Chain Surveying 2019

LINEAR MEASUREMENTS
Direct Measurements:
The various methods of measuring the distances directly are as follows:
(1) Pacing
(2) Measurement with Passometer
(3) Measurement with Pedometer
(4) Measurement by Odometer and Speedometer
(5) Chaining
(1) Pacing: The method consists in counting the number of paces between the two points
of a line. The length of the line can then be computed by knowing the average length
of the pace. The length of the pace varies with the individual, and also with the nature
of the ground, the slope of the country and the speed of pacing. It may also be used to
roughly check the distances measured by other means. However, pacing over rough
ground or on slopes may be difficult.
(2) Passometer: It is an instrument shaped like a watch and is carried in pocket or
attached to one leg. The mechanism of the instrument is operated by motion of the
body and it automatically registers the number paces, thus avoiding the monotony and
strain of counting the paces, by the surveyor. The number of paces registered by the
passometer can then be multiplied by the average length of the pace to get the total
distance covered.
(3) Pedometer: It is a device similar to the passometer except that, adjusted to the length
of the pace of the person carrying it, it registers the total distance covered by any
number of paces
(4) Odometer and Speedometer: The Odometer is an instrument for registering the
number of revolutions of a wheel. The well-known speedometer works on this
principle. The Odometer is fitted to a wheel which is rolled along the line whose
length is required. The number of revolutions registered by the odometer can then be
multiplied by the circumference of the wheel to get the distance. Since the instrument
registers the length of the surface actually passed over, its readings obtained on
undulating ground are inaccurate. If the route is smooth, the speedometer of an
automobile can be used to measure the distance approximately.
(5) Chaining: Chaining is a term which is used to denote measuring distance either with
the help of a chain or a tape and is the most accurate method of making direct
measurement.

Instruments for Chaining

The various instruments used for the determination of the length of line by chaining
are as follows:
(1) Chain or Tape
(2) Arrows
(3) Pegs
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(4) Ranging rods

(5) Offset rods
(6) Plasterer’s lath
(7) Plumb bob
(1) Chain: Chains are formed of straight links of galvanized mild steel wire bent into
rings at the ends and joined each other by three small circular or oval wire rings.
These rings offer flexibility to the chain. The ends of the chain are provided with
brass handle at the end with swivel joint, so that the chain can be turned without
twisting. The length of a link is the distance between the centers of two consecutive
middle rings, while the length of the chain is measured from the outside of one handle
to the outside of the other handle.

Fig: 1.2 Chain with links, rings and handle

Following are various types of chains in common use:
(i) Metric chain
(ii) Gunter’s chain or Surveyor’s chain
(iii) Engineer’s chain
(iv) Revenue chain
(v) Steel band or band chain
(i) Metric chain: Metric chains are generally available in lengths of 5, 10, 20 and
30 meters. To enable the reading of fractions of a chain without much
difficulty, tallies are fixed at every meter length for chains of 5m and10m
lengths and at every five meters length for chains of 20m and 30m lengths. In
case of 20 m and 30 m chains, small brass rings are provided at every meter
length, except where tallies are attached.

Fig: 1.3 Different types of tallies present in an 10m chain

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(ii) Gunter’s chain or Surveyor’s chain: A Gunter’s chain or surveyor’s chain is

