UNIT - II

3Surveying and Levelling

Syllabus ofdistances - angles - levelling- determination ofareas- contours - examples.
Objects - classification -principles - measurements

Contents 3-2
3.1 Introduction 3-2
3.2 Object of Surveying Dec.-15
.3-2
3.3 Classification of Surveying
3-3
3.4 Principle of Surveying May-15
..3-3
Measurement
3.5 Measurement of Distances / Linear
3- 17
3.6 Measurement of Angles/Angular Measurement Dec-16

3- 36
3.7 Levelling. May-15, 16
3- 63
3.8 Calculations of Areas
3- 70
3.9 Contours. Dec.-16

.3- 74
3.10 Two Marks Questions and Answers.
3- 75
3.11 University Questions with Answers

(3- 1)
 Basic Civil and
Mechanical Engineering 3-2 Surveying and Levelling
3.1 Introduction "Geodetic surveying is carried out for large area where
" Surveying is an art of determining the measurements are taken by considering line as curved
relative positions line.
of different objects on the surface of earth by
measuring
the horizontal distances between them and " The triangle formed by any three points is considered a8
preparing a
map to any suitable scale. spherical triangles and angles of triangle are assumed to
" Measurements are taken only in be spherical triangles.
horizontal plane.
Distance measurements are taken using simple distance " Geodetic surveying is conducted by survey of India
measuring instruments like chain, tape or advanced department.
equipments like Electromagnetic Distance Measurements " Generally, for area greater than 250 km, geodetic
(EDM) or tacheometers. Angle measurements are taken surveying is done.
using compass (prismatic or surveyor's) or theodolite.
Sr.
Plane Surveying Geodetic Surveying
3.2Object of Surveying AU : Dec.-15 No.

"The basic aim/object of surveying is to Barth curvature is not Earth curvature is

prepare a map to
show the relative positions of the objects on the surface considered. considered.
of earth. 2 It is carried out for small It is carried out for large
" Map shows location of different features on the earth in area (area < 250 km 2) area (area < 250 km')
symbolic form like natural feature eg. forests, hills, Plane triangles are Spherical triangles are
valleys and/or man made features like buildings, roads, formed. formed.
railways. Plane angles are used. Spherical angles are
u_ed
3.3 Classification of Surveying It is done by state It is done by survey of
agencies like PWD, India department.
A) Primary classification Surveying is primarily irigation department.
classified as ,
a) Plane surveying b) Geodetic surveying B) Secondary Classification :

a) Plane surveying: a) Based on instruments used:

" Plane surveying is type of surveying in which curvature i) Chain surveying,
of earth is not considered while taking measurements.
ii) Compass surveying,
"It is carried out for small area where all measurements
ii) Plane table surveying,
are taken by considering line as straight line.
"The triangle formed by any three points is considered as iv) Theodolite surveying,
plane triangle and angles of triangle are assumed to be v) Tacheometric surveying,
plane angles. vi) Photogrametric surveying.
" Plane surveying in conducted by state agencies like
b) Based on methods used :
public works department, irigation department.
" Generally, for area less than 250 km, plane surveying i) Triangulation surveying,
is done. i) Traverse surveying

b) Geodetic surveying : c) Based on object :

" Geodetic surveying is types of surveying in which i) Geological surveying,
curvature of earth considered while taking
i) Mine surveying,
measurements.
i) Archeological surveying,

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iv) Millitary surveying. c Electronic Distance Measurement (EDM) or total
station.
d) Based on nature of fleld :
"In direct methods, chain or tape and accessories are used
i) Land surveying,
to measure distance between two points directly.
ii) Marine surveying, " In indirect method, theodolite is used to observe the
ii) Astronomical surveying readings. From the observations and trigonometric
Land surveying is again classified as Tapographical formulae, distance is determined. Height can also be
determined in this method.
surveying, Cadastral surveying, City surveying, and
Engineering surveying. " In Electronic Distance Measuremnent (EDM) or total
station distance between two points is directly measured
3.4Prlnciple of Surveying AU : May-15 by use of laser.
The general principles of surveying are 3.5.1.1 Comparison between Three Methods
a) To work from the whole to the part.
Method Instrument Accuracy Use
" According to this principle, the whole area is first
marked by main survey stations and boundary line is Direct Chain/Tape Accurate Base line
measurement,
surveyed with greater accuracy. General
" The area is then divided into well conditional triangles distance
measurement
(explained later), mostly equilateral triangles are
Inditect Theodolite or Less Tapographic
prefered. level accurate survey, General
"Then the interior area is surveyed with less accuracy. traversing
" The purpose of this process is that the error Electronic EDM, total Most Trilateration,
station accurate General
accumulation gets restricted to certain area. distance
measurement
" The error is localised and can always be detected and
removed.
b) To locate a new station by at least two measurement
3.5.1.2 Other Methods
(linear or angular) from fixed reference point. 1)By pacing or stepping :
" According to this principle, at least two reference " For rough and speedy work distances are measured by
points are required to fix any new station. this method. i.e by counting the numbers of walking step
of a man.
"Linear measurements refer to horizontal distances
measured by chain and tape and angular measurements " The walking step of a man is considered as 2.5 ft or
refer to magnetic bearing or horizontal angle taken by 80 cm. This method is generally employed in the
reconnaissance survey of any project.
prismatic compass or theodolite.
2) By passometer / pedometer :
3.5Measurement of Distances / Linear "A small instrument just like stop watch, the passometer
Measurement is used for counting the number of steps automatically by
some 'mechanical device.
3.5.1 Methods of Dlstance Measurement
"Based on type of instrument used there are three methods
" It offers an improvement over the normal pacing method
of determining linear distances as follows : when a very long distance is to be measured and when it
becomes very tedious to count and extremely difficult to
a) Direct method
remember the number of steps.
b) Indirect method
3) By speedometer:
" This is used in automobiles for recording distance.
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Square
4) By perambulator : 2 to 4 cm
on edge Nail
handle. The wheel is
t 1s a wheel fitted with a fork and
graduated and shows a distance per revolution. There 1S a
2 cm
dial which records the number of revolutions. 12 cm Dia. 10 cm
M.S.
5) By chaining :
method of measuring
T2 cm to 3cm
" This is an accurate and common 4cm
distance. Wooden peg Metalpeg
measured directly on
" In this method, the distances are Fig. 3.5.1 Survey pegs
field by chain or tape. 2. Ranging rods
" The various types of chains and tapes
are used for (1.¬. the process of
" The rods used for ranging purpose
measurement of distance like engineers chain, gunter ranging rods.
making a straight) are known as
hand, choth
chain, revenue chain, metric chain and steel " These rods are made of seasoned
wood or metal with
or linen tape, metallic tape, steel tape, invar tape diameter about 25 mm and length of 2-3 m.
respectively. black/red and white band
" The rod is alternately coloured
from a long
3.5.2 Types of Linear Measurements of 20 cm divisións so that the rod is visible

" The other commonly used distance measuring method distance.

