Linear Measurements

Linear Measurements
Lecture Notes

Unit-I
Linear Measurements
Syllabus
• Different types of ranging, tapes, chains, linear
measurements, approximate, direct, optical and
electronic methods, Chain Surveying, Minor
Instruments for setting out right angle.

Ranging
• When a survey line is longer than a chain
length, it is necessary to align intermediate
points on chain line so that the measurements
are along the line. The process of locating
intermediate points on survey line is known as
ranging. There are two methods of ranging
viz., direct ranging and reciprocal ranging.

Direct Ranging
• If the first and last points are intervisible this method is
possible.
• Stations A and B in which an intermediate point C is to
be located. Point C is selected at a distance slightly less
than a chain length. At points A and B ranging rods are
fixed. The assistant holds another ranging rod near C.
Surveyor positions himself approximately 2 m behind
station A and looking along line AB directs the assistant
to move at right angles to the line AB till he aligns the
ranging rod along AB. Then surveyor instructs the
assistant to mark that point and stretch the chain along
AC.

Indirect or Reciprocal Levelling
• Due to intervening ground, if the ranging rod at B is not
visible from station A, reciprocal ranging may be
resorted. Figure shows this scheme of ranging.
• It needs two assistants one at point M and another at
point N, where from those points both station A and
station B are visible. It needs one surveyor at A and
another at B. To start with M and N are approximately
selected, say M1 and N1. Then surveyor near end A
ranges person near M to position M2 such that AM2N1
are in a line. Then surveyor at B directs person at N, to
move to N2 such that BN2M2 are in a line. The process
is repeated till AMNB are in a line.

Indirect or Reciprocal Levelling

Linear Measurements
• The determination of the distance between two
points on the surface of the earth is one of the
basic operation of surveying. Measurement of
horizontal distances or measuring linear
measurement is required in chain surveying,
traverse surveying and other types of surveying.

Linear Measurements
• Methods of making linear measurements
• Direct methods
• Optical methods
• E.D.M methods

Linear Measurements
• In the direct method, the distance is actually
measured during field work using a chain or a
tape. This is the most commonly used method
for linear measurements.
• In the optical methods, principles of optics are
used. The distance is not actually measured in
field but it is computed indirectly. The
instrument used for making observations is
called tacheometer.

Linear Measurements
• Electronic Distance Measuring (E.D.M)
instruments have been developed quite
recently.
• These are practically replacing the
measurement of distances using chains or tapes.
There is a large variety of such instruments and
depending upon the precision required the
instruments should be used.

Electronic Distance Measuring (E.D.M)
EDM
P

Linear Measurements
Approximate methods
• The methods given below may be used in
reconnaissance or for detecting major mistakes in
linear measurements obtained with a chain or a
tape.
Pacing
• A distance between two points can be
approximately be determined by counting the
number of paces and multiplying it with average
length of the pace.

Linear Measurements
Passometer:
• It is a small instrument which counts the
number of paces.
Pedometer:
• This instrument directly gives the distance by
multiplying the number of paces with the
average pace length of the person carrying the
instrument.

Linear Measurements
Odometer
• An odometer is a simple device which can be
attached to the wheel of a bicycle or any such
vehicle. The odometer registers the number of
revolution made by the wheel. The distance
covered is equal to the product of the number
of revolutions and the perimeter of the wheel.

Linear Measurements
Speedometer
• This is used in automobiles for measuring
distances.
Measuring Wheel
• It is a wheel fitted with a fork and handle. The
wheel is graduated and shows a distance per
revolution. There is a dial which records the
number of revolution. Thus the distance can be
computed.

