-6. The plotting chart

Distortion of the printed chart

Charts are liable to slight distortion at various stages in the process of
reproduction but the effect is seldom sufficient to affect navigation. Any
distortion may be observed by checking the dimensions (see page 114). If
there is distortion, bearings of objects, however accurate, may not plot
correctly, particularly if those objects are at a distance as displayed on the
chart. The larger the scale of the chart, the less becomes the effect of
distortion.

Information shown on charts

Number of the chart. This is shown outside the bottom right-hand and top
NAVIGATIONAL CHARTS 113

left-hand corners of the chart, and in the thumb-label on the reverse of the
chart.
Title of the chart. This is shown in the most convenient place so that no
essential navigational information is obscured by it, and in the thumb-label
on the reverse of the chart.
Survey data. This will either be given under the title of the chart, thus:

‘Torbay and the plans of Torquay Harbour and Brixham Harbour from
Admiralty surveys of 1950 with subsequent corrections. Soundings
in upright figures are taken from older surveys. Teignmouth Harbour
from an Admiralty survey of 1962. The topography is taken chiefly
from the Ordnance Survey.’ or

A source data diagram (Fig. 6-7) will be published on the chart. These
diagrams indicate the source, date and scale of the survey in each part of the
chart.
Satellite derived positions. The datum shift (see page 103) is published
on many charts adjacent to the title, indicating the amount by which a
position obtained from a satellite navigation system should be moved to agree
with the chart.
Date of publication. This is shown outside the bottom boarder of the
chart in the middle, thus:

Published at Taunton, 14th November 1980

Fig. 6-7. A source data diagram

114 CHAPTER 6 -CHARTS AND CHART OUTFITS

New Edition. When a chart is completely or partly revised, a New Edition

is published, the date being shown to the right of the date of publication, thus:
New Edition 23rd February 1979
Large Correction. Until 1972 charts were revised by either New Editions
or Large Corrections; the former term was used when the chart was revised
throughout, and the latter when only a portion of the chart was revised. Since
1972 the term New Edition has been used for all revisions of the chart but,
where a Large Correction has been made to a chart, the notation will remain
on the chart until its next revision.
The date on which a Large correction was made appears to the right of the
date of publication under the date of the New Edition (if any), thus:
Large Correction 10th Feb., 1969
Small Corrections. These give essential information for navigation
published in Admiralty Notices to Mariners, or information of secondary
importance which is added to the chart plates by Bracketed Correction as
opportunity affords.
Admiralty Notices to Mariners from which charts have been corrected are
indicated by the year and number of the Notice in the Small Corrections
outside the bottom left-hand corner of the chart, thus:
Small Corrections 1980 ) 1556
Admiralty charts corrected for Australian or New Zealand Notices to
Mariners have the number of the Notice, prefixed AUS or NZ, entered in
sequence in the list of small corrections.
Bracketed Corrections. Until 1986, bracketed corrections were used to
give information of use to the mariner but not essential for navigation. This
was done by an unpromulgated correction to the plate at a routine printing of
the chart; thus, any mariner replacing his copy before the next New Edition
got the benefit of the information concerned.
A Bracketed Correction is shown outside the bottom left-hand corner of
the chart, thus:
Small Corrections 1980 ) [15.7]
This indicates that on 15th July 1980 the chart plate received a minor
correction.
Date of printing. This is shown by the date in the thumb-label on the
reverse of the chart, thus:
Printed November 1980
Identification of chart plates. The type of printing plate used for the
black detail of the chart, with its year of preparation, together with the month
and year of preparation of the black and magenta printing plates, is indicated
outside the bottom right-hand corner of the chart.
Chart dimensions. The figures in parentheses shown outside the lower
right-hand border of the chart, thus: (630.0 x 980.0 mm) or (38.43 x 25.49)
express the dimensions in millimetres or inches of the plates from which the
chart is printed. The dimensions are those of the inner border of the chart
(neat lines) and exclude the chart borders. In the case of charts on the
NAVIGATIONAL CHARTS 115

gnomonic projection, dimensions are quoted for the north and south borders,
and on the transverse Mercator projection for all four borders.
Corner co-ordinates. Co-ordinates expressing the latitude and longitude
of the limits of Admiralty charts published after 1972 are shown at the upper
right and lower left corners of the chart. Charts corrected by New Edition
after 1972 also display corner co-ordinates.
Scale of the chart. The natural scale is shown beneath the title. A scale
of kilometres is shown in the side margins of certain charts of scale larger
than 1:100,000 to facilitate the plotting of ranges from radar displays
graduated in this way.
Abbreviations and symbols. Standard abbreviations and symbols used on
Admiralty charts are shown in Chart Booklet 5011 which in RN ships is
supplied with Chart Folio 317/318, Miscellaneous Charts, Diagrams and
Tables. An extract from this Chart Booklet is reproduced in Fig. 6-8 (pages
116-17).
Wreck symbols. Examples of wreck symbols are shown in Fig. 6-8. The
criteria used to determine what depths are dangerous to shipping have
changed since 1960 from 8 fathoms (48 feet) in 1960 to 28 metres in 1982.
The wreck symbol is not necessarily updated when the chart is revised and a
‘dangerous wreck’ alludes to the depth criteria in force in the area at the time
of survey, which can be determined from the source data diagram (see page
113).
Depths. The unit in use for depths is stated in bold lettering below the
title of the chart. It is also shown, in magenta, outside the bottom right and
top left-hand corners of metric charts.
On all charts, the position of a sounding is the centre of the space
occupied by the sounding figure(s). On metric charts, soundings are
generally shown in metres and decimetres in depths of less than 21 metres;
elsewhere in whole metres only. Where navigation of deep-draught vessels
is a factor and where the survey data are sufficiently precise, soundings
between 21 and 31 metres may be expressed in metres and half-metres.
On fathom charts, soundings are generally shown in fathoms and feet in
depths of less than 11 fathoms, and in fathoms elsewhere. In areas used by
deep-draught vessels where the depth data are sufficiently precise, charts
show depths between 11 and 15 fathoms in fathoms and feet. Some older
charts show fractional parts of fathoms in shallow areas and a few older
charts express all soundings in feet.
Depths in charts are given below chart datum. On metric charts for which
the UK Hydrographic Department is the charting authority, chart datum is a
level as close as possible to Lowest Astronomical Tide (LAT), the lowest
predictable tide under average meteorological conditions. On earlier charts
and those based on foreign charts, chart datums are low water levels which
range from Mean Low Water to lowest possible low water in tidal waters; in
non-tidal waters, such as the Baltic, chart datum is usually Mean Sea Level.
A brief description of the level of chart datum is given under the title of
metric charts.
Large and medium-scale charts contain a panel giving the heights above
chart datum of either Mean High and Low Water Springs and Neaps, or Mean
Higher and Lower High and Low Water, whichever is appropriate.
Depth contours. On charts, all soundings less than and equal to certain
depths are enclosed by appropriate metre or fathom lines, as in Fig. 6-9 (page
118).
116 CHAPTER 6 -CHARTS AND CHART OUTFITS

Fig. 6-8. Extract from Admiralty Chart 5011

NAVIGATIONAL CHARTS 117
 118

Fig. 6-9. Depth contours on Admiralty charts

CHAPTER 6 -CHARTS AND CHART OUTFITS
NAVIGATIONAL CHARTS 119

Heights. All heights except those shown by underlined figures (see

Drying heights) are given in metres or feet above a stated vertical datum,
usually Mean High Water Springs, or Mean Higher High Water or, in places
where there is no tide, Mean Sea Level. In most instances, the position of the
height is that of the dot alongside the figure, thus: .135. Heights which are
displaced from the feature (e.g. a small islet) to which they refer, or which
qualify the description of a feature (e.g. a chimney) are placed in parentheses.
Drying heights. Underlined figures on rocks and banks which uncover
(see Fig. 6-8) give the drying heights above chart datum in metres and
decimetres or in feet, as appropriate.
Tidal stream information
1. All information about tidal streams, whether in tables, or in notes giving
the times of slack water and the rate of the tidal streams, is given in some
convenient place on the chart and referred to by a special symbol ) e.g.
" ) at the position for which the information is given.
2. This information may be shown by means of tidal stream arrows on
certain charts when insufficient data for constructing tables are available.
Colours used on charts
A variety of colours is now used on Admiralty charts, as in Fig. 6-10 (page
120). Shallow water areas are distinguished by a flat blue tint between the
coastline and an appropriate depth contour; the tint includes all isolated
patches within this depth range. In addition, a ribbon of blue tint is
commonly employed to emphasise the limit of water of slightly greater depth.
Drying (intertidal) areas are shown in a green tint on metric charts. Magenta
is used for the emphasis of certain details, notably lights and radio aids and,
nowadays, to distinguish numerous features superimposed on the basic
hydrography.
To describe a particular copy of a chart
When describing a particular copy of a chart, state in the following order:
1. The number of the chart.
2. Title.
3. Date of publication
4. Date of the last New Edition
5. Date of the last Large Correction (if applicable).
6. Number (or date) of the last Small Correction.
Distinguishing a well surveyed chart
Source data diagrams (see page 113) are the key to how well the area shown
on the chart has been surveyed, bearing in mind the opening remarks in this
chapter on lines of soundings and wrecks (pages 101 to 102). If such
information is not available, then bear in mind the following points:
1. The survey should be reasonably modern (see date given in title notes).
2. Soundings should be close together, regular, with no blank spaces.
3. Depth and height contour lines should be continuous, not broken.
4. Topographical detail should be good.
120 CHAPTER 6 -CHARTS AND CHART OUTFITS

Fig. 6-10. Colours used on Admiralty charts

THE ARRANGEMENT OF CHARTS 121

5. All the coastline should be completed, with no pecked portions indicating

lack of information.

The reliability of charts

As mentioned previously, no chart is infallible; every chart is liable to be
incomplete in some way or another. Charts based on lead-line surveys are
particularly fallible; a single lead-line sounding, which surveyed at best a few
centimetres on the sea-bed, may be reflected by a figure occupying several
hectares of ground depending on the scale of the chart. Any such chart being
used for pilotage would have to be treated with the greatest suspicion.
The degree of reliance to be placed on a chart must depend upon the
character and completeness of the original survey material and on the
completeness of reports of subsequent changes. Apart from any suspicious
inconsistencies, e.g. errors in geographical position (latitude and longitude),
matters which must be taken into account are the scale of the chart, its
soundings in relation to the dates of the surveys or authorities from which it
has been compiled and examination of the chart itself. Even these
considerations can only suggest the degree of reliance to be placed on the
chart. The chart must never be taken for granted.

Hints on using charts

Each Admiralty chart, or series of charts, is designed for a particular purpose.
Large-scale charts are intended for entering harbours or anchorages or for
navigating close to potential hazards. Medium-scale charts are intended for
coastal navigation, while small-scale charts are intended for offshore
navigation. Always use the largest scale chart appropriate to the purpose.
For passage along a coast, use the continuous series of medium-scale
charts provided for that purpose. Transfer to the larger scale chart where this
more clearly depicts potential hazards close to the intended route.
There is usually no need to transfer for short distances to a larger scale
chart intended for entering an adjacent port or anchorage. Although the
larger scale chart depicts information in more detail, the next smaller scale
shows all the dangers, traffic separation scheme, navigational aids, etc. that
are appropriate to the purpose for which the smaller scale chart is designed.
Remember that the sea-bed is likely to correspond to the adjacent land
features, even when the chart gives no hint of irregularities of the bottom.
Thus, off an area where sharp hillocks and rocky, off-lying islands abound,
the sea-bed is likely to be equally uneven and old surveys must be even more
suspect than off a coast where the visible land if flat and regular. There are
also likely to be uncharted dangers on or near the rim of a saucer-like plateau
surrounding a coral group.

THE ARRANGEMENT OF CHARTS

The chart folio

Ships may be supplied either with individual charts or with charts made up
into folios. These folios are issued in numbered geographical sets, the charts
in each folio being arranged as far as possible in numerical order, and
contained in a buckram cover.
122 CHAPTER 6 -CHARTS AND CHART OUTFITS

Lists of folios are given in the Hydrographic Supplies Handbook (NP

133) and in the Catalogue of Admiralty Charts and other Hydrographic
Publications (NP 131), and their approximate limits are shown on an index
chart in those publications.
On the outside cover of each folio is:
1. A folio label, H119, showing the folio number, the dates of issue, the
correction state, and the names of ships, etc. to which it was issued. H82
label is used for Fleet folios.
2. A folio list showing the numbers and titles of the charts contained in the
folio, the navigational publication (NP) numbers and titles of the
appropriate volumes of Admiralty Sailing Directions and of the Admiralty
List of Lights and Fog Signals and, sometimes, any other appropriate
publication.
Duplicate folio lists are supplied and kept together in a buckram
envelope.
A small label, known as the thumb-label, is printed on the back of each
chart. The thumb-label shows the number, title and printing date of the chart,
and provides space for notation of the folio number.

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The scheme of chart folios
Navigational chart folios are divided into two categories:
1. Standard folios which together provide cover for the whole world. Each
folio contains all the navigational charts published for the area
concerned. Where Racal-Decca charts have been published, these are

VOL 7
supplied in place of the non-latticed chart, unless there is a request to the
contrary.
2. Local and special folios provide for local services in the vicinity of
dockyard ports and for particular requirements not readily met by
standard folios. The folio numbers (all in the 300 series) or their
geographical limits are not related to the standard folios.
Special folios contain Loran, Omega, Routeing charts, etc.
The Hydrographic Supplies Handbook (NP 133)
This handbook contains information for Navigating Officers and others
regarding the supply and correction of Admiralty charts (except classified
charts) and navigational publications.
The Chart Correction Log and Folio Index (NP 133A, 133B)
This contains:
1. A preface listing the contents and instructions for use.
2. A folio check list.
3. Sheets for logging new charts and New Editions as promulgated in
Notices to Mariners.
4. As Part I: a folio correction sheet for each navigational folio held,
showing charts in numerical order, and with space for logging Notices to
Mariners.
5. As Part II: a numerical index of all Admiralty (navigational, 5000 series,
Loran and Fleet), Australian and New Zealand charts (in BA folios) and
US Loran and Omega charts showing the folios in which they are
contained.
OTHER TYPES OF CHARTS AND DIAGRAMS 123

The Catalogue of Admiralty Charts and Other Hydrographic

Publications (NP 131)
This catalogue, published annually, is supplied to all warships down to and
including coastal survey vessels. It contains details of all the navigational
charts published by the Hydrographer of the Navy including adopted
Australian, New Zealand and International charts, grouped in numerical
sequence under different geographical areas. All navigational publications
used (Sailing Directions, Lists of Lights, astronomical, radio, tidal material
and so on) are included as are all other charts and diagrams (Decca, Omega,
Loran-C, Routeing and so on). The catalogue also lists Admiralty Chart
Agents who are required to supply RN ships with any items ordered in an
emergency.

Classified charts
Certain charts normally classified Restricted, including all Fleet charts, are
contained in folios numbered in the 700 series. Other classified charts may
be contained in the miscellaneous folios (see page 126).
The folio and serial numbers of charts classified Confidential and above

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and the copy numbers of any similarly classified hydrographic department
publications held on charge, should be recorded on CB Form R held by the
Navigating Officer.
A Catalogue of Classified and Other Charts and Hydrographic
Publications (NP 111) is issued to all frigates and above. These charts and

VOL 7
publications are not normally available for sale.

OTHER TYPES OF CHARTS AND DIAGRAMS

Astronomical charts and diagrams

A very small number of azimuth diagrams and star charts are produced for
use in astro-navigation.

Co-tidal charts
Five of these are available, three of waters around the UK and two of other
areas where tidal conditions are of particular significance. Instructions for
their use are printed on each one. (See Chapter 11.)

Gnomonic charts
Small-scale ocean charts (one covering each of the major ocean areas) are
available on the gnomonic projection. These charts are in outline only and
are intended for use in plotting ocean courses. A great-circle course between
two points is represented on them by a straight line. This course can be easily
transferred to a navigational chart, on the Mercator projection, by plotting the
latitude and longitude of the ends of sections of convenient length. Special
versions of these charts are also available, overprinted with curves showing
the true bearings, from all parts of the chart, of certain well used destinations,
such as Bishop Rock, Panama, and Gibraltar.
124 CHAPTER 6 -CHARTS AND CHART OUTFITS

Magnetic charts
There are twelve magnetic charts, six of which show the magnetic variation
and the annual rates of change in variation. Of these one is a world chart,
four cover the main ocean areas and the sixth covers the north and south polar
areas. The polar sheet is on the polar stereographic projection, and all the
others are on the Mercator projection. These charts are renewed every five
years. The other six charts show other magnetic elements, e.g. inclination or
dip (I); they are renewed every ten years.

Routeing charts
Routeing charts include the following data:
1. Limits of load line zones (load line rules).
2. Routes an distances between ports.
3. Ocean currents
ü
4. Wind roses ý data supplied by the Meteorological Office.
5. Ice limits þ
6. Air, dew point, and sea temperatures, barometric pressure, and the
incidence of fog, gales and storms.

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In this series there are five regional sheets on the Mercator projection,
covering the North Atlantic, South Atlantic, Indian, North Pacific and South
Pacific Oceans. Each of these sheets is published in a separate version for
each month of the year, there being 60 sheets in all. They are corrected by
Notices to Mariners and occasional New Editions.

VOL 7
Passage planning charts
A guide chart (BA 5500) has been published by the Hydrographer of the
Navy, bringing together in text and diagrams much information necessary for
those planning to navigate the English Channel and the Dover strait.

Ships’ boats’ charts

These charts are issued for use in ships’ boats as a survival kit for mariners
in case of shipwreck. For many years they were printed on tough linen, but
they are now printed on a water-resistant plastic.
There are six charts, all on the Mercator projection, covering the North
and South Atlantic, the North and South Pacific, and the Indian Ocean. For
the Indian Ocean only, there are separate versions for the periods May to
October and November to April. Each chart is folded into a waterproof
wallet complete with simple plotting tools.
The charts carry a simplified outline of the surrounding land masses and
details of winds, ocean currents, ice and magnetic variations, as well as
compass roses. On the backs are printed full notes on their use including
information about plotting a position and laying a course by simple graphical
means. Information is also given on the management of boats, and on the
effect of winds, weather and currents.
The charts are corrected by New Edition at intervals of between ten and
fifteen years, though it is planned to reduce this period. They are not
corrected by Notices to Mariners and make no claim to be ordinary
navigational charts, being purely for use in an emergency.
OTHER TYPES OF CHARTS AND DIAGRAMS 125

Instructional charts and diagrams

Some of the sheets of the navigational chart series, covering a selection of the
navigable waters of the world, are reproduced and printed on thin, tough
paper for instructional purposes. A few diagrams used in navigation are also
included in the series. These items are not kept corrected and are sold on the
condition that they are not to be used for navigation.
Details of instructional charts are given in the Catalogue of Admiralty
Charts (NP 131) (see page 123). More than 30 charts are available on
various scales, including the 1:75,000 and 1:150,000 intricate or congested
coastal waters scale. Some of the charts are printed with the Racal-Decca
Navigator overlay; an increasing number are metric charts.

Ocean sounding charts

The Hydrographic Department maintains a series of ocean sounding charts,
covering the world’s oceans. Their content is limited to observations made
seaward of the outer edge of the Continental Shelf. True depths are shown
on the charts, all observed soundings having been corrected for the variable
velocity of sound in water. Most of the sheets are now in metric units.

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Ocean sounding charts are used extensively for the compilation of small-
scale navigational charts, such as the International charts published by
various Hydrographic Offices under the auspices of the IHO. Other users of
ocean sounding charts include cable-laying ships, deep-sea drilling operators,
geophysicists and oceanographers.
Further details of the numbers and limits of the ocean sounding charts are

VOL 7
given in the Catalogue of Admiralty Charts (NP 131). Arrangements for
obtaining copies are also described in the catalogue.

Practice and exercise area (PEXA) charts

PEXA (Q series) charts show the maritime areas off the coast of the United
Kingdom which are in use, or available for use, by the Ministry of Defence
for firing practice and exercises. There are six sheets at a scale of 1:500,000.
They are a development of the firing danger area charts first produced during
World War II, when practice areas become so numerous that it was no longer
practicable to show them on navigational charts.
Two broad categories of information are displayed:

1. Danger, prohibited and restricted areas which extend above ground/sea

level (i.e. airspace reservations).
2. Similar exercise areas in which the activities are at surface and sub-
surface levels.

In addition, the charts show the authority (Navy, Army, Air Force, MOD
Procurement Executive, etc.) controlling each area.
The charts are compiled from several sources, including the UK Air Pilot,
Air Notices, aeronautical information circulars, and RAF flight information
publications. Correction is by Notices to Mariners and New Editions.
These charts are in addition to those issued to RN ships and are in the 300
series of folios (see page 122).
126 CHAPTER 6 -CHARTS AND CHART OUTFITS

Meteorological working charts

The Hydrographic Department publishes about 40 meteorological working
charts in all, comprising surface working charts (see below), upper air
working charts, charts for use with radio facsimile transmissions and radial
charts for pilot balloon observations.

Surface working charts

There are about 30 of these charts, of varying sizes and scales, which cover
the world, except for the Arctic regions north of western Canada and eastern
Asia, and the Antarctic regions south and east of Australasia. There is a large
degree of overlap between them, and some areas, such as UK home waters,
feature on a number of sheets at different scales. The largest area covered by
any one chart embraces half of the Northern Hemisphere. A large selection
of meteorological observation stations are marked on the charts in their
appropriate locations.

Miscellaneous folios

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Chart Folio 317 (or 318, abridged set) is supplied to HM Ships. This contains
a quantity of miscellaneous charts, diagrams and tables for general use,
ranging from the Weir’s azimuth diagram to foreign fishing rights and
concessions within the fishery limits of the United Kingdom.
Other miscellaneous items such as Folio 320, Plotting Diagrams are also
supplied to HM Ships.

VOL 7 UPKEEP OF CHART OUTFITS

Full information is given in the Hydrographic Supplies Handbook (NP 133).

This is regularly amended and should therefore be taken as the authority on
the upkeep of chart outfits.

First supply
The Hydrographic Department at Taunton holds and maintains the main stock
of all charts, navigational and meteorological publications and Admiralty
Notices to Mariners. It also arranges for the supply through Chart Depots of
this material.
Correspondence on matters of supply should be addressed to: The Ships
Section, Hydrographic Department, Ministry of Defence, Taunton, Somerset,
TA1 2DN.
The requirements of HM Ships on commissioning are normally met by
a local Admiralty Chart Depot which is in the charge of a Chart Supply
Officer. There are three of these, one each at Plymouth, Portsmouth and
Rosyth.
It is the Commanding Officer’s responsibility to ensure that adequate
charts are held on board for the service on which the ship may be employed,
and that these are ordered in good time. The Ships Section, Hydrographic
Department normally arranges the first supply of chart and publication outfits
without demand.
UPKEEP OF CHART OUTFITS 127

State of correction upon supply

Charts supplied in navigational and Fleet folios are corrected for Permanent
Notices only. Corrections will have been made up to the Notice to Mariners
number shown on the folio correction sheets in NP 133B, the folio labels and
on the copy of the supply note H62 which accompanies the outfit.
The charts will therefore need to be corrected in pencil from Temporary
(T) and Preliminary (P) Notices in force, a list of which is published in
Notices to Mariners at the end of each month. To enable this to be done, the
following are supplied with the outfit:

1. The Annual Summary of Admiralty Notices to Mariners in force on 1st

January of the year in question, which gives full details of all (T) and (P)
Notices in force at that time.
2. A set of Weekly Editions of Notices to Mariners from No. 1 of the
current year, which includes full details of all (T) and (P) Notices
published since the first of the year.

Charts should also be corrected in pencil for radio navigational warnings

in force. A complete reprint of all radio navigational warnings in force at the

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beginning of the year is published in Weekly Edition No. 1 of Notices to
Mariners. NAVAREA I warnings in force, together with full details of the
latest warnings, are published weekly in Notices to Mariners. Selected
important warnings from other NAVAREAS are reproduced on a weekly
basis, while the numbers of those in force are listed once a month usually in

VOL 7
the last Weekly Edition of the month.
When a chart has been cancelled by a new chart or New Edition which is
not available when the outfit is issued, the obsolescent chart is included in the
appropriate folio after being corrected as far as possible and is stamped with
the following cautionary note:

‘CAUTION. This chart will shortly be replaced by a new chart or New

Edition and in the meantime is to be used with caution for navigational
purposes.’
Admiralty Sailing Directions are issued with the latest supplement, where
appropriate. Each volume of the Admiralty List of Radio Signals is issued
from Chart Depots with a recapitulatory supplement containing corrections
which have arisen whilst the publication has been in print, together with sets
of further corrections promulgated to date in Section VI of Notices to
Mariners. Each volume of the Admiralty List of Lights is issued with
subsequent corrections published in Section V of Notices to Mariners. All
these publications should be checked against the list of current hydrographic
publications published quarterly in Section II of Weekly Notices to Mariners
at the end of March, June, September and December.
If a List of Radio Signals is supplied for use by radio operators, a second
copy of the supplement to each volume and a set of separate Section VI of the
Weekly Edition of Notices to Mariners are supplied for the radio operators to
correct their list up to date.
Corrections to Sailing Directions are published in Section IV of the
Weekly Edition of Notices to Mariners. A summary of corrections in force
is published at the end of each month and in the Annual Summary.
128 CHAPTER 6 -CHARTS AND CHART OUTFITS

Action on receipt of the chart outfit

1. Check the folios against the Supply Note H62.
2. Check the associated publications against NP 133, and against the latest
quarterly list of current hydrographic publications.
3. Check the charts in each folio against the folio list.
4. Check the charts’ labels to ensure no chart is incorrectly labelled.
5. Check classified publications against NP 111.
6. Sign and return the duplicate copy of Supply Note H62 to the issuing
Chart Depot.
7. Insert, in pencil, the folio number on thumb-labels.
8. Record relevant details of charts and publications classified Confidential
and above on CB Form R.
9. Correct charts for any permanent notices published since the number
shown on the Supply Note H62.
10. Correct charts for (T) and (P) Notices, and radio navigational warnings,
starting with the folios in use. It saves unnecessary work if (T) and (P)
Notices and radio navigational warnings for other areas are left to the
time when the ship will be operating there.
11. Correct the publications, in particular Sailing Directions, List of Lights,

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List of Radio Signals.

Action on receipt of a newly published chart or a New Edition

The first intimation that a new chart or a New Edition of an existing chart has
been published will be a Notice to Mariners at the beginning of Section II of

VOL 7
the Weekly Notices. The action to be taken at this time is as follows:

1. Make a notation in the Chart Correction Log and folio Index (NP 133A,
133B) on the sheet for logging new charts and New Editions.
2. Amend the Catalogue of Admiralty Charts (NP 131) and the relevant
Sailing Directions (new charts only).
3. Note any Notices to Mariners affecting the chart between publication date
and date of receipt.

Action will normally be taken by the Ships Section, Hydrographic

Department (see page 126), to issue without demand new charts and New
Editions to ships as required; nevertheless, it is the Commanding Officer’s
responsibility to ensure that new charts or New Editions necessary for service
are held on board.
On receipt of the new chart or New Edition, take the following action:

New chart
1. Note the arrival in the Chart Correction Log and Folio Index.
2. Note the arrival on the folio and spare folio lists.
3. Correct for any outstanding Notices to Mariners, (T) and (P) Notices and
radio warnings.

New Edition
1. Change the New Edition for the old one in the folio concerned.
2. Note the arrival in the Chart Correction Log and Folio Index.
UPKEEP OF CHART OUTFITS 129

3. Correct for any outstanding Notices to Mariners, (T) and (P) Notices and
radio warnings.
4. Cancel the old chart.
Action on transfer of chart folios
Transfers of chart folios, navigational publications, etc. between officers,
ships or establishments or to a Chart Depot should be notified immediately
on Form H11, (Transfer and Receipt Certificate, in book form, for chart
folios, etc.), copies of which are included in the Small Envelope containing
H forms (NP 129). Prompt reporting of transfers is essential so that Notices
to Mariners can be diverted without delay.
As all necessary replenishments, etc. are supplied for their maintenance
chart folios and navigational publications are considered to be up to date and
available for transfer at any time to other ships or establishments.
Subsequent upkeep of chart outfits
After the first supply of a chart outfit from a Chart Depot, maintenance items,
as set out below, are issued automatically direct from the Hydrographic
Department, Taunton. Discrepancies should be reported to the Ships Section,

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Hydrographic Department (see page 126).
1. Notices to Mariners, Weekly Edition. Their regular receipt may be
checked by noting whether they are in sequence. HM Ships also receive
Fleet Notices to Mariners, Weekly Edition.
2. Charts. New charts, New Editions and, occasionally, corrected reprint
copies, are supplied when published and the receipt of such charts to

VOL 7
which a ship is entitled should be checked from the weekly list included
in Section II of Weekly Notices to Mariners, or from detail recorded in
the Chart Correction Log and Folio Index (NP 133A, 133B, see page
122). Details of Confidential Fleet charts issued to HM Ships should be
checked against Fleet Notices and CB Form R in a similar manner.
3. Publications. New editions of Sailing Directions, supplements to Sailing
Directions, Lists of Lights, Lists of Radio Signals and their supplements,
Tide Tables, etc. are supplied when published and the receipt of such
publications to which a ship is entitled should be checked from the
quarterly list in Section II of Notices to Mariners.
4. Replacements for worn or damaged charts and publications, or any
additional charts required, for example for blind navigation, are issued on
demand.
Demands for charts on form H262C and for publications on form H262B
(held in the Small Envelope, NP 129) should normally be sent in duplicate to
the Ships Section, Hydrographic Department, (see page 126) or in triplicate
to the Admiralty Chart Depot if the requirement is urgent. Items should be
listed in numerical sequence. The reason for demand should be stated in full
in such instances on the appropriate demand form. Requests for charts and
publications should be signed by the Navigating Officer.
Disposal of chart outfits
When a ship is to pay off and recommission immediately, charts and
publications should be retained on board. If the ship is proceeding to a
130 CHAPTER 6 -CHARTS AND CHART OUTFITS

different station or is to go on different service, arrangements will be made

and notified by the Hydrographic Department regarding the adjustment of the
chart outfit.
On reducing to reserve, the charts should be returned to the nearest Chart
Depot. Instructions regarding publications will be notified by the
Hydrographic Department.
If undergoing long refit or extensive repairs, charts and publications
should be returned to the nearest Chart Depot.
If undergoing short refit, publications should be retained on board, and
charts returned to the nearest Chart Depot. If recommissioning on a different
station or for different service, instructions should be requested from the
Hydrographic Department.

Chronometers and watches

Chronometers and watches, etc., which were formerly issued by and returned
to the Chart Depots, are now dealt with as valuable and attractive stores in the
Naval store account. Demands and returns should be made to the appropriate
Principal Supply and Transport Officer (Naval) (PSTO(N)).

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NAVIGATIONAL WARNINGS

Two main systems are used to provide the mariner with the latest navigational
information. These are Admiralty Notices to Mariners, and, for more urgent
information, radio navigational warnings. A third system, Local Notices, may

VOL 7
be used by commercial or Naval Harbourmasters for their local port area.
Around the United Kingdom, HM Coastguard also operates a Local Warning
Service covering the gap between the limits of one port or harbour and the
next.

Admiralty Notices to Mariners

Admiralty Notices to Mariners, containing important information for the

mariner and enabling him to keep his charts and books corrected for the latest
information, are issued daily to Admiralty Chart Depots and certain
Admiralty Chart Agents by the Hydrographic Department, and are published
in Weekly Editions for issue to ships.
Since Australian and New Zealand Notices are now the sole authority for
correcting all Admiralty, Australian and New Zealand charts of Australian
and New Zealand waters, such Notices as are relevant are included in the
Weekly Notices. But Temporary and Preliminary Australian and New
Zealand Notices are not usually republished: they can be obtained from
Australian and New Zealand Chart Agents.
Notices, and the Weekly Editions containing such Notices, are each
numbered consecutively, commencing at the beginning of each year.
Temporary and Preliminary Notices are identified by the addition of (T)
and (P) respectively after their consecutive numbers. An asterisk preceding
the number of a Notice indicates that the Notice is one based on original
information, as opposed to one that republishes information from another
country.
NAVIGATIONAL WARNINGS 131

Notices can be consulted in the ports listed in the relevant Notice in

Annual Summary of Admiralty Notices to Mariners. The Weekly Notices can
be obtained gratis from Admiralty Chart Agents and Depots (see the relevant
Notice in the same Summary), and from British Mercantile Marine Offices
and Custom Houses, or they can be despatched regularly by surface or air
mail from Admiralty Chart Agents.
Weekly Editions
Each Weekly Edition consists of the following sections:
I Index.
II Admiralty Notices to Mariners.
III Navigational warnings.
IV Corrections to the Admiralty Sailing Directions.
V Corrections to the Admiralty List of Lights and Fog Signals.
VI Corrections to the Admiralty List of Radio Signals and the Notices in
the Annual Summary of Admiralty Notices to Mariners relating to
those volumes (3, 3A, 3B ) Official Messages to British Merchant
Ships).

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Each Weekly Edition is bound by staples to enable Temporary and
Preliminary Notices and Sections III to VI to be detached for filing, or to
facilitate the correction of books. Section VI can be obtained separately.
In addition to the Notices for the correction of charts, the following
information is regularly contained in Weekly Editions.
New charts and publications

VOL 7
New charts and New Editions of charts published during the week, and any
charts withdrawn, are listed in a Notice near the beginning of Section II. This
Notice also mentions other charts affected by these changes, and gives notice
of forthcoming publications and withdrawals.
The publishing of new editions of volumes of the Sailing Directions or
their supplements, List of Lights, List of Radio Signals, Tide Tables and other
publications, are announced in Notices immediately following the above
Notice.
In the Weekly Editions at the end of March, June, September and
December, a Notice at the beginning of Section II gives the dates of the latest
editions of the various volumes of the Sailing Directions, List of Lights, List
of Radio Signals, certain other miscellaneous publications, and any
supplements affecting them. The Notice also indicates which books and
supplements are under revision and in the press.
Temporary and Preliminary Notices
Temporary (T) and Preliminary (P) Notices are found at the end of Section II.
Once a month, usually in the last Weekly Edition of the month, all Temporary
and Preliminary Notices in force are listed in a Notice near the end of Section
II. All (T) and (P) Notices in force at the end of the year are reprinted in
Annual Summary of Admiralty Notices to Mariners.
Notices affecting Sailing Directions
Corrections to Sailing Directions which cannot await the next supplement are
promulgated in Section IV of the Weekly Notices.
132 CHAPTER 6 -CHARTS AND CHART OUTFITS

Navigational warnings
Long-range navigational warnings issued during the week are reprinted in
Section III. These reprints quote only the most appropriate chart, though
others may be affected by the message.
All such warnings in force on 1st January are reprinted in Section III of
Weekly Edition No. 1 of each year.

Admiralty List of Lights

The volumes of the Admiralty List of Lights are corrected by Section V,
which includes any relevant alterations mentioned in Section II.

Admiralty List of Radio Signals (ALRS)

The volumes of the Admiralty List of Radio Signals, and the Notices in the
Annual Summary of Admiralty Notices to Mariners relating to those volumes,
are corrected by Section VI, which also includes any relevant alterations
mentioned in Section II.

Cumulative List of Admiralty Notices to Mariners (NP 234)

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A Cumulative List of Admiralty Notices to Mariners was introduced in
January 1986 and is issued at intervals of approximately six months. It
records the date of issue of the current edition of each chart and of subsequent
relevant Notices to Mariners issued during the previous two years.

Annual Summary of Admiralty Notices to Mariners

VOL 7
The first few Notices of each year are included in the Annual Summary,
published on 1st January of each year, and not in Weekly Edition No. 1. Most
of these important Notices are Annual Notices which deal with the same
subject each year.
The Annual Summary also contains all Admiralty Temporary and
Preliminary Notices and a reprint of corrections affecting Sailing Directions
only, as well as any Australian and New Zealand Temporary and Preliminary
Notices which have been republished, and which are in force at the end of the
preceding year. It is obtainable in the same way as Weekly Notices.

Fleet Notices to Mariners

When required, Fleet Notices to Mariners are published in Weekly Editions
to promulgate information or details of corrections affecting classified charts
or publications. Each issue is allocated the number corresponding to its week
of publication; in appropriate cases, the number of those weeks in which no
issue was made is quoted so that it is possible to check that all published
editions have been received.

Small Craft Editions of Notices to Mariners

Covering an area in NW Europe from the Elbe to the Gironde including the
British Isles, this quarterly edition was introduced in December 1978. An
improved service to yachtsmen results from careful selection of Notices,
which are reprinted in full, together with relevant block insertions. For ease
of reference they are divided into eight geographical areas and are well
indexed.
NAVIGATIONAL WARNINGS 133

Distribution of Notices to HM Ships

Every HM Ship holding a chart outfit is supplied with the Weekly Edition.
HM Ships holding Fleet folios are supplied with the classified edition of Fleet
Notices.
Supply is started automatically from the Hydrographic Department on
notification of the issue of the chart outfit to the ship concerned and is
continued until the outfit is returned.
Radio navigational warnings
Radio navigational warnings are designed to give the mariner early
information of important incidents which may constitute a danger to
navigation, such as particulars of recent dangerous wrecks, shoal depths,
casualties or alterations to major navigational aids, salvage and survey
operations in congested waters, movements of oil drilling rigs, extensive
maritime exercises, significant malfunctioning of radio-navigation aids, etc.
There are three types of radio navigational warnings: coastal, local and
long-range. Coastal and long-range warnings are primarily for international
shipping and local warnings are for vessels operating inshore.
Coastal radio warnings

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Coastal radio navigational warnings for all parts of the world are broadcast
from the country of origin. Particulars are given in Volume 5 of the
Admiralty List of Radio Signals (ALRS), where times, frequencies and other
relevant information may be found. This publication is corrected by Section
VI of the Weekly Notices to Mariners.
For waters around the British Isles, coastal radio navigational warnings

VOL 7
of a temporary nature are broadcast from British Telecom coast radio stations
by WT and RT (see ALRS, Volume 5 and the Annual Summary of Admiralty
Notice to Mariners). Warnings originated by the Ministry of Defence (Navy)
are numbered sequentially in the WZ series. Other warnings are unnumbered.
The information is primarily to assist the mariner in coastal navigation
and between ports as far as the port outer limits. Information of a less
essential nature and matters within a harbour entrance, which may form the
subject of a Notice to Mariners or local harbour warning, might not be
broadcast.
Local radio warnings
Local radio warnings, usually referred to as local radio navigational
warnings and primarily affecting vessels in inshore waters, are normally
issued by Port and Harbour Authorities within their respective limits. Around
the United Kingdom, the inshore gap between the limits of one port or
harbour and the next is covered by a Local Warning Service operated by HM
Coastguard.
Local Naval port radio warnings
HM Naval bases issue their own numbered series of local port navigational
warning signals containing important navigational information for the port
area.
Long-range radio warnings
Details of the procedure adopted by various countries for the dissemination
of long-range radio warnings are given in ALRS, Volume 5.
 134

VOL 7
SEE BR 45
Fig. 6-11. ‘NAVAREAs’ of the Worldwide Navigational Warning Service
CHAPTER 6 -CHARTS AND CHART OUTFITS
CORRECTION OF CHARTS AND PUBLICATIONS 135

The World-wide Navigational Warning Service

The World-wide Navigational Warning Service of long-range radio
navigational warnings, which became fully operational in April 1980,
comprises 16 geographical sea areas termed NAVAREAS identified by
Roman numerals (Fig. 6-11).
The authority charged with collating and issuing warnings to cover the
whole of an area is known as an area co-ordinator. The limits, area co-
ordinator and transmitting stations of each NAVAREA are given in ALRS,
Volume 5. Details are also to be found in the Annual Summary of Admiralty
Notices to Mariners.
NAVAREA I is co-ordinated by the United Kingdom. The text of the
week’s warnings together with a numerical list of those in force is included
in Section III of the Weekly Notices to Mariners. This list includes warnings
cancelled when superseded by a Notice to Mariners.
A Navigational Information Telex Service (NAVTEX) is available in
NAVAREA 1. This service provides shipping with the latest urgent
information on navigation, weather warnings and initial distress messages, by
means of an automatic direct print-out from a dedicated NAVTEX receiver.
This service is also available outside NAVAREA 1; full details may be found
in ALRS, Volume 5.

SEE BR 45
Long-range warnings issued by the United States
In addition to NAVAREA IV and NAVAREA XII warnings, the United
States issues HYDROLANT and HYDROPAC warnings for the remainder
of the Atlantic and Pacific/Indian Ocean areas respectively.
Details are given in ALRS, Volume 5 and in the Annual Summary of

VOL 7
Admiralty Notices to Mariners.
Correction of charts for long-range radio warnings
The correction of charts for radio navigational warnings and the frequency of
publication in Notices to Mariners is covered on page 127.
Local Notices to Mariners
Local Notices to Mariners are issued by commercial and Naval
Harbourmasters and contain navigational information for the local port area.
Each Notice has a local serial number. HM Ships are required to keep Local
Notices for their base port and any other dockyard that they are likely to visit
regularly.
Local Notices are not supplied automatically, except in a ship’s base port,
and application for them should be made to the local Harbourmaster.
List of Local Notices in force are issued from time to time.
CORRECTION OF CHARTS AND PUBLICATIONS
Navigational warnings and chart and publication corrections are brought to
the mariner’s notice by a number of different methods depending on their
urgency and importance; the following methods are available, all of which
have been discussed earlier in this chapter.
Annual Notices to Mariners. Fleet Notices to Mariners
Weekly Notices to Mariners. Local Notices to Mariners
Radio navigational warnings )long-range, coastal and local.
136 CHAPTER 6 -CHARTS AND CHART OUTFITS

Correction and warning system

The following items are required to run a satisfactory correction and warning
system.
1. Chart Correction Log and Folio Index (NP 133A, 133B).
2. Temporary and Preliminary Notices Log Book.
3. Local Notices File divided into areas with totes.
4. Long-range Radio Navigational Warning Log divided into the 16
NAVAREAS, HYDROLANTS and HYDROPACS, with totes and Log
Book.
5. Coastal and Local Radio Navigational Warning Log (WZs, etc) divided
into areas with totes.
6. Local (Naval) Port Navigational Warning Log divided into areas with
totes.
7. Wall chart to record radio navigational warning signals.
8. Fleet Notices to Mariners File with totes (HM Ships only).
Tracings for chart correction
Tracings to facilitate the correction of chart outfits are supplied automatically
to certain HM Ships and Royal Fleet Auxiliaries carrying large chart outfits.

SEE BR 45
They are used extensively by all Admiralty Chart Depots and Admiralty Chart
Agents who sell corrected charts.
When tracings are supplied, they are provided for all permanent
navigational chart corrections promulgated in the Weekly Edition of
Admiralty Notices to Mariners, except when a block correction only applies.
Each tracing is a pictorial presentation of the printed notice and contains in

VOL 7
addition the following details:
The chart number.
The Notice to Mariners number for the current correction.
The previous correction.
The standard folios in which the chart is contained.
Copies of these tracings are reprinted by the British Nautical Instrument
Trade Association and may be purchased through most Admiralty Chart
Agents. The text of the printed Notice must invariably be consulted when
using tracings.
Hints on correcting charts
Chart corrections, except those from Temporary or Preliminary Notices,
should be neatly made in waterproof violet ink on the charts affected. (The
recognised abbreviations shown on Chart 5011 should be used.) Notation of
the year (if not already shown) and number of the Notices inserted should be
made, also in waterproof violet ink, in the bottom left-hand corner of the
chart. Always check that the previous Notice has been inserted ) its number
is given in brackets against the number of the chart at the bottom of the
Notice.
Erasures should never be made but the details should, when necessary, be
crossed through in waterproof violet ink.
If several charts are affected by one Notice, the largest scale chart should
be corrected first. Correct the chart folios in use first.
Whenever possible, writing should be inserted clear of the water unless
the relevant objects are on the water, and care should be taken not to
CORRECTION OF CHARTS AND PUBLICATIONS 137

obliterate any information already on the chart. Unless cautionary, tidal or

other such notes are inserted, they should be written in a convenient but
conspicuous place, preferably near the title where they will not interfere with
other details.
Generally speaking, the amount of information which should be inserted
on a chart should be in accordance with that already shown. The insertion of
excessive detail not only clutters the chart, but can lead to errors. The amount
of detail inserted from each Notice on each of the charts affected should be
reduced as the scale of the chart decreases.
Detail is inserted on charts in accordance with the following principles,
depending upon the purpose of each chart, its scale and complexity. These
principles have been defined for the guidance of the mariner hand-correcting
his charts without overlay correction tracings, which make due allowance for
the reduction of detail.
On large-scale charts, the full details of all lights, light-buoys and fog
signals are inserted, together with the year dates of obstructions, reported
shoals, swept areas, dredged channels and depths on bars in shifting channels.
On coastal charts, full details of only the principal lights and fog signals,
and those lights, fog signals, light-vessels, lanbys and light-buoys that are
likely to be used for navigation on the chart, are inserted.

SEE BR 45
The usual order for omitting detail from light descriptions as the scales
of charts decrease is:

1. Elevation. 2. Period. 3. Range.

VOL 7
Details should be retained if a shortened description would result in
ambiguity between adjacent aids.
On coastal charts, navigational aids in harbours and other inner waters are
not usually shown. If the use of a larger scale chart is essential (e.g. for
navigation close inshore or for anchoring), details are given of those aids
which must be identified before changing to it, even though short-range
navigational aids and minor sea-bed obstructions are usually omitted.
However, it sometimes happens that a small-scale chart is the largest
scale on which a new harbour can be shown, in which case it might be
appropriate to insert on it full details of certain aids, such as a landfall buoy.
On ocean charts, normally only those lights which have a range of 15
miles or over are inserted and then only their light-stars and magenta flares.
Radio aids are inserted only on the charts in which they may be found
useful. Radiobeacons are therefore omitted from large-scale charts where
their use would be inappropriate. Similarly, on small-scale or ocean charts
only the long-range radiobeacons are charted.
On metric charts, and certain fathom charts which have had recent New
Editions, the limits of larger scale charts are shown in magenta.
Admiralty Notices to Mariners are occasionally accompanied by
reproductions of portions of charts (known as ‘blocks’) for pasting on the
chart. When correcting charts from blocks the following points should be
borne in mine:

1. A block may indicate not only the insertion of new information, but also
the omission of matter previously shown. The text of the Notice should
invariably be read carefully.
138 CHAPTER 6 -CHARTS AND CHART OUTFITS

2. Owing to distortion the blocks do not always fit the charts exactly. Care
should therefore be taken when pasting a block on to a chart that the more
important navigational corrections fit as closely as possible. This can
best be assured by fitting the block while it is dry and making two or
three pencil ticks round the edges for use as fitting marks. Paste should
then be applied to the chart and not to the block to avoid distortion of the
latter.
Corrections from Temporary or Preliminary Notices to Mariners should
be inserted on the charts in pencil. The year and number of each Notice
should be shown against it, e.g NM 625/1981 (T), and also outside the bottom
left-hand corner of the chart, in pencil, below the Small Corrections notations.
Temporary corrections should be rubbed out when the Notice cancelling them
is received, and Preliminary corrections should be replaced by the final
information when the Notice is received reporting that the changes have been
made. Similar action should be taken with radio navigational warnings and
Local Notices.
Charts stocked by the Hydrographic Department, Admiralty Chart Agents
and Admiralty Chart Depots are not corrected for Temporary or Preliminary
Notices and, when charts are received from one of these sources, they should

SEE BR 45
be corrected in pencil as necessary from the copies of such Notices already
held, or from those supplied with the charts.
Corrections from information received from authorities other than the
Hydrographic Department may be noted, in pencil, on the charts affected, but
no charted danger should be expunged without the authority of the
Hydrographer of the Navy.

VOL 7
Certain Admiralty Chart Agents provide a chart correcting service which
enables charts to be brought up to date, either from Notices to Mariners, or
by replacement if charts have been superseded by New Editions or new
charts.
Hints on correcting publications
Corrections are not made to publications stocked by the Hydrographic
Department or Admiralty Chart Depots (except to folio correction sheets NP
133B at Depots).
Arrangements for the supply of corrections for Admiralty Sailing
Directions, Admiralty List of Lights and Fog Signals, and Admiralty List of
Radio Signals have already been referred to in this chapter.
It is recommended that pages of Sailing Directions be annotated in pencil,
giving a reference to the relevant corrections promulgated in Section IV of
the Weekly Edition of Admiralty Notices to Mariners. It may be helpful to
record brief details (Weekly Edition number, title of the correction, page
number of the Sailing Directions) on a tote kept inside the front cover of the
relevant Sailing Directions.
Sections V and VI of the Weekly Notices contain corrections to the List
of Lights and Fog Signals and the List of Radio Signals respectively. The
amendments from these two sections should be cut out and stuck into the
appropriate volume, ensuring that the amendment is in the correct numerical
position. The left-hand edge only should be stuck down so that information
underneath may still be read. Manuscript amendments are sometimes
required as well; these should be inserted in ink in the appropriate volume.
HYDROGRAPHIC REPORTS 139

HYDROGRAPHIC REPORTS

Since the intervals between published surveys may be long, it is essential that
hydrographic notes are rendered whenever necessary by ships,
Harbourmasters and so on, to ensure that the charts issued by the
Hydrographer are kept up to date.

Forms
Hydrographic notes are rendered on Forms H102 and H102A. Completed
examples may be found in The Mariner’s Handbook (NP 100) and may be
obtained gratis from the Hydrographic Department, Ministry of Defence,
Taunton, Somerset TA1 2DN, or from Admiralty Chart Depots and principal
Chart Agents. Smaller copies of these forms, issued at the end of each month
in the Weekly Notices to Mariners, may also be used. These forms are issued
to HM Ships with the chart outfit as part of the Small Envelope containing
hydrographic forms (NP 129). Instructions for HM Ships on their use are
given in The Mariner’s Handbook and in Volume IV of this manual.

General remarks
Every opportunity should be taken to obtain information which may be of
value to the Hydrographic Department for the correction of charts and other
publications.
Ships can also be of great assistance in planning re-surveys by reporting
on the adequacy or otherwise of existing charts and plans and the need for re-
surveys or new surveys in the light of new development and possible future
strategy. In this connection, the views and requirements of Harbour
Authorities and pilots are of great assistance. A short letter giving the
reasons for surveys or re-surveys or for the proposed withdrawal of an
obsolete chart of plan, the authority and if possible a priority 1, 2 or 3
(bearing in mind that each Harbour Authority considers his own area of
paramount importance) is all that is required.
The Captain of a ship employed on special service, such as an
experimental cruise, or on a visit to an unfrequented place, is to forward a
hydrographic report with his Report of Proceedings. This should contain all
matters which may be of interest to the Hydrographer and which have not
been included in a report on Form H102/102A. A copy is to be sent direct to
the Hydrographer.
Officers rendering hydrographic notes should be guided by the following
points in addition to those in Volume IV of this manual, The Mariner’s
Handbook and on the forms themselves:

1. If a new anger is reported, its position should be accurately plotted on the

chart and two tracings of the portion of the chart in question should be
made. One copy should be forwarded to the Commander-in-Chief or
Senior Officer and the other direct to the Hydrographer at Taunton.
Similarly, any error detected on a chart or any improvement being
suggested should be plotted on the chart and tracings made and
transmitted as above.
140 CHAPTER 6 -CHARTS AND CHART OUTFITS

In all cases, as much of the adjacent coastline should be included as

will enable the tracing to be laid accurately over the chart affected,
marking also the true meridian line, the number of the chart, the date of
the last New Edition or the date of publication, whichever is the later, and
the most recent Small Correction.
Tracings should always be accompanied by a hydrographic note.
2. The Admiralty charts and navigational publications should be compared
constantly with the conditions found actually to exist.
3. Information, to be of value, must be as precise and up to date as possible.
However, ships should not hesitate to forward information unavoidably
obtained to a lower degree of accuracy, provided that full details of the
method by which it has been obtained are given. The date of the
information should invariably be given.
4. The amount of useful information which can be supplied will generally
be greatest when ships visit unfrequented places. Confirmation of matter
already appearing in the Admiralty Sailing Directions is very acceptable.
The volume and page of the Sailing Directions affected must always be
given, not only when some correction is made to a passage in the book,
but also when information is entirely new and cannot be placed under any
heading appearing on the relevant page.
5. The number of the largest scale chart affected should always be quoted.
When any chart is specifically mentioned in the report, the date of the last
New Edition or Large Correction is to be stated, together with the date or
number of the last Small Correction, as shown on the copy used.
6. True course and bearings are invariably to be given, measured in degrees
(clockwise) from 000° to 360°.
7. When photographs, sketches, tracings, etc. are sent in, they should be
included as enclosures. (See also Sketches and photographs, page 145).
8. Reports should be forwarded on separate sheets and arranged so that the
subject-matter proper to each of the numbered sections can be used
separately.
9. When information is supplied which leads to the correction of an
Admiralty chart or plan of a place in foreign waters for which a
recognised hydrographic authority exists, credit will not be given, in the
title of that chart or plan, to the ship or officer supplying the information,
because reference to the national authority concerned is always made
before chart action is taken.
10. Since the value of the material supplied will depend principally on the
extent to which it can be used for the improvement of hydrographic
publications, officers should take care that all objects quoted, when fixing
positions or for other purpose of reference, can be identified on the chart
without any risk of ambiguity.
11. When dredging operations or building work ) such as that on
breakwaters, wharves, docks and reclamations ) are described, a clear
distinction should be made between work completed, work in progress,
and work projected. An approximate date for the completion of
unfinished or projected work is valuable.
HYDROGRAPHIC REPORTS 141

Information for charts and Admiralty Sailing Directions

Newly discovered dangers

The position and extent of any shoal or danger discovered, especially of one
upon which a vessel has struck or grounded, should be determined, if
practicable, by five horizontal sextant angles between well selected objects;
and a careful true bearing to one of these objects should be given. The least
depth should be obtained whenever possible and, if there is shoal water, the
nature of the bottom.
Reports of shoal soundings, uncharted dangers and navigational aids
which are out of order should, if urgent, also be made by radio to the nearest
coast radio station. The draught of modern tankers is such that any uncharted
depth of less than 30 metres may be of sufficient importance to justify a radio
message.

Soundings
When soundings are recorded, the methods of sounding are always to be
stated, as well as the dates and times and the tidal reductions used.
Soundings are to be reduced to the level of the datum of the Admiralty
chart or, when this is not known, to a level below which the tide will seldom
fall. Details of the datum used must be given. Soundings may also have to
be corrected for the velocity of sound in water: see the remarks on echo
sounders in the revised Volume III of this manual and The Mariner’s
Handbook (NP 100). Corrections to true depth may be found from the Echo
Sounding Correction Tables (NP 139).
In order that the Hydrographer can make use of echo-traces forwarded
from ships, the following points should be noted:

1. Mark the trace each time a fix is obtained either by means of a fix marker,
if one is provided, or by annotating the record.
2. Number the fix and note the time.
3. Insert the recorded depth of all peak soundings.
4. On completion of soundings using a ‘wet paper’ echo sounder, and before
rolling up the paper, draw in the bottom trace and transmission line and
dry the paper, preferably in a dim light. This will ensure that, when the
trace fades, the record will remain clear.
5. Mark conspicuously all changes of phase.
6. Insert the make and type of echo sounding machine and:
‘Transmission correctly set at x metres.’
‘Add (subtract) y metres increased (decreased) draught.’
‘Speed set to suit 1500 m/sec sounding velocity.’
Also, mark the graduations of the depth scale at convenient intervals.
7. It is recommended that an indelible pencil or ball-point pen should be
used for all writing on the echo sounding trace. All writing or marking
should be kept well clear of the bottom trace.

When depths are found that are at variance with charted depths, the value
of the report will be much enhanced by continuing to run the echo sounder
142 CHAPTER 6 -CHARTS AND CHART OUTFITS

until reasonable, or even approximate, agreement with the chart is reached,

as this will enable shoal depths which are false to be identified.
When reports of shoals are received in the Hydrographic Department,
they are carefully considered in the light of accompanying or other evidence
before any action is taken to amend the charts. In the past, much time and
effort has been wasted by surveying ships searching for non-existent shoals.
When unexpected shoal soundings are obtained in waters where the charted
depth gives no indication, even though discoloured water may be seen, the
only certain method of confirming their existence is by taking a cast of the
lead. It has often been found that an apparent shoal sounding in relatively
deep water has been the result of a double echo.

Shoals
If an unexpected shoal is encountered, every endeavour should be made to
run back over the same ground, provided the ship is not endangered, to get
a further sounding with, if possible, an accurate fix of its position. If further
time can be spared, several lines of soundings running across the shoal area
and recorded by the methods described above would make a very useful
report, especially if the least depth on the shoal is obtained and the limits of
the shoal area defined.

Discoloured water
The legend ‘discoloured water’ appears on many charts, particularly those of
the Pacific Ocean where shoals rise with alarming abruptness from great
depths. Most of these legends remain on the charts from the last century,
when very few deep-sea soundings were available and less was known of the
causes of discoloured water. Only a few of the reports of discoloured water
have proved on examination to be caused by shoals; the remainder have been
caused by such things as plankton, cloud reflections etc.
Today, such reports can be compared with the accumulated information
for the area concerned, a more thorough assessment made and, as a result the
legend ‘discoloured water’ is now seldom inserted on charts.
Discoloured water should be approached as closely as possible, in order
to ascertain whether or not the discolouration is due to shoaling, whilst
having due regard to the safety of the ship. If there is good reason to suppose
that the discolouration is due to shoal water, a hydrographic note should be
rendered to the Hydrographer of the Navy accompanied by an echo sounder
trace and any other supporting evidence. Reports of discolouration due to
other causes should be forwarded to the Meteorological Office, London Road,
Bracknell, Berks.

Port information
When opportunity occurs, Admiralty publications should be checked for
inaccuracies, out of date information and omissions. Port regulations,
pilotage, berthing and cargo handling, provisions and water and other
facilities are frequently subject to change, and it is often only by reports from
visitors that charts and publications can be kept up to date for such
information. The value of such reports is enhanced if they can be
accompanied by the local Port Handbook.
HYDROGRAPHIC REPORTS 143

When reference is made to piers or wharves, the depths at the outer end
and alongside are the most important items of information that can be given
(although all dimensions are useful).
The length and bearing of any extension should be given in such a way
that they can be plotted with as great a precision as the scale of the chart
permits. The position of any new lights on the extension should be stated
exactly, and the removal or continuance of any lights charted on the pier or
breakwater before extension should be mentioned.
Where dredged channels exist, the date of the last dredging and the depth
obtained should be noted.
A Port Officer sometimes has a large-scale manuscript plan of the harbour
and approaches, which is merely his own enlargement of the plan published
by the government. The value of such a plan can, however, be judged only
by the comparison with the Admiralty chart and a copy should, if possible, be
forwarded to the Hydrographer for evaluation. It is important to note whether
the datums for heights and sounding, the scale and the true north are given,
and then to check them ) or to supply them if not given.
Lights
When reporting on lights, the simplest way to ensure a full report is to follow
the columns in the Admiralty List of Lights and Fog Signals, giving the
information required under each heading; some details may have to be
omitted for lack of data whilst others might be amplified, at the discretion of
the observer. Characteristics should be checked with a stopwatch.
The numbers assigned to lights in the List of Lights, prefixed by the
volume letter, e.g. G0153.4, are the international numbers adopted in
accordance with the resolutions of the International Hydrographic
Organisation. These letter-figure combinations should be quoted whenever
lights are referred to.
Buoys
Buoys should be checked against the details given on the latest large-scale
chart. Where possible, the position of a buoy should be checked by range and
bearing or other suitable method and details forwarded as described below.
Beacons and marks
For new marks, the position should be fixed by ‘shooting up’ from seaward,
verified where possible from the responsible authorities in the area, who
should be quoted in the report.
Conspicuous objects
Reports on conspicuous objects are required frequently since objects which
were once conspicuous might later be obscured by trees, other more
conspicuous buildings, etc. The positions of conspicuous objects can
sometimes be obtained from local authorities, but more frequently must be
fixed from seaward as stated above.
Wrecks
Stranded wrecks showing any portion of the hull or superstructure at the level
of chart datum should be fixed by the best available method and details
144 CHAPTER 6 -CHARTS AND CHART OUTFITS

recorded. The measured or estimated maximum height of a wreck above

water, or the amount which it dries, should be noted together with the date
and time of observation (for tidal correction purposes). The direction of
heading and the extremities of large wrecks should be fixed if the scale of the
chart is sufficiently large.
Submerged wrecks can usually only be located by vessels fitted with the
necessary searching equipment.

Channels and passages

When reports are made on a discrepancy in the charting of a channel, or a
passage between islands, and when information is supplied about one shore
only of a strait, or about some island in such water, every effort should be
made to obtain a connection by angle or bearing between the two shores. The
absence of such a connection may have been the original cause of the
discrepancy reported, and may cause serious difficulty in making proper use
of the information supplied.

Positions
Observations of positions of little-known places are always welcomed,
especially if the reporting officer has reason to question the charted position.
Full details of observations should be given, in order that their value may be
assessed. When practicable, the position should be linked with some existing
triangulation or known position. Care should always be taken to dispel
uncertainty about the existence, extent and precise position of reported
dangers and doubtful islands, and to obtain the least depth where appropriate.
Careful examination of such objects is of the greatest importance, both in the
general interests of navigation and for the maintenance of the reputation of
the Admiralty charts for accuracy and completeness of information.
Whenever a search or examination is made, the state of the weather and
light should be described fully if they are likely to have had any influence on
the result.
It cannot be emphasised too strongly that, in general, the only effective
method of obtaining evidence about the existence of reported dangers is to
take positive soundings in the vicinity and, if possible, to obtain specimens
of the bottom.

Tidal streams
Observations of tidal streams should be obtained whenever possible. If only
a general description can be given, care must be taken to avoid any ambiguity
that might arise from the use of the terms ‘flood’ and ‘ebb’ streams. It is
generally preferable to give the direction of the stream, e.g. ‘east-going’ or
‘west-going’. The time of the change of stream should always be referred to
high water; for instance, ‘the north-going stream begins two hours after high
water’. When the time of local high water is not known, the turn of the
stream should be referred to high water at the nearest port for which
predictions are given in the Admiralty Tide Tables.
HYDROGRAPHIC REPORTS 145

Ocean currents
Much useful knowledge of ocean currents can be obtained by ships on
passage. Form H568 (Sea Surface Current Observations) is designed for the
collection of such information and is obtainable gratis from the Hydrographic
Department or from the principal Chart Agents. This form is issued to HM
Ships as part of the Small Envelope (NP 129).
Instructions for rendering the form, which are carried on it, call mainly
for a record of courses and distances run through the water, together with
accurate observations of the wind to enable this component of the ship’s drift
to be eliminated in analysis, and sea surface temperature readings to enable
the observed current to be related to different water masses.
Though primarily intended for reporting unexpected currents, the form
can be usefully maintained on a routine basis for all passages outside coastal
waters to give valuable information of predicted currents.

Magnetic variation
In many parts of the world, precise information for the plotting of isogonic
curves on charts is still inadequate. Observations for variations made at sea,
preferably using Form H488 (Records of Observation for Variation), are
valuable, particularly where the isogonic curves are close together or change
quickly, or where there are local magnetic anomalies. These forms are issued
to HM Ships as part of NP 129.
Reports should be forwarded to the Hydrographic Department.

Information concerning radio services

Reports should be made of any irregularities in radio signals that have not
already been announced. Any other information that may be useful for the
Admiralty List of Radio Signals should be forwarded.
If radiobeacons are observed to have characteristics differing from those
given in ALRS, as amended by the latest Notice to Mariners, an attempt
should be made to ascertain locally whether these alterations are permanent.
Similarly, any changes observed in the time or type of transmission of
weather bulletins and storm warnings, navigational aids, warnings or time
signals, should be verified locally, and confirmation sought that these
alterations are permanent.

Zone time
Information should be supplied concerning the time kept locally, if it differs
from that given in the most recently published ALRS (Volume 5), or The
Nautical Almanac (NP 314).

Sketches and photographs

Sketches and photographs form a very valuable adjunct to the Admiralty
Sailing Directions, and every opportunity should be taken of adding to them.
The existing views in the Sailing Directions, or on charts, should be
examined for possible improvements ) for example the addition of a
conspicuous object.
146 CHAPTER 6 -CHARTS AND CHART OUTFITS

Sketches and photographs of navigational interest may be divided broadly

into three classes.

1. General views of a coast or anchorage, showing the principal charted

features. These enable the mariner, when making land or approaching the
anchorage, to identify these features more readily than can be done from
a written description.
2. Views of leading marks or anchoring marks.
3. Sketches or photographs of special objects that cannot easily be described
in words.

In the case of (1) and sometimes in the case of (2) also, a photograph will
have to be taken from a considerable distance, and will usually give poor
results unless enlarged or taken with a telephoto lens. Even when enlarged,
the photograph will usually require treatment in order to emphasise the
desired conspicuous features. This can be done satisfactorily only by the man
on the spot, either when he is in a similar position on a subsequent occasion,
or by his referring to an outline sketch made at the time the photograph was
taken. Alternatively, a photograph may be used for the purpose of improving
or correcting a sketch.
If an outline sketch is made in order to supplement a photograph, the
names or descriptions of the conspicuous objects shown on it can
conveniently be inserted against them, and it can then be attached to the
photograph. The vertical scale on outline views should be 1½ times or twice
as large as the horizontal ) i.e. the heights of objects should be exaggerated
somewhat; but this should be done with discretion, especially if there are any
objects, such as islets, in the foreground.
When no outline sketch has been made, the names can be inserted on the
photograph itself but, when this is done, a second print without names should
be attached.
Always state, in the report and on the photograph or sketch itself, the
exact position from which the photograph was taken or the sketch made, the
date and time.
Sketches and photographs forwarded with a view to reproduction should
never be gummed or pasted to the pages of a report, but should be placed in
an envelope which should be attached securely to the report.

NAVIGATIONAL FORMS

Contents of the Small Envelope (NP 129)

One of these is supplied with the chart outfit and contains various quantities
of the forms listed in Table 6-1.
Form H62 (see page 128) is used by the Hydrographic Department or the
Admiralty Chart Depot for the issue and receipt of chart folios and
publications.

THE PRODUCTION OF THE ADMIRALTY CHART

Data for use in the compilation of Admiralty charts are received from many
sources. The permanent archives of the Hydrographic Department at Taunton
THE PRODUCTION OF THE ADMIRALTY CHART 147

Table 6-1. Forms contained in the Small Envelope

NUMBER TITLE REMARKS

H11 Transfer and Receipt Certificate, Used for chart and map folios
in book form, for chart folios etc. and navigational publications.
See Upkeep of chart outfits (in
this chapter), page 129.
H102 Hydrographic note ü
ï
ý See Hydrographic reports (in
H102A Hydrographic note for port ï this chapter), pages 139 to 146.
information þ

H262B Demand Form for publications ü

ï
(pads) ý See Upkeep of chart outfits (in
ï this chapter), page 129.
H262C Demand Form for charts (pads) þ

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H488 Record of Observation for See page 145.
Variation
H493 Record of Observations of
Magnetic Declination (variation)
H568 Observation of Sea Surface See page 145.

VOL 7
Currents
) Tracing paper For use with hydrographic
notes, etc.

hold over half a million documents, and modern surveying techniques have
resulted in a 10% increase in the annual rate of data acquisition, thereby
giving rise to a considerable problem in maintaining the published charts up
to date. Surveys are continually being carried out by the ships of the Royal
Navy Hydrographic Service, which operates in various parts of the world.
Similar work is carried out by foreign hydrographic authorities. Close
international co-operation between the member nations (50 in 1981) of the
International Hydrographic Organisation ensures a free exchange of data
including copies of surveys, foreign charts, and Notices to Mariners. In
addition, the Hydrographic Department at Taunton receives surveys from
ships, Harbour Authorities and commercial companies, hydrographic reports
from naval and mercantile vessels, land maps, air photographs and many
other relevant documents from a great variety of sources throughout the
world.
When a decision is made to produce a new chart ) perhaps because an
extensive hydrographic re-survey has been carried out, or because a port
development project, including new terminals and dredged approach chan-
148 CHAPTER 6 -CHARTS AND CHART OUTFITS

nels, has been completed ) a period of approximately 18 months will pass

before the chart is ready for publication. A scheme is prepared indicating the
scale at which the chart will be constructed, its geographical limits, and the
general layout of the information it will contain. The source material is
obtained from the archives or is sought from other authorities who may also
have supplementary data. Specifications are written for the compilation
draughtsman, who selects the required detail and assembles it in accordance
with approved policies governing the display of information on Admiralty
charts. After the draft of the chart has been fully edited and verified,
reproduction processes take over and transform the compilation, the approved
draft, into a printed image. Automated cartography, and photographic and
mechanical techniques, are employed where possible, but successful chart
making still depends primarily on the skill of the compiler and the
reproduction craftsman.

Reproduction methods
In the past, charts were always engraved on copperplate, printed copies being
taken directly off the plate. This was a slow process which involved
dampening the paper to obtain the best impression. Thus, there was

SEE BR 45
consequent shrinking of the chart as the paper dried out. Such instability in
paper size was unacceptable when the use of colours was introduced into
chart making. This created the need for the exact registration of each colour
plate during the printing process, and led to the replacement of direct
copperplate printing by lithographic reproduction. The earliest lithographic
printing used the surface of a flat polished stone; this was subsequently

VOL 7
replaced by a zinc plate and then by aluminium. For some time, copperplate
continued in use as the base or master plate, the image being transferred to
the printing plate by either a transfer or a photographic process. Media other
than copper were subsequently used as master plates; one such was an
aluminium sheet spray-coated with white enamel. This type of surface was
ideal for drawing by hand and the resulting image was directly photographed
and photo-printed on the printing plate and also on a fresh enamel as a
permanent record. Correction of such a base was easier and quicker than with
copper.
The residual use of copperplate bases finally ceased in 1981, having been
overtaken by the plastics revolution of the 1970s, the increasing application
of modern scribing methods, photo-typesetting and computer-assisted
cartography. Enamel coated aluminium plates are still used as the master
plates for some Admiralty charts. The charts themselves are printed using the
off-set process (the image is transferred from the plate to a rubber cylinder,
then to paper), on a rotary printing press which will print up to four colours
in succession as the paper is threaded automatically through the machine.
Additional detail in other colours can be overprinted by repeating this
process.
Since the metrication of the Admiralty charts began in 1967, the standard
method of chart production has been on plastic, using automated techniques.
A brief summary of the production process is set out below.

1. A computer is programmed to produce the necessary tapes for an

automatic plotter to scribe on a specially prepared film negative the
graduated border, meridians and parallels, to the required projection,
scale and limits.
THE PRODUCTION OF THE ADMIRALTY CHART 149

2. Using an image from this negative, the new chart compilation is prepared
on a sheet of plastic. After rigorous checking of all details, the
compilation is put through a series of photographic processes using both
negative and positive film to produce an image of printing quality.
During these processes, certain details are scribed by hand ) coastline,
contours, roads, towns, etc; other standard details ) compass roses,
soundings, symbols, etc. ) are added, together with all the type matter
particular to that chart. These type requirements are photo-set on a thin
film which is then cut and patched in position.
3. The production of an increasing number of new charts is partly
automated. The detail of the compilation is digitised and the tape output
from the digitiser processed by the computer, which controls the
automatic plotter to plot all the digitised details. The resulting film
positive has the type matter patched to it and the chart then continues in
the same production stream as those produced entirely by hand.
4. Once the chart has been proofed, checked throughout in detail and up-
dated as necessary, the final production negatives are prepared. These

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negatives are then contact printed to sensitised aluminium printing plates,
one for each of the colours to be used. Standard metric charts are printed
on a four-colour off-set rotary printing press.

Plate correction

VOL 7
Limited corrections and additions can be made to the printing plates prior to
printing, either at the proof stage of new charts and New Editions or,
subsequently, when amendments announced in Notices to Mariners have to
be inserted. However, this process has certain technical limitations and, on
average, after 5 or 6 printings, a plate will have to be replaced. Thus, in the
case of many popular charts, reprinted 3 or 4 times each year, new printing
plates are required every 1½ to 2 years.
 150 CHAPTER 6 -CHARTS AND CHART OUTFITS

| INTENTIONALLY BLANK
 151

CHAPTER 7
Publications

Publications used by the Navigating Officer are divided into two categories:

1. Publications supplied by the Hydrographer (the NP series).

2. Textbooks, reference books, handbooks and forms obtained from the CB
Officer or the Supply Department (CBs, BRs, and ‘S’ series forms).

PUBLICATIONS SUPPLIED BY THE HYDROGRAPHER

Sets of navigational publications

Navigational publications (NPs) are made up into sets, details of which are
given in the Hydrographic Supplies Handbook (NP 133), already mentioned

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in the previous chapter. All major war vessels are supplied with a complete
set of NPs. Ocean-going Royal Fleet Auxiliaries and chartered merchant
ships are supplied with an abridged set; mine countermeasures vessels, tugs
and other small craft employed in home waters are supplied with a Home
Local Service set; similar ships employed abroad with a Foreign Local

VOL 7
Service set. In addition, the appropriate Admiralty Sailing Directions (Pilots)
and Admiralty List of Lights and Fog Signals are issued automatically with
each chart folio, as indicated at the bottom of the folio list.

State of correction upon supply

Navigational publications are not corrected on supply, but the latest
supplements, summaries of Notices, etc. are automatically included with the
set (see Chapter 6, page 127).

Meteorological publications
A list of these publications together with the scale of issue is given in the
Oceanographic and Meteorological Supplies Handbook, W1 (NP452).
The handbook Meteorology for Mariners (NP 407) is issued to all HM
Ships and ocean-going RFAs except some smaller warships. This publication
covers:

The meteorological element.

Climatology.
Weather systems.
Weather forecasting.
Ocean surface currents.
Ice and exchange of energy between sea and atmosphere.
152 CHAPTER 7 - PUBLICATIONS

The Naval Oceanographic and Meteorological Service Handbook, W11

(NP 510) is issued to all major HM warships. It includes chapters on:

Meteorological and oceanographic equipment and stores including

instructions for the precision aneroid barometer.
Publications and charts.
Reports and returns.

Aviation publications
Details of air charts, air chart folios, plotting sheets and reference chart folios
and their scale of issue are given in the Catalogue of Admiralty Air Charts
(NP 110). Issue is limited to larger warships, Royal fleet Auxiliaries and
Front Line Squadrons. The catalogue and a set of Air Notices are supplied
to these ships with the initial chart outfit, after which Air Notices are supplied
automatically when published.

Navigational publications
Books published by the Hydrographic Department are listed in the Catalogue
of Admiralty Charts and Other Hydrographic Publications (NP 131) and the

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Hydrographic Supplies Handbook (NP 133). They fall into the following
subject groups:
Sailing directions.
Lights and fog signals.
Radio signals.

VOL 7
Tides and tidal streams.
Astronomical observations.
Catalogues.
Hydrographic practice and symbols.
Nautical almanacs.
Oceanography.
Admiralty marine science publications.
Miscellaneous.
Brief details of the more commonly used publications are given below.
Details of publications concerning charts are given in Chapter 6.

Admiralty Sailing Directions (NP 1 to 72)

Admiralty Sailing Directions, also called Pilots, were first regularly published
in 1829 after some agitation by the Fleet for officially published books to
complement Admiralty charts. During the nineteenth century, the volumes
gradually grew in size and in numbers from fairly small publications of
‘Hydrographical Notices’ of surveyors’ reports on areas surveyed, to some 70
volumes by the end of the century. This growth corresponded with the
expansion of the chart series, which by this time covered virtually all the
navigable waters of the world except for the polar regions. Present-day titles
and the area covered by each volume are shown in NP 131 and NP 133.
Each volume of the Sailing Directions contains descriptions of the coast
and off-lying features, notes on tidal streams and currents, directions for
navigation in intricate waters, and other relevant information about the
channels and harbours. In addition, each book includes information about
PUBLICATIONS SUPPLIED BY THE HYDROGRAPHER 153

navigational hazards, buoyage systems used in the area covered, pilotage,

regulations, general notes on the countries within the area, port facilities and
a general summary of seasonal current, ice and climatic conditions with direct
access to the sea except Great Lakes of Canada and USA. The indices of the
various volumes provide a fairly comprehensive gazetteer of coastal names.

Uses and users.

The Sailing Directions should be read in conjunction with the appropriate
Admiralty charts quoted in the text. They are intended to aid the mariner in
navigation at sea and are for all classes of vessel, from sea-going small craft
up to the largest super-tankers. The books are also convenient works of
reference for shore-based maritime authorities, in connection with planning
and for general information.

Sources of information
Sailing Directions were originally compiled from first-hand reports and
descriptions of the coast, mainly from British ships. In foreign waters where
British ships had not navigated, foreign charts and publications were used.
Subsequently, the books have been kept up to date on a regular basis from the

SEE BR 45
latest editions of charts, maps, foreign sailing directions and other
publications, and also from reports of surveys, reports from ships, and notices
to mariners issued by other countries and maritime authorities.
Each volume is completely revised at intervals of from 12 to 15 years. In
the intervening period, each is kept up to date by supplements issued at

VOL 7
regular intervals of 1½ to 2 years. Each new supplement is cumulative and
incorporates all previous corrections. A number of corrections to Sailing
Directions are also issued in the Weekly Editions of Admiralty Notices to
Mariners. Notices in force affecting Sailing Directions are listed in the last
Weekly Edition of each month. (See Chapter 6, page 138 for advice on
correcting Sailing Directions.)
When a supplement to a volume has been issued, a copy of the
supplement accompanies that volume on first supply of the chart outfit. Each
supplement should be kept intact, and should invariably be consulted when
using the volume to which it refers.
Of the vast amount of information needed to keep charts up to date, only
the most important items can be used to correct the charts by Notices to
Mariners. Less important information, though it may not reach the chart until
its next major correction, is nevertheless included in Sailing Directions or
their supplements, if appropriate.
Editions of Sailing Directions published after the end of 1972 use metric
instead of Imperial units when describing depths, heights and distances on
land. Where the large-scale chart quoted in Sailing Directions is still in
fathoms and feet, depths and dimensions printed on the chart are given in
Sailing Directions in brackets so that chart and Sailing Directions can be
more easily compared.

Views for Sailing Directions (NP 140)

This publication contains guidance and requirements for taking photographs
for Sailing Directions.
154 CHAPTER 7 - PUBLICATIONS

The Mariner’s Handbook (NP 100)

This book contains information of general interest to the mariner an dis
complementary to the Sailing Directions. The contents include: general
remarks on charts and publications; notes on orthography and terms used; use
of charts and navigational aids, observing and reporting; notes on offshore
hazards and restrictions to navigation; tides, currents, characteristics of the
sea, magnetic anomalies and sea-bed sound waves; basic meteorology and
navigation in ice; a selection of conversion tables.
The Handbook is reviewed and updated regularly by the Hydrographic
Department. It is corrected by supplements and by new editions at intervals
of about 5 years.

Ocean Passages for the World (NP 136)

This book is intended for planning an ocean passage. It gives recommended
routes and distances between the principal ports of the world, with details of
winds, weather, currents and ice hazards that may be encountered. It links the
various volumes of the Sailing Directions. Much useful information is
included which will not be found in the Sailing Directions since the latter are
concerned mainly with coastal waters.

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The book is corrected periodically by supplements, in the same way, but
less frequently, as the Sailing Directions. It is accompanied by diagrams
showing the main ocean routes for power vessels and sailing ships, world
charts of climate and ocean currents, and by Diagram D6083 (Load line rules,
zones, areas and seasonal periods) relating to the Merchant Shipping (Load

VOL 7
Line) Rule, 1968. If required, separate copies of these diagrams are
obtainable from Admiralty Chart Agents.

Admiralty Distance Tables (NP 350(1), (2), (3))

The Admiralty Distance Tables give the shortest navigable distance in
international nautical miles between focal points and chief ports of the world.
This distance may differ from the distance in sea miles by up to ½% at the
equator or at the poles. These routes are not necessarily the quickest and
most suitable route for a particular passage, as other routes may offer more
favourable currents or better conditions of sea, swell or weather. Remarks on
the various routes will be found in Ocean Passages for the World or in the
Admiralty Sailing Directions while Routeing charts show the principal
commonly used routes.
Most routes are available for ships drawing 10 m; where this depth is not
available, as may be the case where there are off-lying shoals or in the
harbour approach, the deepest recommended channel has been used.
Volume 1 covers the North and South Atlantic Oceans, the Arctic Ocean,
Baltic Sea, North-west Europe, Mediterranean Sea, Black Sea, Caribbean and
the Gulf of Mexico. Volume 2 covers the Indian Ocean, and part of the
Southern Ocean from South Africa to New Zealand, Red Sea, Persian Gulf
and the Eastern Archipelago. Volume 3 covers the Pacific Ocean.
Full instructions for use are given in the Introduction to the Distance
Tables.
PUBLICATIONS SUPPLIED BY THE HYDROGRAPHER 155

Use of the Distance Tables

To find the distance from Devonport to Gibraltar
Locate the nearest terminal points by referring to the appropriate chartlets.
Devonport ) Plymouth sound: Part I North-west Europe
Gibraltar ) Europa Point: Part II Atlantic Ocean
As these two places are in adjacent tables, find a suitable place common
to both tables, in this case Ushant (Île d’Ouessent).
Table 1c, North-west Europe, Channel:
Plymouth Sound ) Ushant (10'W)
123
Table 2a, Atlantic Ocean, NE Atlantic:
Ushant ) Europa Point (6'S) 929
Distance from Plymouth Sound to 6 miles south
of Europa Point passing 10 miles west of Ushant (n miles) 1052
If places are in non-adjacent areas, Part IV, the Link Tables, may be used

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provided the places concerned are marked by an asterisk in the tables.
Admiralty List of Lights and Fog Signals (NP 74 to 84)
The Admiralty List of Lights and Fog Signals is published in eleven volumes
giving a worldwide tabulation of all lighthouses and lights of navigational
significance. Also listed are lightships, lit floating marks 8 metres and over

VOL 7
in height, and fog signals; but not buoys of a height of less than 8 metres.
The areas covered by each volume are:
Volume A (NP 74) British Isles and north coast of France.
Volume B (NP 75) Southern and eastern sides of North Sea.
Volume C (NP 76) Baltic Sea.
Volume D (NP 77) Eastern side of Atlantic Ocean.
Volume E (NP 78) Mediterranean, Black and Red Seas.
Volume F (NP 79) Arabian Sea, Bay of Bengal and North Pacific
Ocean.
Volume G (NP 80) Western side of South Atlantic Ocean and East
Pacific Ocean.
Volume H (NP 81) Northern and eastern coasts of Canada.
Volume J (NP 82) Western side of North Atlantic Ocean.
Volume K (NP 83) Indian and Pacific Oceans, south of the equator.
Volume L (NP 84) Norwegian and Greenland Seas and the Arctic
Ocean.
For each light the following details are given. (For further information,
see Chapter 10).
1. Number, used for index purposes.
2. Name and descriptive position, e.g. Longships. Highest rock off Land’s
End.
3. Approximate latitude and longitude.
4. Characteristics. Intensity may be shown when nominal range is not used.
5. Elevation of the light in metres above Mean High Water Springs level.
156 CHAPTER 7 - PUBLICATIONS

6. Range of visibility in sea miles.

7. Description of the structure on which the light is situated and the height
of the structure above the ground in metres.
8. Phases, sectors, arcs of visibility, periods of illumination, important
temporary information, and other relevant remarks ) also any minor
associated lights which do not merit separate numbering.

In addition, each volume contains tables for the calculation of the

geographical and luminous ranges of lights; definitions of, and general
remarks on, the characteristics of lights and fog signals; and a list of foreign
language equivalents of the abbreviations used in light descriptions. In some
volumes, special comments are found on problems peculiar to the areas
covered by them. Items covered include off-shore oil rigs, light vessels and
distress signals.
While the main details of important lights are also shown on Admiralty
charts, item (1) above is not shown on charts, (2), (7) and (8) are sometimes
not shown, and other details are progressively omitted from charts as the scale
decreases. Complete information about lights and the minor and temporary
amendments which are made to them (see below) can therefore only be
obtained from the List of Lights volumes.

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Sources of information
The volumes of the List of Lights are compiled from information received
from the following sources:

VOL 7
1. Lighting authorities in home waters (Trinity House, Northern Lighthouse
Board, Commissioners of Irish Lights), Harbourmasters and Port
Authorities.
2. Foreign lights lists and notices to mariners.
3. Ships’ reports and hydrographic surveys.
4. Foreign charts.

On receipt of information about important changes to lights which affect

the safety of navigation, a Notice to Mariners is issued for the correction (or
temporary correction) of charts. Each week these Notices, together with
temporary alterations and many other minor changes to lights, are included
in Section V of the Weekly Edition of Notices to Mariners. They are
arranged in numerical order and are intended for cutting out and pasting into
the printed books. Changes to lights shown on charts are made by Notices in
Section II of the Weekly Editions, which are usually published later than the
corresponding information in Section V, as chart-correcting Notices take
longer to produce. The List of Lights should therefore invariably be
consulted whenever details of a light are required.
A new edition of each volume of the List of Lights is published at
intervals of about 18 months, the previous edition being thereby cancelled.
The Weekly Notices announcing the publication of a volume will contain all
corrections in Section V received between the date of going to press and the
date of issue. From the latter date, correction by Section V of the Weekly
Notices is resumed. The requisite up-dating corrections are readily available
through Chart Agents.
PUBLICATIONS SUPPLIED BY THE HYDROGRAPHER 157

Admiralty List of Radio Signals

The Admiralty List of Radio Signals (ALRS) consists of six volumes of text
and four booklets of diagrams.

Volume 1: Coast Radio Stations (2 parts)

This volume contains particulars of coast radio stations, including call signs,
hours of service, transmitting and receiving frequencies, and the times of
traffic lists. Stations are listed in geographical sequence.
Other sections of this volume give information on: medical advice by
radio; arrangements for quarantine reports, pollution reports, and locust
reports; the INMARSAT Maritime Satellite Service; regulations for the use
of radio in territorial waters; distress, search and rescue procedures; the
AMVER ship rescue organisation; a brief extract from the international radio
regulations.
Part 1 (NP 281(1)) covers Europe, Africa and Asia (excluding the
Philippines and Indonesia).
Part 2 (NP 281(2)) covers the Philippines, Indonesia, Australasia, the
Americas, Greenland and Iceland.

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Volume 2: Radio Navigational Aids
Volume 2 (NP 282) contains particulars of radiobeacons including aero radio-
beacons in coastal regions; radio direction-finding stations; coast radio
stations providing a QTG service (the transmission of signals on request for
use with ships’ DF); calibration stations (stations giving special transmissions

VOL 7
for the calibration of ships’ DF); radar beacons (racons and ramarks).

Volume 2a: Diagrams relating to Radiobeacons

Volume 2a (NP 282a) contains diagrams showing the location of
radiobeacons throughout the world (marine radiobeacons in black, coastal
aero radio-beacons in red), also a diagram for obtaining the half-convergency
correction for DF bearings.

Volume 3: Radio Weather Services

Volume 3 (NP 283) contains particulars of radio weather services and related
information, including certain meteorological codes provided for the use of
shipping. Frequencies and times of transmission of storm warnings and other
weather messages, including the transmission of facsimile maps, are also
given. Details of ships’ weather reports are also given in this volume.

Volume 3a: Diagrams relating to Weather Reporting and Forecast Areas

Volume 3a (NP 283a) shows the regions, zones and coast radio stations for
the collection and dissemination of ships’ weather reports, also the limits of
forecast areas covered by radio weather transmissions.

Volume 4: Meteorological Observation Stations

Volume 4 (NP 284) comprises a list of world-wide meteorological
observation stations giving the number, location and elevation of each station
158 CHAPTER 7 - PUBLICATIONS

and serving as a key to meteorological working charts on which selected

station numbers appear.
Volume 5: Radio Time Signals: Radio Navigational Warnings: Position-
fixing Systems
Volume 5 (NP 285) contains particulars of: standard (legal) times, including
the dates between which daylight-saving time is observed in certain
countries; radio time signals, including details of co-ordinated Universal
Time (UTC), and a list of stations providing radio time signals giving the
frequencies and times of transmission and the system employed by each
station; radio navigational warnings including details of the world-wide
navigational (NAVAREA) Warning Service (see page 135); national
practices; ice reports; reports of transmission failure in position-fixing
systems; a list of stations transmitting radio navigational warnings giving the
frequencies, times of transmission and area covered by each station;
electronic position-fixing systems (Decca, Consol, Loran-A, Loran-C,
Omega, Differential Omega, and satellite navigation).
Volume 5a: Diagrams relating to Radio Communications and Position-fixing
Systems

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Volume 5a (NP 285a) comprises diagrams for radio communications and
electronic position-fixing systems. Radio communication diagrams include
details of: international radio watchkeeping periods; standard time zone chart
of the world; the format of radio time signals; the limits of NAVAREAS,
HYDROPAC and HYDROLANT areas; details of the transmissions of
navigational warnings by RT in the Baltic and North-west Europe. Electronic

VOL 7
position-fixing system diagrams show the fixing accuracy and coverage of the
various systems (except Consol) in use throughout the world.
Volume 6: Port Operations, Pilot Services and Traffic Management (2 parts)
Volume 6 contains particulars of: stations working in the Port Operations and
Information Services; services to assist vessels requiring pilots; services
concerned with traffic management. Details of various ship movement report
systems such as MAREP (English Channel) are also given in this volume.
Further information is contained in Volume III of this Manual of Navigation
Part 1 (NP 286(1)) covers NW Europe and the Mediterranean.
Part 2 (NP 286(2)) covers Africa and Asia (excluding Mediterranean
coasts), Australasia, Americas, Greenland and Iceland.
Volume 6a: Diagrams relating to Port Operations, Pilot Services and Traffic
Management
Diagrams (NP 286a) accompanying traffic management systems described in
Volume 6, Parts 1 and 2, are provided.
Sources of information
The information contained in ALRS is taken from the relevant international
publications (of the International Telecommunication Union and the World
Meteorological Organisation) and from radio lists, sailing directions, and
notices to mariners published by other national Hydrographic Offices.
Information is also obtained through enquiries to operating authorities and
administrations.
PUBLICATIONS SUPPLIED BY THE HYDROGRAPHER 159

A few items, of major importance to the safety or convenience of

shipping, are issued in the series of long-range radio navigational warnings.
These items, together with others of lesser urgency, are also included in
Section VI of the Weekly Notices to Mariners.
New editions of these volumes are published annually, except for Volume
4, which is revised every 3 years.
Tide and tidal stream publications
Tide and tidal stream publications are dealt with in detail in Chapter 11.
Admiralty Tide Tables
Admiralty Tide Tables (ATT) are published in three volumes annually as
follows:
Volume 1 European waters (including Mediterranean Sea).
Volume 2 Atlantic and Indian Oceans.
Volume 3 Pacific Ocean and adjacent seas.
Volumes 2 and 3 (Admiralty Tide Tables and Tidal Stream Tables)

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contain, in addition to tidal predictions, a number of predictions of tidal
streams. Harmonic constants for some tidal streams are also published in all
three volumes.
Each volume is divided into three parts. Part I gives daily predictions of
the times and heights of high and low water for a selected number of standard
ports. Part II gives time and height differences for prediction of high and low

VOL 7
water at a much larger number of secondary ports. Part III gives the
harmonic constants for use with the Simplified Harmonic Method of Tidal
Prediction for those ports, where they are known. Details showing how this
method can be used on any programmable calculator or computer are
published in the Introduction to each volume of ATT.
The tables for the secondary ports vary considerably in completeness and
accuracy. In general, where full information is given, it can be assumed that
predictions will satisfy the normal demands of navigation; where information
is incomplete, it is prudent to regard it as approximate only.
Outside the British Isles, it is the general principle to publish only a
selection of the standard port predictions from foreign tide tables and these
should be consulted where necessary. Foreign tide tables are obtained from
the appropriate national Hydrographic Office, and usually from national
agencies at the larger ports. A note of those places for which daily
predictions are given in foreign tide tables is included in Part II of all three
volumes.
Admiralty Tide Tables are corrected annually by Notice to Mariners No.
1 contained in Annual Summary of Admiralty Notices to Mariners.
Other tidal publications
A list of Admiralty tidal publications is given at the end of Admiralty Tide
Tables. These include tidal stream atlases covering the whole of the British
Isles and selected areas elsewhere, miscellaneous tidal charts, forms for
predicting tides and instructional handbooks on tidal subjects. In addition,
HM Ships are supplied with Home Dockyard Ports ) Tides and Tidal Streams
(NP 167). The information in this publication is supplementary to that given
in ATT, tidal stream atlases and Admiralty Sailing Directions.
160 CHAPTER 7 - PUBLICATIONS

Astronomical publications
Sight Reduction Tables for Marine Navigation (NP 401)
Sight Reduction Tables for Marine Navigation are published in six volumes,
each covering a band of 15° of latitude. They contain the data necessary for
the solution of sights of heavenly bodies. Values of altitude and azimuth are
tabulated for all combinations of latitude, local hour angle and declination at
intervals of 1 degree. The calculated altitude and azimuth of the heavenly
body being observed is extracted from the tables and compared with the true
altitude to obtain a position line.
The explanation of the tables includes instructions on how to solve great-
circle problems.

Sight Reduction Tables for Air Navigation

The Sight Reduction Tables for Air Navigation (AP 3270) consist of three
volumes (NP 303(1) to (3)) of tables of altitude and azimuth designed for the
rapid reduction of astronomical sights. Volume I contains the tables for
selected stars for all latitudes and a new edition is issued about every 5 years.
Volume 2 (latitude 0° to 39°) and Volume 3 (latitudes 40° to 89°) contain

SEE BR 45
tables for integral degrees of declination providing for sights of the sun,
moon and planets; these tables are permanent. The tables are published by
the United States as Pub. No 249, Sight Reduction Tables for Air Navigation.
The United Kingdom edition (published by HMSO) is a reproduction of the
US publication and an Introduction conforming to RAF usage.

VOL 7
The Nautical Almanac (NP 314)
The Nautical Almanac is compiled jointly by HM Nautical Almanac Office,
Royal Greenwich Observatory, and the Nautical Almanac Office, United
States Naval Observatory, and published annually by HMSO. It is issued by
the Hydrographic Department to HM Ships and RFAs, and is available to
merchant ships through most Admiralty Chart Agents. It tabulates all the data
for the year required for the practice of astronomical navigation at sea.

Star Finder and Identifier (NP 323)

The Star Finder and Identifier consists of a star chart on which are printed
the navigational stars and on which the positions of planets and other stars
may also be plotted. The elevation and true bearing of a star at any time can
be obtained by inspection, using a superimposed transparent grid.

Miscellaneous publications
Norie’s Nautical Tables (NP 320)
Norie’s Tables consist of a set of navigational and mathematical tables which
include:

Meridional parts.
Logarithms.
Log of trigonometrical functions and natural functions of angles.
Haversines.
OTHER BOOKS OF INTEREST TO THE NAVIGATING OFFICER 161

A B and C azimuth tables.

Bearing amplitudes and corrections.
Ex-meridian tables I to IV.
Dip of sea horizon.
Refraction.
Sun, star and moon total corrections.
Radar range.
Distance by vertical angle.
Distance of the sea horizon.
Ports of the world.

Norie’s Tables are issued without demand to HM Ships by the Hydrographer

and are available to merchant ships through most Admiralty Chart Agents.

The Decca Navigator Mark 21 Operating Instructions (NP 315)

This publication contains information on the Decca Mark 21 receiver (QM
14) fitted in HM Ships.

The Decca Navigator Marine Data Sheets (NP 316)

SEE BR 45
This publication contains general information on the Decca system including
the accuracy of Decca fixing; data sheets for individual chains showing the
areas covered, the accuracy of position fixing within the chain, fixed error
corrections for the individual patterns. It is issued to ships direct from the
Racal-Decca Navigator Co., although amendments are issued by the
Hydrographer.

VOL 7
Publications on other radio aids (satellite navigation, Loran-C, Omega,
etc.) are usually issued to HM Ships as technical books of reference (BRs)
(see page 163).

OTHER BOOKS OF INTEREST TO THE NAVIGATING OFFICER

In addition to the five volumes of the Admiralty Manual of Navigation, there

are a number of BRs issued through the Supply Department of interest to the
Navigating Officer. Some of these are on sale to the public.

The Queen’s Regulations for the Royal Navy (QRRN, BR 31)

Regulations laid down in QRRN and in Volume IV of this manual include the
following subjects which are of concern to the Navigating Officer:

The authority of the Officer of the Watch.

Special Duties Officers, Seamen specialists ) Certificates of
Competence, Watchkeeping and Ocean Navigating Certificates.
Officers, general ) Bridge Watchkeeping Certificates.
Officers, general ) Ocean Navigation Certificates.
Regulations for the conduct of courts martial ) evidence on
navigational matters.
Speed of ships.
Instructions to Captains.
Instructions to officers ) Officers of the Watch.
162 CHAPTER 7 - PUBLICATIONS

Navigation ) instructions to Navigating Officers; collisions and

groundings; definitions of terms to be used at sea.
Classification of speed and power.

Admiralty Manual of Seamanship, Volumes I to IV (BR 67(1) to (4))

Volume I is the basic book of seamanship for officers and men joining the
Royal Navy. Volume II contains more technical detail and is a general
textbook and reference book for ratings seeking advancement and for junior
officers. Volume III is intended mainly for officers. It covers such essential
seamanship knowledge as the handling of ships and also information on a
variety of subjects that could be classed as advanced seamanship, such as aid
to ships in distress. The following chapters in Volume III are of particular
interest to the Navigating Officer:

Chapter 6 Towing at sea.

9 Officer of the Watch in harbour.
11 Officer of the Watch at sea.
12 Propulsion and steering of ships.
13-16 Handling ships in narrow waters; in company; in heavy

SEE BR 45
weather; while replenishing at sea.

Volume IV amplifies information in Volumes I to III for RN purposes

only and is not available to the public.

Rules for the Arrangement of Structures and Fittings in the Vicinity of

VOL 7
Magnetic Compasses and Chronometers (BR 100)
This book sets out the rules for the siting of equipment in the vicinity of
magnetic compasses and chronometers. It tabulates the minimum distance at
which magnetic material that is part of the ship’s structure, electrical
equipment, and so on, should be sited from the compass. It also grades the
position for the magnetic compass dependent on its function; for example, a
standard compass providing the primary means of navigation is a Grade I
compass while an Emergency Compass fitted for the purpose of conning or
steering the ship after action damage or breakdown is a Grade IV compass.
This publication is not available to the public.

Collisions and Groundings (and Other Accidents) (BR 134)

This book contains cases of groundings, collisions, berthing incidents and
other accidents affecting the safety of men and ships. There is a narrative of
each incident, followed by comments and a summary of the lessons to be
learned from it.
This publication is required reading for all officers in HM Ships. It is not
available to the public.

A Seaman’s Guide to the Rule of the Road (BR 453)

This is a programmed book designed to teach Royal Navy and Merchant
Navy personnel sufficient theoretical knowledge of the Regulations for
Preventing Collision at Sea to meet the needs of the Officer of the Watch.
‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER 163

Tactical publications
Certain tactical publications are of interest to the RN Navigating Officer,
covering such matters as:

Formations, manoeuvres, sea manners and customs.

Evasive steering ) zigzag plans.
Search and Rescue.
Replenishment at Sea.
Nuclear Fallout Forecasting and Warning Organisation.

These books are not on sale to the public. Certain tactical publications
may be issued to selected British merchant ships in times of war or other
emergencies.

Classified books
Certain books classified Confidential or higher are of interest to the RN
Navigating Officer. These books cover such matters as:

SEE BR 45
Particulars of Royal Fleet Auxiliaries.
Operational endurance data.
Fleet data.
Maritime Law and claimed territorial seas.
Fleet Operating Orders.

VOL 7
Technical publications
There are a number of technical BRs covering the whole range of
navigational equipments available to the RN Navigating Officer. These cover
such items as echo sounders, radio aids to navigation (satellite navigation,
Loran-C, Omega, Decca, etc.), bottom logs, compasses and automated
navigation systems.

‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER

There are a number of ‘S’ forms, supplied from PSTO(N), HM Naval Base,
Portsmouth, and demanded through the ship’s supply department, which are
of interest to the Navigating Officer. These are summarised in Table 7-1
(p.164) and brief details of individual forms follow.

Report of Collision or Grounding (S232)

The procedure for reporting collisions or groundings in HM Ships is laid
down in QRRN. The initial signalled report is to be followed without delay
by a written report on Form S232. Whether or not legal claims or
proceedings are anticipated, the form is to be rendered as follows:
Original to be completed and forwarded by the Captain direct to the
Treasury Solicitor, Central Buildings, Matthew Parker Street, London SW1.
Copies to be forwarded to the Administrative Authority for transmission,
through Commander-in-Chief Fleet to the Ministry of Defence (Naval Law
Division), and the Area Flag Officer.
164 CHAPTER 7 - PUBLICATIONS

Table 7-1. ‘S’ forms of interest to the Navigating Officer

NUMBER TITLE

S232 Report of Collision or Grounding

S322 Ship’s Log
S322A Cover for current Ship’s Log
S374A Record of Observations for Deviation
S376 Manoeuvering Form (pads)
S387 Table of Deviations
S425(4) Inspection Report ) Navigation
S428(6) Inspection Report (Submarines) ) Navigation and AIO
S529 Mership and Fish Vessel Sighting Report
S548A Navigating Officer’s Note Book
S553 Order Book (used for Captain’s Night Orders)
S580 Record Book for Wheel and Engine Orders
S1176 Fishing Vessel Log
S1301 Report on Damage to Fishing Gear (Attended or Unattended)
Alleged to have been Caused by HM Ships, etc.
S1372 Order of the Court and Report of Navigation Direction

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Officers at Trial on Navigational Charge
S1750-1775 Degaussing Forms
S2040 Ship Activity Return
S2624 Formex 110 ) Wheelhouse Record
S2677 Navigational Data Book

VOL 7
S3020A/B/C Turning, Starting and Stopping Trials
S3034 Navigational Record Book

The Ship’s Log (S322)

‘The Navigating Officer, or other such officer or senior rating to whom the
Captain has approved he should delegate this duty, is to have charge of the
Ship’s Log, Form S322, and is to present it weekly for the Captain’s
signature ...’ (BR 45(4)). Instructions for compiling the Ship’s Log are laid
down in Volume IV of this manual and in the front of the Log Book itself.
A complete account of the ship’s movements is kept in the Ship’s Log or in
the Navigational Record Book (S3034) by noting navigational information
in sufficient detail for the track of the ship at any time to be reconstructed
accurately.
A specimen log illustrating sea and harbour usage is in Fig. 7-1 (pp.166-
7).

Record of Observations for Deviation (S374A) and Table of Deviations (S387)

Form S374A is supplied for the purpose of keeping a record of the deviation
of all the magnetic compasses installed in one of HM Ships. Anything likely
to affect the compass which has occurred since the previous occasion of
rendering the form (such as alterations in the ship’s structure or armament),
or anything likely to affect the accuracy of the swing which is being recorded
(such as the nearness of other ships, or the rapidity of the swing) should be
noted in the ‘Remarks’ space of the form.
‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER 165

Form S387 is an abridged version of this form and is intended to be kept

on the bridge if necessary and in the vicinity of the compass concerned.
Full details on the use of these forms are given in Volume III of this
manual.
Manoeuvring Forms (S376)
These forms are supplied in pads. Each form consists of a spider’s web of
254 mm (10 inch) diameter suitable for plotting the positions of ships in
company; it also gives various scales, and a tote to record such things as the
stations of ships in company, the base course, the zigzag plan, flying course,
PIM (position and intended movement) and so on. It is a very useful form for
calculating courses and speeds for changing station, particularly when on a
tactical screen or for precise manoeuvres such as taking station from ahead.
Navigating Officer’s Note Book (S548A)
The Navigating Officer is to ‘keep a Navigating Officer’s note book (S548A)
containing full and sufficient pilotage information to enable him to conduct
the navigation of the ship in safety along predetermined tracks in pilotage
waters’ (BR 45(4)). He should also use this Note Book for all his
navigational planning including ocean and coastal navigation as well as
pilotage and anchorages. Instructions for using the Note Book are given in

SEE BR 45
Chapters 12 and 13.
Captain’s Night Order Book (S553)
It has long been the custom for the Captain of HM Ships to keep a Night
Order Book in which he puts instructions for the Officers of the Watch and
Principal Warfare Officers of the night watches. He also gives information

VOL 7
about the special circumstances of the night, states when he wishes to be
called and also usually draws attention to his Standing Orders on calling.
Instructions for calling the Captain are pasted inside the front cover. The
Night Order Book is an essential link between the Captain and his OOWs and
PWOs, who should initial it on taking over their watch. It is also used in
harbour to implement instructions from the Captain for particular
circumstances; for example, weather precautions, getting under way. (See
also Chapter 19 of this volume.)
Record Book for Wheel and Engine Orders (S580)
Volume IV of this manual states that: ‘A Bridge record is kept of wheel and
engine orders given whenever the ship is operating close to danger’ (land,
other ships, etc.). ‘Should automatic recording equipment not be available,
the Record Book for Wheel and Engine Orders (S580) should be used for this
purpose.’
Fishing Vessel Log (S1176); Report on Damage to Fishing Gear (S1301)
The Fishing Vessel Log is used to record passing through or near a fishing
fleet; if possible, the names and distinguishing numbers of the fishing vessels
are to be entered. In the event that damage to gear may have been caused by
an HM Ship, the circumstances are to be recorded in the Log. These details
may subsequently be needed if it becomes necessary for a Fishery Officer to
render a report on Form S1301, Report on Damage to Fishing Gear (Attended
or Unattended) Alleged to have been Caused by HM Ships, etc.
The Fishing Vessel Log provides a useful table of port distinguishing
letters displayed by fishing vessels.
166 CHAPTER 7 - PUBLICATIONS

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VOL 7

Fig. 7-1. The Ship’s Log

‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER 167

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VOL 7
168 CHAPTER 7 - PUBLICATIONS

Order of the Court and Report of Navigation Direction Officers at Trial on

Navigational Charge (S1372)
In the event of a court-martial arising from the loss, stranding, hazarding, etc.
of an HM Ship, the court will direct one or more Navigating or other
competent officers to work up the ship’s position from the time when her
position was last accurately ascertained and render a report on this form. A
copy or tracing of the chart by which the ship was navigated is also delivered
to the court.

Navigational Data Book (S2677)

In order to maintain a complete record of the performance of an HM Ship
under all conditions of wind and weather from one commission to the next,
the Navigating Officer is to keep the Navigational Data Book (BR 45(4)).
This book should contain details of items listed at the start of each section of
the book. These items are reproduced here as follows:

Section 1. Dimensions and Tonnage

All details of length, breadth, height and draught, including the amounts by
which any fittings protrude below the keel.
Heights of eye (six foot man) for the various decks from which sights may be
taken.
Distance from bridge pelorus, emergency conning position (ECP) pelorus and
navigational radar aerial to stem and stern.
Distances at which buoys are in transit with the base of the jackstaff, etc.
(shadow diagram).
Standard and full load displacement: net, gross and Danube Rule (for Suez
Canal) tonnages.
Tracing of end elevation (from astern) of ship’s stern, showing proud
propellers.
Tonnes per centimetre immersion (TPC).
Visibility diagram (carriers and similar ships).

Section 2. Anchors and Cables

Details of size, age, weight, capacity and all tests and ranging of anchors,
cable and cable-holders.
Diagram showing the positions of each shackle within its cable (a series of
these diagrams after each ranging will assist in maintaining an even rate
of wear).
Speed of weighing anchor in minutes per shackle.

Section 3. Engines
Make and power.
Economical speed range.
Maximum revolutions ahead and astern and standard revolutions for Slow
Ahead and Slow Astern.
Drill for disconnecting and connecting engines and shafts (if applicable).
Drills for operating variable-pitch propellers (if applicable).
Drills for blowing soot.
Working-up rates and any special limitations.
‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER 169

Section 4. Revolution Tables and Full Power Trials

Table and/or graph of engine revolutions/speeds after various periods out of
dock.
Tables and/or graphs of speeds available (Table 7-2) and optimum
revolutions for different combinations of engines connected (if
applicable).
All available information on engine revolutions for speeds when various
shafts are stopped or trailed.
Brief details of each Full Power Trial: date, position, depth, water
temperature, power developed and speed through the water.
Details of speed lost/gained by using stabilisers in varying weather conditions
(if applicable).

Table 7-2. Revolutions for specific speeds (BR 45(4))

CLASSIFICATION PERCENTAGE OF FULL APPROX. PERCENTAGE REVS
POWER OF FULL SPEED

At full speed (authorised full 100 100

power)
With all despatch (maximum) 85 96.5
continuous sea-going power)
With despatch 60 87
With all convenient despatch 40 77
With moderate despatch 15 62.5
(unless below economical
speed)
At economical speed As determined by trial for fuel economy
and for optimum gas turbine life.

Section 5. Fuel Oil Capacity and Consumption Data

Total theoretical quantity of fuel that can be carried and total practical
quantity of fuel oil normally embarked.
Details of any quantity of fuel oil that cannot be used (due to design of tanks
or other reason).
Graphs of consumption (in tonnes/hour)/speed, in both temperate and tropical
waters.
Graph of range/speed allowing for 20% usable fuel remaining.

Section 6. Turning Trials

Report of Turning Trials (S3020A/B/C) from which should be prepared:

Table and/or graph for taking station from the bow and templates
for use on the radar display.
Losing ground diagram.
Amount of wheel for altering course, including tactical diameter
at selected speeds for various rudder angles.
Time taken to turn at rest.
170 CHAPTER 7 - PUBLICATIONS

Starting and stopping data, including working rules for gain/loss

in speed in yards per knot.

Section 7. Shiphandling Characteristics

Standard distance at which to reduce speed, stop and go astern when
approaching an anchorage, buoy or alongside berth.
Recommended positions for handling the ship during different evolutions.
Recommended revolutions to be used when manoeuvring, including
limitations while turning at rest, going astern or on one boiler.
Limitations on shiphandling and blind pilotage caused by compass repeater
and radar blind arcs.
Effect of wind at various speeds ahead and astern.
Amount of leeway for various directions of relative wind.
Steerage way at various speeds ahead and astern.
Record of tricky berthing, with solution to each problem.
Towing speeds attained (and revolutions required) when towing different
classes of ships, and amount of cable veered with depth of water.
Man Overboard ) diagrams to show shiphandling action for various directions
of relative wind, including the Williamson turn.
General observations from experience.
PIM table (carriers only).
Turning-into-wind graph (carriers only).

Section 8. Berthing Information

All special features of the ship with regard to berthing, e.g. catamarans for
berthing a carrier port side to, proud propellers, minimum length of
catamarans as dictated by frame spacing.
Recommended brow lengths.
Section 9. Replenishment
Diagram of ship’s replenishment positions (on same scale as ATP 16 for
RFAs).
Recommended method for approaching the close-aboard position.
Distance usually maintained for various rigs.
Abnormalities of interaction, particularly in shallow water, and notes of
experience gained.
Section 10. Conning Positions
Bridge ) large-scale diagram of layout, with explanatory notes.
Other conning positions ) a brief description of all communications, chart
tables and compasses available at these positions.

Section 11. Navigational Communications

Full details of intercommunication system, voice pipes and telephones (with
simple diagrams).