" The ranging rod is provided with an iron
shoe at its
are

1) By stepping or pacing 2) By stadia method bottom and carries flag at the top.

3) By speedometer 4) By odometer wheel 3. Offset rods

" The methods and techniques used for distance " The offset rods are similar to the ranging rod with the
measurement depends on type of distance and accuracy only difference that the flag at the top is replaced by a
of measurement required. hook for pulling the chain and narrow slits for aligning

3.5.3 Accessories for Linear Measurement the offset lines. (Refer Fig. 3.5.2)
Flag
" The various accessories used for linear measurement are
as follows Hooks
1. Survey pegs 2. Ranging rods
3. Offset rods 4. Line ranger
5. Chains 6. Tapes Height Slits
2 m or 3 m
7. Cross staves 8. Plumb bob for both

1. Survey pegs
" The survey pegs are circular or rectangular in shape, White
20 cm colour
made up of wood or metal are used to fix the position of
survey station/points on the ground.
"The pegs are driven in the ground with the help of 20 cm Red/black
colour
hammer with suficient length projecting outside the
ground but firmly fixed in ground.
20 cm
" Nowdays, metal pegs are used because of the advantage
of their strength and durability. However, wooden pegs 5cm Metal shoe
can be easily manufactured on site.
Offset rod
Ranging rod (No flag used)
" For level ground, rock etc only scratch is made on (Flag may or may
not be used)
ground to indicate station.
Fig, 3.5.2 Ranging rods and offset rod
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4. Line ranger
"It is small handy device consist of pair of right angled triangular prisms of which hypotensual faces retlect
the rays coming fom ranging rods.

Groove

-Handles (brass)

Links 4 mm

5m
Brass ring at every m
One link
L.C. = 20 cm

5m

Brass tags at every 5 m

5m

Central 3 legged tag 5

5m
4 mm o
o 2Legged tag hardened
steel

5m
40 cm
o1Legged tag

-Three connecting rings 4 mm o

5m
(b) Arrow
Shorter links at handles

Eye bolt with swivel joint

(a)30 m metric chain

Fig. 3.5.3
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5. Chain
7. Tapos
"A chain is made with 100 to 150 pieces of galvanised " The mnost commonly used and suitable accessory for
mild steel wire of diameter 4 mn. linear measurement is chain. But to avoid large mumbe
" The ends of pieces are bent to fom loops and then of arrows in chain survey, tapes are used.
connected together with the help of three oval rings to (Refer Fig. 3.5.4.)
make chain flexible. (Refer Fig. 3.5.3 on previous page.) " Metal ring is provided at the outer end of tape which is
"Two brass handles are provided at the two ends of the inchuded is length of tape.
chain to hold the chain. " Tape is available in 10m, 20 m, 30 m for survey work
" Talies are provided at every 10 or 25 links for facility (other lengths are used for other purposes).
of counting. One link means the distance between the " Other end of tape is fixed inside the circular waterproof
centres of adjacent middle rings. plastic case and manual or automatic (spring) winding
" Groove is made n the outer face of handle to fix the device is provided to the box (case) of tape.
arrow or chain pin. Refer Fig. 3.5.3 (a) on previous The tape is made up of different materials with different
page.) (Explained later in section 3.5.4.) least count. i.e. cloth/linen, metallic, plastic or synthetic
6. Arrows with 1mm to 1 cm least count.
" Arrows are used to mark the end of each chain during (Explain later in section 3.5.5.)
the process of chaining. (pegs are used to mark the 8. Cross staves
stations whereas arrows are used to mark the end of each " The cross staff is used for finding the foot of the
chain).
perpendicular from a given point of a line and for setting
" Arrows are, also called as marking chains or chain pin. out a right angle at a given point of a line.
(Fig. 3.5.3 (b) on previous page.) " There are three types of cross staves nanmely open french
or octagonal cross staff and adjustable or circular cros
staff (Explained later in section 3.5.6.)

Rivet L.C.=1 mm
Other
end
6 7 8 9 10
Lm...3olm
Ring 16,13,9.5 or 6 mm

Metal strip
Steel tape

10cm L.C. = 1 cm 16 mm

Hard drawn Leather strengthening piece (Stitched) Other end

brass ring fixed in
cOver (Case)
Metal wired (Metallic) tape

Fig. 3.5.4 Common tapes

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9. Plumb bob
ber " Plumb bob is used for centering and marking a point
Engineer's
chain
100 ft Previously used for
engincering works
vertically below the instrument.
Gunter's chain 66 ft Previously used to
. It is conical metal piece attached at the bottom of thread measure in miles and
to be suspended below the instrument. (Fig. 3.5.5) furlongs
Drk. Thread
Revenue chain 33 A Cádastral survey

3.5.5 Types of Tapes used in Dlstance

DOf Measurement

" Following types of tapes are used in distance

measurement.

Survey tapes
Bob

Cloth or Metal Metal Plastic / Synthetic

linen tapes tapes wired tapes fibre glass tapes
Fig. 3.5.5 Plumb bob

3,5.4 Types of Chains used In Linear

Measurements Steel Invar
tapes tapes
" The different types of chains based on their length and
h pupose are as follows : a) Cloth or linen tape
a) Metric chain " This tape is made of closely woven linen and varnished
S
to resist moisture.
b) Steel band
"It is 12-15 mm in width and 10-30 m in length.
c) Engineer's chain
" This type of tape easily gets affected by pull, temperature
d) Gunter's chain and moisture/dampness.
e) Revenue chain " It is very flexible and light weight. It is used for minor
"The metric, engineer's chain and gunter's chain are or ordinary works.
divided in 100 links while revenue chain is in 16 links.
b) Steel tape
"Engineer's chain is 100 ft long, Gunter's chain is 66 t " The steel tape is made of stee! ribbon of width varying
long and revenue chain is 33 ft long. Metric chains are from 6-10 mm in width and 10-50 m in length.
either 20 m or 30 m (Fig. 3.5.3 (a))
" This tape is used for standardising chains.
" Steel band consists of ribbon of steel of width 16 mm
"It is affected to small extent only by temperature.
and length of 20 m or 30 m. It has brass handle at each
end. It is graduated in meters, decimeters and centimeters " It breaks if twisted/folded
on one side and 0.2 m links on other side. " Not flexible.