66ft. long and consists of 100 links, each link being 0.6 ft or 7.92 inches long.
The length of 66 ft was originally adopted for convenience in land
measurement since 10 square chains are equal to 1 acre. Also, when linear
measurements are required in furlongs and miles, it is more convenient since
10 Gunter’s chains equal to 1 furlong and 80 Gunter’s chain equal to 1 mile
(iii) Engineer’s Chain: The Engineer’s chain is 100 ft long and consists of 100
links, each link being 1 ft long.
(iv) Revenue Chain: The revenue chain is 33 ft long and consists of 16 links, each
link being 2 ft long. The chain is mainly used for measuring fields in
cadastral survey
(v) Steel Band or Band Chain: The steel band consists of a long narrow strip of
blue steel, of uniform width of 12 to 16 mm and thickness of 0.3 to 0.6 mm.
Metric steel bands are available in lengths of 20 or 30 m.
Tapes: Tapes are used for more accurate measurements and are classed according to
the material of which they are made, such as follows
(i) Cloth or Linen tape
(ii) Metallic tape
(iii) Steel tape
(iv) Invar tape
(i) Cloth or Linen Tape: Cloth tapes of closely woven linen, 12 to 15 mm wide
varnished to resist moisture, are light and flexible and may be used for taking
comparatively rough and subsidiary measurements such as offsets. A cloth
tape is commonly available in lengths of 10m, 20m, 25m, and 30m, and in 33
ft, 50 ft, 66ft and 100 ft. The end of tape is provided with small brass ring
whose length is included in the total length of the tape. A cloth tape is rarely
used for making accurate measurements because of the following reasons:
 Its length gets altered by stretching
 It is likely to twist and tangle
 It is easily affected by moisture or dampness and thus shrinks
 It is not strong
(ii) Metallic Tape: A metallic tape is made of varnished strip of waterproof linen
interwoven with small brass, copper or bronze wires and does not stretch as
easily as a cloth tape. Since metallic tapes are light and flexible and are not
easily broken, they are particularly useful in cross-sectioning and in some
methods of topography where small errors in length of the tape are of no
consequence. Metallic tapes are made in lengths of 2, 5, 10, 20, 30 and50
meters.
(iii) Steel Tape: Steel tapes vary in quality and accuracy of graduation, but even a
poor steel tape is generally superior to a cloth or metallic tape for most of the
linear measurements. A steel tape consists of a light strip of width 6 to 10mm
and is more accurately graduated. These are available in lengths of 1, 2, 10,
20, 30 and 50 meters. A steel tape is a delicate instrument and is very light and
therefore, cannot withstand rough usage. It should be oiled with a little mineral
oil, so that it does not get rusted
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(iv) Invar Tape: Invar tapes are used mainly for linear measurements of a very
high degree of precision, such as measurement of base lines. It is made with an
alloy of nickel (36%) and steel, and has very low coefficient of thermal
expansion. These are normally 6mm wide and are available in lengths of 20,
30 and 100 m. The difficulty with invar tapes is that they are easily bent and
damaged. They must, therefore, be kept on reels of large diameter.
(2) Arrows: Arrows or marking pins are made of stout steel wire, and generally, 10
arrows are supplied with a chain. An arrow is inserted into the ground after every
chain length measured on the ground. Arrows are made of good quality hardened and
tempered steel wire 4mm in diameter. The length of arrow may vary from 25 cm to 50
cm, the most common length being 40cm. one end of the arrow is made sharp and
other end is bent into a loop or circle for facility of carrying.
(3) Pegs: Wooden pegs are used to mark the positions of the stations or terminal points of
a survey line. They are made of stout timber, generally 2.5 cm or 3 cm square and 15
cm long, tapered at the end. They are driven in the ground with the help of a wooden
hammer and kept about 4 cm projecting above the surface.

Fig: 1.4 Arrow Fig: 1.5 Peg

(4) Ranging Rods: Ranging rods have a length of 2 m or 3m, the 2m being more
common. They are shod at bottom with a heavy iron point, and are painted in
alternative bands of either black and red or red and white in succession, each band
being 20 cm deep so that on occasion the rod can be used for rough measurement of
short lengths. Ranging rods are used to range some intermediate points in the survey
line. They are circular or octagonal in cross-section of 3 cm nominal diameter.
(5) Offset Rods: An Offset rod is similar to a ranging rod and has a length of 3 m. The
cross-section of the rod is circular and is shod at bottom with heavy iron point and
provided with a notch or a hook at the other. The hook facilitates pulling and pushing
the chain through hedges and other obstructions. The rod is mainly used for
measuring rough offsets nearby.
(6) Plasterer’s Laths: These are made with soft wood of 0.5 to 1m long. They are light in
colour and weight, and can be easily carried. They are very useful for ranging out a
line when crossing a depression from which the forward rod is invisible or in
temporary marking of contour points

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(7) Plumb Bob: While chaining along sloping ground, a plumb-bob is required to transfer
the points to the ground. In addition, it is used as centering aid in theodolites,
compass, plane table and a variety of other surveying instruments.
ERRORS DUE TO INCORRECT CHAIN:
If the length of the chain used in measuring length of the line is not equal to the true
length or the designated 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, therefore, be negative and the correction is positive. Similarly,
if the chain is too short, the measured distance will be more, the error will be positive and
the correction will be negative.
Let, L = True or designated length of the chain or tape
L1= Incorrect (or actual ) length of the chain or tape used.