Instruments Used in Chaining
• The following instruments are used while chaining.
• Chains
• Tapes
• Arrows
• Ranging rods and offset rods
• Laths & Whites
• Pegs
• Plumb bob
• Line Ranger

Chains
• Various types of chains used in surveying are
• Metric Chain
• Gunter‟s Chain or Surveyor‟s Chain
• Engineer‟s Chain
• Revenue Chain
• Steel Band or band chain

Metric Chain
• Normally this chain consists of galvanized
mild steel wire of 4 mm diameter known as
link. The ends of the links are bent into
loop and connected together by means of
three oval rings which provide the flexibility
to the chain and make it less liable to
kinking. Both ends of the chain have brass
handle with swivel joint so that the chain
can be turned round without twisting

Metric Chain
• In a metric chain at every one meter interval of
chain, a small brass ring is provided. Brass tallies
are also provided at every 5.0 m length of chain.
Each tally has different shape which indicates 5 ,
10, 15m from any one side of the chain, metric
chains are available in 20 m and 30 m length.
• A 20 m chain has 100 links each of 20 cm and 30
m chain has 150 links. Length of chain is
embossed on the brass handles of the chain.

Günter's chain
• A 66 feet long chain consists of 100 links each
of 0.66 ft it is known as Gunter‟s Chain
• Here, 10 sq chain are equal to 1 acre,
• 10 chains= 1 furlong and 8 furlongs = 1 mile
• This chain is suitable for taking length in miles
and areas in acres.

Engineer‟s Chain
• A 100 ft chain of 100 links each of 1 foot is
known as Engineer‟s chain. Brass tags are
fastened at every 10 links. This chain is used to
measure length in feet and area in square yards.

Revenue Chain
• Revenue chain is 33 ft long chain consisting of
16 links. This chain is used for distance
measurements in feet & inches for small areas.

Steel Band or Band Chain
• Steel bands are preferred than chains because
they are more accurate, but the disadvantages is
that they get broken easily and are difficult to
repair in the field. They are 20 and 30 m long,
12 to 16 mm wide and 0.3 to 0.6 mm thick.
They are numbered at every metre and divided
by brass studs at every 20 cm

Testing and Adjustment of Chain
• During continuous use, the length of a chain
gets altered. Its length is shortened chiefly due
to the bending of links. Its length is elongated
either due to stretching of the links and joints
and opening out of the small rings. For accurate
work it is necessary to test the chain time to
time. The chain can be thus tested by a steel
tape or by a standard chain. Sometimes, it is
convenient to have a permanent test gauge
established where the chain is tested.

• When the length of a chain is measured at a
pull of 8 kg at 20 0C the length of the chain
should measure 20 m ± 5 mm and 30 m ± 8
mm for 20 m and 30 m long chain shall be
accurate to within 2 mm. Following measures
are taken to adjust the length of a chain.

If chain is found to be too long
• It can be adjusted by;
• Closing up the joints of the rings if found to be
opened out
• Reshaping damaged rings
• Removing one or more small rings
• Adjusting the links at the end.

• If the chain is found to be too short
• Straightening the bent links
• Opening the joints of the rings
• Replacing one or more small circular rings by
bigger ones.
• Inserting new rings where necessary.
• Adjusting the links at the end.

Measuring Tapes
• Tapes are used for more accurate
measurement. The tapes are classified based on
the materials of which they are made of such as:
• Cloth or linen tape
• Fibre Tape
• Metallic Tape
• Steel tape
• Invar Tape

Measuring Tapes
Cloth or linen Tape
• Linen tapes are closely woven linen and
varnished to resist moisture. They are generally
10 m, 20 m, 25 m and 30 m long in length and
12 to 15 mm wide. They are generally used for
offset measurements. These tapes are light and
flexible.

Measuring Tapes
• Fibre Glass Tape
• These tapes are similar to linen and plastic
coated tapes but these are made of glass fibre.
The tapes are quite flexible, strong and non-
conductive. These can be used in the vicinity of
electrical equipment. These tapes do not stretch
or shrink due to changes in temperature or
moisture. These tapes are available in length of
20 m, 30 m and 50 m length.

Measuring Tapes
• Metallic Tape
• A linen tape reinforced with brass or copper wires
to prevent stretching or twisting of fibres is called a
metallic tape. As the wires are interwoven and tape
is varnished these wires are visible to naked eyes.
This is supplied in a lather case with a winding
device. Each metre length is divided into ten parts
(decimetres) and each part is further sub-divided
into ten parts. It is commonly used for taking offset
in chain surveying.