Table 3.5.1 Types of chains and purpose c) Invar tape

" Invar tape is made of an alloy of Nickel (36 %) and
IVpe of chaín Length Purposehuse Steel (64 %) having very low thermal coefficient.
Therefore it is not affected by change in temperature.
Metric 20 m or 30 m To moasure distance
on level ground. These are available in 8 mm width and 30, 50 and
100 m length.
Steel band 20 m or 30 m Projects where more
accuracy is required. " It is used at places where maximum precision is required.

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Cross TWo saW-Cuts

wires Pin
holes
Wooden head
Metallic head
(a) Open cross staff

Eight slits

Open cross staff on leg

(b) French cross staff
Other observer Object

VOne otbserver
Main and
vernier sScales
i Chain line

Adjustable
Screw

(c) Adjustable cross staff

B
(d) Use of open cross staff

Fig, 3,5.6 Cross staves and use of open cross stafi)

d) Metallic tapes/ Metal wired tapes
" Two pairs of arms are at right angle. One arm fixed
" Metallic tapes are linen tapes reinforced with brass or
along the survey line and other along the direction of
copper wires to make it durable.
" This tape is available in 15, 20 and 30 m lengths.
object by keeping cross staff vertically at the
approximate position.
" These are used for all survey work with accurate
" To bisect the object and ranging rod simultaneously the
measurement requirement. cross staff may be moved forward or backward along the
e) Plastic or synthetic tapes chain line (Refer Fig. 3.5.6 (a) and (b))
" These tapes are bad conductor of heat or electricity. b) French cross staff
Therefore can be used under different circumstances.
"It consists of four pair of arms for sighting, Hence
3.5.6 Types of Cross Staff offsets at angle in the multiple of 45° are also possible.
" The cOSS staff is simple instrument used for setting out
(Refer Fig, 3.5.6 (b)
right angles. c) Adjustable cross staff
" There are three types of cross staves " In this type of cross staff, adjustable screw is provided
a) Open cross staff upper portion of cylinder head can be rotated relative to
the lower. Hence can be used for setting out angles of
b)French cross staff
any magnitude. (Refer Fig. 3.5.6 (©))
c) Adjustable cross staff
" The results are approximate considering to the closeness
a) Open cross staff of the sights.
" This is the simplest form of cross staff consists of 4
arms with vertical slits for offsetting.
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3.5.7 Concept of Ranging ii) Assistant should follow the direction given by hand
Defnition : The process of establishing intermediate points signals of main surveyor.
on a straight line (when length of survey line is more than "Following are the hand signals for direction to assistant
he maximum available length of tape/chain) between two during ranging.
end points is called as ranging. Table 3.5.1 Direct ranging by hand signals

Ranging
Sr. Hand signal by main Action by assistant
no surveyor
When end stations When end stations are
are visible not visible 1. Rapid sweep of left or Long/considerable movement
right hand. to left or right side
respectively.
Direct method Indirect method
(reciprocal ranglng) 2 Slow swveep of left or Short/slow moverment to left
No instrument use Instrument use right hand. or ight side respectively.
3 Left or right arm Keep/continue moving to lef
Eye and Use of Use of extended out. or right side respectively.
hand signals line ranger theodolite
msthod
Left armm up and moved Position is ok but make rod
to the lef. vertical by tilting to left.
3.5.7.1 Types of Ranging Right arm up and Position is ok but make rod
a) Direct ranging : moved to the right. vertical by tiltíng to ight.
" When intermediate ranging rods are fixed on a straight Both hands raised and Position and plumb line are
line by direct observation from end stations, the process brought down. correct.
is known as direct ranging.
Both hands extended Rod is to be ixed at that
"This method is useful when end stations are inter visible. forward and depressed position.
rapidly down
"Assume A and B are end stations of survey/ ranging line.
Main surveyor at A stands 1 to 2 m behind rod in such
b) Indirect /Reciprocal ranging :
way that both rods are collinear to him. "When end stations are not intervisible due to high ground
" The assistant at point C (intermediate point) holds (hill) between them, then intermediate ranging rods are
another ranging rod by his judgement on the line. Now, fixed on the line in an indirect way, known as indirect
main surveyor directs assistant by hand signals till rod at ranging or reciprocal ranging.
A, C and B are collinear. Thus rod from C and C is
gradually shifted to point C.
"Suppose points A and B are two end stations which are
not intermediate due to high ground in between them.
"The procedure is repeated for more number of points. "Two assistants R1 and S take their position with
(Refer Fig. 3.5.7)
ranging rods.
1-2m " Initially, assistant at R1 direct assistant S1 till R1, S2
(Main
Surveyor) A (assistant) B (End point) and B are in some line. After that the assistant at ST
direct assistant ofR, till A, R, and ST are in same line.
" By directing alternately in this manner, they change their
Fig. 3.5.7 Direct ranging
position every time untill finally come to positions R and
" Precautions to be taken S which are in straight line AB. (Refer Fig. 3.5.8)
i) Ranging rod should be held/erect vertically.
iü) Hand signals by main surveyor should be clear.

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A B

S1
R2i
A R

Fig. 3.5.8 Indirect ranging (Reciprocal ranging)

|3.5.7.2 Differences Distances along chain Distances across chain line
a) Direct and indirect distance measurement line are called as are called as ofsets.
chainage. (zero at first
b) Chaining and offsetting station)
c) Direct ranging and indirect ranging
No types of chaining. There are short, oblique
a) Direct and indirect distance measurement
and perpendicular offsets.
iN) Every point has only Single point can have
Sr. on chainage. more than one offset.
No
Direct measurement Indirect measurement
c) Direct and indirect ranging
Horizontal distances Horizontal distances between
between station or points stations or points are
are obtained directly. obtained indirectly y Sr. No Direct ranging Indirec ranging
calculations.
Useful when stations are Required when stations
Commonly adopted Commonly adopted method intervisible. are not nteryisible.
method in chaining. is trigonometric observations
(slope angle and sloping ) Methods used are hand
istance to calculate Reciprocal ranging is
signals, line ranger and used
horizontal distanc). theodolite.
ii) No angle measurement is At least one angle
required. More accurate. Comparatively less
measuring device is
required. accurate.
iv) Results are more Results are approximate.
accurate. 3.5.8 Chain Surveying
" Chain is simple instrument used for linear measurement.
b) Chaining and offsetting Chain, corrected for errOrS, gives most appropriate
results.
Sr. No Chaining Offsetting
i) It is measurement of It is measurement of
distances along chain distance at right angle to
line. chain line.