(i)Correction to measured length:

Let, l1 = Measured length of the line

l = actual or true length of the line

Then, true length of line = measured length of line x

Or l = l1x
(ii)Correction to Area:

Let, A1 = Measured (or computed) area of the ground

A = Actual or true area of the ground.

Then, True Area = measured area x () 2

Or A = A1 x () 2

Alternatively, = =1+
Where, δL = Error in length of chain, let it be ‘e’

Therefore, A = A1 x () 2
= A1 x (1+e)2
But (1+e) = 1+2e+e ~ 1+ 2e, if e is small
2 2

Therefore, A = (1+2e) A1

(iii)Correction to Volume:

Let, V1 = Measured (or computed) area of the ground

V = Actual or true area of the ground.

Then, True Volume = measured volume x () 3

Or V = V1 x () 3

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Alternatively, = =1+
Where, δL = Error in length of chain, let it be ‘e’

Therefore, V = V1 x () 3
= V1 x (1+e)3
But (1+e) = 1+3e+3e +e ~ 1+ 3e, if e is small
3 2 3

Therefore, V = (1+3e) V1
CHAINING ON UNEVEN OR SLOPING GROUND:
For all plotting works, horizontal distances between the points are required. It is
therefore, necessary either to directly measure the horizontal distance between the points or to
measure the sloping distance and reduce it to horizontal. Thus, there are two methods for
getting the horizontal distance between two points:
(1) Direct Method: In the direct method (or the method of stepping), the distance is
measured in small horizontal stretches or steps. Fig: 1.6 illustrates the procedure,
where it is required to measure the horizontal distance between the two points A and
B.

Fig: 1.6 Method of stepping (Direct Method)

The follower holds the zero end of the tape at A while the leader selects any
suitable length l1 of the tape and moves forward. The follower directs the leader for
ranging. The leader pulls the tape tight, makes it horizontal and the point 1 is then
transferred to the ground by a plumb bob. The total length D of the line is then equal
to (l1+l2+…..). In the case of irregular slopes, this is the only suitable method.
(2) Indirect Method: In the case of a regular or even slope, the sloping distance can be
measured and the horizontal distance can be calculated. In such cases, in addition to
the sloping distance, the angle of the slope or the difference in elevation (height)
between the two points is to be measured.
Method (i): In the Fig: 1.6 let l1 = measured inclined distance between AB and θ1 =
Slope of AB with horizontal. The horizontal distance D1 = l1 cos θ1
Similarly, for BC, D2 = l2 cosθ2
The required horizontal distance between any two points = ∑l cos θ
The slope of the lines can be measured with the help of a clinometers (Minor
instrument used for measuring the slopes)

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Fig: 1.7 Indirect Method (Regular or Even Slope)

Method (ii): Sometimes, in the place of measuring the angle θ, the difference in the
level between the points is measured with the help of a leveling instrument and the
horizontal distance is computed.
Thus, if h is the difference in level, we have D = l2 – h2
Method (iii): (By Hypotenusal allowance) If only the horizontal distance between A
and B is required, the horizontal distance can be computed after chaining is completed
using either Method (i) or Method (ii), discussed above. However, if intermediate
points are also to be located on the line AB, it is better to use the method based on
hypotenusal allowance (Fig:1.8)

Fig: 1.8 Hypotenusal allowance Method

The follower holds the zero end of the chain at A while the leader holds the
forward end at C1. The leader does not insert the arrow into the ground at Cl but
inserts it at point C, in advance of the end of the chain. The distance ClC by which the
arrow is advanced is called hypotenusal allowance.
Let the length of the chain be 20m(=100links). In the right angle triangle
ACllC, the slope distance AC for a horizontal distance ACll equal to 100 links, is given
by
AC = ACll sec θ = 20 sec θ meters = 100 sec θ links
CCl = (20 sec θ – 20) meters = 100 ( sec θ – 1) links
The next chain length starts from the point C. The follower holds the zero end
of the chain at C and the process is repeated till the end point B is reached. The total
horizontal between A and B is equal to the number of chains laid and measured.
Expanding sec θ as 1+ (θ2/2) +(5θ4/24)+ ……….≈ 1+ (θ2/2)
Then, CCl = 100 [ { 1+ (θ2/2)}-1] = 100 θ2/2 = 50 θ2 links, where θ is in
radians.

