Chain Surveying is that type of survey in which only linear measurement are made in the field. This type of surveying is suitable for surveys of small extent.
Table of Contents
Principle of Chain Survey:
The principle of chain survey is to provide a skeleton (or) frame work consisting of a number of connected triangles, as the triangle is the only simple figure that can be platted from the length of its sides measured in the field.
To get a good result in platting, the framework should consist of triangles which are as nearly equilateral as possible.
Terms and definitions:
Survey Stations:
A survey station is a prominent points on the chain line and can be either at the beginning of the chain line or at the end of the chain line. Such station are known as main station.
Survey lines:
The line joining the main survey station are called main survey lines. The biggest of the main survey line is called the base line and the various survey station are platted with reference to base line.
Check lines:
The check lines (or) proof lines are the lines which are run is the field to check the accuracy of the work.
Offset:
It is the lateral distance of an object (or) ground features measured from a survey line.
By method of offsets the points (or) object is located by measurement of a distance and angle from a points on the chain line. If the angle of offset is 90^{0}, it is called perpendicular offset and if the angle is other than 90^{0} it is called an oblique offset.
Instruments for chaining:
 Chain or tape,
 Arrows,
 Pegs,
 Ranging rods,
 Offset rod,
 plumb bob.
Cross staff:
The simple instrument used for setting out light angles is a cross staff. It consist of either a frame (or) box with two points of vertical slits and is mounted on a pole for fixing in the ground.
Eg: (a) Open cross staff, (b) French cross staff, (c) Adjustable cross staff.
Optical square:
 Optical square is accurate instrument than the cross staff for setting out a line at right angle to other line.
 It consist of circular box with three slits at E, F and G. In line with the opening E and G a glass is silvered at the top and unsilvered at the bottom, is fixed facing the opening E.
 opposite to the opening F a silver glass is fixed at A making an angle 45^{0} to the previous glass.
 A ray from the ranging rod at Q passes through the lower unsilvered portion of the mirror at B and is seen directly by eye at the slit E another ray from the object at P is received by the mirror at A and is reflected towards the mirror at B which reflects it towards the eye.
 Thus the image P and Q are visible at ‘B’. If both the image are in the same vertical line the line PD and QD will be at right angle.
Let the ray PA makes an angle α with the mirror at A.
ACB = 45^{0} or ABC = 180^{0} – (45^{0}+ α) = 135^{0} – α
By law reflection
Ebb_{1} = ABC = 135^{0} – α
ABE = 180^{0} – 2 (135^{0}α) = 2α90^{0}
DAB = 180^{0} – 2 α
From ∆^{le} ADB ADB=180^{0} – (2α – 90^{0}) – (180^{0}2α)
ADB = 180 – 2α + 90 – 180^{0 }+ 2α = 90^{0}
thus if the image of P and Q lie is the same vertical line, then the line PD and QD will be at right angle to each other.
Obstacle in chaining:
Obstacle to chaining prevents chainman from measuring directly between 2 points and give raise to a set of problems in which distance are found by indirect measurements.
Obstacle to chaining are of three types
1) Obstacle to ranging but not chaining
This type of obstacle in which the ends are not intervisible is quite common except in flat country.
There are 2 cases of this obstacle.
 Both ends of the line may be intervisible from intermediate points on the line.
 Both ends of the line may not be visible from intermediate points on the line.
2) Obstacle to chaining but not ranging:
There are 2 cases of this obstacle
a) When it is possible to chain round the obstacle ie. pond.
Methods (a): select 2 points A and B on either side. Set out equal perpendicular AC and BD. Measure CD then CD= AB
Methods (b): set out perpendicular to the chain line measure AC and BC the length of AB is calculated from the relation AB = √(BC^{2}AC^{2 })
Methods (c): By optical square (or) cross staff find a point which subtends 90^{0} with A and B. measure AC and BC. Then the length of AB is AB =√(AC^{2}BC^{2})
Methods (d): Select 2 points C and D to both side of ‘A’ and is the same line measure. AC, AD, BC and BD, let angle BCD be θ from ∆^{le} BCD.
Method (e): Select any point ‘E’ and base ‘C’ is line with ‘AE’ making AE=EC range ‘D’ in line with BE making BE=ED measure CD; then AB=CD
Method (f): select any suitable point ‘E’ and measure AE and BE mark ‘E’ and D on AE and BE such that
CE =AE/n and DF =AE/n
Measure CD; then
AB = n x CD.
b) When it is not possible to chain round the obstacle eg. River.
Method (a): select point ‘B’ on one side and A and C on the other side. erect AD and CE as perpendicular to ‘AB’ and range B, D and E in one line. Measure AC, AD and CE. If a line DF is drawn parallel to AB and AB, cutting CE in F perpendicularly. Then the ∆le ABD and FDE will be similar.