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60 60° A60° 80 )25° 135°

(a) Wellconditioned triangle (b) Il conditioned triangle

Fig. 3.5.9 Well and ill conditioned triangle

3.5.8.1 Objective " Ill conditioned triangles are not used in chain surveying
" Chain survey is the simplest method of surveying. In this because their apex points are not sharp and well defined,
method only measurements are taken in the field. Rest of which is why a slight displacement of these points may
work is done in the office. This method is most suitable cause considerable error in plotting.
for small areas and if carefully done, it gives quite (Refer Fig. 3.5.9.)
accurate results.
|3.5.8.4| Definitions
|3.5.8.2 Principle A) Survey stations
The basic principle of chain surveying is triangulation. " Survey stations are the points at the begining and end of
i) The whole area to be surveyed to divided into a chain line. Survey stations may also be taken at any
skeleton of framework consisting of a number of convenient points on the chain line.
well connected network of well conditioned
"In other words, the points taken as reference for plane
triangles. land survey are called as survey stations.
ii) The sides of triangles are directhy measured on field "Types of survey stations are
by chain or tape and no angular measurements are
a) Main stations
taken. Hence tie lines and check lines control the
b) Subsidary stations
accuracy of work.
c) Tie stations
|3.5.8.3 Well Conditioned and illConditioned Triangles
a) Main stations
" When no angle in triangle is less than 30° and greater
than 120° then the triangle is called as well conditioned "Stations taken along the boundary of an area
controlling points are known as main stations.
triangle.
"Equilateral triangle is considered to be the best "The main survey lines should cover the whole area to be
surveyed.
conditioned triangle or ideal triangle.
" The main stations are denoted by 'A with letters like A,
" Well conditioned triangles are preferred because their
apex points are very sharp and can be located by single B, C, D etc
dot. " The chain line are denoted by
"A triangle in which an angle is les than 30° or more b) Subsidary stations
than 120° is said to be ill conditioned triangle. "Subsidary stations are stations which are on the main
survey lines or any other survey lines.

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D

POND

Base line S2
Check line Tie line

Building

Main survey line

G A R D E N

Fig. 3.5.10 Index sketch showing survey

"
stations
These stations are selected to
run auxiliary lines for 5) Survey lines should pass
covering the details of area which are not possible through a level open ground
main lines. from as far as possible so that
chaining can be done easily.
"These stations are denoted by 6) The main survey
() with latters S1, S2, S3 lines should pass close to the
etc. boundary line of the area to be surveyed.
7) The survey lines should be
c) Tie stations taken close to the objects
so that they can easily be located by
" These are also short offsets.
subsidary stations taken on main survey 8 The
lines to join tie lines. subsidary stations should be suitably selected for
"
taking check lines.
Sometimes tie stations are taken to locate interior details.
9) Station should be SO selected that
" Tie stations are denoted by )
with letters T1, T, Ta chaining are avoided as far as possible. obstacles to
ete. (Refer Fig. 3.5.10.) 10) The survey lines should not
A] Selection of be very close to main
survey stations roads, as survey work may then be
Following points should be remembered during the traffic. interrupted by
selection of survey stations. B] Survey lines
1) The stations should be " An imaginary line while
so selected that the field work is being carried out,
principle of surveying may be strictly followed. general joining survey stations is known as survey line.
2) The main stations " It is designated as line
should be mutually intervisible so AB, bc etc depending on the
that ranging can be done easily. stations which it joins.
3) The stations should be " The types of
selected in such way that well survey lines in the surveying are
conditioned triangle may be formed. a) Base lines
4) The base line should be b) Main lines
the longest of the main
survey lines that runs through the middle of the c) Subsidary or tie lines
area.
d) Check lines
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a) Base lines
a) By swinging the tape from object to the chain line.
The line on which the tramework of the survey is built is The point of minimun reading on the tape will be
known as the 'Base line' the base of perpenducular (Refer Fig. 3.5.11 (a).
" It is the most important line of the
survey
b) By setting a right angle in the ratio of 3:4:5 (Refer
"It is measured very accurately and precisely. Fig. 3.5.11(b).
.Generally, base line is the longest of the main survey
c) By setting a right angle with the help of tri-square
lines roughly pass through center of area at right angles (Refer Fig. 3.5.11 (c).
to esch other.
d) By setting a right angle by cross staf or optical
b) Main lines square.
.Except base line, other survey lines joining main survey
stations are called as main lines. ii) Oblique offsets
"Oblique offset is offset other than perpendicular offset.
c) Tielsubsidary/secondary lines
aO(Object)
" The lines joining tie stations are called as
tie/subsidary/secondary lines.
(a)
. These are selected to complete all the measurement of
building, compounds, roads etc.
d) Check/proof lines P(Base of perpendicular)
" The lines joining the apex point of a triangle to some Chain line
fixed pont on its base is known as check line.
O(Object)
" These lines are important to complete check on the
survey work and also to locate interior details.
(b)
C] Offsets -Builders
" The lateral measurement taken from an object to the square

chain line is known as Offset'.

" Offsets are taken to locate obiects with reference to the
Chain line
chain line.
The classification of offsets is as follows : "O (Object)

Survey offsets
Based on angle of (c)
Based on length measurement
5 m
3m
90°
4 m B

Long offset Perpedicular Oblique Chain ine

Short offset
offset offset

Building

" Short and long offsets are explained later in

Oblique (d)
offset
section 3.5.8.5 (b).
i) Perpendicular offsets
"When lateral measurements are taken perpendicular to the
-Chain line
chain line, known as perpendicular offset.
"Perpendicular offsets may be taken in the following Fig 3.5.11 Types of offsets
ways.
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"Oblique offsets are set up when objects are at a long ) Only one ii) Requlre two number for
distance from the chain line or when perpendicular offset perpendicular offset locating a point or objoct.
0s sufficient.
is not possible due to some difficulties.
" Two long offsets are setup to fix any point. (Refer ii) Cross staff, optical i) Only tape is required for
square eto are taking oblique offsets.
Fig. 3.5.11 (d).
necessary along wvith
3.5.8.5| Diferences tape.

a) Base Line and Tie Line.