Measuring Tapes
• Steel Tape
• The steel tape is made of steel ribbon of width
varying from 6 to 16 mm. The commonly
available length are 10 m, 15 m, 20 m, 30 m
and 50 m. It is graduated in metres, decimetres,
and centimetres. Steel tapes are used for
accurate measurement of distances.

Measuring Tapes
• Invar Tape
• Invar tape are made of alloy of nickel 36 % and
steel 64 % having very low co-efficient of
thermal expansion. These are 6 mm wide and
generally available in length of 30 m, 50m,
100m. It is not affected by change of
temperature therefore, it is used when high
degree of precesion is required.

Arrows
• Arrows are made of tempered steel wire of
diameter 4 mm. one end of the arrow is bent
into ring of diameter 50 mm and the other end
is pointed. Its overall length is 400 mm. Arrows
are used for counting the number of chains
while measuring a chain line. An arrow is
inserted into the ground after every chain length
measured on the ground.

Ranging Rods and Offset Rods
• Ranging rods are used for ranging some intermediate
points on the survey line. Ranging rods are generally 2 to
3 m in length and are painted with alternate bands of
black or white or red and white colour with length of
each equalizing 20 cm. The location of any survey
station can be known from long distances only by means
of ranging rods. If the distance is too long, a rod of
length 4.0 to 6.0 m is used and is called ranging pole.
• The offset rod is similar to ranging rod with the
exception that instead of the flag, a hook is provided at
the top for pushing and pulling the chain or the tape. It
is also used for measuring small offsets

Laths & Whites
Laths
• Laths are 0.5 to 1.0 m long sticks of soft wood. They are
sharpened at one end and are painted with white or light
colours. They are used as intermediate points while
ranging or while crossing depressions.
Whites
• Whites are the pieces of sharpened thick sticks cut from
the nearest place in the field. One end of the stick is
sharpened and the other end is split. White papers are
inserted in the split to improve the visibility. Whites are
also used for the same purpose as laths

Pegs
• Pegs are made of timber or steel and they are
used to mark the position of the station or
terminal points of a survey line. Wooden pegs
are 15 cm long and are driven into the ground
with the help of a hammer.

Plumb Bob
• Plumb-bob is used to transfer points on the
ground. It is also used for fixing the instruments
exactly over the station point marked on the
ground by checking the centre of the
instrument whether coincides with the centre of
the peg or station not, by suspending the
plumb-bob exactly at the centre of the
instrument under it. Plumb bob is thus used as
centring aid in theodolites and plane table.

Line Ranger
• It is an optical instrument used for locating
a point on a line and hence useful for
ranging. It consists of two isosceles prisms
placed one over the other and fixed in an
instrument with handle. The diagonals of
the prisms are silvered so as to reflect the
rays.

Line Ranger
• Its advantage is it needs only one person to
range. The instrument should be occasionally
tested by marking three points in a line and
standing on middle point observing the
coincidence of the ranging rods. If the images
of the two ranging rods do not appear in the
same line, one of the prism is adjusted by
operating the screw provided for it.

Line Ranger
• To locate point C on line AB (ref. Fig.) the surveyor
holds the instrument in hand and stands near the
approximate position of C. If he is not exactly on line
AB, the ranging rods at A and B appear separated as
shown in Fig. (b). The surveyor moves to and fro at
right angles to the line AB till the images of ranging
rods at A and B appear in a single line as shown in Fig.
(c). It happens only when the optical square is exactly
on line AB. Thus the desired point C is located on the
line AB.

Chain Surveying
• Chain surveying is the type of surveying in which
only linear measurements are taken in the field.
• This type of surveying is done for surveying of
small extent to describe the boundaries of plots of
land and to locate the existing feature on them.
• It is the method of surveying in which the area is
divided into network of triangles and the sides of
the various triangles are measured directly in the
field with a chain or a tape and no angular
measurements are taken.

Principles of Chain Surveying
• The principle of chain surveying is to divide the
area into a number of triangles of suitable sides. As
a triangle is the only simple plane geometrical
figure which can be plotted from the length of the
three sides even if the angles are not known. A
network of triangles is preferred to chain surveying.
• Triangulation is the principle of chain surveying. If
the area to be surveyed is triangle in shape and if
the lengths and sequence of its three sides are
recorded, the plan of the area can be easily drawn.