Section 12. Steering and Stabilising Equipment

Full details of steering arrangements and equipment.
Orders for steering gear breakdowns.
‘S’ FORMS OF INTEREST TO THE NAVIGATING OFFICER 171

Drill for operating active rudders (if fitted).

Brief description of stabilisers (if fitted), including position and amount they
protrude, and drills for operating.

Section 13. Compasses

MAGNETIC COMPASSES ) DETAILS OF THOSE FITTED
Record of swings for adjustment of compasses (Form S374A): all swings
done by the compass directorate should be kept, plus the last two swings for
each similar latitude.
Details of special communications and other requirements during compass
adjustment.
Details of abnormal performance, with description of remedies taken.
GYRO-COMPASSES ) DETAILS OF THOSE FITTED.
Details of abnormal performance, with description of remedies taken.
REPEATERS ) WHERE FITTED.
Drills for changing over in the event of compass failure, including AIO.

Section 14. Echo Sounder

Details of fitting.
Record of calibration (see Handbooks).

Section 15. Bottom Log and Plotting Tables

Details of fitting.
Record of measured mile runs and other log calibrations, with table of errors
for the log and plotting tables on each occasion.

Section 16. Degaussing Equipment and Ranging

Details of fitting, including diagram showing layout of compass corrector-
coil resistances.
Record of occasions on which ship is ranged, wiped and depermed.
Chart of the most recent DG ranging (DG Chart No. 1).
Reference: The Manual of Degaussing (BR 825).

Section 17. Navigation Lights

Pattern numbers and location of all mains and battery-operated lights, with
location of all switches (simple diagram useful).
Details of dimmer settings for Close A/S Action, etc. (if applicable).

Section 18. Radio Aids

Details of all equipment fitted (including navigational radars), with comments
on failures, irregular performance and interference experienced.
Comments on accuracies achieved.
Blind pilotage organisation.

Section 19. Special Sea Dutymen

Full details of all personnel, with their positions and tasks. (Details of all
fixing teams for entering and leaving harbour should be entered here.)
List of reports to be made to the Bridge when Special Sea Dutymen close up.
172 CHAPTER 7 - PUBLICATIONS

Section 20. Ship’s Narrative

Steaming table (to show following details):

Year Month Distance Hours Total distance Total hours

steamed underway steamed this underway
commission this com-
mission

Brief narrative of the ship’s employment:

EXAMPLE

Year From Details To Remarks

1986 20 Feb GIBRALTAR 3 Mar CinC Fleet embarked 24-28
February.
3 Mar Exercise ATLANTEX 12 Mar Convoy exercise with USN.
12 Mar PORT EVERGLADES 18 Mar Navy Days 15 & 16 Mar.

Note: Information gained during visits to foreign ports or on passage which

would be of general interest to all ships (not just to the next commission)
should be reported as:

1. Amendments to the Station Guide Book or

2. Hydrographic notes or
3. Amendments to Port Information Sheets, etc.

Each passage should be analysed and lessons to be learnt recorded, e.g.

Tidal streams, currents or weather different from that expected.

Whether time in hand allowed for at the planning stage was adequate
or not.

Turning, Starting and Stopping Trials (S3020A/B/C)

These forms are used to record details of the ship’s turning, starting and
stopping characteristics and the necessary detail is then transcribed into the
Turning Trials section in the Navigational Data Book (see page 169).
Guidance on carrying out these trials is given in Volume IV of this manual
and in BR 67(3), Admiralty Manual of Seamanship, Volume III.

Navigational Record Book (S3034)

The Navigational Record Book is an official record complementary to the
Ship’s Log, designed for use on the Bridge and for recording at first hand.
The Officer of the Watch is to ensure that a complete account of the ship’s
movements is kept in the Ship’s Log or in the Navigational Record Book by
noting navigational information in sufficient detail for the track of the ship
to be reconstructed accurately.
It is the responsibility of the Navigating Officer to arrange for the
necessary records to be kept to allow this accurate reconstruction.
 173

CHAPTER 8
Chartwork

SYMBOLS USED IN CHARTWORK

Chartwork must be clearly intelligible to all who practise it: thus, standard
symbols should be used for all forms of chartwork, including both the
planning and passage phases, blind as well as visual.

Positions and position lines

Fig. 8-1 sets out the standard symbols used in the Royal Navy to display
positions and position lines.

Arrowheads on position lines (Fig. 8-1)

A position line obtained from a bearing of a terrestrial object, visually or by
means of a navigational aid (e.g. DF bearing), is distinguished by a single
arrow at the outer end.
A position line obtained from an astronomical observation or from the
range of a terrestrial object is distinguished by a single arrow at both ends.
A position line that is transferred (see Chapter 9) is distinguished by a
double arrow at the outer end for a terrestrial object and at both ends for an
astronomical observation.

Positions (Fig. 8-1)

The fix is shown on the chart as a dot surrounded by a circle, with the time
alongside, and the position lines, if appropriate, passing through the position
of the fix. A suffix may be added to the fix to indicate it has been obtained
by a method other than by visual bearings.
The Dead Reckoning (DR) position is shown on the chart as a small line
across the course being steered, with the time alongside. A small cross may
be used to originate the DR if a fix or Estimated Position is not available.
The Estimated Position (EP) is shown on the chart as a dot surrounded
by a small triangle, with the time alongside, the estimated track of the ship
over the ground (the ground track) passing through the dot.
The Position Probability Area (PPA, see page 181) may be shown on the
chart as an ellipse with a major and a minor axis.
174 CHAPTER 8 - CHARTWORK

Fig. 8-1. Positions and position lines ) symbols in use in the Royal Navy
DEFINING AND PLOTTING A POSITION 175

DEFINING AND PLOTTING A POSITION

Plotting a position
A position may be expressed by its latitude and longitude, or as a range and
bearing from a specific object. It may be plotted on the chart using a parallel
rule, dividers, and the scale of latitude and longitude appropriate to the chart
itself. The detailed techniques of plotting are given in BR 454, Notes on
Navigation, which is available on sale to the general public.

Transferring a position
When transferring a position from one chart to another, it is best to use
bearing and distance from a distinguishing feature common to both charts,
such as a point of land or light. This should then be checked by latitude and
longitude to ensure no error has occurred (see page 195).

Position by observation
The position line
The navigator finds his position using landmarks, heavenly bodies or radio
aids and, from his observations, obtains what are known as position lines.
A position line is any line, drawn on the chart, on which the ship’s
position is known to lie. It may be straight or curved. The methods of
obtaining a position line are described in the next chapter.
The simplest form of position line is the line of bearing obtained from a
terrestrial object of known position.
Suppose, for example, that a lighthouse (L in Fig. 8-2) is seen to bear
065° at 1030. A line drawn in the direction 065° passing through L is the
position line. In chartwork, it is only necessary to draw the position line in
the vicinity of the ship’s position, the arrowhead being placed at the outer
end. This arrowhead indicates the direction in which the observer must lie
from the observed object.

Fig. 8-2. The terrestrial position line

176 CHAPTER 8 - CHARTWORK

The fix
If two or more position lines can be obtained at the same moment, the
position of the ship must be at their point of intersection. The position thus
obtained is known as a fix. The position lines, as discussed in Chapter 9, may
be obtained from a variety of sources: visual bearings, horizontal sextant
angles, radio navigation aids, radar, astronomical observations and so on, and
the fix is usually given a suffix (D), (O), (L), (M), (S), Obs, HSA, etc. to
indicate it has been obtained by a method other than by visual bearings or
radar ranges (Fig. 8-1). Position lines obtained from different sources may
often be combined for the purposes of fixing the ship.
The observed position
It is desirable to distinguish between the position obtained by observation of
terrestrial objects and that obtained by observations of heavenly bodies. For
this reason, the position decided by the point of intersection of two position
lines derived from astronomical observations, or derived from a number of
such position lines, is known as an observed position and is marked ‘Obs’
(Fig. 8-1).
CALCULATING THE POSITION
When it is not possible to obtain the ship’s actual position by fixing, a
position may be worked up based upon the most recent fix.
Dead Reckoning (DR)
Dead Reckoning is the expression used to describe that position obtained
from the true course steered by the ship and her speed through the water, and
from no other factors.
The DR position* is thus only approximate for, while the speed through
the water will allow for the amount by which the ship’s speed is reduced or
increased by wind and sea, there is no allowance for leeway, tidal stream,
current, or surface drift.
True course steered through the water may be obtained from the plotting
table or course recorder if either is available. If not it can only be determined
by the Officer of the Watch by very close observation of the course being
steered.
Speed through the water may be obtained from the log, provided the latter
is reliable and the error known and allowed for. If the log is unreliable or not
available, then the average engine revolutions over the hour must be used.
These revolutions may be converted into speed through the water having
regard to:
1. The graph † of engine revolutions/speed (power percentage/speed for
* In practice, the term Dead Reckoning is occasionally used to describe the Estimated Position. Such a practice
is incorrect and should be avoided.
† Many merchant ships have the data provided in the form of a revolution/speed/ percentage slip table usually
ranging between 0% and 15%. Experience will be the best guide in establishing what is the apparent percentage
slip for various situations; this will vary according to the draught, trim, state of the ship’s underwater hull and so
on. It should be possible to establish the various slips with a considerable degree of accuracy during the first
eighteen months of service. The percentage slip to be used should be based upon recent ship performance in similar
conditions; for example, a ship operating in tropical waters will usually suffer much greater fouling than in colder
waters.
CALCULATING THE POSITION 177

controllable-pitch-propeller-driven ships) for time out of dock, as

obtained from the Navigational Data Book (page 169).
2. The wind and sea reducing or increasing the ship’s speed through the
water. Such data should be recorded in the Navigational Data Book and
subsequently analysed, so that a quick and accurate assessment of this
effect may be made in any given situation. It is rare for a stern sea to
increase ship’s speed by any appreciable amount because yawing, which
usually accompanies this situation, tends to reduce ship’s speed through
the water. A head wind and sea, however, will invariably reduce the
speed of a ship. In full gale conditions, the reduction can be as much as
50% even in large ships.
Estimated Position (EP)
This position is the most accurate that the navigator can obtain by calculation
and estimation only. It is derived from the DR position adjusted for the
estimated effects of leeway, tidal stream, current and surface drift. The EP
must always remain an approximate position, because these four variable
factors are difficult to determine exactly, although experience goes a long
way to resolving them. It is essential for the navigator to estimate the effects
as accurately as possible; each is now described.
Leeway
Leeway is the effect of wind in moving a vessel bodily to leeward at right
angles to the course steered. The effect of wind in reducing or increasing the
ship’s speed through the water has already been described under Dead
Reckoning.
The effect of wind varies with every type of ship. The navigator should
collect as much information as possible concerning the effects of the force
and direction* of the wind on the behaviour of his own ship and record such
data in the Navigational Data Book.
Leeway depends upon a number of factors:
1. Own ship speed: the higher the speed, the less the leeway.
2. Wind speed: the higher the component of wind speed at right angles to
the course, the greater the leeway.
3. Longitudinal area: the greater the ratio of fore and aft area above the
waterline to that below, the greater the leeway.
4. The depth of water: the shallower the depth of water in relation to the
draught, the less the leeway.
Leeway is thus a complex relationship and, whilst attempts have been
made to quantify it in mathematical terms, it is probably best for the navigator
to rely on his own experience and on the data in the Navigational Data Book.
As a rough guide, in modern warships, which have a high ratio of
longitudinal area above the waterline to that below, one would normally
expect leeway to vary between about ¼ knot in a 10 knot beam wind at 10
knots speed, and up to 3 knots in a 30 knot beam wind while lying stopped,
as shown in Table 8-1. Exact leeway will vary with ship class.
* The system of naming the direction of the wind is exactly the opposite to that of naming tidal streams and
currents. A northerly wind, for example, blows from the north, while a northerly or north-going current set to the
north.
178 CHAPTER 8 - CHARTWORK

Table 8-1. An approximate guide to leeway in HM Ships

BEAM WIND 10 KNOTS 30 KNOTS
SPEED

SHIP
SPEED LEEWAY

Stopped 1 knot 3 knots

10 knots ¼ knot ¾ knot
20 knots Less than ¼ knot
0.1 knot

In ships not fitted with an automatic pilot, an inexperienced or careless

helmsman is likely to steer a course two or three degrees off that ordered,
usually to windward as most ships tend to ‘fly’ into the wind. This may
compensate for the effect of leeway, and may be gauged by comparing the
course ordered with that registered on the plotting table or the course
recorder, or by close observation over a period of time. This ‘boring to
windward’ is particularly noticeable in light craft running with the wind and
sea on the quarter.
As HM Ships are frequently proceeding at a whole range of different
speeds, it is usual to quantify leeway in terms of a leeway vector (e.g. 120°
½ knot). In merchant ships, which normally proceed at a set service speed,
leeway is normally quantified in terms of leeway angle ) the angular
difference between the ship’s course and her track through the water (water
track).

Tidal streams
A tidal stream is the periodical horizontal movement of the sea surface caused
by the tide-raising forces of the sun and moon.
Information concerning tidal streams is given on Admiralty charts, in the
Admiralty Sailing Directions, in tidal stream publications and in special tidal
stream atlases. The various methods of estimating the direction and strength
of the stream are described in Chapter 11.*
Tidal stream data must always be used with caution, particularly at
springs and around the calculated time of change-over from ebb to flood and
vice-versa. It will often be found that the tidal stream experienced is different
from that calculated.

Currents
A current is the non-tidal horizontal movement of the sea due mainly to
meteorological, oceanographical or topographical causes. In some areas this
movement may be nearly constant in rate and direction (e.g. the Gulf Stream)

* The direction of a current or tidal stream is always given as the direction in which the water is moving. If,
for example, it is said to set 150° 2 knots, a ship that experiences such a stream for 3 hours will be set 6 miles
in a direction 150°.
CALCULATING THE POSITION 179

while in others it may vary seasonally or fluctuate with changes in

meteorological conditions (e.g. the Arabian Sea).
Information concerning currents is given on Admiralty charts, in the
Sailing Directions, on the Routeing charts, in Ocean Passages for the World
(NP 136), in The Mariner’s Handbook (NP 100), in Meteorology for
Mariners (NP 407), in current atlases such as the Straits of Gibraltar: Surface
and Sub-surface Water Movements (NP 629), and Volume II of this manual.
The main cause of most surface currents in the open sea is the direct
action of the wind on the surface of the sea. A current formed in this way is
known as a drift current, and a clear correlation exists between the directions
of the prevailing drift currents and the prevailing winds.

Surface drift
Sometimes, however, there may be no recorded data on wind currents, or the
wind itself may be in a contrary direction to that normally prevailing. It may
therefore become necessary to make an estimate for surface drift which may
or may not, depending on the circumstances met with at the time, be in
addition to that already made for currents.
Surface drift can only be estimated from experience and with a
knowledge of the meteorological conditions in the area through which the
ship is steaming.
The matter is a complex one and studied more fully in Volume II, but
some guidelines are set out here.
The maximum rate of surface drift approximates to 1/40 of the wind speed.
However, the strength of the surface drift depends on how long the wind has
been blowing and upon the fetch* of the wind. The build-up of surface drift
in response to wind is slow and a steady state takes some time to become
established. With light winds the slight current resulting may take only about
6 hours to develop, but with strong winds about 48 hours is needed for the
current to reach its full speed. Hurricane force winds may give rise to a
current in excess of 2 knots, but it is rare for such winds to persist for more
than a few hours without a change in direction. The piling up of water caused
by a storm near a coastline may lead to particularly strong currents parallel
to that coast.
The effect of the rotation of the Earth (Coriolis force) is to deflect water
movement to the right in the Northern Hemisphere and to the left in the
Southern Hemisphere. This produces a direction of the surface flow inclined
at some 20° to 45° to the right of the wind direction in the Northern
Hemisphere and to the left in the Southern Hemisphere.
If, for example, the wind has been blowing steadily from the north-east
at 20 knots for several days, the rate and direction of the surface drift in the
Northern Hemisphere may be expected to be of the order of ½ knot in a
direction between 245° and 270°.

Plotting the track

Plotting the Estimated Position (EP) from a known position is carried out in
two steps (Fig. 8-3).

* Fetch is the extent of open water over which the wind has been blowing before it reaches the observer.
180 CHAPTER 8 - CHARTWORK

1. Plot the course steered and the speed through the water, thus arriving at
the Dead Reckoning (DR) position.
2. Plot on from the Dead Reckoning position the effect of:
(a) leeway;
(b) tidal stream;
(c) current;
(d) surface drift;
thus arriving at the Estimated Position (EP).

Fig. 8-3. Plotting the Estimated Position (EP)

Fig. 8-3 also displays the navigational terms used. Those that have not
already been described are defined in Table 8-2. In the figure the effects of
leeway, tidal stream, current and surface drift have been purposely
exaggerated for the sake of clarity.

Arrowheads on tracks (Fig. 8-3)

A single arrow denotes course steered, water track, leeway vector.
A double arrow denotes ship’s ground track.
A treble arrow denotes tidal stream, current, surface drift and drift.

Quantification of set and drift

Set and drift result from the combined effects of tidal stream, current and
surface drift. They are quantified in terms of direction and distance, e.g. 103°
3.5 miles. Drift may also be given a rate measured in knots; e.g. if the time
over which the drift of 3'.5 has been determined is 2 hours, the rate would be
1.75 knots. Thus, set and drift would be defined as set 103°, drift 3'.5, rate
1.75 knots.
CALCULATING THE POSITION 181

Table 8-2

TERM DEFINITION

Track The path followed or to be followed, between one position and

another. This path may be that over the ground (ground track) or
through the water (water track). When radar plotting (Chapter 17),
this path may also be a relative track or a true track.
Track angle The direction of a track.
Track made good The mean ground track actually achieved over a given period.
Set The resultant direction towards which current, tidal stream and
surface drift flow.
Drift The distance covered in a given time due solely to the movement
of current, tidal stream and surface drift.
Drift angle The angular difference between the ground track and water track.
Sea position The point at the termination of the water track.

Position Probability Area (PPA)

The Position Probability Area (PPA) is the area derived from a combination
of appropriate position lines obtained from available navigational aids
(including log and compass), after applying the relevant statistical error
correction to each position line in turn. It may be shown on the chart in the
form of an ellipse with a major and a minor axis (Fig. 8-1). Within the PPA,
the Navigating Officer determines his Most Probable Position (MPP) which,
dependent on the quality of the input, he should treat as a fix, an EP or a DR.

Allowing for wind, tidal stream, current and surface drift

Most of the examples which follow are given for tidal stream only; the same
method of solution applies to problems associated with leeway, current or
surface drift.

To shape a course to steer allowing for a tidal stream

When the navigator knows the direction of the place he wishes to reach and
the direction and strength of the tidal stream he will experience on passage,
he must then find the course to steer.

EXAMPLE
What course must a ship steer, when steaming at 12 knots, to make good a
track 090° if it is estimated that the tidal stream is setting 040° at 3 knots?
Lay off the course to be made good (AB in Fig. 8-4). From A lay off the
direction of the tidal stream AC. Along AC mark off the distance the tidal
stream runs in any convenient interval on a chosen scale. In Fig. 8-4 a 1 hour
interval* has been allowed: thus, AD will be 3 miles.

* The dimensions of the triangle used are to a large extent controlled by the scale of the chart. On a large-
scale chart a ½ hour interval may suffice, while on a smaller scale it may be necessary to use a 2 or even a
3 hour interval.
182 CHAPTER 8 - CHARTWORK

Fig. 8-4. To shape a course allowing for tidal stream (drawing not to scale)

With centre D and radius equal to the distance the ship runs in the same
interval (12 miles), and on the same scale, cut AB at E. Then DE (101°) is the
course to steer.
AE (13.7 miles) is the distance made good in an 090° direction in 1 hour.

To reach a position at a definite time, allowing for a tidal stream

EXAMPLE
What course must a ship steer, and at what speed must she steam, to proceed
from A to a position B in 1½ hours, allowing for a tidal stream setting 150°
at 3 knots?
Join AB, as shown in Fig. 8-5. This determines the course and distance
to be made good in 1½ hours: 090° 15 miles; thus, the speed to be made good
is 10 knots. Mark a position D along AB using a convenient time interval
depending on the scale of the chart, say 1 hour: in this case AD will be 10
miles.
From A lay off AC using the direction and rate of the tidal stream for the
same interval: 150° 3 miles. Join CD. CD will give the course (073°) to steer
and the speed (8.9 knots) at which to proceed.

Fig. 8-5. To reach a position at a definite time, allowing for a tidal stream
CALCULATING THE POSITION 183

To clear a point by a given distance and find the time when an object will be
abeam, allowing for a tidal stream.
EXAMPLE
A ship at A (Fig. 8-6) steers so as to clear a lighthouse L by 2 miles,
allowing for a tidal stream setting 345°. When will the lighthouse L be
abeam?

Fig. 8-6. To clear a point by a given distance

From L draw the arc of a circle, radius 2'. From the ship’s present
position draw a tangent to the arc. This is the course to be made good, AD.
Find the course to steer BC by the method explained above. The light is
abeam when it bears 90° from the course steered, that is to say, when the ship
is at E and not when she is in position D (the point at which she passes closest
to the lighthouse). The time elapsed will be the time taken to cover the
distance AE at a speed represented by AC, the speed made good.

To find the direction and rate of the tidal stream experienced between two fixes
EXAMPLE
A ship is at A at 0100, as shown in Fig. 8-7, and steering 110° at 10 knots.
At 0300 she fixes herself at B. What is the direction and rate of the tidal
stream from 0100 to 0300?
Plot the ship’s course 110° for a distance of 20' from A. The difference
between the Dead Reckoning position C and the observed position B at 0300
gives the direction of the tidal stream CB (025°) and the distance it has
displaced the ship in 2 hours (7.6 miles). From these data the tidal stream
may be calculated as setting 025° at 3.8 knots.

Fig. 8-7. Finding the direction and rate of the tidal stream
184 CHAPTER 8 - CHARTWORK

To determine the Estimated Position (EP) allowing for leeway, tidal stream,
current and surface drift*

EXAMPLE
The ship’s position is fixed at 0700, course and speed ordered are 090°,
revolutions for 15 knots. At the end of 1 hour, course steered as recorded by
the plotting table is 090½°, speed through the water as recorded by the log,
allowing for the error in the instrument, is 14.7 knots. Estimated tidal stream
(tidal stream tables) is 295° 1.5 knots. Estimated current (current charts) is
060° 0.75 knots.
The wind has been blowing steadily in the area from the south at about
20 knots over the past 2-3 days. Leeway as deduced from the data in the
Navigational Data Book is ¾ knot. Plot the Estimated Position after 1 hour,
and deduce the estimated course and speed made good, and the set and drift
from the combined effects of tidal stream, current and surface drift. The ship
is in the Northern Hemisphere. From a study of the area and the data
available it is estimated that surface drift will be in addition to the predicted
current.
The leeway vector will be at right angles to the course steered; thus, in
this case it will be 000½° ¾ knot. (The leeway angle is 3°.) Estimated
surface drift will be 020° to 045° ½ knot; allow for 030°.
Plot the DR position B at 0800 from the course steered 090½° at the
speed through the water 14.7 knots ) AB in Fig. 8-8 (lay the parallel ruler
through 091° and 270° on the compass rose to achieve 090½°).
Plot the leeway, BC, 000½° 0.75 knot (parallel ruler through 000°/181°
on the compass rose).
Plot the tidal stream CD, 295° 1.5 knots.
Plot the current DE, 060° 0.75 knot.
Plot the surface drift EF, 030° 0.5 knot.

Fig. 8-8. Determining the Estimated Position

F is the Estimated Position at 0800, AF is the estimated ground track

(course and speed made good over the ground) and CF is the estimated set
and drift.
The estimated course and speed made good is 082° 14.4 knots; the set and
drift are estimated to be 343° 1.5 miles, rate 1.5 knots.

* The example shows the resolution of all four factors, although frequently only one or two at a time will be
met with, in practice.
CALCULATING THE POSITION 185

Allowing for the turning circle

When a group of warships in manoeuvring, alterations of course are
frequently so numerous, and the distance run on each course so short, that the
curves described by the ship while making the various turns form a large
proportion of the plot, and it is therefore essential that allowances should be
made for the turning circle and the loss of speed while turning, if the
reckoning is to be accurate.
At any time during manoeuvres, it may be necessary for the ship to shape
a course for a particular position, so it is essential that the reckoning should
be kept in such a way that her position at any moment may be plotted on the
chart with the least possible delay.
When the ships form part of a group within easy visual touch of the
Guide, and are unlikely to be detached during the manoeuvres it is advisable
that they should also plot the Guide’s track, for the following reasons:
1. The Guide’s less frequent alterations of course and steadier speeds reduce
the chance of errors.
2. The times recorded in the signal log give a valuable check on the times
taken for the plot.
3. If the ship is detached unexpectedly, a range and bearing of the Guide
should at once give the ship’s position.
4. The alterations of course can often be plotted before it is necessary for
the Navigating Officer to devote his attention solely to the handling of his
own ship.
When HM Ships are engaged in manoeuvres or exercises, it is usual to
establish the DR by obtaining the course steered and distance run through the
water from the plotting table at regular intervals, adjusting for gyro and log
errors as appropriate. If, however, the plotting table is not available, the
turning circles will have to be plotted on the chart or plotting sheet by hand.
The turning circle must always be allowed for in pilotage waters (Chapter
13), also in coastal waters (Chapter 12), where the turning circle of the ship
and the scale of the chart are such that the turning circle forms a measurable
part of the estimated track. Further offshore, when the scale of the chart is
small, and if the alterations of course are few, it may be possible to disregard
the turning circle, whilst remaining within the bounds of the required
accuracy.
Before the various methods of allowing for the turning circle are
considered, it is necessary to define the terms which are used, and these are
illustrated in Figs 8-9 and 8-10 (pp. 186, 187).

The advance is the distance that the compass platform of a ship had
advanced in the direction of the original course on completion of a turn (the
steadying point). It is measured from the point where the wheel was put over.

AD = the advance

The transfer is the distance that the compass platform of a ship is

transferred in a direction at right angles to the original course.

DB = the transfer
186 CHAPTER 8 - CHARTWORK

Fig. 8-9. Turn turning circle ) terms used

The distance to new course is the distance from the position of the
compass platform when the wheel was put over to the point of intersection of
the original course produced and the new course laid back.

AC = the distance to new course

The perpendicular distance between the ship’s original course and her
position when she has turned 180°, is called the tactical diameter.*

BD = the tactical diameter

The final diameter is the diameter of the approximately circular path

which a ship describes if the wheel is kept over.

EF = the approximate final diameter

* Tactical diameter will vary with both speed and rudder angle.
CALCULATING THE POSITION 187

Fig. 8-10. Tactical and final diameter

The length of the arc is the distance from point to point along the path
actually described by the ship when turning.
All the above data for a ship can be obtained from Turning Trials (see
Volume IV of this manual and BR 67(3), Admiralty Manual of Seamanship,
Volume III for details).
Either the advance and transfer method or the distance to new course
method should be used when plotting the track by hand (Fig. 8-11). In
coastal and pilotage waters, an allowance for the tidal stream may also have
to be made and this is discussed in later chapters.

Method 1. Advance and transfer

In Fig. 8-11, a ship is steering a course 000°. If the wheel is put over to alter
course to 120° when in position A (at 0900), she will follow the curve AEB
and will be steady on her new course 120° at the point B.
With data obtained from the Turning Trials, the point B can be plotted
and the time taken to travel from A to B along the arc can be found.
During the turn from A to B, the ship will lose speed so that, when steady
on the new course, she will be moving at less than her original speed. It will
not be correct, therefore, to continue plotting from the point B, unless some
allowance is made for this loss of speed.
The additional distance which must be travelled at the original speed to
regain each knot of speed lost may be between 15 and 60 yards in an HM
Ship. such data are normally recorded in the Navigational Data Book and
known as the speed factor.
Suppose that a warship (in Fig. 8-11), with an original speed of 15 knots
and a speed factor of 60 yards per knot, loses 3 knots on the turn. She will
then be moving at 12 knots when she steadies on the new course at B, and
will have to regain 3 knots. This can be allowed for by making her cover an
additional 3 x 60 = 180 yards, at 15 knots; i.e. she may be plotted on at 15
188 CHAPTER 8 - CHARTWORK

Fig. 8-11. Plotting a turn

knots from a position 180 yards 300° from B. Her position on the plot will
then be correct when she has regained her speed of 15 knots.
To obviate the additional plotting, a time correction is provided which
takes this additional distance into consideration. It consists of the time taken
to turn plus the time taken to cover the additional distance at the original
speed, and should be added to the time of ‘wheel over’ to give a time of
arrival at B which will enable the ship to be plotted on from B at her original
speed.
All subsequent positions can now be laid off along the new course and
worked from the point B, the time interval being calculated from the corrected
time.
A table may be constructed from the turning data to give the advance and
transfer and time correction for any alteration of course, for different speeds
and rudder angles.
CALCULATING THE POSITION 189

Table 8-3 is an example of such a table, constructed for a warship

steaming at 15 knots, using 20° of rudder.

Table 8-3. Advance and transfer

AMOUNT OF ADVANCE TRANSFER TIME
ALTERATION CORRECTION

degrees yards yards min s

20 332 26 0 42
40 516 110 1 12
60 640 233 1 41
80 719 415 2 12
100 735 612 2 42
120 674 803 3 12
140 546 964 3 41
160 366 1064 4 09
180 175 1107 4 38

If this table is used, point B may be plotted from A using an advance of

674 yards and a transfer of 803 yards, and a corrected time of arrival at B of
0903¼ (odd seconds being ignored).

Method 2. Distance to new course

If this method is used for the turn shown in Fig. 8-11, the ship plots her new
course from the point C, where the new course laid back cuts the original
course produced, although in fact she puts her wheel over at A, as before, and
steadies on the new course at B.
If the time taken to travel the distance CB at the original speed is
subtracted from the time correction previously described, then the time of
arrival at the imaginary point C is obtained. This calculation is incorporated
in another time correction, which is again added to the time of ‘wheel over’
so that the ship in this case may be plotted on from C at her original speed
although it is clear that the ship does not in fact pass through the point C at
all.
Table 8-4 is an example of a ‘distance to new course’ table constructed
for the same warship, speed 15 knots, using 20° rudder.

Table 8-4. Distance to new course

ALTERATION DISTANCE TO TIME
OF COURSE NEW COURSE CORRECTION

degrees yards min s

20 261 0 33
40 385 0 52
60 505 1 09
80 646 1 22
100 843 1 28
120 1138 1 22
190 CHAPTER 8 - CHARTWORK

If this table is used, the point C in Fig. 8-11 is plotted 1138 yards along
the original course 000°, and the time of arrival at this imaginary point is
0901½ (odd seconds being ignored).
This method involves only two simple corrections:
1. A distance to be plotted along the original course.
2. A time correction to be added at the time of ‘wheel over’ in order to
obtain the corrected time at the point C.
Its disadvantage is that it cannot be used for alterations of course over 120°
or so, because beyond this point the distance to new course becomes excessive.
Correction for change of speed
The gain or loss of distance when speed is altered while on a straight course
must also be allowed for when plotting by hand. The actual correction for
any ship is found during acceleration and deceleration trials and recorded in
the Navigational Data Book (see Volume IV of this manual and BR 67(3),
Admiralty Manual of Seamanship, Volume III).
CHARTWORK PLANNING
At the planning stage, the following symbols should be used for chartwork
(Fig. 8-12). Blind pilotage symbols are to be found in Chapter 14.
(a) Planned track. Draw the planned track boldly, writing the course along
the track with the course to steer in brackets alongside and the speed in
a box, north orientated, underneath. The figures for course and speed should
be sufficiently far away from the track to permit the necessary chartwork.
(b) Tidal stream. Indicate the expected tidal stream, showing the direction
by a three-headed arrow, the strength in a box, and the time at which it is
effective. This symbol can also be used for ocean currents and surface
drift although the following symbol is often used instead:
0.3

(c) Dangers. Emphasise dangers near the track by outlining them boldly in
pencil (or coloured ink if the chart is to be used often). In pilotage
waters, the safe depth sounding line should be drawn in to show the
limits of the navigable channel. Remember that this will vary with the
height of the tide.
(d) Clearing bearings (see Chapter 13). Draw in clearing bearings boldly,
using solid arrowheads pointing towards the object. NLT ... (not less
than ...) or NMT ... (not more than ...) should be written along the arrow
line. A clearing bearing should be drawn sufficiently clear of the danger
so that the ship is still safe even if the bridge is on the bearing line but
turning away from danger. Allow for the bridge being on the line with
the stem or stern on the dangerous side of it, whichever is the greater
distance.
(e) Distance to run. Indicate the distance to run to the destination,
rendezvous, etc. Numbers should be upright.
(f) Planned position and time. Indicate the time it is intended to be at
particular positions at regular intervals, using ‘bubbles close to but clear
of the track.
CHARTWORK PLANNING 191

Fig. 8-12. Chartwork planning symbols

192 CHAPTER 8 - CHARTWORK

It is suggested that ocean passages be marked every 12 hours (0001 and

1200 or 0600 and 1800), coastal passages more frequently, every 2 or 4
hours.
(g) Sunrise and sunset. Indicate the times of sunrise and sunset at the
expected positions of the ship at those times.
(h) Visual limits of lights. Indicate the arcs of the visual limits of lights that
may be raised or dipped ) the rising/dipping range.
(i) Position and time of ‘wheel over’. Show position and planned time of
‘wheel over’ for alterations of course. The amount of wheel can be
stipulated if this differs from standard.
(j) Change of chart. The positions of changes of chart should be indicated
by double parallel lines, either vertical or horizontal.

CHARTWORK ON PASSAGE

Fixing
The various methods of fixing the ship are described in Chapter 9. The visual
fix is the foundation of all coastal navigation, once a sound plan has been
made. Fixes are vital, yet their observation and plotting takes the eye of the
Navigating Officer or Officer of the Watch away from other vital tasks of
lookout.
Plotting the ship’s position
The DR from the last fix must always be maintained for some distance ahead
of the ship and an EP must be derived from all available information of tidal
stream, current, etc. As soon as a new fix is obtained, the fix position must
be compared with the DR and EP to ensure that there has been no mistake in
identifying features ashore, and also to obtain an estimate of the strength and
direction of any stream or current since the last fix. It is particularly
important to generate a DR or EP after an alteration of course.
Use of a DR may be acceptable when wind, tidal stream and current are
negligible but, when these are significant, the EP must be generated. This
should happen in any case once an appropriate course has been determined,
to make good a track allowing for these factors.

Frequency of fixing
Frequency of fixing should depend on the distance from navigational hazards
and the time the ship would take to run into danger before the next fix. This
depends mainly on the ship’s speed. For example, at passage speeds, say 10
to 15 knots, a fix every 10 to 15 minutes on a 1:75,000 coastal chart gives a
position every 2 to 3 inches on that chart; this is normally sufficient. At
higher speeds or on a larger scale chart, the time interval will need to be much
less and may require a fixing team.
It is recommended that fixes should be taken at times coinciding with DR
or EP times on the chart. This practice will make immediately apparent the
effects of leeway, tidal stream, etc. and whether or not the effects experienced
are the same as those expected.
A 6 minute interval between fixes is convenient for converting distance
CHARTWORK ON PASSAGE 193

to speed made good because the multiplier is 10; e.g. 1.35 miles in 6 minutes
equals 1.35 x 10 or 13.5 knots.
Useful fixing intervals for easy conversion of distance to speed are shown
in the following table. The multipliers are all whole numbers.

Interval 3 4 5 6 10 12 15 20
(minutes)
Multiplier 20 15 12 10 6 5 4 3

For example, if the distance run in 4 minutes is 0'.82, the speed made
good is 15 x 0'.82 = 12.3 knots.
At speeds of about 15 knots, a useful rule of thumb is to fix every 20
minutes (5 miles approx.) when navigating offshore on the 1:150,000 coastal
chart; every 10 minutes (2½ miles approx.) when coasting closer inshore on
the larger 1:75,000 chart; and every 4 minutes (1 mile approx.) when
approaching a port using a 1:20,000 chart. On entering the pilotage stage of
the passage, a different fixing technique is required and this is described in
Chapter 13.

Speed
The speed ordered (rung on) is normally shown in a box north orientated
alongside the track. It should be remembered that the speed made good along
the water track (sea speed) or along the ground track (ground speed) is not
usually shown against the track worked up on the chart. Ground speed may
be deduced from the distance run between successive fixes, or it may be
estimated from the expected effects on the speed ordered of wind, sea, tidal
stream, current and surface drift. Actual or estimated ground speed should
always be used when projecting the EP ahead. Ground speed is liable to
fluctuate when any sea is running, also when the strength or direction of the
tidal stream is changing.

Time taken to fix

The time taken to note the bearings and the time, plot the fix on the chart,
check the DR and lay off further DR, verify time to ‘wheel over’ (if
applicable) and return to lookout, should not be more than 2 minutes. A
practised navigator should be able to complete the task within 60 seconds.
If it is essential to reduce the fixing time further, an assistant or a team should
be used. Using an assistant, the time can be reduced to less than 30 seconds.

Keeping the record

A complete record, showing navigational information in sufficient detail for
the track of the ship at any time to be reconstructed accurately, is to be kept
in the Navigational Record Book (S3034). An example is given in Fig. 8-13.
The following symbols may be employed:

left-hand edge (of land, etc.)

right-hand edge (of land, etc.)
Port (5c) abeam to port (5 cables)
Stbd (1'.2) abeam to starboard (1.2 miles)
194 CHAPTER 8 - CHARTWORK

Further information on the record is given in Chapter 12.

Fig. 8-13. The Navigational Record Book

CHARTWORK ON PASSAGE 195

Establishing the track

A fix must always be taken immediately after altering course and a further fix
taken shortly after (see page 192). From them the following conclusions may
be drawn:

1. Whether the ship is on track or not.

2. The course and speed being made good, and hence the effect of wind,
tidal stream and current.

From this information the following questions arise:

1. Is the actual track the same as that intended and is it safe?

2. Should the course be adjusted now to regain the intended track?
3. Can the divergence (if any) from the intended track be accepted until the
next alteration of course?
4. When is the next alteration of course?

Time of arrival
During the final stages of a passage, show the exact times at which it is
intended to pass through regular positions so that speed may be quickly
adjusted to achieve the correct time of arrive (Fig. 8-14).

Fig. 8-14. Time of arrival

Plan when to change from regular chart fixing to ‘Note Book’ pilotage
(i.e. to keeping on a predetermined track).

General points on chartwork

1. Always show the time of the next alteration of course as a four-figure
time at the appropriate position on the ship’s track. This should be done
as early as possible.
2. Transfer positions from one chart to another by bearing and distance from
a point common to both charts, and check by latitude and longitude. This
is most necessary as a check against mistakes, as the graduations on the
two charts may differ. However, it must be remembered that the charts
may be based on different geographic datums, and small differences in
position between the two transfer methods may arise.
3. Always obtain a fix as soon as possible after the ship’s position has been
transferred from one chart to another.
196 CHAPTER 8 - CHARTWORK

4. Always use the nearest compass rose, because:

(a) There will be less effect of distortion, and the correct variation will
be used.
(b) An error will be avoided if the chart used is drawn on the modified
polyconic (gnomonic) projection.
5. Remember the changes of variation printed on each compass rose.
6. Keep only one chart on the chart table, to avoid the error of measuring
distances off the scale of a chart underneath the one in use.
7. Make certain whether the units denoting soundings on the chart are
fathoms, feet or metres.
8. When measuring distance by the latitude scale, measure as far as possible
the same amount on each side of the mean latitude of the track being
measured.
9. The surface of the chart can best be preserved )and plotting will be most
clear )if a 2B pencil and a soft rubber are used. In wet or hot and humid
weather, it is a good plan to place a towel along the front of the chart
table when working on the charts, and to remove dripping headgear.

SUMMARY

The necessity for developing the DR and the EP has been emphasised in this
chapter. Despite the world-wide availability of a whole range of
sophisticated and accurate navigational aids, it is nevertheless true that a high
proportion of groundings still result from a failure to work up a proper
DR/EP. An accurate DR/EP over which the Navigating Officer has taken
care will often prevent a potentially dangerous grounding situation from
developing in the first place.
 197

CHAPTER 9
Fixing the Ship

Fixing the ship was introduced in Chapter 8 in connection with chartwork.

This chapter sets out the methods of fixing the ship by the use of position
lines obtained mainly by visual observation of terrestrial objects. It is worth
remembering, however, that a visual bearing of a terrestrial object may
sometimes be combined with a position line from some other navigational
source to produce a fix; for example, the echo sounder, radar or a radio aid.
For this reason, position lines from these sources will be covered to a greater
or lesser extent, although how they are obtained is dealt with in detail
elsewhere in this manual. Radar is covered in Chapter 15 of this volume, and
the echo sounder and radio fixing aids in Volume III.

Fig. 9-1. Azimuth circle

198 CHAPTER 9 - FIXING THE SHIP

Taking bearings
The azimuth circle shown in Fig. 9-1 is designed so that the accurate
alignment of the circle itself is not essential, and therefore a foresight is not
fitted. The optical principles on which the instrument is designed are such
that, provided the object is seen through the V, the correct bearing can be
read, whether or not the circle itself is aligned to point at the object. A line
is engraved on the face of the prism to facilitate the reading of the bearing.
An example of a bearing being taken of a chimney is given in Fig. 9-2. It is
not absolutely essential for the azimuth circle and repeater to be horizontal
when the bearing of a surface object is being taken, and a slight skew will not
affect the reading. In both cases in Fig. 9-2, the bearing of the chimney is
355°.

Fig. 9-2. Taking a bearing

To take a bearing of an object at high altitude, the reflection of the object

in the reflector should be sighted through the V sight, and the circle trained
until the reflection is on the engraved line on the reflector. The bearing is
then read on the engraved line on the prism. During this operation, care
should be taken to keep the circle horizontal by means of the bubble level.
It is sometimes difficult to read off the bearing of a terrestrial object when
observing into strong sunlight. Usually a judicious manipulation of the
sighting prism and the reflecting mirror will overcome this problem.

METHODS OF OBTAINING A POSITION LINE

A position line may be obtained from:

1. A compass bearing.
2. A relative bearing.
METHODS OF OBTAINING A POSITION LINE 199

3. A transit.
4. A horizontal angle.
5. A vertical sextant angle of an object of known height.
6. A range by distance meter when the height of the object is known.
7. A range by rangefinder.
8. A rising or dipping range.
9. Soundings.
10. A radio fixing aid.
11. A radar range.
12. An astronomical observation.
13. A sonar range.

Compass bearing
When the compass bearing of an object is taken, the position line thus
obtained is called a line of bearing (see page 175).
When a bearing of the edge of an object is taken, it is usual to distinguish
the right-hand edge with the symbol and the left-hand edge with the
symbol . A vertical edge gives the best bearing. Allowance must
be made for the height of tide when taking the bearing of a sloping edge of
land, as the charted edge is the high water line (Mean Sea Level in areas
where there are no tides).
Details of taking bearings by radar are given in Chapter 15.

Relative bearing
A line of bearing may be obtained by noting the direction of an object relative
to the direction of the ship’s head.
If the lighthouse shown in Fig. 9-3 is observed to be 60°on the starboard
bow (Green 60° or 060° Relative) when the ship is steering 030°, the true
bearing of the lighthouse is 090°, which may be drawn on the chart.

Fig. 9-3. Position line by relative bearing

200 CHAPTER 9 - FIXING THE SHIP

Transit
If an observer sees two objects in line, then he must be somewhere on the line
which joins them, as shown in Fig. 9-4. Ideally, the distance between the
observer and the nearer object should be less than three times the distance
between the objects in transit. The transit is then sufficiently ‘sensitive’ for
the movement of one object relative to the other to be immediately apparent.
It can of course be used at greater distances. It is also most useful for
checking the error of the compass (see page 219).
The symbol φ is used for a transit. The symbol … is used by the
Hydrographer to designate transits on Admiralty charts, and shown in Chart
Booklet 5011, Symbols and Abbreviations used on Admiralty Charts.

Fig. 9-4. Position line by transit

Horizontal angle
Since all angles subtended by a chord in the same segment of a circle are
equal, it follows that, if the observer measures by sextant or by compass the
horizontal angle between two objects, he must lie somewhere on the arc of a
circle which passes through them and which contains the angle observed.

Fig. 9-5. Position line by horizontal angle

METHODS OF OBTAINING A POSITION LINE 201

In Fig. 9-5, the angle between the lighthouse A and the chimney C has been
measured by sextant and found to be 80°. The ship’s position must therefore
lie on the arc of the circle ABC along which the angle between A and C is
always 80°.
Horizontal sextant angles are dealt with more fully later in this chapter
(page 224).

Vertical sextant angle of an object of known height

If the angle subtended at the observer’s eye by a vertical object of known
height is measured, the solution of a right-angled triangle will give the
observer’s distance from the base of the object. The position line will then
be the circumference of a circle which has this distance as its radius
(Fig. 9-6). A vertical sextant angle may be used as a ‘danger angle’, as may
be a horizontal sextant angle, to clear a danger (see Chapter 12).

Fig. 9-6. Position line by vertical sextant angle

Whole of the object above the horizon

In Fig. 9-6, DE is the required distance, AD is the height of the observer, BE
is the height of the object, while CE is the distance from the shoreline to the
point below the object. The observer measures the angle BAC. The required
angle is BDE but, provided that DC is greater than BE and BE greater than
CE, no appreciable error* is introduced if BAC is used instead.

* If the point observed is vertically over the shore horizon, and DE is greater than BE, the error in position will
be less than the height of eye AD. If the point is not vertically over the shore horizon as in Fig. 9-6, provided DC
is greater than BE and BE greater than the horizontal distance CE, the error in position is less than 3 times the height
of eye AD.
202 CHAPTER 9 - FIXING THE SHIP

The distance DE may be expressed as follows:

DE = BE cot BAC . . . 9.1
The charted height is given above the level of MHWS or MHHW (see page
119) and so this must be adjusted for the height of tide. If no such allowance
is made, the calculated distance will be less than the actual distance.
It should be remembered that the charted height of a lighthouse is taken
from the centre of the lens and not the top of the structure.
Norie’s Nautical Tables solve the triangle for ranges between 1 cable and
7 miles and heights between 7 metres (23 feet) and 600metres (1969 feet).
EXAMPLE
A vertical sextant angle of a lighthouse, charted height above MHWS 40
metres, is 0°46'.2. The height of tide is calculated as being 2.12 metres below
MHWS. The Index Error of the sextant is + 1'.2. What is the range of the
light?
observed angle 0°46'.2
index error +1'.2
corrected angle 0°47'.4 (0°.79)
charted height 40 metres
+ 2.12
corrected height 42.12m (0'.02274 n miles) . . . (9.1)
range = corrected height x cot corrected angle
= 0.02274 cot 0°.79
= 1.65 n miles
Norie’s Tables give a distance of 1.65 n miles.
Base of the object observed below the observer’s horizon
It is sometimes useful to be able to obtain a position line from an object such
as a distant mountain peak, where the base is below the observer’s horizon.
The method of obtaining a position line in such circumstances is set out in
Appendix 6.
Long-range position lines obtained in this way are of little value if
refraction different from normal (see Volume II of this manual) is suspected.
Abnormal refraction is likely to be present when the temperatures of the water
and air differ considerably.
Range by distance meter when the height of the object is known
This method is based on the principle of the vertical sextant angle.
The various types of distance meter supplied to HM Ships are described
in Volume III of this manual. They are useful because no calculation is
needed, the range being obtained by a direct reading.
Range by rangefinder
The rangefinder is described in Volume III. This method is useful for finding
the distance of a single light at night, or the distance of an object unsuitable
for a vertical sextant angle.
METHODS OF OBTAINING A POSITION LINE 203

Rising or dipping range

This method is useful at night for finding the distance of a light when it first
appears above or dips below the horizon.
The theoretical distance of the sea horizon for a height of h metres is
1.92 h sea miles, but the effect of normal atmospheric refraction is to
increase this by about 8%. Thus, the distance of the sea horizon may be
found from the formula:
distance = 2.08 h sea miles . . . 9.2
where h is measured in metres, or
distance = 1.15 h sea miles . . . 9.3
where h is measured in feet.

The distance of the ship from the horizon and the light beyond the
horizon can both be found by this method. These ranges added together give
the distance of the ship from the light. The distances may also be found from
Norie’s Tables or the Geographical Range Table in the Admiralty List of
Lights and Fog Signals (see Chapter 10). As these tables make different
allowances for refraction,* the distances obtained will be different. Such
ranges must be treated with caution (see Chapter 10).

EXAMPLE
A short light 40 metres above the water is observed from the bridge to dip
below the horizon. Height of eye is 12 metres. What is the range of the light?

Fig. 9-7. Position line from a dipping range

From formula (9.2), the following ranges are obtained:

range of horizon for height of eye of 12 metres 7.21 sea miles

range of horizon for height of eye of 40 metres 13.16 sea miles
range of light 20.37 sea miles

The range given in the Geographical Range Table in the List of Lights is
19.9 sea miles. Thus, the range at which the light dips is approximately 20
miles.

* Norie’s Tables use the formula: distance of the sea horizon d = 2.095 h where h is the height in metres.
The List of Lights uses the formula: d = 2.03 h , where h is the height in metres, or d = 1.12 h , where h is
the height in feet.
204 CHAPTER 9 - FIXING THE SHIP

When abnormal refraction exists (page 202), this method of obtaining a

range is inaccurate.
As the height of a light is given above MHWS or MHHW (page 119), a
correction to the height should be made for the height of tide.
Soundings
Soundings are frequently of value in establishing a position line. In areas
where a particular depth contour on the chart is sharply defined and
reasonably straight, or in approaches to the land where there is a steady
decrease in depth, a position line may be obtained. Good examples of this are
in the south-western approaches to the British Isles, where the depth
decreases rapidly from 2000 to 200 metres in a distance of some 10 to 20
miles, or in the southern approaches to Beachy Head, where the depth shoals
from 50 to 30 metres in about 1½ miles. In the latter case, it will be necessary
to allow for the height of tide, and to ensure that the echo sounder (see
Volume III) is reading accurately.
Radio fixing aids
Position lines from radio fixing aids may be in the form of a bearing, for
example MFDF, or in the form of a hyperbolic position line, for example
Decca or Omega. Full details of radio fixing aids are given in Volume III.
Radar range
Radar may be used to obtain a position line in the form of a circular arc at
both short and long ranges off the land. Full details are given in Chapter 15.
Astronomical observation
Position lines may be obtained from the observation of heavenly bodies&the
sun, moon, stars and planets. Although the position line is circular, to all
intents and purposes it may be treated as a straight line, except in the case of
very high altitudes. Full details of astronomical observations are given in
Volume II.
Sonar range
Provided that the ship is fitted with sonar equipment, it is possible to obtain
a range of an underwater object such as a rock which can be used for
navigational purposes as a position line in the form of a circular arc. It is,
however, often impossible to determine precisely from which part of the sea-
bed the range is being obtained.
THE TRANSFERRED POSITION LINE
Suppose, as shown in Fig. 9-8, that a lighthouse bears 034° from the ship at
1600 and that the ship is steaming 090° at 8 knots. What information is
available about the ship’s position at 1630? There is no tidal stream or
wind.
Draw a line ACE in a 214° direction from the light. This is the position
line at 1600. The position at 1600 is unknown, although the ship must be on
the position line ACE. Assume the ship is at A, C and E in turn and project
AB,
THE TRANSFERRED POSITION LINE 205

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Fig. 9-8. The transferred position line |
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CD, EF, respectively in a direction equivalent to a 30 minute run, in this case
090° 4 miles. Join BDF.
The ship must be on the line BDF at 1630. BDF is known as the
transferred position line and is parallel to the original. It is distinguished by
a double arrowhead at the outer end.
If the ship is set by tidal stream during the run, the point through which
to draw the position line must be determined in two steps, as shown in Fig.
9-9.
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Fig. 9-9. The transferred position line, allowing for tidal stream |
 206 CHAPTER 9 - FIXING THE SHIP

1. Lay off, from any point on the original position line, the course and
distance (AB) steamed by the ship in the interval.
2. From B lay off BK, which is the direction and distance the ship is
estimated to have been set, in the interval, by the tidal stream. The
position line is now transferred through K.

The use of a single transferred position line

When two position lines cannot be obtained, a single one may often be of use
in clearing some danger or making a harbour. For example, suppose that the
course to be steered up a narrow and ill-defined harbour is 080°, as
in Fig. 9-10.
The ship, steaming 180°, observes the time at which the lighthouse L
bears 080°. The time taken to run to the ‘wheel over’ point B (see page 185)
is calculated, allowing for wind and stream, and at the end of this time the
ship alters course to 080°. It is clear that, no matter where the ship was on the
original position line AL, she will turn on to the transferred position line CK,
which will lead her into harbour, provided that the run between A and B has
been calculated accurately.
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| Fig. 9-10. The use of a single transferred position line

FIXING THE SHIP

A fix is the position obtained by the intersection, at a suitable angle, of two

or more position lines from terrestrial objects. Unless the position lines are
obtained at practically the same time, one or more of them must be
transferred, as described later.
FIXING THE SHIP 207

The most common methods of obtaining a fix are as follows:

1. Cross bearings.
2. A bearing and a range.
3. A bearing and a sounding.
4. A bearing and a horizontal angle from which a range may be calculated.
5. A transit and an angle.
6. Two bearings of a single object, with a time interval between
observations (running fix).
7. A line of soundings.
8. Two or more ranges.
9. Radio fixing aids (described in Volume III).
10. Astronomical observations (described in Volume II).

Fixing using horizontal sextant angles and bearing lattices is described

later in this chapter (page 224).

Fixing by cross bearings |

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Fig. 9-11. Fixing by cross bearings |
208 CHAPTER 9 - FIXING THE SHIP

When bearings are obtained from two different objects at the same time, the
ship’s position must be at the point of intersection of the two lines of bearing.
For example, in Fig. 9-11, assuming that the lighthouse bore 049° and at
the same time the church bore 132°, the point of intersection of these two
bearings is the ship’s position.
To avoid error, a third bearing (called a check bearing) should always be
taken at the same time and should pass through the point of intersection of the
other two bearings. In Fig. 9-11, a check bearing of the beacon was 099°.

The cocked hat

When three bearings are taken from a moving ship, the resulting position
lines may not meet in a point but are more likely to form a triangle known as
a cocked hat. This is illustrated in Fig. 9-12.
Three bearings are taken from a ship steaming 180° at 20 knots. The
beacon bore 057° at 1059½, the chimney 127° at 1059¾ and the rock
084° at 1100. If the three position lines are plotted without any consideration
being given to the course and distance being steamed between 1059½ and
1100, a cocked hat will be formed; its size depends on the time taken to fix,
the course and speed of the ship and scale of the chart. If, however, the
position lines for the beacon and the chimney are transferred the correct
amount for the distance steamed (180° 0'.17 for the beacon and 180° 0'.08 for
the chimney), the cocked hat disappears and the ship’s position is found at X
at 1100.
The cause of a cocked hat may be any of the following:

1. Time interval between observations.

2. Error in identifying the object.
3. Error in plotting the lines of bearing.
4. Inaccuracy of observation resulting from the limitations of the compass.
5. Inaccuracy of the survey or the chart.
6. Compass error unknown or incorrectly applied.

If the cocked hat is large, the work should be revised to eliminate (1), (2)
and (3). Error (1) may be eliminated by reducing the time interval or by
applying the ‘run’ , as in Fig. 9-12.
Error (4) should never be greater than ¼° with modern compass repeaters
and may generally be disregarded.
Error (5) may be judged as described in Chapter 6.
Methods of eliminating error (6) are described later in this chapter (page
219).
A more detailed treatment of errors in lines of bearing is given in
Appendix 7.

Fixing by a bearing and a range

A visual bearing may be combined with a range to obtain a fix. Examples of
position lines from ranges have already been given in this chapter.

Fixing by a bearing and a sounding

On approaching the land, a position may be obtained in places where the
FIXING THE SHIP 209

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Fig. 9-12. The cocked hat |

depth is changing steadily, by observing a visual bearing and a sounding

simultaneously. Before plotting the sounding position line, an allowance
must be made for the height of the tide and also the draught of the ship if the
echo sounder is set to read depths below the keel and not the waterline.
The fix will not be reliable unless the depth contours are clearly defined
and crossed as nearly as possible at right angles.
This type of fix is illustrated in Fig. 9-13 (page 210).
At 1000 St Anthony’s Head bears 342½° at the same time as a depth
below the keel of 47 metres is recorded on the echo sounder. Draught is 6.1
metres, height of tide 3.1 metres. The sounding position line is drawn along
the 50 metre depth contour (47 + 6.1 - 3.1 = 50m) and where it intersects with
the bearing of 342½° is the position at 1000.

Fixing by a bearing and a horizontal angle from which a range may be

calculated
This method is useful when the ship is passing a small island, the compass
bearings of the two edges giving too small an angle of cut, and a ranging aid
210 CHAPTER 9 - FIXING THE SHIP

Fig. 9-13. Fixing by a bearing and a sounding

FIXING THE SHIP 211

such as radar or rangefinder is not available. In such a case, observe the

bearing of one edge and take a horizontal sextant angle between the edges.
From the width of the island as measured on the chart, the range of the ship
may be calculating.

EXAMPLE
The sextant angle between the extremes of an island 0.7 miles wide (Fig. 9-
14) was found to be 7°, and at the same time the left-hand edge bore 085°.
To find the distance of the ship from the island, let R miles equal the
distance. Then, since arc = radius × the angle in radians, |
and 1° = 2π radians: |
360 |
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2π x 7 360 x 0.7
then 0.7 = R x ∴ R= |
360 2π x 7 |
ˆ R = 5.73 miles |

Fig. 9-14. Fixing by a bearing and a horizontal angle

Fixing by a transit and an angle

A transit is observed at the same time as a horizontal sextant angle is taken
between the nearer object of the transit and a third object. The position is the
intersection of the transit and the arc of the circle obtained from the
horizontal sextant angle (see Fig. 9-5).
Such a position has the advantage that no compass is required when using
this method.

Fixing by two bearings of a single object, with a time interval between

observations (running fix)
If two position lines are obtained at different times, the position of the ship
can be found by transferring the first position line to the time of taking the
bearing for the second position line, as described on page 204. The point of
intersection of the second position line and the transferred position line is the
ship’s position at the time of the second observation.
 212 CHAPTER 9 - FIXING THE SHIP

Method 1. To obtain a fix from two position lines obtained at different times,
when the tidal stream is known*

EXAMPLE
(See Fig. 9-15.) A ship is steering 090° at 8 knots. the tidal stream is
estimated as setting 135° at 3 knots.
At 1600 a lighthouse bore 034°. AT 1630 the same lighthouse bore 318°.
Find the position of the ship at 1630.
A is any point on the first position line.
AB is the course and distance run by the ship in 30 minutes.
BC is the amount of tidal stream experienced in 30 minutes.
The point where the first position line, transferred and drawn through C,
cuts the second position line is the ship’s position at 1630, D.
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| Fig. 9-15. The running fix

Method 2. To obtain a fix from two position lines obtained at different times,
when the tidal stream is unknown but a previous fix has recently been
obtained†

EXAMPLE
(See Fig. 9-16.) At 1700 a ship was fixed at A, and was steering 180°.
At 1800 observed bearing of R was 090°. At 1836 observed bearing of
R was 053°. Required: the fix at 1836 and the stream experienced from
1700 to1836.
Draw AE, the course steered, cutting the first position line in B. On the
line AE insert C such that BC is 36 minutes run at the speed given by AB.

* The accuracy of this fix will depend on the accuracy of the estimated run between bearings, and it is therefore
essential to make due allowance for the wind and stream experienced by the ship during this interval.
† This method should only be used over a period, or in an area, in which it is certain that the strength and direction
of the stream remain constant. Otherwise the fix will be inaccurate.
FIXING THE SHIP 213

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Fig. 9-16. The running fix with unknown tidal stream |

Transfer the first position line through C. The point P, where this cuts the
second position line, is then the fix at 1836. AP is the course and distance
made good between 1700 and 1836.
To obtain the tidal stream, plot D, the DR at 1836, along AE at the speed
of the ship through the water. Join this to P; then DP is the direction and set
of the stream between 1700 and 1836.
Proof. Since the triangles ABO and ACP are similar, AO/OP = AB/BC.
AO and OP represent the speeds made good in 1 hour and 36 minutes
respectively. The line AE could have been drawn in any direction which cuts
the two position lines and, provided the proportion AB:BC remained the
same, the transferred position line would always cut the second one at P. The
tidal stream cannot, however, be found unless AE is plotted as described
above.

Method 3. Doubling the angle on the bow: the four-point bearing

This special type of running fix may be plotted as a conventional running fix
but using a quicker method as follows:
The angle between the ship’s head and the bearing of an object is
 214 CHAPTER 9 - FIXING THE SHIP

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measured; suppose it to be α° (Fig. 9-17). Note the time when the angle
doubles to 2α°. The distance from the light CB is equal to the distance run
between the two bearings AB, since ABC is an isosceles triangle.
If the angle α° is equal to 45°, the distance run AB is equal to the beam
distance when the relative bearing has doubled to 90°. This method of fixing
the ship when the object is abeam is known as the four-point bearing.
Doubling the angle on the bow will not give an accurate position if there
is any leeway, tidal stream, current or surface drift across the course. In that
event, the observation should be plotted as a running fix.
The general theory of doubling the angle on the bow in a current or tidal
stream is set out in Appendix 7.

Method 4. Estimating the distance at which a ship will pass abeam of an object

The four-point bearing suffers from Table 9-1

the disadvantage that the distance an
object will pass abeam is not known φ
until the object is abeam. Certain θ
pairs of angles shown on the table 26½° 45°
will give this distance. 30° 53¾°
35° 67°
40° 79°
FIXING THE SHIP 215

Provided that the difference between the cotangents of the two measured
angles is 1, the distance run between the two angles equals the distance at
which the object will pass abeam. This is illustrated in Fig. 9-18.

Fig. 9-18. To estimate the distance at which a ship will pass abeam of an object

y
cot θ =
x

x+ y
cot φ =
x
x+ y y
cot φ − cot θ = −
x x
cot φ − cot θ = 1 . . . 9.5

A great number of pairs of angles will satisfy this requirement, although

the limitations of the equipment in use will frequently prevent one or other
bearing being measured to the degree of accuracy required, and in any case
it is undesirable to use this procedure when the object is too fine on the bow
as the change in angle required is very small. Once again, leeway, tidal
stream, etc. across the course will prevent an accurate fix being obtained.
The first pair of angles, 26½° and 45° is useful, as the distance run
between the two observations, AB, not only equals the abeam distance CL, but
also equals the distance to go until the object is abeam, BC.
A further method of estimating the distance that an object will pass
abeam, but not involving a running fix, is given on page 327.
216 CHAPTER 9 - FIXING THE SHIP

Fig. 9-19. Finding the position by a line of soundings

FIXING THE SHIP 217

Fixing by a line of soundings

When there are no objects suitable for observation, it is sometimes possible
to obtain a position from soundings. Although this method does not strictly
conform to the definition of a fix as previously given, in that it does not
involve the intersection of two or more position lines, a positive indiction of
the ship’s position can be obtained as follows.
Sound at regular intervals, noting the depth. Correct the soundings for
the height of tide, also for draught if measured below the keel. On a piece of
tracing paper draw in a meridian of longitude and a parallel of latitude. Lay
off the ship’s estimated ground track at the scale of the chart in use. Along
this track plot the reduced soundings at the scale of the chart in use. Place the
tracing paper on the chart in the vicinity of the ship’s Estimated Position and,
using the meridian and the parallel as a guide in keeping it approximately
straight, move it about until the soundings on the tracing paper coincide with
those on the chart.
The frequency at which soundings should be taken depends on the speed
of the ship and the spacing and nature of the soundings on the chart.
The procedure is illustrated in Figs. 9-19 and 9-20.
Caution: The approximate position found from a line of soundings
should always be used with caution, because it is often possible to fit a line
of soundings in several positions on a chart.

Fig. 9-20. A line of soundings

218 CHAPTER 9 - FIXING THE SHIP

EXAMPLE
At 0900 a ship is in the estimated position shown in Fig. 9-19, believed to be
accurate within 5 miles. She is on a course of 335° 12 knots. Tidal stream
is estimated to be setting 080° 1 knot, and her estimated course and speed
made good are 340° 11.7 knots. The following soundings, corrected for the
height of tide are obtained:

0900 71 m 0930 55 m
0905 68 m 0935 50 m
0910 66 m 0936½ 47 m
0915 56 m 0939 50 m
0920 62 m 0940 54 m
0925 60 m

Determine the position at 0940.

The soundings are plotted (Fig. 9-20) on a sheet of tracing paper along
the estimated ground track, 340° 11.7 knots at the scale of the chart. A
meridian of longitude and a parallel of latitude are also plotted to help keep
the line of soundings lined up to the track.
From a study of the chart concerned, of which Fig. 9-19 is an extract, it
is immediately evident from the initial sounding at 0900 that the ship is either
further back along the track (2') or is some distance off to the south-east (3'),
or south-west to west (2' to 4'). The soundings at 0905 and 0910 eliminate
the possibility that the ship is to the east of track. The soundings at 0915
onward indicate that the ship may be on track but some 2¼ to 2½ miles astern
of the estimated position. The 0915 sounding indicates that the ship is
passing over or close to a wreck or other obstruction on the sea-bed.
However, the possibility that the ship may be on track but astern or some 4'
to the west is eliminated by the soundings between 0935 and 0940, which
clearly indicate the ship is passing over the bank 2½ miles long by ¾ miles
wide lying to the west of the 0930 estimated position. The tracing may now
be matched to the charted soundings and the positions at 0900, 0935 and
0940 plotted, showing that the ship is some 2 miles to the west and 1 mile
astern of the estimated position.
This example shows that it may take some time to establish a position
from a line of soundings with a reasonable degree of confidence.

Fixing by two or more ranges

This usually becomes necessary when visual bearings are not available. The
intersection of the range arcs fixes the ship’s position. This is the normal
method of fixing using radar and is described in detail in Chapter 15.

Radio fixing aids

Full details on fixes obtained from radio fixing aids are given in Volume III.
General comments on the use of radio fixing aids for coastal navigation may
be found in Chapter 12.
ERROR IN THE COMPASS AND ELIMINATING THE COCKED HAT 219

It should also be appreciated that it is quite possible to determine the position

separately by a radio aid and by visual means, yet find a significant (more
than 100 metres) difference in the latitude and longitude in each case. This
discrepancy may arise from the use of different geographical datums for the
different fixing sources, or it may arise from unknown errors in the radio aid
itself. So the navigator may have to adjust his radio aid fix to the visual one.
Such information may be available on the chart in the form of a datum shift.
If not, the discrepancy can be largely eliminated by comparing the radio aid
position line or fix with an accurate visual fix, adjusting the former to tie in
with the latter.
ERROR IN THE COMPASS AND ELIMINATING THE COCKED HAT
If it seems certain that the cocked hat is caused by compass error alone, then
the error must be determined and a correction applied to the plotted bearing.
In the first instance, check that any known error has been correctly
applied. A gyro error high must be subtracted from, and a gyro error low
added to, the gyro bearing (see Chapter 1). Variation and deviation westerly
must be subtracted from, and variation and deviation easterly added to, the
magnetic compass bearing (see Chapter 1). The deviation to be applied must
be for the compass course and not the compass bearing & this is a frequent
cause of error in the plotted bearings using a magnetic compass.
The error in the gyro compass and the deviation in the magnetic compass
may be checked by any of the following methods:
1. By a transit. The compass bearing of two charted objects is observed
when they are in line (see page 200) and the true or magnetic bearing
obtained from the chart. The difference between them will be the gyro
error or deviation of the gyro or magnetic compass respectively. For
example:
charted transit 079°
gyro compass bearing 081°
gyro error 2° high

charted transit (magnetic) 123°

magnetic compass bearing 120°
deviation (CADET) 3° east (Error East Compass Least)

2. By azimuth of a heavenly body. The error of the compass may be found

by comparing the observed bearing of a heavenly body with that
calculated. Details of the procedure are given on Weir’s azimuth diagram
(to be found in the Miscellaneous Chart Folio 317, see page 126) and in
Norie’s Tables (ABC Tables or Amplitudes and Corrections), and also
covered in the revised edition Volume II of this manual. The Amplitudes
Table (and Corrections) for the rising and setting heavenly body is the
most accurate procedure of the three. The HP-41CV calculator, outfit
PDQ, may also be used to calculate the true bearing of a heavenly body
using the Sight Reduction Table (SRT) sub-routine.
220 CHAPTER 9 - FIXING THE SHIP

3. By bearing of a distant object. The ship may be fixed by horizontal

angles, or may be in a known geographical position, e.g. South Railway
Jetty, Portsmouth Dockyard. An observed compass bearing of a distant
object* may then be compared with the bearing taken from the chart and
the error deduced.
4. By reciprocal bearings with another ship of known compass error.
5. By reduction of the cocked hat. If it seems certain that the cocked hat is
due to compass error alone, and none of the above four methods is
available to resolve it, then the cocked hat may be reduced and the error
found, as follows.
Assume the error has a definite sign (+) or (-) and is the same for
each bearing.† Although the actual bearings may be incorrect, the true
angles between the objects are known. Two angles may be obtained from
three objects. These angles may then be set on a station pointer or drawn
on a Douglas protractor (both instruments are described in Volume III)
and the position found by rotating the instrument until the arms or lines
go through the charted position of each object. The bearing of the
furthest object may then be taken from the chart and compared with the
observed bearing, the difference being the error in the compass. The
following example illustrates the procedure.

EXAMPLE
The following gyro bearings are taken:

Beacon Pt 342½°
Bolt Tail 048°
Bolt Head 094°

What is the gyro error?

The three bearings are plotted (Fig. 9-21) and a cocked hat is obtained.
The three bearings are drawn on the matt side of the Douglas protractor (Fig.
9-22), page 222), or the angles between the bearings, 65½° and 46°, are set
on the station pointer.
The protractor is placed on the chart, matt side down, and rotated until all
three lines are in contact with the charted objects. The position A may then
be pricked through on to the chart. A similar procedure is followed with the
station pointer.
If a station pointer or a Douglas protractor is not available, then a sheet
of tracing paper should be used instead (see page 225). Alternatively, each
bearing should be rotated in the same direction, the amount of rotation
varying directly with the estimated distance, until all three bearings pass
through a point (see Fig. 9-21).

* ½° subtends 100 yards at 6 miles. Provided that one’s position is known accurately to within 50 yards, it
should be possible to determine the error to the nearest ½°, using an object 6 miles away.

† The circumstances in which the errors in the three bearings may be separate and unequal are discussed in
Appendix 7.
ERROR IN THE COMPASS AND ELIMINATING THE COCKED HAT 221

Fig. 9-21. Reduction of the cocked hat

222 CHAPTER 9 - FIXING THE SHIP

Fig. 9-22. Douglas protractor

The true bearing of the furthest object is obtained from A and compared
with the observed bearing, e.g.

true bearing Bolt Head 097°

observed bearing Bolt Head 094°
gyro error 3° low

Revised bearings of 345½° and 051° are plotted from Beacon Point and
Bolt Tail respectively to confirm the error.
This example illustrates the danger of assuming that the position of the
ship must be somewhere inside the cocked hat. This may frequently not be
ERROR IN THE COMPASS AND ELIMINATING THE COCKED HAT 223

so, and an assumption on these lines could well place the ship in danger. In
Fig. 9-21, the correct position and the centre of the cocked hat are ¼ mile
apart.
If, however, the cocked hat is very small, then it should normally be safe
to assume the ship is in the centre. If, on the other hand, the cocked hat is
large yet it seems clear that the error is not due to any of the causes set out on
page 208, then almost certainly the fix should be disregarded, and either
another fix obtained, or reliance placed upon the EP. If the ship is in the
vicinity of danger, it may well be necessary to stop the ship and obtain an
accurate position.
If a cocked hat results from an inaccuracy of the survey or the chart as
may be the case, for example, in a channel where the charted sides do not
correlate, the position should be taken as that corner of the cocked hat which
puts the ship closest to danger, dependent upon her subsequent movements.
This is illustrated in Fig. 9-23. If, for example, the ship is intending to steer
to the northward, the position should be taken as X. If she intends rounding
the rocks to the southward, her position should be taken as Y, so that she has
sufficient advance before altering course. As a further precaution, the course
chosen from Y should be safe to clear the rocks had she actually been at Z.
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Fig. 9-23. Setting a safe course from a cocked hat fix |

In practice, where it is known that such inaccuracies exist, a sensible

precaution is to fix using one side of the channel only. If, in Fig. 9-23, the
224 CHAPTER 9 - FIXING THE SHIP

ship is intending to steer to the northward, then marks on the north side of the
channel should be chosen, and if steering to the southward, marks on the
south side. A cocked hat should not normally be created by accurate bearings
in these conditions. It is also a reasonable supposition that the position of the
off-lying rocks will probably be tied in with the survey of that particular piece
of coastline.

HORIZONTAL SEXTANT ANGLES (HSA) AND VISUAL BEARING

LATTICES
It sometimes becomes necessary to navigate to a higher degree of accuracy
than that obtainable from normal fixing, while at the same time plotting the
fix quickly and maintaining an accurate record of the ship’s movements.
Examples of the occasions when this may be necessary are mine
countermeasures operations, pilotage operations and the anchoring of ships
in company.
Two visual methods are available for this type of fixing !horizontal
sextant angles and bearing lattices. Radar and radio aids may also be used,
and the use of these is described in Volume III.
Fixing by horizontal sextant angles

This method fixes the ship’s position by the intersection of two or more
position lines; these are found by observing with a sextant the horizontal
angles subtended by three or more objects. The method is extremely useful
for fixing the ship accurately when moored or at anchor, and for fixing the
ship accurately at sea when two trained observers are available.
The advantages of the HSA fix are:
1. It is more accurate than a compass fix, because a sextant can be read more
accurately than a compass.
2. It is independent of compass errors.
3. The angles can be taken from any part of the ship.

The disadvantages are:

1. It can take longer than fixing by compass bearings.
2. Three suitable objects are essential.
3. If the objects are incorrectly charted or incorrectly identified, the fix will
be false and the error may not be apparent. For this reason, when a
poorly surveyed chart is used, the ship’s position should normally be
fixed by compass bearings, because inaccuracies in the charted positions
of objects will become apparent when lines of bearing drawn on the chart
from each object do not meet at a point.
Errors in HSA fixes are discussed in Appendix 7.

Horizontal sextant angles

A, B and C (Fig. 9-24) are three objects on shore approximately in the same
horizontal plane as the observer, and the angles between A and B, B and C are
measured. The ship must lie on the arc AOB containing the observed angle
between A and B, and on the arc COB containing the observed angle between
HORIZONTAL SEXTANT ANGLES (HSA) AND VISUAL BEARING LATTICES 225

B and C. The arcs intersect at B and O; thus, O is the ship’s position, as the
ship clearly cannot be at B.

Fig. 9-24. Fixing by two horizontal sextant angles

To plot the fix, the angles between A and B and between B and C are
drawn on a Douglas protractor or set on a station pointer as described on page
220. The instrument is then placed over the chart so that OA, OB and OC
pass through the charted positions of A, B, and C. O is then the ship’s
position.
To guard against incorrect identification, a check angle may be taken
between the centre object and a fourth object (D in Fig. 9-24). When a station
pointer is used, the fourth angle may be plotted after the fix has been
obtained ! by holding the instrument steady and moving the appropriate leg
to the check angle. This leg should then pass through the fourth object.
The fix shown in Fig. 9-24 would be recorded as follows:

A 39°12' B 50°47' C
B 73° 49' D

If a station pointer or Douglas protractor is not available, a piece of

tracing paper will suffice. The measured angles are drawn from any point on
the sheet of tracing paper. The paper is then placed on the chart and rotated
until all the lines are in contact with the charted objects. The position may
then be pricked through the tracing paper on to the chart.

Strength of the HSA fix

The strength or weakness of an HSA fix may be assessed by the angle of cut
between the position circles !the closer to 90°, the better the fix. A major
disadvantage of plotting the fix by station pointer or Douglas protractor or
tracing paper is that none of these methods shows the position circles.
The position circles may be drawn on the chart using a simple
geometrical construction and the angle of cut assessed as shown in Fig. 9-25.
226 CHAPTER 9 - FIXING THE SHIP

A fix is recorded as follows:

A 34°15' B 51°16' C

The perpendicular bisectors to AB and BC are drawn !HF and KG

respectively. The centres O1 and O2 of the two relevant position circles
through AB and BC may be found as follows (see formula A6.2):

½d
DO1 = x1 = = 37.45 mm
tan 34° .25

½e
EO2 = x2 = = 30.48 mm
tan 51° .2667

where d is the distance on the chart between A and B and e the distance
between B and C.
The two position circles, radii AO1 and BO2, may now be plotted and the
fix at L established.

Fig. 9-25. Plotting the HSA fix

HORIZONTAL SEXTANT ANGLES (HSA) AND VISUAL BEARING LATTICES 227

The angle of cut between the two position circles is immediately apparent
and the closer this is to 90°, the stronger the fix. The angle of cut should if
possible never be less than 30°. In Fig. 9-25, the angle of cut as L is about
70°.
If the two angles are small, say about 20° and 30°, the weakness of the fix
may be overcome to a greater extent by plotting a third position circle through
the two outer marks. (This would be a circle through A, L, C, in Fig. 9-25).

Choosing objects
Objects should be chosen so that at least one of the following conditions
applies:

1. Objects are either all on or near the same straight line, and the centre
object is nearest the observer (Fig. 9-26).
2. The centre object is nearer the ship than the line joining the other two
(Fig. 9-27, p.228).
3. The ship is inside the triangle formed by the objects or on the outer edge
(Fig. 9-28, p.228).
4. At least one of the angles observed changes rapidly as the ship alters
position.

The sum of the two angles should be more than 50°. Better results will
be obtained if neither angle is less than 30°.

Fig. 9-26. Suitable objects for a station pointer fix (1)

228 CHAPTER 9 - FIXING THE SHIP

Fig. 9-27. Suitable objects for a station pointer fix (2)

Fig. 9-28. Suitable objects for a station pointer fix (3)

HORIZONTAL SEXTANT ANGLES (HSA) AND VISUAL BEARING LATTICES 229

When not to fix using horizontal angles

If the ship and the objects observed are all on the arc of the same circle (Fig.
9-29), the two position circles become one and the two angles will cut at any
point on the arc. A horizontal angle fix is impossible in these circumstances.
In Fig. 9-29, the beacon should have been chosen and not the chimney.
It should also be noted that, if such a fix is attempted using bearings and
there is an unknown error in the compass, this error will not be revealed by
plotting. The angles between the objects will be correct but the plotted
bearings will always meet at a point on the arc of the circle. The plotted
position will differ from the actual position dependent on the amount of the
unknown error.
Never fix the ship by horizontal angles or bearings when the ship and the
objects observed are all on the arc of the same circle.

Fig. 9-29. When not to fix by HSA or bearings

230 CHAPTER 9 - FIXING THE SHIP

Rapid plotting without instruments

To enable fixes obtained from HSAs to be plotted rapidly without
instruments, a lattice of HSA curves (Fig. 9-30) may be constructed on the
chart. Sets of curves are plotted from each of two pairs of marks and, if the
angle between each pair is observed simultaneously, the fix may be plotted
immediately at the intersection of the two curves.
The construction of the HSA lattice is given in Appendix 6.

Fig. 9-30. Lattice of HSA curves

Bearing lattices

The bearing lattice is illustrated in Fig. 9-31. An interlocking lattice of

bearing lines from two visual conspicuous objects suitably placed to give an
acute angle of cut as close as possible to 60° to 90° (a minimum angle of cut
of 30° is acceptable) is drawn on the chart to be used. In Fig. 9-31, the acute
angle of cut varies between 55° and 90°. Depending on the distance of the
objects and the scale of the chart, lines may be drawn 1° to 5° apart. In Fig.
9-31, the lines are drawn 5° apart, while two ‘boxes’ are illustrated at 1°
apart.
HORIZONTAL SEXTANT ANGLES (HSA) AND VISUAL BEARING LATTICES 231

Fig. 9-31. Bearing lattice

232 CHAPTER 9 - FIXING THE SHIP

If the intended track is then drawn on the chart, in this case 315° towards
an anchorage in Cawsand Bay, a simultaneous reading and plotting of the two
bearings will give the ship’s position immediately and thus the distance off
track. For example, if the two bearings are 340° and 055°, it will be seen at
once that the ship is some 50 yards off track to port. The intersection of two
bearings 343½° and 082½° shows that the ship is 160 yards to starboard of
track. If the two bearings at the time of anchoring are 001° and 088°, the ship
is slightly to starboard of track by about 30 yards.
To ensure as accurate a track as possible, it is essential that the error of
the gyro-compass is checked and allowed for. It is as well to remember that
the error does not necessarily remain constant (see Volume III) and so it is
important to check the compass on each leg of the run.

THE SELECTION OF MARKS FOR FIXING

Choosing objects
Chosen marks should be at least 30° apart in bearing. Ideally, when three
objects are observed, they should be 60° apart, two objects, 90°.

Fig. 9-32. Effect of a 5° error at various angles of cut

Fig. 9-32 illustrates the difference in position caused by an error of 5°

with two cuts of 90° and 20°, A being the correct and B the incorrect position.
The closer the object, the less will be the difference in position resulting
from any error in the bearing.
The chosen marks should not be on the circumference of the same circle
as the ship, because any unknown error in the compass will not be revealed
when the bearings are plotted (see Fig. 9-29).
Marks should also be charted, identifiable, visible from the same repeater
if possible, and ahead of the ship rather than astern. When navigating in
channels, marks should be selected from one side only to avoid any possible
discrepancy arising from a different geographical datum, etc.
THE SELECTION OF MARKS FOR FIXING 233

Fixing procedure*
1. Look at the chart and select likely marks.
2. Check from the present position (DR or EP) the bearings of the objects
to be used.
3. Look out from the bridge and find the marks. It may be necessary to look
along the expected bearing with the binoculars if the object is difficult to
see. Have at least three marks available; it is no use taking the bearing
of one and then having to cast about to find the others.
4. Write down the names of the objects in the Note Book.
5. Observe the bearings as quickly as possible, those ahead and astern first,
those for objects whose bearing is changing most rapidly last.† Ideally,
the time of the last bearing, which is the time of the fix, should coincide
with a DR/EP time on the chart (see page 192). Subsequent chartwork is |
simplified.
6. Note the bearings and the time in the Note Book (see Fig. 8-13).
7. Plot the fix using the correct symbols (see Chapter 8) and the time. If
using the magnetic compass, remember that the deviation to be applied
is that for the ship’s head at the time of observation.
8. Check the DR/EP, verify tidal stream, etc., lay off further DR/EP. Assess
the expected bearings of marks for the next fix.
9. Verify time to ‘wheel over’ (if applicable).
10. Return to lookout.

This procedure should not take the practised navigator more than 1 minute
(see page 193).
If the fix does not fit, it must not be fudged. It needs to be reworked to
eliminate errors (see page 208) or retaken. If there is doubt about the ship’s
position and one is in the vicinity of danger, it may well be a wise precaution
to stop the ship. This may prevent a grounding.
The fix shows where the ship was, and the chartwork is not complete
until the DR/EP has been laid off from it. The present DR/EP must always
be on the chart, also the predicted track at least as far ahead as the time of the
next intended fix and the next ‘wheel over’ if within a reasonable time, say
15 to 20 minutes. (See also the section in Chapter 8 on chartwork on
passage.)

Short cuts to fixing

With experience the navigator will develop short cuts to fixing. Examples of
these are as follows, but it should be emphasised that these are not
recommended for beginners.
1. The fastest changing bearing will be observed at the exact intended time
for the fix: the other bearings will be observed just before or just after
this time.
2. The last two digits only of each bearing will be noted, all three bearings
being written in the Note Book after the last has been taken.
3. Immediate corrective action, if necessary, will be taken on plotting the
fix; the DR/EP will then be generated, and finally the Note Book
completed.

* Fixing procedure using an assistant is described in Chapter 13.

† A slightly different procedure is desirable when anchoring (see Chapter 13).
234 CHAPTER 9 - FIXING THE SHIP

Fig. 9-33. ‘Shooting up’ shore objects

THE SELECTION OF MARKS FOR FIXING 235

‘Shooting up’
The navigator must always think ahead as to the next suitable object to use
for fixing, when navigating along the coast. The procedure to identify suitable
marks is known as ‘shooting up’. There are several methods available.

1. DR/EP
(a) Check from the DR/EP the bearing of a suitable object selected from
the chart.
(b) Look along the bearing at the appropriate time, and identify the
object. This is illustrated in Fig. 9-33. A fix is obtained at 0900,
course 060° speed 15 knots. It is required to identify Caerhays
Castle. From the DR position at 0906, Caerhays Castle should bear
002° and just be visible east of the 50 m contour line.
2. Transits
(a) Check from the chart the bearing of the chosen object when it comes
into transit with a known one.
(b) When the known object is on this bearing, the chosen object should
be seen to be in transit (assuming the error in the compass is
known).
In Fig. 9-33, Crinnis Hotel ¾ mile ENE of Charlestown Harbour may be
identified by its transit with Gwineas Rock, 008½° just before 0920.
3. Bearings
(a) Take the bearings of three known objects and at the same time
observe the bearing of a fourth object requiring identification.
(b) Plot the fix.
(c) From the fix plot the fourth bearing and identify the object.
In Fig. 9-33:
þ Dodman Point 271½°
ï
0928 ý Gwineas Rock 318°
ï
ü Crinnis Hotel 355°
At the same time, a large red and white beacon bore 018°. This may be
identified by plotting 018° from the fix and is seen to be the conspicuous
daymark on Gribbin Head.

Identification of uncharted objects

It sometimes happens that a shore object or buoy is visible from the ship but
is not shown on the chart. Its position may be determined by bearings or
transits in a similar manner to that already described. Fig. 9-34 illustrates the
determination of the position of an uncharted buoy, first by bearings, secondly
by transits.
Once a shore object has been identified and plotted in this manner, it may
be used for fixing the ship.
 236 CHAPTER 9 - FIXING THE SHIP

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 237

CHAPTER 10
Visual and Audible Aids to Navigation

This chapter deals in detail with four aids to navigation: lights, buoys and
beacons, and fog signals, introduced earlier in Chapters 6 and 7.

LIGHTS

Details of lights may be found as follows:

1. On Admiralty charts, where they are distinguished by a light star and a

magenta flare. The greatest detail will usually be found on the largest
scale charts; the amount of detail reduces as the scale of the chart
decreases, as explained in Chapter 6.
2. In the Admiralty List of Lights and Fog Signals (NP 74 to 84), where
additional information not given on charts is included.
3. In the Admiralty Sailing Directions (NP 1 to 72), where only the height
and a description of the light structure is usually to be found.

Characteristics of lights
In order to be correctly identified, a light must maintain a consistent character
and exhibit a distinctive appearance. This appearance is called the character
or characteristic of the light. The principal characteristics are usually the
sequence of light and darkness and, in some cases, the colour of the light.
The colour of a light may be: Blue (Bu); *Green (G); Red (R); White (W);
Violet (Vi); Yellow or Orange (Y).* The letters in brackets are the
recognised international abbreviations printed on charts and in the List of
Lights and Fog Signals. The symbol (W) is sometimes omitted from the
description on the chart.

Classes of light
Lights may be divided into three classes, fixed, rhythmic and alternating.
Fixed lights are those exhibited without interruption. Rythmic lights are those
showing a sequence of intervals of light and dark, the whole sequence being
repeated at regular intervals. The time taken to complete one sequence is
called the period of the light. Each element of the sequence (e.g. a flash, an
eclipse) is called a phase. The characteristic of a rhythmic light may be
flashing, quick flashing, isophase or occulting (see Table 10-1, pages 238-
241)according to the relative duration of light and darkness. At short
distances in clear weather, flashing lights may show a faint continuous light.
Alternating
(Text cont. on page 242)

*Abbreviations for blue and orange lights which may still be found on some older Admiralty charts are Bl and Or
respectively.
238 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

Table 10-1. Characteristics of lights

LIGHTS 239
240 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

Table 10-1 (cont.)

LIGHTS 241
242 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

lights are rhythmic lights showing different colours during each sequence.
The period of an alternating light is the time taken to exhibit the complete
sequence including the change of colour.
The table, which the reader should study closely, gives details of the
various lights and includes a representation of the characteristics of different
types of light. It also shows the abbreviations to be found on modern charts.

Admiralty Lists of Lights and Fog Signals (NP 74 and 84)

A summary of the information available in the Admiralty List of Lights and
Fog Signals was given in Chapter 7. The full description of a light is
tabulated in the List of Lights in eight columns:

Column 1 (number). The number assigned to the light, and prefixed by

the List volume letter, is the International Number and should be quoted when
the light is referred to.
Column 2 (name and position). The place, e.g. FALMOUTH
HARBOUR, is printed in capitals. Those lights with a range of 15 miles and
over are printed in bold type. Light-vessels are printed in ITALIC
CAPITALS, all other floating lights* in italics. The letter in brackets after the
name indicates the authority responsible for maintaining the light; e.g. in
Volume A, (T) is Trinity House, London, (N) the Northern Lighthouse Board,
(I) the Commissioners of Irish Lights, and so on.
Column 3 (latitude and longitude). The latitude and longitude given for
the light are approximate.
Column 4 (characteristics and intensity). Lights with differing intensities
may appear to change their character at different distances because a part of
the character may not be visible. Lights exhibiting a very short flash may not
be visible at the maximum range calculated from the luminous range diagram
(see page 248). The intensity of lights may also be given in this column in
some volumes; if so, the candle power in candelas is given in italics.
Intensities are not listed for lights in countries where nominal range (see
below) is used. The duration of light and darkness is subject to some degree
of fluctuation caused by slight variations in the working speed of the
apparatus. The duration of a flash may also appear to be less than normal
when seen from a great distance, and haze has the same apparent effect.
Column 5 (elevation in metres). The elevation of the light is the vertical
distance between the focal plane of the light and the level of Mean High
Water Springs or Mean Higher High Water, whichever is given in Admiralty
Tide Tables (see Chapter 11) or, where there is no tide, above Mean Sea
Level.
Column 6 (nominal range, luminous range). The range of visibility is
dealt with in details below. A rhythmic light produced by a rotating
apparatus may be detected by its loom at ranges greater than that calculated.
Loom is the diffused glow observed from a light below the horizon caused by
atmospheric scattering. It is possible on occasion to obtain a satisfactory
bearing from the loom.
*Details of light-buoys, etc. of an elevation of less than 8 metres are occasionally included in the List of
Lights.
LIGHTS 243

Column 7 (structure and height in metres). The height is normally

measured from the top of the structure to the ground although this may be
different for some areas as shown in the volumes. Where the colour divisions
of the structure are horizontal, the term bands is used, where vertical, stripes
and, where the marking is in the form of a spiral, diagonal stripes. The shape
of top marks is often shown diagrammatically, e.g. ‘Orange on white
structure’, ‘Red and white on white mast’.

Column 8 (Remarks). Phase is normally expressed to tenths of a second

and printed in italics.
The limits of sectors and arcs of visibility and the alignment of direction
lights and leading lights are given as seen by an observer from seaward. All
bearings refer to the true compass and are measured clockwise from 000° to
359°.

Sometimes a light shows the same colour over separate sectors but with
a different intensity. The ranges corresponding to the different intensities
will be listed in column 6, while details of the less intense or unintensified
sector will be listed in column 8. The different intensity values may also be shown.
Fig. 10-1 (page 244) shows a chart extract giving details of Saint
Anthony Head Light. The relevant List of Lights (Volume A) contains the
following information:

Column 1 0062
Column 2 Saint Anthony Head
(T)
Column 3 50 08.4
5 00.9
Column 4 OcWR 15s
Horn 30s
Column 5 22
Column 6 W22
W20
R20
Column 7 White 8-sided tower
19
Column 8 ec 3.7. W295° - 004° (69°), R004° - 022° (18°) over
Manacle rocks, W (unintens) 022° - 100° (78°), W100°
- 172° (72°). Fog Det Lt LF1 W 5min (fl 5s) 18m. 16
M. Vis 148.2° - 151.3° (2.5°). Shown throughout 24
hours.
bl 3

Saint Anthony Head Light is occulting with a period of 15 seconds,

showing a white or red light over different sectors (column 4). The period
consists of two elements (phases): 3.7 seconds darkness (ec - eclipse 3.7,
column 8) and 15 - 3.7 = 11.3 seconds light. The light changes its colour in
various sectors as set out in column 8. These sectors are also shown on the
chart. The ranges of the light are given in column 6: 22 and 20 miles for the
white sectors, 20 miles for the red sector. The unintensified white sector
where the range is 20 miles is detailed in column 8 and is also shown on the
chart.
244 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

Fig 10-1. Saint Anthony Head Light including the light sectors
LIGHTS 245

Details of the fog detector lights (see below) are given in column 8 and
those of the fog signal (see page 266) are given in column 5 and 8.
The elevation of the light is 22m above Mean High Water Springs
(column 5) and the light is displayed from a white eight-sided tower 19m high
(column 7).

Minor lights
Column 8 in the List of Lights also gives details of minor lights. These have
special uses; some are shown in Fig. 10-2.

1. Sector lights. These are lights presenting different appearances, either of

colour or character, over various parts of the horizon.

Fig 10-2. Light symbols on fathoms and metric charts

246 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

2 Leading lights. Two or more lights are positioned so as to form a leading

line (see Chapter 13). Lights described as ‘Lts in line’ are particular
cases intended to mark limits of areas, alignment of submarine cables,
etc.
3. Directional light. This is a light showing over a very narrow sector,
forming a single leading light. This sector may be flanked by sectors of
greatly reduced intensity, or by sectors of different colours or character.
Directional lights are also used to mark the limits of areas, etc. in the
same way as Lts in line. Some directional lights have a moiré effect.
These show the observer if he is on the centre line, or the alteration of
course to regain the track.
4. Vertical lights. These are two or more lights disposed vertically (or
horizontally, or in a geometric shape) to give a character or appearance
different from normal (single) lights.
5. Fog detector lights. The purpose of fog detector lights is to detect fog
automatically and to switch on fog signals. Visibility range at the station
may be automatically transmitted to a data centre for broadcast to
mariners. Fog detector lights may be fitted to the structure of a light
station or may be positioned some distance from the light. There are a
variety of types in use, some only visible over a narrow arc, some
exhibiting a powerful bluish white flash; others may sweep back and
forth and can therefore be mistaken for signals. Fog detector lights
operate by day and night.
6. Emergency lights. Emergency lights are automatically actuated by a
failure of the main light and are usually or lesser intensity. They may
well have a standard character for the country concerned. Some countries
(e.g. Canada) have installed them.

Range of lights
There are two criteria for determining the maximum range at which a light
can be seen. First, the light must be above the horizon. This depends on:
1. The elevation of the light.
2. The curvature of the Earth.
3. The height of eye of the observer.
Secondly, the light must be powerful enough to be seen at this range. This
depends on:
1. The power (intensity) of the light.
2. The prevailing visibility.
Various terms are used to describe the range of a light and these are set out
below.

Geographical range
Geographical range* is the maximum distance at which a light can reach an
observer as determined by the height of the observer, the height of the
structure and the curvature of the Earth. Geographical range is tabulated in
the List of Lights and an extract is shown in Table 10-2.
*Until 1972, the geographical range of a light for an observer’s height of 5m or 15ft was inserted on charts
unless luminous range was less, in which case the latter was inserted. New Editions of charts published since
31st March 1972 show luminous or normal range.
LIGHTS 247

Table 10-2. Geographical Range Table

Elevation Height of Eye of Observer in feet/metres

in
ft 3 7 10 13 16 20 23 26 30 33 39 46 52
m 1 2 3 4 5 6 7 8 9 10 12 14 16

Range in Sea Miles

0 0 2.0 2.9 3.5 4.1 4.5 5.0 5.4 5.7 6.1 6.4 7.0 7.6 8.1
3 1 4.1 4.9 5.5 6.1 6.6 7.0 7.4 7.8 8.1 8.5 9.1 9.6 10.2
7 2 4.9 5.7 6.4 6.9 7.4 7.8 8.2 8.6 9.0 9.3 9.9 10.5 11.0
10 3 5.5 6.4 7.0 7.6 8.1 8.5 8.9 9.3 9.6 9.9 10.6 11.1 11.6
13 4 6.1 6.9 7.6 8.1 8.6 9.0 9.4 9.8 10.2 10.5 11.1 11.7 12.2
16 5 6.6 7.4 8.1 8.6 9.1 9.5 9.9 10.3 10.6 11.0 11.6 12.1 12.7
20 6 7.0 7.8 8.5 9.0 9.5 9.9 10.3 10.7 11.1 11.4 12.0 12.6 13.1
23 7 7.4 8.2 8.9 9.4 9.9 10.3 10.7 11.1 11.5 11.8 12.4 13.0 13.5
26 8 7.8 8.6 9.3 9.8 10.3 10.7 11.1 11.5 11.8 12.2 12.8 13.3 13.9
30 9 8.1 9.0 9.6 10.2 10.6 11.1 11.5 11.8 12.2 12.5 13.1 13.7 14.2
33 10 8.5 9.3 9.9 10.5 11.0 11.4 11.8 12.2 12.5 12.8 13.5 14.0 14.5
36 11 8.8 9.6 10.3 10.8 11.3 11.7 12.1 12.5 12.8 13.2 13.8 14.3 14.9
39 12 9.1 9.9 10.6 11.1 11.6 12.0 12.4 12.8 13.1 13.5 14.1 14.6 15.2
43 13 9.4 10.2 10.8 11.4 11.9 12.3 12.7 13.1 13.4 13.7 14.4 14.9 15.4
46 14 9.6 10.5 11.1 11.7 12.1 12.6 13.0 13.3 13.7 14.0 14.6 15.2 15.7
49 15 9.9 10.7 11.4 11.9 12.4 12.8 13.2 13.6 14.0 14.3 14.9 15.5 16.0
52 16 10.2 11.0 11.6 12.2 12.7 13.1 13.5 13.9 14.2 14.5 15.2 15.7 16.2
56 17 10.4 11.2 11.9 12.4 12.9 13.3 13.7 14.1 14.5 14.8 15.4 16.0 16.5
59 18 10.6 11.5 12.1 12.7 13.2 13.6 14.0 14.4 14.7 15.0 15.7 16.2 16.7
62 19 10.9 11.7 12.4 12.9 13.4 13.8 14.2 14.6 14.9 15.3 15.9 16.5 17.0
66 20 11.1 12.0 12.6 13.1 13.6 14.1 14.5 14.8 15.2 15.5 16.1 16.7 17.2
72 22 11.6 12.4 13.0 13.6 14.1 14.5 14.9 15.3 15.6 15.9 16.6 17.1 17.7
79 24 12.0 12.8 13.5 14.0 14.5 14.9 15.3 15.7 16.0 16.4 17.0 17.6 18.1
85 26 12.4 13.2 13.9 14.4 14.9 15.3 15.7 16.1 16.4 16.8 17.4 18.0 18.5
92 28 12.8 13.6 14.3 14.8 15.3 15.7 16.1 16.5 16.8 17.2 17.8 18.3 18.9
98 30 13.2 14.0 14.6 15.2 15.7 16.1 16.5 16.9 17.2 17.5 18.2 18.7 19.2
115 35 14.0 14.9 15.5 16.1 16.6 17.0 17.4 17.8 18.1 18.4 19.1 19.6 20.1
131 40 14.9 15.7 16.4 16.9 17.4 17.8 18.2 18.6 18.9 19.3 19.9 20.4 21.0
148 45 15.7 16.5 17.1 17.7 18.2 18.6 19.0 19.4 19.7 20.0 20.7 21.2 21.7
164 50 16.4 17.2 17.9 18.4 18.9 19.3 19.7 20.1 20.5 20.8 21.4 22.0 22.5
180 55 17.1 17.9 18.6 19.1 19.6 20.0 20.4 20.8 21.2 21.5 22.1 22.7 23.2
197 60 17.8 18.6 19.3 19.8 20.3 20.7 21.1 21.5 21.8 22.2 22.8 23.3 23.9
213 65 18.4 19.2 19.9 20.4 20.9 21.4 21.7 22.1 22.5 22.8 23.4 24.0 24.5
230 70 19.0 19.9 20.5 21.1 21.5 22.0 22.4 22.7 23.1 23.4 24.0 24.6 25.1
246 75 19.6 20.5 21.1 21.7 22.1 22.6 23.0 23.3 23.7 24.0 24.6 25.2 25.7
262 80 20.2 21.0 21.7 22.2 22.7 23.1 23.5 23.9 24.3 24.6 25.2 25.8 26.3
279 85 20.8 21.6 22.2 22.8 23.3 23.7 24.1 24.5 24.8 25.1 25.8 26.3 26.9
295 90 21.3 22.1 22.8 23.3 23.8 24.2 24.6 25.0 25.4 25.7 26.3 26.9 27.4
312 95 21.8 22.7 23.3 23.9 24.3 24.8 25.2 25.5 25.9 26.2 26.8 27.4 27.9
328 100 22.3 23.2 23.8 24.4 24.9 25.3 25.7 26.1 26.4 26.7 27.3 27.9 28.4
Luminous range
The luminous range is the maximum distance at which a light can be seen,
determined only by the intensity of the light and the visibility at the time.
Luminous range takes no account of elevation, observer’s height of eye or the
curvature of the Earth. A luminous range diagram is to be found in the List
of Light (Fig 10-3, p.248).
248 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

Fig 10-3. Luminous range diagram

LIGHTS 249

Nominal range
Nominal range is normally the luminous range for a meteorological visibility
of 10 miles, and is the one most frequently used for the range of lights shown
in the List of Lights and on Admiralty charts. The relationship between
candle power (candelas) and nominal range may be seen from Fig 10-3. For
each, a light with the candle power of 1 million candelas has a nominal range
of just under 26 miles, while a light with a candle power of only 1000
candelas has a nominal range of just over 9 miles.

Range displayed in the List of Lights

The type of range used for the light is given in the ‘Special Remarks’ section
of the appropriate volume. As a rule, the ranges given in column 6 of the
tables are nominal ranges (e.g. the British Isles) but there may be exceptions
(e.g. Cuba) where the range given is luminous range and, in these cases, the
intensity of the light in candelas will usually be displayed in column 4.
Countries using luminous range generally use a meteorological visibility of
20 miles for determining the range of the light in column 6, and not 10 miles
as it is the usual practice for nominal ranges.

Determining the maximum range of a light

The range at which a light will be seen by the observer will be either the
geographical or the luminous range, whichever is the less. It is necessary to
work out each range.

EXAMPLE 1
Height of eye 12 metres, estimated visibility 15 miles; disregarding height of
tide, at what range should the Lizard Light (A0060) be sighted? The
elevation of the light is 70 metres (column 5). Nominal range (column 6) is
29 miles.
Geographical range. This can be read off directly from the Geographical
Range Table for a height of light 70 metres and height of eye 12 metres.
Geographical range* is 24'.0.
Luminous range. Enter the luminous range diagram (Fig. 10-3) from the
top border for 29 miles nominal range and determine where the vertical line
from this point cuts the visibility range curve for 15 miles (which must be
interpolated between the 20 mile and 10 mile visibility curves). From this
second point move horizontally to the left-hand border and read off the
luminous range. In this case, luminous range is 38 miles.
This means that, although the intensity of the light and the visibility
would give a range of 38 miles, because of the height of the eye the light must
be well below the horizon at this range and therefore cannot be seen by the
observer. The loom of the light may of course be visible.
The range at which the light itself will be sighted is therefore the lesser
of the geographical and luminous ranges, 24'.0.

* The Geographical Range Table in the List of Lights is based upon a particular allowance for refraction (see
Chapter 9, page 203).
250 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

EXAMPLE 2
Given the same situation as in Example 1 but with the visibility now down to
5 miles, at what range should the light be sighted?
As before, geographical range is 24'.0.
Luminous range. Follow the same procedure as in Example 1, but this
time drop vertically to the point where the 29 miles nominal range cuts the 5
mile visibility curve and read across to the left-hand border, where the
luminous range may be found in this case 16'.5.
This time, although the light will be above the horizon at a range of 24
miles, because of the 5 mile visibility, the intensity of the light is such that it
should be seen at 16'.5.
Once again the range at which the light will be sighted is the lesser of the
two, 16'.5.
It will be noted from these two examples that lights may be sighted at a
range in excess of the estimated meteorological visibility, dependent on the
light’s intensity.
Luminous range, intensity given in the List of Lights
When the range given in column 6 of the List of Lights is luminous rather
than nominal, the range diagram should be entered from the bottom border
for the intensity (column 4 of the List) followed by the same procedure as
before.
EXAMPLE 3
Height of eye 10 metres, estimated visibility 5 miles. Disregarding height of
tide, at what range should Punta Gobernadora Light (J4836) be sighted?
Height of the light is 33 metres, luminous range (column 6) 46 miles,
intensity (column 4) 3 million candelas.
Geographical range is 18'.0.
Luminous range. The luminous range diagram (Fig. 10-3) is entered from
the bottom border for 3 million candelas, vertically up to the 5 mile visibility
curve, then horizontally to the left-hand border, where the luminous range
may be found, 16'.4.
The range at which the light should be sighted is again the lesser of the
two, 16'.4.
Luminous range, intensity not given in the List of Lights
If the candle power or intensity of the light is not listed, the range may be
found as follows.
Enter the diagram (Fig. 10-3) at the left-hand border with the luminous
range given in column 6 of the List of Lights, move horizontally to the right
until the 20 mile visibility curve (see page 249) is reached, then vertically up
or down until the actual visibility curve is met, then read back across to the
left-hand column, where the range at which the light may be seen to the
prevailing visibility may be obtained. Either this or the geographical range,
whichever is the less, will be the expected sighting range.
Light-vessels, lanbys, light-floats
A light-vessel is a manned vessel anchored as a floating aid to navigation,
from which is exhibited a light which may have any of the characteristics of
a lighthouse except sectors.
LIGHTS 251

A lanby (large automatic navigational buoy) is a very large unmanned

light-buoy used as an alternative to a light-vessel to mark offshore positions
important to navigation. Lanbys vary in size up to a displacement of 140
tonnes and a diameter or height of 12 metres.
A light-float is a boat-like structure used instead of a light-vessel or light-
buoy in waters where strong tidal streams or currents are experienced. Light-
floats may vary considerably in size from the size of light-vessels or lanbys
down to ordinary light-buoys. They are unmanned.
The regulations concerning light-vessels are normally found in the special
remarks section of the List of Light. Fully details of light-vessels, lanbys and
light-floats may be found in the body of the List of Lights, provided that the
structure is more than 8 metres high. Brief details are also to be found in the
Admiralty Sailing Directions. Details are also given on the Admiralty chart,
as for lights in general (see page 237).

Remarks on light-vessels, etc

The following remarks refer to light-vessels and lanbys off the coats of the
British Isles, also light-floats where these are listed in Volume A of the List
of Lights. Information relating to other areas of the world may be found in
the appropriate List of Lights or Sailing Directions.

1. Light-vessels, lanbys and light-floats are painted red with the name in
white letters.
2. The elevation given in column 5 of the List of Lights is the distance from
the waterline to the centre of the lantern.
3. A fixed white riding light is exhibited from the forestay, 2 metres above
the rail, to show the direction in which the floating structure is swung.
This direction gives a useful indication of the direction of the tidal
stream.
4. If for any reason the usual light characteristics cannot be shown while on
station, the riding light only is shown.
5. A light-vessel watch buoy is sometimes laid to give an indication of
dragging. These buoys are conical, painted yellow, with ‘LV Watch’ in
black letters.
6. If a light-vessel is off her proper station, the light characteristics are not
shown, nor the fog signal sounded. In addition, the following signals are
displayed:
By day: Two large black balls, one forward, one aft; the International
Code signal ‘LO’ meaning ‘I am not in my correct position’ should be
hoisted where it may best be seen.
By night: A fixed red light will be shown at the bow and stern; in
addition, red and white flares will be shown simultaneously every 15
minutes or more frequently on the approach of traffic.
7. During fog or low visibility, on the near approach of any traffic, the bell
of the light-vessel will be rung rapidly in the intervals between sounding
the normal fog signals. If the normal fog signal is made by hand horn,
the period of the signal is shortened as shipping approaches, becomes
continuous in a dangerously close situation.
8. Neither 6 nor 7 applies to light-floats and lanbys, which are unmanned.
However, an automatic shore monitoring system may be available which
252 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

keeps the position of these floating structures under surveillance. If the

structure is observed to move off station, an appropriate radio
navigational warning is sent out.
9. Light-vessels, lanbys and light-floats are liable to be withdrawn for
repairs without notice and, in some cases, are not replaced by a relief
vessel. Relief vessels usually carry the word ‘Relief’ or ‘Reserve’.
10. Details of distress signals made from light-vessels may be found in the
List of Lights.

Lights on oil and gas platforms, drilling rigs and single point moorings
Details of lights displayed by permanent platforms and drilling rigs may be
given in the appropriate volume of the List of Lights. For example, in waters
around the British Isles, details are given in the ‘Special Remarks’ section
and also in the body of Volume A. Notification of the movement and
position of drilling rigs is given in radio navigational warnings issued for
NAVAREA I (see Chapter 6). Further details are given in the Annual
Summary of Admiralty Notices to Mariners. Permanent oil and gas
installations are shown on the Admiralty chart, where scale permits.
Not all light lists give full details of these lights. For example, in Volume
J of the List of Lights, despite the fact that numerous oil rigs may be found in
the Gulf of Mexico, details are not given in this volume other than a few
general remarks. Recourse must be had to the appropriate charts of the area
and radio navigational warnings.
The Sailing Directions should always be consulted for information on
permanent platforms, drilling rigs, etc.

Other types of light

Details of other types of light that may be encountered at sea are given below.

Aeromarine lights. These are marine type lights in which a part of the
beam is deflected to an angle of 10° to 15° above the horizon for the use of
aircraft. These lights are usually listed as ‘Aeromarine’ in column 8 of the
List of Lights.
Aero lights. These lights are displayed primarily for the use of aircraft
and are often of greater intensity and elevation than lights used for marine
navigation. Those likely to be seen from seaward are detailed in the List of
Lights; their character (column 4) is always preceded by the word ‘Aero’.
These lights should always be used with caution, as any changes may not be
promptly notified to the mariner.
Obstruction lights. These mark radio towers, chimneys and other
obstructions to aircraft. They are not maintained for marine navigation; thus,
they should be used with caution, as for aero lights. They are usually red and
may be fixed, flashing or occulting.
Obstruction lights of high intensity, and likely to be visible from seaward
for some distance, are listed with the character preceded by ‘Aero’ in column
4 and with the legend ‘Obstruction’ in column 8. Those of less intensity are
classified as minor lights and mentioned in column 8.
Daytime lights. These are lights which are exhibited throughout the 24
hours without change of character. Information is given in column 8 of the
LIGHTS 253

List of Lights. If by day there are any differences in the character, these are
preceded by the word ‘By day’ in column 4. By day, the intensity may be
increased,
Fog lights. The characteristics of lights shown only in reduced visibility
are preceded by the words ‘In fog’ in column 4.
Occasional lights. These are lights exhibited only when specially needed.
Examples are:
Tidal lights, exhibited only when the tide serves.*
Fishing lights, for the use of fishermen.
Private lights, maintained by a private authority for its own purpose.
Notes on using lights
The following points should be remembered when using lights for navigation.
1. The characteristics of the light must always be checked on sighting.
2. The refraction and the height of tide may well alter the geographical
range. The raising or dipping range of the light can only be approximate,
and must be used with caution if being used as a position line (see
Chapter 9).
3. Lights placed at a great height - for example, on the Spanish coast - are
often obscured by cloud.
4. The distance of an observer from a light cannot be estimated from its
apparent brightness.
5. The distance at which lights are sighted varies greatly with atmospheric
conditions. It may be increased by abnormal refraction. It will be
reduced by fog, haze, dust, smoke or rain - a light or low intensity is
easily obscured in any of these conditions, and even the range of a light
of great intensity may be considerably reduced. Thus ranges at which
lights first appear can only be approximate. It should be remembered that
there may be fog or rain in the vicinity of the light even though it is clear
at the ship.
6. In cold weather, and more particularly with rapid changes of weather, the
lantern glass and screens are often covered with moisture, frost or snow,
which can greatly reduce the sighting range. Coloured sectors may
appear more or less white, the effect being greatest with green lights of
low intensity.
7. The limits of sectors should not be relied upon and should always be
checked by compass bearing. At the boundaries of sectors there is often
a small arc in which the light may be obscured, indeterminate in colour,
or white. However, some modern sector light boundaries are defined to
a much greater degree of accuracy than for older lights.
8. The limits of arcs of visibility are rarely clear cut, especially at short
ranges.
9. In certain atmospheric conditions, white lights may have a reddish hue.
10. Glare from background lighting reduces considerably the range at which
lights are sighted. The approximate sighting range in such circumstances
may be found by first dividing the intensity of the light by 10 for minor
background lighting, 100 for major background lighting, and then using
the luminous range diagram (Fig 10-3).