3.5.8.6| Errors and Comectlons In Dlstance Measurement
b) Short Offset and Long Offset.
" The errors in linear measurement may oCcur due to
c) Perpendicular and Oblique Offset.
following reasons :
a) Base Line and Tie Line i) Due to natural cause (accidental)
ii) Personal errors (mistake)
Base Line Tie Line
iü) Instrumental (cummulative)
) t is main line passing i) It is secondary
through center of area subsidary survey line. A] Types of Errors
" The types of errors are as follows
ii) Generally, base line is ii) Tie. lines are lesser in
the longest survey line length than base lines.
Errors in surveying

ii) Necessary for control iiü) Necessary to mark interior

and accuracy of work. details and making long Compensating Cummulative
offsets short. errors errors Mistakes
iv) These are measured iv) These are measured with
most accurately with common methods.
special instruments Positive erors Negative errors

a) Gompensating errors
" The error which occur in both directions (positive and
b) Short and Long Offset
negative) and finally tend to compensate each other are
Short Offset Long Offset known as compensating errors.
"These errors do not affect surveying work.
i) These offsets are i) These offsets are greater
generally less than than 15 m in length. " Compensating errOrS may cause due to
15 m in length. i) Incorrect holding of the chain.
i) Most accurate, ii) Less accurate, SO ii) Horizontality and verticality of steps not being
mostly prefered. generally avoided. properly maintained during the stepping operatoin.
ii)Preferably taken as iii) Oblique offset of 2 no. ii) Inaccurate measurement of right angles with chain
perpendicular offsets, are taken. and tape.
" Compensating errors are proportional to VL where, L is
c) Perpendicular andObllque Offset length of the chain.
Perpendicular Ofset Oblique Offset b) Cummulatlve errors
1) Offsets are taken at i) Offsets are taken at any " The erTOrs which occur in one direction and finally teno
right angles to the to accumulate are said to be
angle with respect to survey cummulative errors.
survey line. line. "Cummulative errors seriously affect the
surveying work.
" These errors are in proportional to length of
the line (L
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Basic Civil and Mecharical Engineering 3-15 Surveying and Levelling
eThere are two types of cummulative errors
if the adjustment is done in the begining, correction need
i) Positive eTor to apply for measurement.
ii) Negative error " The corrected length and area are to be calculated as -
i)Positive Errors True length/Correct length x Measured length
" The eTOr said to be positive, when measured length is
more than actual length (i.e. chain is too short)
True area/Correct area ×Measured area
Positive eTor occurs due to
oThe length of chaintape being shorter than actual. where, L = Standard or true length of chain, m
o Slope correction is not applied. L' =Actual length of chain, m
o Correction for sag is not applied.
=Lt em (e = error)
oMeasurement is taken on faulty alignment or during
high wind when tape is in suspension. em

i) Negative Errors ep = Eror at end, m

The error is said to be negative, when measured length is
e, = ErrOr at begining,
less than actual length (i.e. chain is too long).
If chain is too long, use + sign
The increase in length of chain/tape is greater than the
standard length due to following reasons, which causes If chain is too short, use - sign.
negative errors
C] Correction for Slope
i) Opening of joints.
" Slope correction is to be applied when groumd runs in
iü) Elongation of links due to heavy pull. long slopes.
iüi) Applied pull is much greater than standard pull.
0v) The field temperature uring measurement is much B.
higher than the standard temperatures.

c) Mistakes
"Mistakes are the errors occuring due to carelessness of
the chainman.
A B

"Mistake occurs due to following reasons

i) Afull chain length may be omitted or added due to Fig. 3.5.12 Measuring along the slope
wrong counting of arows.
"The slope angle is first measured by angle measuring
iü) The number may read from the wrong direction. i,e instrument i.e. abney level or clinometer.
number '6 may read as 9'.
" CorrectTrue length = cos x Measured length
iü) Wrong calling of numbers, i.e. 30.3 may called as
AB = AC cos 0
"Thirty-Three' without decimal point.
iv) Interchanging of numbers while entering into the where 9 = measured slope angle
field book. i.e. 367 written as '376.
" Suppose L = True length of tape
B] Correctlon in Length and Area AB = AB, = L
"When chain is used for measurements, becomes too long
or too short (i.e: actual length is more or less than the AB
COs =
designated or nominal length of chain respectively) even AC

AC = AB sec = L sec0

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B,C = AC - AB1 ii) Correction for Pull (C,)
" During measurement, the correct tension need
= L sec - L to be
applied to the chain/'tape by attaching a spring balance
= L (sec -1) the handle at one end. (the pull at which
" The amount L (sec -1) is called
Hypotenusal
standardised) tape/chain
allowance. This allowance is always added to
tape
If standard tension is not applied, neceSsary comecti.
length. should be made.
"While chaining, " The correction given by expression
hypotenusal allowance is added in per
tape length. i.e tape ends at B, but (Pm - P,) L
arrow is placed at C
after adding allowance and next AE
point C not B,.
chainage is taken from
where,
D] Gorrections for Tape
Following corrections are applied for Cp = Pull correction, (m)
tapes - measurement with = Applied pull during measurement, (kg)
P'm
i) Correction for temperature P, =Standard pull, (kg)
ii) Correction for pull L =Length of tape, (m)
iii) Correction for slope
iv) A = Cross-sectional area, (cmn')
Correction for sag.
E= Modulus of Elasticity, (kg / cm²)
I) Correctlon for
"
Temperature (C)
Temperature correction needs to be applied when there is (2.1x106 kg/ cm, when not given)
increase or decrease in chain/tape length due to rise "If the pull applied during
or
fall of temperature during
measurement. measurement is greater than
"The standard pull (Pm >P) then more ground will be
temperature correction is given by the expression. and reading will be less, taped
Cf = aL (Tm -T,) indicating negative error.
Therefore positive corrections is thus required.
where, " If pull applied
during
standard pull (Pm <P) measurement
is lesser than
Cf = Temperature correction, (meters.) then negative correction is
required.
a = Coefficient of thermal ii) Correction for Slope
expansion, (/°C)
"When the
(Use 11x10 /°C, when not given). measurements are taken on slope, the extra
distance is measured than actual
Tm =Temperature
during measurement, (°C) Therefor corection for slope need to behorizontal distance.
T, =Standard applied.
Temperature, (°C)
L =Length of tape, (m)
"If the
temperature during measurement is greater than
standard temperature (Tm >T,) then more ground will be
h
taped and reading will be less, indicating
negative eror.
Therefore positive correction is thus required.
" If the temperature during C D
measurement is lesser than
standard temperature (m< lo, negative corection is
required. Fig. 3.5.13 Slope
correction
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 Basic Civil and Mechanical Engineering 3-17 Surveying and Levelling

. The expression for slope correction is Sr. Types of Sign of

Formula correction
No. correction
Ch = 1(1- cose) - (exact)
1. Temperature C= aL(Tm -T) Im > To tve
h2 Tm < T -Ve
(approx)
2/
2 Pull (Pn-P)L Pm > P tve
AE Pm < Po -ve
where, |= One tape length measured, (m)
Ch= I(1- cose)
e = Slope angle (exact)
3. Slope Always -ve
h = Vertical height, (m) h2
27 (approx)
Ch =Slope correction,(m) LW?
"Correction for slope is always negative. C=
24n'P
v) Correction for Sag/Catenary (C,) (Total wt. is given)
4. Sag Always -ve
" If the highest accuracy is required, the tape can be w²1
C,=
suspended at certain distance from ground and corection 24n²P
for sag the tape is applied. (Unit wt is given)