Terms related to Chain Surveying
Survey Stations
• Survey stations are the points at the beginning
and at the end of a chain line they may also
occur at any convenient position on the chain
line. Such station may be
• Main Stations
• Subsidiary Stations
• Tie Stations

• Main Station Stations along the boundary of an
area as controlling points are known as „Main
Stations‟ The lines joining the main station are
called „ Main Survey Lines‟. The main survey
lines should cover the whole area to be
surveyed. The main stations are denoted by Δ.

• Subsidiary Stations: Stations which are on the
main survey lines or any other survey lines are
known as „ Subsidiary Stations‟ these stations
are taken to run subsidiary lines for dividing the
area into triangles, for checking the accuracy of
triangles and for locating interior details.

• Tie Stations:
• These stations are also subsidiary stations taken
on the main survey lines. Lines joining the
stations are known as „ Tie lines‟ Tie lines are
taken to locate interior details.

Main Survey Lines:
• The line joining the main stations are called
main survey lines or chain lines.

• Base Line: The line on which the framework of the
survey is built is known as „ Base line‟. It is the most
important line of the survey. Generally the longest of the
main survey lines is considered as the base line. This
lines should be taken through fairly level ground, and
should be measured very carefully and accurately.

• Check Line
• The line joining the apex point of a triangle to
some fixed points on its base is known as „
Check line‟. It is taken to check the accuracy of
the triangle. Sometimes this line helps to locate
interior details.

• Tie Line
• A line joining tie stations is termed as a tie line.
It is run to take the interior details which are far
away from the main lines and also to avoids
long offsets. It can also serve as check line.

Selection of Survey Station
• The following points should be considered while
selecting survey stations:
• It should be visible from at least two or more
stations.
• As far as possible main lines should run on level
ground.
• All triangles should be well conditioned (No angle
less than 30º).
• Main network should have as few lines as possible.

Selection of Survey Station
• Each main triangle should have at least one
check line.
• Obstacles to ranging and chaining should be
avoided.
• Sides of the larger triangles should pass as close
to boundary lines as possible.
• Trespassing and frequent crossing of the roads
should be avoided

Operation in Chain Surveying
• The following operations are involved in chain
surveying.
• Chaining
• Ranging
• Offsetting
• These three operations are done
simultaneously during chain Surveying.

Chaining
Chaining on Level Ground
• The method of taking measurement with the help
of chain or tape is termed as chaining.
Chaining involves following operations
• Fixing the stations
• Unfolding the chain
• Ranging
• Measuring the distance (Survey Line)
• Folding the Chain

Fixing of Station
• Stations are first of all marked with pegs and
ranging rods to make them visible.
Unfolding of a Chain
• To open a chain, the strap is unfastened and the
two brass handles are held in the left hand and the
bunch is thrown forward with the right hand. Then
one chainmen moves forward by holding the other
handle until the chain is completely extended.

Ranging
• The process of establishing intermediate points
on a straight line between two end points is
known as ranging. Ranging must be done
before a survey line is chained

Ranging ( Code of Signals)
Sr. No. Signal by the Surveyor Meaning of the signal to the assistant
1 Rapid Sweep with right hand Move considerable towards left
2 Slow Sweep with right hand Move slowly towards left
3 Right arm extended Continuously move towards left
4 Right arm up and move to the right Plumb the rod towards left
5 Rapid Sweep with left hand Move considerable towards right
6 Slow Sweep with left hand Move slowly towards right
7 Left arm extended Continuously move towards right
8 Left arm up and move to the right Plumb the rod towards right
9 Both hand above head and brought
down
Ranging is correct
10 Both arm extended horizontally
and brought down quickly
Fix the ranging rod

Measuring the distance (Survey Line)
• Two persons are required in this operation, i.e.
Leader and Follower.
• The chainman at the forward end of the chain
who drags the chain forward, is known as the
leader
• The chainmen at the rear end of the chain, who
holds the zero end of the chain at the station, is
known as the follower.