*A tide serves when it is at a suitable height for ships entering and leaving harbour
254 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

BUOYS AND BEACONS

Buoys
Buoys are floating structures, moored to the bottom, used to mark channels
and fairways, shoals, banks, rocks, wrecks and other dangers to navigation,
where permanent structures would be either uneconomical or impracticable.
Buoys have a distinctive colour and shape, they may carry a topmark and
exhibit lights; all of these are of great importance because they indicate the
buoy’s purpose. Buoys may also be fitted with radar reflectors and may
sound bells, gongs, whistles or horns (see Fog signals, page 266).

Beacons
A beacon is a navigational mark constructed of wood, metal, concrete,
masonry or glass-reinforced plastic (GRP), or a combination of these
materials, erected on or in the vicinity of danger, or onshore, as an aid to
navigation. To indicate their purpose, beacons are often surmounted by
topmarks and may have a distinctive colour and may also exhibit lights.
These features all have the same meaning as for buoys. Large unlit beacons
are often referred to as daymarks (daybeacons in the USA and Canada).
Beacons frequently have distinguishing marks or shapes (referred to as
‘daymark’ in the USA and Canada) built into their structure. Beacons may
be fitted with radar reflectors. In its simplest form, a beacon is known as a
pile beacon and consists of a single wooden or concrete pile identified only
by colour and possibly a number.

Sources of information
The best guide to buoys and beacons for any area is the largest scale chart of
the place concerned. The Admiralty Sailing Directions describe the buoyage
system in use in the area covered by the volume and frequently refer in the
text to individual light-buoys without giving a detailed description. Details
of beacons may also be found in the Sailing Directions. The Admiralty List
of Lights and Fog Signals gives details of lighted beacons, and of light-buoys
of an elevation of 8 metres or more.

The International Association of Lighthouse Authorities (IALA) System

IALA is a non-governmental body which brings together representatives from
the aids to navigation services of various countries to exchange information
and recommend improvements.
The IALA Maritime Buoyage system covers the world in two regions,
Region A and Region B, as shown in Fig. 6-1 (page 105). The only
difference between the two regions is with regard to the colours of lateral
marks (page 258).
The implementation of the IALA System in Region A is expected to be
completed in the mid-1980s, Region B several years later.
A description of the buoyage system in Region A is set out below. For
full details of the world-wide system in Regions A and B, mariners should
refer to IALA Maritime Buoyage System (NP 735) and the relevant volume of
the Sailing Directions, all issued by the Hydrographer of the Navy. In areas
where the IALA system has not yet been implemented, it is particularly
important to consult the Sailing Directions for details of the buoyage system
BUOYS AND BEACONS 255

Fig. 10-4. General direction of buoyage around the British Isles

 256 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

in use. Dates of implementation of the IALA System in the two regions are
given in Admiralty Notices to Mariners.
Application of the IALA System in Region A
The IALA system in Region A applies to all fixed and floating marks other
than lighthouses, sector lights, leading lights and marks, light-vessels and
lanbys. The system is used to indicate the limits of navigable channels, and
to mark natural dangers and other obstructions such as wrecks (all of which
are described as ‘New dangers’ when newly discovered) and other areas or
features of importance to navigation.
Fixed marks
Most lighted and unlighted beacons, other than leading marks, are included
in the system and, in general, beacon topmarks have the same shape and
colour as those used on buoys.
Types of mark
The system provides five types of mark; lateral marks, cardinal marks,
isolated danger marks, safe water marks and special marks. These are now
described. Fig. 10-4 shows the general direction of lateral buoyage around
the British Isles.
Lateral marks
Lateral marks (Fig. 10-5) are used in conjunction with a conventional
direction of buoyage. This direction is defined in one of two ways:
1. Local direction of buoyage. The direction taken by the mariner when
approaching a harbour, river, estuary or other waterway from seaward.
2. General direction of buoyage. The direction determined by the buoyage
authority following a clockwise direction around continental land masses.
This direction is frequently shown on the chart, particularly if there is any
likely doubt about that direction, and may also be given in the Sailing
Directions.
In some places, particularly straits, the local direction may be overridden
by the general direction.
Starboard and port hand
The terms starboard hand and port hand are also used to describe lateral
marks. Starboard hand means that side of the channel which will be on the
right-hand side of the navigator when entering harbour, estuary or river from
seaward, or when proceeding in the general direction of buoyage. Port hand
means that side which will be on the left hand in the same circumstances.

| Shape and colour of lateral marks (Region A)

The shape of the lateral buoy is as important as its colour.
Red can-shaped buoys are generally used to mark the port hand side of
the channel and green conical-shaped buoys to mark the starboard hand. If
the buoy does not conform to these shapes - e.g. it is a spar or pillar* buoy, then
*Pillar buoys are buoys, smaller than lanbys but much taller than the conventional can- and conical-shaped buoys,
with a structure rising from the centre.
BUOYS AND BEACONS 257

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Fig. 10-5. IALA Region A lateral marks |
 258 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

it must have a topmark of the appropriate shape and colour, red can or green
cone. This topmark also applies to beacons.
| In Region A, by night a port hand buoy is identified by its red light and
a starboard hand buoy by its green light; any rhythm may be used, except that
used for a preferred channel buoy.
A preferred channel buoy is used where a channel divides into two, to
indicate the preferred route.
If marks at the sides of a channel are numbered or lettered, the numbering
or lettering should follow the conventional direction of buoyage.
Special marks (see page 260) with can or conical shapes but painted
yellow may be used in conjunction with lateral marks for special types of
channel marking.
Lateral marks in Region B
In Region B, the colours of lateral marks and their lights are reversed, but the
shape remains the same; e.g. green can-shaped buoys mark the port hand side
of the channel and red conical-shaped buoys mark the starboard hand.
| Cardinal marks (Regions A and B)
Cardinal marks (Fig. 10-6) indicate that safe navigable water lies to the
named side of the mark. In other words, the navigator should be safe if he
passes north of a north mark, east of an east mark and so on. It may of course
be safe to pass on other sides as well (e.g. a north mark may have navigable
water not only to the north but also to the east and west), but the navigator
will need to refer to the chart to confirm this.
A cardinal mark may be used to indicate that the deepest water in an area
is on the named side of the mark, or to indicate the safe side on which to pass
a danger (such as rocks, shoals or a wreck), or to draw attention to a feature
in a channel such as a bend or junction, or the end of a shoal.
Black double-cone topmarks (one cone vertically above the other) are the
most important feature, by day, of the cardinal marks. Cardinal marks are
always painted in black and yellow horizontal bands conforming to the points
of the topmarks as follows:

NORTH Points up Black above yellow

EAST Points out Black about yellow

SOUTH Points Black below yellow

down

WEST Points in Black between yellow

The points of the triangle always indicate the position of the black section
of the structure relative to the yellow.
Cardinal marks do not have a distinctive shape, but the buoys are
normally pillar or spar.
When lighted, a cardinal mark exhibits a white light; its characteristics are
based on a group of quick (Q) or very quick (VQ) flashes which distinguish
BUOYS AND BEACONS 259

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Fig. 10-6. IALA cardinal marks |
 260 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

it as a cardinal mark and indicate the quadrant. The rhythm follows the
pattern of a clock face as follows:

NORTH Continuous flashing Twelve o’clock

EAST 3 flashes in a group Three o'clock
SOUTH 6 flashes in a group followed by a long flashSix o’clock
WEST 9 flashes in a group Nine o’clock

| Isolated danger marks (Regions A and B)

Isolated danger marks (Fig. 10-7) are erected on, or moored on or above, an
isolated danger of limited extent surrounded by navigable water. On the
chart, the position of the danger is the centre of the symbol or sounding
indicating that danger; the symbol for the buoy will be slightly displaced.
A black double sphere topmark (one vertically above the other), is, by
day, the most important feature.
The colours used are black with one or more red horizontal bands. The
shape of an isolated danger buoy may be either pillar or spar.
When lighted, an isolated danger mark exhibits a white flashing light
showing a group of two flashes (Fl(2)).

| Safe water marks (Regions A and B)

Safe water marks (Fig. 10-7) are used to indicate that there is navigable water
all around the mark. Such a mark may be used, for example, as a mid-channel
or landfall mark.
Safe water marks have an appearance quite different from danger marking
buoys. First, they are spherical in shape. Secondly, they are the only type of
mark to have vertical stripes (red and white). If pillar or spar buoys are used,
then these should have a single red sphere topmark.
Lights, if any, are white, using isophase, occulting, one long flash every
10 seconds, or Morse ‘A’ rhythm.

| Special marks (Regions A and B)

Special marks (Fig. 10-7) are not primarily intended to assist navigation but
are used to indicate a special area or feature usually referred to on the chart
or in the Sailing Directions, for example:

Ocean Data Acquisition System (ODAS) marks.

Traffic separation marks where use of conventional channel marking may
cause confusion.
Spoil ground marks.
Military exercise zone marks.
Cable or pipeline marks, including outfall pipes.
Recreation zone marks.
A channel within a channel, for example a deep draught channel in a wide
navigable estuary where the normal limits are marked by red and
green lateral marks. The deep channel boundaries would be indicated
by yellow buoys of the appropriate lateral mark shape, or the
centreline would be marked by yellow spherical buoys.
BUOYS AND BEACONS 261

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Fig. 10-7. IALA other marks |
262 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

Fig. 10-8. Chart of Port Able

BUOYS AND BEACONS 263

Fig. 10-9. Perspective view of Port Able

264 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

Special marks are always yellow in colour. If lit, yellow is used, and of
any rhythm other than those used for the white lights of cardinal, isolated
danger and safe water marks. The shape is optional, but must not conflict
with that used for a lateral or safe water mark.

New dangers
A new danger is a newly discovered hazard to navigation not yet shown on
charts, nor included in the Sailing Directions nor sufficiently promulgated by
Notices to Mariners. The term includes naturally occurring obstructions such
as sandbanks or rocks, or man-made dangers such as wrecks.
A new danger is marked by a lateral or a cardinal mark in accordance
with the region rules. If the danger is considered to be especially grave, at
least one of the marks will be duplicated as soon as practicable by an identical
mark to give extra warning until notice of the danger has been sufficiently
promulgated.
If a lighted mark is used for a new danger, it will have an appropriate
cardinal (white) or lateral (red or green) quick or very quick light.
A new danger may also be marked by a racon (see Chapter 15), coded
Morse ‘D’, showing a signal length of 1 mile on the radar display.

Buoyage around the British Isles

A charted representation of buoys and marks used in Region A (Fig. 10-8,
p.262) shows the entrance to an imaginary port in the British Isles and the
method of buoyage. Opposite is a perspective view of the same port
(Fig. 10-9), which shows what the navigator should see by day and which
marks are illuminated by night. It will be noted that a new danger, not yet on
the chart, is visible south of the entrance to the harbour.

Charted buoy and beacon symbols

Fig. 10-10 illustrates the symbols used on fathoms and metric charts to
display the IALA System for Regions A and B.

USING FLOATING STRUCTURES FOR NAVIGATION

The use of light-vessels, lanbys and light-floats for fixing the ship’s position
must always be subject to caution, taking care that all other data tie in, e.g. the
DR/EP, the recorded depth of water and so on. After a strong gale has been
blowing in the area, a floating structure may have dragged. It would be
dangerous to rely on it for fixing the ship. Sometimes, however, the floating
structure may be the only visual aid available (apart possibly from buoys), in
which case the mariner has little alternative, but in such circumstances he
must always proceed with caution.
If shore marks are available and identifiable, these should be used in
preference to floating marks (but see (4) below).
If reliable radio fixing aids (e.g. SATNAV, Decca, see Volume III) of
known error are available within the area concerned, these may be used in
preference to floating marks, provided that the degree of accuracy of the radio
aid concerned is adequate for the task in hand (but see (4) below). A radio
aid fix from Decca or SATNAV may be accurate enough for coastal
navigation, but not accurate enough for pilotage waters.
USING FLOATING STRUCTURES FOR NAVIGATION 265

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Fig. 10-10. IALA System, charted symbols for buoys and beacons |
266 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

The various factors which should be taken into account when deciding
how reliable the position of one of these structures may be, are set out below:

1. Most light-vessels, lanbys and light-floats are anchored by a long scope

of cable and therefore the size of their swinging circle around the charted
position may be considerable. The position of the floating structure
moves around its charted position depending on the scope of cable, the
charted depth, the height of tide, the strength and direction of the tidal
stream, current and wind.
2. Under certain conditions of weather and tidal stream, light-vessels are
subject to sudden and unexpected sheers. It is therefore unwise to pass
them close aboard.
3. Gales in the area could well have caused the structure to drag or break
adrift, and warning signals to that effect may not have been made.
4. The structure may have been moved in any case to take account of
extending shoals; a warning signal or notice to that effect may not have
been received. Thus, a fix by shore objects will not necessarily give a
safe position relative to those shoals.
5. If the structure is not large enough to be quoted in the List of Lights (i.e.
it is less than 8 metres high), then it should be treated like any other buoy.

Buoys
The position of buoys and small-size floating structures must always be
treated with caution even in narrow channels. In deciding how reliable their
positions are, account should be taken of those same five factors set out
above for light-vessels, etc. Remember in particular that buoys can quite
easily drag or break adrift; that they are frequently moved as a shoal extends;
and that they may not always display the correct characteristics.
Remember also that the chart symbol can only show the approximate
position of the buoy mooring, as there are practical limitations in placing and
keeping buoys in the exact position.
Buoys should not be treated as infallible aids to navigation, particularly
when in an exposed position. Whenever possible, navigate by fixing from
charted shore objects; use the echo sounder; check the DR/EP against the
position; use but do not rely implicitly on buoys.

FOG SIGNALS

Information concerning fog signals may be found in complete detail in the

Admiralty List of Lights and Fog Signals. Brief details are also given on the chart.

Types of fog signals

The following types of fog signals are likely to be encountered.

Diaphone. The diaphone uses compressed air to issue a powerful low note
with a characteristic ‘grunt’ at the end of the note (a brief sound of suddenly
reduced pitch). If the fog signal does not end in this ‘grunt’, the Remarks
column (8) in the List of Lights will mention it.
Horn. The horn uses compressed air or electricity. Horns exist in many
FOG SIGNALS 267

forms, differing greatly in sound and power. Some forms, particularly those
at major fog signal stations, simultaneously produce sounds of different pitch
which are often very powerful. Some produce a single steady note, while
others vary continuously in pitch.
Siren. The siren uses compressed air and exists in many forms varying
greatly in sound and power.
Reed. The reed uses compressed air and emits a weak (particularly if hand-
operated) high-pitched sound.
Explosive. This signal produces short reports by means of firing explosive
charges.
Bell, gong, whistle. These may be operated by machinery, producing a
regular character; by hand, giving a somewhat irregular character; or by wave
action, sounding erratically. Bells, gongs and whistles are frequently used as
fog signals on buoys.

Morse Code fog signals

Morse Code fog signals consist of one or more characteristics of the Morse
Code. In a similar manner to lights, the abbreviation for Morse (Mo) may be
included in the abridged description of fog signals; e.g. Horn Mo (N) 90s,
Siren Mo (A) 120s. Oil and gas production platforms often use a Morse Code
fog signal; those off the British Isles and the north coast of France use Horn
Mo (U) 30s.

Using fog signals for navigation

Fog signals give invaluable warning of danger but their use for navigation is
limited. In the vicinity of fog signals, make full use of available aids, e.g.
radar, radio aids, soundings. Place lookouts in positions (e.g. bow and aloft)
where noises in the ship are least likely to interfere with the hearing of a fog
signal.
Sound travels through air in an unpredictable way. The following points
should therefore be noted when using fog signals for navigation:

1. Fog signals may be heard at greatly varying distances; the strength of the
signal is no guide to the rang, nor does an change of intensity necessarily
indicate a similar change of range.
2. The apparent direction of a fog signal is not always a correct indication
of the true direction.
3. If a fog signal is a combination of high and low notes, one of the notes
may be inaudible in certain atmospheric conditions.
4. There are occasionally areas around a station in which the fog signal is
quite inaudible.
5. Fog may exist a short distance from a station and not be observable from
it, so that the signal may not be operated.
6. Some fog signals cannot be started on a moment’s notice.
 268 CHAPTER 10 -VISUAL AND AUDIBLE AIDS TO NAVIGATION

| INTENTIONALLY BLANK
 269

CHAPTER 11
Tides and Tidal Streams

This chapter deals with the causes and effects of the tides, in theory and in
practice, and with tidal streams and currents, and the Admiralty Tide Tables.
Tides. Tides are periodic vertical movements of the water on the Earth’s
surface.
Tidal streams. In rising and falling the tides are accompanied by periodic
horizontal movements of the water called tidal streams. (In American usage,
tidal stream is called tidal current.)

TIDAL THEORY

Tides are caused by the gravitational pull of a heavenly body on the Earth and
on the water over the Earth. The magnitude of the pull is defined in
Newton’s Universal Law of Gravitation, which states that, for any two
heavenly bodies, a force of attraction is exerted by each one on the other, the
force being:

1. Proportional to the product of the masses of the two bodies.

2. Inversely proportional to the square of the distance between them.
3. Directed from the centre of the one to the centre of the other.

This law may be expressed as

m1m2 . . .11.1
F∝ 2
d
where F is the force, m1 and m2 the masses of the two bodies and d their
distance apart.
The two heavenly bodies have the greatest tide-raising effect are the Sun
and the Moon, while the effect of other heavenly bodies is negligible.

The Earth-Moon System

The Earth and Moon may be considered as forming an independent system
rotating about a common centre of gravity known as the Earth-Moon
barycentre (Fig. 11-1, p.270). The barycentre lies on a line joining the centres
of gravity of the Earth and Moon at a point about 1000 miles below the
Earth’s surface.
The Earth describes a very small ellipse about the Earth-Moon
barycentre, while the Moon describes a much larger ellipse about the same
270 CHAPTER 11 -TIDES AND TIDAL STREAMS

barycentre, taking 27½ days approximately to complete one orbit.* As

explained in Volume II of this manual, the Moon revolves around the Earth
with respect to the Sun approximately once every 29½ days. This period is
known as the lunar month.

Fig. 11-1. The Earth-Moon system

Fig. 11-2. The gravitational force of the Moon acting on the Earth

*In a similar manner, the Earth-Moon barycentre describes, an elliptical orbit around the Earth-Sun barycentre (Fig.
11-13) located inside the Sun. It takes one year (365¼ days approximately) for the Earth to complete one orbit
around the Sun.
TIDAL THEORY 271

The gravitational force

The gravitational force of the Moon acts on the Earth as a whole affecting the
structure of the Earth itself, on the atmosphere and on the water on the Earth’s
surface, and it is this latter phenomenon which is relevant when considering
the causes of tides.
In Fig. 11-2, MM1 is the diameter of the Earth on the line joining the
centres of the Earth and Moon, M being the point on the Earth’s surface
directly under the Moon and known as the sublunar point. M1 is on the
opposite side of the Earth away from M and is known as the antipode. A and
B are two points on the great circle whose plane is perpendicular to MM1, and
at all points on this circle the distance from the Moon may be considered as
the same* as that from the centre of the Earth. Hence the gravitational force
exerted by the Moon anywhere on AB is the same and is denoted by G. At M
the distance to the Moon has decreased; thus, the gravitational force acting
at M is increased by a small amount δG, while at M1 the gravitational force
has decreased by a similar amount. Thus, the total gravitational force acting
at M is (G + δG) and that at M1 is (G - δG).
Assuming for our purpose that the Earth is a smooth sphere completely
covered by water, the force acting on the waters may be considered as the
difference between the gravitational force G acting at the centre of the Earth
and the actual force anywhere else on the Earth’s surface; this is shown in
Fig. 11-3.

Fig. 11-3. The differential gravitational force on the Earth’s surface (1)

It will be observed that, at the antipode M1, the differential gravitational

force is negative, i.e. - δG. This is equivalent to saying that the differential
force at M1 is positive but acting in the opposite direction, as shown in
Fig. 11-4.

* The distance of A and B from the Moon is very slightly more than that at C but, as the radius of the Earth is small
compared with the distance of the Moon (1:60 approximately), this fact may be safely disregarded.
272 CHAPTER 11 -TIDES AND TIDAL STREAMS

Fig. 11-4. The differential gravitational force on the Earth’s surface (2)

At some other point D on the Earth’s surface (Fig. 11-4), the differential
force acting on the waters at this point must be somewhere between δG and
zero. If D is φ ° above the sublunar-antipodal plane, then the differential
gravitational force at D is equal to δG cos φ °. Similarly, at D1 the force is
also equal to δG cos φ °, but acting in the opposite direction.

The tide-raising force

If once again it is assumed that the entire surface of the Earth is covered with
a uniform layer of water, these differential forces may be resolved into a
vertical component at right angles to the Earth’s surface and a horizontal
component directed towards the sublunar or antipodal points, as shown in
Fig. 11-5.

Fig.11-5. Resolution of the differential forces

TIDAL THEORY 273

The vertical force is only a very small portion of the Earth’s gravity, so
that the actual lifting of the water against gravity is infinitesimal. It is the
horizontal component which produces the tides, by causing the water to move
across the Earth and pile up at the sublunar and antipodal points until an
equilibrium position is found. The horizontal component of the differential
gravitational forces is known as the tide-raising or tractive force. Its
magnitude at a given point (X in Fig. 11-5) may be expressed as:

3 m2 r
FH ∝ X 3 sin 2φ ...11.2
2 d

where FH is the magnitude of the tide-raising (horizontal) force;

m2 is the mass of the Moon;
r is the radius of the Earth;
d is the distance between the Earth’s and Moon’s centres;
φ is the angle at the centre of the Earth between the line joining the
sublunar and antipodal points, and the line joining the Earth’s
centre and X.

It should be noted that the tide-raising force caused by the Moon varies
directly as the mass of the Moon and the radius of the Earth, and is inversely
proportional to the cube of the distance between Earth and Moon.
The effect of the tide-raising or tractive force is illustrated in Fig. 11-6.
The tide-raising force is zero at the sublunar and antipodal points M and
M1 and along the great circle AB the plane of which is perpendicular to MM1.
The maximum tide-raising force may be found along the small circles EF and
GH, which are 45° from the sublunar point and antipode respectively.

Fig. 11-6. The effect of the tide-raising force

274 CHAPTER 11 -TIDES AND TIDAL STREAMS

Equilibrium is reached when the tides formed at the sublunar and antipodal
points are at such a level that the tendency to flow away from them is
balanced by the tide-raising force. The tide caused in these circumstances is
known as the lunar equilibrium tide (Fig. 11-7), with a high water at M and
M1 and a low water at A and B.

Fig. 11-7. The lunar equilibrium tide

Effect of Earth’s rotation

Fig. 11-8 shows the tide-raising effect on the Earth when the Moon is above
the Earth’s equator, i.e. declination* 0°.
The Earth rotates relative to the Moon once every lunar day of 24 hours
50 minutes approximately and thus, during this period, an observer at point
M will experience two high waters once every 12 hours 25 minutes,
interspersed with two low waters also 12 hours 25 minutes apart. This is
illustrated in Fig. 11-9.

*Declination is defined in Volume II. It is the angular distance of a heavenly body north or south of the celestial
equator, and corresponds to latitude on the Earth.
TIDAL THEORY 275

Fig. 11-8. The effect of the Earth’s rotation

Fig. 11-9. The lunar equilibrium semi-diurnal tide, declination 0°

High water takes place shortly after the Moon’s transit (upper and lower)
of the meridian* of the place. The slight delay is a side effect of the Earth’s
rotation.
The range of this equilibrium tide at the equator - that is, the difference
in height between successive high and low waters - is less than 1 metre.
When the declination is zero, the tide-raising forces on the equator will
be equal. At any other point P on the Earth’s surface north or south of the
equator, the tide-raising forces will still be equal but not so great as at the
equator, and will vary approximately with the cosine of the latitude. The

* This is the time at which the Moon crosses the meridian of the place and is described in Volume II.
276 CHAPTER 11 -TIDES AND TIDAL STREAMS

time intervals between successive high and low waters will still be the same
as those on the equator, 6 hours 12½ minutes approximately.
Such tide-raising forces, producing two equal maxima and two equal
minima per lunar day at equal time intervals, are termed semi-diurnal (one
cycle per half-day). When the Moon’s declination is zero, the tide-raising
forces are semi-diurnal for all latitudes.

Change of Moon’s declination

The effect of the Moon’s declination is shown in Fig. 11-10. The maximum
tide occurs as before at the sublunar and antipodal points M and M1. At any
point P on the Earth’s surface, not only are the heights of successive high and
low waters different, the time intervals also change, as illustrated in Fig. 11-
11. This effect is known as the diurnal inequality, a phenomenon commonly
found in tides.

Fig. 11-10. Effects of the Moon’s declination

Fig. 11-11. The diurnal inequality

TIDAL THEORY 277

At another point Q on the Earth’s surface (Fig. 11-10), where the latitude
is greater than 90° minus the Moon’s declination, the tide-raising force never
reaches zero. This effect is illustrated in Fig. 11-12.

Fig. 11-12. The diurnal tide

At Q there is only one high water and one low water every lunar day and
this type of tide is called diurnal (one cycle per day). The Moon’s declination
changes from a maximum* north to a maximum south and back again once
every 27a days approximately; thus, a similar effect on the tide caused by the
Moon’s declination alone will be experienced roughly every fortnight.

The distance of the Moon

As the Moon rotates around the Earth (Fig. 11-1) approximately once every
27½ days, the tide-raising force is strongest when the Moon is closest to the
Earth, that is, at perigee (perigean tide). The tide-raising force is weakest
when the Moon is furthest away, that is, at apogee (apogean tide). The
variation in the Moon’s distance can cause a difference in the lunar tide-
raising force of between 15% and 20%; thus, tides at perigee are likely to be
appreciably higher than those at apogee.

The Earth-Sun system

The Earth and Sun may be considered as forming another independent tide-
raising system rotating around the Earth-Sun barycentre (Fig. 11-13, p.278).
Although the Sun has a much greater mass than the Moon, the Sun’s tide-
raising force is nevertheless only about 45% that of the Moon. This is
because the tide-raising force is inversely proportional to the cube of the
distance.
The tide-raising effects of the Sun on the Earth are similar to those of the
Moon, though of lesser magnitude. Thus, the tides caused by the Sun will
vary according to:

1. The Earth’s rotation. The solar day is approximately 24 hours; thus, the
solar equilibrium semi-diurnal tide, when the sun’s declination is

*Over an 18.6 year cycle, the Moon’s maximum monthly declination oscillates between about 18½° and 28½° and
back again.
278 CHAPTER 11 -TIDES AND TIDAL STREAMS

Fig. 11-13. The

Earth-Sun system

zero, will have two high waters 12 hours apart, interspersed with two low
waters also 12 hours apart. The time interval between successive high
and low waters will be 6 hours.
2. Change of Sun’s declination. The Sun’s declination changes much more
slowly than that of the Moon and reaches a maximum of about 23½°
north and south of the equator on about 22nd June and 22nd December
respectively, these dates being known as the solstices.
3. The distance of the Sun. It takes the Earth about 1 year, 365¼ days
approximately, to complete its elliptical orbit around the Sun. Perihelion,
when the Earth is closest to the Sun, occurs about 2nd January, and
aphelion, when the Earth is furthest away, is about 1st July. Thus, the
Sun’s tide-raising force will be at its maximum in January and at its
minimum in July. The variation in this force is, however, very small
indeed, of the order of 3%.

Springs and Neaps

When the tide-raising effects of the Moon and Sun are combined, they
sometimes work together and sometimes against each other.

Spring tides
Twice every lunar month, the Moon and Sun are in line with each other and
with the Earth, as shown in Fig. 11-14.
At new Moon, the Moon is passing between the Sun and the Earth; the
Moon and Sun are said to be acting in conjunction. About 14¾ days later, at
full Moon, the Earth is between the Moon and Sun, which are now acting in
opposition.
TIDAL THEORY 279

The net result in both cases is a maximum tide-raising force, producing what
is known as a spring tide. At spring, therefore, higher high waters and lower
low waters than usual will be experienced, these occurring at about the time
of new and full Moon.

Fig. 11-14. Spring tides

Fig. 11-15. Neap tides

Neap tides
Twice every lunar month, i.e. about every 14¾ days, the Moon and Sun are
at right angles to each other, as shown in Fig. 11-15. At these times the
Moon and Sun are said to be in quadrature.
280 CHAPTER 11 -TIDES AND TIDAL STREAMS

This situation occurs when the Moon is in the first and last quarters, and
at this time the lunar and solar tide-raising forces are working at right angles
to each other. The net result in both cases is a minimum tide-raising force,
producing what is known as a neap tide. At neaps, lower high waters and
higher low waters than usual will be experienced, these occurring at about the
time of the first and last quarters of the Moon.
Frequency of springs and neaps
From the foregoing it may be seen that two spring tides will occur each lunar
month interspersed with two neap tides, the interval between successive
spring and neap tides being about 7½ days. This phenomenon is found at
many places in the world, although other inequalities sometimes occur to alter
these timings.
It is usual for springs and neaps to follow the relevant phase of the Moon
by two or three days. This is because there is always a time-lag between the
action of the force and the reaction to it, caused by the time taken to
overcome the inertia of the water surface and friction.
Springs and neaps will occur at approximately the same time of day at
any particular place, since the Moon at that time is in a similar position
relative to the Sun.
Equinoctial and solstitial tides
When the declinations of the Moon and the Sun are the same, the tide-raising
force of each will clearly be acting more in concert than when the
declinations are not the same.
At the equinoxes in March and September, when the declinations of
Moon and Sun are both zero, the semi-diurnal luni-solar tide-raising force
will be at its maximum, thus causing the equinoctial tides. At these times,
where semi-diurnal tides are concerned, spring tides higher than normal are
experienced.
At the solstices in June and December, when the declinations of Moon
and Sun are both at maximum, the diurnal luni-solar tide-raising force will be
at its maximum, thus causing the solstitial tides. At these times, diurnal tides
and the diurnal inequality are at a maximum.
Note: As explained on page 277, the Moon’s declination changes rapidly
over a 4 week period. It can be at any value at the actual equinox or solstice,
although it is bound to reach zero or maximum declination respectively
within a few days.
Priming and lagging
It was explained earlier that the effect of the Earth’s rotation and that of the
Moon relative to each other is to cause a high water at intervals of about 12
hours 25 minutes. The effect of the Earth’s rotation and that of the Sun
relative to each other is to cause a (smaller) high water at intervals of about
12 hours. Thus, when the effects of both Moon and Sun are taken together,
the intervals between successive high and low waters will be altered.
When the Moon is in a position between new/full and quadrature, the
Sun’s effect will be to cause the time of high water either to precede the time
of the Moon’s transit of the meridian or to follow the time of the Moon’s
transit. This is known as priming and lagging and is illustrated in Fig. 11-16.
THE TIDES IN PRACTICE 281

The tide is said to prime when the Moon is between the new and the first
quarter, and between full and the last quarter; high tide then occurs before the
Moon’s transit of the meridian.
The tide is said to lag when the Moon is between the first quarter and full,
and between the last quarter and new; high tide then occurs after the Moon’s
transit of the meridian.

Fig. 11-16. Priming and lagging of the tides

Summary of tidal theory

Tidal theory may be summarised as follows.
The semi-diurnal tide-raising force is maximum when the Moon’s
declination is nil, and minimum when the Moon’s declination is at its
greatest. The diurnal tide-raising force is nil when the Moon’s declination is
nil and maximum when the Moon’s declination is greatest. The same is also
true of the effect of the Sun’s declination but, whereas the Moon’s declination
attains a maximum value north or south of the equator every 15 days or so,
the Sun only reaches a maximum twice a year, in June and December at the
solstices.
As the orbits of the Moon around the Earth and the Earth around the Sun
are elliptical, changes in their distances from the Earth cause variations in the
tide-raising force, that for the Moon being significant, that for the Sun being
minimal.
Spring and neap tides occur at intervals of about 14 to 15 days, caused by
the Moon and Sun either working together at full and new Moon (springs) or
against each other at first and last quarters (neap).
The Sun’s tide-raising force is always a great deal less than that of the
Moon, approximating to some 45% on average.

THE TIDES IN PRACTICE

In practice, the tides may differ considerably from the luni-solar equilibrium
tide just discussed. This is because of the size, depth and configuration of the
ocean basins, land masses, the friction and inertia to be overcome in any
particular body of water, and so on.
282 CHAPTER 11 -TIDES AND TIDAL STREAMS

For an appreciable tide to be raised in a body of water, it is essential to

generate a large enough tide-raising force. To achieve this, the body of water
must be large. The great oceans of the world - the Pacific, the Atlantic and
the Indian Ocean - are large enough to permit tides to be generated, although
none of these tides appears to be a single oscillating body, but rather a
number. The natural period of oscillation is the decisive factor in
determining whether the water responds to the diurnal or the semi-diurnal
tide-raising force or a mixture of the two. Hence, tides in practice are often
referred to as being semi-diurnal, diurnal or mixed.
The Atlantic tends to be more responsive to semi-diurnal forces; thus,
tides on the Atlantic coat and around the British Isles tend to be semi-diurnal
in character (two high waters and two low waters per day) and are more
influenced by the phases of the Moon than by declination. Large tides occur
at springs near full or new Moon. Small tides occur at neaps near the
quarters. The largest tides of the year occur at springs near the equinoxes
when the Sun and Moon are on the equator.
The Pacific is on the whole more responsive to the diurnal forces, and so
tides in this part of the world tend to have a large diurnal component. In
these areas, the largest tides are associated with the greatest declination of
Sun and Moon, that is, at the summer and winter solstices. Areas in the
South-west Pacific off New Guinea, off Vietnam and in the Gulf of Tonking,
and in the Java Sea are predominantly diurnal.
Mixed tides, where the diurnal and semi-diurnal tide-raising forces are
both important, tend to be characterised by a large diurnal inequality (Fig. 11-
11). This may be apparent in the heights of successive high waters, low
waters or both. Occasionally the tide may even be diurnal. Such tides are
common along the Pacific coast of the United States, the east coast of West
Malaysia, Borneo, Australia and the waters of South-west Asia.
The Mediterranean Sea and the Baltic, as bodies of water, are too small
to enable any appreciable tide to be generated. The Strait of Gibraltar is too
restricted to allow the Atlantic tides to have any appreciable effect other than
at the extreme western end. The maximum tides are to be found in the
Adriatic, where they are predominantly mixed, with a diurnal inequality at
high and low water. The range may exceed 0.5 metre in several places in the
Adriatic, but is rarely greater than 1 metre.

Shallow water and other special effects

As a tidal wave enters shallow water, it slows down. The trough is
retarded more than the crest; thus, there is a progressive steepening of the
wave front accompanied by a considerable increase in the height of the wave.
This distorts the timing, in that the period of rise becomes shorter than the
period of fall. These shallow water effects are present to a greater or lesser
degree in the tides of all coastal waters.
The amplitude (height) of the tidal wave increases even more as it travels
up an estuary which narrows from a wide entrance. This may result in a very
large tide such as those to be found in the Bay of Fundy in Nova Scotia, the
Severn Estuary and around the Channel Islands.
THE TIDES IN PRACTICE 283

Where a river is fed from such an estuary with a large tidal range, a
phenomenon known as a bore (Old English - eagre) may be found. The crest
of the rising tide overtakes the trough and tends to break. Should it break, a
bore occurs in which half or more of the total rise of the tide occurs in only
a few minutes. Notable bores are in the Severn, Seine, Hooghly and Chien
Tang Kiang.
At certain places, shallow water effects are such that more than two high
waters or two low waters may be caused in a day. At Southampton,
for example (Fig. 11-17), there are two high waters with an interval of about
2 hours between them. Further west, at Portland, the predominating factor is
a double low water (Fig. 11-18. p.284). Double tides also occur on the Dutch
coast and at other places. The practical effect of this is to create a longer
stand* at high or low water.

Fig. 11-17. Tidal curves at Southampton

* The stand of the tide is the period at high or low water between the tide ceasing to rise (fall) and starting to fall
(rise).
284 CHAPTER 11 -TIDES AND TIDAL STREAMS

Fig. 11-18. Tidal curves at Portland

Because of the distortion of the tidal wave caused by shallow water

effect, special curves based on low water have had to be prepared for
determining the height of tide on the south coast of England between
Swanage and Selsey. The curves and instructions for their use are to be
found in Volume 1 of the Admiralty Tide Tables. The tidal curve at
Southampton, a standard port, is also based on low water because of the
complexity of the tide around high water.

Meteorological effects on tides

Meteorological conditions which differ from the average will cause
corresponding differences between the predicted and the actual tide.
Variations in tidal heights are mainly cause by strong or prolonged winds and
by unusually high or low barometric pressure. Differences between predicted
and actual times of high and low water are caused mainly by wind.
Statistical analysis indicates that 1 standard deviation (see Chapter 16) of
the differences between observed and predicted heights and times amounts
to 0.2 metre and 10 minutes respectively.

Barometric pressure
Tidal predictions are computed for average barometric pressure. A difference
from the average of 34 millibars can cause a difference in height of about 0.3
metre. A low barometer will tend to raise sea level and a high barometer will
tend to depress it. The water level does not, however, adjust itself
immediately to a change of pressure and it responds, moreover, to the average
change in pressure over a considerable area. Changes in level due to
barometric pressure seldom exceed 0.3 metre but, when Mean Sea Level is
raised or lowered by strong winds or by storm surges, this effect can be
important.
THE TIDES IN PRACTICE 285

Effect of wind
The effect of wind on sea level - and therefore on tidal heights and times - is
very variable and depends largely on the topography of the area. In general,
it can be said that wind will raise sea level in the direction towards which it
is blowing. A strong wind blowing straight onshore will pile up the water
and cause high waters to be higher than predicted, while winds blowing off
the land will have the reverse effect. Winds blowing along the coast tend to
set up long waves which travel along the coast, raising sea level where the
crest of the wave appears and lowering sea level in the trough. These waves
are known as storm surges and are discussed below.

Seiches
Abrupt changes in meteorological conditions, such as the passage of an
intense depression or line squall, may cause an oscillation in the sea level
known as a seiche. The period between successive waves may be anything
between a few minutes and about 2 hours and the height of the waves may be
anything from 1 centimetre or so up to 1 metre.

Positive and negative surges; storm surges

A change in sea level is often caused by a combination of wind and pressure,
such changes being superimposed on the normal tidal cycle. A rise in sea
level is often referred to as a positive surge and a fall as a negative surge. A
storm surge is an unusually severe positive surge.
Both positive and negative surges may appreciably alter the predicted
times of high and low water, often by as much as 1 hour.
A positive surge will have the greatest effect when it is confined to a gulf
or bight such as the North Sea. It rarely increases the general sea level height
by more than 1 metre, although greater heights are not unknown (see below
on storm surges). In a bight such as the North Sea, northerly winds will raise
the general sea level at the southern end, causing a positive surge.
Negative surges are of great importance to large vessels navigating with
small under-keel clearances. These surges are most evident in estuaries and
areas of shallow water, and appear to occur when strong winds are tending to
blow water out of a bight or similar area. For example, in the North Sea,
strong southerly winds will tend to cause a negative surge in sea level at the
southern end. Falls in sea level of up to 1 metre are not uncommon, while
falls of as much as 2 metres have been recorded.
Storm surges occur in bights or estuaries when the speed of the tidal wave
is reduced by shallow water effect to that of the speed of the storm. The tidal
wave is thus being ‘fed’ by the storm and gradually increases in amplitude.
In certain circumstances, it may attain a considerable height - 3 metres is not
unknown and, if this peak occurs at high water springs, considerable flooding
and damage may be caused along the coastline.
A storm surge may be anticipated when an intense depression moves at
a critical speed across the head of a bight with storm force winds blowing into
the bight. Such surges have been experienced in the southern North Sea and
in the Bay of Bengal. They may be preceded by an abnormal stand at low
water.
286 CHAPTER 11 -TIDES AND TIDAL STREAMS

Seismic waves (tsunamis)

A seismic wave or tsunami (often popularly but erroneously called a ‘tidal
wave’) is usually the result of an undersea earthquake which sets up waves
entirely unconnected with the tides. These waves travel with great rapidity
in the deep waters of the oceans, reaching speeds of over 400 knots, a
wavelength of over 100 miles (thus, a period of about ¼ hour) and a height
of only ½ to 1 metre. On reaching shallow water, however, they increase
rapidly in height, often reaching destructive proportions. Heights of 15 to 17
metres have been recorded.
The first wave is often preceded by a very rapid lowering of the water
level, a warning that the tsunami will arrive in a few minutes. The tsunami
typically consists of a series of waves, the second and third being higher than
the first, the rest gradually decreasing over a period which may be as little as
a few hours and as long as several days.
Tsunamis usually originate in the earthquake zones of the Pacific basin
and travel for enormous distances. They have been known to reach the
English Channel, although by that time the amplitude has fallen to just a few
centimetres.

TIDAL PREDICTION

To predict with accuracy the height of tide at any place, extensive tidal
observations must be carried out and the results analysed.

Harmonic constituents
The tidal observations at a place are analysed and used to identify a number
of constituent parts making up the tide-raising forces at that place. The tide-
raising forces may be considered as the resultant of a large number of
harmonic cosine curves, the periods and relative amplitudes of which can be
calculated from astronomical theory. Some 400 harmonic constituents have
been calculated but, in practice, it is unnecessary to use so many. As many
as 60 are used for major tidal stations.
If a periodic force such as a tide-raising force is applied to a body of
water, that water will respond by oscillating with the same period. The
response is, however, modified by topographical conditions which can retard
or advance the tidal wave, and raise or lower the amplitude. There is some
response to all the harmonic constituents of the tide-raising force and no
regular response to other forces.
The harmonic constituents are given symbols from which their general
significance may be deduced. For example, the letter M is used for lunar
constituents, S for solar constituents, the subscript 1 for diurnal and the
subscript 2 for semi-diurnal components.

Principle of harmonic tidal analysis

The longer the period of tidal observation at a place, the better the analysis
is likely to be. Because of the various cycles involved, a period of 18.6 years,
equal to the longest cycle, is desirable if all the necessary harmonic
constituents are to be identified. However, for standard port predictions in
the Admiralty Tide Tables, the general rule is for at least 1 complete year’s
TIDAL PREDICTION 287

observations to be analysed; this allows an adequate number of constituents

to be identified with sufficient accuracy. At secondary ports, analysis of at
least 1 month’s observations is the aim, as this permits the identification of
the four major harmonic constituents.
The four principle constituents with which the user will come into contact
are:
M2 The principle lunar semi-diurnal constituent. This component
permits calculations of the amplitude caused by a theoretical Moon
in circular orbit around the Earth at the average speed of the real
Moon, halfway between apogee and perigee and at an average
northerly or southerly declination.
S2 The principal solar semi-diurnal constituent. This component
permits calculation of the amplitude caused by a theoretical Sun in
similar circumstances to that for the Moon above,
K1 A luni-solar declinational diurnal constituent. This component
allows for part of the Moon’s and Sun’s declination.
O1 A lunar declinational diurnal constituent. This component allows
for the remainder of the Moon’s declination.

Each harmonic constituent has a speed, an amplitude and a phase. The

speed is given in degrees per hour, one complete cycle being 360°. Details
of the four main constituents are given in Table 11-1.

Table 11-1
CONSTITUENT NO. OF CYCLES SPEED (DEGREES TIME TO COMPLETE
PER DAY PER HOUR 1 CYCLE
M2 2 28°.98 12 h 25 min
S2 2 30° 12 h 00 min
K1 1 15°.04 23 h 56 min
O1 1 13°.94 25 h 50 min

The amplitude H is equal to half the range, the range being the difference
in height between the maximum and minimum of each oscillation.
The phase of a constituent is its position in time in relation to its
theoretical position as deduced from astronomical theory. The tide-raising
forces do not act instantaneously (see page 280, frequency of springs and
neaps); thus, each constituent has a time or phase lag g.
The purpose of tidal analysis is to determine the amplitude H and the
phase lag g.

Tidal prediction
Tidal prediction is carried out by electronic computer using an appropriate
number of harmonic constituents. In many places, for example Portsmouth,
the shallow water constituents are very complex and additional corrections
have to be applied. The authority for the observations, constants and
predictions, the method of prediction and the year of observation are all
shown in the Admiralty Tide Tables.
 288 CHAPTER 11 -TIDES AND TIDAL STREAMS

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TIDAL PREDICTION 289

Simplified Harmonic Method of Tidal Prediction (NP 159)

Provided that the four main harmonic constituents M2, S2, K1 and O1 are
known, the user may obtain his own curve of predicted tidal heights, using
the various forms in the Simplified Harmonic Method of Tidal Prediction.
This method calculates the M2 and S2 semi-diurnal components, the shallow
water correction (if applicable) and the K1 and O1 diurnal components,
combining all these to determine the predicted tidal curve for the place. Full
instructions are given in NP 159.
M2, S2, K1 and O1 are tabulated in the Tide Tables for most standard and
secondary ports and are referred to as harmonic constants. The daily values
of these four components, which are determined by the position of the Moon
and Sun, are also tabulated. These latter values have been amended to
include a number of minor semi-diurnal and diurnal harmonic constituents.
In some areas of the world, an apparent seasonal variation may occur in
the larger harmonic constants M2 and S2, both for amplitude and for phase.
This phenomenon may be found in areas where there is a large seasonal
variation in seal level, or where there are marked meteorological changes as
is the case with the monsoons. It has also been found in other parts of the
world such as the British Isles. It is only possible to identify the effects if at
least one complete year’s tidal observations have been made.
Such seasonal change must be taken into account when extracting the
harmonic constants for a relevant port from the Tide Tables.
As mentioned above, NP 159 permits the inclusion of shallow water
effect. To this end, data on shallow water corrections are included in the Tide
Tables. At certain ports with large shallow water effects, the change in Mean
Sea Level can be quite significant, dependent on the date relative to springs,
and this needs to be taken into account when using NP 159. Details are given
in the Tide Tables.
A variation of this method of tidal prediction may also be carried out on
a pocket calculator, in preference to the graphical solution using NP 159. Full
details are given in the Tide Tables. A calculator with a polar rectangular
conversion facility is particularly useful. Details are also given in the Tide
Tables on the use of programmable calculators for this method of prediction.
Co-tidal charts
Co-tidal and co-range charts show lines of equal time and range of tides
(Figs. 11-19a, b). They are available for certain areas around the world - the
British Isles (and in particular the Dover Strait and southern North Sea), the
Malacca Strait, the Persian Gulf. Such charts provide a means of predicting
tidal information in the open sea in these areas. Instructions for their use with
an example are provided on the charts, and exercises on their use are given
in Volume V of this manual.
Co-tidal lines (12h, 11h, 10h, etc.) are drawn through points of equal
Mean High Water Interval (MHWI). MHWI is the mean time interval
between the passing of the Moon over the meridian of Greenwich and the
time of the next high water at the place concerned. Co-range lines (5m, 4m,
3m, etc) are drawn through positions of equal mean range (MSR). MSR is
the difference in level between Mean High and Low Water Springs and is
given in metres.
290 CHAPTER 11 -TIDES AND TIDAL STREAMS

Co-tidal lines tend to radiate outwards from an amphidromic* point while

co-range lines surround it. Near amphidromic points in the areas covered by
these charts, the range of the tide may alter considerably within a short
distance.
Such charts are of great importance to deep-draught ships with small
under-keel clearances navigating the areas concerned. The reliability of the
information depends on the accuracy and number of tidal observations made
in the area concerned. Since it is difficult to position tide-gauges in suitable
sites, offshore data often depend more on interpolation from inshore stations
than on direct measurement; thus, the data must be used with caution.

TIDAL STREAMS AND CURRENTS

A careful distinction must be drawn between tidal streams (sometimes
referred to as ‘tidal currents’ in the US and elsewhere) and currents (called,
in some countries, ‘non-tidal’ currents). In practice, a combination of tidal
stream and current is frequently experienced.
Tidal streams are horizontal movements of the water in response to tide-
raising forces and may be predicted for any period in the future. Currents, on
the other hand, are caused by meteorological factors such as wind and
barometric pressure, by oceanographical factors such as water of differing
salinity or temperature, and by topographical factors such as irregularities in
the sea-bed. The assessment of currents is set out in Chapter 8. Ocean
currents are discussed in Volume 4 of this manual.
In rivers and estuaries, there is often a permanent current caused by the
flow of river water; such currents are included in the tidal stream tables.

Types of tidal streams

Tidal streams are of two main types, rectilinear and rotary. The first has only
two directions (with perhaps small variations), which may be called the flood
(the incoming tidal stream) or the ebb (the outgoing tidal stream) or,
preferably, east-west going, north-south going, etc. Rotary tidal streams are
continually changing in direction; they rotate through 360° in a complete
cycle. The rate of the tidal stream usually varies throughout the cycle, with
two maxima in approximately opposite directions interspersed with two
minima about halfway between the maxima in time and direction.
In port approaches, estuaries, channels and straits, where the direction of
the flow of the tidal stream is constricted by the surrounding land and shoals,
the tidal streams are rectilinear. Offshore, where such restrictions no longer
exist, the tidal streams are rotary.
Tidal streams, like tides, have semi-diurnal and diurnal components
(including a diurnal inequality) and may be analysed harmonically or non-
harmonically. In European waters, tidal streams are for the most part of the
same type as the tides, that is, they are semi-diurnal in character. The rates
of the stream are related to the range of the tide, and the times of slack water
are related to but not necessarily identical with the times of high and low
water at
*An amphidromic system is a tidal system, the centre of which is known to be an amphidromic point where the
range of the tide is nil or very small, increasing outwards. The times of high and low water progress clockwise or
anticlockwise around the centre.
TIDAL STREAMS AND CURRENTS 291

the nearest standard port. For example, at Devonport, the turn of the tidal
stream occurs within about an hour of the times of high and low water.
However, further out into the open waters of the English Channel south of
Plymouth, slack water occurs at about half-tide, that is, about 3 to 3½ hours
before and after high water at Devonport. Indeed, along open coats, it is more
usual for slack water and the turn of the tidal stream to be at half-tide rather
than at high and low water.

Tidal stream data

Tidal streams which are semi-diurnal in character may be predicted by
reference to a suitable standard port and are displayed in tables printed on the
published chart. There is no necessity for daily predictions to be published.
These tables show the rate and direction of the predicted tidal stream of
springs and neaps by reference to the time of high water at a suitable standard
port. The rate at times other than at springs and neaps may be found by
interpolating between the two.
In other part of the world, such as the Malacca and Singapore Straits,
where the diurnal inequality of the tidal stream is large, the above procedure
is not possible. Daily predictions for important areas are published in the
Admiralty Tide Tables and Tidal Stream Tables, Volumes 2 and 3 (ATT).
Harmonic constants for some tidal streams are also published in all three
volumes so that predictions may be made using NP 159.

Tidal stream atlases

Where the tidal stream may be related to a standard port and when there is
sufficient data, atlases are available showing rates and directions over a wide
area. Such atlases, showing the tidal streams in pictorial form, are available
for all the waters around the British Isles, and also for other part of the world
such as the west coast of France and Hong Kong. Certain countries may
make the use of such atlases compulsory for ships proceeding to and from
their ports; for example, US Port Authorities require their port and tidal
current tables, charts and diagrams to be held by visiting ships.
Instructions for the prediction of the rate of tidal stream are given inside
the front cover of the atlas.
RN ships are also issued with Home Dockyard Ports - Tides and Tidal
Steams (NP 167, which covers the home dockyards Portsmouth, Devonport,
etc. This information supplements that given in the Tide Tables and Sailing
Directions. The publication also contains information on eddies and slack
water.

Tidal stream observations

The observation of tidal streams presents greater difficulties than the
observation of tides. However, in the case of tidal streams, the degree of
accuracy necessary for tidal prediction is unnecessary as well as
impracticable. For example, the tidal stream tables to be found on charts
around the British Isles, are generally speaking, based on a series of
observations extending over a period of 25 hours. In the case of coastal
observations, any residual current is removed before the tables are compiled.
As mentioned earlier, the permanent current in rivers and estuaries is included
in the tables.
292 CHAPTER 11 -TIDES AND TIDAL STREAMS

Because of the rapidly changing effect of sea-bed topography on the

direction and rate of the tidal stream, it is often impossible to give more than
an indication of how a ship will be affected by tidal streams when on passage.
In a narrow channel, for instance, the stream may be running at 3 knots in the
centre with virtually no stream or even a stream running in the opposite
direction, at the edges of the channel: the stream may vary from nil to 3 knots
in the navigable part of the channel. Tidal stream predictions for any given
position in the channel should be correct for that position, but may well be
incorrect for a position a few yards either side. While the tidal stream
predictions must be accurate enough for navigational purposes, the methods
of prediction are not required to be so complex as for tidal predictions.

Tidal streams at depth

It is sometimes of interest to HM Ships, deep-draught merchant ships, oil rig
operators, and those engaged in underwater operations, to know how the tidal
streams may vary in strength and direction from the surface down to lower
depths. Published tidal stream data normally refer to the uppermost 10 metre
layer of the sea, which is that layer of particular interest to the average ship.
Tidal streams at greater depths tend to be very similar to those on the surface*
until a depth is reached approximating to three-quarters the total depth
although times of turn many be different (usually early but occasionally late)
by as much a 1 hour compared with those on the surface. Tidal streams then
fall away in strength to a value which may be about 50% to 60% of the
surface rate at about 1 metre above a smooth sea-bed, and also change
direction slightly by about 10° to 20°. In the bottom few centimetres of
depth, tidal streams may undergo a marked change from those on the surface.
Published data is available for surface and sub-surface tidal streams in the
Strait of Gibraltar (NP 629). Data is also available for a few other areas of
the world from the Hydrographer. Some of the data is available, in relevant
operating handbooks, to HM Ships only. Commercial companies usually
apply direct to the Hydrographer or the Institute of Oceanographic Science
for whatever information they may require.

Eddies, races and overfalls

Eddies, tide-rips, overfalls and races are different forms of water turbulence
caused by abruptly changing topography of the sea bed, the configuration of
the coastline, the constriction of channels or sudden changes in tidal or tidal
stream characteristics.
An eddy is a circular movement of water, the diameter of which may be
anything from a few inches to a few miles. For an example of the latter, see
the Tidal Stream Atlas of the Approaches to Portland, where there is an anti-
clockwise eddy of the tidal stream east of Portland between 1 hour after and
5 hours after high water at Devonport.

*This situation may be quite different in ports which are fed by river water in addition to the tides, e.g. Devonport.
The strength and direction of the stream may vary considerably with depth, this being dependent on the amount of
fresh water flowing down-river, and the depth to which it penetrates.
ADMIRALTY TIDE TABLES (ATT) 293

An overfall is another name for a tide-rip and is caused by a strong stream

near the sea-bed being deflected upwards by obstructions on the bottom, thus
causing a confused sea on the surface.
A tidal race is an exceptionally strong stream, usually caused by the
constriction of water passing round a headland or where tidal streams from
different directions converge. The tidal stream atlas for Portland shows an
almost permanent race south of Portland Bill.
Where the effect of eddies, etc. are of a permanent nature, they are taken
into account when predicting tidal streams.
ADMIRALTY TIDE TABLES (ATT)
A brief description of the Admiralty Tide Tables is given in Chapter 7.
Standard ports
Each volume of the Tide Tables has a selected number of standard ports, a
total of about 240 in all three volumes. For standard ports in the British Isles
and Commonwealth, observed tide-gauge readings have been made, where
possible, over at least a year. The harmonic constants for these ports are
computed from the analysis of the readings. Changes in Mean Sea Level,
which are included in the standard port data, are observed and analysed where
possible over at least a 3 year period. Predictions for most standard ports
outside the British Isles are obtained from National Authorities. The method
of prediction is not always known but it may be assumed that the predictions
should be adequate for normal navigational purposes in reasonable weather.
In Volume 1, European Waters including Mediterranean Sea, each
standard port has a diagram from which the height and time other than at high
water may be predicted. In Volume 2, The Atlantic and Indian Oceans, and
Volume 3, The Pacific Ocean and Adjacent Seas, one standard curve
covering all the standard ports is included at the beginning of the volume. An
explanation of the use of the diagram is given in the instructions for the use
of the tables in each volume. The four main harmonic constants for the
standard ports are also tabulated in all three volumes.
Secondary ports
Each volume of the Tide Tables has a selected number of secondary ports,
there being about 8000 in all three volumes. Generally speaking, tidal
information on a secondary port is based on that at a nearby standard port and
is tabulated as time and height differences from the standard port. The four
main harmonic constants are also tabulated in all three volumes for about
5000 secondary ports. Predictions for secondary ports are made by applying
time and height differences to predictions at the relevant standard port, or by
using the four harmonic constants and NP 159. The data on which the
differences are based are variable in quality; where possible, observations
have been carried out over at least 15 and preferably 30 days. Where this is
not the case, the harmonic constants are annotated accordingly.
The standard port on which the secondary port is based has similar tidal
characteristics, to ensure that the average time and height differences for the
secondary port are as accurate as possible. In some cases, therefore,
294 CHAPTER 11 -TIDES AND TIDAL STREAMS

a standard port has been chosen which is very remote from the secondary
port. For example, a number of secondary ports in Antarctica are based on
Galveston, Texas. In other cases, the tides at a secondary port cannot be
referred to any standard port, and the tide must be predicted using the
harmonic constants and NP 159.

Using the Tide Tables

The time and height of high and low water, and the height of the tide at times
between high and low water, may be found from the Tide Tables for all
standard and secondary ports. Full instructions on using the tide tables are
given. Suitable exercises may be found in Volume V of this manual.

High and low water at secondary ports

The times of high and low water at secondary ports are obtained by applying
the tabulated time differences to the daily predictions for the relevant
standard port. Where the tide is mainly semi-diurnal in character, the
differences are tabulated for Mean Spring and Neap levels at the standard
port. When the diurnal inequality is large, the tabulations are made for Mean
Higher and Mean Lower, High and Low water (see page 297).
For certain ports no suitable standard port is available and predictions
must be made using NP 159. The Tide Tables are annotated accordingly.

Height of tide at times between high and low water

ATT, Volume 1. Intermediate times and height are best predicted by the use
of the Mean Spring and Neap curves* given for each standard port. For
secondary ports, where there is little change of shape between adjacent
standard ports, and where the duration of rise or fall at the secondary port is
not very different from the relevant standard port, intermediate times and
heights may be found by using the Mean Spring and Neap curves for the
relevant standard port.
Between Swanage and Selsey, the tide is of great complexity and special
curves and instructions are provided.
At some other secondary ports, where indicated in the tables, NP 159
should be used.
ATT, Volumes 2 and 3. The standard curve may be used for all ports
provided that:

1. The duration of the rise or fall of the tide is between 5 and 7 hours.
2. There is no shallow water correction.

If either of these criteria is not met, NP 159 should be used.

Offshore areas and places between secondary ports

Tidal predictions for offshore areas and stretches of coastline between
secondary ports should be obtained by the use of co-tidal charts (see page
289), if these are available.

*The neap curves at ATT, Volume 1 have been adjusted to allow the calculation of intermediate heights and times
and do not, therefore, reflect the true relationship between spring and neap tides at the relevant standard port.
LEVELS AND DATUMS 295

Admiralty Tidal Prediction Form (NP 204)

The Admiralty Tidal Prediction Form is a form designed for the majority of
time and height calculations. Copies of the form are to be found in the back
of the Tide Tables volumes, and further copies in booklet form may be
obtained from Admiralty Chart Depots and Agents.

Supplementary information in the Tide Tables

Supplementary information provided in the Tide Tables in addition to that
already mentioned in this chapter is as follows:

Heights of chart datum relative to Ordnance Datum in the Unit Kingdom

(Volume 1 only).
Heights of chart datum relative to the land levelling system in countries
outside the United Kingdom (Volume 1 only).
Tidal levels at standard ports.
Astronomical arguments for use with the semi-graphic method of
harmonic analysis of 30 days tidal observations (NP 112).
Tidal stream tables (Volumes 2 and 3 only).

LEVELS AND DATUMS

Datum of tidal prediction
Soundings on Admiralty charts are given below the level of chart datum,
which is defined in Chapter 6 (page 115). By international agreement, chart
datum is defined as a level so low that the tide will not frequently fall below
it. The datum for tidal predictions must be the same as the datum for
soundings, to ensure that the total depth of water is equal to the charted depth
plus the height of the tide. The levels at which datums have been established
at standard ports vary widely, however, and the datums do not conform to any
uniform tide level. Modern practice is to establish datum at or near the level
of Lowest Astronomical Tide (LAT, see below) but Table V in the Tide
Tables should always be referred to when planning passages, etc. as this
shows many datums different from LAT. For areas where the Hydrographer
of the Navy is the surveying authority, datums have been adjusted to
approximate to LAT.
It is always advisable to check that chart datum and the datum for tidal
predictions are the same. This can easily be done by comparing the tide
levels printed on the chart with those in the Tide Tables.

Chart datum and land survey datum

To determine how tidal levels vary along any given stretch of coastline, all
levels must be referred to a common horizontal plane. Chart datum is not a
suitable reference because it is dependent on the range of the tide. In Great
Britain, the Ordnance Datum at Newlyn may be regarded as a suitable
horizontal plane and should be used if comparisons of absolute height are
required. On large- and medium-scale charts for which the Hydrographer is
the primary authority, the panel giving tidal height may also tabulate the
difference between chart and ordnance datums for the area. Other countries
have their own land survey datums; some of these are listed in Table IV of
Volume 1 of the Tide Tables.
296 CHAPTER 11 -TIDES AND TIDAL STREAMS

If absolute heights are required at a point on the coast where no tidal data
are given, or where there is no connection to land survey datum, they should
be obtained by interpolation from heights obtained from places on either side
where data is available.

Tide levels and heights

A number of these are shown in Fig. 11-20.

Some old charts show Bench Marks which may be based on Ordnance or Chart Datum

Fig. 11-20. Tide levels and heights

Heights
Heights on Admiralty charts are given above a particular vertical datum. This
is Mean High Water Springs in areas where the tides are semi-diurnal and
Mean Higher High Water where there is a diurnal inequality. Mean Sea
Level is used in places where there is no tide. (See also Chapter 6, page 119).
LEVELS AND DATUMS 297

Tide levels
These levels are all referred to chart datum, which is the same as the zero of
tidal predictions. Definitions of various levels are set out below.

Highest Astronomical Tide (HAT), Lowest Astronomical Tide (LAT).

These are the highest and lowest levels respectively which can be predicted
to occur under average meteorological considerations and any combination
of astronomical conditions. HAT and LAT are not the extreme levels which
can be reached; storm surges (page 285) may cause considerably higher and
lower levels to occur. The values of HAT and LAT are obtained by
inspection over a period of years.
Mean High Water Springs (MHWS), Mean Low Water Springs (MLWS).
The height of Mean High Water Springs is the average of the heights of two
successive high waters during those periods of 24 hours (approximately every
fortnight) when the range of the tide is greatest. This is computed throughout
the year when the average maximum declination of the moon is 23½°. The
height of Mean Low Water Springs is the average height obtained from two
successive low waters during the same period.
Mean High Water Neaps (MHWN), Mean Low Water Neaps (MLWN).
The height of Mean High Water Neaps is the average throughout the year, as
above, of the heights of two successive high waters during those periods
(approximately every fortnight) when the range of the tide is least. The
height of Mean Low Water Neaps is the average height obtained from two
successive low waters during the same period.
Mean Tide Level* (MTL). Mean Tide Level is the mean of the heights of
MHWS, MHMW, MLWS and MLWN.
Mean Sea Level* (MSL). Mean Sea Level is the average level of the sea
surface over a long period, preferably 18.6 years, or the average level which
would exist in the absence of tides.
Mean Higher High Water (MHHW). The height of Mean Higher High
Water is the mean of the higher of the two daily high waters over a long
period of time. When only one high water occurs in a day, this is taken as the
higher high water.
Mean Lower High Water (MLHW). The height of Mean Lower High
Water is the mean of the lower of the two daily high waters over a long period
of time. When only one high water occurs on some days, ª is printed in the
MLHW column of the Tide Tables to indicate that the tide is usually diurnal.
Mean Higher Low Water (MHLW). The height of Mean Higher Low
Water is the mean of the higher of the two daily low waters over a long period
of time. When only one low water occurs on some days, ª is printed in the
MHLW column of the tide table to indicate that the tide is usually diurnal.
Mean Lower Low Water (MLLW). The height of Mean Lower Low Water
is the mean of the lower of the two daily low waters over a long period of
time. When only one low water occurs on a day, this is taken as the lower
low water.

*The Mean Level (ML) tabulated in the Tide Tables is Mean Tide Level in Volume 1 and Mean Sea Level in
Volumes 2 and 3. Mean Sea and Tide Levels at any one place may differ because of distortion in the tidal curve
resulting from shallow water effects.
298 CHAPTER 11 -TIDES AND TIDAL STREAMS

The average values of MHWS, MHWN, MLWS, MLWN, MHHW,

MLHW, MHLW and MLLW vary from year to year in a cycle of
approximately 18.6 years. The tide levels shown in Table V of the Tide
Tables are average values over the whole cycle.
 299

CHAPTER 12

Coastal Navigation

Navigational passages must be carefully planned. Everyone is liable to make

mistakes; over three-quarters of all groundings are attributable to human error
of some kind. A sound passage plan may not prevent a grounding, but it does
reduce the chances of making mistakes.
This chapter takes the reader through the various stages of a coastal
passage; the preparatory work, making the plan and finally the execution.
The chapter concludes with remarks on passages in fog and thick weather and
navigation in coral waters.

PREPARATORY WORK
There are many points that the navigator must consider before undertaking
a coastal passage.

Charts and publications

All the charts and publications necessary for the passage must be selected and
assembled.

Charts
The charts to be used are selected by studying the Catalogue of Admiralty
Charts (NP 131) and the relevant Admiralty Sailing Directions. HM Ships
may also need to study the Catalogue of Classified and Other Charts (NP
111) for classified charts. Remember that the largest scale charts appropriate
to the purpose (see page 121) should always be used; for a coastal passage,
a series of overlapping medium-scale charts are provided. A small-scale chart
is also required covering the whole passage; the intended track throughout the
voyage should be plotted on it. If possible, the whole route should be shown
on one small-scale chart.
All the charts must be corrected up to date for Permanent, Temporary and
Preliminary Notices to Mariners, radio navigational warnings and relevant
Local Notices. Consult the Chart Correction Log (NP 133A, 133B); it
should be up to date for all charts and folios held on board.
Extract the charts from the relevant folios and list them in the Navigating
Officer’s Work Book* in the order in which they will be used.

*Any hard-bound lined A4 size book will suffice as a Work Book

300 CHAPTER 12 - COASTAL NAVIGATION

Certain miscellaneous charts may also be required. These include

Symbols and Abbreviations Used on Admiralty Charts (Chart Booklet 5011);
co-tidal and co-range charts; passage planning charts; practice and exercise
area charts; charts of surveyed areas, offshore oil and gas operations, fishery
limits, etc.
In some overseas areas, charts of other national Hydrographic Offices
may be required, particularly the large-scale ones (see page 102).

Publications
Relevant publications (which must be corrected up to date) include the
following:
Admiralty Distance Tables.
Admiralty Sailing Directions. These are a mine of useful information for
passage making. They give information on ports; recommended
routes; meteorological conditions including gales and fog;
conspicuous fixing marks; sketches and photographs of the coastline
and suitable navigational marks; tidal and tidal stream information.
The Nautical Almanac (for times of sunrise, sunset, etc.).
Admiralty Tide Tables.
Tidal stream atlases.
Co-tidal atlases.
Home Dockyard Ports - Tides and Tidal Streams (HM Ships only).
Admiralty List of Lights.
IALA Maritime Buoyage System
The Mariner’s Handbook.
Annual Summary of Admiralty Notices to Mariners.
Admiralty List of Radio Signals (particularly Volumes 2, 5 and 6).
IMO (International Maritime Organisation) Ships’ Routeing, details of
which may also be found in Sailing Directions, The Mariner’s Handbook,
the Annual Summary of Admiralty Notices to Mariners, and on the charts
(including passage planning charts).
The Decca Navigator Operating Instructions and Marine Data Sheets for
ships so fitted.
Fleet Operating Orders, procedures and programmes (HM Ships only).
Navigational Data Book.
Department of Transport A Guide to the Planning and Conduct of Sea
Passages.
IMO Recommendation on Basic Principles and Operational Guidance
Relating to Navigational Watchkeeping.

Information required
In addition to the information given on the charts, the Navigating Officer will
need to find details of some or all of the following items from the
publications available.
The distance between ports of departure and destination.
The likely set and drift to be experienced on passage resulting from the
combined effect of tidal stream, current and surface drift.
Times and heights of the tide along the route.
Advice and recommendations along the route obtainable from the Sailing
Directions.
PLANNING THE PASSAGE 301

Routeing and traffic separation schemes to be encountered along the

route.
Past, present and likely future weather; in the event of bad weather, the
likely diversionary ports or anchorages.
Duration of daylight and darkness; times of sunset and sunrise, etc.
Radio aids available during the passage.
Likely ship’s draught, fore and aft, at the beginning, during and at the end
of the passage, and the requirements for under-keel clearance.
Search and Rescue arrangements along the route.

All necessary information should be noted in the Navigating Officer’s

Work Book.

Appraisal
Having assembled all the necessary information, the Navigating Officer
carries out an appraisal of the passage. He will need to study the charts
covering the route and its vicinity and the lights likely to be sighted. Some
of these lights may be positioned outside the limits of the selected charts. At
the same time, the Sailing Directions covering the area concerned must be
consulted. A good plan is to tab the pages relevant to that part of the coast
off which the ship will pass, inserting references to the latest supplement and
to corrections listed in Part IV of the Weekly Notices to Mariners. Study the
relevant portions of the Sailing Directions in conjunction with the charts, List
of Lights, tidal publications, List of Radio Signals, local orders, etc. to obtain
a clear mental picture of what may be expected along the route - the
appearance of the coastline and suitable navigational marks, dangers, tidal
streams, radio aids, etc. Such study will also provide information on port
traffic signals, signal stations and local weather signals, depths of water over
bars at harbour entrances, details of anchorages, berths, landing places and
other local information. The charts should be annotated accordingly, e.g.
brief descriptions of light structures and conspicuous buildings, the colour of
cliffs, suitable fixing marks.
Relevant information should be noted as necessary in the Work Book.

PLANNING THE PASSAGE

Choosing the route

Having established the dangers along the route in relation to the draught of
the ship, the Navigating Officer is now in a position to decide on the precise
route to be taken. There are a number of factors which may affect the choice
of route and the timing of the passage.

1. Times of departure arrival. These may be subject to tidal considerations

and also to port restrictions of various kinds (working hours, etc.).
Courtesies to the country being visited (gun salutes, official calls, etc.)
are also factors that need to be taken into account.
2. The possibility of fog or low visibility, particularly in narrow waters, and
the effect this will have on passage speed.
3. The likelihood of bad weather along the route, the direction from which
it is likely to come, the effect on passage speeds, whether it may be
302 CHAPTER 12 - COASTAL NAVIGATION

necessary to seek shelter, or heave to, etc. A passage to leeward of the

coast (e.g. an island) in the prevailing weather is preferable to a passage
along the windward side.
4. Ships’ routeing and traffic separation schemes may apply along part of
the route. Traffic separation schemes are discussed later in this chapter,
and are dealt with in detail in Part 6 of Volume III of this manual.
5. The presence of fishing vessels/fleets along the route. Concentrations of
fishing vessels should be avoided if possible.
6. A requirement to pass through narrow or ill-lit channels. By adjusting
the times of arrival or departure, or the passage speed, it may be possible
to avoid passing through such channels at night. An alteration of a few
revolutions during the night watches will often ensure that the vessel
arrives at the start of a particular passage at dawn. The possibility of
breakdown (main engines, steering gear, compasses, etc.) in such areas
must be borne in mind.
7. Focal points for shipping. Traffic bottlenecks and density of shipping
must be taken into account. If the coast is on the starboard hand, the
planning of the track should allow sufficient room to be able to alter
course to starboard to avoid other shipping and still be navigationally
safe. A ship may often be forced repeatedly to starboard by heavy traffic
and sometimes the only way to counter this is by means of a bold
alteration to seaward as soon as traffic density allows.
8. Operations or exercises. Where possible, these must be planned in
advance and the times allowed for. For example:

Replenishment at Sea.
Rendezvous with other ships.
Flying operations.
Weapon exercises and any need to avoid exercise or range areas while
on passage.
Damage control exercises.
Machinery (including steering gear) breakdown exercises.
Equipment (including compasses) breakdown exercises.
Ship handling exercises and Officer of the Watch manoeuvres.
Seaboat (man overboard) exercises.
Full power trials.
Oil-rig patrols.
Fishery protection assistance.
9. Speed, endurance and economical steaming. There may be restrictions
on the speed allowed to save costs on fuel. If the passage is long, there
may be a need to refuel while on passage to avoid falling below laid
down fuel margins required for operational or safety reasons.
10. Clearance from the coast, and under-keel clearances. These are
discussed later in this chapter.
11. Territorial limits. Territorial limits claimed by countries are given in the
Annual Summary of Admiralty Notices to Mariners and are updated from
time to time in the Weekly Notices. HM Ships and their aircraft should
keep clear of these limits if intending to exercise, otherwise diplomatic
clearance will have to be obtained.
PLANNING THE PASSAGE 303

12. Mined areas (see the Annual Summary of Admiralty Notices to

Mariners). There are a few minefields still in existence from the Second
World War; they are not believed to be anymore dangerous than any
other of the usual hazards to navigation whilst on passage. However,
certain areas are still highly unsafe with regard to anchoring, fishing or
any other form of submarine or sea-bed activity. Details of these may be
found in the relevant Sailing Directions.
It is always possible for minefields to be laid in times of tension
between nations; thus, there is no guarantee that minefields may not be
encountered at some time or other.

Clearance from the coast and off-lying dangers

When coasting, the general rules to be followed are:

1. Be sufficiently close in, to identify shore objects easily.

2. Be far enough off to minimise the risk of running ashore as a result of
error or machinery breakdown.
3. Keep in a safe depth.

When deciding the distance to pass from the coast and from off-lying
dangers, the track chosen should be such that, if fog or mist should obscure
the coastal marks, the ship may still be navigated with the certainty that she
is not running into danger. As a general principle, a course parallel to
dangers should be chosen rather than one converging with them.
The following points should be borne in mind when laying off the ship’s
track on the chart.
1. When the coast is steep-to and soundings fall away sharply, pass at a
distance of 1½ to 2 miles. At this range, objects will be easily recognised
in normal (10 miles) visibility.
2. When the coast is shelving, pass outside that depth contour line which
gives the ship an adequate safety margin beneath the keel.
Ships drawing less than 3 metres (10 feet) should aim to pass outside
the 5 metre (3 fathom) line.
Ships drawing between 3 and 6 metres (10 and 20 feet) should aim to
pass outside the 10 metre (5 fathom) line.
Ships drawing between 6 to 10 metres (20 and 33 feet) should aim to
pass outside the 20 metre (10 fathom) line.
Ships drawing more than 10 metres (33 feet) should pass in a depth of
water which gives a safe allowance under the keep (see p.308).
3. Unmarked dangers near the coast, where fixing marks are adequate,
should be passed at least 1 mile distant provided there is sea-room.
4. Light-vessels, lanbys, light-floats, and buoys should be passed at 5 cables
(½ mile) provided there is sea-room.
5. Unmarked dangers out of sight of land should be passed at about 5 to 10
miles, dependent on the time interval since the last fix and the tidal
stream or current likely to be experienced. By night this distance should
be increased.

Remember that distances may have to be adjusted for the prevailing

weather (a greater depth of water will be needed in rough weather to allow for
 304

Fig. 12-1. Traffic separation schemes, one-way lanes and inshore traffic zones
CHAPTER 12 - COASTAL NAVIGATION
PLANNING THE PASSAGE 305

the scend), tidal stream, etc., the nature of the coast, the off-lying dangers,
and the opportunities for fixing. The height of tide may also be a factor
which should be taken into account when considering a safe depth.

Ships’ routeing and traffic separations schemes

Details of ships’ routeing and traffic separation schemes (TSS) adopted by
IMO (the International Maritime Organisation) may be found in Ships’
Routeing, published by IMO. IMO is a United Nations organisation set up
to deal with international regulations and recommendations relating to
maritime safety (including navigation) and pollution.
The subject matter of routeing and TSS is also dealt with in some detail
in Part 6 of Volume III of this manual. Details of the traffic separation
schemes on Admiralty charts are given in the Annual Summary of Admiralty
Notices to Mariners, which also lists the national authority for schemes not
adopted by IMO. Further information may also be found in the Sailing
Directions, The Mariner’s Handbook (NP 100) and on passage planning
charts. Brief details, sufficient for those planning navigational passages, are
given below.

SEE BR 45
The aim of ships’ routeing is to increase the safety of navigation in areas
where the density of traffic is heavy, or where the traffic converges, or where
restricted sea-room prevents freedom of manoeuvre. To achieve the aim,
some or all of the following measures are in force.

VOL 4
1. One-way traffic lanes, separated by a zone which ships are not normally
allowed to enter other than those crossing the lane (Fig. 12-1). In narrow
passages and restricted waters, a separation line may be used instead of
a zone to allow a greater width of navigable water in the lanes. Opposing
streams of traffic may sometimes be separated by natural obstructions,
e.g. Le Colbart or The Ridge in the Diver Strait.
2. Inshore traffic zones (ITZ) to separate local and through traffic (Fig. 12-
1). These inshore zones may be used by local traffic proceeding in any
direction and are separated from traffic in the adjacent one-way system
by a separation zone or line.
3. Approaches to focal points, e.g. port approaches, entrances to channels
and estuaries, landfall buoys, etc., may be split into different sectors, each
sector having its own traffic separation scheme (Fig. 12-2, p.306).
4. The routeing of traffic at places where routes meet may be dealt with by
means of a roundabout (Fig. 12-2), the traffic proceeding around a
central point or separation zone in an anti-clockwise direction, or a
junction. An alternative method is to end the one-way systems before
they meet. The area enclosed by the end points is called a precautionary
area (Fig. 12-2) to emphasise the need to navigate with caution and may
be indicated by the symbol .

5. Other methods of routeing are deep water (DW) routes for deep-draught
ships (the least depth along the recommended route may be displayed on
the chart), two-way routes, recommended tracks and routes and areas to
be avoided. Through traffic of medium and shallow draught must keep
away from DW routes and avoid inconveniencing very large vessels on
these particular routes.
306 CHAPTER 12 - COASTAL NAVIGATION

SEE BR 45
VOL 4
Fig. 12-2. Sectors, roundabouts, precautionary areas

Conduct of ships in traffic separation schemes

The conduct of ships in traffic separation schemes adopted by IMO is
governed by Rule 10 of the International Regulations for Preventing
Collisions at Sea, 1972, as amended to 1995, and this is set out below.

Rule 10
Traffic Separation Schemes

(a) This Rule applies to Traffic Separation Schemes adopted by the Organization and does not
relieve any vessel of her obligation under any other Rule.

(b) A vessel using a Traffic Separation Scheme shall:

(i) proceed in the appropriate traffic lane in the general direction of traffic flow for that
lane;

(ii) so far as practicable keep clear of a traffic separation line or Separation Zone;

(iii) normally join or leave a traffic lane at the termination of the lane, but when joining
or leaving from either side shall do so at as small an angle to the general direction of
traffic flow as practicable.

(c) A vessel shall so far as practicable avoid crossing traffic lanes, but if obliged to do so shall
cross on a heading as nearly as practicable at right angles to the general direction of traffic
flow.
PLANNING THE PASSAGE 307

(d) (i) A vessel shall not use an Inshore Traffic Zone when she can safely use the
appropriate traffic lane within the adjacent Traffic Separation Scheme. However,
vessels of less than 20 m in length, sailing vessels and vessels engaged in fishing may
use the Inshore Traffic Zone.

(ii) Notwithstanding subparagraph d(i), a vessel may use an Inshore Traffic Zone when
en route to or from a port, offshore installation or structure, pilot station or any other
place situated within the Inshore Traffic Zone or to avoid immediate danger.

(e) A vessel other than a crossing vessel or a vessel joining or leaving a lane shall not normally
enter a Separation Zone or cross a separation line except:

(i) in cases of emergency to avoid immediate danger;

(ii) to engage in fishing within a Separation Zone.

(f) A vessel navigating in areas near the terminations of Traffic Separation Schemes shall do so
with particular caution.

(g) A vessel shall so far as practicable avoid anchoring in a Traffic Separation Scheme or in areas

SEE BR 45
near its terminations.

(h) A vessel not using a Traffic Separation Scheme shall avoid it by as wide a margin as is
practicable.

VOL 4
(i) A vessel engaged in fishing shall not Impede the passage of any vessel following a traffic
lane.

(j) A vessel of less than 20 metres in length or a sailing vessel shall not Impede the safe passage
of a power-driven vessel following a traffic lane.

(k) A vessel Restricted in her Ability to Manoeuvre when engaged in an operation for the
maintenance of safety of navigation in a Traffic Separation Scheme is exempted from
complying with this Rule to the extent necessary to carry out the operation.

(l) A vessel Restricted in her Ability to Manoeuvre when engaged in an operation for the laying,
servicing or picking up of a submarine cable, within a Traffic Separation Scheme, is
exempted from complying with this Rule to the extent necessary to carry out the operation.

Rule 10 is intended to minimise the development of collision risks by

separating opposing traffic flows, but the other Rules also apply. The fact
that a ship is proceeding along a route does not give that ship any special
privilege or right of way. When risk of collision is deemed to exist, the
collision regulations apply in full.
The one-way traffic lanes are mainly for through traffic, which should not
normally use the inshore traffic zone.
Special rules and recommendations may apply to certain areas (see the
relevant Sailing Directions and passage planning guide); e.g. for Ushant, see
the Channel Pilot (NP 27), also the English Channel Passage Planning
Guide, Chart 5500).
A number of traffic separation schemes have not been adopted by IMO.
The regulations governing their use are laid down by the national authority
establishing them. These rules may not only modify Rule 10, but also other
Rules of the 1972 regulations. Details may be found in the appropriate
Sailing Directions or on the charts concerned. (See also the Annual Summary
of Admiralty Notices to Mariners).
308 CHAPTER 12 - COASTAL NAVIGATION

Certain traffic separation schemes may lay down rules on which routes
or parts of routes may be used by vessels carrying hazardous or noxious
cargoes. The latter are defined in the MARPOL Rules, the international
regulations set up to prevent oil pollution of the sea. Details are given in the
relevant Sailing Directions, the appropriate passage planning chart and The
Mariner’s Handbook.
Ships should, as far as practicable, keep to the starboard side in two-way
routes, including DW routes.

Under-keel clearances
All ships have to be navigated at some time or other in shallow water, and an
appropriate safety margin under the keel must be allowed. Vessels with
draughts approaching 30 metres have to navigate considerable distances in
coastal waters with a minimum depth below the keel.
As a ship proceeds through shallow water, she experiences an interaction
with the bottom, more often known as shallow water effect and quantified in
terms of squat. The ship’s speed in shallow water leads to a lowering of the
water level around her and a change in trim, which together result in a

SEE BR 45
reduction in the under-keel clearance. These phenomena are extensively
covered in BR 67(3), Admiralty Manual of Seamanship, Volume III.
Squat is extremely difficult to quantify; the following figures must be
used with caution, but they serve as a useful guide.
Squat may be expected to occur when the draught/depth of water ratio is

VOL 6(1)
less than 1:1.5, e.g. for a ship drawing 6 metres, a depth of water of 9 metres
or less, or for ships drawing 30 metres, a depth of water of 45 metres or less.
The following rules of thumb are available:

squat = 10% of the draught OR

= 0.3 metres for every 5 knots of forward speed OR

(usually an over estimate for fine warships hulls, but

suitable for merchant ships with fully forms)

whichever is the greatest.

EXAMPLE
A ship drawing 6 metres is proceeding at 10 knots in less than 9 metres of
water; what is the likely squat?

squat = 10% of 6 = 0.6 m OR

10
= 0.3 x = 0.6 m OR
2 5
10
= = 1m
100
Thus, squat is likely to be about ½ to 1 metre. Allow the greater figure.
Similarly, a ship drawing 30 metres at 10 knots in less than 45 metres of
water might expect her squat to be of the order of 3 metres.
PLANNING THE PASSAGE 309

Additional under-keel allowances may have to be made for the following:

1. Reduced depths over pipelines which may stand as much as 2 metres
above the sea-bed.
2. Reduced depths due to negative surges which may be as much as 1 to 2
metres, as described in Chapter 11.
3. Increased draught due to rolling or pitching. For example, a large ship
with a beam of 50 metres can be expected to increase her draught by
about ½ metre for every 1° of roll. The trim of the ship is also likely to
be affected by shallow water effect, and allowance must be made for any
increased draught.
4. Inaccuracies in charted offshore depths and predicted tidal heights.
5. Inaccuracy in the estimated draught if coming to the end of a long
passage.
6. Alterations in the charted depth since the last survey. This applies to
areas where the bottom is known to be unstable, and particularly those
part of the world where sandwaves (see below) are a common occurrence,
such as the southern North Sea including the Dover Strait, parts of the

SEE BR 45
Thames Estuary, the Persian Gulf, the Malacca and Singapore Straits, in
Japanese waters and in the Torres Strait.
Sandwaves in water are rather like sand dunes on land. The sea forms the
sea-bed into a series of ridges and troughs which are believed to be more or
less stationary. The size can vary tremendously, from the ripples seen on a
sandy beach by the water’s edge to sandwaves up to 20 metres in amplitude
and several hundred metres between peaks. In the southern North Sea,
sandwaves rising 5 metres above the general level of the sea-bed are quite

VOL 6(1)
common.
Details of known sandwave areas will be found in the relevant Sailing
Directions and are also marked on the charts. Sandwaves may be expected
to occur in shallow seas where there is relatively fast water movement and
where the sea-bed is of a sedimentary type, usually sand. General remarks on
sandwaves are given in The Mariner’s Handbook. Ships navigating in
sandwave areas with little under-keel clearance must proceed with the utmost
caution.
From time to time a considerable under-keel allowance may be necessary.
When planning a passage through a critical area, ships should take advantage
of such co-tidal and co-range charts as are available; nevertheless, as already
mentioned in Chapter 11, the data from such charts must be used with
caution, since offshore data more often depend on the interpolation of inshore
data than on direct measurement.
Various authorities may lay down an under-keel allowance for certain
areas. In coastal waters these apply especially to deep-draught ships. The
figure usually takes into account an allowance for squat up to a particular
speed. For example, in the Dover Strait, a static under-keel allowance of
about 6.5 metres should be arrived at, including a squat allowance for speeds
up to 12 knots.
The difference between the calculated depth of water and the ship’s
draught when stopped must be equal to or more than the static under-keel
allowance. Thus, the least charted depth a ship should be able to cross in
safety may be found as follows:
under-keel + ‘static’ draught = least charted + predicted height
allowance depth of tide
310 CHAPTER 12 - COASTAL NAVIGATION

Port Authorities also issue a minimum under-keel clearance which must

be observed by all ships under way regardless of squat or height of tide. For
example at Portsmouth, when under way in the harbour or the approaches,
ships should have at least 2 metres under the keel at all times.

The passage plan

The following procedure should be followed when planning a navigational
passage. Details, calculations, etc. are entered in the Work Book. Try to
keep the plan as simple as possible; the more complicated it is, the more
likely it is to go wrong.

Times of arrival and departure

1. Determine the distance between departure and destination from the
Admiralty Distance Tables. Add an amount, which may vary between 1-
2% and 10%, to allow for al the likely divergences from the shortest
navigable route as previously mentioned, e.g. operational or exercise
requirements, under-keel clearances, traffic separation schemes, etc.
2. Consider the factors affecting the timing of the passage in terms of hours
gained or lost (usually the latter). These are often operational or exercise
requirements.
3. Consider the factors which may be calculated in terms of speed rather
than time: the overall effect of tidal stream, current and weather.
4. Calculate the time to be taken on passage, taking into account any
restriction on speed which may have been imposed, e.g. a requirement to
proceed at economical speed in order to save fuel. Allow something in
hand for unforseen eventualities; the amount will vary depending on the
nature of the passage. With all other factors allowed for, a figure of
between ½ and 1 knot over the required passage speed, or 1 to 1½ hours
per day in hand, is a reasonable allowance. Distance divided by total
passage time gives the speed of advance (SOA) required. The time in
hand at various SOAs may then be calculated if desired; this also gives
a cross check against the calculations.
5. Determine the Estimated Time of Departure (ETD) and the Estimated
Time of Arrival (ETA). The SOA or the route may have to be adjusted
to make the ETA and ETD convenient. Cross-check that this does not
place the ship in a narrow or ill-lit channel at a bad time. If it does, the
ETA, the ETD or the SOA will have to be adjusted, or the risk accepted.
Do not forget to allow for any change in zone time while on passage.
The allowance for all these matters is illustrated below.

Torbay to Bishop Rock 129 miles

add for divergence from the route 4
total planning distance 133 miles
delaying time for exercises and operations
en route 3 hours
PLANNING THE PASSAGE 311

overall effect of tidal stream throughout

the passage nil
weather: likely weather, force 3-4 from
the south-west, estimate that it will set
the ship back an average of ¼ knot against
overall speed restriction owing to the need
for economical steaming 15 knots
allow for unforseen eventualities ½ knot against

Time to allow for the passage is:

133
+ 3 hours
15 − (¼ + ½)
= 12¼ hours (rounded to nearest ¼ hour)
SOA = 10.86 knots (133 miles in 12¼ hours)

Once the passage time has been calculated, the ETA and ETD may be
determined, e.g.

ETD 13 0800 (-1)

ETA 13 2015 (-1)

The passage chart

Having established suitable times for departure and arrival, plot the intended
track (see Note below) throughout the passage on a small-scale chart. In Fig.
12-4 (page 313) the plan for a passage from Torbay to Bishop Rock shows:

Distance from destination along the track; this provides a valuable cross-
check against the overall planned distance which should be amended
if necessary, with times and SOA adjusted as appropriate.
The times of alterations of course.
Suitable time intervals along the track, e.g. 1600/13.
Tidal streams and, if relevant, currents.
Areas and times where it is planned to conduct operations or exercises;
the position of the ship at the start of these operations or exercises and
her intended movement during them (PIM) should be drawn on the
chart.
Times of sunrise, sunset, moonrise, moonset, periods of darkness along
the track.
Positions where radio fixing aid chains (e.g. Decca) may change.

Note: Keep the track to multiples of 5 or 10 degrees where possible.

This makes life easier for the Officer of the Watch, the helmsman and others
concerned.
Relevant data should then be extracted from the Work Book and
summarised in the Navigating Officer’s Note Book (S548A or equivalent).
This is illustrated in Fig. 12-3 (page 312).
The overall plan must ensure that the needs of the ship’s departments are
met.
312 CHAPTER 12 - COASTAL NAVIGATION

Fig. 12-3. Coastal passage plan: NO’s Note Book

 PLANNING THE PASSAGE

Fig 12-4. Coastal Passage - The Passage Chart

313
314 CHAPTER 12 -COASTAL NAVIGATION

Fig. 12-5. The Passage Graph

PLANNING THE PASSAGE 315

The passage graph

Having determined the ETA and ETD and prepared the small-scale chart, the
navigator may drawn up a passage graph. This is an invaluable aid to the
planning and the execution of a passage of any distance or complexity.

Constructing the graph (Fig 12-5)

1. Plot the time along the X axis and distance to run (DTR) along the Y
axis, using the largest possible time and distance scales for the graph.
2. Construct the speed scale as follows:
(a) Choose a convenient point of origin P, and a convenient horizontal
time scale PQ, using the time scale of the graph; e.g. in Fig. 12-5, PQ
is the equivalent of 6 hours.
(b) Plot vertically downwards from Q the distances run for each speed
required during the time selected, using the distance scale of the
graph; e.g. the distance run in 6 hours at 15 knots is 90 miles; thus,
QR = 90 miles.
(c) The slope of the line joining these points to the origin P represents the
SOA at the scale of the graph.

Using the passage graph as an aid to planning

The passage from Torbay to Bishop Rock (Figs 12-3 and 12-4) is drawn up
on the graph as follows:
1. Plot A, the ETD (13 0800A) against the DTR, 133'.
2. Plot D, the arrival point, ETA 13 2015A. It may often be advisable to use
an ‘arrival gate’ (see page 329) in preference to the final ETA.
3. Join AD by means of a pecked line. The slope of AD gives the overall
SOA required, in this case 10.86 knots. AD’s slope may be measured
against the speed scale using a parallel ruler.
4. Plot horizontal lines at the appropriate DTRs to represent important
navigational features (e.g. Start Point at 114' and Lizard Point at 51' to
go).
5. If necessary, plot vertical lines representing favourable and unfavourable
tidal stream ‘windows’ (e.g. off the Lizard, the tidal stream is not
favourable until about 1700 on 13th April). This is particularly important
in difficult waters with strong tidal streams such as the Pentland Firth or
Dover Strait.
6. Plot rendezvous (R/Vs), exercises, etc. Point B is an R/V at 13 1000A,
B C a 6 hour exercise period with a low SOA. If a zero SOA is
required, as is sometimes the case during an exercise period, the slope of
the graph will be horizontal.
If planning for a group of ships, the graph may also be used to select
suitable rendezvous times and positions.
7. Find the speed required for each section of the passage, by joining the
relevant points A, B, C, D on the graph and measuring the slopes to
determine the SOA. The SOA between A and B is 15 knots; between B
and C it is 6.8 knots; and between C and D it is 14.5 knots.
8. The graph may also be used to find the ship’s position at selected times,
including sunrise and sunset, and these may be cross-checked against the
passage chart as necessary.
 316 CHAPTER 12 -COASTAL NAVIGATION

Large-scale charts
1. Plot the intended track and time on the selected large-scale charts in
sequence of use. Part of the track is illustrated in Figs 12-6 and 12-7
(page 318). Mark the DTR to the destination at suitable intervals.
2. In addition, plot:
Times of alteration of course and speed
Tidal streams (and currents if applicable).
Times and ranges of raising or dipping lights.
Sunrise and sunset.
Where to change charts.
3. Take the small-scale chart, passage graph and appropriate harbour plans
(see Chapter 13) to the Captain for approval. Advise on the writing up
of the Captain’s Night Order Book (see page 165). Be prepared to adjust
the plan for last minute changes to the ship’s programme.

EXECUTION OF THE PASSAGE PLAN

The execution of the passage plan must involve a well-organised bridge
procedure to detect any error in sufficient time to prevent a grounding. In
open waters, it is normally sufficient to proceed from point to point, fixing
the ship’s position at intervals. The permissible deviation from the track, and
the speed of the ship, determine the frequency and required accuracy of the
fixes. The choice of fixing method depends upon the accuracy and reliability
of the systems available, the time between successive fixes, and the time
taken to fix. This in turn will depend, in part, on the accuracy and reliability
of the ship’s navigational equipment: compasses, logs, radars, etc.

| Defence Watch OOW (wearing an infra-red COL headset) at the chart table (T23)
PLANNING THE PASSAGE 317

Fig 12-6. Coastal passage plan: large-scale chart (1)

318 CHAPTER 12 -COASTAL NAVIGATION

Fig 12-7a. Coastal passage plan: Large-scale chart (2)

PLANNING THE PASSAGE 319

Fig 12-7b. Coastal passage plan: Large-scale chart (3)

 320 CHAPTER 12 -COASTAL NAVIGATION

| A ‘Traditional’ T23 Bridge (at Action Stations) with aft facing SNAPS table

| A ‘Later’ T23 Bridge (at SSDs) with forward-facing radar and SNAPS table
PLANNING THE PASSAGE 321

Method of fixing
The standard method of fixing on a coastal passage is by visual compass
bearings, while maintaining a DR and EP ahead of the ship. Visual fixing,
plotting the position, frequency of fixing, time taken to fix, keeping the
record and establishing the track are all covered in Chapter 8 in the section
on ‘Chartwork on Passage’.
A back-up or secondary method of fixing should also be available, which
may be used to cross-check or monitor the standard method. This is usually
radar or a radio fixing aid such as Decca.
In restricted visibility, when it becomes no longer possible to use visual
bearings, radar fixing usually becomes the standard method, with a radio
fixing aid such as Decca being used as an independent (secondary) check.
When radar ranges are being used, consider the use of the parallel index
technique as described in Chapter 15. Sometimes the visibility is such that
a mixture of visual bearings and radar ranges will be used as the standard
method, with a radio fixing aid as a back-up.
The echo sounder is a further check against any possible error and its use
must not be overlooked. In coastal waters, particularly when the range of the
tide is large, an allowance should also be made for the height of tide.
If there is doubt about the ship’s position when close to danger, it is
usually wise to stop the ship and establish the position before proceeding.

Selecting marks for fixing

Chapter 9 refers to the selection of likely marks for fixing. A study of the
chart together with the Sailing Directions usually reveals a number of marks
suitable for fixing, visually and by radar.
For example, a study of the Channel Pilot reveals that, in addition to
those objects such as lighthouses, prominent headlands, left- and right-hand
edges, off-lying rocks and islets, the following conspicuous objects in Figs
12-6 and 12-7 (pages 317, 318) may be seen between Berry Head and Yealm
Head:

1. Day beacon at Dartmouth.

2. Water tower at Dartmouth.
3. Stoke Fleming church tower.
4. Two tall radio masts, 1 mile north-west of Start Point.
5. Radio masts, 1 and 3 miles north-west of Bolt Head. |
6. Malborough church spire.
7. Bigbury church spire.
8. CG lookout (disused) south-east of Yealm Head. |

A conspicuous object is a natural or artificial mark which is outstanding,

easily identifiable and clearly visible to the mariner over a large area of sea
in varying light. Conspicuous objects are indicated on the chart by the legend
written alongside the feature in bold capital letters, e.g. TOWER, SPIRE,
HOTEL, etc. On older charts, the term ‘conspic’ may still be found, printed
alongside a conspicuous feature. Buildings are sometimes blocked in on the
chart in black, but only a few of these may be conspicuous.
Other objects, not necessarily conspicuous may also be found suitable for
fixing: e.g. the monument at Slapton Ley (9), or Thurlestone church tower
(10).
322 CHAPTER 12 -COASTAL NAVIGATION

It is often helpful to write on the chart a brief description of the object,

taken from the Pilot or List of Lights. For example, Start Point lighthouse is
a white round granite tower, 28 metres in height. Bolt Head is a very
prominent headland connected to Bolt Tail by a high ridge faced by abrupt,
dark rugged cliffs.
The topography of the chart, together with the Pilot (including
photographs and sketches) will also usually reveal a number of suitable marks
for fixing, both man-made and natural: e.g. steep-to river valleys, road and
railway bridges, peaks of hills and mountains, cliff edges and so on. The
topography itself may frequently be a guide to the identification of
objects&particularly when there are two similar objects close together of
which only one is visible. Chimneys, flagstaffs, radio masts, and even
churches, can cause confusion if there are a number in close proximity, and
great care must be taken when ‘shooting up’. The radio masts north-west of
Bolt Head in (5) above are a good example of this.
Chimneys, flagstaffs and radio masts are also objects which are liable to
change (removal or installation) without notification, particularly flagstaffs.
Visual fixing by night is often dependent on the various lights available
and these will be clearly marked on the chart. It is extremely important to
check the characteristics of lights on first sighting for correct identification.
It may be advisable to use a stopwatch to time the period. If the
characteristics of a light have been changed, this will usually be notified in
Part V of the Admiralty Notices to Mariners before Part II. Do not forget
there may be other lights outside the limits of the chart in use which may be
seen. For example, the Lizard Light (Fig. 12-4) can be seen up to 50 miles
away when the meteorological visibility is of the order of 20 miles, provided
that the height of eye permits. Even when the height of eye is insufficient, the
loom may well be seen at this range.

Fixing using radar, radio fixing aids and beacons

Radar and radar beacons (racons and ramarks) are dealt with in full in
Chapter 15. Coastal radio aids are fully dealt with in Volume III of this
manual; these include Decca, Loran-C, Hyper-Fix, MFDF radio beacons and
directional radio beacons. Particulars of stations and their coverage are given
in Admiralty List of Radio Signals (ALRS) Volume 2 (radio and radar
beacons) and Volume 5 (Decca and Loran-C).
When planning a coastal passage, the coverage of these aids needs to be
taken into account and decisions made as to their usefulness.
Modern radio aids give the mariner his position with sufficient accuracy
to make a landfall and then proceed to port, regardless of the visibility. The
aids must, however, be used intelligently, as the accuracy and range which
may be obtained from these systems vary considerably.
The accuracy of the radio aid fix depends on three things:

1. The distance of the observer from the transmitter(s).

For hyperbolic fixing systems such as Decca and Loran-C:

2. The position of the observer relative to the base-line joining the pair of
stations in use.
PLANNING THE PASSAGE 323

3. The angle of intersection of the hyperbolic position lines emanating from

the stations.

When using radio aids, it is important to be on guard against the vagaries

of radio wave propagation. At night, for example, ground and sky waves
from a transmitter can interfere with each other to such an extent that the
effective range of the system is very much reduced (e.g. MFDF) or ‘lane slip’
occurs (e.g. Decca), giving unreliable fixes. This ‘night effect’ is particularly
severe at dawn and dusk.
Radio waves are usually subject to refraction when crossing the coast.
This can cause a radio wave from a radiobeacon to be deflected by as much
as 5°. With an aid like Decca, the error is published by the company as a
fixed error correction. Decca readings are also subject to variable errors
caused by variations in the propagation effect of the atmosphere, and these
may change from hour to hour, although the maximum extent is usually
predictable.
At best, MFDF is unlikely to give a bearing accurate to within ± 3°, and
this only within about 100 to 150 miles of a radiobeacon by day. The range
is very severely reduced at night to about 75 miles. In many cases the
maximum range of radiobeacons (see ALRS, Volume 2) is only of the order
of 50 miles. Aero radiobeacons suitable for marine use tend to have a longer
range.
The accuracy obtainable from Decca is affected by the time of day and
the season of the year in addition to those factors already mentioned. Under
favourable conditions, the system is capable of giving a position accuracy
correct to within ± 50 metres (95% probability*) up to 100 miles from the
master station; but at longer ranges out to 350 miles and at poor angles of cut
of the position lines, fixing accuracy in full daylight may be far less precise,
of the order of ± 2000 metres (95% probability). At dusk and at night,
dependent on the time of year, the order of accuracy may be even further
reduced, dependent on the range of the master station and the angle of cut of
the position lines. It is important to apply the variable error correction taken
from the tables in the Decca operating instructions to establish the likely
position circle. For example, at night in midwinter at maximum range from
the master station (240 miles), in the SW approaches to the United Kingdom,
the radius of the position circle generated by a Decca fix can be as much as
6 miles in extent (95% probability).
Ground wave ranges from Loran-C of from 800 to 1000 miles are usual,
depending on transmitter power, receiver sensitivity and attenuation over the
signal path. Errors vary from about ± 15 metres to ± 75 metres at 200 to 500
miles from the master station, increasing to ± 150 metres at 1000 miles.
Within the ground wave coverage shown in ALRS, Volume 5, fixing accuracy
can generally be expected to be within ± 500 metres (95% probability).
Information obtained from radio aids can be misleading and should
always be checked whenever possible with position lines or fixes obtained
from visual observations, or with fixes obtained from a different radio aid
(e.g. Decca may be cross-checked with radar and vice versa). A fix from a
radio aid which is markedly different from the EP must be carefully weighed
up, particularly if it is unconfirmed by other fixing means.

* The principles of probability as they affect navigation are set out in Chapter 16.
324 CHAPTER 12 -COASTAL NAVIGATION

Navigational equipment
It is important to ensure that the ship’s navigational equipment is working
correctly and at optimum efficiency. Not only should performance be
checked before sailing but it should also be checked at regular intervals (once
a watch or more frequently) throughout the passage and, in particular, before
entering narrow or ill-lit channels or other hazardous areas. Particular items
of equipment for which performance should be closely monitored are
compasses, radars and radio fixing aids. Compasses and radio fixing aids are
subject to random errors, while the performance of radars may deteriorate
without warning.

Compasses
Methods of ascertaining gyro-compass errors or deviation in the magnetic
compass are explained in Chapter 9. The chart should always be studied for
suitable transits which may be used to check the gyro error or magnetic
compass deviation, and these should be noted on the chart or in the Note
Book. In Fig. 12-6, for example, the following transits can be used to check
the compass error just before an alternation of course and afterwards when
steady on the new track.

Berry Head φ Downend Point 203½°

Dartmouth Water Tower φ Mew Stone 287°
Start Point φ Prawle Point 249°
Prawle Point φ Bolt Head 280½°

Keeping clear of dangers

Clearing marks and bearings, vertical and horizontal danger angles and radar
clearing ranges may be used to keep clear of a danger. These measures are
also discussed in Chapters 13 and 15.

Clearing marks and bearings

Clearing marks are selected objects, natural or man-made which, when in
transit, or just open* of each other, define a clearing line which leads clear of
danger. In Fig. 12-6, Berry Head 021° open of Downend Point
leads east of Skerries Bank (i.e. Berry Head should be ‘kept’ to the right of
Downend Point). Provided a ship takes care not to go inside this line, i.e. the
bearing of Berry Head NMT 021°, but keeps the marks ‘open’, she will pass
clear of the danger.
When clearing marks are not available, a line of bearing may be drawn
on the chart through a clearly defined shore object to pass a safe distance
from a danger. This line of bearing is called a clearing bearing and is
illustrated in Fig. 12-8. Provided the bearing of the church is kept not less
than (NLT) 260° and not more than (NMT) 272°, the ship will pass safely
between the wreck to the north and the shoals to the south on the way in to
the anchorage.

*Marks are said to be open when they are not exactly in transit (see page 349).
PLANNING THE PASSAGE 325

Fig. 12-8. Clearing bearings

Vertical and horizontal danger angles

Vertical and horizontal danger angles may be used to ensure the safety of the
ship in vicinity of dangers.

Vertical danger angles

It is required to pass 5 cables clear of a rock distant 3 cables from a
lighthouse, height 29 metres above MHWS is 5.5 metres above chart datum
and the predicted height of tide is 4.0 metres.
This is shown in Fig. 12-9 (p.326). The height of the light above sea
level is 29 + 5.5 - 4.0 = 30.5 metres. With centre the lighthouse and radius
8 cables, describe an arc of a circle. Norie’s Nautical Tables (Distance by
Vertical Angle) will give the angle subtended between the lantern and sea
level from any point on the arc of the circle. For a corrected height of 30.5
metres and a range of 8 cables, the angle is 1°11'.
Set this angle on the sextant. Provided the reflected image of the lantern
appears below sea level, the ship is outside the arc of the circle and in safety.
If the height of the tide is not allowed for, and the height of the light as
printed on the chart is used instead, the ship will be further from the light than
is apparent, except in the unlikely event of sea level being above Mean High
Water Springs.
In the above example, if 29 metres is used for the height, the vertical
angle is 1°7'. For an actual height of 30.5 metres, 1°7' gives an actual range
of 8.5 cables.
326 CHAPTER 12 -COASTAL NAVIGATION

Fig. 12-9. Vertical danger angle

Horizontal danger angles

The horizontal angle between two objects on shore may be used in a similar
way. Objects should be chosen lying approximately the same distance on
each side of the danger to be cleared (Fig. 12-10). The chart should be
marked at the distance considered safe to pass, and lines should be drawn
from the objects to the mark. The angle thus formed is measured and, if the
angle subtended by the objects is less than that measured, the ship is outside
the danger and in safety.
In Fig. 12-10, the horizontal danger angle for a clearance of 5 cables from
the rock is plotted as 78°. So long as the horizontal angle between the
lighthouse and the CG lookout remains less than 78°, the ship is outside the
danger circle.
If the angle of 78° is set on the sextant, the CG lookout will appear to the
left (the ‘wrong side’) of the lighthouse when the actual angle between the
objects is less than 78°, i.e. when the ship is outside the danger circle.
PRACTICAL HINTS 327

Fig. 12-10. Horizontal danger angle

Radar clearing ranges

The use of radar for keeping clear of dangers is discussed in Chapter 15.

PRACTICAL HINTS

Various ‘wrinkles’ or useful hints when executing a coastal passage are set
out below.

Calculating the distance that an object will pass abeam

It is a help to be able to determine the distance a ship will pass an object
abeam on a certain course, and by how much the course may have to be
changed in order to pass the object a desired distance away. An allowance
must be made for any tidal stream etc. across the track.
An abeam distance of approximately 1 mile (BC in Fig. 12-11, p.328) is
subtended by an angle of 1° (angle BAC) at a distance of 60 miles (AB).
From this rule of thumb may be deduced other useful data, e.g.

An abeam distance of 2 cables is subtended by an angle of 1° at a distance

of 12 miles (12÷ 60 x 10).

An abeam distance of ½ cable is subtended by an angle of 1° at a distance

of 3 miles (3 ÷ 60 x 10).
328 CHAPTER 12 -COASTAL NAVIGATION

Fig. 12-11. The abeam distance subtended by an angle of 1°

EXAMPLE
A light is sighted 10° on the bow at an estimated distance of 12', and it is
desired to pass 4' from the light. What is the clearance from the light on the
present coarse and what alteration of course is necessary?

Fig. 12-12. Alteration of course required to pass at a given distance

If the ship remains on the present course (Fig. 12-12), the distance of the
light when it is abeam, BC, will be (12÷ 60 x 10) = 2 miles.

At 12' the estimated offing per degree is 12 ÷ 60 = 1/5 mile. To pass 4'
off, therefore, alter course 10° outwards from the present course to bring the
light 4 x 5 = 20° on the bow.

The time of arrival

Circumstances nearly always tend to make a ship late rather than early and,
for this reason, it is always wise to allow something in hand for unforseen
eventualities (see page 310). Remember that, when speed has to be adjusted
to arrive at the correct time, there are two factors to be allowed for:

1. The time already lost or gained when the decision to adjust speed is
made.
2. The time the ship will continue to lose or gain if tidal stream and weather,
etc. remain unchanged.