" The expression for sag correction is

3.5.8.7 Precautions in Distance Measurement
When total weight of tape is given, Following precautions needs to be taken to avoid erOrs
LW2 and mistakes -
Cs =
24 P i) Ground should be marked with cross (X) at the paint
of arrow fixed on ground.
When unit weight of tape is given,
i) The zero end of the chain or tape should be properly
L(wL)? w²L3 held.
Cs D2
24 P2 24 Pn iüü) During chaining, the number of arrows carried by the
follower and leader should always tally with the total
where, numbers of arrows taken.
Cs = Sag correction, m 2iv) The chainman should call reading loudly and clearly
and the surveyor should repeat while booking.
L = Length of tape or chain, (m)
v) Measurements should not be taken with the tape in
W = Total weight of tape, (kg) suspension in high winds.
W = Weight of tape per unit length, (kg/m) vi) In stepping operations, horizontality and verticality
should be properly maintained.
W = WIL
vüi) Ranging should be done accurately.
Pm = Pull applied during measurement, (kg)
"Ifn number of spans are used for chaining, then 3.6 Measurement of Angles/Angular
Measurement
LW2 w23 3.6.1 Methods of Angle Measurement
Cs = or
24n P 24n?P Angle measurement
(Horizontal)
" The sign for sag corection is always negative

Direct measurement Indirect measurement

(Theodolite used) (Compass used)

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 Surveying and Level.
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Fore Bearing (F.B.)

Whole Circle
Bearing (W.C.B.)
Designation Direction
Bearings Jof measurement

Quadrantal or
Back Bearing (B.B.)
Chosen meridian
Reduced Bearing
(Q.B/R.B.)

Arbitrary Bearing
Magetic Bearing
True Bearing (A.B.)
(T.B.) (M.B.)

bearings
Fig. 3.6.1Different types of
" In Direct angle measurement method, angle between the
3.6.2 Bearings
line with a fxet
The horizontal angle made by survey "Bearing
survey lines is measured directly by using instrument i.e. of line'
theodolite.
reference line i.e. meridian is known as
designation.
" nlndirect angle measurement method, angle between the The different types of bearings based on
measurement is a
chosen meridian and direction of
survey lines is obtained from the bearings of lines with
follows. Refer Fig. 3.6.1.
reference to meridian i.e. compass.

3.6.1.1 Differences 3.6.2.1 Systems of Bearings

a) Direct angle measurement and Indirect angle " There are two methods or systems of measuring the
measurement. magnetic bearings :
b) Horizontal angle and Vertical angle.
A) Whole Circle Bearing (WCB) system.
B) Qudrantal Bearing (QB) system.
a)
Indirect angle A) Whole Circle Bearing (WCB) system
Sr. Direct angle measurement
No. measurement " The magnetic bearing of line measured clockwise from
Angle are caloulated the north pole towards the line is known as 'whole circle
Angles between survey
lines obtained directly from bearings of lines bearing' of that line.
No meridian is required Meridian is necessary "In other words, the horizontal angle made by survey line
Instruments like theodolite, Instrument lke with magnetic north in clockwise direction is called as
sextant are used is to compass is used to
measure angle measure bearings whole cirlce bearing of that line (Fig. 3.6.2 (a).
" The values of WCBranges from 0° to 360 °.
b
" Prismatic compass is used to measure WCB.
Sr. No. Horizontal angles Vertical angles
B) Quadrantal Bearing system
Angles are measured Angle are measured in
along horizontal plane vertical plane "The magnetic bearing of a line measured clockwise or
counter clockwise from either North or Souti
i) Required for plotting Required with reference
of maps and plans to levelling (whichever is close) to East or West is known as
i.e. Surveying Quantrantal Bearing of that line'. (Fig. 3.6.2 (b)
ii) Measured with Measured with "The complete space is divided into different quadrants 1.
instruments like. instruments like
compass theodolite. NE, NW, SE, SW.

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 Basic Civil and Mechanical Engineering 3-19 Surveying and Leveling

4N Sr.
WCB QB or RB
(360) i(0) No.

Magnetic bearing of Magnetic bearing measured

D line measured from from N or S (whichever is
magnetic north in Dear)-to E or W in
clockwise direction is clockwise or anticlockwise
called as WCB direcion is called as QB or
RB

ii The values ranges The vahues ranges from 0 o

from 0° to 360 °. to 90 along with quadrant

i) Prismatic compass is Surveyor's compass is used

used

Values of angles are Valves of angle and

C B sufficient quadrant are necessary.

3.6.2.2| Conversion of Bearings

Fig. 3.6.2 (a) W.C.B. system " The conversion of bearings from one system to another
system can be done either by drawing a sketch and using
N the geometry or by using following formulae.
(0)
A) Conversion of WCB Into equivalent QB
N-E
N-W
WCB between Quadrant Corresponding QBRB

0° to 90° NE OB = WCB

W- E
90 to 180 SE QB = 180 WCB
(90°) (90°)
180 to 270° SW QB = WCB-180°

S-W S-E 270° to 360 NW QB = 360 WCB

C S(0)

" The QB is to be represented/expressed along with

Fig. 3.6.2 (b) Systems of bearings quadrant eg. N30°E, S S0°1S' Wi.e. values of angle
and quadrant both are necessary.
" The value of QB lies between 0° to 90. In QB,
quadrants should always be mentioned. B) Conversion of QB into equivalent WCB
" The surveyors compass is used to measure QB.
QB or RB Corresponding WCB
Reduced bearing
"When the WCB of line is converted into QB, then it is Na°E WCB = QB = a°
called as Reduced Bearing (RB).
SB°E WCB = 180°-QB = 180- B°
" The RB is similar to QB (values between 0°- 90 9
SW WCB = 180 +OB = 180+ y

N&W WCB = 360 - OB = 360 - 8

"To represent WCB, only magnitude of angle is sufficient.