• To chain the line, the leader moves forward by dragging the
chain line and taking with him ranging rod and ten arrows.
The follower stands at the starting station by holding the
other end of the chain. When the chain is fully extended, the
leader holds the ranging rod vertically at arms length.
• The follower directs the leader to move his rod to the left or
right until the ranging rod is exactly in the line. Then the
follower holds the zero end of the chain by touching the
station peg.
• The leader stretches the chain by moving it up and down
with both hands, and finally place it on the line. He then
inserts an arrow on the ground at the end of the chain and
mark it with cross.

• Again the leader moves forward by dragging the chain
with nine arrows and the ranging rod. At the end of the
chain, he fixes another arrow as before, As the leader
moves further, the follower picks the arrow which were
inserted by the leader. During chaining the surveyor or
an assistant should conduct the ranging operation.
• In this way, chaining is continued, when all the arrows
are inserted the leader has non left with him, the
follower hands over to the leader.
• To measure the fractional length, the leader should drag
the chain beyond the station and the follower should
hold the zero end of the chain at last arrow, then odd
links should be counted.

Folding of Chain
• To fold the chain, a chainmen should move
forward by pulling the chain at the middle. Then
the two halves of the chain will come side by side.
After this, commencing from the central position
of the chain, two pairs of links are taken at a time
with the right hand and placed on the left hand
alternately in both directions. Finally the two brass
handles will appear at top. The bunch should be
then fastened by the strap.

Chaining on Sloping Ground
• The object of survey is to prepare a plan or a map.
In the plan or a map the distance plotted between
any two points is always a straight line. Even if the
chaining is done on a sloping ground, this sloping
distance is converted into horizontal equivalent
distance while plotting.
• There are two methods of finding out horizontal
distance while on a sloping ground.
• Direct Method
• Indirect Method

Direct Method
• This method is also called method of stepping in this method, the
distance is measured in small horizontal stretches. A suitable length of
chain or tape say l1 is taken. The follower holds the zero end of the tape
at a point on the top of the hill or sloping ground. i.e. at point A. The
tape is stretched horizontally from A at small length l1 of 3 to 5 m. The
point at the end of the l1 is dropped and marked on the ground as a1.
From a1, again tape is stretched exactly in a horizontal plane at a
convenient step l2 and drop end of l2 on the ground as b1. Likewise
entire length of line on the sloping ground is measured.
• Finally the total horizontal length of the line AB, i.e. D is obtained
• D= l1 + l2 + l3 + ……… ln
• Where ln= the last step for the given survey line

• Indirect Method
• Indirect method involves calculation from the
directly measured length these methods are briefly
explained here.
Method-1
• Horizontal distance of the segment is calculated by
knowing sloping length of the segment and angle of
inclination of that with horizontal.
• The angle of the sloping surface with horizontal
can be known by a simple handy instrument called
as abney‟s level

• Total Distance D= ∑d = d1 +d2 +….dn, and
• d= l CosӨ for d1 = l1 Cos Ө1
Where,
Ө = angle of sloping surface with horizontal and
l= sloping length.

Method 2
• If elevation difference between two terminal point
and the sloping distance between the two terminal
point is known, the horizontal distance H can be
calculated as,
• H= l2 – D2
• Where,
• l= sloping length
• D= Elevation difference between two points

Method 3
• This method is also known as hypotenusal allowance
method. The chaining is done on the sloping ground,
but instead of putting the end arrow at the actual end of
the chain, it is put at some advanced distance and that
point is considered as the end of one chain length.
• In this method, the chain of 20 m length ends at point B.
Therefore, sloping length l = 20 m, but the actual
horizontal length (H) is less than 20 m and calculation is
required to calculate horizontal distance based on Ө.
Angle of inclination of ground.

