2.2 linear measurement

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

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
l l l
l
l
llP

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.
• The methods given below may be used in reconnaissance or for detecting
major mistakes in linear measurements obtained with a chain or a tape.
Approximate methods

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.

• 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.
Odometer

• This is used in automobiles for measuring distances.
Speedometer

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
• 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

• 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.
• 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.
Metric 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.

• 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.
Engineer’s 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.
Revenue 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
Steel Band or Band Chain

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

• 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.
Cloth or linen 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.
Fiber Glass 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.
Metallic 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.
Steel 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.
Invar Tape

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.

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

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 Stations
• 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.
• 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 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
Chaining:

• Stations are first of all marked with pegs and ranging rods to make them
visible.
Fixing of Station

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.

• 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

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 abbey'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.

Unit-II
Linear Measurements
• 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.

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.

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.

• 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.
Perpendicular Offsets

• 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.
Oblique Offset

• 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

Perpendicular Offsets Using 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

2.2 linear measurement

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2.2 linear measurement