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C) Numerlcal on A) True merldlan and True bearing (T.M. and TB.)
Converslon
i) Convert following WCBs to QBs " The line or plane passing through the geographical
pole, geographical south pole and any point on the norh
Sr. surface of earth is known as True meridian!
WCB OB 'geographical meridian'.
No.
) WCB of AB 45° 30'
" In other words, the line passing through given station a
QB of ABN45° 30' E north as well as south poles of the earth intersects
surface of earth.
the
i) WCB of BC = 125° 45' QB of BC 180° 0 - 125° 45
54° 15 E "The true meridian at a station is Constant.

i) WCB of CD 222° 15' .True meridians through various stations are not parall
QB of CD 222° 15-180
420 15' W but converges to the poles of the earth, but for
smal
Surveys, true meridian are treated as parallel to ent
iv) WCB of DB = 320° 30 OB of DE 360 -320°30 other.
=N 39°30 W
" The horizontal angle between true meridian and surve
line is known as "True Bearing (T.B.)" or "azimuth" of
ii) Convert the following QBs to WCBs
that line. (Fig. 3.6.3)
Sr.
No. QB WCB MN TN ,Magnetic bearing
True meridian
î) QB of AB =S 36° 30' W WCB of AB = 180° 0'436°30 True bearing
216 30 Magnetic meridian.
B
in OB of BC = S 43° 30' E WCB of BO 18O° 0 4330
13630

) OB of CD = N 26° 45'E WCB of CD 26 45

iv) QB of DE = N40° 15 W WCB of DE 360 040° 15S

319° 45 Fig, 3.6.3 True and magnetic meridian and bearing
v) QB of ER = N 3S° 10 W WCB of EF= 360°03$° 10 "Meridian passing through Greenwitch
3249 50 adopted
internationally as the prime meridian or standard
vi) OB of FG S 88° 30 E WCB of FG 1800- 88° 30 meridian.
919 30 " True bearing is obtained by astronomical observations.
B) Magnetlc meridlan and Magnetic bearing
3.6.3 Types of Meridlan and Bearings and M.B.)
(M.M.
" Meridian is the fixed reference line used to measure "The direction indicated by properly balanced freely
bearing of a line. suspended magnetic needle unaffected by attractive forces
" Depending on the type of meridian used, there are four is known as Magnetic Meridian (M.M.) i.e. Magnetic
types of bearings. North - South line (Fig 3.6.3)
A) True meridian and true bearing " The horizontal angle between magnetic meridian ano
B) Magnetic meridian and magnetic bearing survey line, is known as Magnetic Bearing (M.B.)or
C) Arbitrary meridian and arbitrary bearing simply bearing' of the line.
D) Grid meridian and grid bearing " Magnetic bearing at a station always vary depends on
magnetic declination of magnetic North-South pole.

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C) Arbitrary meridlan and Arbitrary bearing (A.M.

and A.B.) "The fore bearing (FB) is also called as front or forward
.For small survey, any convenient line or diection is bearing.
assumed as meridian called as Arbitrary Meridian. (A.M.) " The FB of AB =30° 20, means station/compass is at A
(Fig. 3.6.4) and rod is bisected at B with angle 30° 20 clockwise
from north. (Fig. 3.6.5 (a))

30°20 bearing)
A ( F o rb
ee 0,(Back bearing)
210°20
Survey
direction

Fig. 3.6.4 Arbitrary meridian and bearing

" The horizontal angle between arbitrary meridian and A

survey line is known as Arbitrary- Bearing (A.B.). (a)

" Sometimes the starting line of survey is taken as
100°30'
arbitrary meridian. and arbitrary bearing is useful to find B(Back bearing)
angle between lines.
" Individual value of arbitrary bearing has no significance A

direcStuirovney
due to arbitrary/assumed meridian.
D) Grld meridlan and Grid bearlng (G.M. and G.B.)
DeFore280°30
bearing)

" For preparation of maps, sometimes, some state agencies

assume several parallel lines with respect to true (b)
meridian called 'grid lines' and central line is called as
Fig. 3.6.5 Fore bearing and Back bearing
Grid Meridian' (G.M.).
B) Back Bearing (B.B.)
"The bearing of a line with respect to grid meridian is " The bearing of line measured in opposite direction to the
known as the 'Grid Bearing' (G.B.) of that line.
Survey called as Back Bearing (BB) of that line.
3.6.4 Bearings of Survey Lines " If back station is bisected from particular station, then it
" Usually survey is progressed as per the progress of is called as Back Bearing of that line.
alphabetical order of station i.e. a line joining P and Q " The Back Bearing (BB) is also called as rear
stations is PQ, line joining X and Y stations is XY. (Not backward bearing.
QP and YX) " If BB of line AB = 210° 20, means station/compass is at
"There are two types of bearings with respect to the B and angle is measured clockwise from north upto rod
direction of measurement/progess : at A(210° 201) (Fig. 3.6.5)
A) Fore Bearing (F.B.) " The clear understanding of FB and BB is required in
traversing operation and the position of compass and
B) Back Bearing (B.B.)
ranging rod.
A) Fore Bearing (F.B.)
" The bearing of line measured in the direction of the 3.6.5 Relationship between FB and BB of Line
progress of the survey is called as fore bearing of that i) In WCB system, the difference between the FB and
line. BB is exactBy 180° (if needle of compass is free and
" If from a station, next station is bisected then it is called unaffected due to external forces)
as fore bearing (FB) of that ine. i.e. B.B = FB ± 180

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Ergineering
N

F.B. of AB
F.B. of PCQ
N

B.B, of AB
180

B.B. of PQ
180

B.B. of AB = F.B. of AB -180° B.B. of PQ F.B. of PQ+ 180°

(b)
(a)

Fig. 3.6.6 Relationship between FB and BB (WCB system)

a
Use tve sign when F.B < 180º and -ve sign when
F.B> 180°. (Refer Fig. 3.6.6)
Sr. W.C.B.
No.
Q.B. (RB.)
i) nquadrantal bearing (QB) i.e Reduced Bearing (RB)
system, the F.B and B.B are numerically equal but the Complete circle is Complete circle is tead
quadrants are just opposite e.g. If the F.B is N 30° E divided into four parts or for bearings.
qudrants N-E, S-W and
then B.B is S 30° W. (Refer Fig. 3.6.7) N-W.

3.6.6 Differences Values range from 0° to Values of W.CB. range

90° from 0 to 360°
a) Quadrantal/Reduced Bearing (QB/RB) and Whole As angle and quadrant Very convenient as only
Circle Bearing (WCB). both are necessary for angle is measured.
b) Magnetic bearing and True bearing complete description of
bearing, it is
c) Fore bearing and Back bearing inconvenient.
Measurement of angle is Measurement of angle is
from North and Sourth only in clockwise
towards East or West direction from North.
either clockwise or
anticlockwise.

