To Be A Leader In Maritime Education & Training

CHAPTER C

RATE OF TURN

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RATE OF TURN

 WHEEL OVER POINT

 CONSTANT RATE OF TURN(RoT)
 LINE OF TURN (LoT)

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REFERENCES
Pilotage and Shiphandling, Nautical
Institute

www.Rajnav.com/wheel over calculation

Bridge Procedure Guide, ICS 2007 Edn

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Learning Outcomes

At the end of topic, student should be able

to understand and apply
Type of Turn
Rate of Turn
Wheel Over position
Line of Turn
Constant Rate of Turn
Calculation and Advantages

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Type of Turn

Constant Rudder Angle Turn

Constant Radius Turn

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RoT
Rate of Turn Describes the rate of change of the
ship’s course per unit time.

Determined while the ship completes sea trials

when new.

The navigation bridge would normally have a

‘Rate of Turn’ indicator to permit monitoring of the
ship’s performance during a turning manoeuvre.

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SOLAS Ch-V, Reg 19

All ships of 50,000 gross tonnage and

upwards shall, in addition to meeting the
requirements of paragraph 2.8, have:

- A rate-of-turn indicator, or other means, to

determine and display the rate of turn;

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Constant Rate of Turn

RoT constant from start turning the vessel

until desired course
Vessel will move along the plan path and
called Line of Turn
No overshoot
Not face near miss / danger / incident

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Factors That Affect A Turn

Structural design & length of the vessel.
Draught & trim of the vessel.
Size & motive power of the main
machinery.
Amount of helm used.
Available depth of water.
List
Other factors (Current / Wind etc)

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Tactical Diameter and Ship Condition

A vessel trimmed by stern will steer more easily,
but the tactical diameter of the turn is increased.
Trim by head will decrease the diameter of the
turning circle but it will be difficult to steer the
vessel.
Listed vessel will be subject to delay in turn. A
larger turn will be experienced when turning into
the list.
External forces, wind & current will affect the turn.
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COMPARISM
CONSTANT RUDDER CONSTANT RADIUS TURN
ANGLE TURN
Larger drift angle with a Lesser drift angle & hence
corresponding loss of speed lesser loss of speed

A large rudder angle is At the end of the turn, the

needed to steady the vessel new course can be steadied
on new course with lesser rudder angle

Uncertainty of ship’s Proper control of ship’s posn.

position during the turn during the turn
Higher fuel consumption Lesser fuel consumption, with
due to zigzagging with reserve rudder and engine
excessive use of helm. power available
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Wheel over points

The dangers of interaction are prevalent in

many different situations, but none more
so than when the vessel enters shallows
and is in close proximity to the land.
Tight manoeuvres must be anticipated
through rivers, canals and when making
land falls.

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Wheel over points

The large vessel must anticipate that the
position of the way point is rarely
coincident with the time at which the helm
will be applied.
Masters would be expected to ensure that
passage plans include ‘wheel over points’
when vessels are approaching positions of
course alteration.

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Wheel Over point

Wheel Over point calculation will discuss later.

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RUDDER ANGLE

Probably the most significant factor

affecting the turning circle is the
rudder angle.

The optimum is one which will cause

maximum turning effect without
causing excessive drag.

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RUDDER ANGLE
If a small rudder angle is employed, a large
turning circle will result, with little loss of
speed.

However, when a large rudder angle is

employed, then, although a tighter turning
circle may be experienced, this will be
accompanied by a loss of speed.

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Drift angle and influencing forces

When a vessel responds to helm

movement, it is normal for the stern of the
vessel to traverse in opposing motion.
Although the bow movement is what is
desired, the resultant motion of the vessel
is one of crabbing in a sideways direction,
at an angle of drift.

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DRIFT ANGLE AND INFLUENCING

FORCES
When completing a turning circle, because
of this angle of drift, the stern quarters are
outside the turning circle area while the
bow area is inside the turning circle.

Studies have shown that the ‘pivot point’ of

the vessel in most cases describes the
circumference of the turning circle.
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Why RoT is Required?

The circumstances in which a constant rate turn
is appropriate If overshoot or not follow planned
path, it will create
 Danger of collision in narrow channel /
fairway
 Danger of interaction
 Danger of stranding
Use extra helm and need to control with more
helm and skill
Zig-zag course and speed drop
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The danger of collision when wheel over point is not applied to

the way point and/or not use constant rate of turn
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PLANNING A CONSTANT TURN

Decide turning radius

Calculate difference between new course and
present course
Size of vessel
Calculate required rate of turn
Calculate and plot wheel over point position
Calculate the distances between the reference
target and ship position to set parallel index

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How to judge the correct execution of

a constant rate turn by visual means?

When execute?
How?

Visual approx bearing of reference target

Transit bearing for channel
Buoy on the bow or quarter/astern
Speed of target movement
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RADAR ASSISTANCE
Radar can be used to assist in monitoring a
constant rate turn
Use parallel Index method




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RADAR ASSISTANCE
Radar can be used to assist in
monitoring a constant rate turn
Use parallel Index method
Perpendicular distance off at w/o
position and new course from
target




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Plotting W/O point, (ICS Bridge Procedure Guide)

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Steps to draw W/O point & bearing ICS/BRM)

extend the present course line (3000T)beyond the alter course waypoint
(WPT2)
Mark the intersection of the new course (334°) and present course (300°) as
point 'B‘
From any point on present course (300°), draw a perpendicular, that is, at 90°
to the present course line.
On the perpendicular line, draw a line (shown in green in diagram) parallel to
present course (300°) at a distance equal to transfer (1.3 cables) from the
present course (300°)
The point where this parallel line (green) intersects the new course (334°) is
point C.
Draw a line from point C to the extension of the present course line (300°).
The point where this line intersects the extension of the present course is D.
The distance CD is equal to transfer and line CD is perpendicular to present
course (300O)
From point D beyond point B, on the present course line (300°), draw a line
equal to advance (6.7 cables) as shown in diagram (blue).
This point is called W and is the wheel over point for alteration of course to
3340.
Determine bearing of the light house (Balfe Point Light) and write on chart to
use for commencement of course alteration.