Any error in estimating the time on passage may readily be seen by

comparing the actual time with the planned time shown on the chart.
PRACTICAL HINTS 329

Adjustments in speed may then be made as necessary; the passage graph (Fig.
12-5, page 314) is a very useful aid in this respect. To monitor the ship’s
progress, proceed as follows:

1. Fix the ship, measure the DTR, plot the position on the graph; e.g.
position E, 131200A, DTR 99'.
2. Measure the time ahead/astern of the plan (e.g. EF, 1 hour 24 minutes
astern).
3. Measure the distance ahead/astern of the plan (e.g. EG, 10' astern).
4. An increase in the speed of advance is clearly needed; the graph enables
this to be found quickly and easily.
5. Joint point E to the next required position, in this case point C, the end
of the exercise period.
6. Determine the revised SOA by measuring the slope of EC against the
speed scale, in this case 9.25 knots.
7. Adjust speed as requisite.

To ensure a precise time of arrival without having either to crawl over the
last few miles or to proceed with unseemly haste, gates should be established
some distance before the actual point of arrival through which one should aim
to pass at a particular time. In a destroyer or a frigate, an ETA should be
aimed at a position some 12 to 15 miles from the official arrival point, say 1
hour before the actual ETA. It is then a relatively simple matter to adjust the
speed to make the right time of arrival. For example, if the official time of
arrival is 0900, a gate may be set up 12 miles to go at 0800. If the ship is 5
minutes late at the gate, it is immediately apparent that an SOA of only 13.1
knots is required (an increase in speed of just over 1 knot) to make the ETA
precisely. A further gate at around 0830 will confirm the accuracy of the
calculations and, if any adjustment is necessary, it is bound to be a small one.
In the larger ship, entering ports like Devonport or Portsmouth, two gates
will almost always guarantee an ETA correct to within a few seconds; for
example, Gate 1 may be 11 miles to go, 1 hour before ETA, SOA 12 knots;
Gate 2 at 3 miles to go, 20 minutes before ETA. The second gate, requiring
an SOA of only 9 knots to the entry point, permits the necessary adjustments
to bring the ship down to a suitable manoeuvring speed for entry (of the order
of 6 to 8 knots). For other ports, the timing or positioning of the gates may
be adjusted depending on the desired speed at entry.

Buoys and light-vessels

The use of buoys and light-vessels for navigation has already been covered
in detail in Chapter 10. When shore marks are difficult to distinguish because
of distance (the Thames Estuary for example) or thick weather, buoys and
light-vessels must often be used instead. Treat light-vessels, lanbys and light-
floats with a proper degree of caution; never rely exclusively on buoys.

When not to fix

On occasions when only mountain summits or distant or inconspicuous marks
are visible, an apparent fix may give a position widely different from the EP.
If there is no reason to distrust the EP, a fix in these circumstances should be
330 CHAPTER 12 -COASTAL NAVIGATION

treated with caution. Objects which are distant or difficult to distinguish

should either be ‘shot up’ precisely or disregarded.

Tidal stream and current

When navigating along the coast, an indraught into a bay or bight is common.
Sometimes there is an indraught at one end and an outdraught at the other.
Currents, tidal streams and tides are affected by the wind. Take care,
however, to distinguish between wind effect on the current or tidal stream and
wind effect on the ship; it is easy to confuse the two.
Wind often has a marked effect on the time of change of the tidal stream,
as much as 1 to 2 hours. Wind also affects both the time of change and the
height of tide.
Tidal stream data must always be used with caution; particularly at
springs, tidal streams experienced are frequently different from those
calculated.

The record
An example of keeping the navigational record in the Navigational Record
Book (S3034) is given in Chapter 8.
Any gyro error or total error correction should be shown in the ‘Remarks’
column. The suffices G, T, or C (indicating Gyro, True or Compass) should
be used as appropriate. All transits should show both the observed and the
true bearings.
Other details concerning the stationing of ships in company, manoeuvres,
wind, tidal stream or current, soundings, alterations of clocks and so on
should all be entered in the ‘Remarks’ column.
When courses and speeds are recorded as ‘various’&for example when
entering or leaving harbour, carrying out manoeuvres or Replenishment at
Sea, full details and times of courses and speeds should be recorded on
automatic recording equipment or entered in the Record Book for Wheel and
Engine Orders (S580), so that a complete record is available from which the
track may be accurately reconstructed if required. Do not forget the value of
the plotting table or AIO computer in establishing the DR (Chapter 8) and the
use of tape recorders for records.
At the end of each passage, the Navigating Officer should carry out an
analysis of the navigational records to obtain data about the ship’s
performance under different conditions, and to provide a basis for subsequent
similar passages. Such information should be summarised in the Work Book
and the Navigational Data Book (S2677).

Flat and featureless coastlines

When it is necessary to make a flat coast with few prominent marks (such as
the Dutch coast north of Scheveningen), where radar may not be of much
assistance in identification, it is sound navigational practice to aim at a point
perhaps 10 or 15 miles to one side of the required position. The required
direction for the alteration of course on sighting the coast is immediately
known and, while running parallel to the coast, objects may be identified and
a fix obtained. The availability of radio fixing aids such as Decca may
obviate the need for aiming to one side, but remember the errors to which this
type of aid may be subject.
PRACTICAL HINTS 331

The echo sounder is frequently of great assistance in such circumstances

in giving warning of the coast’s proximity.

Fixing by night
It is surprising how much coastline may be identified visually at night for
fixing purposes. It should not be assumed that navigational lights are the
only visual method of fixing available. Islands often stand out well on dark
clear nights or may be clearly visible by moonlight. For example, those in the
Eastern Archipelago, which are not particularly well lit, can frequently be
seen quite clearly.

Altering course
Before altering course, always look along the bearing of the new course to see
that it is clear. Arrange also for a responsible officer or rating to look along
the appropriate quarter to see that no ship is overtaking from that direction.
When rounding a point of land very close to the ship which is to be kept
at a constant distance during the turn, put the rudder over by an amount
corresponding to the diameter of the turn required, a little before the point is
abeam. Subsequently adjust the rudder angle so that the object remains
abeam throughout the turn.

‘Wheel over’ bearings

Some mariners prefer to use cardinal (000°, 090°, etc.) or half-cardinal (045°,
135°, etc.) bearings to determine the moment of ‘wheel over’ when altering
course on a coastal passage. Others prefer to use a beam bearing. Others use
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 332 CHAPTER 12 -COASTAL NAVIGATION

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PASSAGES IN FOG AND THICK WEATHER 333

a specific bearing closely related to the next course. All three methods have
their uses.
As explained in Chapter 13, it is particularly important in pilotage work
to use a ‘wheel over’ bearing which is as parallel as possible to the new
course, as shown in Fig. 12-13. This gives the best prospect of achieving the
new track. Such bearings, however, are not always available on a coastal
passage.
Beam bearings are very convenient and easy to remember. This method
suffers from two disadvantages:

1. If the ship if off track to start with, the ship may end up off track by as
much or more than previously (Fig. 12-13).

2. Rounding a headland may from time to time require more than one
alteration of course and perhaps more than one abeam object, depending
on the tracks chosen (Fig. 12-14).

Cardinal and half-cardinal points (Fig. 12-15) are also easy to remember
and may be convenient. This method may be of particular value on routes
where traffic separation schemes do not permit the use of beam bearings. The
method suffers from the disadvantage, similar to beam bearings, that if the
ship is off track to start with, the ship will end up off track by as much or
more than previously if the bearing is not nearly parallel to the new course.
Moreover, a bearing abaft the beam may be ‘wooded’ (i.e. not visible from
the pelorus). In any case, it is preferable not to have to look astern for a
‘wheel over’ bearing when altering course.
If the bearing of a single object is changing rapidly, as in Figs 12-13 to
12-15, a useful running fix may be obtained. The time interval for a large
change of bearing is short; thus, the error in the estimated run between
bearings should be small.

Entering shallow water

Do not navigate in shallow water at high speed, particularly if in close
company with other ships. Shallow water effect (page 308) may cause
flooding in own ship if it has a low freeboard. In addition, a severe
interaction effect with other ships may be experienced over several hundred
metres.
A frigate or destroyer of 3500 tonnes at 15 knots will begin to experience
more than normal interaction or shallow water effect in depths of less than 39
metres. The depth at which more than normal interaction or shallow water
effect may begin to be experienced may be found from the formula:

depth (metres) = speed (knots) x 017

. 3 Displacement (tonnes) . . . 12.1

For a supertanker of ¼ million tonnes deadweight, at 10 knots, the depth is

107 metres. A large fast ship (50,000 tonnes at 18 knots) can experience
steering problems in such conditions sufficient to cause alarm.

PASSAGES IN FOG AND THICK WEATHER

The main consideration in fog is usually the proximity of shipping and the
need to avoid getting into a close quarters situation (International
334 CHAPTER 12 -COASTAL NAVIGATION

Regulations for Preventing Collisions at Sea, 1972 (Rule of the Road), Rule
19). The use of radar for collision avoidance is discussed in Chapter 17.
The navigation of coastal passages in fog is hardly more difficult than in
visual conditions due to radar and radio fixing aids. There may be a
reduction in fixing accuracy by having to change from visual means to radar
or radio fixing aid, and this may be a limiting factor when considering a
passage through an area where there are a number of navigational hazards.
There is a further limitation in the event of unreliability or breakdown of
radar or radio aid equipment, and in the effect of random errors in the fixes.
In times of war or international tension, such aids may not be available or
may be subject to jamming.
The necessity for keeping a good EP reinforced by soundings is therefore
most important in fog. A series of visual fixes taken up to the moment a ship
enters fog, especially in areas of strong tidal stream such as the English
Channel, will give a very clear indication of the likely future ground track.
The record (page 330) of similar passages in clear weather is likely to be
of sound value in navigating safely and accurately in fog and thick weather.
The record should include the estimated times on each course and the
estimated currents and tidal streams, together with the actual results
experienced. The reasons for any discrepancies should be investigated at the
end of every passage, so that adjustments may be made to minimise such
errors on subsequent occasions.
It should be remembered that, in thick weather when there is little or no
wind, estimates of tidal streams and currents may be relied on to a greater
extent than in rough weather.
The speed of the ship is an important factor. Although at very low speeds
the ship is much affected by tidal streams and currents, the advantage of
higher speed must be balanced against other dangers, such as risk of collision.
The visibility in fog should be estimated whenever possible, and the
ship’s speed adjusted accordingly. Visibility of buoys can be ascertained by
noting the time or range of passing a buoy and the time or range it disappears
in the fog. Visibility circles, thus estimated and plotted around succeeding
buoys, will show when the latter may be expected to appear. When it is seen
that the ship is about to enter fog, always note the approximate bearing,
distance and course of any ships in sight; and, if possible, obtain a fix.

Before entering fog

1. Reduce to a safe speed (Rule of the Road, Rules 19 and 6).
2. Operate radar and radio fixing aids (Rule of the Road, Rule 7). Ensure
the charts in use are annotated for suitable radar fixing marks.
3. Consider closing up and operating the blind pilotage/safety team (Chapter
15).
4. Station lookouts. Lookouts should be in direct telephonic
communication with the bridge, or should be supplied with portable
radios or megaphones. Forecastle lookouts should be taught to indicate
direction by pointing with the outstretched arm.
5. Operate the echo sounder, and give instructions for depth reporting.
6. In the vicinity of land, have an anchor ready for letting go.
PASSAGES IN FOG AND THICK WEATHER 335

7. Order silence on deck.

8. Close watertight doors and assume the appropriate damage control state
in accordance with the ship’s Standing Orders.
9. Start the prescribed for signal.
10. Warn the engine room.
11. Decide if it is necessary to connect extra boilers, diesels or gas turbines.
12. Memorise the characteristics of fog signals which may be heard.
Remember that sound signals on some buoys are operated by wave
motion and are thus unreliable.
13. Make sure that the siren is not synchronising with those of other ships,
or with shore fog signals.
14. Should radar not be working efficiently, be prepared to take DF bearings
of radiobeacons and of other ships operating radio in the vicinity.
15. If in any doubt about the ship’s position, alter course at once to a safe
course, parallel to or away from the coast.

Visibility
If there is better visibility from the upper deck or masthead than from the
bridge, a relative bearing of an object sighted from either of these positions
(and especially a beam bearing) will almost certainly improve the EP.
When fog is low-lying, the masts or smoke of ships in the vicinity may
frequently be seen above the fog; hence the need for a lookout as high as
possible.

Practical considerations for passages in fog

If a long passage is being undertaken, for example from Portsmouth to New
York, there is little advantage in taking departure for the Atlantic voyage
from Bishop Rock rather than, say, St Catherine’s Point (Fig. 12-16, page
336). The distance from St Catherine’s to the Bishop is of the order of 200
miles while that from the Bishop to New York is more than 2900 miles. It
makes little difference to the landfall off New York whether the last fix on
leaving the United Kingdom was 2900 or 3100 miles from the destination.
There is therefore little reason, except for such matters as operational
necessity, for embarking on a point to point coastal passage in fog to be
followed directly by a long ocean voyage. In such circumstances it is more
sensible to stand well offshore, keeping clear of navigational hazards,
following the elementary jingle ‘Outward bound, don’t run aground’. A great
deal of coastal shipping will also be avoided.
On the other hand, the navigator of a ship that is proceeding in fog from,
say, Portsmouth to Devonport, is faced with the problem of knowing his
position accurately enough to make a safe landfall on approaching the
destination, if he has stood well offshore to avoid shipping and navigational
hazards. If he has reliable radar and radio fixing aids, backed up by a good
echo sounder, his navigational problems are similar whether he stays 2 miles
off the coast or 20. His main concern will be to balance the avoidance of
shipping against the additional distance to be steamed. If, however, radar and
radio fixing aids are not available, the navigator will be in a much stronger
position, as he approaches Devonport, in knowing his position at Start Point,
 336 CHAPTER 12 -COASTAL NAVIGATION

| Fig. 12-16a. English Channel (West)

| Fig. 12-16b. English Channel (East) - on same scale as Fig 12-16a

NAVIGATION IN CORAL REGIONS 337

25 miles from Plymouth breakwater, having heard the fog signal there and
checked his EP against it and the depth of water, than if his last position was
off St Catherine’s Point some 120 miles earlier; similarly, for his position at
Start Point, if he has heard Portland Bill; and so on. Thus, in fog without
radar and radio fixing aids, it is usually wiser to proceed from point to point.
Entering narrow waters in fog, such as the Dover Strait, the ship’s
position must be known accurately before embarking upon the passage. On
approaching such waters, always consider the likely error in position and
what precautions, such as the echo sounder, are available should the
reckoning be incorrect. For example, on a passage from the north-east
through the strait (Fig. 12-1), the ship’s position must be established at South
Falls in order to approach the Goodwins safely. Similarly, the position at the
Goodwins must be verified in order to pass clear of the Varne. Unless
reliable radar or an accurate radio fixing aid is available, the ship’s position
must be determined by the accuracy of the EP, and information from the echo
sounder, from DF bearings and from the various fog signals. Many ships
transit the Dover Strait in fog in safety with a minimum of aids, but care and
prudence along the lines already discussed in this chapter are necessary.
The ship may be ahead, astern, to port or to starboard of the reckoning.
The event of each possibility and its impact on the ship’s navigation must be
assessed. For example, to be more than 1 or 2 miles to port or starboard of
track could be disastrous; alternatively, up to 10 miles to port or starboard of
track could be perfectly safe, yet to be 2 miles ahead of the reckoning could
be fatal. Each possibility has to be considered and adequate safeguards taken
against those errors which could be dangerous.

NAVIGATION IN CORAL REGIONS

Coastal navigation in coral waters can range from relatively simple and short
transits, such as those through the Balabac Strait between Palawan and
Borneo, to lengthy and complex passages, such as the channel inside the
Great Barrier Reef, which lies off the Queensland coast in NE Australia, over
1300 miles in length and varying in width from 40 miles at the southern
entrance to a few cables at the northern end. In the more difficult parts of the
Great Barrier route, navigation becomes more an exercise in pilotage than the
fairly straightforward task of point to point coastal navigation.

Growth of coral reefs

Although depths over many coral reefs can remain unchanged for a long time
(50 years or more), coral growth and the movement of coral debris can
change depths over other reefs and shoals to a great extent. Decreasing
depths from these two causes may be as much as 0.3 metre per year.
Decreases due to coral debris alone have been known to exceed this rate. For
example, some of the small coral heads in Darvel Bay in E Sabah grew from
a depth of 14 fathoms (25½ metres) to within a few feet (less than 1 metre)
of the surface in a period of about 70 to 80 years. The rate of growth of the
massive reefs which could damage even the largest vessels is, however, only
about 0.05 metre per year.
338 CHAPTER 12 -COASTAL NAVIGATION

Windward channels tend to become blocked by debris and by the inward

growth of the reefs, but leeward channels are usually kept clear by the ebb
stream, which is often stronger than the flood and thus deposits the debris in
deep water outside the reefs.
Coral reefs are frequently steep-to and depths of over 200 metres may
exist within 1 cable of the reef’s edge. In such circumstances, soundings are
of little value in detecting the proximity of a reef. In addition, soundings may
shoal so quickly that it is difficult to follow the echo sounder trace,
particularly as the echo is often weak because of the steepness of the gradient.
Coral usually grows to windward and is steeper on the side of the prevailing
wind.
When navigating in coral waters, take into account the likely decrease in
depths since the date of the survey on which the chart is based. If the survey
is an old one, proceed with caution.

Navigating by eye
A common feature of coral regions is the lack of marks for fixing, particularly
those ahead and astern. It frequently becomes necessary to navigate by eye.
Navigate with caution. Place lookouts aloft and on the forecastle. Use
the echo sounder continuously. Coral can best be seen:
1. From the masthead.
2. When the sun is high and behind the observer and unobscured by cloud.
Above 20° elevation is best.
3. When the sea is ruffled by a slight breeze. A glassy calm makes it very
difficult to distinguish the colour differences between shallow and deep
water.
4. When polaroid spectacles are worn. These make the differences in colour
of the water, explained below, stand out more clearly.

Range of sighting
In good weather with a height of eye of about 10 to 20 metres, coral patches
with depths of water less than about 6 to 8 metres should be sighted at a
distance perhaps of about ½ mile. Good communications from the masthead
to the bridge are essential if avoiding action is to be taken in time. Speed
must be sufficiently slow so that the ship may be stopped or anchored
quickly, yet high enough to maintain steerage way and cope with tidal
streams and currents. A speed of about 4 to 8 knots should normally suffice.

Colour of reefs
When the water is clear, the depth over a reef may be estimated by the
following colours:

LIGHT BROWN reefs with depths of less than 1 metre.

LIGHT GREEN reefs with depths of 2 metres or more.
DARK GREEN reefs with depths of 6 metres or more.
DEEP BLUE reefs with depths of 25 metres or more.

Unmarked narrow channels

In narrow channels between coral reefs, try to keep in the centre of the
channel. If no marks are available, the position of the ship relative to the
NAVIGATION IN CORAL REGIONS 339

centre of the channel may be ascertained by placing a man on the centreline

of the ship facing forward in a position where each side of the reef can be
seen. With arms outstretched to the maximum extent on each side of the
body, each arm is pointed down to the edge of the reef. The angle of the arms
will show whether the ship is in the centre of the channel. For example, if the
left arm is pointing further down than the right, the ship is to port of the
centre of the channel; course should be adjusted to starboard.

Disturbed water
If the water is not clear, it will be almost impossible to see the coral reef and
so navigate by eye. The only safe method is to sound ahead of the ship with
boats.

Cloud patches
Cloud patches are often reflected by the sea and look exactly like reefs,
although it may be possible to see their movement across the water.
If the sun becomes obscured by cloud, nearly all the reefs will disappear
from view and the only safe method is to sound ahead with boats.

Cross currents and weather

Currents and tidal streams frequently set across coral channels rather than
along them; examples are the inner route of the Great Barrier Reef and the
Santaren Strait west of the Great Bahama Bank.
Rain squalls are fairly common in coral regions and are frequently so
heavy as to obliterate everything in sight. In such circumstances, it may be
prudent to stop, or anchor and wait for the weather to clear; this usually
happens quickly.

Edges of coral reefs

The windward or exposed edges of coral reefs are often more uniform than
the leeward edges and may also have water breaking over them; they are thus
more easily seen. The leeward sides of reefs frequently have detached coral
heads which are difficult to see.

Passing unsurveyed reefs

Pass on the weather side because the edges and off-lying pinnacles will be
shown by the sea breaking over them.
340 CHAPTER 12 -COASTAL NAVIGATION

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 341

CHAPTER 13
Pilotage

Fig 13-0. A Type 23 Frigate (HMS KENT) entering Portsmouth harbour |

|

Within the Royal Navy, the planning and execution of pilotage is an

important and demanding part of a Navigating Officer’s duties. This chapter
comprises a brief discussion of the regulations for pilotage for HM Ships and
for merchant ships,* followed by detailed instructions for the planning and
execution of pilotage.
In this book, a distinction is drawn between visual pilotage (Chapter 13)
and blind pilotage (Chapter 15); the reader should remember, however, that
the two techniques are complementary to each other and are often used
together.

* To cater for a wider audience.

342 CHAPTER 13 - PILOTAGE

REGULATIONS FOR PILOTAGE

HM Ships
The regulations regarding pilotage in HM Ships are laid down in The Queen’s
Regulations for the Royal Navy(QRRN) and in Volume IV of this manual.
Amplifying information is to be found below.
The Navigating Officer of an HM Ship is in normal circumstances the
pilot of the ship although, if he is not a specialist in navigation, the duty of
pilotage devolves upon the Captain. If no navigation specialist is borne, the
Captain may undertake the pilotage himself or depute any other officer in the
ship to do so, although it is the usual practice for the officer appointed for
navigation duties to undertake the task.
The Captain of an HM Ship is normally authorised to employ at his
discretion a licensed or regular pilot for ports and channels which are difficult
of access or for which charts and directions are insufficient guide, or in
abnormal conditions.
Most British and Commonwealth ports are adequately charted. However,
the charts of a number of foreign ports, particularly the smaller ones, are

SEE BR 45
likely to be inadequate; in that case, it is usually possible to obtain suitable
charts and directions from the appropriate national Hydrographic Office.
It is not compulsory for an HM Ship to take a pilot in United Kingdom
ports. In Commonwealth and foreign ports, HM Ships must confirm to the
local regulations, which may require compulsory pilotage.
When a pilot is employed, the Captain of an HM Ship may use him in an

VOL 4
advisory capacity or direct him to take full control of the handling of the ship.
On the whole pilots are unused to the considerable power available in HM
Ships and for this reason they are more usually employed in an advisory
capacity.

‘The employment of a pilot does not relieve the Captain of his

responsibility for the safety of the ship, and in the event of an
accident which could have been prevented by a common degree of
attention on the part of the Captain or the Navigating Officer, these
officers will be deemed to have neglected their duty.’ (Volume
IV)

Merchant ships
For merchant ships, the regulations for pilotage are laid down by the national
authority or the shipping company, and in the orders for the port concerned.
Recommendations on pilotage are also made from time to time by IMO.
Regulations for merchant ships frequently require compulsory pilotage,
although Masters who have considerable knowledge of a particular port may
be exempted for that port, as may be certain ships regularly trading on the
coast concerned. In most ports, it is the usual practice for the pilot to take full
control of the handling of the ship between the pilot boarding place (usually
shown on the chart) and the berth. Despite the duties and obligations of a
PLANNING AND EXECUTION OF PILOTAGE 343

pilot, his presence on board does not relieve the Master or the Officer of the
Watch from his duties and obligations for the safety of the ship. The general
aim of the Master should be to ensure that the expertise of the pilot is fully
supported by the ship’s bridge team. The Officer of the Watch is required to
co-operate closely with the pilot and keep an accurate check on the vessel’s
position and movements. If there is any doubt as to the pilot’s actions and
intentions, these should be clarified immediately. If any doubt still remains,
it is up to the Master and/or the Officer of the Watch to take the appropriate
action to ensure the safety of the ship.

PLANNING AND EXECUTION OF PILOTAGE

The planning and execution of pilotage, anchoring and mooring described

here and in Chapter 14 assumes that the pilotage is planned and conducted by
the Navigating Officer, without the assistance of a pilot.

PREPARATORY WORK

The preparatory work required is in many respects similar to that for a coastal
passage (see Chapter 12). Full details should always be entered in the
Navigating Officer’s Work Book.

Charts and publications

Chart selection
Select the largest scale charts available including relevant Fleet charts (HM
Ships only). Ensure the charts are corrected up to date for all Permanent,
Temporary and Preliminary Notices to Mariners, radio navigational warnings
and Local Notices&refer to the Chart Correction Log and Folio Index (NP
133A, 133B). If proceeding to a foreign port, it may be necessary to make
arrangements to obtain the large-scale charts and plans published by the
Hydrographic Office of the country concerned. Usually these charts and
plans are available from national agencies at the larger ports and from the
relevant Hydrographic Office (see Catalogue of Admiralty Charts ..., NP 131,
for details). HM Ships arrange their supply through the Hydrographer,
Taunton. Remember that it may be necessary to obtain larger scale charts
produced by the national authority in order to enter the port concerned, e.g.
the United States, Canada. (See the Annual Summary of Admiralty Notices
to Mariners.)
Do not forget that extra charts for the port may have to be obtained for the
following reasons:

1. The departure plan may well be different from the entry plan.
2. The blind pilotage/safety team (Chapter 15) will require their own charts.
3. It may be desirable to have an entirely separate visual fixing team to
cross-check the execution of the pilotage plan; this team will also require
charts.
4. It may be preferable to use additional copies, cut up into appropriate
sizes, for use by the Captain and Navigating Officer instead of sketch
plans in the Note Book.
344 CHAPTER 13 - PILOTAGE

5. Boats’ crews may require a copy of the chart.

Publications
The following reference books should be consulted when preparing a pilotage
plan:

Admiralty Sailing Directions. Information on the directions to be

followed, maximum draught permissible in channels and port
approaches, tidal streams, topographic details, port regulations,
photographs and sketches.
Admiralty List of Lights and Fog Signals. Characteristics of lights (but
not buoys), description of light structures.
Admiralty Tide Tables. Times and heights of tide.
Tidal stream atlases. Details of tidal streams at springs and neaps.
Home Dockyard Ports&Tides and Tidal Streams (HM Ships only).
Recommended times of entry and departure, minimum under-keel
clearances, tidal stream data.
Port Guide/Fleet Operating Orders (HM Ships only). Detailed directions,
regulations, speed limits.
Navigational Data Book. Own ship characteristics (dimensions, draught,
etc.) turning data, etc.
Admiralty List of Radio Signals, Volume 6. Port operations, pilot
services, traffic management, including communication frequencies
and procedures.
Department of Transport Guide to the Planning and Conduct of Sea
Passages. Planning, execution and monitoring of passages under
pilotage.

Times of arrival and departure

The ETA and ETD were discussed in Chapter 12. Remember that the ETA
and ETD may be governed by the height of tide. Operations at many ports
are dependent upon the tide. The height of the tide may apply particularly to
the overall depth available and to the depth of water over dangers, also to the
desired minimum under-keel clearance (see page 308). Local Orders should
be consulted.
The navigator must always know the time limits within which the entry
or departure plan is valid. Tidal time ‘windows’ may be vital for arrival and
departure, particularly for ‘locking in and out’, the approach to the berth and
so on.
The Sailing Directions, the Port Guide or Home Dockyard Ports&Tides
and Tidal Streams may give advice concerning the best time to arrive at a
destination.
There are a number of other factors to be taken into account when
considering the best time of day to arrive. These include:

The period of daylight.

Likely local weather.
Working hours in the port.
Movements of other shipping, including those which keep to a
timetable like ferries.
PREPARATORY WORK 345

Ceremonial: administrative and domestic requirements such as:

Gun salutes.
Official calls.
Storing and fuelling.
Ship’s company leave.

Limiting danger lines

The water in which it is safe for the ship to navigate must be clearly shown
on the chart. This is done by drawing limiting danger lines (LDL) (Fig. 13-1,
p.346), which provide a clear presentation to the Captain and Navigating
Officer of the area of safe water. The LDL may be defined as a line drawn on
the chart joining soundings of a selected depth to delineate the area
considered unsafe for the ship to enter.
The selected depth must obviously provide sufficient water for the ship
to remain afloat, but it is important not to allow too great a safety margin to
the extent that the LDL is disregarded when approached. The following
factors need to be taken into account when determining the safe depth:

Ship’s draught.
Predicted height of tide.
Reliability of the chart and particular reference to the charted depths
(Chapter 6, pp.101 and 121).
The scend in the approach channel that may reduce the effective
depth.
An additional margin for safety.

The choice of the charted depth of the LDL is a matter for judgement and
no hard and fast rule can be laid down. If the chart has been recently
surveyed on a large scale using modern techniques, a great degree of
reliability can be placed upon the charted depths and the ship may be
navigated safely with a minimum depth of water under the keel. In such
circumstances, it will usually be safe for ships to draw the LDL for a charted
depth equal to the draught of ship, plus any allowances for squat, plus 2
metres (6 feet) safety margin minus the height of tide as shown in Table 13-1.

Table 13-1. Determining the LDL

Take Ship’s draught
Add Squat
Add Safety margin (usually 2m)
Total Above factors
Subtract Height of tide
Obtain Charted depth of LDL

Sometimes it may be necessary to reduce the safety margin for

operational reasons.
If the area has been poorly surveyed with perhaps only a sparse number
of soundings taken by lead-line many years earlier, it may not be possible to
346 CHAPTER 13 - PILOTAGE

Fig. 13-1. Limiting danger line

THE PILOTAGE PLAN 347

determine a safe LDL. It would be necessary to sound ahead of the ship

using boats, while proceeding with the utmost caution.
The navigator must decide upon the LDL which he believes will keep the
ship in a safe depth. An LDL approximating to 1½ times the draught of the
ship will usually be safe in the majority of cases but, as mentioned earlier this
can only be a matter for judgement, taking into account all the different
factors.
An LDL of 7 metres is shown in Fig. 13-1. This is for a frigate drawing
6 metres entering Portsmouth at a time when the allowance for squat is ¾
metre and the predicted height of tide is 1¾ metres. The charted depth to use
when drawing the LDL is thus 6 + ¾ + 2 - 1¾ = 7 m.
Appraisal of the passage
The charts and publications should now be closely studied to obtain a clear
mental picture of the passage. Information on directions, cautions, dangers
and tidal streams should be extracted from the Sailing Directions. A brief
description of any conspicuous marks should be entered on the chart. The
List of Lights should be studied for the characteristics and appearance of light
structures and beacons. A plan view of the ship’s hull shape cut to the scale
of the chart should be prepared, to obtain an idea of the relative sizes of the
channels and harbour to the ship and the likely distances from dangers during
the passage.
THE PILOTAGE PLAN
The pilotage plan must be complete in every detail. Pre-planned data are
essential for a passage in confined waters. The track must be drawn on the
chart, using headmarks, if possible. The position along the track must be
instantaneously available from cross bearings. The safe limits each side of
the track must be defined by clearing bearings. With appropriate details
transcribed into a properly prepared Note Book, the Navigating Officer can
give his whole attention to the conning and safety of the ship without having
to consult the chart. Reports from the navigator’s assistant, the echo sounder
operator, the blind (safety) and/or visual fixing teams, serve to confirm (or
deny) the accuracy of the navigation. If time has to be spent poring over the
charts and publications during pilotage instead of conning the ship, it will be
evident either that the plan has not been fully prepared, or that the Navigating
Officer does not have confidence in it.
The plan must be so organised that, at each stage, the Navigating Officer
recognises those factors demanding his attention with sufficient time to deal
with them. For example, the plan will need to include the selection of ‘wheel
over’ points and the observation of transits to determine the gyro error.
Neither of these operations should interfere with the other. These points
concern the execution of the plan rather than the planning, but consideration
of such details at the planning stage will ensure a sounder plan, simpler to
execute.
Selection of the track
Read the Sailing Directions and the Port Guide for advice on selecting the
track.
The track should normally be to the starboard side of the channel as laid
down in The International Regulations for Preventing Collisions at Sea, 1972
348 CHAPTER 13 - PILOTAGE

(the Rule of the Road). This allows vessels coming in the opposite direction
to pass in safety. If the ship is large relative to the size of the channel, it may
be necessary to plan to use the centreline, in which case one of the following
possibilities may arise:
1. The ship may have to move to the starboard side of the channel to allow
room for other ships to pass.
2. Other vessels may have to be instructed by the Port Authority to keep
clear (for example, such instructions are issued when large ships are
entering or leaving Portsmouth).
3. Special regulations may be in force for ‘vessels constrained by their
draught’ as defined in the Rule of the Road. Such special regulations
usually only apply to the larger ships; (of the order of: draught 10 to 10½
metres or more; length 270 metres or more; deadweight 100,000 tonnes
or more).
Details of the regulations governing (2) and (3) above are usually to be
found in the Sailing Directions. See also the remarks at the end of this
chapter (page 379) on canal effect.
Dangers
Make sure the track chosen passes clear of dangers, and that the ship does not
pass unnecessarily close to them. Dangers should already have been
highlighted by the LDL. If the tidal stream is predicted to set the ship
towards a danger, it is usually advisable to allow an increased margin of
safety.
Tidal streams and wind
If the tidal streams across the track are likely to be large, the courses to steer
to counter them should be decided beforehand. A rule of thumb for this is:
at speeds of 10 to 12 knots, allow 5° for each knot of tidal stream across the
course. At a speed of 5 knots, allow 10°. This rule is correct to within about
1° of the course steered for tidal streams up to 3 knots across the track.
Leeway caused by wind must also be considered. This information
should be available in the Navigational Data Book. A rough rule for a frigate
at slow speed is that 20 knots of wind is about equivalent to 1 knot of tidal
stream. When the depth of water under the keel is restricted, leeway will be
considerably reduced and this fact may often be used to advantage.
Distance to run
To assist in arriving on time, distances to run should be marked on the chart
from the berth or anchorage. Distances to run should be marked at every mile
over the last few miles and every cable in the last mile to anchorage or berth.
This will assist in planning when to order reductions in speed.
The times at which it is required to pass through positions to achieve the
ETA at the planned pilotage speed should be marked on the chart at
appropriate intervals. Remember the use of planned gates as described on
page 329.
Night entry/departure
If possible, the tracks chosen should be such that they can equally well be run
by night as by day.
THE PILOTAGE PLAN 349

Blind pilotage
Consider the action to be taken in the event of restricted visibility. The plan
should be equally safe for blind pilotage as for visual conditions. The track
selected should enable the change-over from visual to blind and vice versa to
be made at any time.
Radar can frequently be used to support the visual plan. This is common
practice in merchant ships and warships where the pilotage team is small in
numbers.

Constrictions
If the track has to pass through a constriction (for example, a narrow section
of a channel) plan to steady on the requisite course in plenty of time. This is
most important if there is any strong tidal stream (or wind) across the track.
Furthermore, this precaution gives time to adjust to the planned track on the
correct heading should the ship fail to achieve this immediately on altering
course.

The Sun
Work out the bearing and altitude of the Sun likely to be experienced as
dazzle during the passage. Try to avoid tracks and ‘wheel over’ bearings
which look directly up Sun, especially at low elevations, when it may be
difficult to pick up the requisite marks.

Headmarks
Suitable headmarks should be selected for the chosen tracks. Transits are
best but, if these are not available from the chart, a conspicuous object should
be used instead. Choose an object such as a lighthouse, pier, fort, etc. which
is unlikely to be confused with anything else. Chimneys, flagstaffs, radio
masts and even churches can cause confusion if there are a number in close
vicinity. Flagstaffs are frequently removed or repositioned; chimneys and
radio masts can change without notification. Avoid choosing objects which
may no longer be visible because of changing topography.

Transits
Many harbour plans show two marks which, when kept in line, lead the ship
clear of dangers or along the best channel. Such marks are called leading
marks and are often shown on a chart by a line drawn from them, called a
leading line (Fig. 13-2, p.350).
The leading line is usually shown as a full line (CD in Fig. 13-2) where
it is safe to use the marks, and dotted elsewhere. The names of the objects
and the true bearing from seaward, are usually written alongside the line (see
Chart Booklet 5011, Symbols and Abbreviations Used on Admiralty Charts).
If the two objects chosen are seen to remain in transit (Fig. 13-3(a),
p.350), the ship must be following the selected track&BD in Fig. 13-2. If the
two objects are not in line (Fig. 13-3(b)) the ship must be off track to one side
or the other.
In Fig. 13-3(b), the marks are open, with the monument open right of the
beacon. This means that the observer is on or in the close vicinity of track BE
in Fig. 13-2.
350 CHAPTER 13 - PILOTAGE

Fig. 13-2. Leading marks, leading line

Fig. 13-3(a). Using a transit: objects in transit

Fig. 13-3(b). Using a transit: monument open right of beacon

THE PILOTAGE PLAN 351

The value of a transit is proportional to the ratio of the distance between

the objects in transit to the distance between the ship and the nearer object.
The closer the ship is to the marks, the better the transit. For example, in
AB
Fig. 13-2, if the ship is at D, the proportion is . The larger this ratio the
BD
better the transit; ideally, the ratio should be 1:3 or greater. In Fig. 13-2, the
ratio at D is about 1:2 and is getting larger as the ship enters harbour, so the
monument and beacon form a good or ‘sensitive’ transit (see page 200).
If the chart does not show suitable leading marks, the Navigating Officer
should select his own if possible.

Line of bearing
If no transit is available, a line of bearing should be used instead (Fig. 13-4).

Fig. 13-4. Line of bearing

The track is drawn on the chart to pass through some well defined object
ahead of the ship and the bearing of this line noted. Provided the bearing of
the object remains on the bearing noted, the ship must be on her track. If the
bearing changes, the ship will have been set off the track, and an alteration
of course will be necessary to regain the line of bearing.

Edge of land
Edges of land such as cliffs can be useful headmarks, particularly if they are
vertical or nearly so. If the edge of land is sloping (Fig 13-5, page 352), the
charted edge is the high water mark and it is this which should be used.
352 CHAPTER 13 - PILOTAGE

Fig. 13-5. Using the edge of land as a headmark

Distance of the headmark

The closer the headmark, the better, because it is easier to detect any change
of bearing and thus whether the ship is being set off the line. One degree off
the line is equivalent to a distance of about 35 yards at 1 mile, 100 yards at
3 miles, 350 yards at 10 miles.

No headmark available
If no headmark is available, a mark astern is preferable to none at all but, if
no marks are available, the alternatives are:

1. Fix and Run. Plan to fix the ship’s position as accurately as possible by
bearings (taking into account any gyro error) to confirm the safety of the
course. Any suitable object* on the bearing of the new track should be
observed and used as a headmark when steady on the new course.
2. A bearing lattice (described in Chapter 9). This is easy to prepare and
can be transcribed to a Note Book. Two bearings taken at the same time
by the Navigating Officer at the pelorus will immediately tell him
whether the ship is off track and, if so, by how much.
3. An HSA lattice (described in Chapter 9 and Appendix 6). This is very
accurate but takes time to prepare and requires a fixing team of about
three people independent of the Navigating Officer.

Altering course
When planning an alteration of course, the turning circle must be allowed for
so that the ship, when steady on the new course, may be on the predetermined
track. The position of the ‘wheel over’ is found using either the advance and
transfer or the distance to new course (DNC). These terms were explained
in Chapter 8 (pages 185 to 190).

* The object does not have to be charted. Virtually any object will do provided it is stationary and there is no
likelihood of it being confused with anything else. Buildings, outcrops of rock, even trees can be used.
THE PILOTAGE PLAN 353

The turning data for a ship may be displayed in tabular or graphical form.
For accurate interpolation it is easier to use the graph, drawing separate
curves for advance, transfer, DNC and the time to complete the turn. This is
illustrated in Fig. 13-6.

Speed 10 knots 15° of

Rudder
Amount of Time Advance Transfer DNC
Turn
Degrees Min Sec Yards Yards Yards
30 50 259 57 162
60 1 20 384 178 285
90 1 50 453 338 453
120 2 30 415 515 710
150 3 10 300 645 &
180 3 40 133 711 &

Fig. 13-6. Turning data

 354 CHAPTER 13 - PILOTAGE

Advance and transfer

The advantage of using advance and transfer are:

1. The point at which the ship gains the new track is precisely determined.
This allows a better indication of the track covered by the pivot point.
The path of the ship during the turn may be found by plotting the advance
and transfer for intermediate angles (particularly important for the larger
ship). For example, if a turn of 90° is to be undertaken, the advance and
transfer for 30° and 60° as well as 90° should be plotted on the chart and
the predicted path of the ship during the turn drawn.
2. The data may be used for turns up to 180°.

The disadvantage of this method is that, compared with DNC, it is

slightly slower and more difficult to plot.

Distance to new course (DNC)

The advantage of using DNC is that it is simple to plot. The disadvantages
are that it does not show the point where the ship completes the turn, nor can
it be effectively used for turns of more than 120°.
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| Fig. 13-7. Turning on to a predetermined line (1)

Turning on to a predetermined line

This is illustrated in Fig. 13-7. It is desired to alter course from the 070° track
to a track of 005°. B is the point of intersection of the two tracks. The ‘wheel
THE PILOTAGE PLAN 355

over’ point A and the steadying point C are plotted on the chart, using the
turning data relevant to the speed and intended amount of wheel. For
example, using the data in Fig. 13-6, the figures for a turn of 65° are:

TIME TO ADVANCE TRANSFER DNC

TURN (YARDS) (YARDS) (YARDS)

1 min 24 s 400 200 305

The advance and transfer method of finding the ‘wheel over’ position A
is as follows:

1. Project the 070° track beyond B.

2. Determine points D and C, where DC is equal to the transfer (200 yards)
and DC is at right angles to the original track (070°).
3. From D lay back the advance (400 yards), to find the ‘wheel over’ point
A.
The DNC method of finding the ‘wheel over’ position A consists of one
step:
From B, lay back the DNC, 305 yards to find the ‘wheel over’ point
A.
The ‘wheel over’ bearing at point A must be chosen with care to ensure
that the ship ends up on the required track. This is illustrated in Fig. 13-8(a)
and (b), where two possible ‘wheel over’ bearings are shown.
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Fig. 13-8(a). turning on to a predetermined line (2): ‘wheel over’ |
bearing parallel to new course |
 356 CHAPTER 13 - PILOTAGE

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| bearing not parallel to new course

If the ‘wheel over’ bearing is parallel to the new course as in Fig. 13-8(a),
the ship will fetch up on the planned approach track, whether she is on the
previous intended track or not. If, however, the ‘wheel over’ bearing is not
parallel to the new course, as in Fig. 13-8(b), a large error will result if the
ship is not on the intended track as she comes up to the ‘wheel over’ position.
For this reason, the ‘wheel over’ bearing should be as parallel to the new
track as possible. Frequently an object which has a bearing parallel to the
new track will not be available and, in such circumstances, the headmark for
the new track will generally be the best object to use.
If it is known that the ship is on the correct track on the run up to the
‘wheel over’ position, a ‘wheel over’ bearing which is changing rapidly will
more precisely define the turning point than one which is changing slowly.
In such circumstances, it may be preferable to use the bearing of an object
which is not parallel to the new course, but care must be taken to check the
| bearing of the new headmark to avoid under-shooting or over-shooting the
turn.
The bearing of an object being used to define the ‘wheel over’ position
should therefore:

1. Be as parallel as possible to the new track.

2. Give a high rate of bearing change.
THE PILOTAGE PLAN 357

Always have an alternative ‘wheel over’ bearing available.

To allow for a current or tidal stream when altering course

Allowing for a current or tidal stream when altering course is illustrated in
Fig. 13-9.

Fig. 13-9. Turning on to a predetermined line, allowing for tidal stream

EXAMPLE
A ship at A is making good a track AB, steering to port of the ground track
to allow for the tidal stream setting to the south-east. The ship wishes to turn
to the line CD (where she will have to steer the course shown at X) and must
therefore make an allowance for the tidal stream setting the ship to the south-
east during the turn.
Determine from the turning data the ‘wheel over’ point E for an alteration
of course equal to the difference between the ship’s head at X and at A (for
example, from C, lay back the DNC for this alteration to find point E).
From E plot, in the direction of the tidal stream reversed, the distance that
the tidal stream will carry the ship during the time for the turn. This gives
point F.
Draw FG through F parallel to CD to intersect AB at G. Point G is the
revised ‘wheel over’ position to allow for the tidal stream. The ship will
arrive on the line CD at point K.
358 CHAPTER 13 - PILOTAGE

Use of single position line

Where there is no headmark or where the headmark is difficult to see, a single
position line with a bearing exactly parallel to the intended approach course
may be very useful when turning into an anchorage or channel. This
technique involves the use of a transferred position line and is illustrated in
Fig. 9-10 (page 206). Remember to time precisely the estimated ground track
between the position line and the ‘wheel over’ point, use a stopwatch if
necessary.

Keeping clear of dangers

Clearing marks and bearings, vertical and horizontal danger angles, have
already been introduced in Chapter 12.

Clearing bearings
Once the track has been decided upon, clearing bearings should be drawn on
the chart clear of the limiting danger line. These clearing bearings define the
area of water in which it is safe to navigate.
The clearing bearing needs to be displaced from the LDL (Fig. 13-10) to
such an extent that the ends of the ship (usually the bow or stern) will still be
in safe water if the bridge is on the clearing bearing. But this distance should
not be so great that the clearing bearing is disregarded when approached.

Fig. 13-10. Displacement of the clearing bearing from the LDL

No hard and fast rule for the distance of the clearing bearing from the
LDL can be laid down. It depends on the width of safe navigable water, the
angle between the intended track and the LDL, the weather and tidal stream
and the safety margin already allowed for in the LDL. For example, in Fig.
13-10&a fairly narrow channel where the track is parallel to the LDL&a
clearing line displaced by a distance equal to ¼ of the distance R between the
bridge and the stern should be sufficient to keep the ship clear of danger,
provided that any alteration of course away from the clearing bearing is not
too great. Fig. 13-10 shows a frigate altering course away from shoal water
at an angle of about 15° to the LDL, with the bridge on the clearing bearing.
In such circumstances the stern is right on the LDL, so the only further safety
factor ‘in hand’ is the additional depth margin built in to the LDL.
If there is plenty of room available, the distance of the clearing bearing
from the LDL may be as much as the full distance R between the bridge and
the stern. This permits a 90° alteration of course away from the LDL yet still
allows the stern to be in a safe depth.
 THE PILOTAGE PLAN

Fig. 13-11. Approaching Devonport in a large ship (some chart detail suppressed to aid clarity in this example)
359

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360 CHAPTER 13 - PILOTAGE

If the marks are some distance away, a greater margin of safety between the
clearing bearing and the LDL needs to be allowed.
Clearing bearings should be so constructed as to box in completely the
safe navigable water, while ensuring that the plan remains simple and
manageable (see Fig. 13-14 on page 367). There are two considerations:

1. Avoid restricting the ship unnecessarily.

2. Avoid using too many clearing bearings which make the plan
complicated and unwieldy.

It is most important to make certain that sufficient clearing bearings are

available for the shiphandling phase when the ship is approaching or leaving
the berth. It is useful to have a sketch of these in the Note Book.
When navigating to very narrow limits (where even ¼ R is too great a
margin) the cut-out model of the ship mentioned earlier will be extremely
useful when considering the distance of the clearing bearing from the LDL.
This is particularly important when navigating a long ship in a narrow
channel which bends sharply, as is the case, for example, in the passage from
Plymouth Sound through Smeaton Pass in the approach to Devonport (Fig.
13-11, page 359).
An LDL for a depth of 10 metres has been employed&draught 11 metres,
plus 1 metre for squat, plus 3 metres for safety, minus 5 metres for height of
tide. Clearing bearings marking the edges of safe navigable water have been
drawn close to the LDL to give the maximum area in which to manoeuvre this
ship. Clearing bearings are much closer to the LDL than ¼ R. The more
wheel required for a turn, the further will the stern swing out from the track,
thus necessitating a greater distance of the clearing bearing from the LDL.
For this reason, both turns have been planned suing only 15° of wheel, the
minimum that can be safely used in the circumstances.

Vertical and horizontal danger angles

If no suitable object is available for a satisfactory clearing bearing, it may be
possible to use a vertical or horizontal danger angle instead. The use of these
as safety angles is explained in Chapter 12 (page 325). An assistant may be
required to observe the angle.

Echo sounder
The least depth expected on each leg of the plan must be known, and thought
given to the course of action to be taken if the echo sounder reading falls
below the least depth.
The echo sounder may also be used to provide a clearing depth similar
in use to a clearing bearing. The LDL is based on the depth of water (page
345) but, as with a clearing bearing, a greater allowance is required for a
clearing depth to ensure that the ends of the ship are always in a safe depth.
For example, in Fig. 13-14 (page 367) the clearing bearings are very close to
the edge of the dredged channel of 9.5 metres. This depth may therefore be
used to determine the clearing depth, which is equal to the charted depth plus
height of tide. For a height of tide of 1¾ metres the clearing depth would be
11¼ metres below the waterline.
THE PILOTAGE PLAN 361

It is sometimes possible to determine a single clearing depth which will

suffice for the whole passage. It may often be necessary, however, to have
a clearing depth for each leg and, on occasion, different depths for each side
of the same leg.
Various echo sounder procedures are set out in Volume III. These cover
such things as:

Depths below the keel or the waterline.

Depths in metres or fathoms.
Echo sounder operator standard reports.

Miscellaneous considerations
Gyro checks
Plan frequent gyro checks. The gyro error must be known and applied before
any pilotage run is started. Before leaving a berth, if no transit is available,
the gyro error may be calculated by various methods including the reduction
of the cocked hat (see page 219).

‘Shooting up’
All marks used in pilotage (headmarks, ‘wheel over’ and clearing marks)
should be positively identified, usually by ‘shooting up’ (see page 235). In
pilotage work, the most practical method is by means of transits and these
should be planned beforehand, details being included in the Note Book.

Using radar to support the visual plan

Radar may often be used to support the visual plan. Examples of the uses
which may be made of radar are as follows:

1. Checking the position of buoys and confirming their abeam distance.

2. Confirming that the track is being maintained (the parallel index
technique&see Chapter 15).
3. Identifying beacons, buoys, ships, etc.
4. Confirming the ‘wheel over’ position.
5. Checking the distance to go to ‘wheel over’ along a particular track or the
distance to an anchorage position.
6. Checking the distance of other ships in the vicinity.
7. Identifying the correct anchoring position.
8. ‘Shooting up’ marks and ships at anchor.

Point of no return
There is usually a position in any pilotage plan beyond which the ship
becomes committed to the plan and can no longer break off from it and take
alternative action. This position depends on many factors including the size
of the ship, the weather, the narrowness and complexity of the passage, the
tidal stream, etc., and must be determined during the planning. In an entry
plan, the Navigating Officer needs to consider: ‘Can I break off from this leg,
either to anchor or to turn round and go back out to sea in safety, or does the
situation commit me to continue?’
362 CHAPTER 13 - PILOTAGE

The point of no return can be a long way to seaward, particularly if the

ship is large. For example in a long, deep-draught ship entering Devonport
(Fig. 13-11), the point of no return is well into the Sound, south of Smeaton
Pass and can in certain circumstances actually be south of the breakwater
itself.

Alternative anchor berth

Suitable positions in which to anchor in case of emergency or change of plan
should be considered. For example, in the plan for entry to Portsmouth
Harbour (Fig. 13-14, page 367) it is advisable to have ready a plan to anchor
at Spithead.

Navigating Officer’s Note Book (S548A)

The relevant details of the plan should be summarised in the Navigating
Officer’s Note Book with a sketch (Figs. 13-12 and 13-13, pages 364, 365)
so that the navigator can pilot the ship from the pelorus, using the Note Book,
without recourse to charts and publications (see page 347).
There is no hard and fast rule as to how the Note Book should be laid out
for the pilotage plan but several guidelines are set out below:

1. The book should be uncluttered and precise.

2. Sufficient information must be available to conduct the plan entirely from
the book.
3. The chart or portions of the chart may be used as an alternative to the
sketch and be readily available to the Captain and the Navigating Officer
(see page 343). More than one sketch may be needed.
4. Distances from the planned track of buoys and other navigational aids
should be included, as these may assist in the execution of the plan.

The Note Book must contain sufficient detail for the Navigating Officer
to know:

1. The planned track and headmark.

2. If the ship is off track at any time and by how much.
3. The safety limits defined by the clearing bearings.
4. The distance to the next ‘wheel over’.
5. The proximity of dangers.
6. The tidal stream.
7. The minimum depth expected on any leg.
8. The cross-checks for the next ‘wheel over’ point and headmark.
9. The ‘wheel over’ bearing.
10. The assessment of the turn to the new planned track.

A Note Book layout which has been used many times in practice and
found to be satisfactory is shown in Fig. 13-13.
The Navigating Officer should always transcribe relevant details about
the ship from the Navigational Data Book (S2677) into the front of his Note
Book. For pilotage work, these include:

Ship’s dimensions and visibility diagram (if held).

Turning data.
THE PILOTAGE PLAN 363

Reduction of speed tables for approaches to anchorages, buoys and

alongside.
Special berthing information (e.g. type of catamarans required, length
of brows, etc.).
The amount of cable available on each anchor. Remember that the
amount of cable which can be veered is about one shackle less than
that fitted.

Conning
The point on the approach where the Navigating Officer takes over the con
from the Officer of the Watch, and the Captain in turn takes over from the
Navigating Officer, should be planned beforehand. As a general rule, the
Navigating Officer should take the con from the Officer of the Watch in
sufficient time to have the ‘feel’ of the ship by the time the pilotage stage
begins using the Note Book only (usually when the ship enters the narrow
channel or anchorage approach phase).
The method of passing orders for the final shiphandling phase of the
approach to the berth must be decided. Some Captains prefer to take the con
themselves; some prefer to leave the Navigating Officer at the con, relaying
orders through him rather than directly to the Quartermaster. If the Captain
takes the con himself, he gets the feel of the ship more quickly but may lose
a feel for the overall situation.

Tugs
The requirements for tugs must be decided during planning. The Tugmasters
will require briefing on the intended movement plan, which should include
details of how and where the tugs will be secured. For harbour entry, the
position in the approach where tugs are to meet the ship should be planned.

Final stages of the plan

For the final stages of the plan, decide:

1. The time or position in the approach to:

Close up special sea dutymen and assume the appropriate NBCD
state.
Operate the echo sounder.
Have the anchors ready for letting go.
Have additional boilers, diesels or gas turbines connected, second
steering motor, etc.
2. The details of harbour communications, frequencies, etc.
3. The requirements for special ceremonial procedures, gun salutes, etc.
4. When to raise logs and sonar domes, secure radar sets, etc.

Submit the departure or entry plan to the Captain, including the

shiphandling problems which will be encountered, including the use of tugs.
Carry out any further briefings; e.g. if berthing alongside, brief the
Executive Officer, the various part of ship officers, the Marine Engineer
Officer, etc.
 364 CHAPTER 13 - PILOTAGE

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| Fig. 13-12. Pilotage plan for a frigate entering Portsmouth&the Note Book
| sketch
THE PILOTAGE PLAN 365

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Fig. 13-13. Pilotage plan for a frigate entering Portsmouth&the Note Book |
layout |
366 CHAPTER 13 - PILOTAGE

Check-off lists
It is always advisable to consider the use of check-off lists when preparing a
pilotage plan. These ensure that nothing is likely to be forgotten. An
example of a pilotage check-off list is to be found in Annex A to this chapter.

The plan

Fig. 13-14 illustrates part of a complete plan for a frigate entering Portsmouth
using an LDL of 7 metres.
Fig. 13-12 illustrates a Note Book sketch (more than one should be used
if there is much detail) and Fig. 13-13 an example of how the Note Book
should be laid out (pp.364, 365).
The planned track, ‘wheel over’ points, LDL and clearing bearings are
shown. Distance to run to the berth inside Portsmouth Naval Base are noted
on the chart, together with the expected times of passing key points so as to
arrive alongside at the planned time. Predicted tidal streams and planned
ship’s speed (see NP 167) and an alternative anchorage in Spithead are also
shown on the chart.
For example, it may be seen that a track of 000° on Southsea Castle Light
has been chosen for the first leg of the entry plan. St Jude’s Church being
open to the right. The track lies to the starboard side of the channel. A gyro
check&the signal station at Fort Blockhouse in transit with the left-hand edge
of Spit Sand Fort bearing 336½°&is available at the southern end of this leg.
Clearing bearings mark the safe navigational limits on each side of the
channel, the bearing of Southsea Castle Light being not less than (NLT) 358°
and not more than (NMT) 004½°. The minimum depth to be expected on this
first leg, allowing for the predicted height of the tide, is 10.7 metres. The
ETA at the Outer Spit Buoy (OSB), which should pass 1 cable abeam to port,
is 1530 (-1) on 29th September. On passing OSB, the distance to run to the
berth at Middle Slip in the Portsmouth Naval Base is just over 3 miles, the
ETA alongside being 1552. The ship’s speed on passing OSB should be 10
knots. At this speed, and allowing for the tidal stream which is predicted to
be easterly, weak, the ship should reach the next ‘wheel over’ position, 1
cable south of the Boyne and Spit Refuge buoys, just before 1533.
The next running mark is the War Memorial, and this may be identified
by a transit with Spit Refuge buoy, bearing 347°. When the War Memorial
bears 344°, course should be altered to port, passing between the Boyne buoy
0.45 cable to starboard and the Spit Refuge buoy 0.7 cable to port, to the next
track of 342° on the War Memorial.
In this manner, the ship proceeds up channel and into harbour.
THE PILOTAGE PLAN 367

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Fig. 13-14. Pilotage plan for a frigate entering Portsmouth - the chart |
 368 CHAPTER 13 - PILOTAGE

| INTENTIONALLY BLANK
EXECUTION OF PILOTAGE 369

EXECUTION OF PILOTAGE

The essence of a good plan is knowing the limits within which the ship may
be navigated in safety. The essential questions which the Navigating Officer
must be able to answer at all times during a pilotage passage are:

Is the ship on track?

If not, where is the ship in relation to the track and what steps are
being taken to regain it?
How close is the ship to danger?
How far is it to the next alteration of course?
Are the tidal streams and depths of water as predicted?

Organisation and records

A team effort is needed to execute a pilotage plan in safety; Table 13-2
(p.370) is a recommended organisation for a frigate or destroyer. Other ships
may need to modify this as necessary, dependent on the size of the ship and
the team available.
The pilotage team should produce sufficient records for the ship’s track
to be accurately reconstructed, if required. The fixes and soundings taken
through the passage should provide a series of confirmatory checks to support
the visual picture and DR/EP times to support ‘wheel over’ bearings, etc.

Maintaining the track

An estimate of the distance off track may be made by looking along the
desired bearing of the headmark and then making a direct assessment of how
far the ship is off track. The distance should be quantified; for example, if it
is estimated that the required bearing is 50 yards to the left of the headmark
(Fig. 13-15), then the ship is ‘50 yards to port of track’. Remember that 1°
off the track is equivalent to a distance of about 100 feet at 1 mile, ½ cable
at 3 miles.
When running a mark on a cross-tidal stream, the course steered is bound

Fig. 13-15. Running a headmark: ship to port of track

370 CHAPTER 13 - PILOTAGE

Table 13-2. Pilotage organisation

CAPTAIN In command, overall responsibility
for ship safety.
NAVIGATING Acts as the pilot and takes over as
OFFICER (NO) necessary from the OOW. Executes
the plan at the pelorus from the Note
Book. Has ready access to the chart.
Keeps the Captain fully informed on
the progress of the plan. May take
the bearings for his assistant to plot
fixes on the chart.
OFFICER OF THE WATCH Filters shipping situation and informs
(OOW) Navigating Officer of ships which
may hinder execution of the plan.
Takes bearings and gyro checks as
directed by the Navigating Officer.
Runs the ship’s routine and
ceremonial and deals with matters of
internal safety (of the ship).
Maintains liaison with the blind
safety team in the operations room.
NAVIGATING Carries out the Navigating Officer’s
OFFICER’S ASSISTANT chartwork. Calls for fixes at regular
and frequent intervals in order to
confirm the ship’s position and cross-
checks the EP. Plots fixes and
generates fresh DR and EP. Reports
after each fix:
its reliability: ‘Good’, ‘Bad’, or
‘No fix’ as the case may be;
its distance from the planned
track, and course required to
regain;
whether the echo sounder
reports correlate with
charted depth;
ETA at next ‘wheel over’
position.
BLIND SAFETY OFFICER Monitors ship’s position using blind
(BSO) AND BLIND SAFETY pilotage techniques as a check on the
TEAM (see Chapter 15) ship’s navigational safety; passes
navigational and anti-collision
information.
NAVIGATOR’S Records wheel and engine orders. A
YEOMAN tape recorder on the bridge may be
found useful.
ECHO SOUNDER Makes standard reports
OPERATOR (see Volume III).
EXECUTION OF PILOTAGE 371

to differ from the planned bearing of the mark. Remember the rule given on
page 348. If the correct bearing is not being maintained, the ship is off track;
it must be regained by a bold alteration. When the track has been regained,
a course must be steered which will counteract the tidal stream more
adequately than the original one.
Do not nibble at course corrections to maintain the track and avoid
making successive alterations of 1° or 2°. Alter 10° or 15° to get back on the
correct track quickly, but do not overshoot.
Radar is often a useful aid in confirming whether the ship is on track or
not (Chapter 15).

Running a transit
The rule for running a transit is ‘Follow the front mark’. In Fig. 13-3(b) the
front mark (the beacon) is to port of the rear mark (the monument). Therefore
the alteration of course to get back on track must also be to port.
If the transit is astern, the alteration must be in the reverse direction, e.g.
in Fig. 13-3(b) the beacon is to the left of the monument, therefore the
alteration must be to starboard.

Running a line of bearing

Altering course the wrong way when running a line of bearing is a frequent
cause of mistakes in pilotage. This can be avoided by the following simple
rules:

1. Look down the bearing on which the headmark should be.

2. The headmark will be:
On the mark (Fig. 13-16) or
To starboard of the bearing (Fig. 13-17, p.372) or
To port of the bearing (Fig. 13-18, p.372).
3. If the headmark is off the bearing, alter course in its direction: If the
headmark is to starboard of the correct bearing alter course to starboard
to regain track (Fig. 13-17).
If the headmark is to port of the correct bearing, alter course to port
to regain track (Fig. 13-18).

Fig. 13-16. Running a headmark: ship on track

372 CHAPTER 13 - PILOTAGE

Fig. 13-17. Running a headmark: headmark to starboard of the correct bearing

Fig. 13-18. Running a headmark: headmark to port of the correct bearing

If the mark is astern and the ship is running a back bearing, the alteration
of course must be in the reserve direction; e.g. if the mark in Fig. 13-17 is
astern and appears to the right of the required bearing, the alteration of course
must be to port; if the stern mark appears as shown in Fig. 13-18, the
alteration required must be to starboard.
When the mark is on the correct bearing, note a point on the landscape
which is in transit with it (either in front or behind). By using this transit, it
is possible to see immediately without reference to the compass whether or
not the ship is being set off line.

Fix and run

This procedure is discussed on page 352. Having chosen a suitable object on
which to run, obtain another one in transit with it in precisely the same way as
EXECUTION OF PILOTAGE 373

when running a line of bearing. Radar can often be of great assistance in

confirming the track.

Assessment of danger
Always be alert to the nearest and most immediate danger. This could be a
ship at anchor or a buoy towards which own ship is being set by wind or tidal
stream. The most immediate danger could be a ship approaching down the
next leg of the route which, if she does not alter course as expected, could
present a collision risk.
The chart gives warning of navigational dangers but there are other
hazards&ships, yachts and small craft, emergencies such as steering gear or
main machinery breakdown. The navigator must be alert to all of these
matters, and be constantly thinking ahead and anticipating possible eventualities.

Identification of marks
In pilotage work, there are two quick and simple methods immediately
available for the identification of shore marks.

1. A straightforward comparison of the chart with what is actually visible.

Such a comparison will frequently reveal the marks to be used, without
having to take a single bearing. If there is any possibility of confusion
between adjacent marks (such as churches, chimneys, blocks of flats, etc.)
this may have to be clarified by taking bearings.
2. Identification by means of the transits which shore marks make with the
buoys marking the channel. Even if a buoy differs from its charted
position by as much as 100 yards, the expected bearing of the mark to be
identified will probably not vary by more than 2° or 3°; this is usually
sufficient for identification purposes.

Buoys or beacons can be identified by combining single visual bearing

with a radar range of the mark.

Shipping
When altering course for shipping, take the necessary action in plenty of time.
If action is delayed, the Officer of the Watch in the other ship may become
alarmed and may do something unexpected and dangerous.
Do not pass too close across the bow (upstream) of anchored shipping;
if possible, pass astern. The position of ships at anchor near own ship’s track
can be established by combining a fix with a visual bearing and radar range
of the ship at anchor. With the position of the other ship on the chart, a
decision can then be made to pass ahead or astern, or take some alternative
action such as stopping if, for example, the anchored ship is blocking the
channel.

Use of the echo sounder

The intelligent use of the echo sounder is essential to the safe conduct of
pilotage. The predicted height of tide must be taken into account at all times.
Reports from the echo sounder operator or the reading on the bridge
display unit must be given proper attention. If the reported depths are different
 374
CHAPTER 13 - PILOTAGE

Fig. 13-19. Monitoring a large turn in pilotage waters

EXECUTION OF PILOTAGE 375

from those predicted, the reasons must be considered and the appropriate
action taken, particularly if the depths are close to the limiting depth. It may
be necessary to stop the ship and clarify the situation before proceeding further.

Altering course and speed

When turning on to a new headmark, the wheel must be put over in plenty of
time. If it is put over too soon, it can be quickly eased; if it is put over too
late, more wheel may not be effective. The use of excessive wheel may bring
the ends of the ship closer to the clearing bearing than planned. Excessive
wheel also reduces ship’s speed more than originally intended and this may
create problems particularly in strong winds or when in company with other ships.
When about to turn, make sure that the ship is not tending to swing in the
opposite direction to that intended. Keep the bows in hand (‘smell’ the turn)
by using small amounts of wheel in the appropriate direction just before the
turn, so that the ship ‘wants to go the desired way as soon as the wheel is put
over for the turn itself. When making a large turn in a big ship, it is often
advisable to use plenty of wheel initially to get the ship swinging in the right
direction and then ease the wheel, otherwise the ship may ‘hang’ in the
original direction, particularly in shallow water or when turning out of wind.
Remember that, as a general rule, ships going ahead turn more easily into
wind than away from it, and allowance should be made for this.
Watch the progress of the ship during the turn to ensure that the planned
track is being followed. Are objects coming up ahead on the right bearing?
Does the turn look right? This is particularly important with large turns in
big ships.
The monitoring of a large turn is illustrated in Fig. 13-19. A ship entering
harbour on a course of 020° is required to turn 110° to port to the next leg
(270°). The courses of 020° and 270° both run on a pair of beacons in transit.
The track of the ship between ‘wheel over’ and steady is plotted using the
ship’s turning data. It will be seen that, once the turn has begun, the tower
should come up right ahead on a bearing of 351°, the church on 325° and the
of the hotel (conspic) on 296°, as the ship’s head swings through
those particular bearings. If these bearings do not come up right ahead, the
rate of turn must be adjusted. For example if, in the early part of the turn, the
tower comes up right ahead on a bearing of 355°, the ship is to port of track,
and is turning too fast. The wheel must be eased to bring the ship back on to track.
Before altering course, check to see that the track is clear of shipping and
other obstructions. Look out on the appropriate quarter for any ship
overtaking from that direction.
Always check that the wheel is put over the right way by watching the
rudder angle indicator. If the wheel is put the wrong way, order ‘Midships’
and repeat the original order.
When altering speed, check from the shaft speed indicators or the pitch
angle repeaters that speed has been altered correctly. If the shafts have been
put the wrong way (e.g. astern instead of ahead), order ‘Stop’ and repeat the
original order.
In ships where the Quartermaster is sited at the QM’s console on the
bridge, it is important that the above procedure should be followed and that
all conning orders and replies are made in a formal manner.
376 CHAPTER 13 - PILOTAGE

Buoys
Buoys are an essential aid in pilotage, especially in narrow channels, but their
positions can vary from that charted with the state of the tide. Buoys can
drag, particularly if in an exposed position; they can also be repositioned to
mark an extending shoal or altered channel, without immediate notification.
Use but do not trust buoys implicitly. Check the characteristics by night,
and the name, number, colour or topmark by day. Fix from charted shore
objects in preference to buoys, using the EP as a check. Take care in areas
where it is known that channels shift and the buoys are repositioned
accordingly. The charts and Sailing Directions may give warning of such
areas, for example the channels in the vicinity of the Goodwin Sands and in
the Thames Estuary.
When passing a buoy, its position may be checked by transits with two,
preferably three, charted shore marks. Radar can help in the identification of
buoys and in checking their positions.
Take care if the planned track leads the ‘wrong side’ of a buoy marking
the leg of the channel, e.g. the deep-draught route for heavy ships
approaching Smeaton Pass (Fig. 13-11) from Plymouth Sound which leads
east of the West Mallard Buoy. It may on occasion, for example in strong
winds, be preferable to aim off 2° or 3° as necessary to get the buoy on the
‘correct’ bow. Otherwise the ship could be set dangerously close to the buoy
concerned if she is slow to turn.
The height of the tide may permit a ship to pass outside the line of buoys
yet still be safe. A ship may be forced the wrong side of a buoy by other
shipping. It may be better to take this course if collision cannot otherwise be
avoided. In certain circumstances, it may even be better to ground than risk
a collision.

Tides, tidal streams and wind

For a number of reasons, the predicted height of tide may be different from
that actually experienced, perhaps by as much as 1 or even 2 metres. This is
particularly dependent on the weather, as explained in Chapter 11.
Tidal streams experienced may not always agree with the predictions,
particularly at springs, and the actual time of a change of direction can be as
much as 1 to 2 hours different. Always check the direction and rate by noting
the heading of the ships at anchor and the wash of the tidal stream past
moored objets such as buoys. The eye tends to deceive; the actual strength
of the stream in knots is not always as great as it appears to be.
Make an adequate allowance for cross-tidal stream and wind, because it
is difficult to recover the track having been set downstream of it, especially
when speed is reduced. The less the distance to the next ‘wheel over’
position, the larger must be the correction to regain track. If the ship is
upstream of the line, there is no difficulty in regaining it.
An adequate allowance must be made for tidal streams and wind when
turning; the ‘wheel over’ point may have to be adjusted as explained on page
357. Wind direction and strength affect not only the leeway but also the
turning circle itself. A turn may have to be started early or late, using more
or less wheel as appropriate, depending on the combined effects of stream and
leeway on the turning circle.
EXECUTION OF PILOTAGE 377

Service to the Command

The Navigating Officer must anticipate the Captain’s requirements and
provide him with relevant information and situation report. Such information
should include:

The headmark and its correct bearing.

Whether on or off track. If off track, by how much, and the course
required to regain.
Distance and time to ‘wheel over’.
The minimum depth expected.
The tidal stream and the likely effect of wind.
Advice on the shipping situation.

Action on making a mistake

If a mistake has been made, report it immediately. If this leads to uncertainty
about the ship’s position, consider stopping the ship at once. The Navigating
Officer must always be scrupulously honest and never try to bluff his way out
of an uncertain situation. His Captain may not find him out, but the rocks and
shoals will.

Checks before departure or arrival

Always observe the situation in the vicinity of the ship before leaving
harbour. If alongside, the best way is to walk down the jetty checking the
catamarans, the positions of adjacent ships, etc. The actual height of tide, the
strength and direction of the tidal stream and the wind can be noted, and all
these may lead to an adjustment of the plan.
Such a detailed check cannot be done on entering harbour, but the
situation needs to be observed as accurately as possible.

Miscellaneous considerations in pilotage execution

Taking over the navigation

Take over the navigation of the ship in plenty of time. It is important to get
settled in early, particularly at night or in poor visibility.

Using one’s eyes

Although the execution of pilotage as presented in this chapter is a formal
process involving extensive use of the compass, never neglect the eye. Use
the eye to reinforce the plan; this is particularly important when assessing the
actual effect of wind and tidal stream.

Making use of communications

Make full use of communications to assist in the execution of the plan.
Examples are:

Communications with the Port Authorities.

Communications with the tugs, particularly to find out the
conditions at the berth.
Passing intentions to other shipping.
 378 CHAPTER 13 - PILOTAGE

Personal equipment
The Navigating Officer should make certain that he has the necessary
personal equipment available: Note Book, torch for use at night, Polaroid
sunglasses, binoculars, etc.

The shiphandling phase

| Full details of the handling of ships are given in BR 45(6), Admiralty Manual
| of Navigation, Volume 6. Certain aspects are amplified below.
Planned speed reductions may have to be modified in the light of the
conditions prevailing.
The extent to which the Navigating Officer assists the Captain in
handling the ship when berthing and unberthing depends on the personal
preferences of the Captain. The essential requirement is for the Navigating
Officer to be fully prepared to handle the ship and to have readily available
all the information pertinent to the manoeuvre&for example, the handling
characteristics of the ship, the depth of water, direction and strength of tidal
stream or current, length and line of berth, sea room available. During the
manoeuvre he should be continuously watching the ship’s movements ahead
or astern, and in azimuth, and should be prepared to give the Captain the
range of any object he wishes. He should ensure that the ship cannot drift
unobserved into shoal water. He should check that the Captain’s wheel and
engine orders are correctly transmitted and obeyed. If he considers at any
time that the ship is in danger, he must not hesitate to say so.

Pilotage mistakes
Mistakes often occur during pilotage. The most common ones are reflected
below in a series of reminders to the Navigating Officer.

Do’s
Do have the detailed planning and turning data in use cross-checked&
particularly the tracks, ‘wheel overs’ and clearing bearings.
Do allow adequate clearances between the clearing bearing and the LDL.
Do obtain local knowledge if the charts and publications do not appear
to be a sufficient guide, but always treat such knowledge with a proper degree
of caution.
Do ensure that the organisation for lookouts, radar, echo sounder, etc. is
adequate.
Do pay attention to the shipping situation in addition to the safe
navigation, particularly in crowded harbours.
Do treat old surveys with a great deal of caution, particularly in coral
regions. The depth could be much less than charted.
Do maintain the DR/EP from the fix up to the next ‘wheel over’ point;
always know its time as well as the relevant bearing.
Do pay attention to the soundings and relate them to the soundings
expected.
Do identify (‘shoot up’) the marks.
NAVIGATION IN CANALS AND NARROW CHANNELS 379

Do appreciate correctly which side of the track the ship is, and which way
the correction must be made.
Do allow a sufficient correction for cross-tidal stream and wind,
particularly during large turns.
Do regain track boldly. Don’t nibble.
Do apply the gyro error correctly. Don’t forget that the weakest point in
modern gyro systems is the transmission system.
Do monitor large turns carefully throughout the turn, particularly in big
ships.
Do allow plenty of room when rounding points or shoals&cutting corners
can be dangerous. Don’t, however, take a ‘battleship sweep’ at them&unless
navigating a similarly large vessel.
Do remember the possibility of canal effect (see below).

Don’ts
Don’t neglect the visual situation.
Don’t request new courses without a visual check for navigational safety
and shipping. Don’t forget the quarter.
Don’t press on in hope when there is uncertainty about the position. Stop
instead.
Don’t pass too close upwind or up tidal stream of dangers, anchored
ships, buoys or other obstructions.
Don’t attempt to ‘cut in’ ahead of other ships when approaching the
harbour entrance.

NAVIGATION IN CANALS AND NARROW CHANNELS

Navigation in canals, rivers and similar narrow channels is often more an
exercise in shiphandling than in pilotage. The effects on draught, speed,
steering and the turning circle are much more pronounced than those
experienced in more open shallow waters. The procedure when passing other
ships is usually different from that in more open waters. These aspects are
covered in BR 45(6), Admiralty Manual of Navigation, Volume 6. |
When navigating in a canal, moderate speed should always be the rule to
ensure that squat is not excessive. The critical speed of any particular ship
in a canal, above which her steering becomes increasingly erratic because of
shallow water effects, is termed canal speed. In the Suez Canal, for example,
canal speed of the convoy is limited to about 7 to 7½ knots and this is also
related to maximum permissible draught and beam. Canal speed should never
be exceeded.
Revolutions to achieve a particular ground speed will have to be higher
than usual to counteract shallow water effect and the counter current set up
by the ship’s movement. For heavy ships this reduction in speed may be as
much as 30% to 40%.
Passages through canals and other narrow channels should be planned
and executed in a manner similar to other pilotage passages. The canal bank
itself may be the limiting danger line and, while there may be a number of
marks each side of the canal including milestones (or kilometre stones), there may
380 CHAPTER 13 - PILOTAGE

often be no suitable headmark. The ship should normally be navigated in the

centre of the channel so as to equalise the pressure distribution each side of
the ship to prevent a sheer developing to either side. The ship should only be
moved away from the centreline when it is necessary to pass ships coming in
the opposite direction; the usual recommendation is to pass close aboard.
Such practice helps to counteract the effect of the nearer bank and also makes
it easier to regain the centre of the channel without inducing a sheer.
In some canals, the Suez Canal for example, sections are cut out of the
bank to form sidings where one line of ships may be made fast while another
line passes. There may be a tendency for the passing ships to veer into the
siding, because of the sudden reduction of bank effect on that side of the ship,
causing a collision with one of the berthed vessels. Such a tendency must be
carefully guarded against.
The effects mentioned above apply mainly to large ships. Destroyers and
frigates do not as a rule experience severe canal effects and can often proceed
quite close to the bank of a canal, provided that speed is kept down to a
moderate level.
All passages in canals must conform to local regulations, and it is
essential to know and understand the local signals and communication
arrangements. The Sailing Directions and amendments issued in Part IV of
Admiralty Notices to Mariners and ALRS, Volume 6, are particularly
important in this respect.
 381

ANNEX A TO CHAPTER 13
Pilotage Check-off List

1. SELECT CHARTS Largest scale.

Fully corrected including Temporary
and
Preliminary Notices and warning
2. SELECT messages.
PUBLICATIONS Sailing Directions.
List of Lights.
3. ETA, ETD Tide and tidal stream tables, etc.
4. SELECT LDL Relevance to the pilotage plan.
5. PASSAGE APPRAISAL Draw on charts for selected depth.
Clear mental picture.
Study charts with Sailing Directions,
List of Lights, etc.
Note description of conspicuous objects
6. SELECT TRACKS and lights on the chart.
Starboard side of channel.
Clear of dangers.
Tidal stream and wind allowed for.
Distance to go marked off.
Suitable for night and blind conditions.
Constrictions.
7. HEADMARKS Position of the Sun.
Transits.
Line of bearing.
Edge of land.
Distance.
No headmark available&bearing lattice,
8. ALTERING COURSE HSA lattice, fix and run.
‘Wheel over’ positions.
Advance and transfer.
DNC.
‘Wheel over’ bearings&parallel to new
course, high rate of bearing change;
9. KEEPING CLEAR OF cross-tidal stream or current.
DANGER Clearing bearings&displacement from
LDL, box in navigable water.
Vertical and horizontal danger angles.
382 ANNEX A TO CHAP 13 - PILOTAGE CHECK-OFF LIST

Echo sounder&clearing depth, depths

below keel/waterline, height of
tide.
10. GYRO CHECKS Transits, one on each leg.
11. ‘SHOOTING UP’ Transits.
12. POINT OF NO RETURN Marked on chart.
13. ALTERNATIVE Suitable positions for emergencies/
ANCHOR BERTH change of plan.
14. NOTE BOOK Relevant details of the plan.
Sketch.
15. CONNING Navigating Officer taking over from
Officer of the Watch; Captain from
Navigating Officer.
16. TUGS How many, how secured, where to
meet ship.
17. BRIEFINGS Captain.
Other officers, warrant officers and
senior ratings.
 383

CHAPTER 14
Anchoring and Mooring

This chapter comprises detailed instructions for the planning and execution
of anchoring and mooring.
In many ports or harbours, the shore authority allocates anchoring or
mooring berths. There are, however, numerous occasions when the
Navigating Officer is called on to select and pilot the ship to a suitable berth,
particularly in out-of-the-way places visited by HM Ships.

Choosing a position in which to anchor

A number of factors have to be considered when choosing a position in which

to anchor. The choice is governed very largely by matters of safety, but
administrative or operational reasons may also have to be taken into account.
These factors are:

The depth of water.

The length and draught of the ship.
The amount of cable available.
The type of holding ground.
The proximity of dangers such as shoal waters, rocks, etc.
The proximity of adjacent ships at anchor.
The shelter from the weather given by the surrounding land.
The strength and direction of the prevailing wind.
The strength and direction of the tidal stream.
The rise and fall of the tide.
The proximity of landing places.

The depth of water

There must be an adequate depth of water under the ship at all times. If the
stay is to last for more than a few hours, this safe depth must be available at
all stages of the tide. A limiting danger line (LDL) (Fig. 14-1, p.384) must
therefore be drawn for the anchorage area, taking into account the lowest
height of tide during the stay.
Minimum clearance under the keel should as a rule be at least 2 metres
at the lowest stage of the tide during the stay.

Swinging room when at anchor

A ship at anchor must have room to swing clear of dangers such as shoal
water, rocks, etc. and also to swing clear of adjacent ships at anchor that are
themselves swinging round in their berths.
384 CHAPTER 14 -ANCHORING AND MOORING

Fig. 14-1. Safety swinging circle

Proximity of dangers
To be safe from rocks, shoals, etc., an anchorage position must be chosen so
that the safety swinging circle (Fig. 14-1) is clear of the LDL. The radius of
this circle may be obtained by adding the following.

1. The length of the ship.

2. The maximum amount of cable which can be veered on the selected
anchor (remember that the last shackle of cable will normally be inboard
of the hawse pipe). This allows for the veering of additional cable should
the weather deteriorate, while still maintaining an adequate safety margin.
3. A safety margin. It is impossible to give any definite rule as to how near
danger a ship may be anchored in safety. An ample safety margin must
be allowed, in addition to (1) and (2) above. At single anchor, it is usual
to allow at least one cable (1/10 mile), increased as necessary, to allow
for:
(a) The possibility that the ship may not achieve her intended anchoring
position.
(b) The likelihood of bad weather.
(c) The likelihood of dragging.
(d) The time between ordering the anchor to be let go and it hitting the
bottom.

Anchoring by day in perfect visibility using a large-scale chart, in a flat

calm with a conspicuous headmark and beam marks, should not present any
CHOOSING A POSITION IN WHICH TO ANCHOR 385

great difficulty even to the inexperienced navigator. The possibility that the
ship may not achieve her intended position is slight. But achieving the
planned anchorage position in a minutely charted bay, at night, in a gale, with
difficult marks when the final run-in is only 1 or 2 cables, is an entirely
different matter.
The likelihood of dragging is dependent on: bad weather; whether the
anchorage is open or sheltered; the strength and direction of the tidal stream;
the nature of the bottom; the holding power of the anchor.
The ship is usually moving very slowly at the time of ordering the anchor
to be let go, so the time for the anchor to reach the bottom may normally be
disregarded.*
Rigid application of these considerations would preclude some
anchorages which would be quite safe in good weather or in sheltered
conditions or of a short duration. In such circumstances, it would be
appropriate to accept a smaller margin of safety, consistent with prudence.
Suppose a ship of draught 7.1 m, length 155 m, with 10 shackles (275 m)
of usable cable on each anchor, comes to single anchor. The minimum height
of tide during the stay is predicted at 1.7 m. Assuming that the safety margin
is 1½ cables, her safety swinging circle (SSC) would be as in Table 14-1.

Table 14-1
METRES YARDS

Length of ship 155 170

Maximum usable cable 275 300
Safety margin 275 300
___ ___
Radius of SSC 705 770 or 3.85 cables

Thus, her berth must be at least 3.85 cables from the LDL. The charted
depth of the LDL would be 7.1 + 2 - 1.7 = 7.4 m, allowing for a minimum
clearance of 2 m under the keel.

Amount of cable to be used

The amount of cable to be used (as opposed to the amount available) depends
on a number of factors&the type of cable and anchor, the strength of the tidal
stream and wind, the holding ground. This matter is discussed fully in
BR 45(6), Admiralty Manual of Navigation, Volume 6. |
The majority of HM Ships are fitted with forged steel cable and the
AC 14 anchor, although minehunters and minesweepers are usually fitted
with aluminium silicon bronze cable. |

* An anchor should take about 3 seconds to reach the bottom in 30 m of water. Assuming the whole operation
from ordering ‘Let go’ to the anchor hitting the ground takes 6 seconds, a ship moving at 2 knots will only move
6 m during that time.
386 CHAPTER 14 - ANCHORING AND MOORING

The amount of forged steel cable required for various depths may be
calculated by the following rule, which allows a slight safety margin over the
actual minimum necessary:
amount of cable required (in shackles) = 1½ depth (in metres) . . . 14.1
or = 2 depth (in fathoms) . . . 14.2
For the heavier aluminium bronze cable, which requires less cable for the
depth of water, the approximate rule is:
amount of cable required (in shackles) = depth (in metres) . . . 14.3
or = 1.3 depth (in fathoms) . . . 14.4
The depths referred to above should normally include the maximum
height of tide expected during the time the ship is at anchor. In strong winds
or in very strong tidal streams, more cable will usually be required.
In good holding ground such as clay, soft chalk, sand, sand/shingle, the
holding power of the AC 14 anchor is approximately 10 times its own weight.
In very good holding ground such as a mixture of sand, shingle and clay or
really heavy mud, the holding power may be as much as 12½ times. In poor
ground such as soft silty mud or shingle and shell, holding power may be as
little as 6 times. Rock, coral and weed are particularly bad types of holding
ground.
Distance from other ships
The anchorage position should be selected to ensure there is no danger of
fouling other ships as they swing round their anchors. The minimum
swinging radius to allow against such an occurrence (Fig. 14-2) is the length
of the ship plus the length of cable veered. Thus, the distance apart of
adjacent ships should be twice the minimum radius; this should be sufficient
to allow the following events to take place without danger or difficulty:
1. A ship may approach and anchor in the line without finding an adjacent
ship swung over the point where her anchor is to go.
2. A ship anchored in the line may weigh anchor alone without fouling other
ships.
3. Two adjacent ships may swing towards each other and at the same time
have their cables drawn out to their fullest extent. This is, however, most
unlikely to occur since, if there is a strong wind or stream, the ships will
be lying parallel and drawing out their cables in the same direction. If the
Table 14-2
METRES YARDS

Length of ship 155 170

Length of cable veered 165 180
(say, 6 shackles) ___ ___
Minimum swinging radius 320 350 or 1¾ cables
Distance of ships apart 640 700 or 3½ cables
CHOOSING A POSITION IN WHICH TO ANCHOR 387

Fig. 14-2. Minimum swinging

radius for ships at anchor (1):
ships at two
radii apart

SEE BR 45
ships swing in opposite directions, it is probably because the tidal stream
is on the turn and almost slack, and the wind at the same time is light, so
that their cables are not laid out towards one another.

2.
VOL 6
The distance apart of two similar ships may be calculated as in Table 14-

Space in harbours is often scarce and therefore it is seldom that the

distance apart of two radii, to allow for the third event above, can be allowed.

CHAP 4
If the berths of adjacent ships are placed at one radius apart, however
(Fig. 14-3, p.388), both the other two events can occur without difficulty. It
is therefore customary to place the berths of similar ships at one radius apart,
e.g. A and B in Fig. 14-3. Ships must be on their guard against swinging
towards one another, but the risk is small. However, if two ships of dissimilar
classes are berthed next to one another, e.g. A and C in Fig. 14-3, the distance
between their berths should be at least that of the radius required for the
larger of the two ships.
388 CHAPTER 14 - ANCHORING AND MOORING

SEE BR 45
Fig. 14-3. Minimum swinging radius for ships at anchor (2): ships at one radius
apart

VOL 6
Reducing swinging radius
If space is particularly restricted, the distance apart of ships may be reduced
by allowing a minimum radius (Fig. 14-4) equal to the length of the ship plus

CHAP 4
45 metres (50 yards). In the example given above, the minimum swinging
radius would be as in Table 14-3.
Care must be taken to ensure that anchor cables of adjacent ships do not
foul each other, and the anchoring margin may have to be increased
accordingly.
It should be noted that the safety swinging circles of the ships do not
change when the swinging radius is reduced.
CHOOSING A POSITION IN WHICH TO ANCHOR 389

SEE BR 45
Fig. 14-4. Reduced swinging radius for ships at anchor

VOL 6
Table 14-3

CHAP 4
METRES YARDS

Length of ship 155 170

Anchoring margin 45 50
___ ___
Minimum radius 200 220 or 1.1 cables
390 CHAPTER 14 - ANCHORING AND MOORING

Anchoring a ship in a chosen position

Planning the approach
Before choosing the position in which to anchor the ship, the limiting danger
line should be drawn on the chart round the anchorage and its approach. The
anchorage position may now be chosen taking into account the factors
mentioned earlier. The anchorage plan can then be prepared.
This is illustrated in Fig. 14-5 for a frigate anchoring in Plymouth Sound.
An LDL for 7 metres and a safety swinging circle (SSC) of 2.65 cables have
been determined as follows:

Table 14-4

SSC LDL
Waterline length 120 yards Draught
(anchor to stern) 6m
7 shackles usable cable 210 Safety margin 2m
Safety margin 200 ___
___ Total 8m
Total 530 yards Minimum height of
tide during stay 1m
SSC = 2.65 cables ___
LDL =7m

1. Draw the clearing bearings to box in the approach and the anchorage.
Remember to allow a safe clearance from the LDL (see page 358).
2. Select the headmark, and the approach course to the chosen position,
clear of all dangers. A transit is preferable to a single mark (see page 349
for choice of headmarks). Do not allow the choice of a conspicuous
headmark to override the need for a safe approach course.
The approach course to the anchorage should be long enough to allow
plenty of time to get the ship steady on the correct line. For a frigate or
destroyer, the approach course may be as short as a few cables and still
achieve an accurate anchorage.
3. From the position of the anchor, lay back the distance between the anchor
and the pelorus (often known as ‘stem to standard’) to establish the ‘let
go’ position on the chart, as shown in Fig. 14-5. This distance should be
available from the Navigational Data Book and should be recorded in the
Note Book.
4. From the ‘let go’ position, mark back the distance to run, in cables. This
is usually done for every cable out to 5 cables from the anchorage and
then as necessary, as shown in Fig. 14-5. One mile to go and distances
at which speed is to be reduced should always be marked.
5. Select good beam marks to establish distance to go. This is particularly
important for the ‘let go’ position. Select suitable marks for the
anchorage fix.
6. Note predicted tidal stream and wind, and calculate the allowance needed
for them.
ANCHORING IN A CHOSEN POSITION 391

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Fig. 14-5. An anchorage plan&the chart |
392 CHAPTER 14 - ANCHORING AND MOORING

7. Note the minimum depth expected on each leg.

8. Decide which anchor to use and what length of cable is likely to be
required.
9. Mark ‘wheel over’ position and select ‘wheel over’ marks.
10. Prepare an alternative approach to the anchorage in case the run-in is
fouled; prepare also an alternative anchorage in case the one selected is
occupied. (This is not illustrated in Fig. 14-5.)
11. Re-check that the safety swinging circle is clear of the LDL.
12. Insert the necessary data in the Note Book, as shown in Fig. 14-6.
13. Brief the Captain on the plan and the alternative. Adjust the plan if
necessary. Brief the OOW, Navigating Officer’s assistant, etc.

Approach to an anchor berth: reduction of speed

It is easier to anchor in the exact berth if steerage way can be maintained up
to the moment of anchoring. If ships are anchoring in company, it is essential
to keep steerage way to permit ships to maintain station. For these reasons,
HM Ships usually anchor with headway and lay out the cable under the ship.
This method is known as the running anchorage.
When anchoring with headway, the speed when letting go should not be
more than 2 to 3 knots over the ground. Too high a speed may strain or even
part the cable, while too low a speed will prolong the operations unduly.
The alternative to anchoring with headway is to stop in the berth or just
beyond it and then, having let go the anchor, go astern laying out the cable.
This is known as the dropping anchorage; it is usually adopted by merchant
vessels and, for any HM Ship anchoring independently, this method may well
be more seamanlike than the running anchorage. HM Ships with underwater
fittings near the forefoot are obliged to use the dropping anchorage to prevent
the cable being laid out under the ship and damaging these fittings. For the
same reason, these ships are not permitted to moor.

The advantages of the dropping anchorage over the running anchorage

are:

1. The cable is laid out downwind and/or downstream (the running method
being into the wind and/or stream). This is the best direction for modern
anchors and cables, and there is less risk of damage to the protective
bottom composition and underwater fittings.
2. There is less risk of tumbling or slewing the anchor as the ship lays back
on the wind and/or stream after letting go. (When carrying out a running
anchorage, this risk is reduced if the wind and/or stream are well on the
bow when letting go, since the result will be to widen the bight of cable.)
3. There is less likelihood of dragging after letting go through premature
snubbing by the cable officer.
4. There is less wear on the hawsepipe and cable, and less chance of
damage, since the cable does not turn so sharply at the bottom of the
hawsepipe while it is being laid out.
5. The ship usually gets her cable more quickly.

The disadvantages of the dropping anchorage as compared to the running

anchorage are:
ANCHORING IN A CHOSEN POSITION 393

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Fig. 14-6. An anchorage plan&the Note Book |
 394 CHAPTER 14 - ANCHORING AND MOORING

1. Shiphandling is less precise in the final stages because way is taken off
the ship in the last part of the approach.
2. The cable is not laid out in a bight upwind and/or upstream as it is with
a running anchorage, and so cannot absorb the strain gradually as the ship
falls back on her cable. This was more important with the old Admiralty
Standard Stockless anchor, where the heavier cable provided a larger
share of the holding power.
3. The final moments of anchoring take longer and the operation may not
look so smart as a briskly executed running anchorage.
Table 14-5. Reduction of speed on approach to an anchor berth
Speed and Engine Orders
Distance
from
HM Ship Invincible Assault County Sheffield Broadsword Amazon Leander
Berth
HERMES Class Ships Class Class Class Class Class
in Cables
Carriers* Destroyer Destroyer* Frigate* Frigate* Frigate

10 8 knots 10 knots 8 knots 10 knots 10 knots 10 knots 10 knots 12 knots

6 Slow ahead Slow ahead

4 Stop

3 Stop Stop

2¼ Slow ahead

2 ü Stop Slow ahead Slow ahead Stop

1½
ï Slow Half astern
ý astern
1 ï
¾ Half astern Half astern
ü Astern
½ Half astern
ï power
ý as
In Berth Hal Half
ïnecessary
astern astern þ
* For these classes of ship, information is for a dropping anchorage

SEE BR 45
A rough guide to the reduction of speed on approach to an anchor berth
for various classes of ship is given in Table 14-5. Modifying factors such as
wind and current must always be taken into account.
Executing the anchorage plan
| Most of the remarks on the execution of pilotage (page 369) apply equally to

VOL 6
the execution of the anchorage plan. Particular points relevant to anchoring
are:
1. Check as far in advance as possible that the berth and the planned
approach to it are clear. Plot anchored ships to confirm this. (See page
400 for an example.)
2. Keep a constant check on the speed required to meet the ETA. This is
usually the time of anchoring.
3. Allow additional aim-off for cross-wind and tidal stream as the speed of
the ship is reduced, in order to make good the correct line of approach.
EXECUTING THE ANCHORAGE PLAN 395

This is particularly necessary in heavy ships, which may have to reduce

speed early in the approach. This is also particularly important when
executing a dropping anchorage, where the aim-off in the last few cables
will need to be approximately double that for a running anchorage.
4. As a general rule, try to anchor with the wind or tidal stream (whichever
is the stronger) slightly on the bow. In a frigate, the effect of 1 knot of
tidal stream is roughly equivalent to 20 knots of wind (page 348).
5. Normally plan to use the weather anchor. It is sometimes better to use
the lee anchor in places where the stream is so strong that the ship lies
more easily to the lee anchor. The lee anchor may be used when the wind
is across the stream, otherwise the ship may fall across the weather
anchor in the process of getting her cable, thus causing dragging. If other
ships are already at anchor, it is usually possible, by observing their
cable, to see which is the better anchor to use.
6. If anchoring with the wind abeam, it is often a good plan to cant the bow
into the wind using maximum rudder just before reaching the anchorage
position.
7. The anchor and the amount of cable to be used are normally planned
beforehand. Be prepared to adjust both of these depending on the
conditions encountered.
8. When on course for the anchorage, it is usually better to give the
Quartermaster the course to steer rather than to con him on to it. This
leaves more time for observing marks, ships, etc.
9. Remember the sun’s position (see page 349).
10. Information which the Captain particularly requires in addition to that
given on page 377 includes:

Depth of water.
Nature of the bottom.
State of the tide on anchoring.
Rise and fall of the tide during the intended stay.
Tidal stream on anchoring.
Forecast and actual wind and relative direction on anchoring.
Recommended anchor and scope of cable.
Landing places and their distance from the ship.

11. Fix the ship on letting go the anchor&take beam bearings first for
accuracy&obtain a sounding and note the ship’s head and time. The
sounding provides a check that sufficient cable is being used.
12. The Captain normally works the anchor flags. These are red and green
hand-flags, denoting port or starboard anchor respectively. To avoid any
chance of prematurely letting go the anchor, the flag should be exhibited
steadily from a prominent position at ‘Stand by’ for a few seconds only
before ‘Let go’, when it should be dropped smartly.
13. As the way is taken off the ship, the Navigating Officer must observe
what the ship is doing, either by beam bearings or by objects in transit,
and report this to the Captain.
396 CHAPTER 14 - ANCHORING AND MOORING

14. The correct method of entering details of anchoring in the Ship’s Log and
Note Book is as follows:

‘Came to port (starboard) with Õshackles in Õmetres/fathoms

in No. ÕBerth (or in position Õ )’.

15. The anchor bearings entered in the Ship’s Log should be for the position
of the anchor and not of the bridge on letting go.
16. Once the position of the anchor has been plotted, using the fix taken at
the time of letting go, the direction of the ship’s head at anchoring and
the stem to standard distance, then:
(a) The safety swinging circle should be re-plotted to confirm it is still
clear of the LDL. In Fig. 14-5, the radius is 530 yards (see page
390).
(b) The bridge and stern swinging circles should be plotted for the
amount of cable veered. In Fig. 14-5 the radii are 195 and 270 yards
respectively, arrived at as in Table 14-6.

Fig. 14-7. Plotting the bridge, stern and safety swinging circles from the
anchorage fix
ANCHORING IN DEEP WATER, WIND, TIDAL STREAM 397

Table 14-6
BRIDGE SWINGING CIRCLE STERN SWINGING CIRCLE

Length (stem Waterline length

to standard) 45 yards (anchor to stern) 120 yards
No. of shackles No. of shackles
veered (5) 150 yards veered (5) 150 yards
Radius of ___ Radius of ___
swinging circle 195 yards swinging circle 270 yards

The plotting of the bridge, stern and safety swinging circles,

using the above figures, is illustrated in Fig. 14-7.

Fixes of the position of the bridge must always lie inside the
bridge swinging circle; if they lie outside, the ship must be dragging.
Drawing the stern swinging circle for the amount of cable veered
gives a clear indication of how much safe water there is available all
round between the ship and the LDL.

SEE BR 45
(c) The distances of other ships at anchor or at buoys should be checked
to confirm that there is no danger of fouling them.

Anchoring in deep water, in a wind or in a tidal stream

Fuller details of anchoring in deep water, in a wind and in a tidal stream are

VOL 6
given in Chapter 13 of BR 45(6), Admiralty Manual of Navigation, Volume |
6. |

Anchoring in deep water

Cable must be veered (perhaps 1 shackle or even more) before letting go.
The maximum safe speed of certain classes of HM Ships with cable veered
is limited, while other classes, because of their underwater fittings, must stop
and take all their way off, before veering cable.
When anchoring in fjords which are steep-to, with deep water reaching
almost to the sides, special procedures are necessary. The bottom is often
rock covered by a layer of silt and is frequently uneven. Depths can change
considerably over a short distance. The holding ground is often poor. The
depth of water is such that the standard rules for the amount of cable cannot
be used&for example, anchoring in 60 fathoms (110 metres) requires at least
13½ to 14 shackles. This amount of cable may not be available unless a ship
so fitted is able to use both cables on one anchor. A ship with, say, 9 shackles
of cable available will only be able to put about 4 shackles on the bottom in
60 fathoms (110 metres) of water. Thus, the holding power of the anchor will
be considerably reduced, perhaps by as much as 60% to 70%, and account of
this must be taken.
When an anchorage of this nature has to be planned, it may be preferable
to assign an anchorage area of about 4 to 6 cables diameter within which the
ship may anchor at her discretion, rather than allocate a precise position. It
is desirable to have at least two charted soundings of about 50 fathoms (90
metres) or less within the area. If time allows, the ship should make several
 398 CHAPTER 14 - ANCHORING AND MOORING

echo sounder passes through the area to identify the optimum position.
Having found a suitable position, the ship should approach it at as slow a
speed as effective steerage way will allow. Several shackles of cable may
have to be veered before letting go and this should be done at minimum speed
(2 to 3 knots) or when stopped in the anchorage position.
Anchoring in a tidal stream
A high contrary wind is necessary to overcome the effect of only a moderate
stream; it is therefore more seamanlike to anchor into the stream. Anchoring
with a following tidal stream of more than ½ knot is not usually
recommended, particularly in a heavy ship of deep draught, because of the
strain on the cable and the cable holders, which is greatest as the ship swings
athwart the stream.
Heavy weather in harbour
Advice on the action to be taken in heavy weather in harbour is to be found
| in Chapter 15 of BR45(6), Admiralty Manual of Navigation, Volume 6.
Letting go second anchor
Should a gale arise while riding at single anchor, the ship will normally yaw
to an extent dependent on her size and above-water design. At the end of
each yaw, violet and sudden strains are brought on the cable, thus
considerably increasing the chances of dragging.
To prevent dragging, either more cable should be veered on the existing
anchor or a second anchor should be dropped to stop the yaw, or a mixture of
these two methods should be used. Some HM Ships are fitted with only one
length of cable or only one anchor, in which case they have little alternative
but to veer more cable or get underway.
Remember to redraw the bridge and stern swinging circles if more cable
is veered.
Dragging
Whether or not the ship is dragging may be confirmed by selecting a pair of
fixed objects on the beam and in transit. Such objects need not be charted.
The transit may be tested by walking along the deck to see if it opens quickly
enough.
The safest method of discovering whether or not the ship is dragging is
to fix by sextant angles or compass bearings. The fixes of the position of the
bridge should always lie within the bridge swinging circle drawn for the
length of cable veered. As mentioned earlier, if they fall outside, the ship is
dragging.
Anchoring at a definite time without altering speed
It is always desirable to anchor the ship at the correct or advertised time; but
a drastic increase or decrease of speed may not be possible or desirable, and
it is therefore as well to plan the approach in such a way that the distance
remaining to be steamed can be adjusted by an alteration of course.
The following simple method of dealing with this problem enables the
chart to be prepared beforehand; the navigator can see at a glance, whenever
he fixes the ship’s position, whether he is ahead or astern of time; and last-
minute alterations of speed can be avoided.
ANCHORING AT A DEFINITE TIME 399

EXAMPLE
A ship has signalled her time of anchoring at a position A (Fig; 14-8) as
0800. She proposes to approach the anchorage on a course 180°. Her speed
of approach will be 12 knots, and will not be altered until the engines are
stopped at 3 cables from position A.

Fig. 14-8. Anchoring at a definite time without altering speed

To prepare the chart, calculate the distance the ship will run in the 10
minutes prior to anchoring, making allowance for stopping engines 3 cables
from A.
Lay back this distance AB along the line of approach. B is then the
position to be attained at 0750.
 400 CHAPTER 14 - ANCHORING AND MOORING

Since 5 minutes at 12 knots is equivalent to 1 mile, with centre B lay back

5-minute time circles. The chart is now prepared, and at 0710 the ship,
steering 270° speed 12 knots, fixes her position at F.
At 0715 she is in position E, inside the 0715 circle. Similarly, at 0720
she is at D, inside the 0720 circle; but it is seen that at 0725 she will arrive at
C, on the 0725 circle, at which time it will be necessary to steer the course CB
in order to arrive at B at 0750.
Ensuring that the anchor berth is clear
When approaching an anchorage, always make sure that the anchor berth and
line of approach are clear of other ships. Check the position of any ship
suspected of fouling the anchor berth by one or other of these two methods:
1. Fix own position and plot the other ship by radar range and visual
bearing, or take a radar range and bearing of the ship from a charted radar
conspicuous object on the radar display.
2. Take a bearing of the other ship when it is in transit with a charted shore
object, so obtaining a position line on which the other ship must lie. This
should be done as early as possible and before altering to the approach
course, so that a second or third position line may be obtained by
observing the bearing of the ship in transit with other charted shore
objects. The position of the other ship may then be fixed, as shown in the
following example.
EXAMPLE
A ship (Fig. 14-9), steering 080° and intending to anchor in position Z by
approaching the anchorage on a course 350°, suspects that a ship D is foul
of her berth. At 1100 the ship is observed in transit with a chimney bearing
050°. At 1105 the ship is observed in transit with a flagstaff bearing 026°,
and at 1107½ with the church bearing 000°.
From these three lines of bearing, D’s position may be plotted on the
chart. The position of D’s anchor must then be estimated, after allowance has
been made for the wind and stream at the time.
Anchoring in a poorly charted area
If there is no accurate chart of the anchorage, and the suitability of the berth
is in any doubt, take careful soundings within a radius of at least 3 cables of
the ship to make certain there are no uncharted rocks or dangers.
Anchoring in company
HM Ships frequently have to anchor in company and full details may be
| found in Volume 4 of this manual and also in BR45(6), Admiralty Manual of
| Navigation, Volume 6. Various points to remember are set out below:
1. If ships of dissimilar type are manoeuvring together, the tactical diameter
which is to be used must be signalled to all ships so that they are aware
how much rudder they will require, dependent on their own turning
characteristics.
2. The normal manoeuvring intervals between lines of ships may have to be
reduced considerably if ships are to anchor in formation.
ANCHORING IN COMPANY 401

Fig. 14-9. ‘Shooting up’ a ship at anchor

3. SEE BR 45
A running anchorage rather than a dropping one is to be preferred. It is
much easier for ships to maintain station as shiphandling is more precise.
However, if some of the ships in company are obliged to carry out a

VOL 6
dropping anchorage (page 392), then it is probably best for all ships to
carry out the same procedure. This means that alterations of course
together in the final stages of the approach to allow for tidal stream are
likely to apply correctly for all ships. Remember that wind will have
different effects when ships are dissimilar. If the same anchoring
procedure is used in all ships, anchor cables will all be laid out in the
same direction, so once the ships have all got their cable, they will ‘look
right’. In the final stages of a dropping anchorage, it becomes
progressively more difficult to maintain station; the best course of action
is to order ships to anchor in the allocated berth ‘in accordance with |
previous instructions’ as convenient.
4. When planning the anchor berths for other ships, their ‘let go’ bearings
should if possible be clear of other ships.
5. The Senior Officer’s anchor berth and those of ships in formation should
be signalled early.
6. The Senior Officer’s intentions (approach course, etc.) should also be
 402 CHAPTER 14 - ANCHORING AND MOORING

signalled early, so that other ships can prepare their own charts and
appreciate what the Senior Officer is trying to achieve.
7. The anchoring formation should be taken up in good time, so that
alterations of course can be made by turns together, a much simpler
procedure than wheeling.
8. If possible, plan on a long run-in on the final approach course to the
anchorage. This gives other ships plenty of time to settle down in their
station.
9. On the final run-in, adjust course as necessary by turns of 5° or 10° to
port or starboard. These alterations can be ordered in advance by flag or
voice and executed as required.
10. Ships must be ready to anchor individually if ordered, and each
Navigating Officer should have prepared the necessary plan to do so.

Mooring ship
Most modern HM Ships are unable to moor because of design limitations and
the times when older ships are required to do so are rare. The procedure has,
however, been retained and is set out below. A ship may often find it
necessary to plan on letting go two anchors in predetermined positions, for
example if carrying out a Mediterranean moor,* and the procedures set out
below will generally apply.

Swinging room when moored

SEE BR 45
The object mooring is to conserve space: the minimum swinging radius may
be taken as the ship’s length plus a mooring margin of at least 18 metres (20
yards). Table 14-7 gives an example.

Table 14-7

VOL 6
Length of ship
Mooring margin

Minimum swinging radius

METRES

155
18
___
173
YARDS

170
20
___
190 or 0.95 cables

Care must be taken that anchor cables of adjacent ships do not foul each
other; the mooring margin may have to be increased accordingly, dependent
on the amount of cable veered on each anchor. When planning mooring
berths, it must be remembered that ships may have to moor or unmoor
independently, whatever the direction of the wind or tidal stream. Thus, the
berths may have to be planned at an even greater distance apart. Furthermore,
a safety margin of at least 1 cable from any charted danger must be added to
the radius of each berth.

* A Mediterranean moor is a method of securing a ship at right angles to the jetty, the stern secured to it by
| hawsers, the bow being held by two anchors out ahead, one on each bow. (See or BR45(6), Admiralty
| Manual of Navigation, Volume 6 for full details.)
MOORING SHIP 403

Planning the approach

The same principles apply as for anchoring, modified as follows. The final
stages of the mooring plan are illustrated in Fig. 14-10 (page 404) and show
the position of each anchor relative to the stem.

1. First decide the length of each cable on each anchor when the ship is
moored. As a general rule, this should be at least 5 times the depth of
water. For example a ship mooring in 20 metres (11 fathoms) should use
a minimum of about 3½ shackles on each anchor. Heavy ships should
always use a minimum of 5 shackles on each anchor in any case.
One shackle is usually required to go round the bow so that the
mooring swivel may be inserted. The distance between the two anchors
when let go should therefore be the combined length of cable to be used
on each anchor less one shackle. For example, a ship using 5 shackles on
each anchor should allow a distance of (5 x 2) - 1 or 9 shackles (270
yards) between the anchor positions. In Fig. 14-10, the distance of each
anchor from the middled position A would be ½ x 270 = 135 yards.
2. The direction of the line joining the anchors should coincide, if possible,
with that of the prevailing wind or tidal stream; and each anchor should
be sufficiently far from dangers, and from the anchors of other ships, to
enable it to be weighed without inconvenience whatever the direction of
the wind.

Executing the mooring plan

1. Reduce speed so that the cable on the first anchor is laid out straight and
all way is taken off the ship as the second anchor is let go.
2. The second anchor can be let go from either the forecastle or the bridge.
Given good marks, less than 1 mile distant, the precise moment when the
bridge arrives at the correct position will be known; but even if the cable
is tautly laid out, it will usually be found that the appropriate shackle, the
ninth in the above example, has not reached, or is already outside, the
hawsepipe when the second anchor bearing comes on. It is
recommended, therefore, that the second anchor be let go by a mixture of
‘bearing’ and ‘shackles’, in an endeavour to drop it as near as possible to
the right position without giving the cable officer an impossible task
when middling.
There will be occasions when middling accurately in the assigned
berth is of more importance than middling with the correct number of
shackles on each cable.
3. Let go the weather anchor first, in order to keep the cable clear of the
stem when middling.
4. The ship must make good the correct course between anchors while the
first cable is being laid out.
5. Always avoid excessive strain on the cables.
6. In order to cant the ship in the right direction for middling, the wheel may
be put over about 2 or 3 shackles before letting go the second anchor,
without having any appreciable effect on the berth.
7. Remember that the stem of the ship will fall well to leeward of the line
of anchors when lying at open hawse.
404 CHAPTER 14 - ANCHORING AND MOORING

EXAMPLE
A ship is ordered to moor with 5 shackles on each anchor in position A (Fig.
14-10). Stem to standard: 40 yards.