W. W
N

W W
F.B. of AB =S B° W F.B. of PQ=S a° E
B.B. of AB N'B°E B.B. of PQ= Na°W

Fig. 3.6.7 Relationship between FB and BB (QB/RB system)

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b)
iin) Interior angles are No check is available with
important for check in deflection angles
Sr. Magnetic Bearings traverse
No.
True Bearings
iv) Control on work and Comparatively less control
It is the bearing Measured with reference to accuracy of ploting is and accuracy
measured with geographical or true very good
reference to magnetic meidian.
meridian i.e. N-S line.
2) Interior and Exterior angles
Measured with help It is not measured, but it is
of a compass as to be calculated as TB, - Sr
freely suspended M.BI declination No. Interior angles Exterior angles
magnetic needle gives
the direction of N-S
line. Usually interior Usually exterior angles are
angles are less than more than 180°
180°
ifi) Bearings vary due to TB. does not vary as true
the variation in N-S meridian at a place is For closed traverse, For closed traverse, sum of
line. (i.e. magnetic Constant sum of interior exterior angles should be
declination) angles should be (2n+4)x90, where n is no. of
(2o 4)x90, where n sides of traverse.
is no. of sides of
traverse
Sr. A] When bearings given are in WCB system
No. Fore Bearing Back Bearing
a) When bearings given from same station point
i) Measured in direction Measured in opposite " If two bearings of lines with a common point or station
of survey. direction of survey. are known, then subtract smaller from larger value to get
From a station, next From a station, previous
"included angle". If subtraction is lesser than 180°, then
station is bisected and station (back station) is it is interior angle or else exterior angle (i.e subtraction
bearing is measured. bisected and bearing is is more than 180).
measured.
"If incuded angle between survey line is asked, any
iii) Also called front or Also called as backward answer after subtraction is correct (either interior or
forward bearing. bearing. exterior).
iv) Designated as F.B. of Designated as B.B. of AB N
AB or bearing of PQ. or bearing of QP ete. A

|3.6.7 Angle Calculation from Bearings

650
" Angles between lines can be included angles (i.e. interior
or exterior angles) and deflection angles. 330°
W E
1) Interor and Defiection angles
165°30
Sr.
Interior angles
200°30
No. Defiection Angles

i) These are related to These are related to the

closed traverse open traverse D
C
These are usually less It may have any value Fig, 3.6.8 Bearings of lines (WCB
than 180P system) at common
point
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" When bearings given are not at common point, then
"To find the included angles for the given bearings values, to be obtained
i) Included angle between OB and OC bearings at common point need from
given values of bearing (i.e FB or BB of line). (n
ZBOC = 165° 30' - 65° 00' Fig. 3.6.9)
30' and BC is 65° 30
= 100°30' (interior angle) If bearings of line AB is 45°
to line AB a
to find included angle at station B due
ii) Included angle between OB and OD BCis not (65° 30 - 45°30)) directly.
station B (i.e BB of line An
ZBOD = 200° 30' - 65° 00' "First, bearing of line AB at
obtained by t1800
or FB of line BA) need to be
= 135° 30' (interior angle) bearing of line AB.
ii) Included angle between OA and OB From Fig. 3.6.9,
LAOB =330° 00' - 65° 00' 45°30'
FB of line AB =
= 265° 00 (exterior angle)
then
" Here, angle value is more than 180°, therefore it is AB + 180°
exterior angle. BB of line AB = FB of ine
+ve sign)
" To calculate interior angle, when subtraction of angles is (As FB of line AB is less than 180, use
more than 180° i.e exterior angle 225° 30
BB of line AB = 45° 30 + 180° =
i) Interior angle - 360° - Exterior angle
and
ii) Interior angle = 360°- Larger value of bearing
FB of line AC = 65° 30'
+ Smaller value of bearing
"To find interior angle between OA and OB Now,
Included angle = 330° - 65° included angle ABC = 225° 30' -65° 30

= 265° Exterior angle) =160° (interior angle)

i) Interior angle = 360° 265° = 95° " Note : For clockwise direction, observed angle = (BB of
previous line) - (FB of next line) if the value of
i) Interior angle = 360° - 330° + 65° = 95o difference is negative, it is exterior angle. Then use (360°
b) When bearings given are from different station Value of exterior angle) to get interior angle (only
magnitude of exterior angle is considered)
points.
B) When bearlngs glven are in Q.BIR.B system
" When given/known bearings are in Q.BR.B system, then
to find included angles between lines at common point,
65°30' following rules can be followed or rough sketch can be
N drawn and simple geometry can be used.
Rule - 1

For line lying on same side of same meridian point (^N or

45°30
S) i.e. both lines are in same quadrant.
225°45'
Included angle = Difference between two bearings
A In Fig. 3.6.10 (a), suppose bearing of line

Fig, 3.6.9 Bearings of lines (WCB system) at different OA = N30°30'E and that of line OB = N 49° 45' E
points
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Included angle 180°- Sum of given bearings.

In Fig. 3.6.10 (6), suppose bearing of line
OA = N 30° 30' B and that of the line OB = S 40° 20' E

LAOB = 180° - (30° 30' + 40° 201)

= 109 10 (interior angle)

(a)
Rule -3

N For lines on opposite sides of opposite meridian points

N and S) i.e. both lines are in opposite side of meridian
and in different quadrant.
W E
Included angle = 180° - difference between given

bearings.
(b) In Fig. 3.6.10 (c), suppose bearing of line 0C = S45° E
and that of line OD = N30° W

2COD = 180° (45° - 30)

D:
= 165° (interior angle)

W Rule -4
For lines on opposite sides of same meridian points
-Difference N or S) i.e both the lines are on opposite of meridian and
between
in adjacent quadrant.
bearings
(c) Included angle Sum of given bearings.
In Fig. 3.6.10 (d), suppose bearing of line OA =N30° E
and that of line OD = N40° W
N
LAOD = 40° + 30° = 70° (interior angle)

W
3.6.8 Magnetic Decination
" The magnetic N-S pole is at different position from true
N-S pole causing some angle between magnetic and true
pole/meridian.
(d) " Thus, the horizontal angle between magnetic meridian
and true meridian is known as magnetic declination of
Fig. 3.6.10 Bearings of lines (Q.B/R.B system)
magnetic needle.
LAOB = 49° 45 -30° 30'
. When the north end of magnetic needle is pointed
= 19° 15' (interior angle) towards the east side of the true maridian, the position is
termed as 'Declined East' (0E) and when the north end
Rule 2
of magnetic needle is pointed towards the west side of
For lines ying on same side of different meridian points the true meridian, the position is termed as 'Declined
(N and S) ie. both lines are on same side of meridian but West. (O)
in different quadrants. (Refer Fig. 3.6.11.)

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