AB/AD = DE/ FE
FE = CE – CF = CE – AD and DF = AC
AB/AD = AC/ (CE – AD)
AB = AC X AD / CE – AD
Method (b): erect perpendicular AC and bisect it at D. erect perpendicular CE at ‘C’ and Range ‘E’ in line with BD measure CE then AB = CE
Method (c ) : erect a perpendicular AC at A and choose any convenient point ‘C’ with the help of an optical square, fix a point ‘D’ on a chain line in such a way that BCD is a right angle. Measure AC and AD. ∆le ABC and DAC are similar hence =AB / AC = AC / AD ; AB = AC^{2}/ AD
Method (d): fix point ‘C’ in such a way that it subtends 90^{0} with AB. Range ‘D’ in line with AC and make AD=AC. At ‘D’ erect a perpendicular DE to cut the line in ‘E’ then AB = AE
3) Obstacle to both ranging and chaining.
Choose 2 points A and B to one side and erect perpendicular AC and BD of equal length join CD and Prolong it pass the obstacle. Choose two points E and F on ‘CD’ and erect perpendicular EG and FH equal to that of AC. Join GH and prolong it measure DE evidently BG= DE.
Error due to incorrect chain:
If the length of the chain used in measuring length of the line is not equal to the true length, the measured length of the line will not be correct and suitable correction will have to be applied. If the chain is too long, the measured distance. Will be less. The error will be negative and the correction is positive.
Similarly if it is too short, the measured distance will be more, the error will be positive and correction is negative.
Let L = true length of the chain (or) tape
L^{1}=Incorrect length of the chain (or) tape.
2) Correction to measured length
l^{1} = measured length of the line
l = actual length of the line
True length of line = measured length of line x (l^{1} / l)
l = l^{1} (l^{1} / l)
2) Correction to Area
A^{1}= measured (or) computed area of the ground
A = actual (or) true area of the ground
Then true area = measured area x l^{1} (l^{1} / l)^{2}
3) Correction to volume:
V^{1} = measured (or) computed volume
V= actual (or) true volume
Then, true volume = measured volume x
Error in chaining:
A cumulative error is that which occur in the same direction and tends to accumulate.
A compensating error may occur is either direction and hence tends to compensate.
Error  Type  Sign 

cumulative
cumulative cumulative cumulative cumulative compensating cumulative compensating Blunder Mistake Blunder 
+ (or) –
+ + + + (or) – + 
Tape correction:
We have seen the different sources of errors in line or measurement. In most of the error, proper correction can be applied. Since in most of the cases a tape is used for precise work the correction are sometimes called tape correction.
After having measured length, the correct length of the base is calculated by applying the following correction.
1) Correction for absolute length:
It is the usual practice to express the absolute length of a tape as its nominal or designated length plus (or) minus a correction. The correction for the measured length is
C_{a} = C.L / l
Where Ca = correction for absolute length
L = measured length of a line (m)
C = correction per tape length
l = designated length of the tape (m)
The sign of correction (C_{a}) will be the same as that of ‘C’,
2) Correction for temperature:
If the temperature in the field is more than the temperature at which the tape was standardized, the length of the tape increases, measured distance become less and the correction is therefore additive. Similarly if the temperature is less the length of the tape decreases, measured distance become more and the correction is negative. the temperature correction is given by
C_{t} = α(T_{m} – T_{o}) L
Where:
α = Coefficient of thermal expansion
T_{m} = Mean temperature is the field during measurement
T_{o} = Temperature during standardization of the tape
L = measured length (tape length)
3) Correction for pull (or) tension:
If the pull applied during measurement is more than the pull at which the tape was standardize, the length of the tape increases, measured distance become less and the correction is positive. Similarly if the pull in less, the length of the tape decreases. The measured distance become more and the correction is negative
If C_{p} is the correction for pull we have
C_{p} = (P_{m} – P_{o} )L / AE
P_{m} = pull applied during measurement (N)
P_{o} = standard pull (N)
L = measured length (m)
A = C/s area of the tape (cm^{2})
F = young’s modulus of elasticity (N/cm^{2})
4) Correction for sag:
When the tape is stretched on supports between two points. It takes the form of a horizontal catenary. The horizontal distance will be less than the distance along curve. The difference between horizontal distance and the measured length along catenary is called the sag correction.
l^{1} = length of the tape (in meter) suspended between A and B
C_{s1}=sag correction in m
w= weight of the tape in kg/m
p= pull applied in kg
wl_{1}= weight of the tape suspended between the support
The relation between curved length (l_{1}) and the chord length (d_{1}) of a very flat parabola is given by
Note: sag correction in always negative
5) Correction for slope or vertical alignment
The distance measured along the slop is always greater than the horizontal distance and hence the correction is negative
AB = L = inclined length measured
AB_{1} = horizontal distance
h = difference is elevation between the ends
C_{v} = slop correction