Fig. 14-10. Mooring in a chosen position

It is decided to approach with the windmill ahead on a line of bearing.

This line of bearing will be the ‘line of anchors’ when the ship is moored.
(2 x 5) − 1
From A lay off AB = AC = x 30 yards = 135 yards
2
B and C will be the positions of the first and second anchors.
From B and C lay distances of 40 yards to Y and X.
Y and X are the positions of the standard compass at the moments of
letting go the first and second anchor respectively.
 405

CHAPTER 15
Radar, Blind Pilotage

This chapter contains advice on the use of radar for navigation and blind
pilotage. Naval users should also be conversant with BR 1982, which |
contains information necessary for a proper understanding of radar, in
particular:

The transmission of radio waves, range and range discrimination,

bearing and bearing discrimination.
The radar receiver, video signals, displays.
Propagation and reflection.
Capabilities and limitations.

Some of this information is amplified below.

Naval users should also refer to BR 1982, for detailed information on the |
various navigational radar sets and the video distribution systems in service
in the Royal Navy.
Non-Naval users should refer to standard works on radar such as The Use
of Radar at Sea.
The chapter concludes with remarks on radar beacons, shore-based radar,
and the use of radar in ice.

RADAR WAVES: TRANSMISSION, RECEPTION, PROPAGATION

AND REFLECTION

Radar detection
Sufficient pulses must strike an object during one sweep of the radar to
produce a detectable response, and the usual minimum for this is 6 to 8
pulses. The number of pulses N striking an object during one sweep of the
aerial may be found from the formula:

BW (in degrees) 60
N= x x PRF . . . 15.1
360 aerial rotation speed (in rev / min)
For a 3 cm radar with a beam width (BW) of 1°, aerial rotation of 24 rev/min
and a pulse repetition frequency (PRF) of 1000 pulses per second:
1 60
N = x x 1000 = 7
360 24
406 CHAPTER 15 - RADAR, BLIND PILOTAGE

i.e. 7 pulses every 2½ seconds, or 168 pulses per minute.

Because the object usually has a cross-sectional area relative to the radar
beam, the number of pulses will be increased and the response will therefore
be improved. Thus, for a 3 cm radar, the data rate (the rate at which contact
information is supplied by the radar) is high. When combined with a narrow
beam and short pulses, this permits accurate bearing and range measurement.
The number of pulses per aerial sweep is normally high enough to ensure
positive detection.
There are, however, factors which affect detection: the reflecting area of
the object, attenuation, clutter, etc. The operator must apply a threshold level
of signal, largely determined by experience, to help him decide whether a
paint represents an object or not. There is no absolute guarantee that the
echoes being observed do actually indicate objects, or that objects are not
hidden in the clutter. The operator may, on occasion, select as an object an
echo at relatively short range which is in fact caused by noise or clutter, while
at long range he may initially ignore an echo because of its apparent random
nature when in fact it is an object at maximum detection range.
These factors become important where computer-based automatic
detection is concerned. A receiver output level has to be selected as the
threshold level. If the level is set too low, then random noise exceeding the
level may be received and an object will be indicated, thus creating a false
alarm. On the other hand, if the level is set too high, while there may be no
false alarms, small objects giving a poor echo response may well be missed
altogether.

Range discrimination and minimum range

Range discrimination equals half the pulse length and may be found from the
following formula:

range discrimination = 164 x pulse length . . . 15.2

(in yards) (in Fs)

For example, the range discrimination of a radar set with a pulse length
of 0.25 microseconds (Fs) is 41 yards.
Minimum range, theoretically, equals the range discrimination of the set
for the pulse length in use and, provided that a twin-aerial system is used, the
two values should be the same. However, if a common-aerial system is used,
minimum range will be approximately twice the range discrimination, owing
to the momentary saturation of the receiver by the transmitted pulse. The
minimum range (the ground wave) should always be noted by the user for the
particular set in the prevailing conditions.

Beam width and bearing discrimination

Beam width causes distortion of the radar picture to an extent approximating
to half the beam width, as illustrated in Fig. 15-1. The picture of the coastline
on the radar display is a distortion of the true area, as shown by the shaded
areas (it is purposely exaggerated for the sake of illustration). Small islands
or rocks close to the coast, or inlets, will merge into the general echo if the
beam width is large enough.
RADAR WAVES 407

Fig. 15-1. Distortion caused by beam width

If radar bearings of edges of the land are observed (e.g. A2 in Fig. 15-1),
they must be corrected for half the beam width.
This distortion is minimised in navigational radars by keeping the beam
width, and hence the bearing discrimination, down to the order of 1°.

Video signals
Bandwidth
In a navigational radar, accurate ranging is essential; thus, the bandwidth
must be wide at the expense of greater noise and loss of maximum range.

Amplification
There may be a choice of linear (LIN), logarithmic (LOG) or processed
log/lin amplification.
LIN amplification is ideal for long-range detection and for use in calm
conditions when sea clutter is minimal. Sea clutter may be suppressed by the
use of swept gain, rain clutter or other block echoes by means of the
differentiating circuit (see p.408).
LOG amplification is the best choice for short/medium-range work when
a lot of sea clutter is present. The logarithmic circuit provides an inherent
suppression of sea clutter which is usually better than can be achieved by the
linear receiver-swept gain combination. Usually, however, there is a loss of
maximum detection range.
408 CHAPTER 15 - RADAR, BLIND PILOTAGE

Some radars may have a processed log amplification whereby the video
signal retains the sea clutter suppression characteristics of the logarithmic
receiver, but benefits to an extent from the high signal/noise ratio output of
the linear amplifier. There is, however, a loss of maximum detection range,
and straightforward linear amplification is a much better choice if there is no
sea clutter present. By introducing a differentiation circuit (see below), a
completely clutter cleared video signal may be produced.

Improvements to video signals

Measures to improve video signals are generally concerned with the removal
of clutter, and some of these facilities may be available to the operator.
Clutter varies with the wavelength & the longer the wavelength, the less the
clutter. Clutter also varies with the height of the aerial & the higher the aerial,
the greater the range of the clutter.
Automatic gain control. The gain of the amplifier is automatically
reduced if the signal reaches saturation level; thus, this control is a partial
answer to removing clutter from the display.
Swept gain. This control reduces the amplitude of clutter at short ranges,
gain increasing with range. However, it is very easy to sweep the display
clean not only of sea clutter but also of close-range echoes, like small craft
and buoys, that give a poor echo response. Care must be taken not to use this
control indiscriminately. Swept gain may also be known as sensitivity time
control (STC) or (anti-clutter) sea.
Differentiation. The differentiation control is used to reduce the effect
of rain and other blocks of unwanted echoes. The control operates at all
ranges but the penalty is loss of maximum range. Differentiation may also be
known as fast time constant (FTC), differentiation time constant (DTC) or
(anti-clutter) rain.
Clipping. Clipping is a process which removes the bases of the signals
to allow echoes which are close together to be seen separately on the display
without having to adjust the normal controls (brilliance, focus, gain).
Clipping sometimes also enables echoes to be identified which might
otherwise be lost in clutter, although the differentiation control may be more
satisfactory. The penalties of using the clipping control are to introduce
range errors and to lose all small contacts. As with swept gain, it is
dangerous to use this control indiscriminately.

Atmospheric refraction
The optical (visible) and radar horizons (Fig. 15-2) are greater than the
geometric because of refraction in the atmosphere. The distance of the
horizon under standard atmospheric conditions may be found from the
following formulae:

geometric horizon 1.92 h sea miles . . . 15.2

optical horizon 2.08 h sea miles . . . (9.2)
radar horizon 2.23 h sea miles . . . 15.3
where h, the height of the aerial, is measured in metres; or
geometric horizon 1.063 h sea miles . . . 15.4
RADAR WAVES 409

optical horizon 1.15 h sea miles . . .(9.3)

radar horizon 1.23 h sea miles . . .15.5
where h is measured in feet.

Fig. 15-2. Geometric, optical and radar horizons

Formulae (15.3) and (15.5) and the radar range/height nomograph (page
427) are all based on the assumption of a standard atmosphere, which
approximates to the average state of the atmosphere in temperature latitudes
over the land.
Super-refraction increases the horizon range, and thus maximum
detection range, by a considerable extent. It is likely to occur when either a
temperature inversion (an increase of temperature with height) or a
hydrolapse (a decrease in humidity with height) is present.
A moderate degree of super-refraction is usually present over the sea
because the hydrolapse in the lower levels of the atmosphere over the moist
sea is normally stronger than that over the land. For average conditions over
the sea, radar detection ranges are often increased by as much as 15% to 20%.
Sub-refraction occurs much less frequently; it decreases normal detection
range through a combination of temperature and humidity which causes the
radar wave to be bent upwards instead of downwards. Decrease of
temperature with height may be greater than the standard lapse rate, and
humidity may increase with height. Detection ranges may be reduced to the
point where contacts are visible to the eye but are not displayed on radar.
A summary of types of weather, with the associated types of refraction
and where these are likely to be found, is given in Table 15-1. Two charts of
the world (Fig. 15-3(a) and (b) show those areas where the meteorological
conditions for super-refraction are likely to be fairly common.
410 CHAPTER 15 - RADAR, BLIND PILOTAGE

Fig. 15-3. Favourable areas for super-refraction

RADAR WAVES 411

Table 15-1. Super- and sub-refraction

WEATHER WHERE FOUND

Super-refraction
Average conditions over open sea: an Everywhere in the open sea. The duct
evaporation duct. The air next to the extends up to 18 metres in trade-wind
water becomes damp by evaporation. If zones.
it is overlaid by drier air, a surface duct
is formed practically irrespective of the
type of temperature lapse. The duct may
be 3 to 8 metres high, but wind will
weaken and disperse it.
Subsidence inversions. Subsiding air In anticyclonic conditions, e.g. the
becomes warmer and relatively drier Azores high and the trade-wind zones.
than the air below it. Temperature Tropical subsidence in Horse Latitudes,
inversion and hydrolapse assist each West Africa, Cape Verde Islands. Also
other, causing a more pronounced duct found in ridges of high pressure.
than usual.
Conditions in coastal waters. Offshore The Mediterranean mainly in summer.
winds often carry warm dry air out Off West Africa during the Harmattan.
above the cooler and damper air over the The Arabian Sea, Bay of Bengal, Sri
sea. The coasts adjacent to hot deserts Lanka, Madras. The lee side of coasts in
and on the lee side of warm land masses the zones of prevailing westerlies, or of
will experience ducts. north-east or south-ease trade winds. In
temperature zones in the ridges between
depressions.
After the passage of cold front. Cold In the North Atlantic, behind the cold
northerly air behind a depression, fronts of depressions.
blowing towards warmer waters, creates Note: Polar air arriving from a
a marked hydrolapse forming a shallow westerly or south-westerly direction in
evaporation duct. the North Atlantic is likely to have only a
small hdyrolapse near the surface; thus,
ranges are only average at best.
Sub-refraction
Conditions in the open sea with no In relatively warm air masses over the
evaporation duct. If a belt of warm air sea in temperate regions, e.g. in a south-
lies over the sea, a humidity inversion is westerly air flow over the North Atlantic,
formed. If this is stronger than the particularly in the warm sector of a
temperature inversion, the evaporation depression.
duct disappears, with the result that
detection ranges are below average.
Cold wind conditions. A wind blowing This condition may occur in Arctic or
from a cold land mass over a relatively Antarctic regions.
warm sea may cause sub-refraction.
412 CHAPTER 15 - RADAR, BLIND PILOTAGE

The refraction conditions likely to be experienced on the passage of a

frontal depression in the North Atlantic are illustrated in Fig. 15-4. In
general, depressions are not favourable to long-range radar detection, whereas
anticyclones and ridges of high pressure are.

Fig. 15-4. Refraction experienced during the passage of a frontal depression

The following effects may be experienced during super-refraction.

1. Increased clutter.
2. Multiple (second or third) trace echoes; e.g. the maximum unambiguous
range of a radar set = (81,000/PRF) n miles. If the PRF is 1000, the
maximum unambiguous range of the set is 81 miles. A contact at 90
miles could therefore appear on the PPI at 90 - 81 = 9 miles range.
3. Distortion in the shape of the multiple trace echoes of land masses.

Attenuation of radar waves

Absorption and scattering of radar transmissions by rain and other forms of
precipitation may be considerable. Points to remember are:

1. The attenuation or weakening of the radar beam in rain may be such that
objects at the far end of a rainstorm or beyond may give a much weaker
RADAR WAVES 413

echo than expected, or may give no echo at all. The echoes from rainstorms
(Fig. 15-5) can be so strong that they mask echoes from targets within the
area; 3 cm radars are particularly prone to these effects. In very heavy rain
such as thunderstorms, the reduction in maximum detection range may be as
much as 30% to 35%, considerably more in tropical downpours. The effect
is less on 10 cm radars.

Fig. 15-5. Shower echoes on the radar display

2. As the reflectivity of ice is less than water, the attenuation effects of hail
and snowstorms are much less marked than in rain.

Appearance of weather echoes

The appearance of weather echoes on centimetric radar sets is illustrated in
Figs 15-6 to 15-8. Cold fronts (Fig. 15-6) produce a band or line composed
of a large number of echoes that break up and re-form as the band moves
across the display. Cold fronts may be detected at long range. Warm fronts
(Fig. 15-7) are varied in structure and may produce weak, diffused echoes
covering a large part of the display. Fig. 15-8 is a good example of super-
refraction, obtained during the summer months on 10 cm radar in the southern
part of the North Sea, SE of Flamborough Head. Multiple ship echoes can be
seen out to about 80 miles.
Sand/dust storms produce weak diffused echoes, particularly on 3 cm
radar.
414 CHAPTER 15 - RADAR, BLIND PILOTAGE

Fig. 15-6. Cold front echoes on the radar display

Fig. 15-7. Warm front echoes on the radar display

RADAR WAVES 415

Fig. 15-8. Super-refraction on the radar display

Reflection from objects

Metal and water are better reflectors of radar than are wood, stone, sand or
earth. In general, however, the shape and size of an object have a greater
effect on its echoing properties than its composition. Increasing the size of
an object may give a more extensive but not necessarily a stronger echo. The
shape of the object dictates whether the reflected energy is diffused over a
wide arc or concentrated into a beam directed back towards the radar. A flat
plane may produce a very strong echo when at right angles to the radar beam
but a very weak one otherwise. Curved surfaces tend to scatter the energy
and thus produce a poor echo as, for example, with conical shaped
lighthouses and buoys.
Corner reflectors provide a means of improving the radar response from
small targets such as buoys, boats or beacons, which would otherwise give a
poor echo owing to their size, shape or construction material. Fig. 15-9
illustrates a typical square corner reflector, consisting of three mutually
perpendicular planes.
A transponder may be fitted to small units, for example helicopters, to
enhance the size of the echo. A transponder consists of a separate transmitter
triggered by the arrival of another transmission and transmitting on a specific
frequency. The nature of the reply can be varied, one variation being echo
416 CHAPTER 15 - RADAR, BLIND PILOTAGE

enhancement, in which the transponder transmits a pulse coincident with the

radar echo, so providing a much improved echo signal.

Unwanted echoes
Unwanted echoes consist, for example, of side lobes and double echoes from
contacts at close range, false echoes from obstructions like masts and
superstructure, and also multiple trace echoes (page 412). Such echoes are

Fig. 15-9. Typical square corner reflector

Fig. 15-10. Radar shadow area around a ship contact

RADAR FOR NAVIGATION 417

normally easy to recognise & e.g. the symmetrical nature of side lobe echoes,
the double range and same bearing for double echoes.

Radar shadow
Radar shadow areas cast by mountains or high land may be extensive and
may contain large blind zones. High mountains inland may well be screened
by lower hills nearer the coast and thus not appear on the display.
On the display, each contact is surrounded by a shadow area, which is
governed by the size of the object, pulse length and beam width. This is
illustrated in Fig. 15-10.
A ship 200 yards long, at an angle of 30° and at a range of 4 miles, would
display an echo about 215 yards in length and 235 yards in width (pulse
length 0.25 microsecond, beam width 1°).

RADAR FOR NAVIGATION

The accuracy of navigation using radar depends on the accuracy of the radar
in use and the correct operation of the user controls. Ranges in excess of 5
to 6 miles are rarely required for blind pilotage; therefore the radar should be
adjusted for optimum performance at short range. Where available, short
pulse length and narrow beam width will improve range and bearing
discrimination and picture clarity. The centre spot should be in the centre and
the picture correctly focussed.
Displays used for blind pilotage must be set up to read in n miles and not
in tactical (2000 yards) miles.

Suppression controls
As described on page 408, suppression controls may be used to reduce or
remove rain clutter, sea returns and side or back echoes, but care must be
taken not to eliminate all small contacts. Suppression controls will need to
be adjusted according to changes in the weather and sea states and also
changes in the strength of the echo return from the object.

Radar and the Rule of the Road

The following points concerning The International Regulations for
Prevention of Collision at Sea, (1972) should be remembered when using
radar:

1. Rule 5. ‘All available means’ implies that radar shall be in use in or near
restricted visibility, and that a watch is being kept on appropriate VHF
circuits. Radar plotting must be systematic (Rule 7b).
2. Section II, Rules 11 to 18 only apply to vessels in sight of one another.
3. Section III, Rule 19. If vessels cannot see each other visually, then
neither has the Right of Way. This rule is strongly worded: ‘Shall
proceed ...’, ‘Shall determine ...’, ‘Shall reduce ...’, and so on.
4. The close quarters situation. Rules 8 and 19 make it quite clear that early
and substantial action should be taken to avoid a close quarters situation
with another ship.
418 CHAPTER 15 - RADAR, BLIND PILOTAGE

Other ships’ radar

It is important to guard against making assumptions about another ship’s use
of radar vis-à-vis own ship, for example:
Assuming that the other ship is aware of own ship’s position when in
fact:
Own ship is not painting on the radar. or
The other ship’s radar is not operating or is not being watched.
The other ship may not be plotting own ship’s track correctly; the radar
bearings could be in error (page 424). This could lead the other ship to
misinterpret the correct avoiding action.
Range errors
Index errors
Radar range is a function of time and is measured from the radar aerial.
Ideally, the transmitter and receiver should be adjacent to the aerial but this
is rarely possible. The following factors must therefore be taken into account
before accurate range measurement is possible.
1. The time take for a pulse to travel from the transmitter through the
waveguide to the aerial.
2. the time between reception of the sync pulse at the input of the display
timebase generator and the start of the timebase scan.
3. The time taken for an echo pulse to travel from the aerial to the receiver.
4. The time taken for the echo pulse to pass through the receiver and to be
applied to the cathode ray tube.
These factors form an error called the range index error, which may be
measured by several methods described below. Index error should be
measured on each range scale before each blind passage, and should be
marked on the display and applied in all fixes, cross-index ranges, etc. On
some radar sets, index error may be eliminated (see page 424).
Other design factors
The following factors may affect range measurement in older displays, but are
no longer a problem with modern solid state circuitry:
1. The calibration oscillator must be stable and at the correct frequency,
otherwise the distance apart of the range calibration rings will not be
correct.
2. Linearity. A linear display & that is, one where the physical distance
between the range rings is the same & is essential for accurate ranging
and parallel indexing.
3. Non-synchronisation between the range rings and the range marker.
Using the display
1. The display must be set up correctly & focus, gain and brilliance may
affect ranging.
2. Operator technique. The largest possible scale must be used for ranging,
RADAR FOR NAVIGATION 419

e.g. the 3 mile range scale is preferable to the 6 mile, the 6 mile to the 12
mile range scale, etc., as required by the range of the objects. The
operator should always use a short pulse and should always range on the
near side of the paint.
3. Parallax errors. When the display is viewed from different angles, errors
are introduced by the curvature of the cathode ray tube (crt) and the
separation of the plotting surface from the surface of the crt. The fitting
of reflection plotters has greatly reduced these errors as does the
introduction of electronic plotting and mapping lines.
4. Errors are introduced by certain controls which alter the range of the
contact (e.g. ‘clip’).
5. Inaccuracies are caused by not using the correct range strobe for the scale
in use.

Other causes of range error

Other possible causes of range error are to do with the nature of the object
itself. Examples of this are:

1. Errors caused by the varied reflecting properties of different objects and

their incidence to a radar beam. For example, a vertical granite cliff will
give a much stronger echo than a sloping sandy beach.
2. As the tide rises and falls on a sloping coastline, the appearance of the
radar picture may be very different from that indicated by the chart.

Finding the radar index error

Radar index error is the difference between radar and true range. The
majority of displays under-range, therefore radar index error usually has to
be added to the measured range. Radar index error is not constant and every
opportunity should be taken to obtain a check. After each check, the revised
error must be marked on the display and applied to all subsequent ranges.
Allowance may have to be made for any range difference between the aerial
and the fixing position, normally the bridge. Several methods of obtaining
the index error are available; these are now described. Some methods are
more accurate than others, but the use of any one method is determined by the
facilities available.

Radar calibration chart

This is the most accurate method of calculating radar index error. Charts are
produced by the Hydrographic Department, with additional data for certain
ports, which enable a ship to fix its position to within 10 yards when at
anchor or secured to a buoy. The additional data consist of curves of equal
subtended angle between pairs of charted objects (Fig 15-11, page 420). The
angles are measured by horizontal sextant and, for example in Fig. 15-11, a
sextant angle between A and C of 40° and one between C and B of 50° would
fix the ship’s position at point X.
The true range of a radar-conspicuous mark can therefore be established
from the chart and compared with a radar range taken simultaneously with the
fix. Any difference is the index error. For example:
420 CHAPTER 15 - RADAR, BLIND PILOTAGE

charted range 1550 yards

radar range 1530 yards
Radar index error +20 yards

A correction of +20 yards must be applied to all radar ranges.

Fig. 15-11. Curves of equal subtended angle

Use of the normal chart

If the ship is alongside in a harbour and radar-conspicuous objects are
available, then charted and radar ranges of the object may be compared. The
difference is the index error.

Two-mark method
The two-mark method may be used if two radar-conspicuous objects are
available, the range between them is known accurately from the chart, and the
ship is steaming between the marks.
Radar ranges of both objects (A and B in Fig. 15-12) are taken
simultaneously as the ship crosses the line between them. Both radar ranges
include index error (IE). AB is the charted distance between the two objects;
a is the radar range between the ship and point A; b is the radar range between
the ship and point B.

a + IE + b + IE = AB
2 IE = AB - (a + b)
AB − (a + b)
IE = . . . 15.6
2
RADAR FOR NAVIGATION 421

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Fig. 15-12. Two-mark method |

Three-mark method
When three radar-conspicuous and well charted objects are conveniently
situated around the ship, radar ranges of all three objects may be taken
simultaneously and range arcs from the objects drawn on the chart, producing
a ‘radar cocked hat’, as shown in Fig. 15-13.
The index error equals the radius of the circle drawn tangential to the
three range arcs.

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Fig. 15-13. Three-mark method |
422 CHAPTER 15 - RADAR, BLIND PILOTAGE

Horizontal sextant angle method

This method is carried out underway when running on a transit with a third
fixing mark available on the beam, as illustrated in Fig. 15-14. A table of true
range of the radar mark against sextant angle may be compiled in advance.
Radar ranges are read off as the horizontal sextant angle is measured. The
differences between true and radar range are then averaged to obtain the mean
and the index error obtained.

Fig. 15-14. Horizontal sextant angle method

Two-ship method
The two-ship method involves the use of double echoes, which will usually
be produced by two ships proceeding in line abreast at close range. This is
illustrated in Fig. 15-15.
RADAR FOR NAVIGATION 423

Fig. 15-15. Two-ship method

Range A between own ship and the consort includes index error, but
range B between the consort and the double echo does not. Thus, range B is
the true range and the difference between this and the radar range A must be
the index error.

Three-ship method
Three ships proceed in line abreast and simultaneously measure range from
one another (Fig. 15-16).

Fig. 15-16. Three-ship method

Ship A provides true range BC and ship C provides true range AB; all
three ships may thus obtain their respective index errors.

Standard set comparison method

A weapon radar set with an accurate ranging system may be established as a
reference, with which a navigational radar may be compared to obtain its
index error when both sets range on a given target.
424 CHAPTER 15 - RADAR, BLIND PILOTAGE

Allowing for range index error

Having found the radar index error for the particular radar, the error may be
allowed for as follows:

1. For some sets, the index error is noted on the front of the display and
applied subsequently to all ranges taken by the operator.
2. Other sets can be adjusted by the maintenance staff. In some RN radars
used for navigation, for example, any index error may be adjusted to
about 5 yards and so is virtually eliminated.

Bearing errors

Causes of bearing errors

Bearing errors are invariably present and are hard to estimate, therefore radar
bearings must always be treated with caution. Remember that a 1° error in
bearing is equivalent to about 35 yards at 1 mile range, about 1 cable at 6
miles. Likely causes of bearing error are as follows:

1. Horizontal beam width causes an incorrect picture to be painted, (see

page 406 and Fig. 15-1). Bearings of points of land lying across the radar
beam will be distorted by approximately half the beam width.
2. Parallax errors when using an engraved cursor.
3. Incorrect centring of the display.
4. Using a longer range scale than necessary, bearings being taken too close
to the centre of the display instead of near the circumference.
5. Limitations in the equipment, for example:
(a) Difficulty in lining up the ship’s head marker to an accuracy of less
than ½°. (This also needs to be checked after a course alteration.)
(b) Difficulty in lining up the radar aerial on the masthead to an
accuracy of less than 1°.
(c) Error in the gyro-compass and its transmission system.
(d) Backlash in the aerial training motor.
(e) Squint error. In end-fed slotted waveguide aerials, the beam is
offset from the aerial’s line of sight between ½° and 2½°. This is
known as squint error. Squint error is at a minimum when the radar
is first installed, but the oscillator frequency tends to drift with age,
causing the error to vary. When the magnetron is changed, the
frequency will be different and this may also produce a significant
squint error.

Bearing alignment accuracy check

At regular intervals, when using radar for navigation, the alignment of the
picture and display must be checked as follows:

1. Centre the display.

2. Compare ship’s head marker with the pelorus or gyro-repeater and adjust
if necessary.
3. Compare the radar and visual bearings of a well defined object.
4. If a visual object is not available, compare the radar and charted bearings
between two objects (Fig. 15-17).
RADAR FOR NAVIGATION 425

Fig. 15-17. Checking radar alignment

A bearing accuracy check should be prepared in the planning stage of a

blind pilotage run, marked on the chart and entered in the Note Book.

Comparison of 10 cm and 3 cm radars

Both 10 cm and 3 cm radars may be available for navigation and it is
important to appreciate the fundamental differences between the two.
Generally, 10 cm radars have a longer pulse length and greater beam
width than 3 cm radars. Thus, minimum range, and range and bearing
discrimination, will be larger on a 10 cm than on a 3 cm radar. The distortion
of the radar picture caused by beam width will be slightly worse.
On the other hand, because of the longer wavelength, the effects of
clutter, rain, etc. will be much less on 10 cm than on 3 cm radar. Thus, in bad
weather, it is quite probable that 10 cm radar will give a better picture,
particularly if switched to short pulse length and wide bandwidth in order to
obtain the best minimum range and range discrimination available. Long-
range detection on 10 cm radar is usually better than on 3 cm, particularly
when switched to long pulse.
In RN ships, the aerial of the 10 cm set is often positioned higher than the
3 cm aerial. In this case, the clutter experienced in bad weather on the 10 cm
set, although not as intense as that on the 3 cm set, will extend to a greater
distance (Fig. 15-18). This can mean that small targets at long range may be
lost on 10 cm radar, although visible on 3 cm radar. However, as the contact
closes, giving a stronger echo, it may appear through the clutter on 10 cm
radar, yet disappear inside the much heavier clutter on the 3 cm radar. This
is illustrated in Fig. 15-18.
426 CHAPTER 15 - RADAR, BLIND PILOTAGE

Fig. 15-18. Effect of sea clutter on a small contact on 3 cm and 10 cm radar

LANDFALLS AND LONG-RANGE FIXING

Radar range/height nomograph

A useful guide to the probable maximum range of objects when the height is
known, in standard atmospheric conditions, is given by the radar range/height
nomograph shown in Fig. 15-19. The range R is based on the formulae (15.3)
and (15.5) and may be found as follows:

R = 2.23( h + H ) sea miles . . . 15.7

i.e. H = 0.201( R − 2.23 h ) 2 . . . 15.8

where h, the height of the aerial, and H, the height of the target, are measured
in metres; or

R = 1.23( h + H ) sea miles . . . 15.9

i.e. H = 0.661( R -1.23 h) 2 . . . 15.10

where h and H are measured in feet.

LANDFALLS AND LONG-RANGE FIXING 427

EXPLANATION
This NOMOGRAPH is an Earth Curvature Graph, corrected for refraction of
the RADAR waves. It is used by passing a straight-edge through the points on
two vertical lines representing known quantities and reading off the solution at
the intersection of the third line with the straight edge.

EXAMPLE
Aerial height is 100 feet.
At what range should a 7900 feet peak first be observed?
Method: Join the 100 feet mark in the left
hand column with the 7900 feet
mark in the right hand column.
A range of approximately 120 miles is read off at the intersection of the
straight-edge with the central column.
The Nomograph is constructed for standard atmospheric conditions over land.
For average conditions over the sea, detection ranges may be increased by as
much as 15%.

Fig. 15-19. Radar range/height nomograph

428 CHAPTER 15 - RADAR, BLIND PILOTAGE

When considering the probable detection range of targets, two points

should be borne in mind:
1. Radar will not necessarily detect an object with poor radar reflection
properties at great ranges even though it may be above the radar horizon.
2. Maximum detection range is governed not only by the height of the aerial
and the target but also by the power and performance of the radar set, the
reflective properties of the target, and the atmospheric and sea conditions.

Long-range radar fixes

The radar/range height nomograph is a useful aid when making a landfall or
fixing at long range using radar. Knowing the height of the coastline and
mountains further inland, it is possible to determine the approximate range at
which these should be detected and an example is given in Fig. 15-19.
Remember, however, that for average atmospheric conditions over the sea,
the detection range may be increased by as much as 15%.
The likely range may also be determined from formula (15.7) or (15.9).
If, for example, the height of the aerial is 30 metres and the mountain
concerned 400 metres then, from formula (15.7):
R = 2.23( 30 + 400)
= 56'.8
Note: This range could be as much as 65'.3 for average atmospheric
conditions over the sea, even greater in super-refraction conditions.
This indicates only that the mountain concerned should be above the
radar horizon at this range (depending on the atmospheric conditions). It
does not necessarily mean it will be detected at this range. Even if it is
detected, it may be beyond the maximum unambiguous range of the set
(81,000/PRF n miles) and so appear as a second-trace echo.
Alternatively, when an echo of high land is first detected, the height of
the leading edge may be deduced from the nomograph or formula (15.8) or
(15.10). If the height of the aerial is 30 metres and land is detected at 42
miles, from formula
(15.8): H = 0.201(42 − 2.23 30) 2

= 178.3 m
Once the height of the leading edge of the echo has been determined in
this way, the radar range position line may be plotted from the appropriate
height contour level on the chart. Such long-range position lines must,
however, be treated with caution because it is probable that the atmospheric
conditions will be different from those on which the nomograph and formulae
are based. The assessment of height may therefore be incorrect and the
position line in error (Fig. 15-20), to an extent that depends on the gradient
and thus the distance apart of the height contours on the chart. If, in the
above example, the atmospheric conditions improve detection range by about
15%, then H ought to have been calculated for a smaller range, in this case
36'.5 (36'.5 + 15% = 42' approx.). In which case, from formula (15.8):
H = 118.5 m
LANDFALLS AND LONG-RANGE FIXING 429

Fig. 15-20. Long-range radar position lines

This means that the radar is detecting land at a height of about 120 metres
at a range of 42' instead of 36'.5.
Using the nomograph or the formula, the observer would plot from A, the
178.3 metre contour (Fig. 15-20), the observed range R (42 miles). However,
because of additional refraction, the leading edge of the mountain observed
on the display is actually at B, (118.5 metres). The range R ought to have
been plotted from this point, where AB equals d', the distance between the
two contour lines. Thus, the error in the position line is CD, also equal to d'.
Taking into account the gradient of the height contours, d is unlikely to
be large, but this will depend upon what refraction is actually being
experienced. In the example given for a 15% improvement in detection
range, for a gradient of about 1 in 10, the error in the position line is about a
mile [10(178.3 - 118.5) = 0.32 n mile]. For a gradient of 1 in 30 at a range of
60 miles, the error in the position line could be about 2¼ miles.

Plotting the long-range fix

Generally, it cannot be expected that the position arcs obtained at great ranges
will cut at a point. As in Fig. 15-21 (p.430), they will probably do no more
than indicate an area in which the ship is situated. It is advisable to plot the
radar bearings of such long-range fixes as well because, although there may
be inaccuracies in the bearings, they help to resolve the Position Probability
Area produced by plotting the range arcs.
Note that peak E, though higher than D, is in the latter’s shadow area and
is therefore not visible on the display.
Any fix obtained in such circumstances should obviously be treated with
caution.
 430 CHAPTER 15 - RADAR, BLIND PILOTAGE

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| Fig. 15-21. Fixing by radar ranges and radar bearings of long-range shore objects

The Radar Station Pointer

The Radar Station Pointer (Chart 5028), enables the Navigating Officer to
plot radar echoes to the scale of the chart in use and assists in identifying
these echoes with charted features. The chart is a transparent plotting sheet
inscribed with radial lines from 0° to 360°. It is supplied to HM Ships in the
Miscellaneous Charts Folio 317.
With the Radar Station Pointer orientated correctly, and with the plotted
radar echoes ‘fitted’ on top of the charted objects, the ship’s position is at the
centre of the diagram.
It can also be used for:

1. Determining errors in the orientation of the radar display.

2. Laying off sextant angles as an ordinary station pointer.
3. Plotting position lines.

Instructions, and a table of approximate heights and distances at which

echoes may be detected by radar under standard conditions, are printed on the
diagram.
RADAR IN COASTAL WATERS 431

RADAR IN COASTAL WATERS

Radar is frequently used in coastal waters to supplement fixes by visual

bearings. In low visibility, when shore objects are not clearly visible, fixing
by radar may have to replace visual fixing altogether. Various techniques
using radar in coastal waters are set out below.

Fixing by radar range and visual bearing

Fig. 15-22 shows a fix obtained by a visual bearing of a beacon from which
a range has been obtained by radar. A radar range from the nearest land may
also serve as a check.
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Fig. 15-22. Fix by radar range and visual bearing |
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Fixing by radar ranges

Fixing using radar range arcs is normally the most accurate method of
obtaining a fix using radar information alone.
Fig. 15-23 shows a fix obtained by radar ranges of two conspicuous
headlands A and B, and a further headland C inside the bay. The position of
 432 CHAPTER 15 - RADAR, BLIND PILOTAGE

the buoy marking the rock D may be ‘shot up’ by taking a radar range and
bearing of it at the same time as the fix. It may also be cross-checked if
desired by measuring from the display the radar ranges of the buoy from
headlands, A, C and E. The display shows the use that may be made of the
heading marker as a check that the ship is safely clearing the rock. It should,
however, be appreciated that, if there is a strong tidal stream setting the ship
to starboard, this could be setting the ship down on to the rock, although the
ship’s head may still be pointing to the left of the buoy. Parallel index ranges
(see page 434) on headlands A and E are to be preferred.
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| Fig. 15-23. Fix by radar ranges of three objects
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Three radar ranges should always be taken, if possible, for the radar range
fix. This should ensure that:

Objects are not misidentified.

Ranges are not read off incorrectly.
Any unresolved index error becomes apparent.

Fixing by radar range and bearing

Fig. 15-24 shows a ship off a coast which is obscured by bad visibility. A fix
has been obtained by radar range and bearing of the headland A. In spite of
the possibility of inaccuracy due to the beam width, a radar bearing has been
used because ranges of the land at right angles to the bearing A are
unsatisfactory owing to the poor radar response offered by the sand dunes.
The bearing may be corrected approximately by applying half the beam width
of the radar to the bearing obtained; in this case, it must be added.
Alternatively, a more accurate bearing may be obtained if the gain is
reduced until the headland only just ‘paints’ on the display. Be careful to
readjust the display to the former level for normal operation, otherwise small
contacts may be lost altogether.
RADAR IN COASTAL WATERS 433

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Fig. 15-24. Fixing by radar range and bearing |
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Fig. 15-25. Use of a radar clearing range |
 434 CHAPTER 15 - RADAR, BLIND PILOTAGE

Use of a radar clearing range

When proceeding along a coast, it is often possible to decide on a minimum
clearing range outside which no off-lying dangers should be encountered.
The clearing range is illustrated in Fig. 15-25, and may also be drawn on the
display using the parallel index technique (see below). The ship must remain
outside the clearing range to proceed in safety.

BLIND PILOTAGE

Blind pilotage means the navigation of the ship through restricted waters in
low visibility with little or no recourse to the visual observation of objects
outside the ship. The principal non-visual aid to navigation that enables this
to be done is high-definition warning-surface radar, but all available non-
visual aids are employed. The organisation to achieve this is called the blind
pilotage organisation, comprising a BP team, led by a BP Officer (BPO).

Assessment of the risk involved in a blind pilotage passage

Although normally the accuracy of blind pilotage is such that a ship can be
taken to an open anchorage and anchored within 50 yards of the desired
place, the degree of risk involved, particularly in restricted waters, must be
carefully assessed. Congestion due to other shipping, the consequences of
failure of radar or other vital aids once the ship has been committed to her
passage, and the number and quality of fixing marks must be taken into account.

Parallel index technique

The key to blind pilotage is the principle of the parallel index. The running
of a parallel index line provides real-time information on the ship’s lateral position
relative to the planned track. On the chart (Fig. 15-26), a line is drawn from
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| Fig. 15-26. Parallel index
BLIND PILOTAGE 435

the edge of a radar-conspicuous object, parallel to the planned track. The

perpendicular distance (or cross-index range) from the object to the track is
then measured. The range strobe on the radar is then set to this range, and a
solid chinagraph line drawn on the display parallel to the planned course on
a scale appropriate to the range in use.
Positions 1, 2 and 3 on the chart and radar display show the ship on track
at various instances up to the time that the island is abeam to starboard.
Positions 4 and 5 show the ship off track to port. The exact distance off track
can be measured by dividers from the radar echo of the island to the nearest
point of the chinagraphed parallel index line at the scale of the display. This
can be made easier by constructing scales for each range setting, as shown
below, and mounting them adjacent to the display. (The crosses on the chart
do not represent fixes and only appear in order to illustrate the example.)

Radar clearing ranges

Radar clearing ranges (Fig. 15-27, p.436) are similarly drawn at the maximum
or minimum distances from the radar-conspicuous objects to keep the ship
clear of dangers. These are drawn as broken lines:

Course alterations
‘Wheel over’ positions are calculated and plotted on the chart as for visual
pilotage. A radar-conspicuous mark is selected as close as possible to the
‘wheel over’ position. A pecked line - - - - - - - - - - - is then drawn through
the ‘wheel over’ position (Fig. 15-27A) parallel to the new course, and the
cross-index range measured. This ‘wheel over’ range is plotted on the display
as a pecked line parallel to the new course. When the selected mark reaches
this line, the wheel should be put over and the ship brought round to the new
course, by which time the mark should be on the firm line denoting the
parallel index for the new course.
The standard symbols used for parallel index lines, radar clearing and
‘wheel over’ ranges are shown on page 441.

Blind pilotage in HM Ships

Responsibilities
The Queen’s Regulations for the Royal Navy (QRRN) state that, in normal
circumstances, the Navigating Officer is the pilot of the ship although, if he
is not a navigation sub-specialist, the duty of pilotage devolves on the
Captain, who may either perform it himself or, at his discretion, depute any
officer of the ship’s complement to do so.
 436 CHAPTER 15 - RADAR, BLIND PILOTAGE

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| Fig. 15-27. Clearing and ‘wheel over’ ranges on the chart and the radar display
BLIND PILOTAGE 437

No matter what the blind pilotage organisation may be, the sub-specialist
Navigating Officer (NO) is always the pilot of the ship, and thus he should
also be the Blind Pilotage Officer (BPO).
Where no navigating sub-specialist is borne, the officer appointed for
navigating duties should also be the Blind Pilotage Officer in normal
circumstances. However, as responsibility for pilotage is clearly vested in the
Captain, he may wish to delegate the blind pilotage duty to some other
officer. If so, the Captain must also clearly set out in his standing orders the
circumstances envisaged, to ensure that it is absolutely clear who is
responsible and when. These orders must also take into account the
organisation for blind pilotage in various circumstances envisaged; the
organisation described below may have to be modified.
It must also be decided who is responsible for informing the Captain of
the collision risk with other ships. The NO/BPO will be fully employed
navigating the ship; therefore it is essential that the officer in charge of the
operations room, who already has an anti-collision plot running, should be
made responsible for advising the Captain and OOW on this aspect of safety.

The conduct of blind pilotage

The Navigating Officer should remain on the bridge in poor visibility and
conduct the blind pilotage from there. It is essential to have another officer,
who is suitable by training and experience, as a Blind Safety Officer (BSO)
in the operations room, where he can monitor the blind pilotage and back up
the Navigating Officer on the bridge. The BSO will need to be in touch with
the surface plot to assist with the identification of radar contacts.
The essence of this arrangement is that members of the team do not
change position if the visibility changes. The Navigating Officer conducts
the pilotage from the bridge whatever the weather or visibility. In good
visibility, the BSO acts as a useful check on the visual plan and builds up
confidence in his team and the Command. In marginal visibility, the bridge
team continues to make use of any visual information to supplement
information from the radar. In nil visibility, the NO conducts the blind
pilotage from the bridge radar display, monitored by the BSO. If reports from
the NO and BSO disagree, immediate action to stop the ship may be
necessary until the position has been accurately determined.
The Navigating Officer should not move from the bridge to the operations
room in order to conduct the pilotage from there. This will cause delay and
perhaps confusion, and can be particularly undesirable in marginal visibility,
when a mixture of visual and blind techniques is required.
There may well be circumstances, particularly in large ships, where the
Navigating Officer has already taken or wishes to take the con and therefore
charge of the ship from the Officer of the Watch, in order to conduct the
pilotage where a blind pilotage situation has already arisen or arises
subsequently. In such a situation, it may be undesirable for the NO to move
to the bridge radar display as indicated above. The composition and duties
of the blind pilotage team must therefore have sufficient flexibility built in to
cope with such circumstances. The NO may continue to con the ship from the
pelorus, taking full account of the navigational and collision avoidance
438 CHAPTER 15 - RADAR, BLIND PILOTAGE

information he is receiving from the operations room, the bridge radar display
(which should be manned by a competent officer such as the NO’s assistant)
and other sources, e.g. the bearing lattice team, lookouts, etc. Despite being
at the con, the NO is still the pilot and the Blind Pilotage Officer of the ship
and retains full responsibility for these under QRRN.
Blind pilotage team and duties
Blind pilotage requires a high degree of organisation and team work, so that
not only are the responsibilities of individuals clearly defined but also all
relevant factors may be considered while assessing the ship’s position and her
future movements. Suitable arrangements to achieve this are set out in Table
15-2; these may have to be adjusted depending on the class of ship, the
personnel available, and the above comments.
Table 15-2. Blind pilotage organisation
PLACE PERSONNEL DUTY

Bridge Captain Overall responsibility for ship

safety. May wish to con ship in
certain circumstances.
Bridge OOW Has charge of and cons ship. In
charge of lookouts and sound
signals. Reports all visual
sightings to Captain/NO.
Bridge NO Acts as Blind Pilotage Officer
(BPO). Responsible for all aspects
of pilotage, visual and blind.
Bridge NO Assistant Plots fixes, generates DR/EP.
Advises on times of ‘wheel over’
(WO), etc. Plots visual sightings.
Checks echo sounder (E/S) reports
with charted depth.
As reqd Navigator’s Yeoman Records wheel and engine orders:
the running commentary from the
NO/Blind Safety Officer to the
Captain/OOW which includes
recommended courses and speeds
and information on the ship’s
position by radar relative to the
planned track. Alternatively, this
duty may be satisfied by having a
continuously running tape recorder
on the bridge during pilotage. It is
essential to incorporate a time
check at the beginning of each
tape.
Bridge/ E/S operator Standard reports.
charthouse
As reqd Lookouts Standard reports. Lookouts must
be briefed to listen as well as look.
BLIND PILOTAGE 439

Table 15-2. Blind pilotage organisation (continued)

PLACE PERSONNEL DUTY

Operations Blind Safety Officer Monitors ship’s position as a check

room (BSO) on the ship’s navigational safety,
using the most suitable display.
Co-ordinates navigational and anti-
collision information to bridge.
Although he does not supervise
surface plot, he must keep an eye
on shipping situation.
Operations Blind Safety Officer’s Plots radar fixes and other radio
room assistant aids (e.g. Decca) as appropriate.
Generates DR/EP. Assists in
identification of marks, ships.
Checks E/S reports with charted
depths.
Operations Anti-collision plot A suitably experienced officer or
room the most experienced Ops(R)
Senior Rate in charge. Passes anti-
collision information to bridge, co-
ordinated by BSO.
Sonar control Sonar controller Reports sonar information as
room ordered.

Planning and execution of blind pilotage

General principles
To ensure success, the ship must be accurately navigated along a pre-arranged
track. In comparatively unrestricted waters, this is best done by constant
fixing using radar in conjunction with other aids such as Decca and echo
sounder.
In narrow waters and during the final stages of an anchorage, the delays
inherent in fixing are unacceptable to the BPO. It is therefore necessary, for
anti-collision and navigation in these conditions, to work directly from the
radar display using a prepared Note Book; but it is still necessary to pass
radar information for fixing at regular intervals as a safety check and as an
insurance against radar failure.
The following principles apply:

1. The Navigating Officer should navigate or pilot the ship.

2. The Captain should have easy access to the blind pilotage position and the
NO.
3. The ship should be conned from the compass platform because it is only on
the bridge that the ‘feel of the ship’ can be retained.
4. The Captain, Blind Safety Officer, OOW and the officer in charge of the
anti-collision plot should all be carefully briefed before the passage by the
NO, so that they are all entirely familiar with the visual/blind plan.
440 CHAPTER 15 - RADAR, BLIND PILOTAGE

5. Navigational charts with the NO’s prepared visual/blind plan must be

available on the bridge and in the operations room.
6. The whole pilotage team should be exercised as frequently as possible in
clear weather in visual and blind techniques. Only in this way can the
necessary confidence in the system be built up which will allow runs of
some complexity to be conducted safely in blind conditions.
7. The BSO should be closed up on all occasions of entering and leaving
harbour and passages through narrow waters when special sea dutymen are
closed up; the BP team should be regarded as part of special sea dutymen.
8. There should be good communication between the blind pilotage position
and the BSO and personnel manning navigational aids fitted elsewhere.
9. All members of the team should be encouraged to admit any doubts they
may have regarding the information acquired from sensors.

Blind pilotage planning

1. Normal planning considerations for selection of tracks apply. Blind and
visual tracks should be the same, to enable the transition from visual to
blind or vice versa to be made at any time and also to allow one plan to be
used to cross-check the other.
2. The number of course alterations should be kept to a minimum to reduce
the work load in redrawing parallel and ‘wheel over’ lines.
3. Always try to have two parallel index lines & where possible, one on each
side of the track. These provide a check on measurement, mark
identification and can reveal index or linearity errors.
4. Objects to be used both for parallel index lines and for fixing must be
carefully selected. They should be radar-conspicuous and unchanged by
varying heights of tide. Clearly mark on the chart the objects to be used for
fixing and brief the assistant. Avoid if possible fixing by radar range and
bearing on a single mark.
5. The range scales to be used require careful consideration. Accuracy is
greater at shorter ranges but marks pass more quickly than at a distance,
requiring more lines to be drawn. When operating on short-range scales,
it is essential that the BPO frequently switches to longer ranges to keep
aware of developing situations. Changes of range scales and parallel index
marks should be pre-planned and marked in the Note Book. The stage at
which charts will be changed must also be carefully considered.
6. Tidal streams and currents should be worked out and noted for calculation
of courses to steer and for the calculation of EP. These should be
displayed on the chart and recorded in the Note Book.
7. Expected soundings (allowing for height of tide and calibration of echo
sounder) should be noted for each leg. The possibility of being early or
late should also be borne in mind.
8. All hazards along the track should be boxed in by clearing ranges and their
cross-index ranges listed in the Note Book.
9. Details of all lights and fog signals should be taken from the Admiralty List
of Lights/chart and entered in the Note Book.
10. The chart should be drawn up using standard symbols (Figs. 15-28, 15-29
and 15-31), see Table 15-3.
BLIND PILOTAGE 441

Table 15-3. Blind pilotage symbols

Blind pilotage chartwork Symbol

Parallel index lines to stay on track
Clearing ranges
‘Wheel over’ (WO) ranges -------------

Use the same conventions as above for cross-index ranges.

The term dead range (Figs. 15-28, 15-31) is used to describe the range
of a mark ahead when anchoring in a chosen position. The term may also be
used when measuring the progress of a radar-conspicuous object along a
parallel line, as shown in Fig. 15-31. |
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Fig. 15-28. Blind pilotage symbols |

Radar-conspicuous objects such as buoys should be highlighted to enable

the BPO to have a clear mental picture of what he expects to see on the
display.

11. The Note Book should contain the full plan, neatly and legibly recorded
in chronological order. Sketches of both chart and radar display (Fig. 15-
29), p.442) can be of great assistance to the BPO in evaluating the
picture. A suitable Note Book layout supplementing Fig. 15-29 is shown
in Fig. 15-30 (p.443) as a guide to blind pilotage planning.
12. Tracks plotted for entering and leaving harbour should not appear on the
same chart simultaneously, otherwise confusion will arise.
13. Clearing range should be simple, safe and easily interpreted.
14. Objects used for ‘wheel overs’ should be conspicuous, easily identifiable
and suitably located adjacent to the track.
 442 CHAPTER 15 - RADAR, BLIND PILOTAGE

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| Fig. 15-29. Blind pilotage: preparation of the chart and displays
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Blind pilotage execution

1. Carry out a time check to synchronise clocks and watches.
2. On the radar display, keep one set of parallel index lines drawn up ahead
of those in use. Any more will clutter the display excessively. Rub out
lines as soon as they are finished with.
3. Identify contacts early (by range and bearing from charted object). An
accurate EP is a most useful aid in identification.
4. Fix at frequent intervals and immediately after a change of course.
DR/EP ahead. A suitable fixing procedure is:

BPO assistant ‘Stand by fix in 1 minute’

BPO ‘Roger&using points A, B, C’
BPO assistant writes these in Note Book.
BLIND PILOTAGE 443

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Fig. 15-30. Blind pilotage: layout of Navigating Officer’s Note Book |

BPO/BPO assistant ‘Fix now.’ BPO marks the point on face of the
display.
BPO assistant notes the time.
BPO then ranges off the marks drawn on display
and passes these to BPO assistant.
BPO assistant Records the ranges, plots the fix and generates
fresh DR and EP.

This procedure cuts the time to take a fix and reduces the risk of a
‘cocked hat’ due to ship movement. It may be quicker to interpolate from
the range rings rather than use the range strobe, although the latter will
be more accurate.
5. Ship’s speed. One of the factors affecting the choice of ship’s speed will
be the rate at which the BPO and his assistant are capable of dealing with
the radar information.
6. Commentary and conning advice. Maintain a steady, unhurried and
precise flow of information to the Command:
Distance off track/on track/course to maintain or regain.
Distance and time to next ‘wheel over’, new course.
Present/new course clear of shipping.
Adjacent marks or hazards, expected lights and sound signals.
Expected depth and echo sounding. Minimum depths.
 444 CHAPTER 15 - RADAR, BLIND PILOTAGE

When fixing and result of fix. EP to next alteration.

Manoeuvring limits (e.g. 5 cables clear to stbd, 1 cable to port).
If in any doubt, say so and if necessary stop the ship.

7. It must be appreciated that, whatever the technique employed, a drift off

line is likely to be detected less readily by radar than by visual methods.
8. It is vital to pay attention to the echo sounder and the least depth
expected. The nearest land is usually the bottom.

Blind pilotage exercise

To improve the reality of BP exercises in clear weather, the following points
should not be forgotten:

Safe speed should be maintained.

Fixes should be recorded and plotted at the same frequency as for actual
blind pilotage.
A full de-brief should take place on completion of the practice.

Blind anchorages
A blind anchorage should be planned in the same way as a visual anchorage
but remember to allow ‘stem to radar’ instead of ‘stem to standard’ when
plotting the ‘let go’ position. As shown in Fig. 15-31, parallel index lines
should be used to guide the ship to the anchorage position and she must stay
boxed in by clearing ranges. Distances to run can be obtained by using a
dead range on a suitable object ahead, or by measuring the progress of a
radar-conspicuous object along a parallel index line. Full details must be
shown on the chart and in the Note Book. Distances to run must be marked
on the face of the display.
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| Fig. 15-31. Blind anchorage execution
TRUE MOTION RADAR 445

These can be backed up by the range strobe, but reliance on the strobe alone
is dangerous because the reference is lost as soon as the strobe is required for
any other measurement.
In Fig. 15-31, the dead range of the point of land ahead when anchoring
is 2.3 cables. The distance to run to the anchorage position may be obtained
by subtracting the dead range from the actual range of the point. For
example, if the range of the point is 7.3 cables, the distance to the anchorage
is 7.3 - 2.3 = 5 cables.
Fig. 15-31 also shows that the dead range of the point of land on the
starboard side when anchoring is 3 cables. On the radar display, this point of
land should ‘move’ along the parallel index line drawn 2½ cables to starboard
of the approach track. When the ship reaches the ‘let go’ position, the point
of land should have reached point A, 3 cables beyond the abeam position B.
The distance AB equals the dead range (3 cables).

Navigational records
When carrying out a blind pilotage passage, the Navigating Officer/BPO will
be too busy to maintain a continuous written record. It is essential that such
a record should be kept, and in comparatively unrestricted waters it is
normally sufficient for this record to be kept on the chart itself by plotting
fixes and noting the positions and times of alterations of course and speed
and other relevant data, in addition to the record in the Navigational Record
Book (S3034). This procedure, involving thorough and methodical
chartwork, is in fact no different from that which should be practised during
any pilotage passage.
In more restricted conditions, however, the Navigating Officer/BPO’s
running commentary to the Captain should be recorded on tape if possible,
for example:
‘No. 7 buoy fine on port bow, 8 cables&ship 50 yards to port of
track&steer 136 to regain.’
In conjunction with the Navigating Officer/BPO’s prepared Note Book, the
chart, the recorded fixes and courses and speeds, this record should suffice
for any subsequent analysis required.

Horizontal displays
Where horizontal displays are available in the operations room, the whole
passage may be prepared in advance on a series of overlays, the BSO’s
assistant changing these at appropriate times. The drawback of this method
is that all tracking and other additional marks made by the BSO are lost at
each change. With most horizontal displays in use in the Royal Navy, the
picture is not sufficiently precise for accurate blind pilotage and should not
be used.

TRUE MOTION RADAR

There are various arguments for or against using relative motion (usually
stabilised ‘north-up’ presentation) or true motion radars for navigation. These
arguments are normally to be found in standard works on radar and also in
446 CHAPTER 15 - RADAR, BLIND PILOTAGE

many articles in various navigational periodicals. Some general comments

are set out below. Further comments on the use of radar in the collision
avoidance role may be found in Chapter 17.

Advantages of true motion radar

True motion radar has two important advantages when being used for
navigation, particularly in pilotage waters:

1. Ships underway may be distinguished at once by their echo trails

(Fig. 15-32).
2. Echoes of stationary objects, e.g. buoys, may be distinguished by the
absence of echo trails.

Fig. 15-32. Identification of moving and stationary objects on a ground

stabilized true motion radar

This assumes that the correct allowances for set and drift (tidal stream,
wind, current and surface drift) have been made (see Chapter 8). It also
assumes that the trail of a moving ship will be visible on the display. This
depends on the size of the display, the range scale in use, speed of the target
and duration of the afterglow. For example, if the 3 mile range scale is in use
on a 30 cm display (5 cm to 1') and the minimum length of echo trail required
is 0.5 cm then, if the afterglow lasts for 1 minute, the minimum speed of ship
RADAR BEACONS (RACONS AND RAMARKS) 447

that will produce an echo trail long enough for movement to be apparent is
6 knots. In 1 minute, a ship at 6 knots moves 0'.1, which is equivalent to 0.5
cm at a scale of 5 cm to the mile.
Improved detection range ahead of the ship is also available on true
motion radar, without having to change the scale, by moving own ship’s
position to the appropriate sector of the display (Fig. 15-32). Such a facility
is often also available on relative motion radars by using the off-centring
controls. Targets abaft the beam may, however, be lost and this could be
important.

Disadvantages of true motion radar

The disadvantages of true motion radar for navigation are summarised below:

1. Contacts closing on steady bearings are not immediately apparent.

2. There are breaks in compilation and control every time the position is
reset.
3. Adjustments to remove completely the effects of tidal stream, leeway, etc.
are difficult to determine.

Shifts of picture must be carefully planned to take place after the ship has
settled on a leg and has been fixed on the chart, to enable pilotage to continue
by EP during the short break entailed. Shifts of picture should not be left to
the last moment in case this coincides with a close quarters situation which
requires constant watching.

RADAR BEACONS (RACONS AND RAMARKS)

Radar beacons are transmitters designed to produce a distinctive image on

ship’s radar displays, thus enabling the mariner to determine his position with
greater certainty than would be possible by means of normal radar contacts.
Many Lighthouse Authorities have established radar beacons at lighthouses
and at other sites where it is believed they would give good service to
shipping. These microwave aids to navigation usually operate initially on an
experimental or trial basis and are only permanently established if the service
provided is vindicated by user experience.
Details of racons and ramarks in operation are given in the Admiralty List
of Radio Signals (ALRS), Volume 2.

Racons
A racon is a radar transponder beacon which emits a characteristic signal
when triggered by emissions of ships’ radars. Most racons are of the swept-
frequency kind, that is, the transponder frequency sweeps the frequency range
of the marine radar band. The racon response to a ship’s triggering radar
pulse will therefore appear automatically on the ship’s radar display. Usually,
the ‘racon flash’ takes the form of a single line or narrow sector, extending
radially towards the circumference of the display, from a point slightly
beyond the spot (if any) formed by the echo from the lighthouse, etc. at the
racon site (Fig. 15-33, p.448).
The range may be measured to the point at which the racon flash begins,
but the figure obtained will be greater than the ship’s distance from the racon;
this is due to the slight response delay in the radar beacon apparatus.
448 CHAPTER 15 - RADAR, BLIND PILOTAGE

Fig. 15-33. The ‘racon flash’

Other racons are termed frequency agile, their response always being
within the bandwidth of the ship’s radar receiver. They may cease to respond
for a few seconds each minute to allow radar echoes otherwise obscured by
the racon signal to be distinguished.
The majority of racons respond to 3 cm radar emissions, but a few
respond to both 3 cm and 10 cm radar emissions.
On certain types of racon including some in British waters, the flash is
composed of a Morse identification signal followed by a ‘tail’. Thus Morse
‘S’ would show as . . . __ , and ‘O’ _ _ _ __ . The length of the ‘tail’ is
normally controlled by the number of characters in the Morse identification
signal.

Ramarks
A ramark is a radar beacon which transmits independently, without having
to be triggered by the emissions of ships’ radars. It is otherwise similar to a
racon, except that the ramark’s flash gives no indication of range, as it
extends from the ship’s position to the circumference of the display.
SHORE-BASED RADAR 449

There are relatively few ramarks in service throughout the world, most
are in Japanese waters.

Interference from radar beacons

It may be found that, in certain circumstances, radar beacon emissions can
cause unwanted interference with the normal radar display, particularly at
close range. The operation of the differentiation control may reduce racon
but not ramark interference to acceptable proportions, provided that the
technical characteristics of the beacon have been selected with this in view.

SHORE-BASED RADAR

Shore-based radar systems may be found throughout the world, either as an

aid to traffic using a port, or for the purposes of traffic surveillance or
management in areas of high shipping density like the English Channel or St
Lawrence River. Details of the various systems in force may be found in the
relevant Admiralty Sailing Directions and in the Admiralty List of Radio
Signals (ALRS), Volume 6. Some details of surveillance systems are also
given in Volume III of this manual.

Port radar systems

The aim of a port radar system is to help ships which might otherwise have
to anchor to proceed in restricted or nil visibility, thus avoiding congestion
and delay at the port. Such installations often operate in clear weather to
assist in traffic control. The radar normally operates in the 3 cm band, often
with a narrower beam width and shorter pulse length than sets fitted in ships,
thus giving improved range and bearing accuracy and discrimination. The
necessary VHF communications between shore and ship are also available at
the control centre. The shore-based radar often covers the sea approaches to
the port in addition to the approach channels. This may require remote aerial
sites transmitting data to the control centre.
The shore-based system usually provides the following information to
ships:

1. Information on the arrival, berthing, anchoring and departure of

individual ships.
2. Information on navigational aids, navigation generally, visibility and
safety.
3. Tidal information.
4. General situation and movement reports giving traffic movements, local
navigational warnings and weather reports.
5. When requested, navigational information may be passed to individual
ships:
Information to bring the ship up to and through the harbour
entrance.
Accurate positioning when navigating bends.
Warning of approaching ships.
Position in relation to navigational marks, buoys and beacons.

Certain shore systems, dependent on the installation and siting of the

radar, may also be able to provide berthing assistance in fog.
450 CHAPTER 15 - RADAR, BLIND PILOTAGE

Shore based radar systems also enable the Harbour Authority to:

1. ‘See’ the position of all vessels underway or at anchor in the port and its
approaches.
2. Check the position of all floating navigational marks: buoys, light-floats,
light-vessels.
3. Check the position of any shipping casualties and arrange for the
necessary tugs, firefighting and lifesaving equipment.
4. Monitor the various dredging operations being undertaken in the port and
its approaches.
Positional information
Positional information is usually passed to ships from the control centre by
one or other of the following methods:

1. Distance right or left of the charted radar reference line relative to the
direction of progress.
2. Bearing and distance from the nearest charted object, e.g. pier, jetty,
buoy, etc.

SEE BR 45
This information is normally passed by means of a running commentary
from the control centre, which the ship is required to acknowledge at regular
intervals. Control of the ship remains in the hands of the Captain or Master.

Reporting points within port radar systems

VOL 4
A number of reporting points for inward and outward bound traffic are
usually designated within the area covered by the port radar system, ships
being required to report to the control centre as these are passed.
The orders for the port may require the inbound ship to provide
amplifying information, such as her name and nationality, intended approach
channel, destination, draught, etc. Similar information is also required on departure.

Traffic surveillance and management systems

An advisory and surveillance service using shore-based radar may be used
within a traffic separation scheme (see Chapter 12, p.305ff), where there may
be an adverse combination of navigational factors. The aim of such systems
is to increase the safety of navigation in hazardous areas. Navigational
information is given to ships both by broadcast and by response to individual
requests. Information passed to ships is usually of the following type:
1. Navigational and traffic information of immediate interest.
2. Information on the movement of ships which appear to be navigating the
wrong way within a traffic separation system, contrary to Rule 10 of the
Rule of the Road.
3. Urgent information, e.g. casualties, collisions, etc.
Positions are normally given by means of a range and bearing from a
named navigational mark.
Aircraft, helicopters and ships may all be used to identify vessels
apparently contravening Rule 10.
SHORE-BASED RADAR 451

Position fixing assistance

Ships uncertain of their position may seek assistance from the control centre
to establish their whereabouts, using a combination of VHF, DF and radar.
It should, however, be remembered that, short of fitting some kind of
transponder device in ships, there is often some uncertainty in the
identification of any particular radar echo in poor visibility by the control
centre.

Basis of operation
Traffic surveillance and management systems entail either compulsory or
voluntary compliance by ships. For example, the St Lawrence Vessel Traffic
Management (VTM) System is a mandatory system and applies to all vessels
over gross tonnage 100. On the other hand, the English Channel and Dover
Strait Ship Movement Reporting System (MAREP) together with the Dover
Strait Channel Navigation Information Service (CNIS) only invite certain
categories of ships to take part, as follows:

Loaded oil tankers, gas and chemical carriers of gross tonnage 1600

SEE BR 45
and over.
Any vessel ‘not under command’ or at anchor in a traffic separation
scheme or inshore traffic zone.
Any vessel ‘restricted in her ability to manoeuvre’.
Any vessel with defective navigational aids (compasses, radars, radio
aids, etc.).

VOL 4
The radar coverage of the CNIS system is illustrated in Fig. 15-34 (p.452).
National compulsory schemes may overlap or operate side by side with
voluntary ones. For example, in the south-western approaches to the English
Channel (Fig. 15-35, p.453), covered by the voluntary MAREP scheme, the
French regulations for the control of traffic off the north and west coasts of
France and in the traffic separation scheme of Ushant are mandatory. In
certain circumstances, ships already participating in the MAREP scheme may
be exempt from the French regulations.
Whether the system is on a voluntary or compulsory basis, control of the
ship still remains in the hands of the Captain or Master. Moreover, Rule 10
of the Rule of the Road governing the conduct of ships in traffic separation
schemes (see Chapter 12) still applies.

Reporting points within traffic surveillance systems

A number of ship reporting points, as with port radar systems, are usually
designated within the area covered by the traffic surveillance or management
system. These reporting points may be at each end of the traffic separation
scheme (e.g. Ushant, Casquets), or at various points within the system (e.g.
the St Lawrence VTM System). Details of the information to be sent by ships
may be found in ALRS, Volume 6, and also on Chart 5500 for the English
Channel. It is usually essential that ships with any defects (e.g. ‘not under
command’, defects in propulsion, steering or anchoring equipment, defects
in navigational equipment) report the fact.
 452
CHAPTER 15 - RADAR, BLIND PILOTAGE

Fig. 15-34. Radar surveillance in the Dover Strait

 SHORE-BASED RADAR
453

Fig. 15-35. MAREP and French traffic systems off Ushant

454 CHAPTER 15 - RADAR, BLIND PILOTAGE

USE OF RADAR IN OR NEAR ICE

Ice is a poor reflector of radar waves and, for this and other reasons, radar
does not always detect it in its many forms. Sole reliance must never be
placed on radar for ice warning.
Nonetheless, radar can be of great assistance in giving warning of ice. In
a calm sea, ice formations of most sorts should be detected on radar, from
large icebergs at ranges of 15 to 20 miles down to small growlers at a range
of about 2 miles. Because of the angle of incidence of the radar beam,
however, smooth flat ice sends back practically no return.
In rough weather, it is unsafe to rely solely on radar when sea clutter
extends beyond about 1 mile. Growlers or bergy bits large enough to damage
the ship may be undetectable in the clutter until they are very close and a
danger to the ship, nor will the use of swept gain necessarily reveal their
presence. Small growlers may not be detected at all.

SEE BR 45
Folds of concentrated hummocked pack ice should be detected in all sea
conditions at a range of at least 3 miles. The type of return from pack ice is
similar to that of strong sea clutter, except that the echoes will be fixed and
not continually changing.
Leads through ice will probably not show up on radar unless the lead is

VOL 6
at least ¼ mile wide and free of brash ice. Shadow areas behind ridges are
liable to be mistaken for leads.
Although ice is a comparatively poor reflector, icebergs generally give
detection ranges comparable to those of land of similar height. The strength
of the echo depends as much on the angle of inclination of the reflecting

CHAPTER 7
surfaces as on size and range.
In waters where shipping may be encountered, individual echoes should
be plotted. This may help to indicate whether the echo is a ship, iceberg,
bergy bit or growler. If the echo is classified as an iceberg, it should be given
a wide berth to avoid the growlers which may have recently calved from it.
When using radar in coastal waters, it is quite likely that the appearance
of the coastline will be greatly changed by the presence of fast ice, icebergs,
etc.
 455

CHAPTER 16
Navigational Errors

INTRODUCTION

This chapter discusses navigational errors and how the navigator may
recognise and deal with them. To this end, a broad understanding is needed
of the probability of errors as it affects navigation. The mathematics of one-
and two-dimensional errors are set out in an annex at the end of this chapter.
The quantification of particular errors in terms of distance, given certain
parameters, is set out in Appendix 7.
Every time a position line is obtained from any source (celestial
observation, visual bearing, radar range, radio fixing aid), the navigator must
be able to judge its likely accuracy, and thus the accuracy of the ship’s
position obtained from the intersection of two or more of those position lines.
Similarly, when determining the ship’s DR position or the EP, an assessment
of the likely accuracy of that position must be made.
For example (Fig. 16-1), the ship’s position has been fixed at A at 0600
by celestial observations. The DR, B, and the EP, C, have been plotted on at
0700, as explained in Chapter 8. At 0700, a single visual position line DE is
obtained from the oil production platform F. What position should be chosen
from 0700?

Fig. 16-1. Deriving the ship’s position

456 CHAPTER 16 - NAVIGATIONAL ERRORS

The navigator may consider: ‘I have a good set of stars at 0600. I have
an accurate plotting table and bottom log so that the course steered and speed
steamed through the water, AB, between 0600 and 0700 are, I think, reliable.
I am not quite so sure about my estimates of leeway, set and drift, BC. But
I know that I am on the line DE at 0700. I will therefore, take point G (where
CG is perpendicular to DE and so G is the nearest point to C on the line DE)
as may 0700 EP and work from that for my estimate of future positions.’
Consider, however, the likely errors in the observed position at 0600, in
the DR and the EP at 0700, and in the plotted bearing of the oil production
platform at 0700. The navigator needs to take into account the following:
1. The error in the observed position at 0600. The practised observer can
normally expect to obtain a celestial fix to within about 2 miles of the
true position on almost all occasions. But a poor horizon or refraction
different from the normal can cause larger errors than this from time to
time.
2. The error in the determination of the DR and the EP. Assuming the
availability of a gyro-compass whose error has been recently checked and
a reliable electromagnetic bottom log, residual errors in a gyro-compass
and its associated transmission system could be of the order of ½° to 1°
while the error in the electromagnetic log could be as much as 1% to
2%.* Then there is the error inherent in the evaluation of leeway, tidal
stream, current and surface drift. This depends as much on the quality of
the available data as on the skill of the navigator in interpreting both this
data and the effect of the weather.
It is likely, therefore, that the error in the EP could be as much as 3%
to 5% of the distance run since the previous fix. Occasionally the error
may be more than this.
3. Any residual but unknown error in the gyro-compass together with small
but unpredictable errors in the taking and plotting of the visual bearing
at 0700. These may be as much as ±1°.
The effects are shown in Fig. 16-2.
A position circle, radius 2 miles, is drawn around A to show the likely
area covered by the observed position. By 0700, this position circle will have
grown with time according to the errors in the course steered, the distance
steamed, and errors in the estimation of leeway, and the set and rate of the
tidal stream, current, etc. The bearing of the oil platform DE is plotted
showing the ±1° limits. The navigator can now reduce his position circle at
0700 to the area KLMN.
As the chosen point G also lies within the area KLMN, this rather lengthy
assessment of the position area at 0700 may seem unnecessary. The plotted
bearing of the production platform might, however, fall outside the
navigator’s estimate of the likely position circle at 0700, e.g. PQ in Fig. 16-2.
The navigator must then review the situation to establish what has gone
wrong. Has the observed position been calculated correctly; has the DR been plotted
correctly; has the production platform been properly identified? In different
circumstances, the navigator may be passing close to shoals between him and

* This error assumes that the log has been correctly calibrated.
NAVIGATIONAL ACCURACIES 457

Fig. 16-2. Plotting the position, taking likely errors into account

the production platform and would be wise to choose an 0700 EP in the area
KLMN which assumes the most ‘dangerous’ position, e.g. N in Fig. 16-2,
perhaps calling for corrective action.
All practical navigation work frequently involves dealing with errors of
some kind or other. The navigator needs to be able to discriminate between
an error caused by a mistake, an error in a particular piece of equipment
which can be allowed for in some way (e.g. an error in the gyro-compass),
and an error caused at random.

NAVIGATIONAL ACCURACIES

If ships are to be navigated safely, there must always be a maximum

acceptable limit to navigational accuracy. The ultimate aim in any
navigational system is to ensure that the ship remains within predetermined
acceptable safe limits.

Definitions
The following definitions apply.
Accuracy. Accuracy may be expressed in a number of ways which are
explained later, e.g. root mean square distance (drms); one, two or three sigma
(1σ, 2σ, 3σ); circular error probable (CEP). Equally and more simply, it may
be expressed in terms of a percentage probability. The accuracy limits of
navigation position lines, fixes, etc. should be such that there is a 95%
probability that the actual position line or fix concerned is within the limit
quoted.
Precision. Precision relates to the refinement to which a value is stated.
For example, a celestial position line may be stated to the nearest 0'.2 but,
because of errors in refraction, personal error, etc., it may only be accurate to
±2'.0 (95% probability). Usually, there is little point in tabulating a quantity
to a greater precision than the accuracy required, but calculations involving
a number of fractions should not be ‘rounded off’ too soon, otherwise a
cumulative error may be introduced.
458 CHAPTER 16 - NAVIGATIONAL ERRORS

Absolute position. The absolute position of a ship is that which defines

its position on the Earth and is normally expressed in terms of latitude and
longitude. Where the higher orders of accuracy are required, it is necessary
to state the reference datum used.
Relative position. The relative position of a ship is a means of expressing
its position with reference to a fixed point or other ship. It may be determined
either by direct measurement, or by both ships using the same navigation
system at the same time, or by comparison of measured absolute positions
(see below).
Repeatability. Repeatability is the ability of the same ship or different
ships to return to a particular position to the same degree of accuracy as the
original ship, using the same positional sensors.

TYPES OF ERROR

There are three principal types of error: faults, systematic errors and random
errors.
Faults
Faults can be caused by any of the following:
1. A blunder on the navigator’s part.
2. A malfunction in the equipment. This may often be difficult to recognise.
For example, a gyro may start a slow wander without setting of the alarm
system and it may therefore be some time before the fault is discovered.
3. A breakdown in the equipment. This may be less serious than a
malfunction, on the grounds that no information is better than the wrong
information.
Faults must be guarded against. A reliable cross-check against the
particular source of information is always useful. For example, radar may be
used as a check against the Decca Navigator and vice versa. The DR/EP is
an invaluable means of checking a position line from any source. Regular
checks on the accuracy of the gyro-compass, as described in Chapter 9, may
well indicate whether an error has developed, as may comparison with other
gyros or with the magnetic compass. The navigator may keep a log of
readings from any particular radio navigational aid to ensure that the pattern
of readings is consistent. Any departure from this consistent pattern may well
indicate some kind of malfunction or other fault. For example, suppose the
position line readings from a radio fixing aid at equal time intervals are: 4.5,
5.2, 5.8, 7.5, 7.2, 7.8, 8.5. It should be immediately apparent that the 7.5
reading is an incorrect value as it is inconsistent with all the others.

Blunders
Blunder is the term used to describe a mistake. For example, the navigator
may forget to apply the error in the compass or the deck watch, or he may
apply it in the wrong direction.
Blunders are not easily revealed. Procedures need to be developed which
help to eliminate them. The navigational work should always be cross-checked.
TYPES OF ERROR 459

Desk-top computers and hand-held programmable calculators may be

programmed with routine tasks such as astronomical sight reductions, tidal
calculations, the calculation of rhumb-line and great-circle courses, etc. The
interpolation involved when using tables is a frequent cause of error in
navigation - this may be avoided by the use of suitable programs.

Systematic errors
A systematic error is one that follows some regular pattern, by which means
that error may be predicted. Once an error can be predicted, it can be
eliminated or allowed for.
The simplest type of systematic error is one which is constant, for
example the error resulting from any misalignment between the lubber’s line
of the compass and the fore-and-aft line of the ship.
Other examples of systematic error are errors in the gyro-compass, the
deviation of the magnetic compass, the fixed error in the Decca radio aid.*
Errors in the gyro-compass may be reduced or eliminated electronically by
making the necessary allowances for course, speed and latitude. The
deviation in the magnetic compass may be reduced by placing small magnets
and soft-iron correctors close to the compass and the residual deviation
tabulated in a deviation table. Fixed errors for Decca may be found from the
Decca Navigator Marine Data Sheets (NP 316).
Systematic errors change so slowly with time that they may be measured
and corrected. It may well be, however, that certain errors, while fairly
constant over a matter of hours, may then begin to change. Such errors may
be termed semi-systematic. Examples of such errors might be: any residual
error in the gyro-compass after applying the appropriate corrections; changes
in dip and refraction of celestial bodies observed at low altitudes, caused by
unpredictable changes in temperature and pressure.
In practice semi-systematic errors are, of necessity, treated as random
errors† (see below).

Random errors
Other errors change so rapidly with time that they cannot be predicted. There
are many causes of such errors. The taking and plotting of a visual bearing
is subject to small unpredictable errors. Short-term variations in the
ionosphere affect radio aid readings. A value extracted from a table is only
accurate to within the limits set by the table itself. For example, if a table is
expressed to only one decimal point, an extracted value of 3.4 may lie
anywhere between 3.35 and 3.45.
Such errors are known as random errors and are governed by the laws of
probability. This means that, whereas the sign and magnitude of any particular
* Whilst the fixed error remains constant in any one location, it may change considerably between
relatively close positions. Thus, the error will be experienced in a moving ship as one which varies with time,
the rate of change being dependent on the speed.
†
It is impossible to draw a precise dividing line between random and semi-systematic errors. Similarly,
it is impossible to draw a precise dividing line between semi-systematic and systematic errors. This is
because the difference is to do with the time scale over which the error has occurred. It is therefore quite
possible, for example, for ay unknown residual error in the gyro-compass to be a random or a systematic
error.
460 CHAPTER 16 - NAVIGATIONAL ERRORS

Fig. 16-3. Errors in one dimension

TYPES OF ERROR 461

random error cannot be predicted, the averaging of a number of readings can

help to determine the magnitude of that error.

Composite errors
Faults, systematic (and semi-systematic) errors and random errors may exist
in combination, in which case the error distribution may look like that shown
in Fig. 16-4. The bell-shaped pattern of random errors is explained in the
annex to this chapter.
Systematic errors shift the random distribution curve to the left or right
of the correct value. A fault can be of any size, and therefore the distribution
may be represented by a straight line, so adding a ‘skirt’ to the normal distribution.
In navigation, it is always possible for all these errors to exist in
combination. Faults, systematic and semi-systematic errors can, however, be
reduced, eliminated or allowed for, leaving in many cases only the random
error to be dealt with. Random errors are considered as being in one or two
dimensions; these are discussed below.

Fig. 16-4. Combined errors

In practice, the navigator may not have the time nor the information to
analyse the nature of the errors experienced, nor to calculate them. If,
however, he understands these concepts, he is better equipped to determine
his Position Probability Area (PPA) and his Most Probable Position (MPP).
For example, he should look upon his Estimated Position (EP) not so much
as a position but rather as a 95% probability circle with a radius appropriate
to the situation and expanding with time. If he considers his estimate of speed
along the track to be less reliable than his estimate of the ground track itself,
he may decide to change his Position Probability Area from a circle to an
ellipse, the longer axis being along the track.

Random errors in one dimension

Consider a ship making good an actual ground track of 090° (Fig. 16-3). Her
position is fixed at various times by some navigational aid. Each fix includes
random errors which cause it to fall either north or south of the actual track.
462 CHAPTER 16 - NAVIGATIONAL ERRORS

The error across the track only (cross-track error) is considered, errors to the
north of track being taken as +ve and those to the south as -ve.
The cross-track error is shown at five equally spaced points along the
track. The mean (cross-track_ error value is:
4 + 11 + 6 - 4 - 2
m = + 3m
5
This mean error value is known as the bias. In Fig. 16-3 it is the
difference between the mean apparent ground track and the actual ground
track. The bias is any given set of readings is discussed below.
Bias, however, is insufficient on its own to explain the nature of the
errors. The spread of those errors also needs to be considered. The spread of
errors is obtained by squaring each cross-track error, taking the average, and
then taking the square root, thus obtaining the root mean square (RMS) error.
In Fig. 16-3:
4 2 + 112 + 6 2 + ( -4) + ( -2)
2 2

RMS error =
5
= 6.2 m
This figure is known as the RMS error about the true value.
It is possible to calculate the RMS error about any other value but the
only one of interest is that about the mean error value. This is referred to as
the (linear) standard deviation (SD).

linear standard = RMS error about

deviation (SD) the mean error value
12 + 8 2 + 32 + ( -7) + ( -5)
2 2

=
5
= 5.4 m
It may also be seen that:
2
æ RMS error aboutö
÷ = ( bias) + ( SD)
2 2
ç
è the true value ø . . . 16.1

ie ( 6.2) 2 = ( 3) 2 + ( 5.4) 2
In practice, however, to determine the linear standard deviation
accurately, the errors in a large number of readings are required, as explained
in the annex to this chapter.
Many one-dimensional random navigational errors show a specific bell-
shaped pattern (Fig. 16-4) known as a normal distribution. The normal
distribution of errors is explained and illustrated in the annex (pp.480-1). The
bell-shape of this pattern is fixed by the unbiased estimate of the linear
standard deviation, which is often referred to as the one sigma (1σ) value, as
explained in the annex. It is possible to say what percentage of errors will lie
within any multiple of this standard deviation, and examples of these are set
out in the annex (p. 481).
TYPES OF ERROR 463

In navigation, 95% probability is the value normally used to express the

accuracy of one-dimensional position lines. This value may be considered for
most practical purposes as being equivalent to two sigma (2σ) or twice the
standard deviation (2SD). Thus, if a large number of random measurements
are made which are of a normal distribution, then approximately 95% of these
measurements may be expected to fall within the two sigma (2σ) value or
twice the linear standard deviation about the mean value. There is a 1 in 20
chance (5%) that the position line obtained could lie outside this 2σ limit. For
example, in Fig. 16-2 the navigator should now be able to recognise that:
There is a 95% probability that the plotted bearing of the oil
production platform at 0700 is accurate to within 1°, taking into
account any unknown residual error in the gyro-compass and any
small errors in observing the plotting. There is a 1 in 20 (or 5%)
chance that the position line might lie outside this limit.
When several independent random errors are considered in conjunction,
their individual standard deviations may be combined as explained in the
annex (p.481):

σ = σ 12 + σ 22 + σ 23 + . . . + σ 2n . . . 16.2

where σ1, σ2, σ3, etc. are the individual standard deviations and σ the
composite standard deviation. For example, if a ship is running a line of
bearing when the accuracy of fixing is ±50 metres, assuming a 95% (2σ)
probability but, due to vagaries in course keeping is only maintaining her
required track to an accuracy of ±20 metres (95% probability), the combined
effect of these two errors will be to produce an overall 2σ value of:

2σ = 50 2 + 20 2 = 53.85 m
The chances of the total error being as much as 70 m, which would be the
case if both errors had the same sign and maximum value at the same instant,
would only be 1/20 x 1/20 or 1 chance in 400. The overall error will lie
within the limit of ±54 metres on 95% of occasions. It should never be
assumed that, when two random errors are involved, they must necessarily
have the same sign at any particular moment.
If several small errors are combined with one which is large by
comparison, the small errors can often be disregarded as having little or nor
practical significance. For example (see also p.484), the accuracy of a gyro
bearing allowing for any random gyro error may be ±1°, assuming a 95%
probability and normal distribution. However, the gyro bearing can only be
read to the nearest ½°, i.e. the maximum rounding-off errors is ±¼°. The gyro
bearing itself can be plotted to an accuracy of ±¼°. What is the likely total
95% error?
The standard deviations of these three values are as follows (the full
details are set out in the annex, p.484):
Gyro bearing 0°.5 (2σ1 = 1° ∴ σ1 = 0°.5)
Rounding-off error 0°.15 approx. (σ2 = 0.6 x 0°.25)
Plotting error 0°.15 approx. (σ3 = 0.6 x 0°.25)
464 CHAPTER 16 - NAVIGATIONAL ERRORS

combined standard deviation σ = (0.5)2 + (0.15) 2 + (0.15) 2

= 0° .54
∴ 2σ = 1° .08

The random gyro error of 1° is only increased by a negligible amount

when the taking and the plotting of the bearing are also considered. For most
practical purposes, the total 95% error is still only 1°.
Bias
If a series of readings is taken, a bias in these readings about the true value
may be revealed. This bias can occur for various reasons. The number of
readings may be small, as in Fig. 16-3. The number of readings may be large
but be taken over a relatively short time scale and may include an as yet
unrevealed systematic or semi-systematic error. This systematic or semi-
systematic error, which may well be constant over the time scale concerned,
will be revealed as a bias, that is, a difference between the mean value of the
readings and their true value.
If the errors are truly random, and if an infinite number of observations
are made, then mean and true values of the readings will coincide, that is,
there will be no bias. In practice, however, it is not possible to take an
infinite number of readings. The navigator must always remember, therefore,
that his set of readings, which appears random, may in fact be biased one side
or the other of the true value.
A bias will be present in may readings from radio navigation and inertial
navigation systems. Moreover, this bias will not be constant but will change
with time, the rate of change of the bias depending on the type of navigational
aid. For example, a 24 hour related bias will be experienced with the Ship
Inertial Navigation System (SINS), Omega and also Decca. A more rapidly
changing bias will also be experienced with Decca, the bias being associated
with the course and speed of the ship across the Decca chain.
Random errors in two dimensions
Radial error
Although the navigator is interested in the likely errors in any one position
line, he is also concerned with the likely error in his fix.
Fig. 16-5 shows a situation where a ship stopped in position B has
obtained a series of fixes using some navigational aid. Position A represents
the mean of these fixes, the difference between the individual fix and A being
shown as r1, r2, r3, r4, and r5.
The total error being positions A and B may be regarded as being made
up of one-dimensional distribution in two mutually perpendicular directions,
e.g. N-S and E-W, through the mean position A. Thus, there is a component
of bias in each of these directions, y and x, and these determine the true
position B. If there is no bias, then A and B coincide.
A measure of the spread of these errors is found by calculating the radial
error (σr) about the mean or true position. Radial error is known as the root
mean square (RMS) error, or root mean square distance (drms) about the true
or mean value. The radial error about the mean position is often referred to
as the radial standard.
TYPES OF ERROR 465

Fig. 16-5. Errors in two dimensions

deviation* (radial SD):

radial error about the

mean position (1drms) . . . 16.3

where n is the total number of individual errors. In Fig. 16-5 the radial error
is shown for five values of r (r1 to r5). Also:
2 2
æ radial error about ö æ radial error about ö . . . 16.4
÷ = ( bias) + ç
2
ç ÷
è the true position ø è the mean positionø
For example, suppose the errors around the mean position A are as
follows:
r1 = 40 m; r2 = 24 m; r3 = 30 m; r4 = 18 m; r5 = 23 m. This bias (AB) is 19 m.

For formula (16.3): 402 + 242 + 302 + 182 + 232

=
5
radial error about the
~ 28.03m
mean position (1drms)

For formula (16.4):

(19) (28.03)
2 2
=
radial error about the ~ 3386
. m
true position (1drms)

* Be careful to differentiate between linear standard deviation and radial standard deviation. Both terms are
explained in the annex. The abbreviations used in this chapter are:
1σ linear standard deviation
1drms or σ r radial standard deviation
466 CHAPTER 16 - NAVIGATIONAL ERRORS

Orthogonal position lines

Orthogonal position lines are position lines (Fig. 16-6) intersecting at right
angles where the individual linear standard deviations (1σ) of the error values
in those position lines are the same.
The 95% circle of error around these two position lines may be found, as
shown in the annex (page 487), from the formula:

r = 2.45σ
• 1.25 a
. . . 16.5

where σ is the linear standard deviation of each position line and a if the 95%
or 2σ value of the error in each.

Fig. 16-6. The 95% error circle around two orthogonal position lines

The error ellipse and the equivalent probability circle

Orthogonal position lines do not often occur in practice. It is more likely that
the error distribution will be in the form of an error ellipse (Fig. 16-7), where
the position lines do not cut at a right angle and have different standard
deviations.
TYPES OF ERROR 467

Fig. 16-7. The error ellipse

The two position lines AB and CD intersect at E at an angle α; σ1 is the

linear standard deviation or 1σ value of the error in AB, and σ2 is the linear
standard deviation or 1σ value of the error in CD. The intersection of the
standard deviation position line bands forms a diamond of error FGHJ.
The exact shape of the error ellipse varies with the magnitude of the
errors σ1 and σ2 as well as the angle of cut α. The development of the 95%
ellipse is explained in the annex (page 488).
It is more helpful to the navigator if this error ellipse is adjusted to form
a circle around the position where the probability of error is the same as that
for the ellipse. Such a circle is known as an equivalent probability circle.
The radial error or 1drms (σr) value of this circle may be found from the
formula:

1d rms = cosec α σ 12 + σ 22 . . . 16.6

where σ1 and σ2 are the individual linear standard deviations and α is the
angle of cut between the two position lines. Similarly, the 2drms (2σr) value,
illustrated in Fig. 16-8 (page 468), is:

2d rms = 2 cosec α σ 12 + σ 22 . . . 16.7

= cosec α a 2 + b2 . . . 16.8

where a = 2σ1 and b = 2σ2.

The 2drms value is of particular interest to the navigator because its
percentage probability lies between 95.4% and 98.2%, dependent on the
shape of the ellipse. The navigator may therefore use the 2drms value for the
95% probability circle for most practical purposes as, in so doing, he is
always taking a more pessimistic but safer view of the likely circle of error.
An example is given later in the section on the practical application of
navigational errors.
468 CHAPTER 16 - NAVIGATIONAL ERRORS

Fig. 16-8. The 2drms error circle around the position

Circular error probable (CEP)

The navigator may encounter the term circular error probable (CEP) as the
accuracy of navigational equipment is often expressed using this term. The
CEP may be defined as being the 50% probability circle. That is to say, there
is an equal chance that the position lies outside or within the circle.
When the position lines are orthogonal, the radius of the CEP
approximates to 1.2σ, where σ is the standard deviation of the two position
lines. The 95% probability circle may be found by multiplying the CEP
radius by a factor of approximately 2.1. This factor may also be used to find
the 95% equivalent probability circle from the CEP around an error ellipse,
provided that the latter is not too elongated. The relationship between the
CEP and the shape of the ellipse is set out in the annex (p. 493).

THE PRACTICAL APPLICATION OF NAVIGATIONAL ERRORS

Allowing for faults and systematic errors

Errors arising from faults and systematic errors need to be eliminated or
allowed for. Various ways of achieving this have already been discussed in
this chapter and are summarised below:
1. Cross-checking one system against another. Examples are: cross-
checking radar against the Decca Navigator and vice versa; cross-
checking the DR/EP against a position line from any source.
THE PRACTICAL APPLICATION OF NAVIGATIONAL ERRORS 469

2. Navigational procedures which help to eliminate mistakes, for example,

cross-checking the Navigating Officer’s work.
3. The reduction or elimination of systematic errors in navigational
equipment such as the gyro- and magnetic compasses, radio aids, etc.
Examples are:
(a) The necessary adjustments to the gyro-compass for course, speed and
latitude and the determination of any residual error by the methods
described in Chapter 9.
(b) The reduction of the deviation in the magnetic compass by means of
small magnets and soft-iron correctors and the tabulation of the
residual deviation.
(c) The allowance for fixed errors in the Decca Navigator.
(d) The allowance for personal error

Allowing for random errors

Once faults and systematic errors have been allowed for, the navigator is left
with random errors. In general, these may be expected to have a normal
distribution (Fig. 16-4) and those which are rectangular (p.482) can often be
disregarded because they add so little to the total random error.
As far as random errors in navigation are concerned, the accuracy limits
of a position line or fix should be such that there is a 95% probability that the
actual position line or fix is within the limit quoted. This means that there is
always a 5% or 1 in 20 chance that the position line or fix lies outside this
limit and the practical navigator always needs to bear this in mind. It is a
matter of navigational prudence to choose that position in an area of
uncertainty which places the ship closest to danger.
Because position lines usually cross at an angle other than a right angle
and because the amount of error in individual position lines may well be
different when expressed in n miles, the navigator is often left with a diamond
of error and an error ellipse, as shown in Fig. 16-7. For all practical purposes,
provided the ellipse is not too elongated, he may determine the radius of his
95% probability circle around his position by using the procedure described
on p.489, particularly if that procedure has been programmed as suggested on
p.492. Alternatively, he may use the 2drms formulae (16.7) or (16.8), which
produce a slightly larger error circle and so err on the side of caution.
The navigator may then use the 95% probability circle in preference to the
95% error ellipse. Thus, in Fig. 16-9 (p.470) a position F may be obtained
from the intersection of two position lines AB and CD, each considered
accurate to ±1° (95% probability). AB and CD cut at 65° and the distances of
two objects observed* are: lighthouse 12 miles; chimney 15 miles.
One degree at 12' subtends 0'.2, at 15', 0'.25. From formula (16.8) the
radius of the 2drms probability circle around F is 0'.35. Using formulae
(16.27) and (16.28), the radius of the 95% probability circle is 0'.33.
In the special case where position lines cross at right angles and the
standard linear deviations are the same, a circle of radius 1¼ times the 95%
or 2σ value of the linear error is the 95% probability circle.
* The distances of these objects are greater than would normally be expected in coastal navigation but they
are chosen to illustrate the technique. If the two objects are 3' and 6' away, the radius of the 95% probability
circle is about 230 metres.
470 CHAPTER 16 - NAVIGATIONAL ERRORS

Fig. 16-9. Plotting the 2drms (95% approx.) probability circle

Limits of random errors

As explained earlier, there is a 95% probability that the random error in any
position line is within the two sigma (2σ) value selected; that is to say, there
is a 1 in 20 chance that the position line lies outside this limit. If it appears
that the error in a position line is greater than three sigma (3σ) , for example
from its juxtaposition with other position lines, it is more likely that the error
has been caused by a mistake rather than by a random error. This is because
the likelihood of there being a normally distributed random error equal to 3σ
is only about 0.27% or 1 chance in 370. The likelihood of the error being as
great as 4σ is only about 1 chance in 16,000.
In practice, therefore, if the random error in any one position line appears
to lie between 2σ and 3σ, that position line should be treated with caution.
some kind of mistake may have been made and the possibility should be
investigated. If the error appears to be greater than 3σ, then almost certainly
a mistake has occurred unless there is supporting evidence to the contrary.
The navigator will need to investigate the reason, for example:
He may have made a blunder such as misreading an instrument or
misidentifying an object.
He may have made an incorrect assessment of the sigma values of
one or more of his position lines or position areas.
THE PRACTICAL APPLICATION OF NAVIGATIONAL ERRORS 471

His assessment of external factors such as current and tidal stream

may be in error.
An unsuspected semi-systematic error may have arisen.

Most Probable Position (MPP)

The navigator is now able to determine his 95% Position Probability Area
(PPA). PPA was defined in Chapter 8 (page 181) and four examples of
finding this are given below. Within this area, he needs to choose his Most
Probable Position (MPP) (Fig. 16-10), which he may treat as a fix, an EP or
a DR dependent on the quality of the input. MPP may be defined as that
position which takes into account the probability of error in each piece of
positional information available.
Judgement is all-important when dealing in a practical way with errors in
position lines in order to arrive at an MMP. The magnitudes of the 95%
errors in the DR and the EP, and in the position lines obtained by visual
observation of celestial and terrestrial objects, are largely a matter of
judgement based upon experience. Some idea of the likely extent of these
errors has already been given earlier in this chapter (see page 456) and
example 4 shows how these values may be used.

Example 1
In Fig. 16-10, E is the ship’s estimated position, considered accurate to within
a radius of 3 miles (95% probability). At this time a position line AB is
obtained, considered accurate to within 1½ miles (95% probability). The PPA
will be the sector CDFG, the overlapping area created by the EP probability
circle and the band of error around the position line.

Fig. 16-10. Position Probability Area (1): MMP within the PPA
472 CHAPTER 16 - NAVIGATIONAL ERRORS

If the overall effect of each error is considered to be of a random normal

distribution, the effect of each error is proportional to the square of its size.
Thus, if the likely error in the position line is a miles and that in the EP is b
miles, the Most Probable Position H is nearer the position line AB at a
distance:

a2
d . . . 16.9
a 2 + b2
where d is the perpendicular distance EJ between the EP, E, and the position
line AB in Fig. 16-10.
If a = 1½ miles and b = 3 miles for a 95% probability and EJ is 1', then
H will be:

2.25
× 1' = 0'.2 from AB * . . . 16.10
2.25 + 9
Example 2
If the position line falls outside the probability circle, although the error bands
overlap (Fig. 16-11), the MMP as calculated above may fall outside the PPA.

Fig. 16-11. Position Probability Area (2): MMP outside the PPA

The Most Probable Position H, as calculated above, lies outside the

Position Probability Area CDF. Although the two areas overlap, the fact that

* Although an error band an error circle may intersect, as in Fig. 16-10, it does not always follow that they
can be combined in this way to give a better estimate of the position. Statistical confidence interval tests may
indicate that the two sets of data are inconsistent with each other.
THE PRACTICAL APPLICATION OF NAVIGATIONAL ERRORS 473

AB lies outside the probability circle around the EP means that some kind of
mistake may have occurred, and so the navigator must treat the result with
caution. He needs to investigate the possibility of a mistake and, if possible,
resolve it. All other things being equal, he would probably choose the
position F as the MPP. This is the point where the probability area CDF is
closest to H.

Example 3
If the two error bands do not overlap at all (Fig. 16-12), then almost certainly
some mistake must have occurred which should be investigated. The
Navigating Officer may have erred in his estimate of the 95% probability
limits, or he may have made a blunder.

Fig. 16-12. Position Probability Area (3): error bands do not overlap

If these matters cannot be resolved and the navigator is forced to choose

between the two, his choice of position must depend on the circumstances at
the time. For example, if he is in the vicinity of dangers, he should choose
that position G which puts him closest to these. Alternatively, no dangers
being present, he may choose J, the position on AB closest to E. On the other
hand, if he decides to weight each error in proportion to its square, then he
may choose H as the MPP, calculating this from formula (16.9). In short, no
hard and fast rules as to what the navigator should do can be laid down; he
has to use his own judgement.
 474

Fig. 16-13. Plotting the position, taking probability into account

CHAPTER 16 - NAVIGATIONAL ERRORS
THE PRACTICAL APPLICATION OF NAVIGATIONAL ERRORS 475

Example 4
Consider the application of the principles of probability to the example given
at the beginning of this chapter (Fig. 16-1), and how these principles may be
used to determine the PPA and MPP at 0700 (Fig. 16-13).
The error in the observed position at 0600
Assume this was obtained from two astronomical position lines* each
considered correct to within 1'.5 (95% probability) crossing at 60°. Then,
from formula (16.8):

2d rms = cosec 60° (1.5) 2 + (1.5) 2

= 2'.45
At 0600, therefore, the navigator should be able to assume that there is a
95% probability that his actual position will lie within 2'.45 of position A.
The error in the determination of the EP at 0700
The magnitude of the error in the EP depends upon those factors mentioned
on page 456. Assuming that there is a 95% probability that the error in the EP
is within 5% of the distance run since the previous fix at 0600, this error
should therefore amount to 5% of 17' or 0'.85.
Assuming a 95% probability, the overall error at 0700 is therefore, from
formula (16.2), equal to (2.45) 2 + (0.85) 2 or 2'.59. The radius of the
position circle around C at 0700 is then about 2'.6, again assuming a 95%
probability.
Note: The two errors 2'.45 and 0'.85 must not be added together to obtain
the combined error. The likelihood that the maximum error could be as much
as 2'.45 + 0'.85 = 3'.3 is 1/20 x 1/20 or 1/400 or 0.25%. The probability that
the 0700 position lies within 3'.3 of C is therefore 99.75%, a much higher
percentage than is needed for most practical purposes.
The error in the bearing at 0700
If the bearing of the oil production platform is accurate to within 1°, given a
95% probability, and assuming that the distance of the platform is about 18',
the position line DE will be correct to within 0'.3. The distance CG may be
measured, 1'.2 (CG is perpendicular to DE).
The navigator can now reduce the position circle at 0700 to the Position
Probability Area KLMN. The Most Probable Position H may be calculated,
using formula (16.9), as shown in the example of page 471 (Fig. 16-10).
In Fig. 16-13:
a2
GH = 2 × CG
a + b2
(0.3)2
= × 1'.2
(0.3)2 + (2.6) 2
= 0'.016 ~ 0'.02
* An astronomical fix frequently comprises more than two position lines. The method of obtaining the Most
Probable Position from a number of position lines that are subject to normally distributed errors is given in
the annex.
476 CHAPTER 16 - NAVIGATIONAL ERRORS

Position H may now be plotted and the ship’s future track developed from this
position.
In this particular case, the EP (G) and the MPP (H) are virtually identical,
so for all practical purposes the navigator may plot from G. It would be
unwise, however, to assume that the two positions will always be so close
together, as Examples 1 to 3 make clear. Each position line should be
weighted to take account of its probability of error, before an assessment of
the MPP is made.
 477

ANNEX A TO CHAPTER 16
Navigational Errors

ONE-DIMENSIONAL RANDOM ERRORS

Variance and linear standard deviation

Suppose a series of observations for a single position line are taken from a
radio aid (e.g. the Decca Navigator) receiver at 10 second intervals, the ship
being in a fixed position. After applying any fixed error correction (which
may be considered as the bias in that radio aid) for the area, a sample obtained
from a very large number of observations might be as in Table 16A-1:*

Table 16A-1

CLASS INTERVAL CENTRE OF NO. OF DEVIATION (APPROX)

OF RADIO RADIO AID OBSERVATIONS FROM MEAN VALUE
AID READING LANE READING (x - 0)
8.195-8.205 x1 8.20 f1 2 d1 -0.06
8.205-8.215 x2 8.21 f2 6 d2 -0.05
8.215-8.225 x3 8.22 f3 17 d3 -0.04
8.225-8.235 x4 8.23 f4 50 d4 -0.03
8.235-8.245 x5 8.24 f5 63 d5 -0.02
8.245-8.255 x6 8.25 f6 72 d6 -0.01
8.255-8.265 x7 8.26 f7 76 d7 NIL
8.265-8.275 x8 8.27 f8 73 d8 +0.01
8.275-8.285 x9 8.28 f9 65 d9 +0.02
8.285-8.295 x10 8.29 f10 52 d10 +0.03
8.295-8.305 x11 8.30 f11 16 d10 +0.04
8.305-8-315 x12 8.31 f12 5 d12 +0.05
8.315-8.325 x13 8.32 f13 3 d13 +0.06

Total readings (n) = 500

* This is a hypothetical example illustrating how random errors might occur. The example has not been
derived from any particular set of radio aid readings.
478 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

A mean value x̄ may be calculated from these readings as follows:

. . . 16.10

(8.20)2 + (8.21)6 + (8.22)17 + . . . + (8.32)3

=
2 + 6 + 17 + . . . + 3

= 8.26016 • 8.26

Fig. 16-14. Histogram of lane readings against frequency of observation

If these readings are plotted against the frequency of observation in the

form of a histogram (Fig. 16-14), it may be seen that the frequency of
observation reduces as the readings diverge from the approximate mean value
x̄, 8.26. It may also be seen that a curve drawn through the histogram value
peaks at the mean value x̄ and is roughly symmetrical about this mean.*

* In practice, the curve may be somewhat distorted about the mean lane value and is likely to be skewed one
way or the other.
ONE-DIMENSIONAL RANDOM ERRORS 479

The average error is evaluated by finding the variance (also known as the
mean square deviation). The variance of a set of observations is the average
of the sum (denoted by 3 ) of the squares of the deviation from the mean and
is given by the formula:

variance =
å (x − x ) = å d
2
2 . . .16.11
n n
whereå ( x − x ) = åd = f 1 (d1 ) + f 2 (d 2 ) + f 3 (d 3 ) + ... f 13 (d13 )
2 2 2 2 2 2

The standard deviation (SD) or root mean square (RMS) error about the
mean value of this set of observations is equal to the positive square root of
the variance, i.e.:
å( x − x) åd
2 2

SD = σ n = = . . . 16.12
n n
It is often more convenient to use the alternative and equivalent formula
for variance:

variance =
å x2
= x2
n . . . 16.13

However, these readings are only a sample taken from the whole, and a
better estimate of the variance and the standard deviation of all the readings
is more accurately given by the formula:

variance = σ = 2 å( x − x) 2

=
åd 2

. . . 16.14
n− 1 n−1
1
σ2 =
n− 1
å (
x 2 − nx 2 ). . . 16.15

The square root of this value is known as the unbiased estimate of the
standard deviation and is often referred to as the one sigma (1σ) value:

å ( x − x) åd
2 2

1σ = σ n −1 = = . . . 16.16
n− 1 n− 1

1
or
n− 1
(å x 2
− nx 2
) . . . 16.17

Where n is large, as should be the case when a random sample is being

considered, the difference between n and (n - 1) is not significant and may
often be disregarded. In such circumstances, it is immaterial whether 1σ is
obtained by division by n or by (n -1):
In the above example, from formula (16.16):
480 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

f 1 (d1 ) + f 2 (d 2 ) + f 3 (d 3 ) + ...+ f 13 (d13 )

2 2 2 2
1σ = . . . 16.18

2( − 0.06) + 6( − 0.05) + 17( − 0.04) + ...+ 3( 0.06)

2 2 2 2

−~
499

1σ −~ 0.02 mean lanes

From formula (16.17):

f 1 x12 + f 2 x22 + ... + f 13 x132 n . . .16.19
1σ = − x 2
n−1 n− 1

2( 8.2) + 6( 8.21) + ... + 3( 8.32)

2 2 2
500
= − ( 8.26016) 2
499 499
−~0.02 mean lanes
Random errors of measurement can be shown to follow the Gaussian*
distribution of normal errors which is usually referred to as the normal
probability distribution, as shown in Fig. 16-15. Such a distribution may be
considered as the limited or idealised form of the curve shown in Fig. 16-14
and only differs from it because the curve in Fig. 16-4 was based on a sample
of 500 readings rather than an infinite number.
In the normal distribution curve (Fig. 16-15), errors are symmetrical about
the mean distribution µ, and the probability of obtaining progressively larger
errors falls off in a particular way. The area beneath the curve over a given
interval measures the probability of an error occurring in that interval. The
whole shape of the distribution is fixed by the standard deviation and it is
possible to say what percentage of errors will lie within any multiple of sigma.
The probability density function (pdf) for the general normal distribution
is
y = σ -1 ( 2π ) e [
− ½ − ½ ( x-µ ) / σ ] 2
. . . 16.20
where y is the height of the curve at any point, σ is the standard deviation and
µ the mean of the random variables; π and e are commonly used mathematical
constants.
All values of practical significance lie between X = -3 and X = +3, as
indicated in Fig. 16-15. The important figures are as follows:
50% of the errors fall within 0.674σ of the mean. The 50% error, where
any individual error has an equal chance of being greater or less than this
value, is often referred to as probable error or linear error probable (LEP).
68.27% of the errors fall within one sigma (1σ) of the mean. That is to
say, if a large number of random measurements are made and it is known that

* The German mathematician Gauss (1777-1855) used the normal distribution as a model for the errors in
astronomical observations.
ONE-DIMENSIONAL RANDOM ERRORS 481

Fig. 16-15. The normal distribution of random errors

the error distribution is normal (Fig. 16-15), then 68.27% of these

measurements may be expected to fall within 1σ value or one standard
deviation from the mean.
95% of the errors fall within 1.96σ of the mean.
95.45% of the errors fall within 2σ of the mean.
98% of the errors fall within 2.33σ of the mean.
99% of the errors fall within 2.58σ of the mean.
99.73% of the errors fall within 3σ of the mean.

The 95% error is the value normally used in navigation to express the
accuracy of one-dimensional position lines and this value may be considered
for practical purposes as being equivalent to 2σ.
In the above example, if 1σ = 0.02 mean lanes, then 2σ = 0.04 mean lanes.
There is a 95% probability that the actual position line lies within the limit
quoted, 0.04 mean lanes. In other words, there is a 1 in 20 chance that the
position line could lie outside the limit of 0.04 mean lanes.

Combining one-dimensional random errors

The total one-dimensional error at any particular instant may be found by
summing algebraically the relevant individual errors. Suppose that, at a given
moment, the particular errors in a navigational situation are as follows:
482 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

error in the navigation system in use +35 m

error due to human fallibility -27 m
error caused by the effect of the elements (wind,
water, tidal stream, etc.) +17 m

The total error at this moment will be +35 -27 +17 = +25 metres.
The standard deviations of several independent random errors may also
be combined.
The variance of the sum (or difference) of two or more independent
random variables is equal to the sum of the individual variances, i.e.
σ 2 = σ 12 + σ 22 + σ 23 + . . . + σ 2n . . . 16.21

The standard deviation of the sum (or difference) of these variables is as

follows:
. . . (16.2)
σ = σ 12 + σ 22 + σ 23 + . . . + σ n2
When sigma values are combined, the resultant value is much less than
if the two individual values are added together. This is because the squares
of the two values are added, and then the square root of the sum is taken. An
example of this was given on page 463.

Rectangular errors
Random errors only follow a Gaussian or normal distribution if the error is a
continuous variable. But this is not always the case. The distribution of
random errors can also be rectangular.

Rounding-off errors
Many values in navigational tables are expressed to only one decimal point;
thus, the error in the extracted value may be anywhere between ±0.05 about
that value. Such an error is usually referred to as a rounding-off error.
A rectangular or continuous uniform distribution (Fig. 16-16) has the
probability density function:
. . . 16.22

. . . 16.23

. . .16.24

When a table or instrument reading to the nearest 0.1 value is being used
(a = -0.05, b = +0.05), the variance and standard deviation are as follows:

( 0.1) 2
variance = = 0.000833
12
ONE-DIMENSIONAL RANDOM ERRORS 483

Fig. 16-16. Rectangular error

( 0.1) 2
SD = = 0.029
12

The standard deviation of the error will be approx. 0.6 of the maximum
error or three-tenths of the difference between the graduations. The 95%
error leaves 2.5% at each end of the distribution; e.g. in Fig. 16-16 it lies
between (x - 0.0475) and (x + 0.0475), that is to say, for all practical purposes
it may be considered as being equal to half the difference between the
graduations - in this case 0.05.

Effect of rectangular errors

Provided that rectangular errors of the type described above are small by
comparison with a random error of normal distribution, they can often be
disregarded as having no practical significance. Their effect on the total
random error is small, as illustrated in the following example, which has
already been summarised on pages 463 and 464. |
The accuracy of a gyro bearing allowing for any random gyro error is ±1°,
assuming a 95% probability and normal distribution. However, the gyro
bearing can only be read to the nearest ½°, i.e. the maximum rounding-off
error is ±¼°. The gyro bearing itself can be plotted to an accuracy of ±¼°,
once again assuming a uniform (rectangular) distribution. What is the likely
total 95% error?
484 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

Accuracy of the gyro bearing

2σ 1 = 1°
SD(σ 1 ) = 0° .5
variance (σ 12 ) = 0° .25
Measuring the gyro bearing - rounding-off error
From formula (16.23):
(¼ − ( − ¼) )2
variance =
12
i.e. σ 2 2 • 0°.021

σ 2 • 0°.14
Plotting the gyro bearing
From formula (16.23):
(¼ − ( − ¼) )2
variance =
12

i.e. σ 32 • 0°.021

σ 3 • 0°.14
From formula (16.21):
combined variance = 0° .25 + 0° .021 + 0° .021
σ 2 = 0° .292
From formula (16.2):
combined SD = 0.292
σ • 0°.54
As the rounding-off errors in the combination are not too large by
comparison with the error in the gyro bearing, the combined standard
deviation may be doubled to obtain the total 95% error:
total 95% error = 1° .08
The random gyro error of 1° is only increased by a negligible amount
when the measurement and the plotting of the gyro bearing are also
considered. For all practical purposes, the total 95% error is still only 1°.