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Plotting W/O Point ( NI Pilotage)

First the Master of the vessel has to decide
the radius of turn required, depending on
the manoeuvring characteristics of the
vessel & available sea room.

A reference point such as an island, buoy,

etc. can be also used to decide the radius of
turn.

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To Determine Wheel Over position

1st method
Calculate the distance off wheel over
line from the new course line as per
formula

P = F sin  + R (1 – Cos )

(Ref: Pilotage by Nautical Institute &

rajnav.com)
See details on next slide
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To Determine Wheel Over position

Formula

P = F sin  + R (1 – Cos )
Where,
F = constant for particular ship
R = Radius of the turn
P = Perpendicular distance of wheel over
line from the new course line
 = Angular difference between new course
and old course
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To Determine Wheel Over position

More details for “F”

As per Nautical Institute, scale in mile

F= 0 for quick turning ferry

= 0.1 for normal size ship
= 0.15 for large and heavy container vsl
= >0.15 for VLCC
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Example as per NI
Panamax Container, Speed 20
knots, D

Radius of turn = 2 n-m, Ө Course Alteration

Change of course angle = 45O

P

Ө R
P = F Sin  + R (1-Cos )
F
P = 0.1 Sin 45 + 2 (1-Cos 45) W/O Ө
P = 0.07+0.59 n-m Centre

P = 0.66 n-m
Old Course

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Example as per NI

Plot the W/O position using “P” data

Calculate the RoT to manoeuvre the

vessel during turning

It will follow exactly according to line of

turn
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As per rajnav
To find & mark approx. W/O position:
1st Method
F = 0.1 to 0.15 NM
P = F Sin Ө + R(1-Cos Ө)

2nd Method
Distance to new course = Radius x Tan Ө/2
Wheel over point = F + Dist to new course
Then plot w/o position on the chart

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Example as per rajnav

D
LOA 225m,Speed 20 knots, Ө Course Alteration
Radius of turn = 2 n-m,
Change of course angle = 45O
P
P = F Sin  + R (1-Cos ) Ө R

P = 0.1 Sin 45 + 2 (1-Cos 45) F

P = 0.66n-m W/O Ө
Centre

Dist to new co. = Radius x Tan Ө/2

Old Course
= 2 x Tan 45/2
= 0.83 n-m
Wheel over pt = F + Dist to new co.
= 0.1 +0.83 = 0.93 n-m

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Check two formulas

Sin 45 = 0.66/X 45o

X = 0.66 /Sin 45 0.66

(1st Formula)
X = 0.933 X = 0.93
2nd Formula

Almost the same answer.

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To Determine RoT
To determine the rate of turn for a constant rate turn (Constant
radius Turn) is based on the following formula:

Rate of turn (Degrees/ minute) = 57.3 x V

60 R
where V= Ship’s speed over ground in knots and,
R = Radius of the turn in nautical miles.
We can say, 0.955 x(V/R)
The distance of wheel over point from the point where the turn to
become effective is usually taken as one ship’s length but it is
recommended to find it out by some practice turns on the type of
ship one is serving.

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Example

LOA 225m,Speed 20 knots,

Radius of turn = 2 n-m

RoT = ( 57.3 x V ) / ( 60 x R )
= (57.3 x 20) / (60 x 2)
= 9.55 degree/min

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F = Head Reach – Distance traveled by

vessel after giving wheel over & before
commencing turn, i.e. distance to overcome
inertia. D

Ө Course Alteration
P = Perpendicular distance from wheel over
point to new course extension.
P

D + P = Parallel Index distance at W/O Ө R

position. F
W/O Ө
D = Parallel Index distance from new Centre
course, as obtained from chart.
Old Course

R = Radius of turn.
Ө = Change of course angle.

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Plotting W/O Point

Distance to new course can be found by
the above formulas.

Once the Master has decided on the

radius of turn, a pre calculation may be
prepared for various course change
angles with respective radius.

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Example
LOA 225m,Speed 20 knots,
Radius of turn = 2 n-m,
Change of course angle = 45O

Position of w/o point = F + Distance from a/c point

RoT = We can say, 0.96 x(V/R)

Distance off to set parallel index

New course
Present course

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How To Give Helm Constant Rate Turn?

Lightship condition

Arrive w/o point (parallel index/bearing) /

Give less helm / monitor required RoT and
maintain constantly/ midships before new
course / reverse wheel to counteract / try to
get RoT zero (stop the turn) when vessel
reached on new course

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How To Give Helm Constant Rate Turn?

Fully laden condition

Arrive w/o point (parallel index/bearing) / Give

more helm initially / decrease helm gradually
when response / monitor required RoT /
midships before new course but take earlier
action / reverse more wheel to counteract / try
to get RoT zero (stop the turn) when vessel
reached on new course / parallel index line is
reference
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Constant rate turn is effective in helping a

vessel maintain its planned line of turn.

Less bodily drift and speed drop

Away from danger and near-miss

Know the ship is on safe track without

taking fix position

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SUMMARY
Type of Turns
W/O point
Parallel Index to monitor during turning
RoT and LoT
Radius of Turn, speed, size of vessel and
different of two courses
Formula to plot W/O point and RoT
Advantages

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