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ERRORS IN CHAINING:
Errors that may occur during surveying may be of two types, they are
Cumulative Errors and Compensating Errors.
A Cumulative Error is that which occurs in the same direction and tends to
accumulate while a Compensating Error may occur in either direction and hence
tends to compensate
Errors and mistakes may arise from:
1. Erroneous Length of Chain or Tape: (Cumulative + or - ): The Error due to the wrong
length of the chain is always cumulative and is the most serious source of error. If the
length of the chain is more, the measured distance will be less and hence the error will
be negative. Similarly, if the chain is too short, the measured distance will be more
and error will be positive. However, it is possible to apply proper correction if the
length is checked from time to time.
2. Bad Ranging: (Cumulative, + ): If the chain is stretched out of the line, the measured
distance will always be more and hence the error will be positive. For each and every
stretch of the chain, the error is not very serious in ordinary work if only the length is
required. But if offsetting is to be done, the error is very serious.
3. Bad Straightening: (Cumulative, +): If the chain is not straight but is lying in an
irregular horizontal curve, the measured distance will always be too great. The error
is, therefore, of cumulative character and positive.
4. Non-Horizontality: ( Cumulative, + ): If the chain is not horizontal (specially in case
of sloping or irregular ground), the measured distance will always be too great. The
error is, therefore, of cumulative character and positive.
5. Sag in Chain: (Cumulative, + ) : When the distance is measured by stepping or when
the chain is stretched above the ground, the chain sags and takes the form of a
catenary. The measured distance is, therefore, too great and the error is cumulative
and positive.
6. Variation in Temperature: (Cumulative, + or - ): When a chain or tape is used at
temperature different from that at which it was calibrated, its length changes. Due to
the rise in the temperature, the length of the chain increases. The measured distance is
thus less and the error becomes negative. Due to the fall in temperature, the length
decreases. The measured distance is thus more and the error becomes negative. In
either cases the error is cumulative.
7. Careless Holding and Marking: (Compensating, + or - ): The follower may sometimes
hold the handle to one side of the arrow and sometimes to the other side. The leader
may thrust the arrow vertically into the ground or exactly at the end of chain. This
causes a variable systematic error. The error of marking due to an inexperienced
chainman is often of a cumulative nature, but with ordinary care such errors tend to
compensate.
8. Variation in Pull: (Compensating or Cumulative, + or - ): If the pull applied in
straightening the chain or tape is not equal to that of the standard pull at which it was
calibrated, its length changes. If the pull applied is not measured but is irregular (
sometimes more, sometimes less), the error tends to compensate. A chainman may,
however, apply too great too small a pull every time and the error becomes
cumulative.

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9. Personal Mistakes: Personal mistakes always produce quite irregular effects. The
following are the most common mistakes:
a. Displacement of arrows: If an arrow is disturbed from its position either by
knocking or by pulling the chain, it may be replaced wrongly. To avoid this, a
cross must also be marked on the ground while inserting the arrows.
b. Miscounting chain length: This is a serious blunder but may be avoided if a
systematic procedure is adopted to count the number of arrows
c. Misreading: A confusion is likely between reading a 5m tally for 15m tally, since
both are of similar shape. It can be avoided by seeing the central tag. Sometimes, a
chainman may pay more attention on cm reading on the tape and read the metre
reading wrong. A surveyor may sometimes read 6 in place of 9 or 28.26 in place
of 28.62.
d. Erroneous booking: The surveyor may enter 246 in place of 264 etc. To avoid
such possibility, the chainman should first speak out the reading loudly and the
surveyor should repeat the same while entering in the field book.
Tape Corrections:
A Correction is positive when the erroneous or uncorrected length is to be
increased and negative when it is to be decreased to get the true length.
After having measured the length, the correct length of the base is calculated
by applying the following corrections:
1. Correction for absolute length: If the absolute length (or actual length) of the tape
or wire is not equal to its nominal or designated length, a correction will have to
be applied to the measured length of the line. If the absolute length of the tape is
greater than the nominal or the designated length, the measured distance will be
too short and the correction will be additive. If the absolute length of the tape is
lesser than the nominal or designated length, the measured distance will be too
great and the correction will be subtractive.
Thus, Ca = ( L * c ) / l
Where Ca = Correction for absolute length
L = measured length of the line
c = correction per tape length
l = designated length of the tape
Ca will be of the same sign 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 becomes less, and the correction is therefore, additive.
Similarly, if the temperature is less, the length of the tape decrease, measured
distance becomes more and the correction is negative. The temperature correction
is given by,
Ct = α (Tm - To) L
Where α = Coefficient of thermal expansion
Tm = mean temperature in the field during measurement
To = Temperature during standardization of the tape
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L = Measured length.
To find the new standard temperature Tolwhich will produce the nominal
length of the tape or band:
Some times, a tape is not of standard or designated length at a given standard
temperature To. The tape/band will be of the designated length at a new standard
temperature Tol.
Let the length at standard temperature To be l + δl , where l is the designated
length of the chain
length of the tape.
Let ΔT be the number of degrees of temperature change required to change the
length of the tape by = δl