TWO-DIMENSIONAL RANDOM ERRORS

Probability heap
Consider the special case of a fix E (Fig. 16-17), which is obtained from two
position lines AB, CD, crossing at right angles where the 95% error or 2σ
value of each position is the same, a. Such position lines are known as
orthogonal. Orthogonal position lines rarely occur in practice.
TWO-DIMENSIONAL RANDOM ERRORS 485

Each position line has its own particular error distribution which, if
Gaussian by nature (Fig. 16-15), ma be visualised where they intersect as a
probability heap around the position E. The probability distribution of a
single position line is a function of the area under the curve (Fig. 16-15); thus,
the probability distribution of two crossing position lines is a function of the
volume within the heap.

Fig. 16-17. Error distribution of two intersecting orthogonal position lines

The circle of error

Portions of the heap cut out by cylinders of a particular radius, e.g. r in Fig.
16-17, may be removed. The proportion which the volume of the heap
contained within the cylinder bears to the total volume of the heap determines
the percentage error of the fix. For example, if in Fig. 16-17 the volume of
the heap within the cylinder of radius r equals 70% of the total volume of the
heap, then the radius r determines the 70% probability circle of the fix. Such
a circle may be referred to as a circle of error. The radial error or root mean
square (RMS) error (σr), is a particular case of this circle of error.
The link between percentage errors and standard deviation is not the same
in a two-dimensional probability heap as it is in a linear distribution (page 481).
This is because two sets of conditions are being met simultaneously and the
486 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

probability of this occurring is less than the probability of either set being
satisfied individually. The probability is proportional to the volume of the
heap rather than the area under the curve.
In the special case of orthogonal position lines where the linear standard
deviations (1σ) are the same, the probability P (expressed as a fraction of 1,
e.g. 95% is expressed as 0.95), of being within a radius r may be expressed
by the following formula, which is also shown in the graph in Fig. 16-18.
2
/2σ 2
P = 1 - e -r . . . 16.25
2
/ σ 2r
or P = 1 - e -r

Fig. 16-18. The circular normal distribution

The distribution of errors about the mean point has circular symmetry and
the pattern of distribution is referred to as a circular normal distribution. The
circular normal distribution may be specified in terms of the linear standard
deviation (σ) in each direction. It may also be specified in terms of the radial
error about the mean value.
Values of the circular normal distribution, where two position lines of
equal linear standard deviation (σ) intersect at right angles, are given in Table
16A-2.
TWO-DIMENSIONAL RANDOM ERRORS 487

Table 16A-2
r PERCENTAGE PROBABILITY
1σ 0.71σ r 39.35%
1.1774σ 0.83σ r 50% circular error probable (CEP)
σ 2 σr 63.2% 1drms (radial error)
2σ 1.41σr 86.47%
2.45σ 1.73σr 95%
2σ 2 2σr 98.2% 2drms
3σ 2.12σr 98.89%
3.04σ 2.15σr 99%

Fig. 16-6 (page 466) displays a plan view of the fix in Fig. 16-17. If the
95% or 2σ value of the linear error common to both position lines is a, then:
when a = 2σ
2.45a
r=
2
• 1.25a
Thus, a circle of radius r = 1.25a around E provides the 95% circle of
error for most practical purposes.
The relationship between CEP and other probability circles for the
circular normal distribution may be determined using formula (16.25). The
radii of various percentage probability circles may be found by multiplying
the radius of the CEP circle by the factors in Table 16A-3.

Table 16A-3
% PROBABILITY RADIUS CEP MULTIPLICATION FACTOR
95% 2.079
98% 2.376
99% 2.578

The error ellipse

The error ellipse may be drawn by fitting an ellipse (Fig. 16-19) into an area
of overlap produced by constructing bands of errors around the intersecting
position lines. The relationship between the ellipse probability and the width
of appropriate band may be taken from Table 16A-2, for example:

Table 16A-4
ELLIPSE PROBABILITY WIDTH OF BAND OF ERROR
50% ±1.18 linear SD (1.18σ)
95% ±2.45 linear SD (2.45σ)
488 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

Fig. 16-19. the 95% error ellipse

The 95% error ellipse is illustrated in Fig. 16-19. AB and CD are two
position lines intersecting at E at an angle α. The linear standard deviations
of AB and CD are σ1 and σ2 respectively.
Lines parallel to AB and CD are drawn on each side, 2.45 σ1 and 2.45 σ2
away from the appropriate position line.* The ellipse is now drawn to fit the
parallelogram, as in Fig. 16-19, by making it pass through the points P, Q, R,
S and by making the ellipse cut the diagonals of the parallelogram
approximately seven-tenths of the distance along the diagonal from the centre.
For example, if each position line is a visual bearing, then it may be said
that the 95% error (2σ) value of each bearing is 1°. The standard deviation
(1σ) value of the error equals ½° and may be represented by σ1 and σ2 in Fig.
16-19. The actual width of this ½° error is dependent on the distance of the
fixing mark, as explained in Chapter 12.† σ1 and σ2 may now be expanded
2.45 times (or the 2σ1 and σ2 values 1¼ times approx.) and the ellipse drawn.

* If the 95% or 2σ values of the individual position lines are given these may be expanded (2.45 ÷ 2), or
approximately 1¼ times for most practical purposes.

† ±1° is equivalent to: ±1' at 60'; ±0'.25 at 15'; ±0'.2 at 12'; ±0'.1 at 6'; ±0'.05 at 3'.
TWO-DIMENSIONAL RANDOM ERRORS 489

Equivalent probability circles

An elliptical error distribution is not particularly helpful to the navigator, who
will find that it is of more practical use if he can adjust the error ellipse to
form a circle (Fig. 16-20) where the probability of error is the same as that
formed by the ellipse. Such circles are known as equivalent probability
circles. The terms CEP is also used (page 487) to indicate that circle within
which there is a 50% probability, even though the actual error figure is an
ellipse.

Fig. 16-20. Error ellipse and equivalent probability circles

The radial error (1drms) is illustrated in Fig. 16-20, together with the 1σ
error in the individual position lines. 1drms is equal to the square root of the
sum of the squares of the 1σ error components along the major and minor
axes of the ellipse:

1drms = σ x2 + σ y2 . . . 16.26
1 é 2 ù
whereσ y2 =
2 sin 2 α êë σ 1 + σ 2 +
2
(σ 2
1 + σ 22 ) − 4 sin 2 α (σ 12σ 22 ) ú
2

û
. . . 16.27
490 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

1 é 2 ù
and σ 2y =
2 sin 2 α
2
êë σ 1 + σ 2 - (σ 2
1 + σ 22 ) - 4 sin 2 α (σ 12 σ 22 ) ú
2

û
. . . 16.28

1drms may now be expressed in therms of σ1 and σ2 and the above formulae
simplify to:

1d rms = cosec α σ 12 + σ 22 . . . (16.6)

Other multiples of the radial error may also be derived by using

corresponding values of σ; for example, the 2drms value may be calculated
using the above formulae, using the 2σ error values, i.e.
2d = cosec α a 2 + b 2 . . . (16.8)
rms

where a = 2σ 1 and b = 2σ 2
i.e. 2d rms = 2 cosec α σ 12 + σ 22 . . . (16.7)

The numerical probabilities associated with 1drms and 2drms vary

dependent on the shape of the ellipse and are given in Table 16A-5.*

Table 16A-5. drms and the shape of the error ellipse

LENGTH OF PROPORTIONATE PROPORTIONATE 1drms 2drms
MAJOR AXIS LENGTH OF MINOR VALUE OF PERCENTAGE PERCENTAGE
OF ELLIPSE AXIS OF ELLIPSE 1drms PROBABILITY PROBABILITY
σX σY
σ x2 + σ y2
1.0 0.0 1.0 68.3% 95.4%
1.0 0.1 1.005 68.2% 95.5%
1.0 0.2 1.02 68.1% 95.7%
1.0 0.3 1.04 67.6% 96.1%
1.0 0.4 1.08 67.1% 96.6%
1.0 0.5 1.12 66.2% 96.9%
1.0 0.6 1.17 65.0% 97.3%
1.0 0.7 1.22 64.1% 97.7%
1.0 0.8 1.28 63.5% 98.0%
1.0 0.9 1.35 63.2% 98.1%
1.0 1.0 1.41 63.2% 98.2%

Provided σx and σy have been determined using formulae (16.27) and

(16.28), the radius of the probability circle may be found by multiplying σx
(σx $ σy) by the factors in Table 16A-6 for varying shapes of ellipse.

* See N. Bowditch, American Practical Navigator, Volume I (1977 edition), Appendix Q, Tables Q6a and
Q7e.
TWO-DIMENSIONAL RANDOM ERRORS 491

Table 16A-6

σx MULTIPLICATION FACTOR

SHAPE
OF
ELLIPSE 50% CIRCLE (CEP) 95% CIRCLE 99% CIRCLE
σy/σx

0.0 0.67 1.96 2.58

0.1 0.68 1.96 2.58
0.2 0.71 1.97 2.58
0.3 0.75 1.98 2.59
0.4 0.81 2.01 2.61
0.5 0.87 2.04 2.63
0.6 0.93 2.08 2.67
0.7 1.00 2.15 2.72
0.8 1.06 2.23 2.79
0.9 1.12 2.33 2.90
1.0 1.18 2.45 3.04

Fig. 16-21. The CEP, 95% and 2drms probability circles

492 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

For example, suppose two position lines AB and CD cross at an angle of

50° (Fig. 16-21), where the 1σ value of the linear error is AB is 1' and that in
CD is 1½'. What are the size of the CEP and 95% probability circles?
From formulae (16.27) and (16.28):
σ x = 2'.2
σ y = 0'.9
σy
∴ • 0.4
σx
From Table 16A-6:
radius of CEP circle = 2'.2 x 0.81 = 1'.8
radius of 95% circle = 2'.2 x 2.01 = 4'.4
The diamond of error formed by the 2σ (95%) linear values of the
individual position lines has been shaded in Fig. 16-21 for comparison with
the 95% and 2drms circles. The 95% error ellipse is also shown.
It is a relatively simple matter to program a desk-top computer or
programmable calculator with the necessary data to obtain the radius of the
95% probability circle. Formulae (16.27) and (16.28) are required, the inputs
being σ1, σ2 and α. The values of σy and σx and the ratio σy / σx may now be
obtained. Provided the multiplication factors from the above table are also
fed in to the program, the appropriate factor may be multiplied by σx and the
radius of the 95% probability circle obtained.
The 2drms value, which lies between probability values of 95.5% and 98.2%
dependent on the shape of the ellipse, may be deduced using formula (16.8):
2d rms = cosec α a 2 + b 2
(about the mean value)
where α is the angle of cut and a and b are the 95% (2σ) linear errors for the
two position lines.
The 2drms about the mean value formula will always produce a slightly
larger error circle than the 95% circle, the amount being dependent on the
shape of the error ellipse.
The formula is much easier to use and, if no program as above is
available, the navigator may for most practical purposes use the 2drms formula
to provide the 95% probability circle. He is therefore always taking a more
pessimistic but safer view of his likely circle of error.
Using formula (16.8) in the above example:
a = 2σ 1 = 2'
b = 2σ 2 = 3'
2d rms = cosec 50° ( 2) 2 + ( 3) 2 = 4'.7
The disadvantage of drawing equivalent probability circles is that a
position is more likely to fall within those smaller areas of the ellipse that are
outside the circle than within those larger areas of the circle that are outside
the ellipse.
TWO-DIMENSIONAL RANDOM ERRORS 493

Generally speaking, however, the equivalent probability circle is quite

satisfactory for all practical purposes provided that the error ellipse is not too
elongated.

Circular error probable (CEP)

A useful approximation to determine the CEP for the elliptical error is:

CEP = 0.615σ y + 0.562σ x . . .16.29

when σx > σy as in Fig. 16-20. This is very accurate as long as σy > 0.3σx, so
it is very useful for all but the most elongated of ellipses σx and σy ,may be
calculated using formulae (16.27) and (16.28).
The CEP conversion factors in Table 16A-3 (page 487) may also be used
for elliptical error distribution provided that the σy / σx ratio is close to 1.
However, errors increase significantly both when high values of probability
are desired and when the error ellipse is elongated. Fig. 16-22 shows the
relationship between the CEP multiplication factor and the shape of the
ellipse for a 95% probability.

Fig. 16-22. Relationship between CEP multiplication factor and ellipse shape

It may be seen from Fig. 16-22 that the CEP multiplication factor varies
between 2.08 when σy / σx = 1 and 2.9 when σy / σx = 0.1 for the 95% probability
circle.
494 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

Derivation of the Most Probable Position (MPP)

from three or more position lines
The method used* to derive the Most Probable Position from three or more
position lines (Fig. 16-23) is known as the least squares, minimum variance
or maximum likelihood solution. It is assumed that each position line is
subject to normally distributed random errors † only (Fig. 16-15) and that any
faults and systematic errors have been removed or allowed for. It is also
assumed that the random errors in any one position line are independent of the
random errors in any other position line.

Fig. 16-23. Derivation of the Most Probable Position from three position lines

* In practice, this technique has a number of limitations in that it assumes no auto-correlation on the position
lines nor cross-correlation between position lines. The technique may be modified to account for these
correlation effects but requires a co-variance matrix approach, rather than the relatively simple geometric
solution shown here.

† The least squares method does not require the errors in each position line to be normally distributed.
However, if the errors are normally distributed, the least squares estimates are also the maximum likelihood
estimates.
TWO-DIMENSIONAL RANDOM ERRORS 495

Fig. 16-23 shows three position lines AB, CD and EF, from which any
faults and systematic errors have been removed,* but that a ‘cocked hat’
(caused by normally distributed random errors in the position lines) still
remains. O is the ship’s Estimated Position and it is immaterial to the
calculation whether O is inside or outside the cocked hat (but see Note at the
end of this section. e1 is the perpendicular distance between AB and O; e2 is the
perpendicular distance between CD and O; e3 is the perpendicular distance
between EF and O. θ1, θ2 and θ3 are the angles which e1, e2 and e3 respectively
make with the east-west axis through O and measured from east. P is the Most
Probable Position and is deduced using the least squares method. The most
likely estimate of the co-ordinates of P (x, y) relative to O are . Thus
must be found in order to establish the most likely position of P.
‘1, ‘2 and ‘3 are the mean error estimates between the three position lines and
P. σ1, σ2 and σ3 are the standard deviations of the error distributions
associated with the three position lines AB, CD and EF respectively.
The most likely or best estimates of x and y - that is , are given
by the following equations:
$ 2 + yG
xC $ = Ec . . .16.30
and $ + yS
xG $ 2 = Es . . .16.31
where:
e
Ec = åσ 2 cosθ
e1 e2 e3 en . . .16.32
= cos θ + cos θ + cos θ + ...+ cosθn
σ 12 1
σ 22 2
σ 32 3
σ n2
e
Es = åσ sin θ
2
e e e e
= 12 sin θ1 + 22 sin θ2 + 32 sin θ3 + ...+ n2 sin θn . . .16.33
σ1 σ2 σ3 σn
1
C2 = åσ cos2 θ
2

1 1 1 1
2 cos θ1 + 2 cos θ2 + 2 cos θ 3 + ...+ cos2 θn
2 2 2
=
σ1 σ2 σ3 σ n2 . . .16.34
1
S2 = åσ sin 2 θ
2

1 1 1 1
2 sin θ1 + 2 sin θ 2 + 2 sin θ3 + ...+ sin 2 θn
2 2 2
=
σ1 σ2 σ3 σ n2 . . .16.35

* The ‘cocked hat’ shown in Chapter 9 is reduced, on the assumption that the same error affects all three
position lines equally. Over the time scale involved, the error in the compass may be considered as constant,
affecting all three bearings equally.
496 ANNEX A TO CHAPTER 16 - NAVIGATIONAL ERRORS

1
G= åσ 2 sin θ cosθ
1 1 1 1
= sin θ cos θ + sin θ cos θ + sin θ cos θ + ...+ sin θ n cos θ n
σ 12 1 1
σ 22 2 2
σ 23 3 3
σ n2
. . . 16.36

The simultaneous equations (16.30) and (16.31) may be solved as follows:

EC S2 − GE S
x$ = . . . 16.37
C2 S2 − G 2
C2 E s − GEc . . . 16.38
y$ =
C2 S2 − G 2

Thus, the Most Probable Position P may be found.

Note: Provided e1, e2, e3, etc. are small, i.e. each is less than about 10 miles,
the position lines on the Earth will map on to the plane as straight lines with
negligible distortion. If the errors are greater than 10 miles, however, equations
(16.37) and (16.38) should be recalculated using the values of ‘1, ‘2 and ‘3 instead
of e1, e2 and e3 respectively. It may be necessary to carry out more than one
calculation, substituting fresh values of ‘1, ‘2 and ‘3, although in practice one is
usually sufficient unless O and P are some miles apart. If O lies some distance
outside the cocked hat formed by the position lines, the navigator will need to treat
the results with caution and, if possible, try to analyse why O and P are so far
apart.
 497

CHAPTER 17
Relative Velocity and Collision
Avoidance

This chapter introduces the concept of relative velocity and its application to
collision avoidance. The use of radar is solving collision avoidance problems
is also discussed. Some simple relative velocity problems and their solutions
are given. Details of the Battenberg Course Indicator, a type of mechanical
plotter used within the Royal Navy to solve relative velocity and station
changing problems, are given in Volume IV.

Definitions
Various terms are commonly used in the context of relative velocity and
collision avoidance and also when other ships are being plotted on radar.
These terms are set out below, and supplement those already described in this
book, such as direction, bearing and course (Chapter 1), ground track and
water track (Chapter 8), etc.

Table 17-1
SEA SPEED The speed of own ship along the water
track, expressed in knots.
GROUND SPEED The speed of own ship along the ground
track, expressed in knots.
RELATIVE TRACK OF CONTACT The path of a radar contact as observed
on a relative motion display.
TRUE TRACK OF CONTACT The path of a radar contact as observed
on a surface plotting table or on a true
motion display.
ASPECT The relative bearing of own ship from
another ship, expressed in degrees 0 to
180 Red or Green relative to the other
ship (Fig. 17-1, p.498). Aspect is often
referred to as angle on the bow.
DETECTION The recognition of the presence of a
radar contact.
ACQUISITION The selection of those radar contacts
requiring a tracking procedure and the
initiation of their tracking.
TRACKING The process of observing the sequential
changes in the position of a radar
contact to establish its motion.
498 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Fig. 17-1. Aspect

PRINCIPLES OF RELATIVE VELOCITY

Relative speed
Suppose two ships are approaching each other head-on (Fig. 17-2), the speed
of each being 20 knots.

Fig. 17-2. Relative speed

Own ship may be represented by WO, the other ship by WA. The speed
of one ship relative to the other is 40 knots; in other words, to an observer in
one ship the other ship appears to be approaching at a relative speed of 40
knots. This relative speed may be represented by OA.
One arrowhead is used on own ship’s vector, two on the other ship’s
vector and one arrowhead in a circle on the relative motion vector.
PRINCIPLES OF RELATIVE VELOCITY 499

Relative track and relative speed

Relative speed is also dependent upon the courses being steered by each ship.
For example, if the two ships are steaming in station with one another on the
same course and speed, then the speed of one ship relative to the other is zero.
In order to avoid collisions between ships and also to manoeuver ships
in company safely, the terms relative track and relative speed must be
understood. In Fig. 17-3 ship G is in sight on the starboard bow of own ship
on a crossing course. If the true bearing between the two ships does not
appreciably change, then in accordance with Rule 7 of the International
Regulations for Prevent Collisions at Sea, 1972 (the Rule of the Road), a risk
of collision must be deemed to exist. (In such a case, under Rule 15, own
ship W is required to give way to ship G.)

Fig. 17-3. Relative track

If the true bearing of G from W remains steady, then to the Officer of the
Watch in W, G must appear to be approaching W along the line GW. In other
words, the track of G relative to W (the relative track of G) is GW. The
relative speed is that speed at which G is approaching W along the line GW.
Fig. 17-3 illustrates the case of one ship in sight, crossing, and on a
steady bearing. The collision avoidance problem is easy to solve because the
bearing is steady; the relative track does not have to be computed.
If own ship is obliged to alter course to give way to another, it is
important to be able to assess what effect this manoeuver will have on the
relative track of other ships nearby. For example, in Fig. 17-4 (p.500) own
ship W may consider altering course 30° to starboard to avoid another ship G,
which is approaching on a steady bearing on the starboard bow. What effect
will this alteration have on the relative tracks of H and J? Will the proposed
change of course of 30° put own ship on a collision course with either H or
J, or both?
500 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

If it does, then a different manoeuver may be preferable, for example a much

larger alteration of course or slowing or stopping.

Fig. 17-4. Maneuvering to avoid other shipping

In order to make a proper assessment, it is necessary to find the relative

track and relative speed of the other ships. It may also be necessary to find
their true tracks and speed.

Comparison between relative and true tracks

Relative track
If the track of another ship (G in Fig. 17-5) is plotted on a relative motion
radar display, the relative track of G will be revealed. This is because own
ship remains at the centre of the display: the other ship’s relative track
corresponds to a combination of both movements.
At 0800 (Fig. 17-5) own ship W is steering 340° at 20 knots; another ship
G bears 070°, distance 5 miles. G’s movement is plotted on the radar display
and the following ranges and bearings are obtained:
PRINCIPLES OF RELATIVE VELOCITY 501

0806 082°, 4'.1 (G1)

0812 099°, 3'.5 (G2)
0818 120°, 3'.3 (G3)

Fig. 17-5. Development of the relative track

By joining all four points on the display, G’s relative track is found to be
208° (along the line GH). Between 0800 and 0818, G moves 3'.8 along GH,
hence her relative speed is:
60
× 3'.8 = 12.7 knots
18

It will be seen that G’s relative track is leading her well clear astern of
own ship. If, on the other hand, the relative track had been directly towards,
as in Fig. 17-3 - that is, towards the centre of the radar display, then the two
ships would have been on a collision course.
502 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

This is perhaps the most important feature of collision avoidance using

the relative motion display. If the relative track of another ship is moving
directly towards own ship’s position, then that ship is on a collision course.

True track
If the track of the other ship G is plotted on a plotting table, taking into
account own ship’s track, G’s true track will be revealed (Fig. 17-6). This is
because own ship W is moving over the plot in a direction and at a speed
directly proportional to own course and speed. As ranges and bearings of the
other ship are plotted, so the true track and speed of G is obtained.

Fig. 17-6. Development of the true track

PRINCIPLES OF RELATIVE VELOCITY 503

The plotted track GJ is G’s true track and speed (300°, 15 knots). It
should be noted that this is very different from G’s relative track and speed
(208°, 12.7 knots).

The velocity triangle

Once the relative track and speed of the other ship have been found (Fig. 17-
5), a velocity triangle (Fig. 17-7) may be used to give the other ship’s true
track and speed.
Alternatively, the velocity triangle may be used to find the relative track
once the true track has been determined as in Fig. 17-6, or is known.

Fig. 17-7. The velocity triangle

The velocity triangle consists of three vectors, each vector being a line
drawn in the correct direction to represent the track, the length of the line
being proportional to the speed.
Vector WO represents own course and speed (340°, 20 knots). A
convenient scale may be chosen to represent the speed: for example, if 5 knots
is to be represented by 20 mm, then own speed vector will be 80 mm long.
504 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Vector OA represents the relative track and speed of the other ship (208°,
12.7 knots). The same scale for speed is used. OA will therefore be
(12.7/5)20 = 50.8 mm long.
Vector WA represents the true track of the other ship (300°, 15 knots).
The same scale for speed is used; thus, WA will be (15/5)20 = 60 mm long.
Provided certain rules, as set out below, are followed, there should never
be any difficulty in drawing the velocity triangle correctly, with each vector
in its correct direction.

1. The arrowheads on own and the other ship’s vectors must always diverge
from W-WO and WA in Fig. 17-7.
2. The arrowheads on the other ship’s true and relative vectors always
converge on A-WA and OA in Fig. 17-7.
3. Our own course arrowhead ‘chases’ the relative track arrowhead - WO
‘chases’ OA in Fig. 17-7.

Initial position of ships

The initial positions of the ships do not affect the velocity triangle, which
depends only on the tracks and speed of each ship. However, the initial
positions of the two ships will have very different effects on subsequent
events. Suppose that, in Fig. 17-5, the other ship G had started from a
position K on a bearing of 028° from own ship, instead of starting from
position G. Her relative track of 208° must then pass through the position of
own ship. G is therefore on a collision course.

Relative movement
When considering relative tracks, do not make the mistake of assuming that
a ship points in the direction of her relative track. She is still pointing in the
direction of her course, which may be very different. Visually, a ship often
appears to move almost sideways, or crabwise, along her relative track.

USE OF RADAR

Radar may be used to advantage in solving collision avoidance and

maneuvering problems.
Modern radar, with its high rate of aerial rotation, gives an up to date
picture of other ships’ positions, their bearings and ranges. The afterglow
trails on the relative motion display show the approximate relative tracks.

Radar displays
Radar data for collision avoidance may normally be obtained using the
following methods of display. Detailed information on these radar displays
may be found in standard works on radar.

Relative motion north-up, stabilised.

Relative motion course-up, stabilised.
Relative motion course-up, unstabilised.
True motion north-up, sea-stabilised.
True motion north-up, ground-stabilised.
USE OF RADAR 505

True motion course-up, sea-stabilised.

True motion course-up, ground-stabilised.

A brief discussion on the merits of relative or true motion radar for

collision avoidance is given later in this chapter (p.509).
For collision avoidance, a stabilised method of display is generally to be
preferred to an unstabilised method. Compass bearings of other ships may be
read off directly and echoes do not become blurred when an alteration of
course is made or when a ship yaws about her course.
The type of display used for navigational purposes usually has a
mechanical bearing cursor fitted over the face of the tube. The cursor is
engraved with parallel lines and can be rotated, usually by a manual control.
Range is shown on the face of the tube by range calibration rings and by an
electronic range strobe, which paints a circular trace and is adjusted as
necessary by the range strobe control. The range to which this range strobe
is set is shown on a digital read-out.
A reflection plotter, consisting of a transparent disc provided with side
illumination, is fitted over the face of the display. The design of the plotter
is such that parallax is eliminated, that is to say, manual plotting using a
chinagraph pencil on the face of the plotter coincides with the radar picture
on the face of the tube.
The calibration rings or range strobe may be used to provide the speed
scale, while the rotating cursor provides the parallel lines for transferring
vectors.
Modern navigational radars, such as Naval Radar Type 1007, use
electronic plotting instead of the old-fashioned reflection plotter and
chinagraph pencil. Tracks of specified contacts may be generated giving their
course, speed, closest point of approach (CPA) and time to CPA (TCPA).
Pilotage lines and markers may also be injected electronically. However, the
use of such radars does not alter the principles underlying the solution of
relative velocity problems discussed below.

Using the relative motion stabilised radar display to solve relative velocity
problems
Relative velocity problems may be solved on the radar display by using the
bearing cursor and range strobe and by plotting on the face of the reflection
plotter. The following example uses a relative motion north-up stabilised
display.

EXAMPLE
A ship bears 220°, 8 miles at 0900. Own ship’s course and speed is 150°, 15
knots. Find the other ship’s relative and true tracks and speeds.

1. Set the display on a suitable range scale (Fig. 17-8, p.506) to plot the
relative track of the other ship.
2. Mark the initial position and the time of the other ship, on the reflection
plotter (220°, 8 miles at 0900)
3. Mark the position of the other ship on the reflection plotter as accurately
as possible at regular intervals to obtain her relative track, e.g.:
506 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Fig. 17-8. Finding the true and relative tracks and speeds from a relative
motion radar display (north-up stabilised): velocity triangles based (a) on
other ship’s relative track; (b) on own ship’s position.
USE OF RADAR 507

0903 222°, 7'.0

0906 226°, 6'.1
0909 229°, 5'.2
0912 237°, 4'.3
4. Measure the distance travelled by the contact between 0900 and 0912 (4
miles) and calculate the relative speed: in this case, 4 miles in 12 minutes,
or 20 knots.
5. Rotate the bearing cursor to align the parallel lines to the other ship’s
relative track and measure this using the centre line (022°).
6. The velocity triangle may now be constructed to find the contact’s true
track and speed. The velocity triangle may be drawn on the other ship’s
relative track (already developed on the reflection plotter) or it may be
based on own ship’s position at the centre of the display. The two
procedures are set out below.
7. Velocity triangle drawn on the other ship’s relative track (Fig. 17-8(a))
(a) Mark the initial position of the contact O at 0900.
(b) Draw vector OA along the other ship’s relative track (already
developed for 0900-0912) to represent the contact’s relative track
and speed vector. A distance of 8 miles for the range scale in use on
the display has been used in Fig. 17-8(a), equivalent to a 24 minute
run.
(c) Rotate the bearing cursor to own ship’s course (150°) and plot own
ship’s course and speed vector WO (150°, 6 miles - 15 knots for 24
minutes equals 6 miles).
(d) Join and measure WA, using the bearing cursor to measure the
contact’s true track (070°). The distance WA over the same 24
minute period for the range scale in use equals 6.4 miles. Thus, the
contact’s speed is 16 knots.
8. Velocity triangle based on own ship’s position (Fig. 17-8(b))
(a) Rotate the bearing cursor (alternatively use the ship’s head marker)
to own ship’s course, and adjust the range strobe to represent own
ship’s speed. Draw own ship’s course and speed vector WO (150°,
15 knots) on the reflection plotter.
(b) Rotate the bearing cursor to the relative track (022°) and using the
same scale draw vector OA to represent the contact’s relative track
and speed (022°, 20 knots).
(c) Join and measure WA, using the bearing cursor to measure the
contact’s true track (070°) and the range strobe her speed (16 knots).

The first method, plotting from the other ship’s position, has the
advantage that it uses the existing relative track of the other ship; thus, it is
a very useful method to employ when there are several contacts being plotted
at the same time on the display. The second method, plotting from own
ship’s position, makes use of the range strobe and should be more accurate.
508 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Radar plotting on relative and true motion displays

Radar data obtained from a stabilised or unstabilised relative motion display
or a true motion sea-stabilised display may be plotted on that display as
shown in Fig. 17-9, and the velocity triangle drawn.

Fig. 17-9. Radar plotting on the relative and true motion displays

Radar limitations

The navigator must be aware of the limitations of solving relative velocity

problems using radar. He may be able to draw what appears to be a precise
velocity triangle (Fig. 17-9), but the data he is using is subject to error.
Possible errors are:

1. Plotting errors. Despite the elimination of parallex, manual plotting on

the face of a reflection plotter is subject to error, caused mainly by the
thickness of the chinagraph pencil and the small size of the relative
velocity triangles. This error should be eliminated with electronic
plotting.
2. Own ship’s course and speed vector. Both the gyro-compass and its
transmission system and the bottom log are subject to errors. In RN
ships, the gyro-compass should usually be accurate to ±1°, and the
bottom log should usually be accurate to ±2%.
3. Radar data. Radar may not provide precise and consistent data,
particularly with regard to range and bearing. The ship’s head marker may
USE OF RADAR 509

not be lined up correctly; the gyro compass providing stabilisation of the

radar picture is subject to error; the radar beam may be subject to squint
error.
The accuracy of the data produced by the radar display will only be
within certain limits. In RN ships, the usual navigational radar display
has a bearing accuracy of ±1°, and a range accuracy of ±50 yards or 1%
of the range scale in use, whichever is the greater. In the Department of
Transport Radar Specification, the maximum permissible bearing error
is 1°, while the accuracy of the variable range marker should be within
1½% of the range scale in use or 70 metres, whichever is the greater.

The cumulative effect is to cause errors in both the deduced relative and
true tracks and the speeds of the contact. This is of particular importance
when ships are likely to pass close to one another and also in the head-on
approach. In the latter case, errors could produce a completely misleading
situation, for example giving the impression that a ship is passing clear but
very close down the port side when in fact it is passing down the starboard
side.
The longer a contact is plotted, the more accurate becomes the assessment
of the relative and true tracks. The shorter the range, the less is the effect of
range and bearing errors. However, the longer a contact deemed a collision
risk is plotted, the less time there is to take avoiding action.
It should not be forgotten that the relative and true tracks of a contact
only tell the Officer of the Watch what was happening in the past; they do not
reveal that the contact may be about to alter course or speed. If the contact
alters course, there will be a time delay before this becomes evident on the
radar display, and a further time delay before the new relative and true tracks
can be deduced.

Relative or true motion plotting

Some general comments on the arguments for or against using relative motion
or true motion radars for navigation were set out in Chapter 15 (page 446).
The advantage which a relative motion display has over true motion for
collision avoidance is in giving an immediate indication of which ships are
on a collision course.
On the other hand, whether or not a target is moving or stationary can
usually be more quickly distinguished on a true motion display than on a
relative display.
Generally speaking, from the point of view of collision avoidance, a
stabilised relative motion display is usually preferable to true motion in open
and coastal waters. Whether or not to use relative or true motion in pilotage
waters is a matter of judgement, taking into account the situation at the time
and the organisation available. The organisation in HM Ships usually
includes an operations room team which deals with collision avoidance and
assists with blind pilotage; thus, the need to use true motion radar displays is
limited. Merchant ships, on the other hand, have fewer people to devote to
these two tasks; thus, it is desirable to have both types of display immediately
available. If only one type of display is available, merchant ships may prefer
to use true motion radar in pilotage waters.
510 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Aspect
When deducing another ship’s true track from a plotting table (Fig. 17-6) or
from the relative motion radar display (Fig. 17-8), the deduced aspect (angle
on the bow) - defined earlier - of the other ship may not be the same as the
visual aspect. Several factors can cause this variation. The effects on both
ships of leeway, tidal stream, etc. may be different; own ship’s speed input on
a true motion display may not be correct; there may be a difference between
the actual water or ground track of own ship and that shown on the radar
display.
Always remember that the collision risk is from the approaching ship
whose bearing is steady or does not appreciably change.

Effect of leeway
If the water track and sea speed are used as own ship’s course and speed
vector, the other ship’s true vector will also be her water track and sea speed,
provided there is no difference in the set and drift being experienced by both
ships. The difference between the deduced and visual aspects reflects the
other ship’s leeway and is equal to her leeway angle.
From time to time, leeway may be an important consideration,
particularly if the other ship’s aspect is close to zero, or if the leeway is large,
as may be the case with yachts and ships in ballast.

Effect of drift and set

If the drift and set being experienced by two ships are the same, they should
have no effect on the aspect, provided ground stabilisation is not being used.
If the drift and set are not the same for each ship, then the deduced and
observed aspects of the other ship will differ.
A ground-stabilised motion display may give a misleading picture in a
collision situation in a tidal stream (Fig. 17-10). For the purposes of this
example, it is assumed that neither ship is experiencing leeway.
At 0800, own ship W is on course and speed 000°, 12 knots, tidal stream
setting 090°, 3.5 knots. Own ship’s ground track is 018°, speed made good
12.5 knots. Ship G is on a steady bearing of 010° at a range of 10 miles. Her
course and speed are 202°, 10 knots but, because of the tidal stream, her
ground track is 182°, speed made good 9.4 knots. If no action is taken,
collision will occur at point K at 0828.
On the ground-stabilised true motion display (Fig. 17-11, p.512), ship G
appears to be on own ship’s starboard bow and on an almost parallel and
opposite course, the aspect being Green 8°. This is a misleading picture.
The situation, as shown on the stabilised north-up relative motion display
(Fig. 17-12, p.513), is somewhat different.
Ship G is on own ship’s starboard bow, crossing from starboard to port.
Her aspect is actually Red 12° and not Green 8°. Such a situation should also
be apparent visually and on the sea-stabilised true motion radar display.
USE OF RADAR 511

Fig. 17-10. Collision situation in a tidal stream

512 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Fig. 17-11. The situation as displayed on true motion radar

USE OF RADAR 513

Fig. 17-12. The situation as displayed on the relative motion radar

514 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Automated radar plotting aids (ARPA)

A number of radars available commercially are fitted with automated or semi-
automated aids to plotting and collision avoidance. Such aids to navigation
are discussed in Volume III of this manual and are not dealt with in any great
detail here.
The International Maritime Organisation (IMO) has set out certain
standard amending the International Convention of Safety of Life at Sea, 1974
(SOLAS ‘74) requirements regarding the carrying of suitable automated radar
plotting aids (ARPA). Certain countries, e.g. the United States, have also
enacted legislation on the subject.
A typical ARPA gives a presentation of the current situation and uses
computer technology to predict the future situation. An ARPA assesses
collision risk, proposed manoeuvres by own ship, etc. The following
information is usually provided:
1. True or relative motion radar presentation.
2. Manual acquisition of contacts with automatic tracking of a selected
number (usually about 20). Automatic acquisition is also available when
contacts come within a specified range in a designated sector.
3. True or relative track and speed vectors of other ships, together with a
prediction of their future positions.
4. Digital read-out on specified targets of track, speed, range, bearing,
closest point of approach (CPA) and time to CPA (TCPA).
5. Automatic visible and audible warnings on targets predicted to come
within a chosen CPA and TCPA.
6. The likely effect on the collision situation of a proposed manoeuver by
one’s own ship.
7. Automatic ground stabilisation for navigational purposes, e.g. pilotage.
8. Selected navigational data.
The principal advantages of ARPA are a reduction in the work load of
bridge personnel and fuller and quicker information on selected targets.
ARPA is not infallible, however, and must be used with caution. ARPA
processes radar information much more rapidly than can be done manually,
but that information is still subject to the same limitations mentioned earlier.
The accuracy from inputs such as the compass and the log governs the
accuracy of the displayed data. Using ARPA, the assessment from radar of
the relative and true tracks of a contact is arrived at quickly, but the errors
inherent in radar are still present. ARPA does not resolve the differences
between the deduced and visual aspects caused by leeway and differing tidal
streams, etc. The data presented are historical, and predictions are usually
based on the assumption that courses and speeds of other ships will be
maintained. Radar contacts can be lost or confused. Weather, especially
clutter, imposes its own limitations.
The use of ARPA in inexpert hands can easily breed a false sense of
security as in such circumstances undue reliance may be placed upon the
accuracy of the displayed data.
SOME RELATIVE VELOCITY PROBLEMS 515

Fig. 17-13. Graticule from Manoeuvring Form (RNS 376) /

516 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

SOME RELATIVE VELOCITY PROBLEMS

A number of simple relative velocity problems and their solutions is given in

the following paragraphs. The conventions of the velocity triangle (Fig. 17-
1) - the three rules set out on page 504 - are followed; and the triangle is
based on own ship’s position, as in Fig. 17-8(b). The examples given are
summarised in Table 17-2.

Table 17-2
EXAMPLE TITLE PAGE
12345 Find the true track and speed of another ship from its below
relative movement
Find the closest point of approach (CPA) 517
Find the course to pass another ship at a given 518
distance
Find the time at which two ships steaming different 519
courses and speeds will be a certain distance apart 520
Open and close on the same bearing

These problems may be solved on radar displays, plotting tables, the

Battenberg Mark 5 Course Indicator, or on plotting sheets such as the
Maneuvering Form (S376), briefly described in Chapter 7 and illustrated in
Fig. 17-13 (page 515).

EXAMPLE 1 Find the true track and speed of another ship from its relative
movement.
Own ship’s (W) course and speed are 020°, 20 knots. The following ranges
and bearings of another ship G are obtained from radar as follows:

TIME BEARING RANGE (MILES)

6.000603e+14 040° 8'.00
038° 6'.65
035° 5'.45
030° 4'.25

What is the true track and speed of the other ship?

In Fig. 17-14 the positions of the echo G, G1, G2, G3 are plotted relative
to own ship W at the centre of the graticule or radar display.
The relative track of the other ship is along GG3, 231°/ Between 0600
and 0609, 9 minutes, the echo has moved from G to G3, a distance of 3'.9.
Thus, the relative speed of G along GG3 is:
3.9
× 60 = 26 knots
9
The velocity triangle may now be constructed to find the other ship’s true
track and speed. WO, own ship’s vector, is drawn in a direction 020°, at a
SOME RELATIVE VELOCITY PROBLEMS 517

Fig. 17-14. Other ship’s true track and speed

distance equivalent to 20 knots. OA, the relative vector is drawn from O in

a direction 231° at a distance equivalent to 26 knots. Vector WA represents
the other ship’s true track and speed (280°, 13.5 knots).
Note how all three rules (page 504) have been followed. WO and WA
diverge; WA and OA converge; WO chases OA.
The true track and speed of the other ship is 280°, 13.5 knots.

EXAMPLE 2 Find the closest point of approach (CPA).

Given the information in Example 1, will ship G pass ahead or astern of own
ship W, by what distance and at what time? How close will she come, at what
time and on what bearing?

Project G’s relative track, G, G1, G2, G3 (Fig. 17-15, page 518), along the
relative course of 231°. This track is seen to pass ahead of own ship and
down the port side. When G is ahead, her bearing will be the same as own
course (020°), and her distance WG4 (2'.95). The distance between G3 and G4
may be measured (1'.4). The time of arrival at G4 at G’s relative speed of 26
knots will be:
14.
0609 + x 60 (minutes) = 0612¼ (to nearest ¼ minute)
26
G’s closest point of approach (CPA) is when she reaches position G5, WG5
being at right angles to G’s relative track (231° + 90° = 321°). Measure WG5
(1'.5).
518 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Fig. 17-15. The closest point of approach (CPA)

The total distance from G to G5 is 7'.8, which takes:

7.8
x 60 = 18 minutes at G's relative speed of 26 knots
26
Ship G will pass ahead 2'.95 at 0612¼ and her closest point of approach
will be on own ship’s port side at 0618 on a bearing of 321° at a distance of
1'.5.

EXAMPLE 3 Find the course to pass another ship at a given distance.

Given the information in Example 1, it is decided to alter course at 0609 to
ensure that ship G passes down the port side, keeping outside 3½ miles. At
the same time G alters course 5° to starboard 285°. What is own ship’s new
course? What is the range, time and bearing of the new CPA?

Develop the relative track GG3 as before (231°, 26 knots; Fig. 17-16).
Own ship needs to alter course at 0609 in such a way that the relative track
of G changes to keep outside 3'.5.
Draw the arc of a circle FK, radius 3'.5, centred on W. G’s relative track
from G3 must be tangential to this circle. Construct the tangent G3H, and
measure the new relative track required (266½°).
Construct the velocity triangle.

1. Draw the other ship’s true track vector WA (285°, 13.5 knots).
2. Through A draw the required relative track parallel to G3H
(266½°&086½°).
SOME RELATIVE VELOCITY PROBLEMS 519

Fig. 17-16. The course to pass at a given distance

3. With centre W and radius representing own speed (20 knots), draw an arc
of a circle cutting the required relative track through A, at O.
4. WO is the new course required at 0609 (074°).
5. Measure G’s new relative speed OA from the speed triangle (32.5 knots).

G’s new CPA is now when she reaches G6 WG6 being at right angles to
G’s new relative track (266½° + 90° = 356½°). Measure G3G6 (2'.35). At the
new relative speed of 32.5 knots, this distance will be covered in
(2.35/32.5)60 = 4¼ minutes (to the nearest ¼ minute), so G will reach G6 at
0613¼.
Own ship’s new course at 0609 is 074°, an alteration of 54° to starboard.
G’s CPA is now 3½ miles at 0613¼ on a bearing of 356½°.

EXAMPLE 4 Find the time at which two ships, steaming different courses and
speeds, will be at a certain distance apart.
Own ship’s (W) course and speed are 000°, 16 knots. Another ship G on
bearing 301°, 15 miles, has a true track 040° at 12 knots. When and on what
bearing will ship G be 5 miles away?
Construct the velocity triangle (Fig. 17-17, p.520).

1. Draw own ship’s vector WO (000°, 16 knots).

2. Draw other ship’s vector WA (040°, 12 knots).
3. Join and measure OA, the relative track and speed of the other ship G
(132°, 10.2 knots).
520 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

Fig. 17-17. The time at which two ships will be a certain distance apart

Plot G’s present position (301°, 15 miles) and draw in her relative track
from this point GH (132°, 10.2 knots).
With centre W and radius 5 miles, draw an arc of a circle cutting GH in
K. Measure GK (10'.5).
When ship G has steamed the relative distance GK (10'.5) at the relative
speed (10.2 knots), she will be 5 miles away from W on a bearing of 277°.
The time taken will be (10.5/10.2)60 = 61¾ minutes (to the nearest ¼ minute).
Ship G will be 5 miles away after 1 hour 1¾ minutes, on a bearing of 277°.

EXAMPLE 5 Close and open on the same bearing

Own ship W (Fig. 17-18) is on course and speed 050°, 20 knots. Another
ship G bears 330°, 8', true track and speed 030°, 15 knots. It is desired to
close to 1 mile to identify ship G, then open out to the previous distance of 8
miles while preserving the bearing. What courses are required to close and
open, and how long will each manoeuver take?

Plot G at 330°, 8'. The courses which own ship W will require to steer
will be those to close on a steady bearing of 330° to a distance of 1 mile, 7
miles in all; then to open on the same steady bearing of 330°, to a distance of
8 miles, a further 7 miles. In other words, G must move to H relative to own
ship, 330°, 1 mile away and then back out again to G.
Construct the velocity triangle.

1. Draw the other ship’s vector WA (030°, 15 knots).

SOME RELATIVE VELOCITY PROBLEMS 521

Fig. 17-18. close and open on the same bearing

2. Through A draw the required relative track, 330° & 150°.

3. From W, strike off an arc of a circle, radius equivalent to own ship speed
of 20 knots, to cut the relative track through A in O and O1.
4. Remembering the rules for the arrows:
OA is the relative track and speed (150°, 7.5 knots) when closing on
a steady bearing.
O1A is the relative track and speed (330°, 22.5 knots) when opening
on a steady bearing.
5. WO is the course to steer (011°) to close ship G on a steady bearing.
6. WO1 is the course to steer (109°) to open from ship G on a steady bearing.

The time to close to 1 mile will be the time to travel 7 miles at a relative
speed of 7.5 knots (OA): (7/7.5)60 = 56 minutes. The time to open again to
8 miles will be the time to travel 7 miles at a relative speed of 22.5 knots
(O1A):
(7/22.5)60 = 19 minutes (to the nearest minute).

The course required to close to 1 mile is 011°, time taken 56 minutes.

The course required to open to 8 miles is 109°, time taken 19 minutes.
 522 CHAPTER 17 - RELATIVE VELOCITY AND COLLISION AVOIDANCE

/ INTENTIONALLY BLANK
 523

CHAPTER 18
Surveying

Many Admiralty charts are to this day compiled from the sketch surveys of
the last century, and the Hydrographer is dependent on many and varied
sources of information in his endeavours to keep charts up to date.
Opportunities often exist during the various passages and visits of HM Ships
for valuable data to be collected and forwarded to the Hydrographic
Department. Commanding Officers should, however, be careful to respect
the territorial seas of foreign states and must obtain diplomatic clearance
before embarking on anything which might be construed as surveying.
Guidance can be found in General Instructions for Hydrographic Surveyors
0534, 0752 and 0803.
The purpose of this chapter is to explain to navigating officers of HM
Ships how to carry out various kinds of hydrographic surveying work. The
methods described have been kept as simple as possible, bearing in mind the
limited resources generally available. The chapter starts with a discussion of
those items of surveying work which the Navigating Officer may be required
to undertake within a relatively short time scale. It concludes with some
remarks on conducting a complete minor survey, should he have the
opportunity and time, in an unsurveyed or poorly charted area.
It should be appreciated that hydrographic surveying is neither a
mysterious nor very complicated art and that a lot of valuable work can be
done by Navigating Officers with the relatively simple equipment to be found
in any HM Ship.
Whatever is attempted, it is important that the work itself and the records
later rendered to the Hydrographic Department should be honest and
complete. Details of just how the work was done, what accuracy is judged
to have been attained and what mistakes and omissions were made is vital if
the survey is to earn its place as a worthwhile contribution to the Admiralty
chart of the area. Lack of information on how the work was carried out can
often lead to the discarding of work which might be sound, because it cannot
be checked.
It is important to consider the cartographer who has the task of fitting the
new survey to existing work. The more information that is rendered
concerning scale, orientation and position, the easier it is to evaluate the work
and insert it in its correct position on the chart. A survey may be an example
of superb draughtsmanship and look to be of impeccable accuracy, but at the
same time be virtually useless through lack of essential ‘fitting-on’ data.
Full instructions and advice on carrying out a survey may be found in the
Admiralty Manual of Hydrographic Surveying (AMHS), Volumes I and II,
524 CHAPTER 18-SURVEYING

and the General Instructions for Hydrographic Surveyors (GIHS), to which

frequent reference will be made in the pages that follow. However, both of
these publications may be somewhat forbidding to the non-professional and
an attempt is made here to reduce the various surveying processes to their
simplest terms. AMHS and GIHS are issued to HM Ships as part of their
complete set of navigational publications and may also be purchased from
Admiralty Chart Agents. Advice on rendering hydrographic notes may be
found in Chapter 6.

Types of surveying work

Types of surveying work which lie within the capability of non-surveying
HM Ships are listed below. Those which the Navigating Officer is more
likely to find himself tackling are given first. The guidance on conducting a
minor survey is put last, as the length of time it is likely to take, several days
or up to a week, is not often likely to be available. Despite the listed order,
the reader may find it helpful to read the last item first, as he will acquire a
better understanding of the fundamental principles of surveying on which all
the others depend. The pages which deal with them are given in brackets.

1. Passage sounding (below).

2. Fixing new navigational marks and dangers (below).
3. Disaster relief surveys (page 525).
4. Information on new port installations (page 526).
5. Running surveys (page 527).
6. Searches for reported dangers (page 529).
7. Tidal stream observations (page 530).
8. A complete minor survey (page 532).

It should always be borne in mind that, with hydrographic notes, disaster

relief surveys, running surveys or area surveys, any information however
limited is better than none. Even such brief statements as ‘Harbour
developments have made Chart ... out of date’, or ‘Chimney (conspic) could
not be seen’ are useful, as they prompt the Hydrographer to write to the Port
Authority concerned to seek more detailed information.

PASSAGE SOUNDING

Whenever ships are on a steady passage, particularly outside the Continental

shelf but also in coastal waters which appear poorly charted, they should take
every opportunity to obtain continuous lines of passage sounding. Guidance
and instructions may be found in AMHS, Volume II, Chapter 3; GIHS; The
Mariner’s Handbook and Fleet Operating Orders. A high quality of passage
sounding data is now possible with the introduction of deep echo-sounders
and improved worldwide radio aids such as Omega and SATNAV.

FIXING NEW NAVIGATIONAL MARKS AND DANGERS

There are two main methods of fixing navigational marks and dangers:
intersection and resection. Circumstances may dictate the use of one or the
other, but intersection is preferred as being inherently the more accurate and
easier to check.
DISASTER RELIEF SURVEYS 525

To fix an object by intersection, observations, which may be angles by

sextant, bearings by compass or ranges by radar, are made from fixed
positions into the object. For resection the observations are made at the
object to the fixed.
The fixed position from which an intersecting shot is taken may be the
bridge of the ship or a boat, in which case the ship or boat must be fixed
simultaneously with the observation of the shot. Best of all, the ship or boat
should be fixed by horizontal sextant angles to shore marks with the object
to be fixed in transit with a charted mark. This procedure should be repeated
until at least three shots with different transits and a good cut have been
obtained, and the fixes and shooting up angles can be plotted with station
pointers to fix the object. If suitable transits cannot be found, the intersecting
shot should be the sextant angle between one of the fix marks (preferably the
centre to facilitate plotting with station pointers) and the object to be fixed.
Alternatively, but with less accuracy, the fix and intersecting shot can be
obtained by gyro bearings and/or radar ranges. Similarly, the intersecting
shot may be observed from ashore using a sextant or hand bearing compass
from a well defined charted object such as a beacon or breakwater head.
Resection implies the accessibility, for ship, boat or man, of the object to
be fixed. This method is often suitable for fixing a buoy. A boat is taken
alongside the buoy and the position fixed by horizontal sextant angles. A
new beacon on a jetty may be fixed by the observer standing alongside it and
taking a sextant fix. In every case, a check angle to a fourth mark must be
obtained in addition to the main fix and plotted with the fix to guard against
errors.
Buoys should be fixed on both ebb and flood and a mean position
accepted.
An underwater danger must be fixed either by resection, with the ship or
boat on top of the danger; or by intersection, the danger having been marked
with a dan or pellet, possibly laid by diver.

DISASTER RELIEF SURVEYS

From time to time, earthquakes, tidal waves and hurricanes cause

considerable damage to ports and anchorages. Navigational marks may have
been destroyed or displaced; berths and jetties severely damaged; and the
whole topography of the sea-bed may undergo considerable change with
consequential alterations in the depths. HM Ships sent to the area to afford
relief may well therefore find themselves carrying out essential surveys. This
work may involve any of the following:

1. Helping to erect and establish the position of fresh navigational marks,

e.g. beacons, leading marks, etc.; establishing any errors in position of
buoys and other floating navigational aids.
2. The sounding out of approach channels, recommended tracks and leading
lines for differences in depths from those charted, especially along leads
and over bars. It may even be necessary to try to establish alternative
approaches, setting up fresh leading marks, etc.
3. Sounding out anchorages.
4. The charting of new wrecks and other dangers to navigation which may
be encountered (see GIHS).
526 CHAPTER 18-SURVEYING

5. Amendments to the Admiralty Sailing Directions, together with views

and photographs.

Whatever the particular need, which can only be decided by the

Navigating Officer on the spot, the general surveying principles set out
elsewhere in this chapter will apply.

Reporting new dangers

It is of paramount importance that any new danger to navigation is reported
without delay. This may be done by signal and followed up with a
hydrographic note (Form H102 or H102A, see Chapter 6). Such reports
should also include errors in the position of floating navigational aids, and
lights which are unlit or whose charted or listed characteristics appear to be
in error.

INFORMATION ON NEW PORT INSTALLATIONS

The following information should normally be obtained on new jetties and

wharves.
1. Dimensions.
2. Height (above chart datum or MHWS).
3. Orientation.
4. Depth alongside and at 5, 10 and 20 metres off.
5. Type of construction.
6. Particular berthing and mooring arrangements (e.g. dolphins).
7. Boat landings.
8. Cranes and other facilities.

Sounding out a berth alongside a jetty

A suitable scale for this type of work is about 1:1000 (1 cm to 10 m). If the
jetty is charted on a large scale, its position and orientation may be taken
from the chart. If it is not charted, its position and orientation must be fixed
in the field with reference to the largest scale chart available.

Fig. 18-1. Sounding out a berth alongside a jetty

RUNNING SURVEYS 527

The survey procedure (Fig. 18-1) is as follows:

1. Establish a datum line parallel to the line of the jetty and far enough back
to provide sensitive transits.
2. Paint marks at 5 metre intervals along the datum line with whitewash or
white emulsion. Make similar marks on the face of the jetty, to form
transits with the marks on the datum line at right angles to the line of the
jetty.
3. Additional marks to provide transits for lines around the corner of the
jetty may also be required.
4. Poles or flags are placed or held on the white marks to enable the transits
to be seen while sounding each line.
5. Soundings should be taken alongside and at 5, 10 and 20 metres off. This
work is most easily done in a small dinghy at or near high water, when
the tidal stream is slack. The distance of the leadsman from the face of
the jetty may be obtained by distance line.
6. A line of soundings parallel with the jetty and about 3 metres off should
be run, to ensure that no underwater obstructions exist which might foul
a ship’s bilge keels or propellers.
7. If shoal depths are found in the vicinity of the berth, sounding lines
should be run parallel to the line of the berth to indicate how far these
extend.
8. Details such as cranes, bollards, sheds, railway lines, etc. should be
included on the plan, if time permits.

RUNNING SURVEYS

A running survey, as the name implies, is carried out whilst a ship is on

passage along a coast and does not require the ship to slow down or stop.
The technique can be practised on any coastal passage in well charted waters,
so that the team is worked up should the need for a running survey arise later.
In a running survey, the scale, orientation and geographical position
(page 533) are provided by the ship’s track fixed by the most accurate means
available. It is preferable to fix the ship at the beginning and end of the run
and, if possible, regularly in between, by some means independent of the
adjacent coast that is to be fixed. Ideal for this purpose is any suitable radio
aid (e.g. SATNAV) or, if none is available, astronomical fixes. If the latter
are used, however, at least three reliable observers should obtain the best
agreement possible.
If the run is fixed at each end, scale and orientation for the survey are
provided by the adjusted fair track between fixes. If only one fix can be
obtained, scale and orientation are provided by ‘fixing’ by range and bearing
off one well defined mark ashore. Even if the geographical position of this
mark is unknown, it will provide a stationary reference point from which the
ship’s ground track can be found and plotted. Alternatively, scale and
orientation can be provided less accurately by the water track derived from
log, compass and leeway. It will help if the ship’s course and speed are kept
as steady as possible during a running survey.
The remainder of the running survey procedure is standard, regardless of
the means used to find the ship’s track. DR stations are established at regular
intervals of about 10 minutes and selected objects ashore are ‘shot up’ using
528 CHAPTER 18-SURVEYING

gyro, sextant and radar. The objects selected should be those which best
define the coastline, such as headlands, river mouths, etc., off-lying islands
and rocks, and any useful marks for navigation such as prominent peaks,
buildings and conspicuous natural features.
To minimise ‘cocked hats’ at the shore objects being fixed, it is important
that all observations should be made simultaneously at the instant of the DR
station or, at the most, a few seconds either side. The use of several observers
and recorders will make this easier.
The best way of recording radar data at the stations is by photographing
the radar display. Ideally, range rings should be switched on and, if fitted, the
bearing marker should be pre-set to a fixed bearing, e.g. north; if not, the
ship’s head marker should be used to orient the picture. In the latter case, the
ship’s head should be noted at the instant of each fix, as the radar display
bearing graduations do not always show up well in a photograph. It is
advisable to construct a simple jig of wood or Dexion strip to hold the camera
square to the face of the display and properly centred. This avoids distortion
of the picture and ensures consistency between photographs. Later, ranges
can be read off the photographs by interpolation between the range rings and
bearings read off, by aligning a protractor with the bearing marker or ship’s
head marker. Once the salient points of the coastline have been fixed, the
radar picture can be of great assistance in filling in the shape of the coast in
between.
The scale chosen should be not larger than 1:100,000 or about 18 mm to
a sea mile as, even at this scale, inaccuracies will be very apparent in the plot.
In addition to the observations mentioned above, the ship should run a
line of soundings and obtain photographic views at intervals along the run
(see NP 140).
It is important that all instruments and equipment used (gyro, sextants,
radar, echo sounder, etc.) are calibrated before and after the run.
Fig. 18-2 shows how, in the course of about 1½ hours, an inadequately
charted coastline of about 8 miles could be improved.
At 0800 the ship is fixed by radio aid and simultaneously fixes the
lighthouse by radar range and visual bearing. The ship is then fixed by range
and bearing of the lighthouse (fixes 2 to 15) at 6 minute intervals.
Numerous sextant angles and gyro bearings are taken into the selected
objects ashore, either at these fixes or, to relieve congestion on the gyro, at
accurately plotted DR stations in between. Observations at each station must
be simultaneous or may be taken at accurately timed points and plotted from
the DR between the fixes.
Photographs of the radar display, soundings and photographic views are
also obtained throughout the run. If possible, the aim should be to obtain at
least five shots into each object.
One of the greatest difficulties experienced is that of identifying the
objects consistently as the aspect of the coastline changes with the ship’s
movement along it; a methodical approach to the recording is necessary to
avoid muddle.
If there is no reliable charted object for a fix, such as the light in Fig. 18-
2, the best object available should be chosen instead, e.g. islet A. This should
be fixed as soon as possible, its geographical position being based on the
ship’s position which has been found by astronomical observations or radio aid
SEARCHES FOR REPORTED DANGERS 529

Fig. 18-2. A running survey

(e.g. SATNAV). Islet A would now be used as the datum for subsequent
fixes.
As the ship proceeds along the coast, it is possible to ‘hop’ from one
datum to another, for example from islet A to mosque B, at the same time
endeavouring to establish the ship’s geographical position by other means.
If it is not possible to establish the geographical position in this way, the EP
will have to be used, but it should be remembered that this will become
progressively more inaccurate as the distance increases from the last fix. The
process of ‘hopping’ from one datum to the next may be used on a long
stretch of coast, but it is essential to tie in the ship’s track to a geographical
position at each end of the run.
A full report of survey should be forwarded to the Hydrographer,
describing the methods used, assumptions made and results achieved.
If the scale of the published chart is suitable, the survey should be
forwarded as a tracing to fit the chart; alternatively, a tracing on a selected
scale should be prepared with sufficient graduations to permit accurate
comparison with Hydrographic Office records.

SEARCHES FOR REPORTED DANGERS

A brief study of Admiralty charts will reveal many reported dangers or shoal
soundings. Many of them prove to be false and may not be dangerous to
surface navigation. The Hydrographer is obliged to chart them even though
the evidence for their existence may be poor, but they can only be removed,
or be more positively charted, after a systematic search has been carried out
by a ship whose navigation can be relied upon.
A search out of sight of land is best conducted on an automatic plotting
table provided the log is accurately calibrated. A scale of about 10 cm to
530 CHAPTER 18-SURVEYING

1 mile is generally adequate and the search should usually cover about 100
square miles.
The depth of water governs the distance apart of the lines of soundings,
which should be spaced in accordance with the following rough rules:

general depths of 4000 m 4 miles apart

general depths of 2000 m 1 mile apart
general depths of 1000 m ¼ mile apart

The search track must invariably be adjusted between star sights or other
reliable fixes by radio aid.
If the soundings indicate shoaling, additional lines of sounding should be
run to establish the least depth. If possible, an up and down wire sounding
should also be taken over the shoalest part to guard against false echoes.
Sonar and a helicopter greatly enhance the value of a negative report and
may also contribute to the safety of one’s own ship. A good visual look out
with polaroid sunglasses should also be maintained.
Fuller guidance may be found in AMHS, Volume II, Chapter 3 and GIHS.

TIDAL STREAM OBSERVATIONS

It is normally only practicable to observe tidal streams over a limited period.

In the waters around the British Isles and in other areas where the tide is
predominantly semi-diurnal, a single observation period of 25 hours at
springs is usually enough. In areas where the diurnal inequality is large, a
period of 49 hours during large tides is to be preferred. If this is not possible,
sufficient measurements should be obtained to enable a description to be
inserted in the Sailing Directions and tidal stream arrows to be shown on the chart.
Where the tidal stream is very strong, the method described below will
be unsuitable but, at the very least, if the times of slack water and the
direction from and to which the stream is changing are reported, a valuable
contribution will have been made.

Pole current log

A pole current log should be used to measure tidal stream rates. The pole
should be weighted at the base so as to float vertically with about 45
centimetres above water, the base being at a depth appropriate to the average
draught of shipping using the area. A small light or reflector should be
attached for night observation.
A hole should be drilled through the pole at the waterline so that the
current line may be attached. This may consist of any small buoyant line,
well stretched, and marked with coloured bunting every 3 metres, starting
about 15 metres away from the log to allow it to be well clear of the ship
before observations start (Fig. 18-3).
The log is streamed from the stern. A relative bearing plate or gyro
repeat will be required to observe the direction of the pole and so deduce the
direction of the stream.
TIDAL STREAM OBSERVATIONS 531

Fig. 18-3. Plotting tidal stream data

532 CHAPTER 18-SURVEYING

Observing procedure
Allow the current line to run out to the first mark (15 metres approx.) and
start the watch as the first mark passes outboard. The line is allowed to run
for 2 minutes, or 1 minute if the stream is more than 2½ knots. when the time
is up, the direction of the log and the distance run are noted. The log is then
handed, and a further observation taken 1 hour later, and so on until the total
time is up.
The rate of the tidal stream may be deduced from the formula:
30.9 m/min = 1 knot . . . 18.1
Recording
The following is an example of the record of observations kept. Note that the
time zone used must be recorded.

RELATIVE TRUE
LINE DIRECTION SHIPS HEAD DIRECTION
ZONE
RUN MINUTES OF POLE AT OF POLE AT
TIME
OUT
START FINISH START FINISH START FINISH

1300(A) 130 m 2 R175° G170° 021° 025° 206° 195°

The calculation of the rate and direction of the stream from the above data
is best made graphically on a large-scale plotting sheet or Manoeuvring Form
(S376) and is illustrated in Fig. 18-3.
The position of the anchor is plotted at the centre of the plotting sheet
from which the stern swinging circle (Chapter 14) is plotted. The position
of the stern relative to the anchor and the position of the pole are plotted at
the start and finish of the run. The direction and rate of the tidal stream may
now be calculated. Do not forget to make an allowance for the length of the
stray line when plotting both the start and finish positions.
For the above data, the calculated tidal stream at 1300 is 202°, 2knots.

A COMPLETE MINOR SURVEY

Principles of surveying
The pages that follow describe how a full survey may be conducted with
limited equipment, time and resources. They start with first principles and
should enable the navigator to produce a passable survey of a small area even
in the unlikely event of him finding himself in a totally uncharted and
unmapped part of the world. Almost always, in practice, there will be at least
a chart of the area and, depending on its scale, date of publication and
reliability, there will be one or more of the basic elements of control
mentioned below which can be taken from it.
Control
A hydrographic survey has to present a three-dimensional picture on a two-
dimensional piece of paper.
A COMPLETE MINOR SURVEY 533

In the horizontal dimension all plotted features shown must be:

1. The correct shape; that is, outline features such as islands, bays and
contours must be the correct shape and point features such as depths,
beacons and buoys must be in the correct angular relation to each other.
2. The correct size or distance apart, in accordance with the stated scale of
the survey.
3. In the correct orientation relative to true north.
4. In the correct geographical position in terms of latitude and longitude
and relative to adjacent land masses and existing charts.
These four elements&shape, scale, orientation and geographical
position&form the horizontal control of a survey and permit construction of
a framework of fixed points to which the detail such as soundings, coastline
and topography can be added.
Vertical control is the process whereby depths and heights are referred
to the appropriate vertical datums.

Horizontal control
There are several methods of controlling the shape of the survey, but the one
described here as being most suitable for a navigator carrying out a minor
survey with limited equipment is the classical method of triangulation
(Fig. 18-8, page 543). It relies on the fact that, if the three angles of a triangle
are known, that triangle can only be plotted in one shape. In addition, the
other three requirements of scale, orientation and geographical position are
satisfied if the length and true bearing of one side and the geographical
position of one of the points of the triangle are known. Triangulation takes
advantage of the inherent check that the three angles of a plane triangle sum
to 180° exactly.

Triangulation
To establish the framework to which the survey detail will be added, the
navigator must first simplify. From the irregular coastline and topography he
sees before him, he must select a number of triangulation stations, the lines
of sight between them forming a series of rigidly defined geometric figures
based on the triangle. Having established his main framework of relatively
few stations, he then fixes more stations from these, called sounding marks,
until he has a sufficiently dense network of control points from which his
sounding boat can be fixed and from which a shore party can fix the detail of
the coastline and topography.
The regular methods of triangulation and the elaborate adjustment of the
observations described in AMHS, Volume I cannot be carried out thoroughly
unless ample time and a full equipment of surveying instruments are
available. As a rule, the navigator will measure all angles with a sextant and,
in the small surveys with which he is generally concerned, he should reduce
his system of triangulation to the simplest possible form. For this type of
survey the following points should be noted:

1. The triangulation scheme should as nearly as possible enclose the area to

be surveyed and the positions of the sounding marks. This conforms with
one of the fundamental principles of surveying&that of working from the
534 CHAPTER 18-SURVEYING

whole to the part. By working inwards from the outer framework, errors
are diminished rather than exaggerated.
2. Providing (1) above is observed, the number of triangulation stations
should be the least that will provide an adequate framework to cover the
area to be surveyed. For a small anchorage or harbour, half a dozen
stations should suffice. From these it should be possible to ‘shoot up’
any additional marks required for fixing the soundings and topography.

3. The stations should be grouped so as to form quadrilaterals or polygons

with central stations. By so doing, each will be connected by at least
three shots from adjacent points, and a check is provided against errors
of observation and plotting.
4. The stations should be sited so that most of them are intervisible, and
certainly the three stations forming any one triangle should see each
other.
5. The shots fixing each station should intersect at a strong angle of cut.
6. Natural marks should be used as far as possible, and efforts should be
made to include in the triangulation a selection of well defined points
already shown on the chart. This will greatly assist the cartographer
when he has to incorporate the new survey in existing charted material.
7. The angles of the triangulation should be measured in the horizontal
plane. It may not be possible to site all the stations at about the same
level, but it should be remembered that, if the subtended angle between
two objects is in the region of 90°, the error due to differing elevations
is reduced to a minimum (see page 541 and AMHS, Volume I).

Scale
The choice of scale should be governed by the complexity of the area, the
irregularity of the sea-bed, and the type and size of vessel likely to use the
area. A more complex area requiring more detailed survey will call for a
larger scale. If a large-scale chart of plan of the area already exists, it may
well be advisable to use the same scale. In any case, a study of the chart
folios held on board will help determine a suitable scale for a given type of area.
As a general guide a suitable scale for a coastal survey might be 1:50,000;
for an anchorage or small bay 1:25,000; and for detailed work in a harbour
1:10,000 or even larger. For these large scales, much skill and very careful
observations are needed to ensure accurate results, and the inexperienced
surveyor will be well advised to think very carefully before undertaking any
such work. The larger the scale, the longer the work will take. As a rough
guide, doubling the scale trebles the time.
In choosing a scale, it is also necessary to consider the instruments
available for plotting. Large sheets can be plotted with accuracy only if metal
scales, straight edges and beam compasses are used. If the plot has to be
made entirely with station pointers, the scale should be such that the marks
of the survey are all contained within a sheet of moderate size, say about 15
inches square.
In the absence of a metal scale, there is no exact method of measuring
distances on the paper and the natural scale can only be approximate.
However, the relative positions of every point on the survey can be correctly
plotted and the true scale can be worked out afterwards, provided the length
in metres of one or more of the sides of the triangulation is stated.
A COMPLETE MINOR SURVEY 535

The base line

All surveys depend on a ‘base’ for scale, and this base must be measured as
accurately as possible. There are various methods by which the base line may
be obtained.

1. The published chart

Sometimes it is possible to use the distance on the published chart
between two identifiable objects, thereby providing the scale, orientation
and geographical position in one operation.
It will be seldom, however, that the published chart is on a large
enough scale for a new survey, and the distance obtained will have to be
doubled or trebled. To do this, prick-off the charted length on to the
plotting sheet, draw a fine line through the points on the sheet and extend
it well either side of them; equal distances can then be stepped off to the
left and right of the original two points as required to double or treble its
length. This method is considerably more accurate with limited
equipment than measuring the length on the chart on the distance scale,
multiplying the distance by 2 or 3, and then re-converting into a plotting
distance.
2. Taped base
A base line may be taped out along the ground provided the ground is
reasonably flat. The base length should be at least 300 m over flat
ground&a jetty is ideal. A number of poles may have to be set up in
transit, so that the various fleets of the tape are all in a straight line.
The base should be measured at least once in each direction and the
measurements should agree to within 15 cm. Any discrepancy should be
noted for subsequent inclusion in data rendered at the end of the survey.
A base even 300 m long will only plot 12 mm long at 1:25,000, and
this is too short if the rest of the triangulation is to be plotted by angles
alone as scale error will increase as the plot progresses away from the
base. The measured base must therefore be incorporated into the
triangulation by what is called the base extension, so that the longest side
can be calculated through the successive triangles using the sine formula.
The triangulation can then be plotted from the longest side as described
on pages 542 to 543. The principles and some suitable layouts for base
extension triangulation may be found in AMHS, Volume I. Fig. 18-5 (p.
536) is a simple example of base extension using an even shorter
measured distance.
3. Radar base
Longer bases can be measured by carefully calibrated radar with
reasonable accuracy, providing the marks chosen as targets give a well
defined radar response and that the ship is so tightly moored as to provide
unfluctuating ranges during the period of measurement. The angles
between the marks and the ship must be measured at the same time,
preferably with a sextant, to permit calculation of the triangle involved,
as shown in Fig. 18-4 (p. 536). To avoid parallax, it is important that the
observer’s sextant be as near vertically below the radar aerial as possible
and that the observers ashore use the centre of the aerial as their mark.
536 CHAPTER 18-SURVEYING

Fig. 18-4. Determination of the base length by radar

Fig. 18-5. Determination of the base length by the subtense method

4. Subtense method
If it is impossible to measure a long enough base because of the rugged
nature of the ground, the subtense method (Fig. 18-5) may be used as
follows, DC being the measured distance.

If the distance AB is required, find a point D about midway between A

and B, lay out DC at right angles to AB and measure DC and the angles a and
b. Then, by plane geometry:

AB = DC (cot a + cot b) . . . 18.2

AD and DB should not be more than about 7 times the length DC and the
small angles a and b should be very carefully observed and plumbed directly
over the marks. Observations with a number of different sextants should be
taken if possible.

Orientation
The true bearing of one of the sides of the triangulation must be determined
in order to orient the whole triangulation scheme. This can be done in one of
the following ways:

1. From an existing large-scale chart or plan. Measure the angle between

the base line or another side in the triangulation and a meridian of the
chart, using the most accurate station pointers available.
2. By observing the angle subtended at one end of the line between the other
end of the line and low altitude sun or stars. Accurate times must be
A COMPLETE MINOR SURVEY 537

noted and the mean of several observations accepted. Sun or stars should
be at an altitude of 10° to 30°, and the angle between the other end of the
line and the sun or star as near as possible to 90°. An accuracy of ± 5'
should be aimed at (AMHS, Volume I).
3. By observing along the line from both ends with as accurate a magnetic
compass as available and then correcting for variation and accepting the
mean.
4. By reference to a distant charted object. Take a bearing from the chart
between an identifiable point in the survey area to another well charted
point which may or may not lie in the survey area. For example, in Fig.
18-6 point A is a beacon in the survey area, shown also on the published
chart; point X is a well defined hill summit some miles up the coast, also
charted. The bearing A to X may be taken from the chart, the angle XAB
observed by sextant, and hence the true bearing of the line AB deduced.
The angle XAB should be as close to 90° as possible to avoid errors due
to unequal elevation of the marks.

Fig. 18-6. Orientation of the base line

5. By ship’s compass.
(a) Take a round of compass bearings to the various marks of the survey
from the ship at anchor. Plot the bearings, radiating from a point, on
a piece of tracing paper and obtain the best fit by sliding the tracing
paper over the plotting sheet. Having obtained a position of the ship
relative to the marks, a meridian may be drawn on the plot. The
bearings must be obtained quickly as well as accurately, as the ship
may move appreciably about her anchor.
(b) If two of the plotted marks of the survey are so situated that the ship
can be placed on the transit, the gyro bearing of one from the other
538 CHAPTER 18-SURVEYING

can easily be obtained. The gyro error should be found as close to the
time of observation as possible.

Geographical position
Before the cartographer can incorporate a survey on to the published chart,
he needs to have a means of fitting it on in the right place. Where a survey
is close to the coast, its geographical position is best defined by fitting-on
points. At least two, and preferably more, points should be chosen that are
common to the survey and the largest scale suitable chart. Any well charted
objects such as lighthouses, beacons, church towers, well defined peaks or
points of land may be used. The points should be as widely spaced on paper
as possible, ideally spanning the field work of the survey. If, as could happen
on a featureless desert coast, suitable fitting-on points are not available,
geographical position will have to be observed independently. Depending on
how the ship is fitted, SATNAV, long-range electronic position fixing
systems or astronomical observations may be used. Whichever method is
used, the ship must be fixed relative to a mark or marks of the survey
simultaneously with the observations. In the case of a SATNAV fix, where
the time of fix is not known until after the pass, the ship must be anchored
and fixed at frequent intervals during the pass so that the fix closest in time
to the SATNAV time of fix can be used.

Vertical control
A hydrographic survey shows detail in three dimensions. Not only does it
show the position of land and water features but it also gives the depth of
water and the height of lighthouses and hills.
Soundings are reduced to chart datum; whichever soundings are being
obtained, a record of the height of tide above chart datum must be kept so that
the soundings can be reduced by the height of tide at the time (see page 548).
The elevation of rocks and banks which dry at low water but cover at high
water is measured above chart datum.
Heights are referred to Mean High Water spring (MHWS) (or Mean
Higher High Water (MHHW) where the tide is mainly diurnal).
The method of establishing chart datum in the survey area is given below
(page 550).

The practical survey

Survey equipment
The items of equipment listed below should all be available to the navigating
Officer of an HM Ship, or capable of being made on board. If he has
sufficient notice of the opportunity or requirement to carry out a survey, it is
possible that the Hydrographic Department at Taunton or any surveying ship
may be able to assist with such items as surveying sextants, steel tapes,
portable echo sounders or modern plastic drawing materials and instruments.
Depending on the circumstances, some items may not be needed. For
instance, if a base length is derived from the existing chart, there is no need for
steel tapes.
A COMPLETE MINOR SURVEY 539

The following is a list of equipment likely to be required:

1. Sextants: two or more, preferably fitted with star or surveying telescopes.
2. A device for measuring distance on the ground. Steel tapes are ideal but
linen tapes are not recommended, as they are liable to stretch perhaps by
as much as 15 cm in 15 m. A very serviceable steel ‘tape’ may be made
from a 30 m length of small diameter wire accurately measured against
an engineer’s steel tape on board before starting the survey and again on
completion.
3. A straight edge and a measuring scale for plotting the work. An
engineer’s steel rule is quite adequate, as the average length of line to be
measured will not generally exceed 300 mm.
4. An accurate magnetic pocket compass.
5. Station pointers. These should be graduated in minutes of arc, for
plotting the fixes when sounding, etc. and also for plotting angles when
laying down the framework or triangulation of the survey (AMHS,
Volume II, Chapter 3).
6. Douglas protractors.
7. Lead lines: one for each boat. These may be made up on board,
preferably fitted with a wire heart, and marked in metres or fathoms and
feet depending on the units required. Lead lines should be calibrated
before and after sounding when wet, and corrections for stretch made if
necessary. Bearing-off spars or boat-hook staves may also be marked off
for use in shallow water (AMHS, Volume II, Chapter 3).
8. Tide pole. This should be marked off in metres or feet dependent on the
units of soundings required (page 549 and AMHS, Volume II, Chapter 2).
9. Ten-foot poles. Two or three poles 10 feet in length may be required for
measuring short distances (AMHS, Volume I).
10. Materials for marks ashore. Flags, bunting, boat-hook staves, whitewash
or white emulsion, guys, stakes, etc. (AMHS, Volume II, Chapter 1).
11. A pair of sounding boards. Any flat drawing board mounted with
suitable paper will suffice.
12. One plotting sheet made of thick paper, for example the back of a clean,
flat, cancelled chart. Do not use tracing cloth, as it is liable to become
distorted.
13. Appropriate sounding and field books. Any conveniently sized
Stationery Office note book will suffice.
14. Admiralty Manual of Hydrographic Surveying, Volumes I and II.
15. General Instructions for Hydrographic Surveyors.

Reconnaissance and planning

Plan on the largest scale chart or map available. If there is a Land Survey
Office interested in the area, they will probably be able to supply maps and
other data; they may be able to provide an easily recoverable base for the
survey. If no adequate chart or map exists, a quick reconnaissance may be
worth while to help in the planning of the triangulation. This can usually be
done with sufficient accuracy in a few hours by sketches from ship or boat
stations with the aid of compass and radar. If a helicopter is available, a most
thorough reconnaissance of the area can be quickly obtained together with all-
540 CHAPTER 18-SURVEYING

round oblique photographs from which to plan later. Natural objects, suitable
for inclusion in the triangulation, should be picked out. The best site for a
base and the method of measurement must be decided upon, and also the most
suitable scale.

Marking (AMHS, Volume II, Chapter 1)

For shore marks, white-painted marks or boat-hook staves with flags will,
with the help of natural objects, fulfil most of the requirements of a small
survey. Floating marks are sometimes useful for fixing, particularly as a
centre object when coastlining, and a boat on a taut moor, or a dan buoy, can
often be used to advantage if the scale is not too large. A floating beacon can
easily be improvised using 40 gallon oil drums.
The siting of marks requires a good deal of thought if their numbers are
to be kept within reasonable limits. They must be designed to provide a good
fix at any part of the survey; generally speaking, marks about every 50 to 100
millimetres on paper are desirable. Some marks sited inland can enable a
boat to fix right up to the beach, but remember that the marks used in a fix
should be at approximately the same elevation and as close to water level as
possible.
Before finally deciding where to place marks, refer back to the section on
triangulation (page 533) and AMHS, Volume I.

Observing
Having erected or selected all the marks for both triangulation and sounding
marks, the next step is to observe all the angles of the main triangulation and
those to sounding marks by sextant.
All the angles of the triangulation forming a series of triangles must be
observed wherever possible. If, for some reason, it is not possible to observe
one angle of a triangle, it can be derived by subtracting the sum of the other
two from 180°, but this is not recommended because there is no check on the
accuracy of the angles observed.
The observed angles of any triangle add up to 180° if there is no error of
observation; as a general rule, a triangle should be re-observed if it does not
close within 5'. When observing it is most important that the observer’s eye
should be exactly over the triangulation station. It is also most important that
boat-hook staves carrying flags should be perfectly upright. Most errors of
observation are due to the non-observance of these points.
It follows that an object like a church steeple is not suitable as a main
station but is better fixed as a sounding mark by intersection (page 525). A
church tower, however, with a flat roof, on which an observer can occupy a
station, can be excellent providing there is a precise target such as a flagpole
for shots into the tower from other stations.
The marks of a survey are seldom at the same height and therefore the
angles measured are seldom truly horizontal. For example, if one mark is 4°
above the horizon and the other is on the horizon, and the true horizontal
angle between them is 40°, the angle between them will be 40°10'. This is
termed a ‘cocked-up’ angle. The true horizontal angle maybe obtained from
the cocked-up angle by the following formula (AMHS, Volume I):
A COMPLETE MINOR SURVEY 541

cos true horizontal angle = cos angular distance x sec apparent altitude
. . . 18.3

The error is zero if the angular distance between the two marks is 90°.
Angles should be observed to the nearest ½ minute of arc.
Observed angles at a mark must be consistent with each other; e.g. the
angle at A between B and C (Fig. 18-7 below) added to the angle between C
and D must equal the angle between B and D. Check this before leaving the
mark.

Use of the sine formula

Fig. 18-7 shows a quadrilateral in which the eight angles at A, B, C and D
have been observed by sextant and the length of the side AB is known. In the
triangle ABD the lengths of AD and BD may be found from the sine formula:

AB AD BD
= =
sin ADB sin ABD sin BAD
AB sin ABD
i.e. AD =
sin ADB
AB sin BAD
and BD =
sin ADB
Similarly, once BD is known, the other two sides BC and CD in the
triangle BCD may be found.

Fig. 18-7. Triangulation

542 CHAPTER 18-SURVEYING

Calculation of the longest side

In the type of survey being considered here, the observed angles are plotted
straight on to paper to form the triangulation rather than by computing the
rectangular co-ordinates of stations and plotting on a grid. In order to
minimise errors of plotting, the plot must start with the longest side.
Depending on the method of base measurement used, the measured base may
or may not be the longest side. If it can be so arranged, so much the better
but, if the base is measured by tape, it is unlikely to be longer than about 400
metres, which will only plot at 16 mm at 1:25,000 or 40 mm at 1:10,000.
In most cases, therefore, it will be necessary to calculate the length of the
longest side from the measured base through the triangulation using the sine
formula (page 541 above).
Fig. 18-8 (opposite) represents a small harbour triangulation. At each of
the five main stations, sextant angles between all the other four have been
observed. A check has been made in the field that each of the ten component
triangles sums to within 5' of 180° and any rogue angles have been re-
observed.
AB is the base whose length has been measured, or calculated from a
shorter measured base through a base extension scheme (pages 535-6), and
whose true bearing has been found by one of the methods described above.
In this case, there is little to choose in length between AC and EC but AC
is preferred as the plotting ‘longest side’ because calculation of its length and
bearing involves fewer steps:
AB x sin ABC
AC =
sin ACB
and, the bearing AC = bearing AB + angle BAC

Nevertheless, it is prudent also to calculate AC via another route as a

check on observing errors. For example, the length of AE can be found in the
triangle ABE and then, in the triangle ACE, another value for the length of AC
can be found. The discrepancy between the two values for AC will be due to
errors in the observation of the sextant angles and, providing it is not
plottable on the scale of the survey, it will be quite adequate to accept the
mean of the two values.

Plotting and graduation

Having found the length of AC and converted it via the scale of the survey to
a plotting distance, the plot proceeds as follows:
First, draw a line XY right across the plotting sheet on the approximate
bearing of AC. Prick-off the length AC at the most convenient place along
XY, then lay off the rays from A and C into the other marks B, D and E by
station pointer using the long line XY as zero. Again, make these rays as long
as possible to the edge of the paper to provide accurate alignment for further
plotted rays.
The positions of B, D and E are now each defined by the intersection of
two rays. As a check, the rays from B, D and E into all other stations should
be plotted so that each station including A and C has at least three rays
A COMPLETE MINOR SURVEY 543

passing through it. The size of the resulting cocked hats will indicate the
accuracy of the work.

Fig. 18-8. Triangulation of a small harbour

Plotting of the rays is best done by scribing fine lines with a ‘pricker’ (a
needle secured in a penholder makes a very serviceable one) rather than in
pencil, as even with a ‘chisel edge’ on the pencil lead, it is virtually
impossible to draw a line to coincide with the leg of the station pointer.
Once the main triangulation stations are plotted and checked, any
sounding marks can also be plotted (a, b, c and d in Fig. 18-8).
The method of graduating a sheet is described in AMHS, Volume I
Chapter 6. This cannot be done in satisfactory manner unless the necessary
instruments are available. The navigator is advised to render his survey in the
form of an ungraduated plan; a meridian and scales of latitude, longitude and
544 CHAPTER 18-SURVEYING

metres will be sufficient, provided the geographical position of a plotted

point is given in the title.
The plotting sheet should bear the title and scale of the survey, together
with the name of the ship and the officer in charge of the surveying work.
The geographical position of at least one main station, either from the chart
or map, or from SATNAV or astronomical observations, should be given, and
also a table of the lengths of all measured or calculated sides. The plotting
sheet should be forwarded to the Hydrographer with the fair chart or tracing.

Tracing and field boards

The plotting sheet is the master plot for the survey and should be preserved
from rough handling and risk of getting wet. In order to transfer the plotted
points from the plotting sheet to field boards, which will be taken away in
boats or used to plot the coastline, a ‘prick-through’ tracing is used.
A previously flattened piece of tracing paper is laid over the plotting
sheet, and main stations, sounding marks, scales and meridian are pricked
through. This tracing can now be used as a template for pricking through on
to the field boards.
Field boards are best made by pasting cartridge or chart paper on to
softwood boards or thick plywood.

Sounding (AMHS, Volume II, Chapter 3)

The sounding of the area of the survey is both the most important, and the
most difficult, part to achieve with limited resources. The sounding must be
systematic and cover the area with regularly spaced lines of sounding. Any
irregularities of depth, particularly shoaling, found on these lines must be
investigated by ‘interlines’ and, if necessary, a close examination made using
a pellet as a datum.

Boat sounding
In a Navigating Officer’s survey, soundings will probably be carried out
using the boat’s lead and line. The lead line is described in BR 67(1),
Admiralty Manual of Seamanship . Lead lines used for survey work should
be fitted with a wire heart to ensure they do not stretch in use. The markings
should be checked using a steel tape (see AMHS, Volume II Chapter 3).

Procedure when sounding

A table, on which the sounding board and instruments may be placed, should
be rigged across the boat in a convenient position, preferably sheltered from
spray.
Prepare the sounding board before leaving the ship by ruling on it the
lines along which it is proposed to sound. These should be at right angles to
the general direction of the depth contours, and usually therefore at right
angles to the coast. The recommended method of sounding is to run along
these predetermined lines, fixing at intervals by simultaneous horizontal
sextant angles (HSA). This requires considerable expertise from the whole
sounding team, officers and boat’s crew.
A COMPLETE MINOR SURVEY 545

Using a largely untrained boat’s crew, it is well worth while erecting

transit marks ashore (Fig. 18-9) for each line to be run. The transits assist the
boat to steer along a straight line and also space the lines correctly. Nothing
very elaborate is required. Two men can hold the transit marks&boat-hook
staves with flags&in position while the sounding line is run. If a triangulation
station or sounding mark can be used as one of the transit marks, so much the
better. Fixing the boat is a separate matter and is discussed below.

Fig. 18-9. Sounding, using transit marks

The distance apart of lines is not very critical, but it is usual to run them
some 5 millimetres apart on the sounding board. The front transit mark can
be moved to the position for the next line by pacing out (or measuring by
tape) the appropriate distance. The back transit may be positioned by a
magnetic compass bearing, or by a sextant angle from a distant object.
Quite often it is possible to utilise a distant object (Fig. 18-10) well inland
as a back transit mark; the sounding lines then become a ‘star’ centred on the
distant object; provided it is far enough away, the lines of sounding open out
very little over the area of an average survey.

Fig. 18-10. Sounding, using a distant object

546 CHAPTER 18-SURVEYING

It will be helpful to insert the relevant coastline and topographical detail

on the sounding board if this has been obtained before sounding starts.

Methods of fixing the boat

As mentioned earlier, the recommended method of sounding is to run along
a predetermined line, fixing by simultaneous horizontal sextant angles. There
are various methods of fixing the boat at the necessary intervals along the line
of soundings. These depend on the nature and scale of the survey.

Method 1. Station pointer fixes steering transits

This method was illustrated in Figs 18-9 and 18-10. the boat is steering along
the planned sounding lines by means of shore transits. HSA fixing is carried
out at close intervals, using two observers and one plotter. Fixes are also
taken when crossing important depth contours.
If conditions are suitable, this is probably the best method for the average
small harbour or anchorage survey. For advice on how to choose marks
giving a strong fix, see Chapter 9, also AMHS, Volume II, Chapter 3, part 2.
If an inexperienced officer finds he cannot keep up with the plotting of
the fixes while the line is being run, he can plot them at the end of the line
confident that, with the help of the transit, at least the boat maintained a
steady track. The same is true of Method 2 but not of Method 3.

Method 2. Transits and ‘cut-off’ angle

The boat is steered along planned sounding lines by means of shore transits.
The transit marks must be accurately fixed relative to the triangulation and
plotted on the board. Fixing is now carried out by observing at regular
intervals one horizontal ‘cut-off’ angle between the transit and a suitably
positioned shore mark.
Such a method only requires one practised observer instead of two, plus
one plotter. However, as the transit forms one position line of the fix, it is
essential that the boat maintains the transit. If the boat strays off the line, the
amount cannot be measured and so the line must be run again.

Method 3. HSA fixes without transits

Simultaneous horizontal sextant angles are observed between three fixed
marks and plotted on the sounding board using a station pointer. This method
requires two observers and one plotter, all practised. The helmsman steers by
compass and is conned on to the correct track by the plotter as the result of
plotting each fix immediately after it is taken. To be effective, particularly
in a difficult cross-tide or cross-wind, the fixes have to be plotted, and any
alteration of course made, very quickly after the angles have been observed.
If the plotting and conning order take longer than about 50 seconds, control
will soon be lost and the line will have to be re-run. The smaller the scale
and therefore the larger the interval between fixes, the more time is available
for corrective conning to take effect and the easier this method becomes.

Accurate positioning of soundings

Soundings must be precisely positioned. An error in position is often more
misleading than an error in depth. It is advisable to adjust the speed of the
A COMPLETE MINOR SURVEY 547

boat so that fixes are between 1 and 1½ cm apart on the sounding board and
never more than 2½ cm. The density of soundings along the line should be
about 4 per centimetre. This is illustrated in Fig. 18-11. The accuracy of the
inking in (see below) is increased if fixes are spaced to allow an odd number
of soundings to be inserted between them, as the centre one can be inked in
first and the spaces either side more easily subdivided by eye.

Fig. 18-11. Fixing while sounding

The boat’s speed between fixes must be constant, otherwise the

intervening soundings will be plotted incorrectly. If the boat’s course has to
be altered, it is best to do this at the fixes and not between them.
548 CHAPTER 18-SURVEYING

Recording boat soundings

Each fix position should be given a consecutive fix number as it is plotted on
the board. Details of the fixes and the soundings obtained should be noted
in the sounding book together with the intervening soundings, as follows.
Soundings are in metres and decimetres. The height of tide and reduced
soundings allowing for this are shown in red.

TIME FIX NO. ANGLES AND SOUNDINGS

1015 3 A a b SOUNDING AT FIX

4.0 m
46°21' 52°33' 12
2
12 11 11 8
8 6 2
8 7 7
8 6
1017 4 A a b
56°04' 56°00' 11
4
11 11 10 7
2 8 4
7 7 6
2 8

Reduction of soundings
The recorded soundings must be reduced for the height of tide obtained from
the tidal curve (page 551) before being plotted. The reduced sounding may
also be recorded in the sounding book (see above) but in a different colour.
Soundings are plotted to the nearest decimetre in depths of less than 31
metres, in metres elsewhere. The general principle to be followed is that
depths are never to be shown as greater than they actually are, relative to
chart datum. For example, a recorded depth of 10.2 m, the height of tide
above chart datum being 4.1 m, would be plotted as a reduced sounding of
6.1 m (10.2 & 4.1). A recorded depth of 37.2 m, the height of tide being 3.4
m, would be plotted as a reduced sounding of 33 m: 37.2 m & 3.4 m = 33.8
m, but, to follow the principle set out above, the depth relative to chart datum
must be rounded down to the nearest metre (33 m).
Inking in of soundings
All significant features, particularly pinnacles and other dangers, must be
precisely positioned on the sounding lines when they are inked in on the
sounding board. Once these have been inserted, representative soundings
should be inserted between them to provide as accurate as possible a
depiction of the sea-bed’s topography as allowed by the scale of the survey.
Soundings should be inked in at a density of about 4 per centimetre along the
sounding line.
When the soundings are being inked in, it is important to try to visualise
the underwater terrain as a whole, so that areas requiring further examination
may be identified and soundings which appear to be inconsistent may be
queried and re-examined if necessary. If a shoal is suspected from adjacent
soundings, the area concerned should be marked for interlining and cross-
lining at the first opportunity. Additional soundings may also be needed to
fill in any holidays.
A COMPLETE MINOR SURVEY 549

The ship’s echo sounder

It will sometimes be possible to use the ship’s echo sounder to run lines of
sounding.
The echo sounder must be precisely adjusted and calibrated (see Volume
III of this manual and AMHS, Volume II, Chapter 3). It should be set up to
read depths below the surface and the stylus speed adjusted to suit the
prevailing water conditions.
Calibration should be carried out once the equipment is thoroughly
warmed up. It should be carried out at the start and at the end of a day’s
soundings. The zero setting and speed of the recorder should be checked
regularly throughout the day and noted in the sounding book.
If the moment of fixing and the fix number, together with the phase, are
marked on the echo trace as well as in the sounding book and on the sounding
board, the soundings may subsequently be taken off the trace at any point
between fixes. The greatest care must be taken when soundings are read off
and marked in. Do not forget to reduce them for the height of tide.
Echo sounder traces should be carefully preserved for forwarding with
the survey report. They should be clearly marked with the following
information:

Ship’s name.
Echo sounder type.
Sound velocity and units used.
Scale of survey.
Start date/time ü (or appropriate fix identification with dates and
Finish date/time ý times).
þ
The rendering of echo sounder traces with hydrographic notes is also
covered in Chapter 6.

Tides
Tidal observations
Since all soundings obtained must be reduced to chart datum, a tide pole must
be erected before sounding can begin. The tide pole (Fig. 18-12, p.550)
consists of a length of wood with painted graduations. These graduations are
usually in metres and decimetres (or feet and fifths of a foot), alternate metres
(feet) being painted with black figures on a white background and white on
black.
It is preferable to erect the pole at low water. The following points
should be considered.

1. The readings must be relevant to the area, and not to some very local tide
as in a lagoon.
2. The pole should not be too exposed to heavy weather.
3. The zero of the pole should not dry out at low water.
4. The pole should belong enough to allow readings to be made up to and
including high water.
5. The pole should be positioned so that it can be easily read by the observer.
6. The pole must not move, particularly vertically, during the course of the
survey and must be firmly secured, preferably to a wall, jetty or pier. If
550 CHAPTER 18-SURVEYING

Fig. 18-12. Tide pole, graduated in metres

guyed to the bottom, the latter must be sufficiently firm to ensure that the
pole does not sink into the ground.
7. The pole must be vertical. Any deviation from the vertical will introduce
a scale error into the readings.

Tidal observations to establish chart datum may now be carried out.

Observations to the nearest decimetre (or 0.2 foot) should be made every ½
hour and, near high and low water, every 10 minutes. Observations should
be obtained over a complete tidal half-cycle of at least 6 hours&that is to say,
observations should include at least one high and one low water, and
preferably four (see below).
Tidal observations will also need to be carried on during the times that
the area is being sounded, so that all soundings may be reduced to chart
datum.

Establishing chart datum on the tide pole

If the survey area is very remote from a standard or a secondary port, and
there is no information on chart datum in the area, the lowest level to which
the tide falls on the tide pole during the survey period will have to be used as
chart datum.
More usually, it should be possible to establish a connection between the
tide pole readings and the data for the nearest standard or secondary port,
which may be obtained from the relevant volume of the Admiralty Tide
Tables. The following method should be used (Fig. 18-13).
Observe, on the tide pole, four consecutive high and low waters. From
the eight observations, deduce mean level m above the zero of the tide pole.
Mean level will be half-way between the mean values of the high and low
waters.
Determine from the Tide Tables the times and heights of HW and LW of
the predicted tides for the relevant period for the nearest standard or
secondary port. Derive the level of chart datum on the tide pole from the
following formula:
A COMPLETE MINOR SURVEY 551

Fig. 18-13. Establishing chart datum on the tide pole

r
d = m− M . . . 18.4
R
where:
d is the level of local chart datum relative to the zero of the tide pole.
m is the height of local mean level above the zero of the tide pole.
r is the range (mean HW & mean LW) at the place.
M is the height of mean level at the standard or secondary port (ML or Zo in
the Tide Tables) above chart datum.
R is the range of the predicted tide (mean HW & mean LW) at the nearest
standard or secondary port.

All tidal observations and calculations should be forwarded to the

Hydrographer with the rest of the survey. It is important that the time zone
used is clearly stated throughout.

Tidal curve
While sounding is in progress, readings on the pole should be read at half-
hourly intervals. Subsequently these may be plotted to the nearest decimetre
against time (Fig. 18-14), having been first corrected for the value of chart
datum on the tide pole.
552 CHAPTER 18-SURVEYING

The heights of tide obtained may then be deducted from the recorded
soundings to obtain a corrected depth, reduced to chart datum.

Fig. 18-14. Tidal curve

Coastline
The coastline in a small survey can best be charted by taking a series of HSA
fixes along the high water line. Provided the HW line is fairly smooth and
the fixes close together (about 10 to 15 millimetres apart on the coastlining
board), the coastline between fixes may be drawn in by eye. At every fix,
angles are taken to three of the main triangulation stations plus a check angle
to some other mark. (See Chapter 9, also AMHS, Volume II, Chapter 3, part
2 on how to select marks to obtain a well conditioned fix.)
This is illustrated in Fig. 18-15, which represents part of Fig. 18-8
enlarged. HSA fixes are obtained along the coastline from A to B and at each
fix a check angle is also observed. The fix B, D, A is a strong one in this area
as the observer is inside the triangle formed by the three marks; the angle
from D to E is suitable as a check angle.
If the coastline is rugged or indented (Fig. 18-16, p.554), it will probably
be best to use a sextant and ten-foot pole for fixing the detail between sextant
fixes.
A ten-foot pole is a light pole at the ends of which are secured two targets
whose centres are exactly 10 feet apart. The pole is held vertically or
horizontally, exactly perpendicular to the line of sight from the sextant, and
the angle between the target centres is measured by sextant and then
converted to distance by the use of tables (AMHS, Volume I). For short
distances, a pocket compass may be used to determine the bearing of the pole
from the previous position.
A COMPLETE MINOR SURVEY 553

Fig. 18-15. Fixing a smooth coastline and a summit inland

For example (Fig. 18-16), positions (2) to (6) may be established as

follows:

1. The ten-foot pole is held vertically at position (2) and its position is fixed
as described above by the observer, standing at position (1).
2. The observer moves to position (2) and the pole is then moved to position
(3).
3. The vertical angle and the bearing of the pole are measured to fix position
(3).
554 CHAPTER 18-SURVEYING

Fix 1: HSA Fix using E, H, G, Check Angle to F

Fix 2:
Fix 3: ü Fixes using VSA, 10 ft Pole and Pocket Compass
Fix 4:
ý
Fix 5:
þ
Fix 6: HSA Fix using E, H, G, Check Angle to F

Fig. 18-16. Fixing a rugged or indented coastline

4. This process is continued for positions (4) and (5), a fresh HSA fix being
obtained at position (6).

It is inadvisable to obtain more than four or five such pole and compass
positions without obtaining a proper fix by sextant angles.
A considerable amount of time can sometimes be saved by mooring a
boat off the coast, fixing its position and using it as the centre object of the
fix. This can save a lot of pole work.
On a steep-to, cliff-lined coast, it will probably be easier to fix the
coastline by moving along in a dinghy rather than attempting to walk round
the base of the cliffs.
The nature of the HW line (sand, shingle, etc.), the foreshore and the type
of country immediately inshore of the HW line should be recorded in the field
note book. The drawing of frequent and large-scale freehand sketches of
each section of the coast is recommended to aid subsequent plotting.
A COMPLETE MINOR SURVEY 555

Fixing navigational marks and dangers (see page 524)

Buoys, dolphins, ends of jetties, stranded wrecks, etc. should be fixed by
bringing the boat alongside and taking angles to all visible fixing marks. In
the case of buoys, this must be done on both ebb and flood and a final mean
position shown.
A small buoy or pellet and a sinker should always form part of a sounding
boat’s equipment to provide a visual datum for the examination of any rocks
or shoals which may be encountered.

Topography
It is usual to fix the topography at the same time as the coastline. This is
done by means of sextant ‘shots’ into the object to be charted from the
various fixes on the coastline. For example, the position of the summit f in
Fig. 18-15 may be intersected by horizontal angles from coastline fixes.
Rough contours or form lines may be drawn in at the same time to give an
impression of the relief. Heights of natural features are difficult to obtain
unless a sea horizon is available as the datum for a vertical sextant angle.
Provided that the elevation can be measured accurately from the HW mark,
the height of objects not too far inland may be calculated from the formula
distance in miles x altitude in seconds of arc
height in metres =
1115 . . . . 18.5

Do not attempt too much topography. Fix only those objects that will be
of direct assistance to the mariner. It is better to have two or three easily
identifiable marks (e.g. well defined summits, conspicuous buildings, etc.)
correctly positioned than a large number of objects which have been inserted
by eye to improve the appearance of the chart.
A lot of topography can be scaled down from existing land maps or aerial
photographs. If possible, arrange to have the maps or photographs photo-
reduced to the scale required.

Aerial photography
Vertical photographs from the ship’s helicopter can be most useful for
charting purposes and a useful aid to coastlining on the ground. Instructions
for the pilot should include details of the tracks to be flown, the required
flying height, the approximate lateral and fore-and-aft overlap to be obtained
(usually 30% and 80% respectively), together with other considerations such
as the state of tide at which the photography is to be taken. For more detailed
advice, see AMHS, Volume II, Chapter 6.

Tidal stream observations (see above, page 530)

Admiralty Sailing Directions
All matter appearing in the Sailing Directions relevant to the locality of the
survey should be carefully checked, and any new information which may be
of use to the mariner should be added. This information should be recorded
under the appropriate headings and in the sequence adopted in the Sailing
Directions.
556 CHAPTER 18-SURVEYING

Views for the Sailing Directions obtained from oblique aerial photography
can be most useful. The topography, prominent features and the use made of
the area by shipping, together with the age of the views already published, are
factors which need to be taken into account when considering the need for
photographs. Full details are given in NP 140, Views for Sailing Directions.

Preparing the fair sheet

A tracing is the quickest way of rendering a minor survey, as the navigator
is unlikely to have the materials, instruments or time to draw a fair chart in
the traditional sense. Tracing paper (but not tracing cloth, which is too
unstable) is satisfactory for this purpose. Ozatex, a matt surface transparent
foil, is better, if it can be obtained from a surveying ship or the Hydrographic
Department in time.
All the soundings, coastlining, topography, etc. obtained during the
survey should be transferred to the fair sheet.
Colour washes cannot be used on tracing paper but coloured drawing inks
improve the clarity of detail and light crayon may be used for the land tint if desired.
Details regarding the use of colours and symbols may be found in GIHS
and also in Chart Booklet 5011, Symbols and Abbreviations used on
Admiralty Charts.
If possible, the fair tracing should be graduated for latitude and longitude
but, if not, then it should be enclosed within a plain border. The true
meridian must be shown with the lines of the border parallel and at right
angles to it.
If the sheet is not graduated, it must show a scale of metres (or feet)
and/or latitude and distance and give the geographical position of one fixed
point of the survey.

Report of survey
The report of survey should be rendered to the Hydrographer at the same time
as the fair sheet. It should give a brief description of how the survey was
carried out, notes on whether or not the least depths over shoals have been
found, and comments on omissions or inaccuracies in the existing chart. It
is important that full comments are made on differences between the
published chart and the survey. This ensures that the cartographer is left in no
doubt that detail omitted in the survey is not caused by an oversight. Other items
usually forwarded as appendices to the report are set out below (GIHS 0918):

1. Triangulation data. Information should include a drawing of the scheme

of triangulation, a list of observed angles and triangles used for the main
control of the survey, and a list of observed angles used to ‘shoot up’
other marks.
2. Base measurements. Details of how the base was derived or measured
should be forwarded.
3. Amendments to the Sailing Directions (see above).
4. Tidal observations and data. These should include details of the datum
used for soundings and how it was arrived at, together with all tide
readings obtained.
A COMPLETE MINOR SURVEY 557

Shadwell Testimonial
In memory of Admiral Sir Charles F. A. Shadwell, a prize consisting of
instruments or books of a professional nature of use in navigation is
presented to a Naval or Royal Marine Officer for the most creditable plan of
an anchorage or other marine survey accompanied by sailing directions
received each year. Hydrographic notes and lines of ocean sounding can also
qualify, providing they show sufficient merit and scope. Details are given in
the Navy List.
558 CHAPTER 18-SURVEYING

INTENTIONALLY BLANK
 559

CHAPTER 19
Bridge Organisation and
Procedures

This chapter considers bridge organisation and procedures within the Royal
and Merchant Navies.
More than three-quarters of navigational accidents (collisions,
groundings, berthing incidents) are attributable to human error of some kind.
When these accidents are analysed, it is often evident that one or more of the
following factors has played a major part.

1. Poor planning.
2. Inadequate bridge organisation.
3. Unsound bridge procedures.
4. Failure to make intelligent use of the information available.

Sound navigational planning, the organisation of the bridge for certain

specific tasks e.g. pilotage, and correct navigational procedures have already
been covered in previous chapters.
Effective use must also be made of the considerable information available
to the mariner on the bridge. The DR or EP projected from the last fix may
well show up any misidentification of shore marks. Radar and radio fixing
aids provide a valuable cross-check for visual fixes. The echo sounder
frequently gives advance warning that the ship is being taken into shoal
water. Clearing bearings will do the same. Tides and tidal stream data are
essential for coastal navigation, pilotage and berthing. The errors of the
compasses must be known and either applied or allowed for. Details of
turning and stopping data are essential for the safe planning and execution of
pilotage and berthing. The observation of the bearing of other ships, and the
acquisition of their relative tracks on the radar display, will identify those
ships on a collision course.

BRIDGE ORGANISATION AND PROCEDURES WITHIN THE

ROYAL NAVY

These remarks serve as both instructions and guidance for Captains,

Navigating Officers (NOs), Principal Warfare Officers (PWOs) and Officers
of the Watch (OOWs), reminding them of important regulations and of
principles on which to base their actions. They also show how the duties of
these officers are interdependent.
560 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

Definitions
Certain terms (like ‘command’) are used throughout this section; their
definitions are as follows:
COMMAND (of the ship). This is the overriding authority over the
ship’s movements which the Captain retains at all times. The
circumstances in which he may delegate sea command to
another officer are set out in BR 31, The Queen’s Regulations
for the Royal Navy (QRRN).
CONDUCT. The direction of a team or management of a series of
tasks in the performance of a function, e.g. conduct of the ship;
conduct of navigation; conduct of operations. Conduct includes
planning and may include execution.
CHARGE (of the ship). The authority delegated by the
Commanding Officer or the officer to whom command or
conduct has been delegated, to the Officer of the Watch for the
safety of the ship at sea.
CONTROL. The action of a functional superior in issuing
instructions and guidance in a clearly defined professional field.
CONNING. The act of giving wheel, hydroplane or engine orders.

SEE BR 45
Command responsibilities
The Captain

A number of instructions about the conduct and charge of the ship are
contained in QRRN, with which the Captain and his officers must be

VOL 4
thoroughly familiar. Not only may the Captain delegate sea command in
certain circumstances (see above), he may also, in accordance with QRRN,
delegate the conduct of navigation to the Navigating Officer and the conduct
of operations in his ship or other units under his command to the Principal
Warfare Officer. Advice to the Captain on delegation is to be found in
Volume IV of this manual.
Further advice to the Captain on his general navigational responsibility
is also to be found in Volume IV.
Charge of the ship
The article in QRRN and in Volume IV of this manual concerning charge of
the ship must be carefully studied. At sea, the Officer of the Watch alone can
have charge of the ship. The Captain may, however, authorise other officers
to take charge of the ship from the OOW in certain circumstances. For
example, the Navigating Officer may require to take charge of the ship in the
course of pilotage. When an officer other than the Captain takes charge of
the ship from the OOW in this way, he automatically becomes the OOW.
Charge of the ship returns to the Captain at any time he so directs, and
automatically should he give any conning order either directly or through
another person. In such circumstances the Captain must ensure that there is
a clearly understood division of responsibilities on the bridge. The Captain
should always make it quite clear when he is taking over charge of the ship.
Nothing is more likely to cause an accident than doubt on the bridge as to
who has charge of the ship. For example, if while altering course the Captain
wishes the OOW to use more wheel, he should give the order ‘Use more
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE ROYAL NAVY 561

wheel’ and not ‘Starboard 25’; if the Captain gives a direct wheel or engine
order, he is in effect relieving the OOW of his responsibility for handling the
ship.
At no time may the Principal Warfare Officer on his own authority take
the ship out of the charge of the OOW or absolve him from his
responsibilities as laid down.

Calling the Captain

The Captain’s Standing Orders should leave the OOW/PWO in no doubt as
to when the Captain should be called. If the OOW/PWO begins to think that
the Captain should be called, the effect of the Standing Orders should prompt
him to do so. The OOW should be encouraged to call the Captain if in any
doubt whatsoever about the safety of the ship. The PWO should call the
Captain as soon as an operational situation requiring the Captain’s attention
develops.

Captain’s Night Order Book (S553)

It has long been the custom for the Captain to keep a Night Order Book in
which he puts instructions for the OOWs and PWOs of the night watches and

SEE BR 45
gives information about the special circumstances of the night. The Night
Order Book should state when the Captain wishes to be called and should
draw attention to his Standing Orders on calling. The Night Order Book is
an essential link between the Captain and the OOW and PWO (and the NO)
who should initial it on taking over their watch.