• Horizontal distance H= (l + a) Cos Ө ,
Where,
H is intended to make one chain length,
• Therefore ,
• H= (l + a) Cos Ө
Here, AB= one chain length= l= H= 20 m
• Therefore Put H= l= 20 m
• 20= (20 +a) Cos Ө
• 20 Sec Ө= 20 + a
• a= 20 Sec Ө – 20
• a= 20 (Sec Ө – 1)

• Where a hypotenusal allowance for 20 m chain
• For a chain other than 20 m length,
• a= l (Sec Ө – 1) where l= length of chain in m
• Thus the arrow is inserted at (l+a) distance on
the ground instead of at the end of chain. Thus
the horizontal distance of this sloping distance
on ground is equal to one chain length.

Offsets
• Lateral measurements to chain lines for locating
ground features are known as offsets. For this
purpose
• perpendicular or oblique offsets may be taken .
If the object to be located (say road) is curved
more number of offsets should be taken. For
measuring offsets tapes are commonly used.

Offsets
Perpendicular Offsets
• The offsets which are taken perpendicular to
the chain line are termed as perpendicular
offsets. These offsets are taken by holding zero
end of the tape at the object and swinging the
tape on the chain line. The shortest distance
measured from object to the chain line is
usually the perpendicular offset.

Offsets
Oblique Offset
• Oblique distance is always greater than
perpendicular distance. All the offsets which
are not taken at the right angle to chain line are
known as oblique offsets.

Offsets
• For setting perpendicular offsets any one of the
following methods are used:
• (i) Swinging
• (ii) Using cross staffs
• (iii) Using optical or prism square.

Perpendicular Offset by Swinging
• Chain is stretched along the survey line. An
assistant holds the end of tape on the object.
Surveyor swings the tape on chain line and
selects the point on chain where offset distance
is the least.
• and notes chain reading as well as offset reading
in a field book on a neat sketch of the object

Perpendicular Offset by Swinging

Perpendicular Offsets Using Cross
Staffs
• Three different types of cross staffs used for setting
perpendicular offsets. All cross staffs are having two
perpendicular lines of sights. The cross staffs are
mounted on stand. First line of sight is set along the
chain line and without disturbing setting right angle line
of sight is checked to locate the object.
• With open cross staff (Fig(a)) it is possible to set
perpendicular only, while with French cross staff
• (Fig(b)), even 45º angle can be set. Adjustable cross staff
can be used to set any angle also, since there are
graduations and upper drum can be rotated over lower
drum.

Perpendicular Offsets Using Cross
Staffs

Perpendicular Offsets Using Optical Square
and Prism Square
• These instruments are based on the optical
principle that if two mirrors are at angle „θ‟ to
each other,
• they reflect a ray at angle „2θ‟. Figure shows a
typical optical square.

Perpendicular Offsets Using Optical
Square and Prism Square

Optical Square and Prism Square

3-4-5 Method
• AB is the chain line it is required to erect a
perpendicular at C of the chain line. Establish a pt
D at 3 m distance. 5m & 6m marks are brought to
gather to form a loop .The tape is stretched tight
by fastening the end D and C. The point D is
established such that DE = 5 m and CE= 4 m and
CD = 3 m and DE2 = CD2 + DE2
• i.e. 5 2 = 3 2 + 4 2 = 25 thus Angle DCE = 90 0
• i.e. CE is perpendicular to chain line at C

Field Book
• All observations and measurements taken during chain
surveying are to be recorded in a standard field book. It is a
oblong book, which can be carried in the pocket.
• There are two forms of the book
• (i) single line and
• (ii) double line.
• The pages of a single book are having a red line along the
length of the paper in the middle of the width. It indicates the
chain line.
• All chainages are written across it. The space on either side
of the line is used for sketching the object and for noting
offset distances. In double line book there are two blue lines
with a space of 15 to 20 mm
• is the middle of each book. The space between the two lines
is utilised for noting the chainages.

References
• “Surveying and Levelling” Vol I
Kanetkar and Kulkarni (2011) Pune Vidhyarthi Griha, Pune
• “ Surveying and Levelling”
N.N.Basak (2010) Tata Mcgraw Hill
• “ Surveying Vol- I
Dr. B.C. Punamia Laxmi Publication
• Internet Websites
• http://www.fao.org/docrep/r7021e/r7021e02.htm#TopOfPage

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