Then δl = ( l + δl) α ΔT

ΔT = δl / ( l + δl) α ≈ δl / l α

(neglecting δl which will be very small in comparison to l)

If Tol is the new standard temperature at which the length of the tape will be exactly
equal to its designated length l, we have

Tol = To + ΔT
Tol = To + (δl / l α)
3. Correction for Pull or Tension: If the Pull applied during measurement is more
than the pull at which the tape was standardized, the length of the tape increases,
measured distance becomes less, and the correction is positive. Similarly, if the
Pull is less, the length of the tape decreases, measured distance becomes more and
the correction is negative.
If Cp is the correction for Pull, we have
Cp = (P-Po)L / AE
Where, P = Pull applied during measurement (N)
Po = Standard Pull (N)
L = Measured length (m)
A = Cross-sectional area of the tape (cm2)
E = Young’s Modulus of Elasticity (N / cm2)
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 the curve. The difference between horizontal distance and the
measured length along the catenary is called as “ Sag Correction”.

If l is the total length of tape and it is suspended in n equal number of bays, the
Sag Correction (Cs) per tape length is given by

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Cs = nl1(wl1)2 / 24P2

Where Cs = tape correction per tape length

l = The Total length measured

W = Total weight of the tape (wl)

w = Unit Weight of the tape

n = number of equal spans

P = Pull applied

5. Correction for slope or Vertical Alignment: The distance measured along the
slope is always greater than the horizontal distance and hence the correction is
always subtractive.
Let, AB = L = Inclined length measured
ABl = Horizontal length
h = difference in elevation between the ends
Cv = Slope correction, or correction due to vertical alignment
Then Cv = AB - ABl
= L – (L2 – h2) = L – L(1 – (h2/2L2) -(h4/ 8L4) - …….
= (h2/2L) +(h4/ 8L3) + …….
The second term may safely be neglected for slopes flatter than about 1 in 25.
Hence, we get
C = h2/2L (subtractive)

If the angle θ of slope is measured instead of h, the correction is given by

Cv = L – L cos θ = L (1- cos θ)

6. Correction for horizontal alignment:

a. Bad ranging or misalignment: If the tape is stretched out of line, measured
distance will always be more and hence the correction will be negative. Fig:
1.9 shows the effect of wrong alignment, in which AB = L is the measured
length of the line, which is along the wrong alignment while the correct
alignment is AC. Let d be the perpendicular deviation.
L2 – l2 = d2
(L + l) (L – l) = d2
Assuming L = l and applying it to the first parenthesis only, we get
2L(L – l) ≈ d2
Or (L – l) ≈ d2/ 2L

Hence Correction, Ch = d2 / 2L

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Fig: 1.9 Bad ranging or misalignment

It is evident that smaller the value of d is in comparison to L, the more

accurate will be the result

b. Deformation of the tape in horizontal plane: If the tape is not pulled straight
and the length L1 of the tape is out of the line by amount d, then (as shown in
Fig: 1.10)
Ch = (d2/ 2L1) + (d2/ 2L2)

Fig: 1.10 Deformation of tape in horizontal plane

7. Reduction to Mean Sea Level: The measured horizontal distance should be
reduced to the distance at the mean sea level, called the “Geodetic distance”. If the
length of the base is reduced to mean sea level, the calculated length of all other
triangulation lines will also be corresponding to that at mean sea level.
Let AB = L = measured horizontal distance
AlBl = D = equivalent length at M.S.L (Geoditic M.S.L)
h = mean equivalent of the base line above M.S.L
R = Radius of earth
θ = angle subtended at the centre of the earth, by AB
Then, θ = D / R = L / ( R + h )
D = L [ R / ( R + h ) ] = L [ 1/ (1+(h/R))]
= L [ 1 + (h / R ) ]-1
= L [ 1- (h / R ) ]
= L – (Lh / R )
Therefore, Correction (Cmsl) = L – D = Lh / R (subtractive)

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Fig: 1.11 Reduction to the Mean Sea level

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