VOL 4
Shiphandling
This subject is dealt with in BR 45(6), Admiralty Manual of Navigation
Vol 6.

Importance of a shiphandling plan

Shiphandling requirements should be planned in advance by the Captain
jointly with his Navigating Officer and, for berthing or replenishment, with
other officers concerned.
Circumstances may prove different from those which were anticipated;
it is wise, therefore, not only to have prepared contingency plans but to have
in mind the action to be taken to meet all reasonable eventualities & for
example, a sudden change in wind strength or direction, a mechanical failure
or a fouled berth.
All contingencies cannot be foreseen, however. It is worth remembering
that precipitate departure from the plan increases the risk of undetected
errors.

Supervision of the Navigating Officer

The Captain should supervise the work of the Navigating Officer. When
under stress or when tired, it is easy to make mistakes in laying off or
ordering a course.
The Navigating Officer should insist that the Officer of the Watch checks
the course on the chart and carries out the duty of fixing the ship in coastal
waters, reporting at once if he considers the ship is being set off her intended
track.
 562 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

Training of seaman officers

All seaman officers should be given every opportunity to gain bridge
experience. This includes retaining charge of the ship during manoeuvres
and peacetime exercises. During long periods of operations in peace or war
no Captain or Navigating Officer can remain in sole charge without loss of
efficiency from fatigue. A ‘second eleven’ must be trained and ready to take
responsibility during the relatively quiet periods.
Captains are advised to take the following steps to raise and maintain the
standards of all seaman officers in navigation:
1. Officers should take and work out sights during their periods off watch.
The Officer of the Watch may take sights if a second Officer of the
Watch is on watch.
2. On long passages seaman officers should take turns in carrying out the
duties of the Navigating Officer in addition to the officer appointed.
3. On coastal passages the Officer of the Watch should plan and execute a
passage for his watch between a given point of departure and a given
destination compatible with the overall plan.
4. Before coming to an anchorage, another officer besides the Navigating
Officer should prepare ad carry out the run-in, combining this with a

SEE BR 45
blind approach if appropriate.
5. A plan for departure from anchorage or berth should be prepared by the
Harbour Officer of the Day.

Bridge watchkeeping non-seaman officers

VOL 4
Commanding Officers should make every opportunity available for their
engineer, instructor and supply officers who are medically qualified to obtain
Bridge Watchkeeping Certificates. This task is voluntary and must not be to
the detriment of the officer’s primary role nor his professional training.

The Officer of the Watch

| Instructions for the Officer of the Watch at sea are to be found in QRRN, and
| in Volume 4 of this manual. These instructions may be amplified in
| Captain’s Standing Orders.

Looking out
The officer of the Watch should be constantly looking out ahead and on either
bow and frequently astern. Whenever he leaves the position from which he
can look out, he should see that someone else on the bridge is doing so for
him. He should be continuously alert and be the first to spot anything new
that comes into view. He must watch the bearings of all ships in sight,
including those of giving-way vessels. This visual alertness should not be
diminished in the slightest by the knowledge that lookouts are posted or that
radar is operating.
The limitations of radar. The best plots and radar displays cannot be
more than aids to shiphandling in a close quarters situation, where the human
eye is still far superior in speed, accuracy and completeness of information,
even at night. The tracks of ships take time to mature on a plot, and further
delay occurs in reporting them to the bridge. On a relative motion radar
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE ROYAL NAVY 563

display, the aspects of ships cannot be assessed directly and, as compared

with the eye, there is a considerable delay before the fact that a ship is under
wheel and altering course becomes apparent. The alert and watchful OOW
should appreciate much earlier than the operations room that a dangerous
close quarters situation is arising.
The OOW should keep his lookouts informed about the general situation
and tell them what particularly to look for. He should always acknowledge
their reports and praise them for good sightings. The efficiency of lookouts
is greatly improved by the encouragement and interest of the OOW and,
conversely, they will become uninterested and unreliable if ignored. This
applies equally to the Lifebuoy Sentry, whom many ships call the ‘stern
lookout’ to reflect this equally important responsibility.
Even when his ship is Guide, the OOW must keep an eye on the
movements of all ships in company. To assume that attention can be relaxed
because other ships should keep clear of the Guide is unfortunately a
dangerous fallacy. The OOW must remember his next astern particularly, and
ships astern of him generally, whenever he alters course or speed.
Merchant vessels often cruise at higher speeds than warships, so that it
is essential, particularly in ships where the view astern is restricted, for the
OOW to look astern or check with the stern lookout to discover whether there

SEE BR 45
are ships coming up astern before making any alteration of course or
reduction of speed.

Calls by the Officer of the Watch

The Officer of the Watch must pay particular attention to the Captain’s orders

VOL 4
about calling him. The same applies with equal force to calling the
Navigating Officer. Neither the Captain nor the NO can obtain any real rest
at sea unless they are confident that they will be called, and thoroughly
roused if need be, as soon as they are required. The OOW should never
shrink from making sure that the Captain or NO comes to the bridge if he is
wanted there.
Because the weather usually changes gradually over a number of hours,
the OOW may not always realise when the moment has come to inform the
NO and Captain during the night of a change in the condition of the sea, etc.
Such a change may affect the course and the speed made good and, if action
is postponed until morning, drastic remedies may then be necessary.
An OOW will be unable to retain his Captain’s confidence if his reports
are sloppy or inaccurate. The basic principles which the OOW should follow
are:

First Present the facts in a clear, logical and succinct manner.

Second Propose solution/make recommendation.

In this way the Captain is told what he needs to know and can make the
necessary decisions.

Emergencies
There are many kinds of emergency that may arise suddenly and which will
require the Officer of the Watch to act immediately. He must be thoroughly
familiar with the particular action needed in each emergency. It is good
practice to run over in the mind, during the quiet periods of the watch, the
564 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

correct procedures for each case; then the reaction will be instant and correct
in any dangerous situation.
Some of the emergencies for which the OOW should be prepared are:

Man overboard in own or nearby ship.

Failure of main engines in own or nearby ship, particularly in the
ship next ahead.
Failure of steering in own or nearby ship.
Outbreak of fire.
Approach of fog.
Incorrect action by consorts in carrying out signalled manoeuvres.

The OOW should be equally well versed in the action required of him in
the many types of emergency that may arise in war, e.g. sighting of torpedo
track, detection of submarine, etc.

Equipment failures
In the event of an engine telegraph failure, the Officer of the Watch must
ensure that there is immediate and direct telephone communication available

SEE BR 45
between the bridge and the engine room or MCR. In certain circumstances
this line must be manned continually at both ends by communication numbers
who have no other duties to perform.

Compass failure

VOL 4
The compass alarm system in HM Ships primarily indicates a failure of the
master compass only. A ship’s compass transmission system alarm may also
be incorporated in an integrated compass alarm and indication system.
However, even with this integrated system, the possibility of a fault occurring
in the overall system that does not operate the alarms cannot be completely
eliminated.
A modification to the ship’s compass transmission system is available to
cover those ships with a Mark 19, Mark 23 or Arma-Brown gyro-compass
outfit, in which an integrated system is not fitted. However, this only gives
an indication of loss of power to the transmission system.
It is possible for the compass transmission system to fail and also for a
fault to occur in the overall system (e.g. one introducing a slow wander)
without the alarm system operating. In all ships fitted with more than one
transmitting compass (gyro or magnetic), duplicate repeaters from alternative
sources are provided on the bridge, at main or secondary steering positions
and in the operations room. Comparison of these repeaters will serve to
check the operation of the compasses and transmission system. In some
bridge arrangements, due to space considerations, and in operations rooms,
the repeaters can be switched to either compass. In these instances, ensure
that the repeaters are switched so that both compasses are displayed.

Conning orders
It cannot be emphasised too often that wheel and engine orders must always
be given very clearly and precisely, and that imprecise orders such as ‘Meet
her’ and ‘Nothing to starboard’ should never be used. If the wheel is put the
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE ROYAL NAVY 565

wrong way, the best action is to order ‘Amidships’, followed after a short
pause by a very precisely spoken repetition of the original order. It is unwise
to rebuke the helmsman at the time, because this may unnerve him and cause
further errors. Similarly, if the engines are put the wrong way, the best action
is to order ‘Stop (both) engines’ followed by a repetition of the correct order.
A ‘post mortem’ can be held later, when the ship is clear of dangers.
Details of conning orders may be found in BR 45, Admiralty Manual of
Navigation, Volume 4.
When the automatic (auto pilot) system is being used, the procedure to be
followed by the Officer of the Watch is:

‘Set course port/starboard 305'.

‘Rudder limits 10/15/20 etc. degrees’ (as appropriate & this ensures
the ship will be turned under the required helm).

The auto pilot will then apply rudder and counter-rudder to achieve the
new course. The Quartermaster reports when steering the course ordered:

‘Course 305, Sir.’

SEE BR 45
Note: When the turn is more than 180° and it is intended to go the long
way round, the course must be ordered in two bites, so that each bite is less
than 180°.
The above sequence of events should apply to all course alterations when
the auto pilot is in use. If the helmsman is on the bridge, it is important to

VOL 4
ensure that he is not confused between a specific order to alter course and
general discussion as to what the next course should be.

Action information organisation (AIO)

The Officer of the Watch should always bear in mind that the officer in
charge of the operations room may have better information than he has. He
should make a point, therefore, of seeking information or clarification from
the operations room as necessary. Nonetheless, the OOW has the final
responsibility for the safety of the ship.
When on passage or cruising, the value of information that the OOW
derives from the AIO will be in direct proportion to the interest he takes in it.
In order to produce a comprehensive and clear picture, the operations room
must be supplied from the bridge with up to date information about signalled
courses, speeds, changes of formation; with visual sightings, and visual
confirmation of radar contacts. At the same time, the OOW should insist that
the AIO provides him with whatever information he needs and which it is
capable of providing; for instance, he should see that the AIO tracks any new
ship that is detected and that her track and speed are reported, whether she is
expected to pass clear and, if so, what will be her closest point of approach.

The Navigating Officer

Instructions to Navigating Officers are to be found in QRRN and in Volume
IV of this manual. Some amplifying remarks are set out below.
566 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

Method of navigation
The Navigating Officer who is not methodical in the preparation and
execution of his work will sooner or later endanger the ship. Even in familiar
waters a proper plan is essential. The nearer the ship is to danger, the more
frequently must the NO fix her position, so that he is quite confident that he
knows precisely the track she is making over the ground. Navigation should
never be done ‘by eye’, except in very confined waters when the ship is being
piloted from the pelorus. In that case, the NO will have put all the relevant
data in his Note Book, e.g. headmarks, ‘wheel over’ bearings, clearing
bearings, transits, etc., so that he is in effect conducting the ship along a
predetermined track. The NO must be on the lookout at all times, and
particularly in narrow channels, for any signs of danger, such as the colour
of the water, or the appearance of the waves over a shoal. If he feels from
such portents that he is running into danger, he must be prepared to abandon
his plan on the instant and order the ship to be stopped, or the wheel to be put
hard over, as appropriate. Running the echo sounder continuously in shoal
water is required by the regulations, and soundings often give the only
warning that something has gone wrong with the plan. Too often the echo
sounder is run without an adequate reporting organisation; a well briefed and

SEE BR 45
attentive reporter is required.
It may happen occasionally that the ship is required to enter unfamiliar
waters in an emergency without time for full navigational preparation. The
NO should point out the risk to the Captain, who alone can decide whether
the importance of the task justifies his attempting it immediately.

VOL 4
In doubt
If the Navigating Officer is doubtful about the position of the ship and if the
possibility of grounding exists, he must tell the Captain of his misgivings and
suggest that the ship be stopped at once until the position has been accurately
determined.

Instructions for the Officer of the Watch

Navigating Officer’s Night Order Book. The Navigating Officer must give
precise orders to the Officers of the Watch as to when he is to be called. This
may be done verbally or by keeping a Night Order Book or Call Book, in
which navigational information can be put as well as orders for calls each
night.
Bridge Emergency Orders and Bridge File. These contain information
and instructions for the OOW. The NO is responsible for their compilation.
Changing of steering and conning positions. At the start of the
commission, the NO should agree with the Marine Engineer Officer detailed
drills for changing steering and conning positions in the event of damage or
breakdown. These drills should be submitted to the Captain for promulgation
in his Standing Orders. Subsequently the NO should see that they are
available in brief and handy form on the bridge, and in the various steering
and conning positions. He should also recommend to the Captain that the
drills are exercised frequently, so that all the OOWs are familiar with them.
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE ROYAL NAVY 567

Use of the chart, etc. The NO must make available to the OOW the chart
showing the ship’s track, and must ensure that, in his absence from the
bridge, the OOW attends to the navigation. The OOW must fix the ship in
coastal waters and the NO must see that he enters his observations neatly in
the Navigational Record Book (S3034) and on the chart, and that he also
inserts them as necessary in the Ship’s Log (S322). It must always be
remembered that navigation is a branch of seamanship, and therefore within
the province of every seaman officer. The NO must regard it as part of his
duty to train inexperienced OOWs in pilotage and navigation, and to
encourage the more senior ones to practise it.

The Principal Warfare Officer

The Principal Warfare Officer is not a member of the bridge team as such,
and is to be found in the operations room, where he is the officer in charge.
He has a very close relationship with the Command and with the Officer of
the Watch.
From time to time the PWO may be given control of the ship (see page
560) by the Captain, in which case the PWO gives instructions to the OOW

SEE BR 45
regarding the conduct of operations. In such circumstances, the OOW has
authority to query, modify or delay carrying out any instruction which
appears likely to lead to a dangerous situation.
The PWO is never to con (see page 560) the ship from the operations
room unless directed to do so by the Captain when the ship is at shelter
stations.

VOL 4
The PWO also provides the OOW with any available information, advice
or intentions which may assist him in avoiding collision or grounding or other
hazard.

Essential information from the operations room

To ensure that the Officer of the Watch knows the expected movements of
other ships in the vicinity, and the part to be played by his own ship, it is
essential that the Principal Warfare Officer keeps him fully informed at all
times of what is going on. The OOW will then know what to watch for and
can alert his lookouts accordingly.

Special sea dutymen

Special sea dutymen are a standing party of men, who close up at specified
navigational control positions when the ship is entering or leaving harbour
or at times of other hazardous navigational conditions, such as replenishment
at sea or when negotiating a narrow channel. When the ship is clear of
harbour or other hazard they are relieved by the sea dutymen of the watch on
deck. Some or all of those listed in Table 19-1 (p.568) will be needed,
according to the type and class of the ship.
Special sea dutymen of other departments close up simultaneously with
those of the operations department to operate equipments and provide
services for which their departments are responsible.
568 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

Table 19-1
NAME POSITION OF DUTY

Chief Quartermaster or Coxswain At the wheel.

Quartermaster of the watch and In the forward steering position.
telegraphsmen
Quartermaster longest off watch In the after steering position.
Screw flagmen Aft (visible from bridge).
Boatswain’s Mate of the watch At the main broadcast system, also
required for ceremonial piping.
Telephone operators On the forecastle, quarterdeck and
bridge.
Bridge messenger On the bridge.
Blind pilotage team (radar) As required.
Navigating Officer’s Yeoman On the bridge (recording of wheel

SEE BR 45
and engine orders).
Chief Boatswain’s Mate With Executive Officer.

Standing orders and instructions

VOL 4
Captain’s Standing Orders
Captain’s Standing Orders should include sections on the conduct of the ship
in harbour and at sea. A useful aide-mémoire for these orders is provided in
Volume IV.

Bridge Emergency Orders

Bridge Emergency Orders should contain orders in the form of an aide-
mémoire to assist the Officer of the Watch in taking the correct action in an
emergency. They should be kept on cards in plastic covers or displayed on
boards. Full details of the emergencies to be covered are given in Volume IV
and include the following:

Man overboard.
Steering gear breakdown.
Check list for entering fog.
Machinery and telegraph breakdown.
Compass breakdown.
Internal alarm signals, including fire.
Torpedo countermeasures.
Various helicopter operating emergencies.

Bridge File
The bridge File should contain information of a more routine nature than in
the Bridge Emergency Orders. Volume IV gives full details, including:
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE ROYAL NAVY 569

Extracts from Captain’s Standing Orders (sea and operational

sections).
Extracts from Navigation Departmental Orders.
Navigational Data Book extracts.
Navigational lights, switching arrangements.
Masthead heights.
Salvage aide-mémoire.
ASW procedures.
Submiss/subsunk orders.
Orders for domes, etc.
Bridge weapons safety guides.
Instructions on use of recognition.
Helicopter operations.
Instructions for helicopter drill (COPDRILL).
Replenishment at Sea check-off list.

SEE BR 45
List of maintainers responsible for each radar and navaid.
Leaving and entering harbour, check-off list.

Books and publications

The following list shows those books and publications which should be kept
on the bridge, or should be readily available when at sea, in addition to those

VOLs 4 & 7
already mentioned above:

Fishing Vessel Log (S1176).

The Mariner’s Handbook.
Admiralty List of Lights and Fog Signals
Admiralty Tide Tables ü of appropriate
ï
Tidal stream atlases ý area
Admiralty Sailing Directions ï
þ
BR 45(1) and (4), Admiralty Manual of Navigation, Volumes I and
IV.
The Nautical Almanac.
Admiralty List of Radio Signals, Volumes 5 and 6 and associated
diagrams.
ATP 3, latest edition.
ATP 10, latest edition.
Ship’s Standing Orders.

Navigational Departmental Orders

A useful aide-mémoire for these orders is provided in Volume IV.

Orders for Quartermasters

There are some general instructions for Quartermasters in BR 67(1), (2), (3),
Admiralty Manual of Seamanship, Volumes I to III. The Navigating Officer
should also prepare detailed instructions for Quartermasters to cover their
duties and responsibilities in harbour and at sea. A useful aide-mémoire for
these orders is provided in Volume IV. See BR 9276 - Warfare Department
Standing Orders.
 570 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

Orders for the Navigator’s Yeoman

The Navigating Officer should prepare orders for his Yeoman. These should
include instructions for correcting charts and publications along the lines set
| out in BR 45 Vol 7. It is important that the Navigating Officer checks his
Yeoman’s work frequently for accuracy and for correct dissemination of
information.

BRIDGE ORGANISATION AND PROCEDURES WITHIN THE

MERCHANT NAVY

Many instructions and recommendations are available which deal with the
organisation of ship’s bridges and the navigational procedures to be followed
in British Flat Merchant Ships. These may be found in a number of books
and publications, including the following:

The Merchant Shipping Acts.

Statutory Instruments on merchant shipping safety.
Department of Transport booklets (e.g. A Guide to the Planning and
Conduct of Sea Passages).
Department of Transport Merchant Shipping ‘M’ Notices.
IMO recommendations.
International Chamber of Shipping (ICS) and General Council of
British Shipping (GCBS) recommendations (e.g. the ICS Bridge
Procedures Guide).
Admiralty Chart 5500, English Channel passage Planning Guide.
Company instructions.
Port regulations.

In addition to these items, the Master of a merchant ship usually produces

Master’s Standing Orders and a Bridge Order Book.

Navigation safety
The following remarks on navigation safety in Merchant Ships are taken from
Department of Trade (now Transport) Merchant Shipping Notice M.854
(HMSO, August 1978).

‘... To assist masters and deck officers to appreciate the risks to which they
are exposed and to provide help in reducing these risks it is recommended
that steps are taken to:

(a) ensure that all the ship’s navigation is planned in adequate detail with
contingency plans where appropriate;
(b) ensure that there is a systematic bridge organisation that provides for
(i) comprehensive briefing of all concerned with the navigation of the
ship;
(ii) close and continuous monitoring of the ship’s position ensuring as
far as possible that different means of determining position are used
to check against error in any one system;
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE MERCHANT NAVY 571

(iii) cross-checking of individual human decisions so that errors can be

detected and corrected as early as possible;
(iv) information available from plots of other traffic to be used carefully
to ensure against over-confidence, bearing in mind that other ships
may alter course and speed.
(c) ensure that optimum and systematic use is made of all information that
becomes available to the navigational staff;
(d) ensure that the intentions of a pilot are fully understood and acceptable
to the ship’s navigational staff.’

Bridge organisation
The following remarks on bridge organisation are taken from the ICS Bridge
Procedures Guide (1977) which was issued as a guide to Masters and
Navigating Officers.

‘1.1 General
1.1.1 The competence and vigilance of the Officer of the Watch provides the
most direct means of avoiding dangerous situations. However, analyses of
navigational casualties show that weaknesses in bridge organisation are a
contributory cause in very many cases. Well defined procedures clearly laid
down in company instructions and/or Master’s Standing Orders, supported
by an efficient organisation, are essential.
‘1.1.2 Clear instructions should be issued to cover such matters as:
(a) calling the Master ...;
(b) reducing speed in the event of restricted visibility, or other
circumstances;
(c) posting lookout(s);
(d) manning the wheel;
(e) the use of largest scale charts and navigational aids, such as echo
sounder, radar, etc.;
(f) an established drill for changing over from automatic to manual steering
and, if applicable, change-over from hydraulic to electric steering and
vice versa;
(g) the provision of additional watchkeeping personnel in special
circumstances, e.g. heavy traffic or restricted visibility.’
‘1.1.3 There is a clear requirement that Officers of the Watch should be
in no doubt as to what action Masters expect them to take and therefore it is
good practice to issue the foregoing as standing instructions, supplemented
by a bridge order book.’
‘1.1.4 It is the responsibility of the Master to ensure that, when
practicable, the departing officers ‘hand-over’ correctly to officers joining.
Newly joined officers should read and sign Standing Orders and any other
directives. It is essential they be shown how to set up and operate all
appropriate bridge equipment ...’

‘1.2 Passage Plan

1.2.1 The Master should ensure that a plan for the intended voyage is
prepared before sailing. It is of particular importance that this procedure is
adopted for that part of the voyage in coastal waters. In pilotage waters, it
572 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

may be appropriate to have available a forecast of the times of alteration of

course, speed and sets expected ...
‘1.3 Safety Systems & Maintenance and Training
1.3.1 In addition to the above, the Master should ensure that all safety
systems (for example, life-saving appliances, fire-fighting equipment)
are properly maintained and that Officers of the Watch and other crew
members are trained, as appropriate, in the use of these systems.
Regular drills should be carried out, especially at the early stage of a
voyage.’
Principles of watchkeeping arrangements for navigational watch
The following remarks on keeping a navigational watch on the bridge of a
merchant ship are taken from Department of Trade (now Transport) Statutory
Instrument (SI) 1982 No. 1699, Merchant Shipping (Certification and
Watchkeeping) Regulations 1982 (Merchant Shipping: Safety series, HMSO,
1983) Schedule 1.
‘1. Watch arrangements
(a) The composition of the watch shall at all times be adequate and
appropriate to the prevailing circumstances and conditions and shall take
into account the need for maintaining a proper look-out.
(b) When deciding the composition of the watch on the bridge which may
include appropriate deck ratings, the following factors, inter alia, shall be
taken into account:
(i) at no time shall the bridge be left unattended;
(ii) weather conditions, visibility and whether there is daylight or
darkness;
(iii) proximity of navigational hazards which may make it necessary for
the officer in charge of the watch to carry out additional navigational
duties;
(iv) use and operational condition of navigational aids such as radar or
electronic position-indicating devices and any other equipment
affecting the safe navigation of the ship;
(v) whether the ship is fitted with automatic steering;
(vi) any unusual demands on the navigational watch that may arise as a
result of special operational circumstances.’
‘2. Fitness for duty
The watch system shall be such that the efficiency of watchkeeping officers
and watchkeeping ratings is not impaired by fatigue. Duties shall be so
organised that the first watch at the commencement of a voyage and the
subsequent relieving watches are sufficiently rested and otherwise fit for
duty.’
‘3. Navigation
(a) The intended voyage shall be planned in advance taking into
consideration all pertinent information and any course laid down shall be
checked before the voyage commences.
(b) During the watch the course steered, position and speed shall be checked
at sufficiently frequent intervals, using any available navigational aids
necessary, to ensure that the ship follows the planned course.
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE MERCHANT NAVY 573

(c) The officer of the watch shall have full knowledge of the location and
operation of all safety and navigational equipment on board the ship and
shall be aware and take account of the operating limitations of such
equipment.
(d) The officer in charge of a navigational watch shall not be assigned or
undertake any duties which would interfere with the safe navigation of
the ship.’

‘4. Navigational equipment

(a) The officer of the watch shall make the most effective use of all
navigational equipment at his disposal.
(b) When using radar, the officer of the watch shall bear in mind the
necessity to comply at all times with the provisions on the use of radar
contained in [the applicable regulations for preventing collisions at sea].
(c) In cases of need the officer of the watch shall not hesitate to use the helm,
engines and sound signalling apparatus.’

‘5. Navigational duties and responsibilities

(a) The officer in charge of the watch shall:
(i) keep his watch on the bridge which he shall in no circumstances
leave until properly relieved;
(ii) continue to be responsible for the safe navigation of the ship, despite
the presence of the master on the bridge, until the master informs
him specifically that he has assumed that responsibility and this is
mutually understood;
(iii) notify the master when in any doubt as to what action to take in the
interest of safety;
(iv) not hand over the watch to the relieving officer if he has reason to
believe that the latter is obviously not capable of carrying out his
duties effectively, in which case he shall notify the master
accordingly.
(b) On taking over the watch the relieving officer shall satisfy himself as to
the ship’s estimated or true position and confirm its intended track,
course and speed and shall note any dangers to navigation expected to be
encountered during his watch.
(c) A proper record shall be kept of the movements and activities during the
watch relating to the navigation of the ship.’

‘6. Look-out
In addition to maintaining a proper look-out for the purpose of fully
appraising the situation and the risk of collision, stranding and other dangers
to navigation, the duties of the look-out shall include the detection of ships
or aircraft in distress, shipwrecked persons, wrecks and debris. In
maintaining a look-out the following shall be observed:

(a) the look-out must be able to give full attention to the keeping of a proper
look-out and no other duties shall be undertaken or assigned which could
interfere with that task;
(b) the duties of the look-out and helmsman are separate and the helmsman
shall not be considered to be the look-out while steering, except in small
574 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

ships where an unobstructed all round view is provided at the steering

position and there is no impairment of night vision or other impediment
to the keeping of a proper look-out. The officer in charge of the watch
may be the sole look-out in daylight provided that on each such occasion:
(i) the situation has been carefully assessed and it has been established
without doubt that it is safe to do so;
(ii) full account has been taken of all relevant factors including, but not
limited to:
state of weather
visibility
traffic density
proximity of danger to navigation
the attention necessary when navigating in or near traffic
separation schemes;
(iii) assistance is immediately available to be summoned to the bridge
when any change in the situation so requires.’

‘7. Navigation with pilot embarked

Notwithstanding the duties and obligations of a pilot, his presence on board
shall not relieve the master or officer in charge of the watch from their duties
and obligations for the safety of the ship. The master and the pilot shall
exchange information regarding navigation procedures, local conditions and
the ship’s characteristics. The master and officer of the watch shall co-
operate closely with the pilot and maintain an accurate check of the ship’s
position and movement.’

‘8. Protection of the marine environment

The master and officer in charge of the watch shall be aware of the serious
effects of operational or accidental pollution of the marine environment and
shall take all possible precautions to prevent such pollution, particularly
within the framework of relevant international and port regulations.’

Operational guidance for officers in charge of a navigational watch

Operational guidance for officers in charge of a navigational watch is set out
in a Department of Transport Merchant Shipping Notice M.1102 (HMSO,
March 1984) and the following is an extract:

‘... Taking over the navigational watch

7. ... The relieving officer should not take over the watch until his vision is
fully adjusted to the light conditions and he has personally satisfied himself
regarding:
(a) standing orders and other special instructions of the master relating
to navigation of the ship;
(b) position, course, speed and draught of the ship;
(c) prevailing and predicted tides, currents, weather, visibility and the
effect of these factors upon course and speed;
(d) navigational situation, including but not limited to the following:
(i) operational condition of all navigational and safety equipment
being used or likely to be used during the watch;
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE MERCHANT NAVY 575

(ii) errors of gyro and magnetic compasses;

(iii) the presence and movement of ships in sight or known to be in
the vicinity;
(iv) conditions and hazards likely to be encountered during his
watch;
(v) the possible effects of heel, trim, water density and squat on
underkeel clearance.
8. If, at any time the officer of the watch is to be relieved, a manoeuvre or
other action to avoid any hazard is taking place, the relief of the officer
should be deferred until such action is completed.’
‘Periodic checks of navigational equipment
9. Operational tests of shipboard navigational equipment should be carried
out at sea as frequently as practicable and as circumstances permit, in
particular when hazardous conditions affecting navigation are expected:
where appropriate these tests should be recorded.
10. The officer of the watch should make regular checks to ensure that:
(a) The helmsman or the automatic pilot is steering the correct course;
(b) the standard compass error is determined at least once a watch and,
when possible, after any major alteration of course; the standard and
gyro-compasses are frequently compared and repeaters are
synchronized with their master compass;
(c) the automatic pilot is tested manually at least once a watch;
(d) the navigation and signal lights and other navigational equipment
are functioning properly.’
‘Automatic pilot
11. The officer of the watch should bear in mind the necessity to comply at
all times with the requirements of Regulation 19, Chapter V of the
International Convention for the Safety of Life at Sea, 1974. He should
take into account the need to station the helmsman and to put the steering
into manual control in good time to allow any potentially hazardous
situation to be dealt with in a safe manner. With a ship under automatic
steering it is highly dangerous to allow a situation to develop to the point
where the officer of the watch is without assistance and has to break the
continuity of the look-out in order to take emergency action. The change-
over from automatic to manual steering and vice-versa should be made
by, or under the supervision of, a responsible officer.’
‘Electronic navigational aids
12. The officer of the watch should be thoroughly familiar with the use of
electronic navigational aids carried, including their capabilities and
limitations.
13. The echo-sounder is a valuable navigational aid and should be used
whenever appropriate.’

‘Radar
14. The officer of the watch should use the radar when appropriate and
whenever restricted visibility is encountered or expected, and at all times
in congested waters having due regard to its limitations.
576 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

15. Whenever radar is in use, the officer of the watch should select an
appropriate range scale, observe the display carefully and plot effectively.
16. The officer of the watch should ensure that range scales employed are
changed at sufficiently frequent intervals so that echoes are detected as
early as possible.
17. It should be borne in mind that small or poor echoes may escape
detection.
18. The officer of the watch should ensure that plotting or systematic analysis
is commenced in ample time.
19. In clear weather, whenever possible, the officer of the watch should carry
out radar practice.’
‘Navigation in coastal waters
20. The largest scale chart on board, suitable for the area and corrected with
the latest available information, should be used. Fixes should be taken
at frequent intervals: whenever circumstances allow, fixing should be
carried out by more than one method.
21. The officer of the watch should positively identify all relevant navigation
marks.’
‘Clear weather
22. The officer of the watch should take frequent and accurate compass
bearings of approaching ships as a means of early detection of risk of
collision; such risk may sometimes exist even when an appreciable
bearing change is evident, particularly when approaching a very large
ship or a tow or when approaching a ship at close range. He should also
take early and positive action in compliance with the applicable
regulations for preventing collisions at sea and subsequently check that
such action is having the desired effect.’
‘Restricted visibility
23. When restricted visibility is encountered, or expected, the first
responsibility of the officer of the watch is to comply with the relevant
rules of the applicable regulations for preventing collisions at sea, with
particular regard to the sounding of fog signals, proceeding at a safe
speed and having the engines ready for immediate manoeuvre. In
addition, he should:
(a) inform the master (see paragraph 24);
(b) post a proper look-out and helmsman and, in congested waters,
revert to hand steering immediately;
(c) exhibit navigation lights.
(d) operate and use the radar.
[It is important that the officer of the watch should know the
handling characteristics of his ship, including its stopping distance, and
should appreciate that other ships may have different handling
characteristics.]’
‘Calling the master
24. The officer of the watch should notify the master immediately in the
following circumstances:
(a) if restricted visibility is encountered or suspected;
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE MERCHANT NAVY 577

(b) if the traffic conditions or the movements of other ships are causing
concern;
(c) if difficulty is experienced in maintaining course;
(d) on failure to sight land, a navigation mark or to obtain soundings by
the expected time;
(e) if, unexpectedly, land or a navigation mark is sighted or change in
soundings occurs;
(f) on the breakdown of the engines, steering gear or any essential
navigational equipment;
(g) in heavy weather if in any doubt about the possibility of weather
damage;
(h) if the ship meets any hazard to navigation, such as ice or derelicts;
(i) in any other emergency or situation in which he is in any doubt.
Despite the requirement to notify the master immediately in the foregoing
circumstances, the officer of the watch, should in addition not hesitate to
take immediate action for the safety of the ship, where circumstances so
require.’

‘Navigation with pilot embarked

25. If the officer of the watch is in any doubt as to the pilot’s actions or
intentions, he should seek clarification from the pilot; if doubt still exists,
he should notify the master immediately and take whatever action is
necessary before the master arrives.’

‘Watchkeeping personnel
26. The officer of the watch should give watchkeeping personnel all
appropriate instructions and information which will ensure the keeping
of a safe watch including an appropriate look-out ...’

Routine bridge check lists

It is useful to have bridge check lists for routine navigational matters. The
ICS Bridge Procedures Guide recommends the following:

‘1. Familiarisation with Bridge Equipment

2. Daily Tests and Checks
3. Preparation for Sea
4. Embarkation/Disembarkation of Pilot
5. Master/Pilot Information Exchange
6. Navigation, Coastal Waters/Traffic Separation Schemes
7. Changing over the Watch
8. Navigation, Deep Sea
9. Preparation for Arrival in Port
10. Anchoring and Anchor Watch
11. Restricted Visibility
12. Heavy Weather
13. Navigating in Ice
14. Navigating in Tropical Storm Area.’
578 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

The recommended routines for coastal navigation and the preparations for
arrival in port (Routine Check Lists 6 and 9) are set out below:

‘6 Navigation, Coastal Waters/Traffic Separation Schemes

(a) Corrected charts and hydrographic publications available.
(b) Courses laid off well clear of obstructions.
(c) Following factors taken into consideration:
advice/recommendation in the sailing directions;
depth of water and draught;
tides and currents;
weather, particularly in areas renowned for poor visibility;
degree of accuracy of navigational aids and navigational fixes;
day-light/night-time passing of danger points;
concentration of fishing vessels.
(d) Position fixed at regular intervals, particularly when navigating in, or
near a traffic separation scheme.
(e) The position of buoys or other floating marks to be used with caution.
(f) Error of gyro/magnetic compasses checked whenever possible.
(g) Likelihood of encountering unlit, small craft at night.
(h) Appropriate publications consulted for effect of tidal streams and current.
(i) Effect of “squat” on underkeel clearance in shallow water.
(j) Broadcasts by any local navigational services monitored.
(k) Account taken of 1972 International Regulations for Preventing
Collisions at Sea [as amended by Department of Transport SI 1983 No.
708*], Rule 10 when navigating in, or near the vicinity of, an IMO-
approved traffic separation scheme.’

‘9 Preparation for Arrival in Port

(a) ETA sent to pilot station at appropriate time with all relevant
information required.
(b) Available port information, sailing directions and other navigation
information, including restrictions on draught, speed, entry time, etc.,
studied.
(c) All appropriate flag/light signals displayed.
(d) Minimum and maximum depths of water in port approaches, channels
and at berth calculated.
(e) Draught/trim requirements.
(f) Cargo/ballast re-arranged if necessary.
(g) Large-scale charts for port’s pilotage water prepared.
(h) Latest navigational messages for area received.
(i) All hydrographic publications fully corrected up-to-date.
(j) Tidal information for port and adjacent area extracted.
(k) Latest weather report available.
(l) Radio check for pilot/tugs/berthing instructions.
(m) VHF channels for various services noted.

* The Merchant Shipping (Distress Signals and Prevention of Collisions) Regulations (Merchant Shipping;
Safety series, HMSO).
BRIDGE ORGANISATION AND PROCEDURES WITHIN THE MERCHANT NAVY 579

(n) Availability of pilot ladder/hoist on correct side ...

(o) Master/Pilot information exchange form prepared.
(p) All navigational equipment tested, stabilisers housed.
(q) Engines tested for satisfactory operation ahead and astern.
(r) Steering gear tested in primary and secondary systems.
(s) Course recorder, engine room movement recorder and synchronisation
of clocks checked.
(t) Manual steering engaged in sufficient time for helmsman to become
accustomed before manoeuvring commences.
(u) Berthing instructions, including:
anchoring/berthing;
which side to jetty;
ship or shore gangway;
size and number of shore connections;
derricks required;
mooring boats/mooring lines;
accommodation ladder.
(v) Ship’s crew at stations for entering harbour.
(w) Mooring machinery tested, mooring lines, etc., prepared.
(x) Adequate pressure on fire main.
(y) Internal communication equipment, signal equipment and deck lighting
tested.’

Action in an emergency
The Officer of the Watch must be prepared for any emergency and the
following guidelines are useful:

1. You may have to act on your own initiative.

2. Rehearse beforehand in your mind the action to be taken in an
emergency.
3. Indecision and delay may make it too late.
4. Questions you need to ask yourself:

Are you keeping a good lookout, visually and on radar?

Are you taking seamanlike precautions for the circumstances, e.g.
low visibility, bad weather?
Have you checked the ship’s position, course and speed correctly?
Are you thinking ahead? Is a dangerous situation likely to arise
which action now might prevent?
Have you called the Master in plenty of time?

Procedures for emergencies should be readily available on the bridge, and

they should be printed on a red background. These procedures include:

Man overboard.
Steering gear breakdown.
Approach of fog.
Fire or explosion.
Machinery or compass breakdown.
Collision or grounding.
Flooding.
580 CHAPTER 19 - BRIDGE ORGANISATION AND PROCEDURES

Boat/liferaft stations.
Search and Rescue.
Recommended procedures for ‘Man Overboard’ and ‘Steering Failure’
taken from the ICS Bridge Procedures Guide (Emergency Check Lists 10
and 2) are set out below. These instructions may be amplified as necessary
in the particular ship.

‘10 Man Overboard

(a) Lifebuoy with light, flare or smoke signal released.
(b) Avoiding action taken.
(c) Position of lifebuoy as search datum noted.
(d) Ship manoeuvred to recover person (“Williamson” turn recommended if
sea-room allows).
(e) Lookouts posted to keep person in sight.
(f) Three long blasts sounded and repeated as necessary.
(g) Rescue boat’s crew assembled.
(h) Master informed.
(i) Engine room informed.
(j) Position of vessel relative to person overboard plotted.
(k) Vessel’s position available in radio room, up-dated as necessary.’

‘2 Steering Failure
(a) Engine room informed and alternative/emergency steering engaged.
(b) Master informed.
(c) “Not under command” shapes or lights exhibited.
(d) Appropriate sound signal made.
(e) If necessary, way taken off ship.’
 581

APPENDIX 1
Basic Trigonometry

Trigonometry is that branch of mathematics dealing with the relations

between the angles and sides of a triangle and with the relevant functions
of any angles.

The degree
The angle between two intersecting lines is the inclination of one line to the
other, and this inclination is commonly measured in degrees and sub-
divisions of a degree.
In one complete revolution there are 360 degrees. When the two
arms of the angle are perpendicular, the angle is said to be a right angle, in
which there are 90 degrees.
The sub-divisions of the degree are the minute and second, the
relation between them being:

1° = 60 minutes (N)
1' = 60 seconds (O)

Fig. A1-1. Degrees in one revolution

582 APPENDIX 1 - BASIC TRIGONOMETRY

In navigation, angles are measured clockwise from north 000°, through

east 090°, south 180° and west 270° to north (Fig. A1-1).

The radian
The degree is an arbitrary unit. The principles of trigonometry would not be
altered if its size were chosen so that 100 degrees formed a right angle. The
mathematical unit is the radian, which is defined as the angle subtended at the
centre of a circle by a length of arc equal to the radius.
The number π is defined as the constant ratio of the circumference of a
circle to its diameter and is approximately equal to 3.1415927... From this it
follows that:

1. The angle subtended by an arc equal to the radius is also constant and
equal to 360° ÷ 2π, or approximately 57° 17' 45".
2. The number of radians in a right angle is ½π.
3. The length of any arc is equal to the radius multiplied by the angle in
radians.
The definitions of trigonometric functions
The right-angled triangle
In Fig. A1-2, the triangle ABC is right-angled at C; the sides BC, CA and
AB are of length a, b and c respectively; and the angle CAB is of size θ. For
navigational convenience AC is taken as due north so that the (true) bearing
of B from A is θ.
There are six trigonometric functions. Two of these, the sine and cosine,
are of fundamental importance while the other four, tangent, cotangent,
secant and cosecant are derived from them. The six functions are defined and
abbreviated thus:
side opposite the angle a . . . A1.1
sin θ = =
hypotenuse c
side adjacent to the angle b
cos θ = = . . . A1.2
hypotenuse c
side opposite a a c sin θ
tan θ = = = x = . . . A1.3
side adjacent b c b cos θ
b 1 cosθ . . . A1.4
cot θ = = =
a tan θ sin θ
c 1
sec θ = = . . . A1.5
b cos θ

c 1 . . . A1.6
cosec θ = =
a sin θ

The last four trigonometric functions are defined in terms of sin and/or
cos. The last three functions are reciprocals of the first three.
In Fig. A1-2, where AC is 000° and angle CAB equals θ,
THE DEFINITIONS OF TRIGONOMETRIC FUNCTIONS 583

a = c sin θ
b = c cos θ

Thus, B is c sin θ east of A and c cos θ north of A.

Fig. A1-2. The right-angled triangle Fig. A1-3. Complementary angles

Complementary angles
Angles that add together to make 90° are said to be ‘complementary’.
Thus, if one angle is 34°, its complementary angle is 56°.
In any right-angled triangle the two acute angles are complementary,
since the sum of the three angles, of which one is 90°, must be 180°. Fig. A1-
3 shows this and also:
a
sin θ = = cos (90°− θ ) . . . A1.7
c
e.g. sin 34° = cos 56°
b
cos θ = = sin (90°− θ ) . . . A1.8
c
e.g. cos 34° = sin 56°
a
tan θ = = cot (90°− θ ) . . . A1.9
b

e.g. tan 34° = cot 56°

584 APPENDIX 1 - BASIC TRIGONOMETRY

Trigonometric functions of certain angles

Fig. A1-4 and Table A1-1 show the relationship between the trigonometric
functions of certain angles and the length of sides of right-angled triangles.

Fig. A1-4. Trigonometric functions of certain angles

Table A1-1

θ 0° 30° 45° 60° 90

°

1 3
sin θ 0 0.5 2 • 0.707 • 0.866 1
2

3 1
cos θ 1 • 0.866 • 0.707 0.5 0
2 2
1
tan θ 0 • 0.577 1 3 • 1.732 4
3

The signs and values of the trigonometric functions between 000° and 360°

The definitions given earlier (Formulae A1.1 to A1.6) of the six trigonometric
functions for acute angles may be extended to angles up to 360° as follows.
Bearing and direction are measured clockwise from 000° to 360°.
Northerly and easterly directions may be considered as +ve, southerly and
westerly as &ve (Fig. A1-5). South may be said to be the equivalent of
negative north and west the equivalent of negative east. Tangent, cotangent,
secant and cosecant may be defined in terms of sine and/or cosine (page 582).
THE DEFINITIONS OF TRIGONOMETRIC FUNCTIONS 585

In Fig. A1-5, B1 is at a distance r and on a bearing θ1 from A, where θ1

equals the angle θ. B1 is r sin θ east of A and r cos θ north of A. The sine,
cosine and tangent of the direction θ1 are all positive, as are their respective
reciprocals, cosecant, secant and cotangent.

Fig. A1-5. The signs of the trigonometric functions between 000° and 360°

The six trigonometric functions (A1.1 to A1.6) remain true for angles
between 90° and 360°.
Bearings between 090° and 180° lie between south (&ve) and east (+ve).
Bearings between 180° and 270° lie between south (&ve) and west (&ve).
Bearings between 270° and 360° lie between north (+ve) and west (&ve).
586 APPENDIX 1 - BASIC TRIGONOMETRY

Consider, for example, B3, south and west of A at a distance r on a

bearing θ3 (equal to the angle 180° + θ). B3 is r sin θ west of A, which is
equivalent to -r sin θ. B3 is also r cos θ south of A, equivalent to -r cos θ.
− r sin θ
sin θ3 (sin (180°+ θ )) = = − sin θ
r
− r cosθ
cos θ3 (cos (180°+ θ )) = = − cos θ
r
sin θ3 − sin θ sin θ
tan θ3 = = = = tan θ
cosθ3 − cosθ cosθ
The signs of the three functions, sine, cosine and tangent in the four
quadrants are summarised below: the other three functions, cosecant, secant
and cotangent, are reciprocals of the first three respectively, and take the
same signs.
000°
(C)&Cosine positive
(sine, tangent, negative) (A) - All positive
270° 090°
(T)&Tangent positive (S)&Sine positive
(sine, cosine, negative) (cosine, tangent, negative)
180°
The mnemonic All Stations To Crewe provides a reminder of the signs
of the trigonometric functions.
The value (as distinct from the sign) of any trigonometric function of an
angle greater than 90° is equal to the value of the trigonometric function of
the angle made with the north&south axis. For example, the value of sin 127°
equals sin 53° (180° & 127°), while the value of cosine 296° equals cosine
64° (360° & 296°).
The signs and values of the trigonometric functions of angles in each
quadrant are summarised in Table A1-2 (see also Fig. A1-5).
Table A1-2
DIRECTION ANGLE SINE ANGLE COSINE ANGLE TANGENT ANGLE

θ1 θ sin θ cos θ tan θ

θ2 180° & θ* sin (180°& θ) cos (180° & θ) tan (180° & θ)
= sin θ = &cos θ = &tan θ

θ3 180° + θ sin (180° + θ) cos (180° + θ) tan (180° + θ)

= &sin θ = &cos θ = tan θ

θ4 360° & θ sin (360° & θ) cos (360° & θ) tan (360° & θ)
(= & θ) = &sin θ = cos θ = &tan θ
= sin (& θ) = cos (& θ)

* If θ is an angle, the angle equal to (180° & θ) is known as the supplement of θ. Supplementary angles add
together to 180°.
THE DEFINITIONS OF TRIGONOMETRIC FUNCTIONS 587

Table A1-3, illustrated in Fig. A1-6, gives the sign and value of
trigonometric functions of some angles between 90° and 360°.

Fig. A1-6. The signs and values of trigonometric functions of angles

between 90° and 360°

Table A1-3
ANGLE SINE COSINE TANGENT

106° +sin 74° &cos 74° &tan 74°

233° &sin 53° &cos 53° +tan 53°
341° &sin 19° +cos 19° &tan 19°

The sine, cosine and tangent curves

Although, in navigation, angles outside the range 0° to 360° are rarely
encountered, the definitions given earlier may be extended to angles greater
than 360°. The value 360° (or multiples of 360°) may be subtracted from the
angle concerned to reduce it to an angle between 0° and 360°.
588 APPENDIX 1 - BASIC TRIGONOMETRY

Negative angles may be taken as angles measured anti-clockwise from

due north and brought to an angle between 0° and 360° by the addition of
360° (or multiples of 360°).
The graphs of sin θ, cos θ and tan θ may be deduced for any given range.
Fig. A1-7 shows the graphs of sin θ and cos θ between &180° and +540°, and
the graph of tan θ between &180° and +270°.

Fig. A1-7. The sine, cosine and tangent curves

The following should be noted:

1. Both sin θ and cos θ repeat every 360°.

2. tan θ repeats every 180°.
3. In any 360°, there are two angles which have the same value for any
trigonometric function, e.g.

sin 35° = sin 145°

cos 134° = cos 226°
tan 213° = tan 33°, etc.
THE DEFINITIONS OF TRIGONOMETRIC FUNCTIONS 589

Inverse trigonometric functions

As there are two angles in any 360° which have the same value for any
trigonometric function, it follows that the inverse function has more than one
value. However, a calculator can only give what is called the principal value
of the inverse trigonometric function. The principal value ranges for sine,
cosine and tangent are as follows:

sin-1: &90° # θ # 90°

cos-1: 0° # θ # 180°
tan-1: &90° < θ < 90°

The principal value may not be the one required in a particular problem, and
the graph of the appropriate trigonometric function should be used to
determine other values. For example:

sin-1 +0.5 = 30° (the angle could be 30° or 150°.)

sin-1 &0.5 = &30° (the angle could be 210° or 330°.)
cos-1 +0.866 • 30° (the angle could be 30° or 330°.)
cos-1 &0.866 • 150° (the angle could be 150° or 210°.)
tan-1 +0.577 • 30° (the angle could be 030° or 210°.)
tan-1 &0.577 • &30° (the angle could be 150° or 330°.)

Care must be taken to ensure that the displayed angle reading is adjusted
if necessary to the correct value. This may often be achieved by inspection.
For example, if a bearing θ is such that tan θ • &0.577, but it is also known
that the bearing is in the fourth (north-west) quadrant, then the angle required
must be 330° (and not 150°, nor the &30° given by a calculator).
Alternatively, two trigonometric functions corresponding to the displayed
value may be compared. For example, if the sine of the displayed value is
&ve, while the cosine is also &ve, the angle corresponding to both values can
only be in the third (south-west) quadrant, where sine and cosine are both
negative.

Pythagorean relationships between trigonometrical functions

By the theorem of Pythagoras, the square on the hypotenuse of a right-angled
triangle is equal to the sum of the squares on the other two sides. Therefore
(Fig. A1-3):
a 2 + b2 = c2
i.e. a 2 b2
+ 2 =1
c2 c
or sin θ + cos θ = 1
2 2 . . . A1.10

Further division by cos2 θ gives:

tan2 θ + 1 = sec2 θ . . . A1.11

or, if (A1.10) is divided by sin2 θ:

1 + cot2 θ = cosec2 θ . . . A1.12

590 APPENDIX 1 - BASIC TRIGONOMETRY

These formulae hold for all values of θ, because the square of any quantity is
always positive, although the quantity itself may be negative.

Acute and obtuse triangles

There are several formulae connecting the sides and angles of acute and
obtuse triangles (Fig. A1-8) and the choice of formula is governed, as a rule,
by the data available and the requirements of the problem to be solved.

Fig. A1-8. Acute and obtuse triangles

The sine formula

This formula is established by dropping a perpendicular from any vertex on
to the opposite side. In Fig. A1-8, the perpendicular is CD, denoted by p.
Then:
p
sin A =
b
also = sin B (acute triangle) or sin (180° & B)(obtuse triangle) = sin B

i.e. p = b sin A p = a sin B

∴ b sin A = a sin B
a b
or =
sin A sin B
Similarly, if a perpendicular is dropped from A to BC, or BC produced:
b c
=
sin B sin C
a b c
Hence = = . . . A1.13
sin A sin B sin C
ACUTE AND OBTUSE TRIANGLES 591

If two angles A and B and one side of the triangle are given, the third
angle is 180° & (A + B); and the sine formula gives the remaining sides.
Fig. A1-9 shows that ambiguity arises if the formula is used for solving
the triangle when two sides and an angle other than the included angle are
given, the given angle being opposite the smaller side. If, for example, the
sides b and c and the angle C are given, the angle found from the formula is
either ABC or its supplement AB1C, because the sine of an angle is equal to
the sine of its supplement.

Fig. A1-9. Ambiguity in the sine formula

The cosine formula

This formula is established by applying the theorem of Pythagoras to the
right-angled triangles ADC and BDC in Fig. A1-8. Thus:

a2 = p2 + BD2
b2 = p2 + AD2
ˆ a2 = (b2 & AD2) + BD2
= b2 & AD2 + (c & AD)2
= b2 & AD2 + c2 & 2cAD + AD2
= b2 + c2 & 2cAD
= b2 + c2 & 2bc cos A . . . A1.14

In the same way it can be established that:

b2 = c2 + a2 & 2ca cos B . . . A1.15

c2 = a2 + b2 & 2ab cos C . . . A1.16

This formula is true for any triangle, but it must be remembered that, if
the angle A, B or C is greater than 90°, the angle lies in the second quadrant
and its cosine is negative.
592 APPENDIX 1 - BASIC TRIGONOMETRY

The formula gives the third side when two sides and the included angle
are known, or any angle when the three sides are known.

The area of a triangle

It is known that the area of a triangle is equal to half the base multiplied by
the perpendicular height. The area of the triangle ABC (Fig. A1-8) may also
be found by transposing this value using the sine formula to give the
following:

½ ab sin C . . . A1.17
½ bc sin A . . . A1.18
½ ca sin B . . . A1.19

Functions of the sum and difference to two angles

The trigonometric functions of combined angles may be determined. For
example, the sine, cosine and tangent of the angles A + B in Fig. A1-10 may
be found as follows.

Fig. A1-10. The sum of

two angles

PQR is a triangle right-angled at R. The line QS divides the angle Q into

the angles A and B. PS is a perpendicular from P to QS and SV is a
perpendicular from S to QV. ST is the perpendicular from S to PT. The angle
SPT equals the angle B.

r sin (A + B) = PR = PT + TR = PS cos B + SV
= r sin A cos B + QS sin B
= r sin A cos B + r cos A sin B
ˆ sin (A + B) = sin A cos B + cos A sin B . . . A1.20
ACUTE AND OBTUSE TRIANGLES 593

r cos (A + B) = QR = QV & RV = QS cos B & TS

= r cos A cos B & PS sin B
= r cos A cos B & r sin A sin B
ˆ cos (A + B) = cos A cos B & sin A sin B . . . A1.21
sin ( A + B)
tan (A + B) =
cos ( A + B)
= sin A cos B + cos A sin B
cos A cos B − sin A sin B

Dividing top and bottom by (cos A cos B):

tan A + tan B . . . A1.22
tan (A + B) =
1 − tan A tan B
We may find sin (A & B), cos (A & B), tan (A & B) from these three
formulae by remembering that sin (&B) = &sin B, cos (&B) = cos B and tan
(&B) = &tan B, and substituting these values. Thus:

sin (A & B) = sin A cos B & cos A sin B . . . A1.23

cos (A & B) = cos A cos B + sin A sin B . . . A1.24

tan (A & B) = tan A − tan B . . . A1.25

1 + tan A tan B

Double and half-angle formulae

If A is equal to B, it follows from formulae (A1.20), (A1.21) and (A1.22) that:

sin 2A = 2 sin A cos A . . . A1.26

cos 2A = cos2 A & sin2 A . . . A1.27
= 1 & 2 sin2 A
= 2 cos2 A & 1
2 tan A
tan 2A = . . . A1.28
1 − tan 2 A
In terms of the half-angle these formulae become:

sin A = 2 sin ½A cos ½A . . . A1.29

cos A = cos2 ½A & sin2 ½A . . . A1.30
= 1 & 2 sin2 ½A
= 2 cos2 ½ A & 1
2 tan ½ A
tan A = . . . A1.31
1 − tan 2 ½ A
Sum and difference of functions
The above formulae, relating to the sines and cosines of sums and differences,
may be combined to give other formulae which relate to the sums and
differences of sines and cosines.
594 APPENDIX 1 - BASIC TRIGONOMETRY

By adding (A1.20) and (A1.23), and writing P for (A + B) and Q for

(A & B) so that A is equal to ½(P + Q) and B to ½(P & Q):

sin (A + B) + sin (A & B) = 2 sin A cos B

i.e. sin P + sin Q = 2 sin ½(P + Q) cos ½(P & Q) . . . A1.32

By subtracting (A1.23) from (A.1.20):

sin (A + B) & sin (A & B) = 2 cos A sin B

i.e. sin P & sin Q = 2 cos ½(P + Q) sin ½(P & Q) . . . A1.33

By using formulae (A1.21) and (A1.24), it can be shown that:

cos P + cos Q = 2 cos ½(P + Q) cos ½(P & Q) . . . A1.34
cos P & cos Q = &2 sin ½(P + Q) sin ½(P & Q) . . . A1.35
The sine of a small angle
Certain approximations suggest themselves when the angle is small.
In Fig. A1-11, AOB is a small angle θ, measured in radians. AB is the arc
of a circle which subtends this small angle. The radius of a circle is r, and BC
is perpendicular to OA at C.
On page 582 it was stated that the length of arc of a circle is equal to the
radius multiplied by the angle subtended in radians. That is:
AB = r x θ
AB
or θ =
r
BC
But sin θ =
r
Therefore, when θ is sufficiently small for AB to approximate to BC:
sin θ = θ
If there are x minutes in this small angle of θ radians, then there must be
x 360°
minutes in one radian. But one radian is equal to or 3437.7468 minutes
θ of arc. 2π
x
hence = 3437'.7468
θ
x
i.e. θ=
3437'.7468
The relation sin θ = θ therefore becomes:
x
sin x ' =
3437'.7468
Since this relation holds for any value of x that is small:
ACUTE AND OBTUSE TRIANGLES 595

1
sin 1' =
3437'.7468

∴ sin x ' = x sin 1' . . . A1.36

These adjustments are important when practical results have to be

obtained from theoretical calculations, as in the construction of the ex-
meridian tables described in Volume II of this revised edition of the manual.

Fig. A1-11. The sine of a small angle

The cosine of a small angle

Fig. A1-11 shows that, when θ is small, OC approximates to OA, which is the
same as OB. But:
OC
cos θ =
OB

Therefore, when θ is small, cos θ is equal to 1.

A second approximation can be obtained if cos θ is expressed in terms of the
half-angle, for then:
cos θ = 1 − 2 sin 2 ½θ

i.e. cos θ = 1 − 2(½θ ) 2

∴ cos θ = 1 − ½θ 2 . . . A1.37
596

APPENDIX 2
A Summary of Spherical
Trigonometry

Spherical trigonometry is the science of trigonometry (Appendix 1) applied

to the triangles marked on the surface of a sphere by planes through its centre.

DEFINITIONS

The sphere
A sphere is defined as a surface, every point on which is equidistant from one
and the same points, called the centre. The distance of the surface from the
centre is called the radius of the sphere.

Great circle
The intersection of the spherical surface with any plane through the centre of
a sphere is known as a great circle.

Small circle
When a plane cuts a sphere but does not pass through its centre, its
intersection with the spherical surface is called a small circle.

Spherical triangle
A three-sided figure, ABC in Fig. A2-1, formed by the minor arcs of three
great circles on the spherical surface is known as a spherical triangle.
The side of a spherical triangle is the angle it subtends at the centre of the
sphere and may be measured in degrees and minutes, or radians.
In Fig. A2-1, ABC is a spherical triangle formed by the minor arcs of
three great circles, AB, AC and BC. The length a of the side BC is equal to
the angle subtended at the centre of the sphere, that is, BOC. Similarly, b and
c are equal to the angles AOC and AOB.

Spherical angles
In a spherical triangle (Fig. A2-1), the angle A is the angle between the planes
containing the great circles AB and AC, that is, the angle between the plane
AOB and the plane AOC. Similarly, the angle B is the angle between the
planes AOB and COB, and the angle C is the angle between the planes AOC
and COB.
In a spherical triangle ABC, it is customary to refer to its angles as A, B
and C.
DEFINITIONS 597

Fig. A2-1. The spherical triangle

and to the sides opposite these angles as a, b and c. This is analogous to the
conventions adopted in a plane triangle and set out in Appendix 1.

Properties of the spherical triangle

Certain properties of a spherical triangle are equivalent to those of a plane
triangle. For example, the largest angle is always opposite the largest side, and the
smallest angle is always opposite the smallest side. One side is always less than
the sum of the other two sides, e.g. c < a + b in Fig. A2-1. There is, however, one
very important difference between spherical and plane triangles. The sum of the
three angles of the spherical triangle, A + B + C, is always greater than 180° (π
radians). The sum is always less than 540° (3π). The sum of the three sides of the
spherical triangle, a + b + c, is always less than 360° (2π).

THE SOLUTION OF THE SPHERICAL TRIANGLE

There are six things to be known about a spherical triangle: the sizes of its three
angles and the lengths of its three sides. Various formulae connect these angles
and sides so that, if sufficient of them are given, the rest can be found. The
common problems are those of finding the third side when two sides and their
included angle are known, and finding a particular angle when the three sides are
known.
598 APPENDIX 2 - A SUMMARY OF SPHERICAL TRIGONOMETRY

The cosine and sine formulae

Cosine formula

In Fig. A2-2, O is the centre of the sphere of radius R. AB, BC and CA are the
minor arcs of three great circles forming the spherical triangle ABC on the
surface of the sphere. OA = OB = OC = R.

CD is the perpendicular from C to the plane OAB.

CE is the perpendicular from C to the line OB.
ˆ DE is perpendicular to OB.
and angle CED = spherical angle at B.

Similarly, CG, is the perpendicular from C to the line OA

ˆ DG is perpendicular to OA,
and angle CGD = spherical angle at A.
angle BOC = a angle AOC = b angle BOA = c
GH is the perpendicular from G on to OB, and DJ is the perpendicular
from D on to GH. JD is parallel and equal to HE. Angle JGD = c.
In the triangle COE, which is right-angled at E:
OE
= cos a
OC
∴ OE = R cos a
but OE = OH + HE
= OG cos c + GD sin c
= R cos b cos c + CG cos A sin c
= R cos b cos c + R sin b cos A sin c
ˆ (COSINE RULE) cos a = cos b cos c + sin b sin c cos A . . . A2.1

Similarly:
cos b = cos c cos a + sin c sin a cos B . . . A2.2
cos c = cos a cos b + sin a sin b cos C . . . A2.3

Thus, if any two sides and their included angle are given, the third side
may be found, this side being the one opposite the only spherical angle in the
formula. Such formulae are analagous to the cosine formulae for the plane
triangle set out in Appendix 1.
When all three sides of the spherical triangle are known, the angle may
be found by transposing the relevant cosine formula. For example, from (A2.1):

cos a − cos b cos c

cos A = . . . A2.4
sin b sin c
THE SOLUTION OF THE SPHERICAL TRIANGLE 599

Fig. A2-2. Spherical trigonometry: the cosine and sine formulae

Sine formula
In the triangles CED and CGD, both right-angled at D:
CD CD
= sin B and = sin A
CE CG
thus CE sin B = CD = CG sin A
∴ R sin a sin B = R sin b sin A
sin a sin b
i.e. =
sin A sin B
and, by symmetry:
sin a sin b sin c
(SINE RULE) = = . . . A2.5
sin A sin B sin C
The sine formula for the spherical triangle is analogous to the sine
formula for the plane triangle set out in Appendix 1, and has the same
limitation in that ambiguity arises if it is used to solve the triangle when two
sides and one angle are given. It must be remembered that as sin θ = sin
(180° & θ), there is no way of knowing from the formula alone whether the
quantity found is greater or less than 90°.
600 APPENDIX 2 - A SUMMARY OF SPHERICAL TRIGONOMETRY

Suppose (Fig. A2-3) that a is 66°, b is 50° and B is 40°. From the formula:
sin a
sin A = x sin B
sin b
= sin a sin B cosec b
= sin 66° sin 40° cosec 50°
= 0.76657
A = 50° 02'.8 or 129° 57'.2

Fig. A2-3. Spherical trigonometry & ambiguity in sine formula

Fig. A2-3 shows that ABC and A1BC are possible triangles. The
ambiguity, however, may often be resolved in practice and the formula is
easier and quicker to use on a calculator than the cosine formula. The sine
formula may therefore often be used to find the great-circle course, having
found the distance.
The sine rule is a useful cross-check against the accuracy of the workings
when the complete solution of the spherical triangle is found using the cosine
sin a sin b sin c
formula: , and must all equal the same value.
sin A sin B sin C
Polar triangles
In the same way as the equator is related to the Earth’s axis, which cuts the
Earth’s surface at the North and South Poles, so every great circle has an axis
and two poles.
The polar triangle A1B1C1 of the spherical triangle ABC (Fig. A2-4) is
formed as follows:

A1 is the ‘pole’ of the great circle BC on the same side of BC as A.

OA1 is perpendicular to the plane of the great circle through BC.

B1 is the ‘pole’ of the great circle AC. OB1 is perpendicular to the

plane of the great circle through AC.
THE SOLUTION OF THE SPHERICAL TRIANGLE 601

C1 is the ‘pole’ of the great circle AB. OC1 is perpendicular to the

plane of the great circle through AB.

The two triangles ABC and A1B1C1 are mutually polar.

In the polar triangle A1B1C1,

a1 = π & A A1 = π & a
b1 = π & B B1 = π & b
c1 = π & C C1 = π & c

If these values are substituted in the cosine rule (formula A2.1), the following
formula is obtained:
cos A + cos B cos C
(POLAR COSINE RULE) cos a = . . . A2.6
sin B sin C

Such a formula may be used to calculate a side of the spherical triangle

given all three angles. It may also be used to calculate an angle given the
other two angles and the opposite side.

Fig. A2-4. Polar triangles

The four-part formula

This is a formula the terms of which are four consecutive angles and sides of
any spherical triangle.
602 APPENDIX 2 - A SUMMARY OF SPHERICAL TRIGONOMETRY

In Fig. A2-5, the four parts to be considered are C, a, B and c. The angle
B, contained by the two sides a and c, is called the ‘inner angle’ or ‘I.A.’.
The side a, common to the angles B and C, is called the ‘inner side’ or ‘I.S.’.
The others are the ‘other angle’ C, denoted by ‘O.A.’, and the ‘other side’ c,
denoted by ‘O.S.’.
The four-part formula states that:

cos (I.S.) cos (I.A.) = sin (I.S.) cot (O.S.) & sin (I.A.) cot (O.A.) . . . A2.7
It may be proved thus:

cos b = cos c cos a + sin c sin a cos B

cos c = cos a cos b = sin a sin b cos C

By substituting for cos b:

cos c = cos a (cos c cos a + sin c sin a cos B) + sin a sin b cos C
i.e. cos c = cos c (1 & sin2 a) + sin a cos a sin c cos B + sin a sin b cos C

Therefore, since cos c cancels out and sin a is common to the remaining
terms:
sin a cos c = cos a sin c cos B + sin b cos C

cos c sin b cos C

i.e. sin a = cos a cos B +
sin c sin c
Hence, by the sine formula:
sin B cos C
sin a cot c = cos a cos B +
sin C
i.e. cos a cos B = sin a cot c − sin B cot C

Fig. A2-5. The four-part spherical triangle

THE SOLUTION OF THE SPHERICAL TRIANGLE 603

The four-part formula may be used to find the initial or the final course
direct from the latitude and longitude without first finding the great-circle
distance.

Right-angled triangles
If one angle of a spherical triangle is a right angle, the formulae for solving
the triangle are greatly simplified.
Thus, if the angle C in the triangle ABC is a right angle (Fig. A2-6), the
cosine formula (A2.3) becomes:
cos c = cos a cos b . . . A.28

and the sine formula (A2.5) becomes:

sin a sin b
= = sin c . . . A2.9
sin A sin B
The numerous formulae thus obtainable are best summarised by Napier’s
rules.

Fig. A2-6. Napier’s right-angled triangles

Napier’s mnemonic rules for right-angled triangles

The triangle ABC is ‘extended’ as shown in Fig. A2-6, to form the symbolic
five quantities, a, b, (90° & A), (90° & C), (90° & B), displayed clockwise
around the triangle. These quantities may also be shown as the sectors of a
circle having a vertical radius that represents the right angle at C.
If any one of these quantities is taken as the ‘middle’ quantity, two of the
other four quantities become ‘adjacent’ and the remaining two quantities
become ‘opposite’.
Napier’s rules are:

sin middle = products of tans of adjacents . . . A2.10

= products of cosines of opposites . . . A2.11

604 APPENDIX 2 - A SUMMARY OF SPHERICAL TRIGONOMETRY

In the triangle ABC, right-angled at C, Napier’s rules give the ten

formulae in Table A2-1, which may also be derived from the various
formulae described earlier.

Table A2-1
MIDDLE FORMULA DERIVED FROM

a sin a = tan b cot B Four-part formula

sin a = sin c sin A Sine rule
b sin b = tan a cot A Four-part formula
sin b = sin c sin B Sine rule
(90° & A) cos A = tan b cot c Four-part formula
cos A = cos a sin B Polar cosine rule
(90° & c) cos c = cot A cot B Polar cosine rule
cos c = cos a cos b Cosine rule
(90° & B) cos B = tan a cot c Four-part formula
cos B = cos b sin A Polar cosine rule

Right-angled spherical triangles may be used as follows:

1. To find the position of the vertex on the great circle.

2. To solve an isosceles triangle where two points are in the same latitude,
by bisecting the triangle.
3. To find where a great circle cuts the equator.
4. To solve the composite track.

Quadrantal triangles
A quadrantal triangle is a spherical triangle where one side is equal to 90°,
e.g. c in Fig. A2-7.

Fig. A2-7. Napier’s quadrantal triangles

THE SOLUTION OF THE SPHERICAL TRIANGLE 605

As with the right-angled triangle, the quadrantal triangle may be

‘extended’ and a five-part figure constructed. The symbolic five quantities
are now A, B, (90° & a), (C & 90°), (90° & b). These quantities may also be
combined in accordance with Napier’s rules (A2.10 and A2.11), for example:

sin A = tan B cot b

sin A = sin a sin C
cos a = cos A sin b
(etc.)

The haversine
When using logarithmic tables instead of a calculator, it is more convenient
to solve the spherical triangle using a function called the haversine of the
angle.
This function is half the versine & hence the name haversine & and the
versine of an angle is defined as the difference between its cosine and unity,
that is:
versine θ = 1 & cos θ . . . A2.12
and it follows that:
haversine θ = ½(1 & cos θ) . . . A2.13

The haversine of an angle is thus always positive, and it increases from

0 to 1 as the angle increases from 0° to 180°. Fig. A2-8 shows the haversine
curve in relation to the cosine curve from which it is derived. Norie’s Tables
give the values of the haversine for angles between 0° and 360°.

Fig. A2-8. The haversine curve

The usefulness of the haversine formula is confined to situations where

a solution has to be found from logarithmic tables. If calculators or
computers are available, the previous formulae (cosine rule, sine rule, etc.)
should be used in preference.
606 APPENDIX 2 - A SUMMARY OF SPHERICAL TRIGONOMETRY

The haversine formula

To express the cosine rule in terms of haversines instead of cosines, substitute
for the appropriate cosines their values in terms of the haversines. Thus cos
A can be written (1 & 2 hav A), and the formula becomes:

cos a = cos b cos c + sin b sin c (1 & 2 hav A)

i.e. cos a = cos b cos c + sin b sin c & 2 sin b sin c hav A
= cos (b ~ c) & 2 sin b sin c hav A
Similar substitutions for cos a and cos (b ~ c) give:
1 & 2 hav a = 1 & 2 hav (b ~ c) & 2 sin b sin c hav A
i.e. hav a = hav (b ~ c) + sin b sin c hav A . . . A2.14

The half log haversine formula

This formula, which gives one of the angles when the three sides are known,
is derived from the cosine rule by making substitutions similar to those used
in building the haversine formula.
As before, the first substitution gives:

cos a = cos (b ~ c) & 2 sin b sin c hav A

2 sin b sin c hav A = cos (b ~ c) & cos a

By the rule for the subtraction of two cosines this equation becomes:

2 sin b sin c hav A = 2 sin ½ [a + (b ~ c)] sin ½ [a & (b ~ c)]

Therefore, by division:
hav A = cosec b cosec c sine ½ [a + (b ~ c)] sin ½ [a & (b ~ c)]
But, from the definition of the haversine:
hav x = ½ (1 & cos x) = ½ [1 & (1 & 2 sin2 ½x)]
= sin2 ½x
Therefore, by analogy:

sin ½ [a + (b ~ c)] = hav [a + (b ~ c)]

sin ½ [a & (b ~ c)] = hav [a - (b ~ c)]

By substitution:
hav A = cosec b cosec c hav [a + ( b ~ c) ] hav [a − ( b ~ c) ]

In logarithmic form this is:

log hav A = log cosec b + log cosec c + ½ log hav [a + (b ~ c)]
+ ½ loghav [a & (b ~ c)] . . . A2.15

The haversine solution to the example on page 39 is set out below.

THE SOLUTION OF THE SPHERICAL TRIANGLE 607

A ship steams from position F (45°N, 140°E) to T (65°N, 110°W). Find

the great-circle distance and the initial course.

Fig. A2-9. A great-circle problem

Great-circle distance
It is required to find the great-circle distance between two points, F and T,
with known latitudes and longitudes. The haversine formula (A.2.14) then
becomes:

hav FT = hav FPT sin PF sin PT + hav (PF ~ PT)

= hav (d.long) sin (90° & lat F) sin (90° ± lat T)
+ hav [(90° & lat F) ~ (90° ± lat T)]
This applies to F in either north or south latitudes.
i.e. hav dist = hav d.long cos lat F cos lat T
+ hav (co-lat F ~ co-lat T) . . . A2.16
= hav 110° cos 45° cos 65° + hav (45° ~ 25°)
= hav 110° cos 45° cos 65° + hav 20°

log hav 110° - 182673

.
log cos 45° / 184949
.
162595
.
log cos 65° .$$$$$$$
130217
. 0.20053
hav 20° 0.03015
&&&&&
hav 57°24'.5 0.23068

ˆ G.C. distance = 3444'.5

608 APPENDIX 2 - A SUMMARY OF SPHERICAL TRIGONOMETRY

Great-circle bearing
When it is necessary to find the great-circle bearing of one point on the
Earth’s surface from another (or the initial course when sailing on a great-
circle track from one point to another), the half-log haversine formula (A2.15)
is applied. Thus, the bearing of T from F is given by:

hav PFT
= cosec PF cosec FT hav [ PT + ( PF ~ FT ) ] hav [ PT − ( PF ~ FT ) ]
or
log hav PFT = log cosec PF + log cosec FT + ½ log hav [PT + (PF ~ FT)]
+ ½ log hav [PT & (PF ~ FT)]

i.e. log hav initial course

= log cosec co-lat F + log cosec distance

+ ½ log hav[co-lat T + (co-lat F ~ distance)]
+ ½ log hav[co-lat T & (co-lat F ~ distance)] . . . A2.17
= log cosec 45° + log cosec 57° 24'.5
+ ½ log hav[25° & 12° 24'.5]
+ ½ log hav[25° + 12° 24'.5]
= log cosec 45° + log cosec 57° 24'.5
+ ½ log hav 12° 35'.5 + ½ log hav 37° 24'.5

log cosec 45° 0150515

.
log cosec 57° 24'.5 0.074414
½ log hav 37° 24'.5 1506074
.
½ log hav 12° 35'.5 1040056
.

log hav PFT 2.771059

initial course = N28° 07'.3E

= 028°
 609

APPENDIX 3
The Spherical Earth

MERIDIONAL PARTS FOR THE SPHERE

As was explained in Chapter 4, the meridional parts of any latitude are the
number of longitude units in the length of a meridian between the parallel of
that latitude and the equator. A longitude unit is the length on the chart
representing one minute of arc in longitude.

Fig. A3-1. Construction of the mer. part formula

Construction of the mer. part formula for the sphere

In Fig. A3-1, X is any point on the Earth in latitude φ , and Y is a neighbouring
point differing from it in latitude by the small amount ∆ φ . X1 and Y1 are the
610 APPENDIX 3 - THE SPHERICAL EARTH

corresponding points on the Mercator chart where, since all meridians are
straight lines at right angles to the equator, A1B1 is equal to X1Z1.
The ratio that the chart length A1B1 bears to the geographical distance AB
decides the longitude scale of the chart. That is, when AB and A1B1 are
expressed in the same units, A1B1 is some fraction of AB or, what is the same
thing, AB is equal to kA1B1 where k is some constant. If, for example, AB is
1 minute of arc and A1B1 is 1 mm, 1 mm on the chart is equivalent to 1 minute
of arc or approximately 1,853,300 mm on the Earth, and k is 1,853,300. The
value of k thus determines the size of the chart. For the actual measurement
of meridional parts, however, it is sufficient to know the chart unit that
represents 1 minute of arc along the equator.
In the example quoted, where 1 mm represents 1 minute, the meridional
parts of X1 are simply the number of millimetres in X1A1.
To calculate this chart length and so determine the number of minutes of
arc along the equator to which it is equivalent, consider the distortion that
occurs away from the equator.
XZ is the parallel through X, and XY the rhumb line joining X to Y. On the
chart X1Z1 is the parallel and X1Y1 the rhumb line, both lines being straight.
Then, if all lengths XZ, AB, A1B1 ... are measured in the same units:

XZ = AB cos φ (from formula 2.1)

= kA1B1 cos φ
= kX1Z1 cos φ
1
i.e. X1Z1 = XZ sec φ
k
Any arc of a parallel, the latitude of which is φ , is thus represented on
the chart by a line proportional to the actual length of the arc multiplied by
sec φ , a quantity greater than unity. The distance scale along the parallel is
therefore stretched.
Again, if Y is taken sufficiently close to X for XYZ to be considered a
plane triangle right-angled at Z:

Z1Y1 X 1Z1
=
ZY XZ
1
= sec φ
k
1
i.e. Z1Y1 = ZY sec φ
k
Any small element of a meridian in the neighbourhood of latitude φ is
thus represented on the chart by a line proportional to the actual length of the
element multiplied by sec φ , and the distance scale along the meridian is
therefore stretched.
The actual distance between Z and Y on the Earth, being ∆ φ in circular
measure, is 180 x 60∆ φ , or 3437.747 ∆ φ minutes of arc. Hence:
π
MERIDIONAL PARTS FOR THE SPHERE 611

1
Z1Y1 = 3437.747 sec φ ∆φ
k
in minutes of arc.
But 1 minute of arc is equal to k millimetres, or whatever the scale units
are. Therefore:
æ1 ö
Z1Y1 = ç 3437.747 sec φ ∆φ ÷ k
èk ø
in millimetres or scale units.
The actual chart length of Z1Y1 in millimetres, or whatever the scale units
are, is thus:
3437.747 sec φ ∆φ

The chart length of any particular parallel from the equator, measured
along a meridian is clearly the sum of all the component elements of which
the expression just found is typical. If the latitude of the parallel is LF, this
sum, in the chosen units, is given by:
LF
3437.747 ò0 sec φ dφ
That is, the number of meridional parts or longitude units (a longitude
unit being the length on the chart that represents 1 minute of arc in longitude)
in the length of a meridian between latitude LF and the equator is:

3437.747 log e tan (45° + ½ LF ° )

Evaluation of the mer. part formula
The actual evaluation of this formula may be accomplished more easily if the
logarithm is expressed to base 10. Thus, if y is the number of meridional
parts:
y = 3437.747 log10 tan (45° + ½ LF ) log e 10
= 7915.7045 log10 tan (45°+ ½ LF ° ) . . . (4.1)

Suppose the latitude is 40°. Then:

y = 7915.7045 log10 tan 65°
= 7915.7045 x 0.33132745
= 2622.69

CORRECTED MEAN LATITUDE FOR THE SPHERE

On page 28 it was made clear that, given certain circumstances, the mean
latitude must not be used to determine d.long by means of formula (2.5), but
a correction to that mean latitude must first be applied.
612 APPENDIX 3 - THE SPHERICAL EARTH

Fig. A3-2. The corrected mean latitude

In Fig. A3-2, a ship steams from F to T. Since the departure is greater

than HT and less than FG, it must be exactly equal to the arc of some parallel
UV. The latitude of this parallel is called the corrected mean latitude, and if
it is denoted by L, then:

QR = UV sec L
i.e. d.long = departure sec L

This is an accurate formula, but L must be known before it can be used. The
problem is therefore to find L.
The latitudes of F and T may be denoted by LF and LT, and the difference
of latitude between them, FH, divided into n equal parts of length x. JK is
one of these parts. Then:

d.lat = nx = LT & LF

If parallels of latitude are now drawn through the points J, K . . . ,

intersecting the rhumb line FT in A, B, etc. and the meridians through these
points of intersection in A1, B1, etc., n small triangles are formed. Moreover,
these triangles are equal because in each the side of which AA1 is typical is
x; the angle at A1 is 90°; and the angle at A is the course, which is constant
between F and T. The length of the arc of which A1B is typical is thus the
CORRECTED MEAN LATITUDE FOR THE SPHERE 613

same for each triangle and if the triangles are made sufficiently small (that
is, if n if made sufficiently large) for the conditions for evaluating an accurate
departure to be realised, the departure between F and T is the sum of the
elements A1B. Thus:

departure = ny

where y is the length of A1B. Also, the d.long corresponding to the element
A1B is ab and:
ab= A1B sec (latitude B)

ab= y sec (latitude K)

By adding all these elements ab, bc, etc. the d.long is obtained, the
formula being:
d.long = y[sec (LF + x) + sec (LF + 2x) + . . . + sec LT]
Or, since the departure is equal to ny:
sec ( LF + x ) + sec ( LF + 2 x ) + ... + sec LT
d.long = departure
n
But the corrected mean latitude L is given by:
d.long = departure sec L
Hence, by equating these two values of the d.long:
1
sec L =
n
[ ]
sec ( LF + x ) + sec ( LF + 2 x )+ ...+ sec LT
The quantity sec L is thus the mean of the secants of the latitudes of the
successive parallels.
Written in the integral form in order that the value of sec L may be found,
the equation is:
1
sec L =
nx
[ ]
sec ( LF + x ) + sec ( LF + 2 x )+ ...+ sec LT x

=
1
( LT − LF ) [ ]
sec ( LF + x ) + sec ( LF + 2 x ) + ...+ sec LT x

Then, as n becomes larger, x grows progressively smaller and, in the limit:

1 LT

d.lat ò LF
sec L = sec LdL...
L

1 é æ π Lö ù
T

= log tan ç + ÷ ú if d.lat is expressed in radius

d.lat êë e è 4 2ø û L
F

1 180 x 60
= x
d.lat π
x loge 10 [log10 tan (45° + ½LT°) & log10 tan (45° + ½LF)]
if d.lat is expressed in minutes of arc.
614 APPENDIX 3 - THE SPHERICAL EARTH

It may be seen that:

180 x 60
x loge 10 [log10 tan (45° + ½LT°) & log10 tan (45° + ½LF°)]
π
corresponds to the meridional parts formula (4.1) and is equal to the
difference of meridional parts (DMP). Thus:
DMP . . . (2.7)
sec L =
d.lat (minutes of arc)
 615

APPENDIX 4
Projections

This appendix deals with the following:

1. The conical orthomorphic projection on the sphere.

2. The deduction of the mer. part formula for the sphere.
3. The position circle on the Mercator chart.
4. The modified polyconic projection.
5. The polar stereographic projection.
6. The gnomonic projection.
7. The transverse Mercator projection&conversion from geographical to grid
co-ordinates and vice versa.

THE CONICAL ORTHOMORPHIC PROJECTION ON THE SPHERE

On projections of the simple conical type, all meridians are equally spaced
straight lines meeting in a common point beyond the limits of the chart or
map. The parallels are concentric circles, the common centre of which is the
point of intersection of the meridians. This is illustrated in Fig. A4-1. The
cone AVG is tangential to the sphere along the standard parallel AFGH; AV
is the radius ro of the standard parallel at latitude φ0 on the projection, co-
latitude Zo, and is equal to R tan Zo where R is the radius of the sphere; the
angles EVF and WVF on the projection are equal, each representing 180 of
longitude on the sphere.

The scale
The meridians and parallels of this projection intersect at right angles and
thus angles are preserved. Although this is a necessary condition for
orthomorphism, it is not sufficient. To make the projection orthomorphic, the
scale along the meridian must be equal to the scale along the parallel at any
point on the projection.
In Fig. A4-2, ABCD is an infinitely small quadrilateral on the sphere,
while A1B1C1D1 is its plane representation on the conical projection. The
small change in the meridian on the projection, dθ, is only a fraction of the
equivalent change in the meridian on the sphere, dλ, and this fraction may be
referred to as:

n, the constant of the cone

where dθ = ndλ . . . A4.1

616 APPENDIX 4 -PROJECTIONS

Fig. A4-1. The simple conical orthomorphic projection

The scale along the meridian at A1 is the relationship:

A1 B1 − dr dr
= = . . . A4.2
AB Rdφ RdZ
THE CONICAL ORTHOMORPHIC PROJECTION ON THE SPHERE 617

The negative sign must be allocated to dr if φ is used, because r

increases as φ decreases, and the positive sign must be allocated if Z is used,
when r increases as Z increases.
The scale along the parallel at A1 is the relationship:

A1 D1 rdθ
=
AD R cos φ dλ
rdθ nr
= =
R sin Z dλ R sin Z . . . A4.3

Fig. A4-2. Scale on the conical orthomorphic projection

To be orthomorphic, these two scales must be equal:

dr nr
i.e. =
RdZ R sin Z
1
dr = n cosec Z dZ
r
1
i.e. ò r dr = ò n cosec Z dZ
Z
log e r = n log e tan + C
2
Z
= n log e tan + log e k
2
n
æ Zö
r = k ç tan ÷ . . . A4.4
è 2ø
where k is a constant defining the scale.
618 APPENDIX 4 -PROJECTIONS

The general properties of a system of conformal conical projections may

be defined by this formula (A4.4).

The constant of the cone

From Fig. A4-1, it may be seen that the length of the standard parallel AFGH
is 2πR cos φ0 , whilst the radius of the parallel on the projection is R tan Zo or
R cot φ0 . When this conical shape is displayed for the whole 360° of
longitude for the Earth, the angle on the projection represents 2π. Thus:

R cot φ0 dθ = 2πR cos φ0

dθ = 2π sin φ0
but, in this case, dλ = 2π
so, from (A4.1), 2πn = 2π sin φ0
ˆ n = sin φ0 = cos Zo . . . A4.5

Thus for the simple conical projection, the constant of the cone, n, equals
sin φ0 , the sine of the standard parallel.
Conical orthomorphic projection with two standard parallels
Since the scale at any point not on the standard parallel is too large, two
standard parallels may be chosen, where the scale is correct. This is
illustrated in Fig. A4-3. Between the two parallels, the scale of the chart is
too small, while beyond them the scale is too large. This projection is known
as Lambert’s conical orthomorphic projection.

DEDUCTION OF THE MER. PART FORMULA FOR THE SPHERE

The formula giving the meridional parts of any latitude may be derived from
the general formula for the cone (A4.4).
If Zo is the co-latitude of the standard parallel, the radius of the parallel
on the projection is given by (A4.4).
n
æ Z ö
ro = k ç tan o ÷
è 2ø

The distance between the standard parallel and any other parallel is given by:
éæ Zo ö
n
æ Zö ù
n

ro − r = k ê ç tan ÷ − ç tan ÷ ú
ëè 2ø è 2ø û
æ Z Zö
• kn ç log e tan o − log e tan ÷
è 2 2ø
an approximation obtained by expanding the right-hand side in its
exponential form, given that n ultimately tends to zero.
DEDUCTION OF THE MER. PART FORMULA FOR THE SPHERE 619

Fig. A4-3. Lambert’s conical orthomorphic projection, two standard parallels

620 APPENDIX 4 -PROJECTIONS

The value of k follows at once from the fact that ro cos Zo is equal to R sin
Zo and is given by:
R sin Zo 1
k= x n
cos Zo æ Zo ö
ç tan ÷
è 2ø
and since n = cos Zo
R sin Zo
kn = n
æ Zo ö
ç tan ÷
è 2ø
When the cone becomes a cylinder, the standard parallel becomes the
equator, this being the Mercator projection Zo becomes 90° and:

kn = R

The value of (ro & r), which is now the chart length of a parallel in
latitude φ from the equator, measured along a meridian, is therefore given by:
Z
ro − r = − R log e tan
2
Z
= R log e cot
2
10800 æ π φö
= log e tan ç + ÷
π è 4 2ø
æ 1 ö
= 3437.747 log e tan ç 45°+ φ ° ÷
è 2 ø
æ 1 ö . . . (4.1)
= 7915.7045 log10 tan ç 45°+ φ ° ÷
è 2 ø

THE POSITION CIRCLE ON THE MERCATOR CHART

A position circle is a circle drawn on the Earth’s surface with the

geographical position of the heavenly body as centre. It is a small circle.
When plotted on a Mercator chart, this curve of position will no longer be a
circle, and the problem is to find the equation of the resulting curve.

Fig. A4-4 shows the relative positions of the pole P, the observer Z, and
the geographical position of the heavenly body U, when the true altitude
(obtained from a sextant reading) is a, and the declination is d. The latitude
of Z if φ . Then, if X and x are the easterly longitudes of Z and U, the hour
angle of the heavenly body is (x& X).
The cosine formula applied to the spherical triangle PZU gives:

cos UZ = cos PU cos PZ + sin PU sin PZ cos UPZ . . . (A2.1)

i.e. sin a = sin d sin φ + cos d cos φ cos (x & X)
or cos (x & X) = sin a sec d sec φ & tan d tan φ . . . A4.6
THE POSITION CIRCLE ON THE MERCATOR CHART 621

Fig. A4-4. Position circle

Fig. A4-5. Position circle plotted on a Mercator chart, declination zero

622 APPENDIX 4 -PROJECTIONS

If the co-ordinates of Z on the chart are x and y, x is given by this

equation, and y by:
sec φ = ½(ey + e-y)

and tan φ = ½(ey&e-y)

Hence, by substitution:

2 cos (x & X) = ey (sin a sec d & tan d)

+ e-y (sin a sec d + tan d) . . . A4.7

This is the general equation of the curve on the chart that represents the
position circle, and the curve itself is defined by the values of a, d and X.
Fig. A4-5 shows the curve as it appears on a Mercator chart when the
declination is zero, and Fig. A4-6 shows three typical curves representing
position circles for three values of the altitude when the geographical position
is in latitude 40°N, longitude 60°W.

Fig. A4-6. Three typical position circles

THE MODIFIED POLYCONIC PROJECTION

Although new charts on a scale 1:50,000 or larger are now drawn on the
transverse Mercator projection, there are still many harbour plans and
approaches in general use traditionally described on the chart as being
gnomonic. In fact these plans have been drawn on a modified form of the
polyconic projection.
THE MODIFIED POLYCONIC PROJECTION 623

In the polyconic projection, the central meridian alone is straight and the
distances between consecutive parallels are made equal to the real distances
along the surface of the spheroid, to the scale required for the chart. Each
parallel is constructed as if it were the standard parallel of a simple conical
projection. This means (see Chapter 4) that the circular arcs in which the
parallels are developed are not concentric, but their centres lie on the central
meridian. The other meridians are concave towards the central meridian and,
except near the corners of maps or charts showing large areas, they intersect
the parallels at angles differing only slightly from right angles.
In practice on Admiralty charts, all meridians are drawn as straight lines
and to this extent the polyconic projection has been modified, although the
normal curvature of the limiting meridians would be extremely small in any
case, having regard to the scale of the chart.
The co-ordinates (x, y) of any point Q on the projection (Fig. A4-7) may
be found from the formulae:
x = v∆λ cos φ . . . A4.8
y = ¼v(∆λ)2 sin 2 φ . . . A4.9
where φ is the latitude of the parallel,
∆λ is the difference of longitude from the central meridian,
v is the radius of curvature at right angles to the meridian* at latitude φ .

Fig. A4-7. The modified polyconic projection

These formulae are accurate for projections covering 2° of latitude and

1° of longitude. The projection may be extended to 2° of longitude without
any appreciable inaccuracy by laying off co-ordinates from each of the
extreme meridians, to cover a further 30 minutes of longitude.

* This radius of curvature is sometimes referred to as the transverse radius of curvature and should
not be confused with the meridional radius of curvature ρ described in Chapter 3. For any
spheroid, v = a
(1- e sin 2 φ )
2 1/ 2
624 APPENDIX 4 -PROJECTIONS

THE POLAR STEREOGRAPHIC PROJECTION

The polar stereographic projection (Fig. A4-8) is a perspective conformal

projection on a plane tangential to the sphere at the pole, obtained by
projecting from the opposite pole. Angles are correctly represented; parallels
of latitude are represented by circles radiating outwards from and centred on
the pole. Meridians appear as straight lines originating from the pole.

Fig. A4-8. The polar stereographic projection

If R is the Earth’s radius and φ the latitude of G, the angle PP1G1 is

½(90°& φ °) and the radius PG1 of the projected parallel is 2R tan ½(90°& φ °).
If the radius PG1 is r, and the co-latitude of φ is Z, the scale along the
parallel is G1 is:
r 2 R tan ½ Z
= = sec2 ½ Z
R sin Z R sin Z
The scale along the meridian at G1 where dr is a small increase in r and dz a
small increase in Z is:
dr 2 R ½ sec 2 ½ Z
= = sec 2 ½ Z
Rdz R

The scale is the same in each direction; thus the orthomorphic property
is established.

GNOMONIC PROJECTION

Principal or central meridian

The plane on which the parallels and meridians are projected is a tangent
plane and, to avoid distortion, the tangent point K should be chosen in the
centre of the area to be shown. In Fig. A4-9, its latitude is 20°N.
GNOMONIC PROJECTION 625

Since the gnomonic projection is a perspective projection, the point on

the tangent plane that corresponds to a point on the sphere that represents the
Earth is found by producing the radius at the point until it cuts the tangent
plane. Thus p corresponds to P, the pole, and all points on the meridian PK
project into the straight line pK. PK is known as the principal or central
meridian.
If B is any point and ABC any great circle through it, the arc AB projects
into the straight line ab.
The meridian through B is PBL and, since it is part of a great circle, pbl
is also a straight line. The meridians on the gnomonic graticule are thus
straight lines radiating from p.
The straight line Kl corresponds to the great-circle arc KL.
If φ K and φ A are the latitudes of K and A, then:
KP = 90° & φK = KOP
and AP = 90° & φ A = AOP

Since Kp lies in a plane tangential to the sphere at K, OK, the radius of

length R, is perpendicular to Kp. Therefore:
Kp
= tan KOp = tan KOP
OK
i.e. Kp = R cot φK

Also KOA = KOP − AOP

= φ A − φK
Ka
and = tan KOa = tan KOA
OK
i.e. Ka = R tan (φ A − φ K ) . . . A4.10

Fig. A4-9. Gnomonic projection&the principal meridian

626 APPENDIX 4 -PROJECTIONS

The chart distances of the pole (Kp) and any point on the central meridian
(Ka) from the tangent point are thus known, and it is clear from Fig. A4-9
that, if the latitude of A is greater than that of K, a will lie on the line Kp
between K and p. If the latitude of A is less, a will lie beyond K on pK
produced.
Angle between two meridians on the chart
The difference of longitude between the meridians PBL and PAK in Fig. A4-9
is the angle LPK, denoted by λ, and this angle is projected into the angle lpK,
denoted by α.
Suppose the great circle ABC is chosen so that it cuts the meridian PK at
right angles. Its projection ab will then be at right angles to Kp and, from the
plane right-angled triangle pab:
ab = ap tan α
Also, of the plane of the great circle KLM is made to cut the central
meridian at right angles, the angle pKl is a right angle and, from the plane
right-angled triangle pKl:
Kl = Kp tan α
From the plane right-angled triangles lKO and pKO:
Kl = OK tan KOL
and Kp = OK tan KOP = R cot φK
By Napier’s rules applied to the spherical triangle LKP, right-angled at K:
tan KL = sin KP tan λ
Hence, by combining these relations:
tan α = sin φK tan λ . . . A4.11
From this relation it is apparent that when φ K is 90°, that is, when the
pole is the tangent point, α is equal to λ and there is no distortion in the chart
angles between the meridians: they are equal to exact differences of
longitude. When the tangent point is not at the pole, there is distortion and
the angles between the meridians are not represented correctly on the chart.
If the distance ab is required, it can be found by substitution. Thus:
ab = ap tan α
= (Kp & Ka) sin φ K tan λ
= R [cot φ K & tan ( φ A & φ K )] sin φK tan λ
= R tan λ cos φ A sec ( φ A & φ K ) . . . A4.12
Parallels of latitude
Since the parallels of latitude are not great circles, they form a series of
curves on the gnomonic graticule.
In Fig. A4-10 ABC is a parallel in latitude φ , and b is the projection of
B. As B moves along the parallel, b describes a path which is not a straight line.
GNOMONIC PROJECTION 627

Fig. A4-10. Gnomonic projection&

the parallel of latitude

The problem is to find the equation of the path, and this can be done by
referring b to the rectangular axes KX and Kp.
If the angle AKB is denoted by η, the angle bKp will also be η because the
great circles KB and KP can be regarded as ‘meridians’ radiating from ‘pole’
K which is a tangent point. There is thus no distortion when this angle is
projected. Hence, if x and y are the co-ordinates of b:

x = Kb sin η
and y = Kb cos η
and x2 + y2 = Kb2
From the plane right-angled triangle KOb:
Kb = OK tan KOb
From the spherical triangle PBK, by the cosine formula:
cos PB = cos KB cos KP + sin KB sin KP cos η
i.e. sin φ sec KB = sin φK + tan KB cos φK cos η
For convenience take the radius of the sphere as unity. Then:
sin φ sec KB = sin φK + y cos φK
and tan2 KB = x2 + y2
i.e. sec2 KB = 1 + x2 + y2
ˆ sin2 φ (1 + x2 + y2) = sin2 φ K + 2y sin φ K cos φ K + y2 cos2 φ K
i.e. x2 sin2 φ + y2 (sin2 φ & cos2 φK ) & 2y sin φK cos φK
= sin2 φ K & sin2 φ . . . A4.13

For all points on the parallel ABC, φ is constant. φ K is also constant.

This equation is therefore the equation of the curve that represents the parallel
ABC on the chart.
628 APPENDIX 4 -PROJECTIONS

To construct a gnomonic graticule

When the tangent point is on the equator or at the pole, the graticule admits
of simple geometrical construction. When the tangent point is elsewhere, the
formula just established must be employed.

Fig. A4-11. Gnomonic graticule

Fig. A4-11 shows the graticule when the tangent point is in latitude 45°S,
longitude 120°W. MK is the central meridian, and the other meridians are
inclined to it at angles given by:

tan α = sin φ K tan λ

where φ K is 45° and λ has successive values 10°, 20°, 30°, etc. The position
of the pole (not shown in the figure) is given by:
Kp = OK cot φ K
Kp can therefore be marked according to the chosen scale, and the meridians
drawn as lines radiating from p at the angles discovered.
Again, if b is the point corresponding to latitude 50°S, longitude 130°W,
and ba is the perpendicular from b to MK, the length of Ka in the chosen
scale is given by:
Ka = tan ( φ A & φ K )
in which φ A is the latitude of A, the point that a represents on the chart (Fig.
A4-10).
If φ B is the latitude of B, the point that b represents on the chart, Napier’s
rules applied to the triangle PBA give:
tan φ A = tan φ B sec λ
where λ is the difference of longitude between A and B. This formula gives φ A
since φ B is 50° and λ is 10°. Hence Ka can be found. Also, in the chosen
units:
ab = tan λ cos φ A sec ( φ A & φ K )
i.e. ab = tan 10° cos φ A sec ( φ A & 45°)
GNOMONIC PROJECTION 629

The point b, corresponding to latitude 50°S, longitude 130°W, can

therefore be plotted with other points where this parallel cuts the meridians.
In this way all the parallels can be inserted.

Equatorial gnomonic graticule

When the tangent point is on the equator, φ K is zero, and the general
formulae are simplified considerably. The graticule, however, lends itself to
a geometrical construction.

Fig. A4-12. Gnomonic projection&the equatorial graticule (1)

In Fig. A4-12 the central meridian is KP, and this is represented on the
chart by KM which is at right angles to OK. The equator KA projects into the
straight line Ka at right angles to KM, and any other meridian, AP, projects
into a line at right angles to Ka and therefore parallel to KM.
The distance between the projected meridian ab and the central meridian
is given by:

Ka = OK tan KOA
= R tan (d.long between K and A)

The positions of the meridians can thus be decided.

If B is any point on the meridian AP in latitude φ , B projects into b, and
ab represents this latitude on the chart. Fig. A4-13 shows the geometrical
construction for finding the position of b.
630 APPENDIX 4 -PROJECTIONS

The plane of projection is represented by MKa in the plane of the paper,

and Ka is a tangent to the equatorial circle at K. A is fixed on this circle by
its exact difference of longitude from K, and it projects into a. If ab1 is now
drawn at right angles to Oa, so that the angle aOb1 is equal to the latitude of
B, the triangle aOb1 is equal in all respects to the triangle aOb in Fig. A4-12.
The position of b can thus be marked merely by marking ab equal to ab1.

Fig. A4-13. Gnomonic projection&the equatorial graticule (2)

Other points on the projection of the parallel through B can be found in

the same way. Since, however, a graticule is usually drawn for equal angular
intervals of latitude and longitude, the work can be shortened by drawing
radials at the required interval and using them for both d.long and latitude as
shown in Fig. A4-14.
This same construction can be used for finding the position of the vertex
and the latitude of any point on a great circle, the longitude of which is
known.
Any great circle projects into a straight line. Also, a great circle cuts the
equator in two points 180° apart. In Fig. A4-15, Q is one of these points, and
q its projection. Then, since the longitude of the vertex is 90° from the
longitude of Q, the position of the vertex v is found merely by making the
angle QOU a right angle.
GNOMONIC PROJECTION 631

The angle uOv1 measures the latitude of the vertex.

If the latitude of any point x is required, it can be found in the same way,
that is, by drawing xy at right angles to uq and yx1 at right angles to Oy, and
making yx1 equal to xy. The angle yOx1 then measures the latitude of the
point X on the Earth to which x corresponds on the chart.

Fig. A4-14. Gnomonic projection&the equatorial graticule (3)

632 APPENDIX 4 -PROJECTIONS

Fig. A4-15. Gnomonic projection&

the equatorial graticule (4)

THE TRANSVERSE MERCATOR PROJECTION

Conversion from geographical to grid co-ordinates and vice versa

The formulae to be used in the appropriate computer program for the

conversion of geographical position to grid co-ordinates and vice versa on the
transverse Mercator projection are set out below.

Symbols
The symbols used in these formulae, which correspond to those in use in the
Hydrographic Department, are set out below.

a = semi-major axis of spheroid (metres)

b = semi-minor axis of spheroid (metres)
e = eccentricity of spheroid

a− b
n = a+b

φ = latitude (radians)
THE TRANSVERSE MERCATOR PROJECTION 633

λ = longitude (radians)
λo = longitude of central meridian (CM) of grid (radians)
∆λ = λ & λo
t = tan φ
ρ = radius of curvature of meridian (metres)
a(1- e 2 )
=
(1- e2 sin 2 φ ) 3/2
ν = radius of curvature at right angles to meridian (metres)
a
=
(1 − e2 sin2 φ )1/ 2
v e2 cos2 φ
η2 = − 1=
ρ ( )
1− e2
Sφ = length of meridian arc from equator to latitude i (metres)
sφ
θ =
æ 5n 2 81n 4 ö
b(1 + n) ç 1 + + ÷
è 4 4 ø
φ1 = ‘footpoint’ latitude
t1
ρ1 ü
ï
ν1 ý variables, defined above, corresponding to φ1
η1 ï
þ
E = grid easting (metres)
N = grid northing (metres)
FE = ‘false’ easting of true origin
FN = ‘false’ northing of true origin
Er= ‘true’ easting = E & FE (points east of CM) or FE & E (points west of
CM)
Nr = ‘true’ northing = N & FN
ko = scale factor on CM (= 0.9996 for UTM)
To find the length of the meridional arc given the latitude
This is already set out in formula (5.19) on page 94 and in Appendix 5 (page
643 et seq.), but is repeated here for convenience, in a slightly different form.
é 35 6 æ 15e4 105e 6 ö
Sφ = a(1 − e )ê −
6
e sin 6φ + ç + ÷ sin 4φ
ë 3072 è 256 1024 ø
æ 3e 2 15e 4 525e6 ö
−ç + + ÷ sin 2φ
è 8 32 1024 ø
æ 3e 2 45e 4 175e 6 ö ù
+ ç 1+ + + ÷φ
è 4 64 256 ø úû
634 APPENDIX 4 -PROJECTIONS

To find the ‘footpoint’ latitude, given the true grid co-ordinates

If So is the length of the meridian arc from the equator to the true origin, then:
N'
Sφ 1 = So ±
ko
(+ in N hemisphere, − in S hemisphere)
and φ1 can be found from Sφ 1 using the formula:
8011 5 1097n 4
φ1 = n sin 10θ1 + sin 8θ1
2560 512
æ 151n 3 417n5 ö
+ç − ÷ sin 6θ1
è 96 128 ø
æ 21n 2 55n 4 ö
+ç − ÷ sin 4θ1
è 16 32 ø
æ 3n 27n 3 269n5 ö
+ç − + ÷ sin 2θ1 + θ1 . . . A4.14
è 2 32 512 ø
φ1 being the latitude of the foot of the perpendicular drawn from a point on
the projection to the CM.

To convert from geographical to grid co-ordinates

E' ∆ λ3 cos3 φ
koν
= ∆ λ cos φ +
6
(1− t 2 + η2 )

∆ λ cos φ
5 5

+
120
(5 − 18t 2 + t 4 + 14η 2 − 58t 2η2 )

∆ λ7 cos7 φ
+
5040
( 61 − 479t 2 + 179t 4 − t 6 ) . . . A4.15

and:
N ' Sφ ∆ λ 2 ∆ λ4
=
koν ν
+
2
sin φ cos φ +
24
(
sin φ cos3 φ 5 − t 2 + 9η 2 + 4η 4 )
∆ λ6
+ sin φ cos5 φ(61 − 58t 2 + t 4 + 270η 2 − 330t 2η2 )
720
∆ λ8
+ sin φ cos7 φ (1385 − 3111t 2 + 543t 4 − t 6 ) . . . A4.16
40320

If an accuracy of ± 0.01 m is acceptable, terms containing ∆λ6and higher

powers of ∆λ may be ignored.
THE TRANSVERSE MERCATOR PROJECTION 635

To convert from grid to geographical co-ordinates

φ φ1 ( E ') ( E ')
2 4

3 (5 + 3t1 + η1 − 9t1 η1 − 4η1 )

2 2 2 2 4
= − +
t1 t1 2 ko ρ1 ν1 24 k o ρ1 ν1
2 4

( E ') 6
−
720ko ρ1 ν1
6 5 (61 + 90t 1
2
+ 45t1 4 + 46η1 2 − 252t1 2η1 2 − 90t1 4η1 2 )

(E ) 1 8
. . . A4.17
+
40320k 08 p1v17
(1385 + 3633t 1
2
+ 4095t14 + 1575t16 )

and:
E' ( E ') 3
∆ λ cos φ1 = 3 3 (1 + 2t1 + η1 )
2 2
−
k0v1 6k 0 v1
( E ') 5
+
120k0 v 5 5 (5 + 28t 1
2
+ 24t14 + 6η12 + 8t12η12 )

( E ') 7
−
5040k0 v 7 7 (61 + 662t 1
2
+ 1320t14 + 720t16 ) . . . A4.18
1

In an accuracy of ± 0".001 is acceptable, terms containing (E0)7 and higher powers

of E0 may be ignored.
636

APPENDIX 5
The Spheroidal Earth

This appendix deals with the following:

1. The equation of the ellipse.

2. Geodetic, geocentric and parametric latitudes.
3. The length of one minute of latitude.
4. The length of the meridional arc.
5. Meridional parts for the spheroidal Earth.
6. The length of the Earth’s radius in various latitudes.

THE EQUATION OF THE ELLIPSE

When a point M (Fig. A5-1) moves so that its distance from a fixed point S
(the focus) is always in a constant ratio e (less than unity) to its perpendicular
distance from a fixed straight line AB (the directrix), the locus of M is called
an ellipse of eccentricity e.
The equation of the ellipse takes its simplest form when the co-ordinates
of S are (&ae, 0) and the directrix AB is the line:
a
x= −
e
In Fig. A5-1, by definition:
MS = eMC
a
MC = x +
e
( MS ) 2 = y 2 + ( x + ae) 2
2
æ aö
∴ e ç x + ÷ = ( x + ae) + y 2
2 2

è eø
i.e. (1 − e2 ) x 2 + y 2 = a 2 (1 − e2 )
This may be written in the form:
x2 y2
+ =1 . . . A5.1
a 2 b2
THE EQUATION OF THE ELLIPSE 637

where b 2 = a 2 (1 − e 2 ) . . . A5.2
1/ 2
æ a 2 − b2 ö
i.e. e= ç ÷ . . . (3.2)
è a2 ø
The ellipse corresponds to a cross-section of the Earth, where a is the
equatorial and b the polar radius. As b is less than a, the Earth is ‘flattened’
in the polar regions.

Fig. A5-1. The ellipse

The flattening or ellipticity of the Earth may be defined by a quantity f

where:
a− b
f = . . . (3.1)
a
From (3.1) and (3.2):

e = (2 f − f )
2 1/ 2 . . . (3.3)

The quantities a, e and f are used regularly in the solution of rhumb-line

and great-circle sailing problems on the spheroid.
638 APPENDIX 5-THE SPHEROIDAL EARTH

GEODETIC, GEOCENTRIC AND PARAMETRIC LATITUDES

Geodetic and geocentric latitudes

In Fig. A5-2, as explained in Chapter 3, φ is the geodetic and θ the
geocentric latitude of M.

Fig. A5-2. Geodetic and geocentric latitudes

If the distance of the point M from the polar axis OP is x, and its distance
from the major axis OA is y, these distances or co-ordinates are connected by
the equation of the ellipse on which M lies; that is:

x2 y2
+ =1
a 2 b2
y2 x2
= 1− 2
b2 a
2 x 2b 2
2
y =b − 2
a
dy b2
By differentiation: 2y = − 2x 2
dx a
dy x b2
=−
dx y a2
If ψ is the angle which the tangent MK makes with the X-axis then, since
the slope of the tangent is measured by the differential coefficient:
GEODETIC, GEOCENTRIC AND PARAMETRIC LATITUDES 639

dy b2 x
tan ψ = =− 2
dx a y
But ψ is equal to (φ + 90°) since ML is perpendicular to MK:

hence tan ψ = − cot φ

b2 x
∴ cot φ = 2 . . . A5.3
a y
b2
= 2 cot θ
a
φ and θ are connected by the formulae:
b2
tan θ = 2 tan φ . . . (3.4)
a
= (1 − f ) tan φ
2
. . . (3.5)

= (1 − e 2 ) tan φ . . . (3.6)

The difference between the geodetic and geocentric latitudes is zero at the
equator and the poles and has a greatest value when φ = 45°. For the
International (1924) Spheroid where f = 1/297, the greatest value of the angle
OML (φ - θ ) • 11.6 minutes of arc.

The parametric latitude

Fig. A5-3. Parametric latitude

In Fig. A5-3, as explained in Chapter 3, β is the parametric latitude of M. If

the co-ordinates of M are (x, y) and WBE is a semi-circle of radius a, centre
O.
OH = OU cos β
i.e. x = a cos β
640 APPENDIX 5-THE SPHEROIDAL EARTH

From (A5.1):
y2 x2
= 1− 2
b2 a
= 1 − cos2 β
y 2 = b 2 (1 − cos2 β ) = b 2 sin 2 β
y = b sin β
y b
∴ = tan β
x a
From Fig. A5-2:
y
= tan θ
x
which, from (3.4):
b2
= 2 tan φ
a
b
∴ tan β = tan φ . . . A5.4
a

= (1 − f ) tan φ . . . A5.5

The difference between the geodetic and parametric latitudes is zero at

the equator and at the poles and has a greatest value when φ = 45°. For the
International (1924) Spheroid where f = 1/297, this amounts to 5.8 minutes
of arc approximately.

THE LENGTH OF ONE MINUTE OF LATITUDE

Fig. A5-4. The length of one

minute of latitude (1)
THE LENGTH OF ONE MINUTE OF LATITUDE 641

The length of the sea mile (one minute of latitude on the spheroid) may be
found from the general formula ρ dφ (Fig. A5-4) where ρ is the radius of
curvature in the meridian and dφ a small increase (in radians) in the geodetic
latitude φ .

Fig. A5-5. The length of one minute of latitude (2)

Fig. A5-5 shows an expanded version of Fig. A5-4, where dφ is a very

small increase in φ . The co-ordinates of M are (x, y); those of M1,
representing this small increase, are (x & dx), (y + dy).
The triangle MQM1 may be considered plane and, if the length of MM1 is
denoted by dR then: dl 1
=−
dx sin φ
dl
But, as =ρ
dφ
dl = ρdφ
dx dl
= x
dφ dx
1 dx
∴ρ= − x . . . A5.6
sin φ dφ
642 APPENDIX 5-THE SPHEROIDAL EARTH

dx
may be found as follows:
dφ
From (A5.3):
xb 2
y = 2 tan φ
a
which, from (A5.2):
= x(1 − e 2 ) tan φ
If this value of y is substituted in the general equation of the ellipse
(A5.1) and the value of b from (A5.2) also substituted, then:
x 2 x 2 (1 − e 2 ) tan 2 φ
2

+ =1
a2 a 2 (1 − e 2 )
x 2 + (1 − e2 ) x 2 tan 2 φ = a 2
x 2 (1+ tan 2 φ − e 2 tan 2 φ = a 2 )

x 2 ( sec 2 φ − e 2 tan 2 φ ) = a 2
é 1
2 e2 sin 2 φ ù
x ê − ú = a2
ë cos φ cos φ û
2 2

a cos φ
x=
(1 − e 2
sin 2 φ )
1/ 2

= a cos φ (1 − e2 sin 2 φ )
− 1/ 2
. . . A5.7

Differentiating:
dx − a(1 − e2 ) sin φ
=
dφ (1 − e2 sin 2 φ ) 3/ 2
Substituting in (A5.6):
a(1 − e2 )
ρ= . . . (3.8)
(1 − e
sin φ )
2 2 3/ 2

Thus, when dφ equals 1' of arc:

a(1 − e2 )
lr of latitude = sin 1' . . . (3.9)
(1 − e2 sin2 φ ) 3/ 2
This is the theoretical expression for the sea mile. The expression may
be expanded as follows:
æ 3e2 15e 4 ö
2
lr of latitude = a sin 1' (1 − e )ç 1 + sin φ +
2
sin 4 φ + ...÷
è 2 8 ø
Disregarding terms of e4 (10-5 x 4.5) and higher powers:
THE LENGTH OF THE MERIDIONAL ARC 643

æ 3e2 ö
lr of latitude = a sin 1' ç 1 + sin 2 φ − e 2 ÷
è 2 ø
é 3e 2
ù
= a sin l' ê1 − e 2 +
4
(1 − cos 2φ )ú
ë û
æ e 2
3e 2
ö
= a sin l' ç 1 − − cos 2φ ÷
è 4 4 ø
é e2 ù
= a sin l' ê1 − (1 + 3 cos 2φ )ú
ë 4 û
When figures for a and e for the International (1924) Spheroid are given:

lr of latitude = 1852.28 - 9.355 cos 2φ metres . . . A5.8

which gives a solution for the sea mile correct to the order of 0.001%.*

THE LENGTH OF THE MERIDIONAL ARC

The distance R along a meridian between two latitudes φ1 and φ2 may be

found as follows:
φ2
l= òφ ρdφ
1 . . . (5.17)
φ 1
= a(1 − e )ò
2
3/ 2 dφ
2
. . . (5.18)
φ 1
(1 − e
sin 2 φ ) 2

Expanding by the binomial theorem:

φ2æ 3e2 15e4 35e6 ö
= a(1 − e )ò ç 1 +
2
sin φ +
2
sin φ +
4
sin 6 φ + ...÷ dφ
φ1 è 2 8 16 ø
Each term in the integral may now be integrated separately where:

ò sin 2
φ dφ = ò (½ − ½ cos 2φ ) dφ
φ sin 2φ
−= +c
2 4
æ 3 cos 2φ cos 4φ ö
ò sin4 φ dφ = ò çè 8 − 2 + 8 ÷ø dφ
3φ sin 2φ sin 4φ
= − + +c
8 4 32
æ 10 15 cos 2φ 3 cos 4φ cos 6φ ö
ò sin6φ dφ = çè 32 − 32 + 16 − 32 ÷ø dφ
10φ 15 sin 2φ 3 sin 4φ sin 6φ
= − + − +c
32 64 64 192
* By comparison with NP 240, Spheroidal Tables, formula (A5.8) gives a solution which is correct at the
equator, 0.001% in error at latitude 45° and 0.002% in error at latitude 90°.
644 APPENDIX 5-THE SPHEROIDAL EARTH

é 3e2 æ φ sin 2φ ö
l = a(1 − e )ê φ +
2
ç − ÷
ë 2 è2 4 ø
15e4 æ 3φ sin 2φ sin 4φ ö
+ ç − + ÷
8 è 8 4 32 ø

35e 6 æ 10φ 15 sin 2φ 3 sin 4φ sin 6φ ö ù φ2

+ ç − + − ÷ + ... ú
16 è 32 64 64 192 ø û φ1
This may be expanded in the form:
[
l = a Aoφ − A2 sin 2φ + A4 sin 4φ − A6 sin 6φ + ... φ 1 ]
φ2

. . . (5.19)
[
l = a Ao (φ2 − φ1 ) − A2 (sin 2φ2 − sin 2φ1 )
+ A4 (sin 4φ2 − sin 4φ1 ) − A6 (sin 6φ2 − sin 6φ1 )+ ... ]
. . . A5.9
where φ is measured in radians and
1 2 3 4 5 6
Ao = 1 − e − e − e − ...
4 64 256
3 æ 2 1 4 15 6 ö
A2 = çe + e + e + ...÷
8è 4 128 ø
15 æ 4 3 6 ö
A4 = ç e + e + ...÷
256 è 4 ø
35 2
A6 = e + ...
3072
A computer is ideal for this calculation, and may be programmed to carry
out the computation to as many terms as the user wishes.
Such a calculation may be determined reasonably quickly, and to a high
degree of accuracy, using a pocket calculator and disregarding terms of
e6(10-7 x 3.1) and higher powers. In this case, the meridional arc distance R
from the equator to latitude φ may be found from the formula:
é e 2φ 3e 2 3e 4 3e4 15e4 ù
l = a êφ − − sin 2φ − φ− sin 2φ + sin 4φ ú
ë 4 8 64 32 256 û
. . . (5.24)
Tables may be constructed from the general formula (5.19) as the user
desires by means of a desk-top computer, giving the length of the meridional
arc for any latitude at, say, minute of arc intervals. This may be computed for
any spheroid and may be expressed in metres, n miles, etc. depending on the
unit used for a. The length of the meridional arc between the two different
latitudes can then be measured and the course and distance computed between
two positions using formulae (5.22) and (5.23) (see the example on page 95).
Conversely, if the course, distance and initial positions are known, the final
THE LENGTH OF THE MERIDIONAL ARC 645

latitude may be computed from the length of the meridional arc and the final
longitude from the difference of meridional parts.
EXAMPLE
A ship in position 2°N, 25°W, steers a course of 060° for 600 miles. What are
her latitude and longitude at the end of the run?
If no allowance is made for the spheroidal shape of the Earth, the latitude
and longitude of the final position may be found from formulae (2.3) and
(5.3) respectively:
d.lat = distance cos course = 600' cos 60° = 5°N
d.long = DMP tan course (DMP for the sphere)
which, from formula (4.1):
= 301.03 tan 60° = 521'.4E = 8° 41'.4E
final position = 7°N, 16° 18'.6W
On the International (1924) Spheroid, from (5.23):
R = distance cos course = 300 n miles
R1 for 2°N = 119.412 n miles
ˆ R2 = 419.412 n miles
which, from a table constructed for the spheroid, may be seen to be the
equivalent of:
7° 01'.46N latitude
= 7° 01'.5N
d.long = DMP tan course
which, from NP 239:
= 300.515 tan 60° = 520'.5E = 8° 40'.5E
final position = 7° 01'.5N, 16° 19'.5W
If a computer-produced table for the length of the meridional arc against
latitude is not available, an approximate final latitude may be obtained from
(A5.8), where:
æ 1852.28-9.355cos2( mean lat ) ö
l = d.lat ç ÷ . . . A5.10
è 1852 ø
In the above example, using a mean latitude of 4½°N:
d.lat = 5°01'.5N
final latitude = 7° 01'.5N
This final latitude can now be tested against (5.24) and adjusted as
necessary.
The longitude may now be determined using DMP for the spheroid.
The difference between the two latitudes (1'.5 in this case) illustrates the
error which can arise from the assumption that a distance in n miles can
be said to equate to a d.lat measured in minutes of arc or sea miles. For
646 APPENDIX 5-THE SPHEROIDAL EARTH

the practical navigator, little account need be taken of this difference between
the n mile and the sea mile except when precise distances, particularly near
the equator or the poles, are required, as the maximum error in this
assumption is of the order of 0.5%.

MERIDIONAL PARTS FOR THE SPHEROIDAL EARTH

Certain books of tables (e.g. NP 239, Table of Meridional Parts based on the
International (1924) Spheroid, or Norie’s Tables (Clarke 1880 spheroid)
make an allowance for the oblate spheroidal shape of the Earth.
The table of meridional parts which cartographers use to compute the
graticules for Mercator charts is the table of spheroidal meridional parts; its
use is thus consistent with the use of the chart. Astronomical observations at
sea are made with reference to a horizon which is part of the spheroidal
surface of the Earth; thus, tables of spheroidal meridional parts are consistent
with the co-ordinates of positions found from astronomical observations.
In Fig. A5-6, the elliptic meridional section of the Earth may be
expressed by the equation:
x2 y2
+ =1
a 2 b2

where x = a cos β
y = b sin β

Fig. A5-6. Meridional section of the Earth

MERIDIONAL PARTS FOR THE SPHEROIDAL EARTH 647

At a point M which has co-ordinates (x, y) with reference to O, the centre

of the ellipse, let the geographical latitude be φ . If the radius of curvature
at M is ρ , the length of an element of the meridian is ρ dφ .
In order to measure the meridional parts of φ , the element ρ dφ must be
expressed in terms of the length of 1 minute of longitude at latitude φ .
Now the longitude scale for this latitude is x/a times the longitude scale at the
equator, and the unit of longitude at the equator is the length of that
equatorial element which subtends an angle of 1 minute of arc at the centre
of the Earth. The length of this element is a divided by the number of
minutes in 1 radian, that is:
aπ
10800
The length of a minute of longitude at latitude φ is thus:
x aπ xπ
x or
a 10800 10800
and the number of longitude units in the meridional element ρ dφ is:
xπ 10800 ρ
ρdφ ÷ or x dφ
10800 π x
The meridional parts at latitude L are given by the equation:
10800 L ρ
π òO x
mer. parts L = dφ

which, from (3.8) and (A5.7):

10800 L a(1 − e2 ) 1
=
π ò (1 − e
O 2
sin φ )
2 3/ 2 x
a cos φ (1 − e sin φ )
2 2 − 1/ 2 dφ

10800 L æ 1 − e2 ö
π òO
= sec φ ç ÷ dφ . . . A5.11
è 1 − e 2 sin 2 φ ø
10800
[
sec φ 1 − e 2 cos2 φ(1 + e2 sin 2 φ + e4 sin 4 φ
L
=
π ò
O

+ e6 sin 6 φ + ... ) ]dφ

10800 L
=
π òO
( sec φ − e2 cosφ − e 4 sin 2 φ cos φ

− e 6 sin 4 φ cos φ − ... )dφ

10800 é æ L° ö 1
= ê log e tan ç 45°+ ÷ − e 2 sin L − e 4 sin 3 L
π ë è 2ø 3
1 6 5
− e sin L − ...
5
] . . .(5.21)
648 APPENDIX 5-THE SPHEROIDAL EARTH

For the International (1924) Spheroid, a suitable numerical formula

giving the meridional parts correct to three decimal places is:
æ L° ö
mer. parts = 7915.7045 log10 tan ç 45°+ ÷
è 2ø
− 231108
. sin L − 0.052 sin 3 L . . . A5.12

THE LENGTH OF THE EARTH’S RADIUS IN VARIOUS LATITUDES

In Fig. A5-2 the required geocentric radius is OM and, if this length is

denoted by R, it follows that x is R cos θ and y is R sin θ. Hence, by
substituting for x and y in the equation of the ellipse:
R 2 cos2 θ R 2 sin 2 θ
+ =1
a2 b2
but as b = a (1 − f )
2 2 2

[ ]
R 2 (1 − f ) cos2 θ + sin 2 θ = a 2 (1 − f )
2 2

When terms in f 2 (10-5 x 1.1) are neglected, this equation becomes:

R 2 (1 − 2 f cos2 θ ) = a 2 (1 − 2 f )
1/ 2
æ 1 − 2f ö
R = aç ÷
è 1 − 2 f cos2 θ ø
When the right-hand side is expanded by the binomial theorem, terms in f 2
and higher powers again being omitted, the equation becomes:
R = a(1 − f )(1 + f cos2 θ )

= a(1 − f sin 2 θ )

Since θ varies from φ by a small quantity, R may be expressed in terms

of the geodetic latitude (page 638) without appreciable error by direct
substitution:

i.e. R = a(1 − f sin 2 φ ) . . . A5.13

 649

APPENDIX 6
Vertical and Horizontal Sextant
Angles

VERTICAL SEXTANT ANGLES

Base of the object below the observer’s horizon

A position line may be obtained from the observation of the vertical sextant
angle (VSA) such as a distant mountain peak where the base is below the
observer’s horizon.

Fig. A6-1. Position line by vertical sextant angle&

base of the object below the horizon (1)

This situation is illustrated in Fig. A6-1. O is the centre of the Earth, which
has radius R. AD is the height of eye h. B is the summit of a mountain whose
650 APPENDIX 6-VERTICAL AND HORIZONTAL SEXTANT ANGLES

height BE is H above sea level. DE is the required distance d, while the angle
measured between the mountain top and the observer’s horizon is represented
by the angle CAF. This takes account of the terrestrial refraction r, which
‘bends’ the ray of light as it proceeds through the atmosphere between object
and observer. Thus, the top of the mountain B is seen in the direction AC,
while the horizon G is seen in the direction AF. These two lines AC and AF
are tangential to their respective curved rays of light (pecked in Fig. A6-1).
AK is the horizontal at the observer’s position and the angle KAF is
known as the angle of dip, which may be defined as the angle between the
horizontal plane through the eye of the observer and the apparent direction
of the visible horizon. It is always present when the observer’s eye is above
sea level.
Dip is tabulated in the Nautical Almanac and in Norie’s Tables.
Terrestrial refraction amounts to approximately 1/13 of the distance in n
miles of the object, expressed in minutes of arc. Dip and refraction are
explained fully in Volume II of this manual; both must be subtracted from the
observed altitude of the summit to obtain the true altitude.
Provided that an estimated distance of the object is available, a position
line may be obtained.
The apparent altitude of B as measured from the sea horizon, when
reduced by dip, is the angle CAK, α. The true altitude of B, the angle BAK,
is (α & r), where r is the amount of refraction CAB.

Fig. A6-2. VSA. Base of the object below the horizon (2)

In the triangle OAB (Fig. A6-2):

OA = R* + h
OB = R + H

* R may be found from the formula R = a(1-f sinφ 2

) (see formula A5.13) where α is the equatorial radius, f
φ is the mean latitude between observer and object.
is the compression (flattening) of the spheroid and
VERTICAL SEXTANT ANGLES 651

OAB = 90°+ α − r

OBA = 180° = ( d + 90°+ α − r )

= 90°− d − α + r
sin OBA R + h
=
sin OAB R + H
sin 90°− ( d + α − r ) R + h
=
sin 90°+ (α − r ) R+ H
cos ( d + α − r ) R + h
=
cos (α − r ) R+ H
R+ h . . . A6.1
cos ( d + α − r ) = cos (α − r )
R+ H
The distance d may easily be found from evaluating formula (A6.1) on a
hand-held calculator, as shown by the following example.
EXAMPLE
A mountain 1646 m (5400 ft) high is observed at a range of about 25 miles.
Mean latitude between observer and object is 41°27'. Height of eye is 7.6 m
(25 ft). The vertical sextant angle of the summit is 1°59'.3. Index error of the
sextant is -1'.3. What is the range of the mountain?
observed angle 1°59.3
index error -1'.3
1°58'.0
dip -4'.9
apparent altitude (α) 1°53'.1
refraction correction (r) (25/13 = 1'.9) -1'.9
true altitude (α-r) 1°51'.2 (1°.8533)
R = 3438.9726 n miles
H= 0.8889 n miles
h = 0.0041 n miles
3438.9767
cos ( d + 1° .8533) = cos 1° .8533
3439.8615
d = 2 o .2634 − 1o .8533
= 0° .4101
= 24.6 n miles*
If the estimated distance if found to be much in error, a second
approximation will be necessary.

* This distance may be taken for all practical purposes at sea miles. The maximum error in so doing varies
between zero at about latitude 45° and 0.5% at the equator and the poles.
652 APPENDIX 6-VERTICAL AND HORIZONTAL SEXTANT ANGLES

Long-range position lines obtained in this way are of little value if

different from normal refraction (see Volume II of this manual) is suspected.
Abnormal refraction is likely to be present when the temperature of the water
and that of air differ considerably.
This method of obtaining a position line has a limited application and
while useful in giving a reasonably satisfactory long-range position line on
a single isolated peak, e.g. Tenerife in the Canaries, it should not be used with
a mountain peak which forms part of a mountain chain unless it has been
positively identified.

HORIZONTAL SEXTANT ANGLES

Rapid plotting without instruments

To enable fixes obtained by horizontal sextant angles to be plotted rapidly
without instruments, a lattice of HSA curves may be constructed on a chart.
Each curve gives the constant angle between a pair of suitably placed fixing
marks, and is in fact an arc of a circle. If a set of curves is plotted for each of
two pairs of marks, then, having observed the angle between each pair
simultaneously, the navigator can plot the resultant fix immediately at the
intersection of the two curves corresponding to the two angles. A sufficient
number of curves must be drawn to enable the observed angles to be plotted
conveniently by interpolation between the lattice lines.
Preparing a lattice for plotting HSA fixes
This is illustrated in Fig. A6-3.
Consider the pattern of arcs which may be generated from one pair of
objects A and B. Three arcs are shown: AEB, ADB, ACB. Their centres O,
P, Q respectively, all lie along the perpendicular bisector FQ of the base line
AB. Consider one arc AEB. Let OQ, the distance of the centre of the arc from
the base line, be x. Then:

x = ½d cot θ . . . A6.2
where d is the length of the base line and θ is the angle subtended by the
chord AB on the circumference of the circle through AEB.
This formula may now be used to construct the lattice for all required
angles.
Fixing objects within the boundaries of the chart
Chart D6472, Diagram for Facilitating the Construction of Curves of Equal
Subtended Angles, issued by the Hydrographer with the miscellaneous charts
and diagrams folio 317 (see page 126) enables the Navigating Officer to plot
his own lattice of curves on any chart or plotting sheet, provided that all the
fixing objects lie within the boundaries of the chart. Full instructions as to
how to use Chart D6472 are printed on it.

Fixing objects outside the boundaries of the chart

If the fixing objects do not lie within the area of the chart, the following
procedure will enable the Navigating Officer to plot his own lattice.
HORIZONTAL SEXTANT ANGLES 653

Fig. A6-3. Pattern of arcs generated from one pair of objects

654 APPENDIX 6-VERTICAL AND HORIZONTAL SEXTANT ANGLES

1. Lay out on an appropriate space, such as the floor or deck, the chart or
plotting sheet on which the lattice is required. Represent the HSA marks
with pins placed in their correct relative positions.
2. From the largest scale navigational chart which shows the fixing marks,
measure, as accurately as possible, the distance between them. Convert
these distances to the desired scale of the lattice to obtain the distances
between the pins on the floor. The simplest method for this scaling up is
to find a multiplication factor, e.g. if the navigational chart has a natural
scale of 1:50,000 and the lattice is to have a scale of 1:10,000, then all
50,000
chart lengths taken off the former must be multiplied by = 5.
10,000

In this case, if two objects, A and B, are found to be 150 mm apart of

the navigational chart, the pins should be placed (150 x 5) = 750 mm
apart on the floor.
3. Measure the angle between the base lines (α in Fig. A6-4) and lay this off
on the floor. Measure the appropriate floor lengths and mark the position

Fig. A6-4. Construction of the HSA lattice

HORIZONTAL SEXTANT ANGLES 655

of the third object C. If the grid co-ordinates of the fixing marks are
known, the accuracy of all these measurements should be checked by
calculation.
4. Next, the exact position on the floor for the lattice chart must be found.
On the largest scale navigational chart which shows both the lattice area
and the fixing marks, draw in the limits of the lattice chart. Measure the
distances from each of the fixing marks to all four corners of the lattice
(Aa, Ab, Ad, Ac, Ba, Bb, etc). Scale up these distances by the
multiplication factor found as described above, and then, by striking off
arcs on the floor, fix the positions of the corners of the lattice. Pin down
the outline lattice chart in this position.
5. On the floor draw the base lines and their perpendicular bisectors.
Note: Where the floor surface is unsuitable for drawing, tightly
stretched thread can be used.
6. On the perpendicular bisectors of the base lines mark the centres of the
arcs to be drawn (½d cot θ from the base line).
Strike off two arcs from each pair of objects giving an intersection at
each end of the lattice area. As a check, compare for accuracy the
geographical positions of the intersections thus obtained with fixes
plotted by station pointer using the same angles on a navigational chart
which shows the objects and lattice area. This will reveal any inaccuracy
in the construction of the lattice.
7. Finally, complete the lattice, using red ink for the curves generated from
the left-hand angles as viewed from seaward, and green for the right-hand
angles. On large-scale lattices an alteration of firm and pecked lines in

Fig. A6-5. Lattice of HSA curves

656 APPENDIX 6-VERTICAL AND HORIZONTAL SEXTANT ANGLES

each pattern may improve the clarity of the lattice. If the curves do not
cut at a satisfactory angle or are too widely spaced in any part of the
chart, other objects can be taken and the curves generated from them
drawn in the appropriate area, colours other than red or green being used.
The general form of the completed lattice is shown in Fig. A6-5.
 657

APPENDIX 7
Errors in Terrestrial Position Lines

Chapter 16 and the annex to that chapter discuss how navigational errors
(faults, systematic and semi-systematic errors and random errors) may be
recognised and dealt with. This appendix sets out to quantify particular
errors in terms of distance, given certain parameters: for example, the
displacement in a fix given the angle of cut between the position lines, the
distance apart of the objects, and an assumed constant (or maximum) value
in the error in the bearing of each position line. Errors in terrestrial bearings
and in horizontal sextant angles are quantified in terms of the distance
between the true and the obtained positions. The appendix concludes with
a discussion on how the position is obtained when doubling the angle on the
bow in a current or tidal stream.

SEXTANT ERRORS

Whenever a sextant is used, whether for measuring an altitude or a horizontal

angle, there is a possibility of an error which may be significant. Index error
is easily found, reduced if necessary, and allowed for, but the failure to
eliminate perpendicular error, side error and collimation error may easily
give rise to an unknown error when an observation is made.
In addition to this error, there is the limitation of the sextant itself,
depending on the accuracy aimed at in the observation. The ordinary sextant
reads to the nearest 0'.2.

Personal error
Personal error, as the name suggests, is peculiar to the observer himself, and
affects all his observations. Unless it is abnormal it is of no practical
importance when bearings are measured, but it may be when altitudes are
measured because the precision required is then considerable.

ERRORS IN TAKING AND LAYING OFF BEARINGS

In practical chart work involving observations of terrestrial objects, there is

the possibility that the lines of bearing are plotted inaccurately or to a degree
of accuracy less than that with which the observations were made.
658 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

Bearings taken with a magnetic compass are particularly liable to error

because the deviation is not constant and, although it may be practically
eliminated when the compass is corrected, it may not be negligible or even
accurately known several days later. The effect of sub-permanent magnetism,
the heating of funnels, and change in latitude all combine to vary the
deviation.
The diameter of the card in the standard magnetic compass is 16.5 cm,
and a degree is represented by two lines on the circumference approximately
1.5 mm apart. It is not easy, therefore, to take a bearing with certainty, and
if the ship is unsteady the difficulty is further increased.
In the gyro-compass there is the possibility of an unknown residual error
in the compass itself.
When these sources of error are borne in mind, it is seen that the resulting
error in the line of bearing drawn on the chart may easily reach ½°, and this
may lead to an appreciable displacement of the fix.

Displacement of fix when the same error occurs in two lines of bearing

Fig. A7-1. Errors in two lines of bearing

The fix by two lines of bearing from terrestrial objects is one of the simplest
methods of finding a ship’s position. In Fig. A7-1, A and B are these objects
and AC and BD the two accurate lines of bearing intersecting F, the ship’s
true position.
ERRORS IN TAKING AND LAYING OFF BEARINGS 659

If the errors in the position lines drawn on the chart are the same in
magnitude and sign&that is, the angle CAC1 is equal to the angle DBD1&these
position lines may be represented by AC1 and BD1 and F1, their point of
intersection, is the fix obtained. The displacement is FF1.
Let the error in the bearing be denoted by α and the true angle of cut AFB
by θ. Then the angle of cut actually obtained is also θ since these angles are
in the same segment of which FF1 is the base.
Hence, if errors in the two position lines are the same in magnitude and
sign, F1 will lie on a circle passing through A, B and F.
To find FF1 draw FG perpendicular to BF1. Then:
BF sin GBF = FF1 sin BF1 F
BF sin GBF
i.e. FF1 =
sin BF1 F
But the angles BF1F and BAF are equal, and from the rule of sines:
BF AB
=
sin BAF sin AFB
AB sin GBF
therefore FF1 =
sin AFB
AB sin α
=
sin θ
If α, which is a small angle, is now expressed in radians, the displacement is
given in the form: α AB
FF1 =
sin θ . . . A7.1

Formula (A7.1) shows that the error in the fix resulting from a constant
error in the observation is least when θ is 90°, and increases as θ decreases,
this increase becoming rapid after θ has reached about 30°. When θ is 30°,
the error is αAB cosec 30°, or twice the error when the angle of cut is 90°.

EXAMPLE
It is required to find the errors in the fix obtained when the true bearings of
two points, A and B, 14 miles apart, are (1) 060° and 030°, (2) 010° and
100°, and the errors in the observed bearings are each 1°.

1. The angle of cut, being the difference of the true bearings, is 30° and the
2π
error in each bearing is radians.
360
Hence the displacement of the fix is given by:

2π
FF1 = 14' x x cosec 30°
360
= 0'.5 (approximately)
660 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

2. The angle of cut is 90°, and the displacement is given by:

2π
FF1 = 14' x x cosec 90°
360
= 0'.25 (approximately)
The cocked hat
When the lines of bearing from three objects, observed simultaneously, are
drawn on the chart, it is usually found that they do not meet in a point but
form a cocked hat as explained in Chapter 9.
The cocked hat results from:

1. The unknown and therefore uncorrected error of the compass which may
be as much as 1°.
2. The error in observation resulting from the limitations of the compass,
which may be ¼°.
3. The error in the actual plotting of the lines of bearing, which may also be
¼°.

Of these errors (2) and (3) are fortuitous and may have either sign. That
is, the plotted results could be up to ½° high or ½° low on what the bearings
should be. The remaining error (1), however, has a definite sign and,
although it may be high or low, it is the same in each plotted bearing. It is
thus convenient to investigate this error first.

The cocked hat arising from the same error in three lines of bearing
In Fig. A7-2, F is the true position, and A, B and C are three objects, the true
bearings of which are observed. Suppose these bearings are 221°, 276° and
313°.
If the bearings are taken and laid off correctly, the three position lines
intersect in F, but if there is an unknown compass error of 1° low, say&it is
shown in the figure as 10° for the sake of clarity&the bearings plotted on the
chart are AZ (220°), BX (275°) and CY (312°), and they form the cocked hat
XYZ.
Since the difference between the bearings of A and B will be the same
whether the compass error is applied or not, the angle AZB must be equal to
the angle AFB, and Z, the point of intersection of the two bearings AZ and BZ,
must lie on the circle through A, B and F. Similarly X, the point of
intersection of the two bearings BX and CX, must lie on the circle through B,
C and F; and Y, the point of intersections of the two bearings AY and CY,
must lie on the circle through A, C and F.
The true position F, can be seen to lie outside the triangle XYZ.
The distances of F from the vertices of the triangle are given by formula
(A7.1) on page 659. Thus, if α is the constant error of the bearings in radians
and θ1, θ2 and θ3 are the angles between the bearings of A and B, B and C, and
C and A: α AB
FZ =
sin θ 1 . . . A7.2
ERRORS IN TAKING AND LAYING OFF BEARINGS 661

α BC
FX = . . . A7.3
sin θ 2
α CA
FY = . . . A7.4
sin θ 3

The distances AB, BC and CA can be taken from the chart. If, for
example, they are respectively 2', 5', and 7' and the values of θ1, θ2 and θ3 are

Fig. A7-2. Errors in three lines of bearing (1)

662 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

30°, 90° and 120°, while the constant error is 1°, the separate displacements
of F are given by the above formulae as:

FZ = 0.7 cables
FX = 0.9 cables
FY = 1.4 cables

When the cocked hat results from an inaccuracy in the assumed value of
the compass error (i.e. a constant error), the amount and sign of the error may
be obtained approximately from Fig. A7-2. In this figure Z is the intersection
of the position lines through A and B, and F lies on the circle through A, B
and Z. For similar reasons, F lies on the circles through B, C and X, and C,
A and Y. F is therefore the point of intersection of the three circles.
In this case, the position of F, obtained by this construction, is the true
position of the ship.
It must be borne in mind that the three circles drawn in Fig. A7-2,
irrespective of the number of errors involved and of the differences in
magnitude and sign that may exist between them, will always intersect in one
point. This point, however, will only be the true position of the ship when the
amount and sign of the error are the same on each bearing, i.e. a compass
error as previously explained.

EXAMPLE
It is required to find the compass error when the bearings of three objects,
carefully taken by gyro-compass, are such that the difference between the
bearings of A and B is 45°. AB is 6' and FZ, as measured on the chart, is
0'.4.
From formula (A7.2):
αAB
FZ =
sin θ1
0.4 sin¼π
α= radians
6
= 2° .7
The sign of α can be obtained from the chart.

The cocked hat in general

When errors of observation and plotting are included with the compass error,
the resulting errors in the position lines may all differ, and a cocked hat is
formed as shown in Fig. A7-3.
The constant error α is now replaced by separate and unequal errors α1,
α2 and α3 In this example α1 and α2 have the same sign, which is opposite to
that of α3.
As before, F is the true position of the ship, and AZ, BX and CY are the
lines of bearing actually plotted and forming the cocked hat XYZ.
Unless the errors α1, α2 and α3 are definitely known, it is impossible to
locate the position of F from this cocked hat.
ERRORS IN TAKING AND LAYING OFF BEARINGS 663

The value and sign of α3 may cause the plotted line of bearing CY to pass
through Z. Z is then the fix by observation, but it is still a distance FZ in
error. It is thus clear that, even when all three lines of bearing intersect in a
single point, the resultant fix may be considerably in error. The best estimate
of the true position F can be arrived at using the least squares solution (see
page 494). |
In the practice of navigation, when a cocked hat is obtained, it is
customary to place the ship’s position on the chart in the most dangerous |
position that can be derived from the observations because the existence of
the cocked hat is evidence and the observations are inaccurate and, by
interpreting them to his apparent disadvantage, the navigator gives himself
a margin of safety which he might not otherwise have.

Fig. A7-3. Errors in three lines of bearing (2)

ERRORS IN HSA FIXES

When the horizontal angle subtended by two objects at an observer is

measured, it tells him that his position lies on the arc of a circle passing
through the points. If the angle subtended by one of these objects and a third
object is now measured, a second position circle is obtained, intersecting the
first position circle at the common object. The other point of intersection is
the observer’s position. These position circles can be plotted directly, or the
angles can be set on a station pointer. But, whatever method is used for
664 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

finding the observer’s position, there will be a possibility of error in the

position found owing to:

1. Error in the measurement of the angles.

2. Plotting error, or the instrumental error inherent in the station pointer.
3. Error arising from the fact that, in general, the three objects and the
observer will not lie in a horizontal plane.

In Fig. A7-4, AFB and BFC are the accurate position circles and AF1B
and BF1C are those obtained by observation and plotting. F is the true
position of the observer, and F1 is that obtained.
X is the point in which the circles BFC and AF1B intersect, and BX
produced cuts the circle AFB in Y.
It is assumed that each horizontal angle has the same error α. That is, the
plotted angle AF1B is equal to the true angle AFB plus the error α. The error
α is equal to the angle XAY. Similarly, the plotted angle BF1C is equal to
(BFC + α).
r1 is the ratio of the observer’s distance from the first object A to the
distance of A from B, the middle object, i.e.
AF
r1 =
AB
CF
similarly r2 =
CB
θ is the acute angle of cut between the two circles AFB and BFC; that is
to say, θ is the acute angle between the tangents to the two circles at the point
of intersection F.
The distance between the true position F and the plotted position F1 (i.e.
the error in position F1) may be found from the formula:
αFB . . . A7.5
FF1 = r12 + r2 2 + 2r1r2 cos θ
sin θ
where α is measured in radians.

Maximum errors in the HSA fix

Formula (A7.5) shows that FF1 varies directly as α and the distance of the fix
from the object common to both observations, and inversely as sin θ; FF1 also
depends on the values of the ratios r1 and r2.
When θ is small, cosec θ and cos θ are both large, and FF1 is large.
When θ is equal to 90°, cosec θ is unity, and cos θ is zero, and FF1 is
given by:

αFB r12 + r2 2

For values of r1 and r2 not exceeding 5, and for values of ½(r1 + r2) less than
3, the mean ratio ½(r1 + r2) can be used instead of each separate ratio without
appreciably altering the maximum error, and when this is done, and the value
æ 30 ö
of α is taken as ½°çè 3438 radians÷ø , formula (A7.5) can be adjusted to give
ERRORS IN HSA FIXES 665

Fig. A7-4. Errors in horizontal sextant angles

666 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

a still more approximate value of the maximum error. Thus:

αFB
½(r1 + r2 ) (1 + cos θ )
2
FF1 max =
sin θ
αFB ær +r ö
= x ç 1 2÷
sin ½θ è 2 ø
30 FB ær +r ö
= xç 1 2 ÷
3438 sin ½θ è 2 ø
FB æ r1 + r2 ö
= ç ÷ in miles (approximately)
θ° è 2 ø
distance of middle object . . . A7.6
= x mean ratio
acute angle of cut in degrees
If the distance FB is taken as unity, a table may be constructed in terms
of θ and the mean ratio, giving the values of FF1 and from this table the error
for any other value of FB can be found by multiplying the tabulated error by
that value. The error itself is tabulated in cables instead of decimals of a mile.
Table A7-1. Maximum error in cables of an HSA fix, for each mile of
distance from the middle object and for values of θ and the mean ratio, when
the error in each angle observed is ½°.

ACUTE MEAN MEAN MEAN MEAN MEAN

ANGLE RATIO ½ RATIO 1 RATIO 1½ RATIO 2 RATIO 2½
OF CUT

10° 0.5 1.0 1.5 2.0 2.5

20° 0.3 0.5 0.8 1.0 1.3
30° 0.2 0.3 0.5 0.7 0.8
40° 0.1 0.3 0.4 0.5 0.6
50° 0.1 0.2 0.3 0.4 0.5
60° 0.1 0.2 0.3 0.3 0.4
70° 0.1 0.1 0.2 0.3 0.4
80° 0.1 0.1 0.2 0.2 0.3
90° 0.1 0.1 0.2 0.2 0.3

In Fig. A7-5, A, B and C are three objects. The circles of position

corresponding to the horizontal sextant angles have been drawn, and it is seen
that they intersect at an angle of about 40°. It is also seen that the ratios r1
and r2, being FA/AB and FC/BC, are about 1 and 2. The mean ratio is thus
about 1½.
If, for example, FB is 3', the maximum error in the fix corresponding to
an error of ½° in observation and plotting, is 1.2 cables.

Reliability of HSA fixes

Formula (A7.6) makes it possible to set out rules for deciding whether a
station-pointer fix is reliable or not, and for indicating the extent of its
reliability.
ERRORS IN HSA FIXES 667

Fig. A7-5. Maximum error in the HSA fix

There are three factors to consider: the acute angle of cut θ, the distance
of the fix from the middle object or object common to both observations, and
the mean of the ratios r1 and r2. The formula shows that the error in the fix
will be least when three conditions are fulfilled:

1. The distance of the fix from the middle object is as small as possible.
That is, the nearest of the three objects should be chosen as the middle
object when practicable.
2. The angle of cut should be as near as 90° as possible.
3. The mean ratio should be as small as possible.

As a rule it is unlikely that all three conditions can be fulfilled at any one
time, but it does happen that a reliable fix results even when only two are
fulfilled. The fulfilment of a single condition is not sufficient to determine
the reliability of a fix. The angle of cut, for example, may be 90°, but the
other two factors can easily outweigh this advantage. On the other hand if,
in addition to an angle of cut equal to 90°, the distance from the middle object
is small, the resulting error will be small.

The angle of cut

In order to ensure that the angle of cut shall not be too small, it is desirable
to have an approximate idea of what it will be before the observations are
made. This can be obtained by considering the angle subtended at the middle
object by the other two objects.
668 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

In Fig. A7-6, FL and FM are tangents at F to the position circles. Then

θ is the angle LFM.
Since FL is a tangent to the circle BFC at F, the angle LFB is equal to
the angle BCF. Similarly, the angle MFB is equal to the angle BAF. Hence:

θ = BAF + BCF
= 180° & (AFB + ABF) + 180° & (BFC + CBF)
= 360° & (AFC + ABC)

Fig. A7-6. The angle of cut in an HSA fix

Of these angles, ABC can be measured or estimated from the chart. Also
if E is the estimated position of the ship at the time the observations will be
made, the angles AEC and AFC will be approximately equal (assuming that
E and F are reasonably close together), so that:

θ • 360° & (AEC + ABC) . . . A7.7

The angle AEC can also be estimated from the chart, and a value of θ
obtained before the observations are taken. A glance at Table A7-1 will then
give some idea of the reliability that can be attached to the fix when it is
obtained.
As it stands, formula (A7.7) is not general because θ must be less than
90°, and the sum of the angles AEC and ABC will not always be greater than
270°. When they are not, it can be shown, by adjusting the positions of A, B,
C and F, that:

θ = (AEC + ABC) & 180°

θ = 180° & (AEC + ABC)
ERRORS IN HSA FIXES 669

The rule giving θ is therefore: add the angles AEC and ABC and subtract
the sum from 360° or 180°, or subtract 180° from the sum, so as to obtain a
value of θ less than 90°.

Examples of satisfactory HSA fixes

In the two examples that follow, E denotes the estimated position of the ship
at the time the fix is obtained.
In Fig. A7-7(a), the angle ABC is estimated to be 170°, and the angle AEC
160°. The angle of cut is therefore given by:

360° & (170° + 160°)

= 30°

The ratio r1, being FA/AB or EA/AB approximately, is about ¾; and r2 is

about 5/4. The mean ratio is therefore about unity. Suppose FB is 2', and that
the error in each angle observed is ½°. Table A7-1 shows that the possible
error in the fix is 2 x 0.3 or 0.6 cables.
In Fig. A7-7(b), the angle ABC is estimated to be 100°, and the angle
AEC 190°. The angle of cut is therefore 70°. Also, r1 and r2 are both about
¾, and the mean ratio is therefore about ¾. If the distance FB in this example
is 7', the possible error in the position when the error in each angle observed
is ½°, is seen from Table A7-1 to be 7 x 0.1 or 0.7 cables.
The small and apparently unfavourable angle of cut in the first example
is counterbalanced by the small value of FB. In the second example FB is large,

Fig. A7-7. Satisfactory HSA fixes

670 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

but θ is 70°. The two fixes are thus widely separated in their angle of cut, yet
their reliability is practically the same, and both would be regarded as
satisfactory.

Example of an unsatisfactory fix

When the middle object lies near the circle passing through the other two
objects and the fix, the fix cannot fail to be unreliable because, in the limiting
position when the middle object lies on that circle, it is impossible to obtain
a fix.
Fig. A7-8 shows the middle object badly placed. The angle ABC is about
100° and the angle AEC 60°. The angle of cut is therefore 180° & (100° +
60°) or 20°.
Also, r1 and r2 are each about 1¾. The mean ratio is therefore about 1¾.
If FB is 6', the error in the fix resulting from an error of ½° in each angle
observed is 6 x 0.9 or 5.4 cables, an error sufficiently large to render the fix
unreliable.

Fig. A7-8. An unsatisfactory HSA fix

DOUBLING THE ANGLE ON THE BOW AND THE EFFECT OF

CURRENT OR TIDAL STREAM

It is apparent that if a ship holds a steady course until the bearing of an object
on her bow is doubled, the position at which this occurs forms an isosceles
triangle with the first position and the object, and it is distant from the object
by an amount equal to the run between the observations. If the ship
experiences a current or tidal stream in the meantime, it must be allowed for
in order to avoid an error in her final position.
In practice, it will usually be more convenient to solve a problem of this
type by plotting it on the chart and transferring the position lines as
necessary. The following theory, however, may be regarded as general.
DOUBLING ANGLE ON BOW AND EFFECT OF CURRENT OR TIDAL STREAM 671

Fig. A7-9. Doubling the angle on the bow in a tidal stream

In Fig. A7-9, AB is the course of the ship, and BC is the tidal stream. AB
and BC combine to give the ground track, AC.
Suppose X is some object observed from the ship. When the ship is at A,
the angle on the bow is XAB, denoted by α. When the ship is at C, it is
assumed for the purpose of this problem that the angle on the bow has been
doubled. At this point the fore-and-aft line is in the direction CE, parallel to
AD, and the angle XCE is thus 2α.
EC produced meets AX in F. The angle CFX is therefore equal to the
angle CXF, and FC is equal to CX.
CG is drawn parallel to XA. The angle CGB is therefore equal to α, and,
since FAGC is a parallelogram:

CX = AG = AB & GB

AB, the distance resulting from the ship’s known speed and the duration
of the run, can be found at once, but GB must be calculated from the triangle
GCB.
672 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

Thus:
GB sin GCB
=
BC sin BGC
sin GCB
i.e. GB = BC
sin α
If BC is denoted by d (the amount of drift during the run) and the angle CBD
by φ , the angle GCB is (φ - α ) and:
d sin( φ − α )
CX = AB − ... ( φ > α ) . . . A7.8
sin α
If φ is less than α, CX is given by:
d sin(α − φ ) . . . A7.9
AB +
sin α
These formulae suffice when the current or tidal stream carries the ship
to port, and the object is also to port. They also suffice when the ship is
carried to starboard and the object is to starboard. When, however, the ship
moves to starboard and the object is to port or vice versa, it can easily be
shown that CX is given by:
d sin( φ + α )
AB + . . . A7.10
sin α
The distance of the ship from the object at the instant of the second
observation can therefore be found.

EXAMPLE
At 1000 an object is seen to bear 040° to an observer on board a ship
steaming 075° at 16 knots in a tidal stream setting 300° at 3 knots. At 1030
the same object bears 005°. How far is the ship from the object at 1030?
At 1000 the angle on the port bow is (075°&040°) or 35°. At 1030 the
angle is (075°&005°) or 70°. Also, the angle φ is (75°&300° + 360°) or 135°
The ship’s run in 30 minutes is 8', and d is 1'.5.
Both the set of the tidal stream and the object are to port. The distance
of the ship from the object at 1030 is therefore (formula A7.8):

1'.5 sin (135°− 35° )

8' −
sin 35°
1'.5 sin 100°
= 8' −
sin 35°
= 8' − 2'.6
= 5'.4
The position of the ship at 1030 is thus fixed by a bearing and distance
of 005° and 5'.4, and it is necessary to plot only the true bearing.
 DOUBLING ANGLE ON BOW AND EFFECT OF CURRENT OR TIDAL STREAM 673

If the set had been in the opposite direction, 120°, φ would have been equal
to (120° & 75°) or 45°, and the distance would have been (formula A7.10):
1'.5 sin ( 45°+ 35° )
8' +
sin 35°
= 8' + 2'.6

= 10'.6

Effect of the tidal stream when φ has particular values

The general formula is simplified considerably when φ has certain values.

These values and adjustments are:

1. When φ is equal to zero. This means that the direction of the current or
tidal stream is the same as the course steered. Then, by substitution:

CX = AB + d

2. When φ is equal to 180°. The set is now in a direction opposite to the

course steered, and:

CX = AB & d

3. When φ is equal to α. This means that the direction of the current or

tidal stream is that of the first true bearing, and:

CX = AB

4. When φ is equal to (180° & α). The set is now in a direction opposite to
the first true bearing, and again:

CX = AB

5. When φ is equal to 2α. This means that the direction of the current or
tidal stream is that of the second true bearing, and:

CX = AB & d

6. When φ is equal to (180° & 2α). The set is now in a direction opposite
to the second true bearing, and:

CX = AB + d
674 APPENDIX 7-ERRORS IN TERRESTRIAL POSITION LINES

INTENTIONALLY BLANK
 675

Bibliography

The following books, publications, pamphlets, etc. have been consulted during the
writing of Volume I of the Admiralty Manual of Navigation. These are in addition
to those references from RN sources (e.g. the Admiralty Sailing Directions), which
are not included below.

Aeronautical Chart and Information Centre. Geodetic Distance and Azimuth

Computations for Lines Over 500 Miles. ACIC Technical Report No. 80 US
Air Force, August 1957.
Anderson, E.W. The Principles of Navigation. Hollis and Carter, 1966.
Anderson, N. M. ‘Computer-assisted cartography in the Canadian Hydrographic
Service’, International Hydrographic Review, July 1981.
Appleyard, S.F. Marine Electronic Navigation. Routledge and Kegan Paul, 1980.
Blance, A.G. Norie’s Nautical Tables. Imray, Laurie, Norie and Wilson, 1979.
Bomford, G. Geodesy. 3rd edition. Oxford University Press, 1971.
Bowditch, N. American Practical Navigator, Volumes I and II. Defence Mapping
Agency Hydrographic Centre, 1977 (Volume I), 1975 (Volume II).
Bulmer, B.F. Meteorology for Mariners. Met O.895. HMSO, 1978.
Clarke, G.M., and Cooke, D. A Basic Course in Statistics. Edward Arnold, 1981.
Cotter, C.H. The Elements of Navigation and Nautical Astronomy. Brown, Son
and Ferguson, 1977.
Crenshaw, J.R. Naval Shiphandling. United States Naval Institute Press, 1975.
Cross, P.A., and Walker, A.S. Statistical and Computational Aspects of Multi-
position Line Fixing (MPLF). North East London Polytechnic/RN
Hydrographic School, HMS Drake, 1984.
Fifield, L. W. J. Navigation for Watchkeepers. Heinemann, 1980.
Glansdorp, C., Goldsten, G.H., Kluytenaar, P.A., and Wepster, A. Round the Horn
or Through Magellan. Report No. R109. Netherlands Maritime Institute (undated
but probably 1978/79).

HM GOVERNMENT PUBLICATIONS
Department of Trade. A Guide to the Planning and Conduct of Sea Passages.
HMSO, 1980.
Õ International Convention on Standards of Training, Certification and
Watchkeeping for Seafarers, 1978. Command Paper 7543, Shipping Misc.
No. 6 HMSO, 1979.
Õ Marine Radar Performance Specification, 1982. HMSO, 1982.
Õ Merchant Shipping ‘M’ Notices. HMSO, 1971 to June 1983 (see also
Department of Transport).
Õ Statutory Instruments (Merchant Shipping: Safety series):
676 BIBLIOGRAPHY

SI 1975 No. 700, The Merchant Shipping (Carriage of Nautical Publications)

Rules 1975. HMSO, 1975.
SI 1980 No. 530, The Merchant Shipping (Navigational Equipment)
Regulations 1980. HMSO, 1980. As amended by SI 1981 No. 579, The
Merchant Shipping (Navigational Equipment) (Amendment) Regulations 1981.
HMSO, 1981.
SI 1980 No. 534, The Merchant Shipping (Navigational Warnings) Regulations
1980. HMSO, 1980. As amended by SI 1981 No. 406, The Merchant
Shipping (Navigational Warnings) (Amendment) Regulations 1981. HMSO,
1981.
SI 1982. No. 1699, The Merchant Shipping (Certification and Watchkeeping)
Regulations 1982. HMSO, 1983.
SI 1983 No. 708, The Merchant Shipping (Distress Signals and Prevention of
Collisions) Regulations 1983. HMSO, 1983.
Department of Transport. Merchant Shipping ‘M’ Notices. HMSO, from July
1983 (see also Department of Trade).
SI 1984 No. 1203, The Merchant Shipping (Navigational Equipment)
Regulations 1984. HMSO, 1984. As amended by SI 1985 No. 659, The
Merchant Shipping (Navigational Equipment) (Amendment) Regulations 1985.
HMSO, 1985.
Steering Committee on Pilotage. Marine Pilotage in the United Kingdom.
HMSO, 1974.
International Association of Lighthouse Authorities. Maritime Buoyage System.
IALA, 1980.
International Chamber of Shipping. Bridge Procedures Guide. Wetherby, 1977.
International maritime Organisation. Recommendation on Basic Principles and
Operational Guidance Relating to Navigational Watchkeeping. IMO, 1974.
Õ Ships’ Routeing. 5th edition. IMO, 1984, incorporating amendments 1-6.
Kreyszig, E. Introducing Mathematical Statistics & Principles and Methods. John
Wiley and Sons, 1970.
Maling, D.H. Coordinate Systems and Map Projections. George Philip and Son,
1973.
Maloney, E.S. Dutton’s Navigation and Pilotage. 13th edition. US Naval Institute
Press, 1978.
Moody, A.B. Navigation Afloat. Hollis and Carter, 1980.
Moss, W.D. Radar Watchkeeping. Maritime Press, 1973.
Nautical Institute. Nautical Review (including Seaways and Nautical Briefings),
Volume 1 No. 1, March 1977, to Volume 4 No. 2, February 1980.
Õ Seaways, March 1980 to December 1985.
Nautical Institute/Royal Institute of Navigation. The Selection and Display of
Navigational Information. Proceedings of seminar, December, 1981. Nautical
Institute, 1982.
Õ Aspects of Navigational Safety. Proceedings of seminar, December 1982.
Nautical Institute, 1983.
Nautical Institute/National Maritime Institute/College of Nautical Studies,
Warsash, Southampton. Ship Operations and Safety. Proceedings of
conference, April 1981. Nautical Institute, 1981.
Racal-Decca. The Decca Navigator Operating Instructions and Marine Data
Sheets, Volumes 1 and 2. Decca Navigator Company, 1973 (up to and
including Amendment No. 8).
Õ The Decca Navigator Marine Data Sheets. Racal-Decca Navigator Ltd.
1985.
Õ The Decca Navigator Mark 21 Operating Instructions. Racal-Decca
Navigator Ltd, 1986.
BIBLIOGRAPHY 677

Royal Institute of Navigation. The Journal of the Institute of Navigation,

Volume I No. 1, 1948; Volume IX No. 4, 1956; Volume 23 No. 2, 1970, to
Volume 24 No. 4, 1971.
Õ The Journal of Navigation, Volume 25 No. 1, 1972, to Volume 38 No. 3,
1985.
Õ Navigation Equipment and Training Standards. Proceedings of conference,
April 1985. RIN, 1985.
Royal Institute of Navigation/Royal Institute of Naval Architects. Marine Traffic
Engineering. Proceedings of conference, May 1972. RIN/RINA, 1973.
Skolnik, M. I. Introduction to Radar Systems. McGraw-Hill/Kogakusha, 1962.
Smart, W. M. On a Problem in Navigation. Royal Astronomical Society, 1946.
Tranter, C.J., and Lambe, C.G. Advanced Level Mathematics (Pure and Applied).
3rd edition. Hodder and Stoughton, 1973.
Troup, Sir James A.G. On the Bridge. Hutchinson, 1950.
Vogel, T.J. ‘Horizontal datum for nautical charts’, International Hydrographic
Review, July 1981.
Wylie, F.J. Choosing and Using Ship’s Radar. Hollis and Carter, 1970.
Õ The Royal Institute of Navigation’s ‘The Use of Radar at Sea’. 5th revised
edition. Hollis and Carter, 1978.
678 BIBLIOGRAPHY

INTENTIONALLY BLANK
 679

INDEX

Accuracies, navigational information on lights, 237, 252

absolute position, 458 sources of information, 153
definitions, 457-8 state of correction on supply, 127
precision, 457 supplements, 127, 153
relative position, 458 surveying, 555-6
repeatability, 458 uses and users, 153
Admiralty Distance Tables, 7, 154-5 Views for, 153, 556
Admiralty List of Lights and Fog Signals Admiralty Tide Tables
correction, 132, 138, 156 correction, 159
details of lights, 155-6, 242-5 description and purpose, 159, 293-4
folio list references, 122 secondary ports, 293, 294
hydrographic information, 143 standard ports, 293
ranges, 246-9 supplementary information, 295
rising or dipping range, 203-4 Tidal Prediction Form 295
sources of information, 156 tidal stream data, 291
state of correction on supply, 127 using, 294
volumes of, 155 Advance
Admiralty List of Radio Signals defined, 185
correction, 132, 138, 159 in pilotage planning, 352-8
hydrographic information, 145 plotting, 187-9
sources of information, 158 Aero lights, 252
state of correction on supply, 127 Aeromarine lights, 252
volumes and diagrams, 157-8 Air publications - see Aviation publications
Admiralty Manual of Hydrographic Surveying, Altering course
523 blind pilotage, 435
Admiralty Manual of Seamanship, 162 cardinal and half-cardinal points, 331
anchoring, 385-6 in coastal navigation, 331-3
anchoring in company, 400-2 in pilotage planning, 352-8
Officer of the Watch, 562-5 pilotage execution, 373, 375
Admiralty Notices to Mariners ‘wheel over’ bearings, 331-3
Admiralty List of Lights, 132, 156 when giving way, 490-500
Admiralty List of Radio Signals, 132, 159 Alternating lights, 241, 242
Annual Summary, 127, 132, 159 Amphidromic point, 290
correction of charts and publications, Anchoring
135-8 alternative berth, 362, 392
Cumulative List, 132 amount of cable, 385-6
distribution to HM Ships, 133 approach to berth, 392-4
Fleet, 132 at a definite time, without altering
navigational warnings, 132 speed 398-400
new charts and publications, 131 blind, 444-5
purpose, 130-1 choosing the berth, 383-9
Sailing Directions, 131 depth of water, 383
Small Craft Edition, 132 distance from other ships, 386-8
Temporary and Preliminary, 131 dragging, 398
Weekly Edition, 131-2 dropping anchorage, 392-4, 401
Admiralty Sailing Directions ensuring berth is clear, 394, 400
correction, 127, 131, 138, 153 executing the anchorage plan, 394-7
description and purpose, 152-3
folio list references, 122

hydrographic information for, 141-6

information on buoys and beacons, 254
680 INDEX

Anchoring (cont.) Bearing lattices, 230-2, 352

heavy weather in harbour, 398 Bias, in navigational readings, 462, 464,
in a chosen position, 390-4 465, 477
in a poorly charted area, 400 Blind pilotage
in wind or tidal stream, 397-8 anchorages, 444
in company, 400-2 assessment or risk, 434
in deep water, 397-8 conduct of, 437-8
information required by Captain, 395 course alterations, 435
letting go second anchor, 398 dead range, 441
limiting danger line, 390-2, 396 defined, 434
minimum swinging radius, 386-7 execution, 442-5
one radius apart, 387 exercises, 444
planning the approach, 390-2 general principles, 439-40
proximity of dangers, 384-5 horizontal displays, 445
reduced swinging radius, 388-9 in HM Ships, 435-9
reducing speed, 392-4 navigational records, 445
running anchorage, 392-4, 401 parallel index, 434-5
safety margin, 384 planning, 349, 440-2
safety swinging circle, 384, 385, 390, 396 radar clearing ranges, 435, 436
selecting the headmark, 390 relative v. true motion, radar plotting,
swinging room 383 445-6, 509-13
Andoyer-Lambert method, spheroidal responsibilities, 435, 438-9
great-circle sailing, 97-9 Safety Officer, 437, 439
Angle on the bow - see Aspect team and duties, 438-9
Angles, plane Blunders, 458-9
complementary, 583 Bore (tides), 282-3
cosine of small, 595 bridge check lists, Merchant Navy,
functions of sum and difference of 577-9
combined, 592-3 navigation, coastal waters/traffic
sine of small, 594 separation schemes, 578
supplementary, 586 preparation for arrival in port, 578-9
trigonometric functions of, 584-7 Bridge Emergency Orders - see
Angles, spherical, definition, 596-7 Emergencies
Aphelion, 278 Bridge File, 568-9
Apogee, 277 Bridge organisation and procedures,
Aspect, 497-8, 510 Merchant Navy
Astronomical charts and diagrams, 123 automatic pilot, 575
Astronomical publications books and publications, 570
Nautical Almanac, 160 calling the Master, 576-7
Sight Reduction Tables for Air Navigation, clear weather, 576
160 duties and responsibilities, 573
Sight Reduction Tables for Marine electronic navigational aids, 575
Navigation, 160 emergencies, 579-80
Star Finder and Identifier, 160 fitness for duty, 572
Atmospheric refraction - see Refraction, general remarks, 559
atmospheric look-out, 573-4
Automated radar plotting aids, 514 navigation, 572-3
Aviation publications, Catalogue of navigational equipment, 573, 575
Admiralty Air Charts, 152 navigation in coastal waters, 576
Azimuth circle, 198 navigation safety, 570-1
navigation with pilot embarked, 574, 577
Base line in surveys, 535-6 operational guidance for officers in
Beacons, 254-64 - see Buoys and beacons charge of a navigational watch, 574-7
Bearings passage plan, 571-2
compass, 16 procedures, general, 571
conversion of magnetic and compass to protection of the marine environment, 574
true, 17 radar, 575-6
great-circle, 34, 38 restricted visibility, 576
magnetic, 16 routine bridge check lists, 577-9
radar - see Radar bearings safety systems, maintenance and
relative, 21 training, 572
taking, 197 watchkeeping arrangements,
true, 10, 34 navigational 572-5
visual, errors in 456, 475 watchkeeping personnel, 577
INDEX 681

Bridge organisation and procedures, Chart Correction Log and Folio Index, 122
Royal Navy correction and warning system, 136
calling the Captain, 561 state of chart correction on supply, 127
Captain, 560-2 Chart datum
Captain’s Night Order Book, 165, 561 depths on charts, 115
charge of the ship, 560-1 drying heights, 119
command responsibilities, 560 land survey datum, 295
definitions, 560 Lowest Astronomical Title, 295, 297
general remarks, 559 on the tide pole, surveying, 550-1
Navigating Officer, 565-7 tidal datum, 295
Officer of the Watch, 562-5 Chart depots, supply of charts, 126
Principal Warfare Officer, 567 Chart folios - see Folios, chart
shiphandling, 363, 378, 561 Chart outfits
special sea dutymen, 567, 568 action on receipt of, 128
standing orders and instructions, disposal, 129
568-70 first supply, 126
supervision of the Navigating Officer, 561 legal requirements, 102
training of seaman officers, 562 state of correction on supply, 127
watchkeeping non-seaman officers, 562 subsequent upkeep, 129
Bridge Procedures Guide, ICS, 570 Chart production, 146-9
bridge organisation, 571-2 plate correction, 149
emergencies, 580 reproduction methods, 148-9
routine bridge check lists, 577-9 Chart projections - see Projections
Buoys and beacons Charts
around the British Isles, 255, 262, 264 British policy, 102
cardinal marks, 258-60 classified, 123
description, 254 coastal navigation, 299-300, 311, 316
isolated danger marks, 260 colours used, 119
lateral marks, 256-8 constructing a Mercator chart of the
new dangers, 264 world, 67
pilotage, 376 constructing a Mercator chart on a
safe water and special marks, 260 larger scale, 68
symbols on charts, 264, 265 coverage, 102
use in navigation, 266, 329 datum, 115, 295
Buoyage around the British Isles, 255, datum shift, 103, 113
262, 264 depths, 115
describe a particular copy, 119
distinguish a well surveyed, 119
Canals, navigation in, 379-80 distortion, 112
Captain’s Night Order Book, 165, 561 folios, 121-2
Captain’s Standing Orders, 568 geographical datum, 103-4
Cardinal marks (buoys and beacons), gnomonic projection, 123
258-60 graduation of Mercator, 63
light characteristics, 258, 260 great-circle tracks on Mercator, 70-1
safe navigable water, 258 harbour plans, 109, 110
topmarks, 258 heights, 119
Catalogue of Admiralty Charts, 102, 123 hydrographic information for, 141-6
chart folios, 122 information, 112-19
Hydrographic Department books, 152 International, 104
instructional charts, 125 latticed, 104
ocean sounding charts, 125 measurement of distance on
Charge of the ship, 560-1 Mercator, 63-4
Chart correction, 127, 128, 135-8 Mercator projection, 61-71
blocks, 137 metrication, 102-3
correction and warning system, 136 miscellaneous folios, 126
first supply, 127 modified polyconic (‘gnomonic’)
hints, 136 projection, 108-9
lights, 137 navigational, 106-21
new chart/New Edition, 128-9 new, 127, 128
radio aids, 137 New Editions, 127, 128
radio navigational warnings, 127, pilotage, 343-4
133-5, 138 plotting, 109, 111-12
Small Corrections, 114, 136 reliability, 121
tracings, 136 survey methods, 101
682 INDEX

Charts (cont.) horizontal danger angles, 326

transverse Mercator projection, 109 information required, 300-1
types, 123-6 keeping clear of dangers, 324-7
upkeep, 126-30 navigational equipment 324
using, 121 passage chart, 311, 313
work of Hydrographic Department, 101 passage graph, 314-16
Chartwork, Chapter 8 passage plan, 310-16
allowing for the turning circle, 185-9 practical hints, 327-33
allowing for wind, tidal stream, current preparatory work, 299-301
and surface drift, 181-4 publications, 300
blind pilotage symbols, 441 record, 330
calculating the position, 176-90 routeing and traffic separation, 302,
defining and plotting a position, 175, 176 304-8
establishing the track, 195 selecting marks for fixing, 321-322
general points, 195-6 tidal streams and current, 330
on passage, 192-6 times of arrival/departure, 301, 310,
planning and planning symbols, 190-2 328-9
summary, 196 under-keel clearances, 308-10
symbols used in, 173, 174 vertical danger angles, 325
time of arrival, 195 when not to fix, 329
Chronometers and watches Cocked hat
siting, near magnetic compass, 162 causes, 208, 660-2
supply and return, 130 description, 208
Circle of error, 485-7 eliminating, 208, 219-24, 660
circular normal distribution, 486 in general, 662-3
equivalent probability circles, 489-93 Most Probable Position, 494-6
radial error, 465, 485 reduction, 220-2
Circular error probable, 468 Co-latitude, 34
determining, 493 Collisions and Groundings (and Other Accidents),
equivalent probability circles, 489, 492 162
relationship with other probability Collision avoidance
circles, 487 bearing, 510
Clearing bearings and marks close quarters, 562
anchoring, 390 relative v. true motion radar plotting,
coastal navigation, 324 509-13
pilotage planning, 358-60 relative track, importance, 502
symbols for, 190, 191 stabilised relative motion radar display,
Clearing depths, 360, 383 509
Clearing ranges, radar Collision/grounding reports, 163
blind pilotage, 435, 436, 441 Command responsibilities, Royal Navy,
coastal waters, 327, 433, 434 560
Closest point of approach Compass
find, 517-18, 519 bearing, 16, 199
track generation, 505 course, 16
using automated radar plotting aids, 514 definition, 12
Coastal navigation, Chapter 12 errors, 219-24, 324, 361, 456
altering course, 331-3 failure, 504
appraisal, 301 gyro-compass, 12
buoys, light-vessels, 329 magnetic, 13
charts, 299-300, 316, 576 Navigational Data Book, 171
choosing the route, 301-3 rules for siting, 162
clearance from the coast and off-lying unknown error in, 229, 456
dangers, 303-5 Composite errors, 461
coral regions, 337-9 Composite track sailing, 36, 91-3
distance an object will pass abeam, Conical orthomorphic projection
214-15, 327-8 constant of the cone, 615, 618
entering shallow water, 333 description, 615
execution of the passage plan, 316-27 Lambert’s two standard parallels,
fixing by night, 331 618-19
fixing methods, 321 scale, 615-17
fixing using radar, radio aids, beacons, Conspicuous objects
322-3, 431-4 coastal navigation, 321
flat and featureless coastlines, 330 radar, 435, 441
fog and thick weather, 333-7 Coral regions, navigation in, 337-9
INDEX 683

Corrected mean latitude sailing, 27-30 Degree, 581-2

formulae, 28, 614 Departure, 24
for the sphere, 611-14 Depths
on the spheroid, 93-4 of water when anchoring, 383
Cosine on charts, 115
curves, 587-8 Deviation
formula, plane triangle, 591-2 curve, 15
formula, spherical triangle, 598-9, 603 checking, 20
definition, 582 definition, 13
method, great circles, 37, 39, 40 record of observations, 164
of a small angle, 595 table, 14, 164
polar rule, great circle, 601 Diameter of turning circle, final/tactical, 186
rule, great circle, 598 Diamond of error, 467
Co-tidal charts, 289-90, 294 Difference
Course of latitude, 4
compass, 16 of longitude, 4
conversion of magnetic and compass to of meridional parts, 28, 33, 67, 85
true, 17 Dip, vertical sextant angles, 650
find the compass, from true, 20 Direction
great-circle, 38, 40 compass north, 13
gyro, 12 magnetic and compass course and
heading, 11 bearing, 16
magnetic, 16 magnetic north, 13
on the Mercator chart, 106 on the Mercator chart, 106
true, 10 relative, 21
Currents true, 10
cause, 290 true bearing, 10
chartwork, 178 true course, 10
coastal navigation, 330 true north, 10
coral regions, 339 Disaster relief surveys, 525-6
pilotage, 357 reporting new dangers, 526
Displays, radar - see Radar displays
Distance
Danger angles - see Horizontal and Vertical cable, 7
danger angles comparison of, 99-100
Danger lines - see Limiting danger lines geographical mile, 7
Dangers - see Marks and dangers, great-circle, 34, 37, 39
navigational international nautical mile, 7
Datums measurement on Mercator chart, 63, 108
chart, 115, 295 minute of latitude, 44, 640-3
datum shift, 50, 103, 113 minute of longitude, 45
geodetic, 45 object will pass abeam, 213, 214-15,
geographical, on charts, 103-4 327-8
horizontal, 45 on the spheroid, 93-9
Ordnance, Newlyn, 295 rhumb-line, 24-33
Ordnance Survey, 79 sea mile, 6, 641, 642, 643
reference, 48 statute mile, 7
tidal prediction, 295 Distance to new course
vertical, 45 defined, 186
Datum shift (on charts), 50, 103, 113 in pilotage planning, 352-8
discrepancies between visual and radio plotting, 189
aid fixes, 219 Distortion
Daymark, 254 charts, 112
Daytime lights, 252 projection, 51
Dead Reckoning Doubling angle on the bow, 213-14
calculating the position, 176 effect of current and tidal stream, 670-3
errors in, 456 Douglas protractor
need for developing, 196, 559 HSA fixing, 225
on passage, 191 reduction of cocked hat, 220
symbol in chartwork, 173 Drift
Decca defined, 181
charts, 104 radar plotting, 510-13
fixing by, 322-3, 458 qualification, in chartwork, 180, 181
Navigator publications, 161 Dropping anchorage, 392-4, 401
684 INDEX

Earth limit of random errors, 470-1

as a sphere, 9 Most Probable Position, 461, 471-6,
axis, 2 494-6
equator, 2 observed position, 456, 475
‘flat’, 54 orthogonal position lines, 466, 468
flattening or ellipticity, 41, 637 position areas, 456
great circle, 9, 33 position circle, 456
meridians, 2 Position Probability Area, 471-6
poles, 2 practical application, 468-76
prime meridian, 2 radial error in the fix, 464
radius in various latitudes, 648 sextant, 657
spheroidal shape, 1, 41 taking and laying off bearings, 657-63
Earth-Moon system - see Tides, effect of terrestrial position lines, 657-73
Earth-Sun system- see Tides, effect of unknown, in compass, 229, 456
Ebb (outgoing tidal stream), 290 visual bearings, 456, 475
Eccentricity, 42, 636 Errors in taking and laying off bearings,
Echo sounder 657-63
blind pilotage, 439 cocked hat, 219-24, 660-3
clearing depths, 360 displacement in the fix, 658-60
coastal navigation, 331 Errors in terrestrial position lines, 657-73
in fog, 334, 335-7 Estimated Position
operational guidance, Merchant Navy, calculating, 177-9
575 composite errors, 461
pilotage execution, 373, 375 currents, 178
pilotage planning, 360 definition, 177
surveying, 549 determine, allowing for leeway, tidal
Eddies (tidal stream), 292 stream, etc., 184
Ellipse errors in, 456
eccentricity, 42, 636 in fog, 334
equation, 636-7 leeway, 177-8
flattening or ellipticity of Earth, 41, 637 need for developing, 196, 559
Emergencies, 563-4 on passage, 192
Merchant Navy, 579-80 plotting, 179-81
Royal Navy, 568 surface drift, 179
Equator, 2 symbol, chartwork, 173
Equinoctial tides, 280 tidal streams, 178
Equivalent probability circles, 467, 489-93
Equipment - see Navigational equipment
Error ellipse, 466-7, 487-93 Faults, 458-9, 468-9
Errors Final diameter, turning circle, 186
blunders, 458-9 Fix
composite, 461 definition, 205
faults, 458-9, 468-9 observed position, 176
navigational - see Errors in navigation radial error in, 464-5, 467
random - see Random errors; Random setting a safe course from a cocked hat,
errors in one dimension; Random 223-4
errors in two dimensions symbol, chartwork, 173
systematic, 459, 468-9 time taken to, 193
types of, 458-68 see also Fixing; Fixing the ship
see also detailed entries below Fixed lights, 237, 238
Errors in HSA fixes, 663-4 Fixed marks (beacons), 256
Errors in navigation Fixing
allowing for faults/systematic errors, choosing objects, 232
468-9 coastal navigation, 321-3, 576
allowing for random errors, 469-70 conspicuous objects, 321
cocked hat, 219-24, 660-3 coral regions, 338-9
compass, 12, 324, 456 establishing the track, 195
Dead Reckoning, 456 frequency, 192, 576
diamond of, 467 methods, 205-19
doubling angle on the bow, current or on passage, 192, 195
tidal stream, 670-3 procedure, 233
Estimated Position, 456, 475 radar, radio fixing aids, radio beacons,
general remarks, 455-7 322-3
HSA fixes, 663-70 selection of marks for, 232-6, 321-2
INDEX 685

Fixing (cont.) Four-part formula, 601-3

‘shooting up’, 235-6 Four-point bearing, 213-14
short cuts, 233
surveying by boat, 546 General Information for Hydrographic Surveyors,
visual observation, 197 523
Fixing the ship, methods of, 206-19 Geocentric latitude, 43, 638-9
bearing and horizontal angle, 209-11 Geodesic, 45, 97-9
bearing and range, 208 Geodetic datum, 45
bearing and sounding, 208-10 Geodetic latitude, 43, 47, 638-9
bearing lattices, 230-2 Geodetic longitude, 47
cocked hat, 208, 220-4 Geographical mile, 7
coral regions, 338-9 Geographical range of lights
cross bearings, 207-8 description, 246-7
fix and run, pilotage waters, 352, 372-3 determining, 249-50
horizontal sextant angles, 224-30, 652-6 rising or dipping range, 203-4
line of soundings, 217-18 Geoid, 46
radar ranges - see Radar fixing Gnomonic projection/chart, 59, 73-7, 123
radio fixing aids, 218, 322-3 angle between two meridians, 626
running fix, 211-16 description, 73
running surveys, 527-9 equatorial gnomonic latitude, 629-31
transit and angle, 211 modified polyconic, 61, 108-9, 622-3
Flood (incoming tidal stream), 290 parallels of latitude, 626-9
Fog and thick weather, navigation in practical use, 77
action on or before entering fog, 334, principal or central meridian, 624-6
335, 576 tangent point, 73, 108
choosing the route, 301 transfer of great-circle tracks to Mercator
general remarks, 333-4 chart, 74
practical considerations, 335-7 Great circle
visibility, 334, 335 bearing, 34
Fog lights, 253 cosine formula and rule, 598-9
Fog signals, 266-7 cosine method, 37, 39, 40
passages in fog, 335-7 course/bearing, 38
Folios, chart definition, 9, 33, 596
Fleet, 127 distance, 34, 37, 39
label, 122 haversine method, 607-8
list, 122 polar cosine rule, 601
local and special, 122 sailing, 33, 35
miscellaneous, 126 sine formula and rule, 599-600
scheme of, 122 sine method, 40
standard, 122 solutions, 37
state of correction on supply, 127 tracks and Mercator charts, 70-1, 74,
transfer, 129 89-91
Forms, navigational (‘S’ forms) vertex, 36
Captain’s Night Order Book, 165 Great-circle sailing, 33, 35
Fishing Vessel Log, 165 composite track, 91-3
Hydrographic Notes, 139 on the spheroid - see Spheroidal great-
Manoeuvring, 165, 575-6 circle sailing
Navigating Officer’s Note Book, 165 PLOTTING ON Mercator chart using the
Navigational Data Book, 168-72 vertex, 89-91
Navigational Record Book, 172 vertex, 36, 88-9
Order of the Court and Report of Grids
Navigation Direction Officers at Trial convergence, 79
on Navigational Charge, 168 conversion between geographical and
Record Book for Wheel and Engine transverse Mercator grid co-ordinates,
Orders, 165 634-5
Record of Observations for Deviation, definition, 51
164 description, 77-8
Report of Collision or Grounding, 163 National Grid, 78, 79
Report on Damage to Fishing Gear, 165 on transverse Mercator projection, 80-1
Ship’s Log, 164 transferring grid positions, 81
Small Envelope, 145, 146, 147 Ground speed, 497
Table of Deviations, 164 Ground track, 180, 181, 497
Turning, Starting and Stopping Trials, Gyro-compass
172 checks, pilotage, 361
686 INDEX

Gyro-compass (cont.)
definition, 12
error, 12, 456 Ice, navigation in, using radar, 454
failure, 564 Instructional charts and diagrams, 125
Interaction with other ships, in shallow
Harbour plans, 109, 110 water, 333
Haversine, 604 International Association of Lighthouse
formula, 606 Authorities
great-circle solutions, 607-8 maritime buoyage system, 106, 254-65
half log haversine, 606 marks, 256-64
Heights Region A, 256-64
drying, 119 Region B, 258
of tide, 294, 296, 376, 390 International charts, 104
on charts, 119, 296 International Hydrographic Organisation,
highest Astronomical Tide, 297 104
Horizontal danger angles International nautical mile, 7
coastal navigation, 326 Isognoic charts/lines, 13
pilotage, 360 Isolated danger marks (buoys and
Horizontal sextant angles beacons), 260
angle of cut, 667-9
charting a coastline, 552-4 Knot, 7
choosing objects, 227
errors in, 663-6 Lagging, of tide, 280-1
fixing by, 224-30 Lanby, 251, 264, 266, 329
fixing by bearing and, 209-11 Lateral marks (buoys and beacons), 256-8
fixing objects on the chart, 652 Latitude
fixing objects outside the chart, 652, 654-6 calculation of d.lat, 5
lattice for plotting fixes, 652-6 co-latitude, 34
lattice, pilotage planning, 352 definition, 2
obtaining a position line, 200-1 difference of, 4
radar index error, 422 geocentric, 43, 638-9
rapid plotting without instruments, 230 geodetic, 43, 47, 638-9
652 length of Earth’s radius, 648
reliability of fixes, 666-7 length of minute of, 44, 640-3
satisfactory fixes 669-70 linear measurement of, 7
strength of fix, 225-7 meridional parts, 65, 609
surveying by boat, 546 parallels of, 2
transit and, 211 parametric, 43, 639-40
unsatisfactory fixes, 670 small circle, 2, 9
when not to fix, 229 Latticed charts, 104
Hydrographic Department, 101 Leading marks and lines
supply of charts, 126 anchoring, 390
Hydrographic reports, 139-46 pilotage planning, 349-51
beacons and marks, 143 Least squares, deriving Most Probable
buoys, 143 Position, 494-6
channels and passages, 144 Leeway, 177-8, 510
conspicuous objects, 143 Levels, tide - see Tides
discoloured water, 142 Light-float, 251, 264, 266, 329
forms (hydrographic reports), 139 Lights, 237-53
general remarks, 139 Admiralty List of Lights and Fog Signals,
information on radio services, 145 155-6, 242-6, 247
lights, 143 alternating, 241, 242
magnetic variation, 145 areas of visibility, 243
newly discovered dangers, 141 characteristics, 237, 238-41, 242
ocean currents, 145 classes, 237-42
port information, 142-3 determining maximum range, 249-50
position, 144 fixed, 237, 239
shoals, 142 intensity, 242, 243
sketches and photographs, 145 loom, 242
soundings, 141-2 minor, types of, 245-6
tidal streams, 144 notes on using, 253
wrecks, 143-4 on permanent platforms, drilling rigs
zone time, 145 and single point moorings, 252
Hydrographic Supplies Handbook, 122, 126, 152 period, 237
INDEX 687

Lights (cont.) surveying, 524-5,555

phase, 237, 243 Marks and dangers, navigational
range, 242, 245-50 buoys and beacons, 264
rhythmic, 237, 238-40 fixing, surveying, 524-5
sectors, 243, 245 intersection, 525
specialised types, 252-3 reporting, 526
structure, 243 resection, 525
Light-vessels, 250, 264, 266, 329 Maximum likelihood, deriving Most
Limiting danger lines Probable Position, 494-6
anchoring, 390, 396 Mean High Water, various levels of, 115,
pilotage planning, 345-7, 348 119, 296, 297
use with clearing bearings, 358-60 Mean latitude sailing, 27
Line of bearing Mean Low Water, various levels of, 115,
pilotage planning, 351 296, 297
running a, anchoring, 394-5 Mean Sea Level, 115, 296, 297
running a, pilotage execution, 371-2 Mean Tide Level, 297
Linear error probable, 480 Mediterranean moor, 402
Local Notices to Mariners, 135 Mercator projection/chart, 56
Longitude charts drawn on, 106-8
calculation of d.long, 5 constructing, 67-70
definition, 3 description, 61, 106
difference of, 4 distances on, 63-4, 108
geodetic, 47 graduation of charts, 63
length of minute of, 45 great-circle tracks, 70-1, 89
linear measurement of, 7 longitude scale on, 63, 107-8
scale on harbour plan, 109, 110 meridional parts, 64-7
scale on Mercator chart, 63 orthomorphism, 67, 107-8
Loran-C position circles on, 620-2
charts, 104 principle, 61-3
fixing by, 322-3 Mercator sailing, 33
Loxodrome, 24 course and distance from meridional
Lowest Astronomical Tide, 115, 295 parts, 85-8
Luminous range of lights on the sphere, 85-8
description, 247-8 on the spheroid, 93
determining, 249-50 Meridian
nominal, 249 definition, 2
magnetic, 13
prime, 2
Magnetic charts, 124 Meridional arc, length, 94, 643-6
isogonic, 13 Meridional parts
Magnetic compass course and distance, Mercator sailing,
compass north, 13 85-8
conversion of magnetic and compass deduction for the sphere, 618, 620
course and bearing to true, 17 defined, 64
definition, 13 differences of, 28, 33, 67, 85, 95
deviation, 13 evaluation of, 612
graduation of older magnetic compass for any latitude, 65, 609
cards, 16 formula, sphere, 609-11
magnetic and compass courses and for the spheroid, 94-6, 646-8
bearings, 16 tables of, 64, 67, 94-5, 646
magnetic meridian, 13 Meteorological effects on tides, 284-6
magnetic north, 13 Meteorological publications, 151-2
practical application of compass errors, 17 Meteorology for Mariners, 151
variation, 13 Naval Oceanographic and Meteorological
Maps, 54, 83 Service Handbook, 152
Mariner’s Handbook, 154 Oceanographic and Meteorological Supplies
hydrographic forms, 139 Handbook, 151
hydrographic reports, 139 Meteorological working charts, 126
soundings, 141 Metric charts, 102-3
Marks - see also Buoys and beacons Middle latitude - see Corrected mean
for surveys, 540-1 latitude
identification of, pilotage 373 Mile
selecting, for fixing, coastal navigation, geographical, 7
321-2 international nautical, 7
688 INDEX

Mile (cont.) Navigational Data Book

sea, 6, 641, 642, 643 anchors and cables, 168
statute, 8 berthing information, 170
Mined areas, 303 bottom log and plotting tables, 171
Minimum variance, deriving Most compasses, 171
Probable Position, 494-6 conning positions, 170
Miscellaneous folios, charts, 126 degaussing equipment and ranging, 171
plotting diagrams, 126 details required for anchoring, 390
Miscellaneous publications details required for pilotage, 362-3
Decca Navigator Marine Data Sheets, 161 dimensions and tonnage, 168
Decca Navigator Mk 21 Operating Instructions, echo sounder, 171
161 engines, 168
Norie’s Nautical Tables, 160 fuel oil capacity, consumption data, 169
radio aids, 161, 163 navigational communications, 170
Spheroidal Tables, 6 navigation lights, 171
Mistakes - see Blunders radio aids, 171
Modified polyconic (‘gnomonic’) projection replenishment, 170
- see Polyconic projection revolutions for specific speeds, 169
Mooring revolution tables, full power trials, 169
executing the plan, 403-4 shiphandling characteristics, 170
Mediterranean moor, 402 ship’s narrative, 172
mooring ship, 402-4 special sea dutymen, 171
planning the approach, 403 steering and stabilising equipment, 170
swinging room 402 Turning Trials, 169-70
Morse Code in fog signals, 267 Navigational Departmental Orders, 569
Most Probable Position Navigational equipment
composite errors, 461 compasses, 324
defined, 181 failures, 564
derivation from three or more position in coastal navigation, 324
lines, 494-6 regulations for use, Merchant Navy, 573,
determining, 471-6 575
Navigational marks and dangers - see
Marks and dangers, navigational
Navigational publications, 152-61
Napier’s rules correction, 135-8
quadrantal triangles, 604, 605 kept on the bridge, 569, 570
right-angled spherical triangles, 603 sets of, 151
Nautical Almanac, 160 state of correction on supply, 151
Navigating Officer, 566-7 Navigational Record Book, 193, 194
Navigating Officer’s Note Book blind pilotage, 445
anchorage plan, 392, 393 coastal navigation, 330
anchoring, 390, 396 pilotage, 369
authority for use, 165 ship’s movements, 164, 172
blind pilotage, 442-3, 444, 445 Navigational warnings, 130-5
coastal navigation, 311, 312 Admiralty Notices to Mariners, 130-3
pilotage plan, 362-3 Local Notices to Mariners, 135
Navigating Officer’s Work Book radio, 127, 130, 133-5
coastal navigation, 299, 310, 311 Navigator’s Yeoman
pilotage, 343 correcting charts and publications, 135-8
Navigation orders for, 570
definition, 1 Neap tides, 279-81
in canals and narrow channels, 379-80 Nominal range of lights, 249
in coastal waters, 299-333, 576 Norie’s Nautical Tables, 30, 64, 160
in coral regions, 337-9 Notices to Mariners - see Admiralty
in fog and thick weather, 333-7, 576 Notices to Mariners
in ice, using radar, 454
in pilotage waters, 341-82
radar for, 417-54
safety, merchant ships, 570-1 Observed position, 176
using floating structures for, 264, 266 errors in, 456, 475
using fog signals, 267 Obstruction lights, 252
watchkeeping, merchant ships, 572-3 Occasional lights, 253
Navigational accuracies - see Accuracies, Ocean Passages for the World, 7, 154
navigational Ocean sounding charts, 125
INDEX 689

Officer of the Watch Pilotage execution

action information organisation, 565 action on making a mistake, 377
bridge organisation and procedures, altering course and speed, 375
562-5 assessment of danger, 373
calls by, 563 buoys, 376
compass failure, 564 checks before departure or arrival, 377
conning orders, 564-5 communications, 377
emergencies, 563-4 do’s and don’ts, 378-9
equipment failures, 564 echo sounder, 373, 375
keeping a navigational watch, Merchant essential questions, 369
Navy, 572-4 fix and run, 372-3
looking out, 562, 573-4 identification of marks, 373
operational guidance, Merchant Navy, information required by the Captain, 377
574-7 maintaining the track, 369, 371
Omega charts, 104 miscellaneous considerations, 377-8
Operations room, 567 mistakes, 378-9
Organisation, bridge - see Bridge organisation and records, 369, 370
organisation and procedures personal equipment, 378
Orthogonal position lines, 466, 468, 484-5 running a line of bearing, 371-2
Orthomorphism running a transit, 371
maps, 83 shiphandling, 378
Mercator chart, 67, 107-8 shipping, 375
transverse Mercator chart, 73, 109 taking over the navigation, 377
Overfalls or tide-rips (tidal stream), 292 tides, tidal stream, wind, 376
using one’s eyes, 377
Pilotage planning
Parallel of latitude, 2 advance and transfer, 354
Parallel index, radar, 433-5 allowing for tidal stream or current when
Parallel sailing, 24 altering course, 357
Parametric latitude, 43, 97, 639-40 altering course, 352-8
Passage alternative anchor berth, 362
appraisal of, pilotage waters, 347 appraisal of the passage, 347
blind pilotage, planning and execution, bearing lattice, 352
439-45 blind, 349, 440-2
canals and narrow channels, 379-80 chart selection, 343
coastal, chart, 311, 312 check-off lists, 366, 381-2
coastal, execution, 316-27 clearing bearings, 358-60
coastal, graph, 314, 315 clearing depths, 360
coastal, plan, 301-16 conning, 363
fog and thick weather, 333-7 constrictions, 349
pilotage execution, 369-79 dangers, 348
pilotage plan, 347-67 distance of the headmark, 352
plan, Merchant Navy, 571-2 distance to new course, 354
Passage graph distance to run, 348
constructing, 315 echo sounder, 360
monitoring ship’s speed/progress, 328-9 edge of land, 351-2
planning aid, 314, 315 example, 366
Passage planning charts, 124 final stages, 363
Passage soundings, 524 fix and run, 352
Perigee, 277 gyro checks, 361
Perihelion, 278 headmarks, 349-52
Pile beacon, 254 HSA lattice, 352
Pilotage Keeping clear of dangers, 358-61
appraisal of the passage, 347 leading lines, 349
blind, 349, 434-45 limiting danger lines, 345-7, 348, 358-61
canals and narrow channels, 379-80 line of bearing, 351
execution, 369-79 miscellaneous considerations, 361-6
pilots, 342-3, 574, 577 Navigating Officer’s Note Book, 362-3
plan, 347-67 night entry-departure, 349
preparatory work, 343-7 point of no return, 361
regulations, HM Ships, 342 preparatory work, 343-7
regulations, merchant ships, 342-3 publications, 344
visual, 341-82 radar, 361
see also detailed entries below selection of the track, 347-9
690 INDEX

Pilotage planning (cont.) on the spheroid, 45, 47

shiphandling, 363 plotting, 175
‘shooting up’, 361 probability area - see Position Probability
single position line, 358 Area
Sun, 349 sea, 180, 181
tidal stream and wind, 348 symbols used in chartwork, 173, 174,
time of arrival, 344-5, 348 190-1
time of departure, 344-5 transferring, 175, 195
transits, 349-51 Position circle, errors in, 456
tugs, 363 Position line
turning on to predetermined line, 354-7 arrowheads, 173
vertical and horizontal danger angles, definition, 175
360 likely accuracy, 455-7
Pilots, 342-3, 574, 577 methods of obtaining - see entry below
Plane sailing, 25 orthogonal, 466, 468
formula, 26 MPP from three or more, 494-6
on the spheroid, 93-4 symbols used in chartwork, 173, 174
Plane triangles - see Triangles, plane transferred, 173, 204-6, 358
Planning Position line, methods of obtaining,
anchoring, 390-2 198-206
blind pilotage, 440-2 astronomical observation, 204
coastal passage and plan, 301-16 compass bearing, 199
complete minor survey, 539-40 distance meter range, 202
passage graph, 315 horizontal angle, 200-1
pilotage, 343-67 radar range, 204
Plotting radio fixing aids, 204
allow for advance and transfer, 187-9 rangefinder range, 202
allow for distance to new course, 189 relative bearing, 199
clear a point by a given distance, 183 rising or dipping range, 203-4
correction for change of speed, 190 sonar range, 204
course to steer, allowing for a tidal soundings, 204
stream, 181-2 transferred, 204-6
Dead Reckoning, 176-7 transit, 200
establishing the track, 195 vertical sextant angle, 201-2
HSA fixes, 224-30, 652-6 Position Probability Area
position, 175 composite errors, 461
reach a position at a definite time, defined, 181
allowing for tidal stream, 182 determining, 471-6
relative and true motion radar displays, error in navigation, 456
508 symbol in chartwork, 173
relative v. true motion radar, 509-13 Practice and exercise area (PEXA) charts,
ship’s position on passage, 192 125
surveying, 542-4 Prime meridian, 2
track, Estimated Position, 179-81 Priming (of tide), 280-1
Plotting chart, 109, 111-12 Principal Warfare Officer, 567
Polar stereographic projection - see Probability heap, 484-5
Stereographic projection Procedures, bridge - see Bridge
Polar triangles, 600-1 organisation and procedures
polar cosine rule, 601 Projections
Pole current log, 530 conical orthomorphic, on the sphere,
Poles, 2 615-18
Polyconic projection, 60 definitions, 51
modified (‘gnomonic’), 61, 108-9, 622-3 distortion, 51
Port installation surveys, 526-7 ‘flat Earth’, 54
Position Gauss conformal - see transverse
close objects, 10 Mercator
expressing, 4 gnomonic, 57, 73-7, 123, 624-31
fix, 176 graticule, 51
hydrographic information, 144 Lambert’s conical orthomorphic, 56,
‘let go’ anchoring, 390 618
most probable - see Most Probable Mercator’s 56-7, 61-71, 106-8
Position modified polyconic (‘gnomonic’), 61,
observed, 176 108-9, 622-3
on the Earth’s surface, 1 of the sphere, 54
INDEX 691

Projections (cont.) coastal waters, 322-3, 431-4

of the spheroid, 56 comparison of 10 cm and 3 cm radars,
orthomorphism or conformality, 54, 67, 425-6
73, 82, 108, 109 fog, 334, 335-7
polyconic, 60-1 ice, 454
skew orthomorphic, 57 landfalls, long-range fixing, 426-30
transverse Mercator, 57, 71-3, 109. limitations, 562
632-5 other ships’, 418
Universal Polar Stereographic, 57, 60, radar index error, 419-24
624 range errors, 418-19
used for maps, 83 relative motion, 445-7, 504, 505-8,
Publications 509
Admiralty Distance Tables, 154 relative velocity, 504-14
Admiralty List of Lights and Fog Signals, Rule of the Road, 417
155-6 setting up the display, 417
Admiralty List of Radio Signals, 157-9 shore-based, 449-54
Admiralty Manual of Seamanship, 162 suppression controls, 408, 417
Admiralty Sailing Directions, 152 true motion, 445-7, 509-13
astronomical - see Astronomical use by Officer of the Watch, Merchant
publications Navy, 573, 575-6
Catalogue of Admiralty Charts and Other visual pilotage, 361
Hydrographic Publications, 123 see also detailed entries below
Catalogue of Admiralty Air Charts, 152 Radar beacons
Chart Correction Log and Folio Index, 122 details, 447
classified, 163 interference from, 449
coastal navigation, 310 racons, 447-8
Collisions and Groundings (and Other ramarks, 448-9
Accidents), 162 Radar bearings
Hydrographic Supplies Handbook, 122 alignment accuracy check, 424
kept on the bridge, 569, 570 causes of errors, 424
Mariner’s Handbook, 154 coastal waters, 432
meteorological, 151-2 long-range fixing, 429-30
miscellaneous - see Miscellaneous squint error, 424
publications Radar clearing ranges - see Clearing ranges
Ocean Passages for the World, 154 Radar displays
pilotage, 344 horizontal, 445
Queen’s Regulations for the Royal Navy, 161-2 parallax errors, 419
Rules for the Arrangement of Structures and radar plotting, 528
Fittings in the Vicinity of Magnetic relative motion stabilised, 505-7
Compasses and Chronometers, 162 relative v. true motion, 509-13
Seaman’s Guide to the Rule of the Road, 162 relative velocity, 504-5
tactical, 163 setting up, 417
technical, 163 suppression controls, 408, 417
tide and tidal stream, 159 using, 418-19
Views for Sailing Directions, 153, 556 Radar fixing
base line, surveying, 535
blind pilotage, 442-3
Quadrantal triangles, Napier’s rules, 604 coastal waters, 322-3, 431-4
Quartermasters, orders for, 569 landfalls, 428
Queen’s Regulations for the Royal Navy, 161-2 long-range, 428-9
blind pilotage, 435 Radar Station Pointer, 430
charge of the ship, 560 range/height nomograph, 426-8
command, 560 ranges, 218, 431-2
pilotage, 342 traffic surveillance systems, 451
Radar in coastal waters, 431-4
clearing range, 434
Racal-Decca - see Decca fixing by radar range and bearing, 432
Races (tidal stream), 292 fixing by radar range and visual bearing,
Racons - see Radar beacons 431
Radar (for navigation) fixing by radar ranges, 431-2
beacons (racons and ramarks), 447-9 parallel index, 434-5
bearing errors, 424-5 running surveys, 528
blind pilotage, 434-45 Radar index error, 418-24
clearing ranges, 327 allowing for, 424
692 INDEX

Radar index error (cont.) Radial error

calibration chart, 419 circle of error, 485
defined, 418 equivalent probability circles, 489-93
finding, 419-24 in the fix, 464-5, 467
find using normal chart, 420 Radian, 582
horizontal sextant angle method, 422 Radio (fixing) aids
standard set comparison method, 424 fixing, 218, 322-3, 330
two/three-mark method, 420-2 fog, 334, 335-7
two/three-ship method, 422-3 Navigational Data Book, 171
Radar in relative velocity operational guidance, merchant ships,
aspect, 510 575
automated plotting aids, 514 position line, 204
displays, 504-5 Radiobeacons, 322-3, 334, 335-7
drift, 510-13 Radio navigational warnings
leeway, 510 Admiralty Notices to Mariners, 132
limitations, 508-9 chart correction, 127, 135, 138
plotting on relative and true motion coastal, 133
displays, 508 local, 133
relative motion stabilised display, 505-7 local, Naval port, 133
relative v. true motion plotting, 509 long-range, 133-5
set, 510-13 purpose, 133
Radar range errors United States, 135
design factors, 418 World-Wide Service, 135
index errors, 418, 419-24 Ramarks - see Radar beacons
linearity, 418 Random errors
other causes, 419 allowing for, in navigation, 469-70
using the display, 418-19 described, 459-60
Radar ranging limits of, in navigation, 470-1
clearing ranges 327, 434 rectangular, 482-4
errors, 418-19 see also detailed entries below
fixing by - see Radar fixing random errors in one dimension, 461-4
position line, 204 bias, 462, 464, 477
Radar waves combining, 463-4, 481-2
amplification, 407-8 linear error probable, 480
atmospheric refraction, 408-12 mean value, 478
attenuation, 412 normal (Gaussian) distribution, 462,
automatic gain control, 408 480-1
bandwidth, 407 rectangular, 482-4
beam width, 407 root mean square error, 462, 479
bearing discrimination, 406-7 sigma values, 462, 463, 479, 480-1
clipping, 408 standard deviation, linear, 462, 479
corner reflectors, 415, 416 variance, 479
detection, 405 Random errors in two dimensions
differentiation, 408 bias, 464-5
double echoes, 416-17 circle of error, 485-7
linear amplification, 407 circular error probable, 468, 487, 489,
logarithmic amplification, 407 492, 493
minimum range, 406 circular normal distribution, 486
processed log/lin amplification, 408 diamond of error, 467
pulse repetition frequency, 405, 412 equivalent probability circle, 467, 489-93
radar shadow areas, 416, 417 error ellipse, 466-7, 487-9
range discrimination, 406 orthogonal position lines, 466, 468
reflection from objects, 415 484-5
side lobe echoes, 416-17 probability heap, 485
swept gain, 408 radial error, 464, 465, 467, 485
transponders, 415-16 radial standard deviation, 464-5, 467
unwanted echoes, 416-17 root mean square error/distance, 464,
video signals, 407-8, 417 467, 485
weather echoes, 413-15 Range errors, radar - see Radar range
Radar weather echoes, 413-15 errors
cold fronts, 413-14 Range of lights, 242, 246-50
sand/dust storms, 413 Record
super-refraction, 413, 415 blind pilotage, 445
warm fronts, 413-14 coastal navigation, 330
INDEX 693

Record (cont.) Root mean square error

keeping, chartwork on passage, 193, 194 about the mean value, 462, 479
pilotage execution, 369 about the true value, 462
Record Book for Wheel and Engine Orders radial 464, 465, 467, 485
authority, 165 Rotary tidal streams, 290
blind pilotage, 438 Rounding-off errors, 482-3
coastal navigation, 330 Routeing and traffic separation schemes,
pilotage, 370 302, 304-8, 450
Rectangular errors, 482-4 traffic surveillance systems, 450-3
effect, 483-4 Routeing charts, 124
rounding-off, 482-3 Rule of the Road
Rectilinear tidal streams, 290 close quarters situation, 562
Refraction, atmospheric, 408-12 fog, 333-4
abnormal, 652 pilotage planning, 347, 348
average conditions over the sea, 409 radar, 417
hydrolapse, 409 risk of collision, 499, 510
radar horizon, 408-9 Rule 10, traffic separation schemes,
standard atmosphere, 409 306-8
sub-refraction, 409-11 Seaman’s Guide to, 162
super-refraction, 409-11, 413, 415 Running anchorage, 392-4, 401
temperature inversion, 409 Running fix
terrestrial, 650 doubling angle on the bow, 213-14,
weather and, 411-12 670-3
Relative bearing, 21, 199 methods of obtaining, 211-16, 332
Relative track Running surveys, 527-9
compared with true track, 500-3
radar plotting, 181, 497-500 Safety margin, anchoring/mooring, 384,
velocity triangle, 507 402
Relative velocity Safety swinging circle, anchoring, 384, 385,
aspect, 497-8 390
automated radar plotting aids, 514 Safe water marks (buoys and beacons),
comparison between relative and true 260
tracks, 500-3 Sailing Directions - see Admiralty Sailing
definitions, 497-8 Directions
initial position of ships, 504 Sailings
problems - see entry below composite track, 36, 91-3
radar limitations, 508-9 corrected mean latitude, 27
relative movement, 504 departure, 24
relative v. true motion plotting, 509-13 loxodrome, 24
relative speed, 498-500 mean latitude, 27
relative track, 499-500 Mercator, 33, 85-8
use of radar, 504-14 parallel, 24
velocity triangle, 503-4 plane, plane formulae, 25, 26
Relative velocity problems rhumb-line, 23
closest point of approach, 517-18 spherical great-circle, 33, 35, 88-91
index to, 516 spheroidal great-circle, 97-9
open and close on the same bearing, spheroidal rhumb-line, 93-6, 645-6
520-1 traverse, 30
pass a ship at a given distance, 518-19 Sandwaves, 309
time at which ships on different courses Satellite geodesy, 48
and speeds will be a certain distance Satellite navigation, 48, 50
apart, 519-20 Sea mile, 6, 641, 642, 643
true track and speed of another ship, Sea position, 180, 181
516-17 Sea speed, 497
Reported dangers, searches for, 529-30 Secondary ports, 159, 293-4, 550-1
Rhumb line, 23 Seiches, 285
loxodrome, 24 Seismic waves (tsunamis), 286
on the Mercator chart, 106 Set
on the spheroid - see Spheroidal rhumb- defined, 181
line sailing quantification, in chartwork, 180
Rhythmic lights, 237, 238-40 radar plotting, 510-13
Right-angled spherical triangles Sextant errors, 657
cosine and sine formulae, 603 ‘S’ forms, 163-72 - see Forms, navigational
Napier’s rules, 603 Shadwell Testimonial, 557
694 INDEX

Shallow water, 308 revolutions for specific, 169

canals and narrow channels, 379-80 sea, relative velocity, 497
effect, 308 through the water, 176-7
entering, 333 Sphere
pilotage, 345-7 definition, 596
Shiphandling, pilotage, 363, 378, 561 projection of, 54
Ships’ boats’ charts, 124 Spherical angles - see Angles, spherical
Ship’s Log, 164, 166-7, 172 Spherical triangles - see Triangles,
Ships’ Routeing, 305 spherical
Shore-based radar Spheroid
details, 449 datum shift, 50, 103, 113
port radar systems, 449 eccentricity, 42, 636
positional information, 450 flattening of the Earth, 41, 637
reporting points, 450 geodesic, 45
traffic surveillance and management geodetic datum, 45
systems, 450-3 geoid, 46
‘Shooting up’, 235-6 great-circle sailing on the, 97-9
bearings, 235 International (1924), 1, 6, 7, 9, 43, 95, 98
blind pilotage, 442 meridional parts, 94-6, 646-8
Dead Reckoning/Estimated Position, 235 oblate, 1, 41
identification of uncharted objects, 235 position on the, 45, 47
pilotage planning, 361 projection of the, 56
transits, 235 reference, 48
when anchoring, 400 rhumb-line sailing on the, 93-6, 645-6
Simplified Harmonic Method of Tidal Prediction, satellite geodesy, 48
159, 289 World Geodetic System (WGS), 48
Sine Spheroidal great-circle sailing, 97-9
curves, 587-8 Spheroidal rhumb-line sailing
definition, 582 course and distance, 94-6, 645-6
formula, plane triangle, 590-1 length of the meridional arc, 94, 643-6
formula, spherical triangle, 599-600, 603 meridional parts, 94-5, 646-8
formula, surveying, 541 Spheroidal Tables, 6
method, great-circle solutions, 40 Spring tides, 278-9, 280-1
of a small angle, 594 Squat, 308, 345-7, 379
rule, great circle, 599 Standard deviation
Small circle, 2, 9, 596 combining, 463-4, 481-2
Solstitial tides, 280 linear, 462, 479
Soundings one sigma value, 462, 479, 480-1
along a berth, 526 radial, 464-5
blind pilotage planning, 440 rectangular errors, 482-3
complete minor survey, 544-8 two sigma value, 463
fixing by a line of, 217-18 variance, 479
fixing by bearing and, 208-10 Standard ports, 159, 286-7, 293, 294,
in fog, 334, 335-7 550-1
on passage, 524 Standing orders and instructions (Royal
position line from, 204 Navy)
running surveys, 528 books and publications, 569
searching for reported dangers, 530 Bridge Emergency Orders, 568
Source data diagram, 113 Bridge File, 568-9
Special marks (buoys and beacons), 260 Captain’s Standing Orders, 568
Special sea dutymen, 171, 567, 568 Navigational Departmental Orders, 569
Speed orders for Navigator’s Yeoman, 570
blind pilotage, 443 orders for quartermasters, 569
canals, narrow channels, 379-80 Station pointer, 220, 225
chartwork on passage, 193 Statue mile, 8
correction for change of, 190 Stereographic projection, 57
find, from relative movement, 516-17 Universal Polar, 57, 624
fog, 334 Surface drift, in chartwork, 179
ground, relative velocity, 497 Surges, tidal, 285
loss of, when turning (speed factor), Survey, complete minor, 532-57
187-90 Admiralty Sailing Directions, 555-6
pilotage, 375 aerial photography, 555
reduction of, when anchoring, 392-4 base line, 535-6
relative, 498 chart datum, 550-1
INDEX 695

Survey, complete minor (cont.) amplitude, 287

coastline, 552-4 co-tidal charts, 289-90, 294
control, horizontal/vertical, 532, 533, 538 datum, 295
echo sounder, 531, 549 harmonic analysis, 286-7
equipment, 538-9 harmonic constituents, 286
fair sheet, 556 method, 287-9
fixing marks and dangers, 555 offshore areas, 294
fixing the boat, 546 principal constituents, 287
geographical position, 538 Simplified Harmonic Method, 289
graduation, 543-4 time (phase) lag, 287
longest side calculation, 542 Tidal stream observations, 530, 532
marks, 540 Tidal streams
observing, 540-1 allowing for, altering course, pilotage
orientation, 536-7 planning, 357
planning, 539-40 at depth, 292
plotting, 542-4 atlases, 291, 292
principles, 532-8 blind pilotage, 440
procedure, 544-6 data on, 291, 292
reconnaissance, 539-40 definition, 269, 290
report, 556 diurnal, 290-1
scale, 534 during anchoring, 396, 398
Shadwell Testimonial, 557 during coastal navigation, 330
sine formula, 541 during pilotage, 348, 376
sounding marks, 533 eddies, races and overfalls, 292-3
soundings, 544-8 effect of, radar plotting and collision
subtense method, 535-6 avoidance, 510-13
ten-foot pole, 552-4 find direction and rate, 183
tidal curve, 551-2 in chartwork, 178, 190, 191
tidal observations, 549-50 information on charts, 119
tide pole, 549-50 observation, 291-2, 530-2
tracing and field boards, 544 semi-diurnal, 290-1
triangulation, 533-4 true motion radar, 446
topography, 555 types, 290-1
Surveying Tidal theory
Admiralty Manual of Hydrographic Surveying, Earth-Moon system, 269-77
523 Earth-Sun system 277-8
complete minor survey, 532-57 Newton’s Universal Law of Gravitation,
disaster relief, 525-6 269
General Instructions for Hydrographic springs and neaps, 278-81
Surveyors, 523 summary, 281
general remarks, 523-4 Tide and tidal stream publications, 159
navigational marks and dangers, 524-5, Admiralty Tidal Prediction Form 295
555 Home Dockyard Ports&Tides and Tidal
passage sounding, 524 Streams, 159-291
port installations, 526-7 tidal stream atlases, 291, 292
running surveys, 527-9 Tide pole, 549-52
searches for reported dangers, 529-30 Tide-raising (tractive) forces
tidal stream observations, 530-2 diurnal, 277
types of, 524 effect, in practice, 281-2
Symbols lunar equilibrium tide, 274, 275
blind pilotage, 441, 442, 445 neap tides, 280
chartwork planning, 191, 192 of the Moon, 272-4
conversion between geographical and of the Sun, 277
grid co-ordinates, 632-3 semi-diurnal, 276
standard, position and position lines, spring tides, 278-9
173-4 Tide-rips or overfalls, 292
Systematic errors, 459, 468-9 Tides
cause, 269
defined, 269
Tactical diameter, turning circle, 186 during pilotage, 376
Ten-foot pole, in surveying, 552-4 effect of wind, 285
Territorial limits, 302 heights, 294, 296, 376, 390
Tidal prediction in practice, 281-6
Admiralty Tidal Prediction Form 295 levels, 297-8
696 INDEX

Tides (cont.) Transit, 200

meteorological effects, 284-6 anchorage planning, 390
seismic waves (tsunamis), 286 checking error in the compass, 219, 324
shallow water effects, 282-4 fixing by angle and, 211
surveying, 549-52 pilotage planning, 349-51
tidal windows, 344 running a, pilotage waters, 371
see also detailed entries below use of, for identification, 373
Tides, effects of Earth-Moon system, Transverse Mercator projection/chart, 57,
269-77 109
antipode, 271 analogy with the Mercator projection, 73
apogee, 277 conversion between geographical and
barycentre, 269, 270 grid co-ordinates, 632-5
description, 269, 270 description, 71-3
diurnal, 277 grids, 80
diurnal inequality, 276 ‘footpoint’ latitude, 634
Earth’s rotation, 274-6 length of the meridional arc, 633
lunar equilibrium tide, 274, 275 Traverse sailing, 30
lunar month, 270 Traverse table, 30, 32
Moon’s declination, 276-7 Triangles, plane
Moon’s distance, 277 acute and obtuse, 590-5
Moon’s gravity, 271-2 areas, 592
perigee, 277 cosine formula, 591-2
semi-diurnal, 276 right-angled, 582-3
stand, 283 sine formula, 590-1
sublunar point, 271 Triangles, spherical
tide-raising (tractive) force, 272-4 cosine formula, 598-9
Tides, effects of Earth-Sun system 277-8 defined, 596
aphelion, 278 four-part formula, 601-3
description, 277 half log haversine formula, 606-7
distance, 278 haversine, 605-8
Earth’s rotation, 277 Napier’s rules, right-angled, 603-4
perihelion, 278 polar triangles, 600-1
Sun’s declination, 278 properties, 597
Tides, types of quadrantal, 604-5
apogean, 277 right-angled, 603
diurnal, 277 sine formula, 599-600
diurnal inequality, 276 solution, 597-608
equinoctial, 280 Triangulation, 533-4
lunar equilibrium, 274 Trigonometric functions
luni-solar equilibrium, 281 combined angles, 592-3
neap, 279-80 complementary angles, 583
perigean, 277 definitions, 582-90
semi-diurnal, 276 double and half-angle formulae, 593
solstitial, 280 inverse, 589
spring, 278-9, 280 of certain angles, 584
Time Pythagorean relations between, 589-90
arrival and departure, 195, 301, 310-11, right-angled triangles, 582-3
328-9, 344-5 signs and values, 584-7
of arrival when anchoring, 394 sine, cosine and tangent curves, 587-8
Track sum and difference of, 593-4
defined, 181 Trigonometry
establishing, 195 basic, 581-95
planned, 190, 191 spherical 596-608
plotting, 179-81 True bearing, 10, 34
relative - see Relative track True course, 10
Traffic separation schemes, 304-8, 450 in chartwork, 176
Traffic surveillance systems, 450-3 True motion radar
Transfer advantages and disadvantages, 446-7
defined, 185 pilotage, 445-7, 509
pilotage planning, 352-8 plotting, collision avoidance, 508, 509-13
plotting, 187-9 relative v. true motion, 445-6, 509-13
Transferred position line, 204-6 True track
in chartwork, 173 compared with relative track, 500-3
single, 206 find, from relative movement, 516-17
INDEX 697

True track (cont.) other ship’s relative track, 507

when radar plotting, 181, 497 own ship’s relative track, 507
Tsunamis, 286 rules, 504
Turning use in solving relative velocity problems,
advance and transfer, 187-9 516-21
allowing for turning circle, in chartwork, vectors, 503
185-90 Vertex, of great circle, 36, 88-91
distance to new course, 189-90 Vertical danger angles, 325, 360
on to a predetermined line, 354-7 Vertical sextant angle, 201
speed factor, 187-8 base of object below horizon, 649-52
time correction, 188 dip, 650
Turning data, 169, 172, 353 obtaining a position line, 201-2
terrestrial refraction, 650, 652
Visual pilotage - see Pilotage
Under-keel clearances
allowances, 309-10 Water track
sandwaves, 309 defined, 181
shallow water effect, 308, 333, 345-7, in relative velocity, 497
379-80 leeway, 178
squat, 308, 345-7, 379 plotting, 180
Universal Transverse Mercator grid, 80, 81 ‘Wheel over’
anchoring, 392
bearings, coastal navigation, 331-3
Variance, 479 blind pilotage, 435, 441
rectangular errors, 482-3 pilotage planning, 352-8
Variation, 13, 145, 147 symbols in chartwork, 191, 192
Velocity triangle World Geodetic System (WGS), 48
description, 503 international geographical datum, 103