Unit 1

Surveying-1
UNIT-1
INTRODUCTION AND CHAIN SURVEYING
D.PARTHIBAN/AP-CIVIL

WHAT IS SURVEYING?
Surveying is the branch of civil engineering which deals with measurement of
relative positions of an object on earth’s surface by measuring the horizontal
distances, elevations, directions, and angles.
Surveying is defined as the science of making measurements of the earth
specifically the surface of the earth. This is being carried out by finding the
spatial location (relative / absolute) of points on or near the surface of the earth.
Different methods and instruments are being used to facilitate the work of
surveying.
The primary aims of field surveying are :
to measure the Horizontal Distance between points.
to measure the Vertical elevation between points.
to find out the Relative direction of lines by measuring horizontal angles with reference
to any arbitrary direction and
to find out Absolute direction by measuring horizontal angles with reference to a fixed
direction.
These parameters are utilised to find out the relative or absolute coordinates of
a point / location.

Importance of Surveying to Civil
Engineers
The planning and design of all Civil Engineering projects such as
construction of highways, bridges, tunnels, dams etc are based upon
surveying measurements.
Moreover, during execution, project of any magnitude is constructed
along the lines and points established by surveying.
Thus, surveying is a basic requirement for all Civil Engineering
projects.
Other principal works in which surveying is primarily utilised are
to fix the national and state boundaries;
to chart coastlines, navigable streams and lakes
to establish control points
to execute hydrographic and oceanographic charting and mapping
to prepare topographic map of land surface of the earth.

Objectives of Surveying
To collect field data;
To prepare plan or map of the area surveyed;
To analyse and to calculate the field parameters for setting out
operation of actual engineering works.
To set out field parameters at the site for further engineering
works

Divisions of Surveying
The approximate shape of the earth can best be defined as
an oblate tri-axial ovaloid.
But, most of the civil engineering works, concern only
with a small portion of the earth which seems to be a
plane surface.
Thus, based upon the consideration of the shape of the
earth, surveying is broadly divided into two types.
Geodetic Surveying
Plane Surveying

Classifications of Surveying
Based on the purpose (for which surveying is being conducted), Surveying has
been classified into:
Control surveying : To establish horizontal and vertical positions of
control points.
Land surveying : To determine the boundaries and areas of parcels of
land, also known as property survey, boundary survey or cadastral survey.
Topographic survey : To prepare a plan/ map of a region which includes
natural as well as and man-made features including elevation.
Engineering survey : To collect requisite data for planning, design and
execution of engineering projects. Three broad steps are
1) Reconnaissance survey : To explore site conditions and availability of infrastructures.
2) Preliminary survey : To collect adequate data to prepare plan / map of area to be used
for planning and design.
3) Location survey : To set out work on the ground for actual construction / execution of
the project.

Route survey : To plan, design, and laying out of route such as
highways, railways, canals, pipelines, and other linear projects.
Construction surveys : Surveys which are required for
establishment of points, lines, grades, and for staking out
engineering works (after the plans have been prepared and the
structural design has been done)
Astronomic surveys : To determine the latitude, longitude (of the
observation station) and azimuth (of a line through observation
station) from astronomical observation.
Mine surveys : To carry out surveying specific for opencast and
underground mining purposes

Principles of Surveying
The fundamental principles upon which the
surveying is being carried out are
working from whole to part.
after deciding the position of any point, its
reference must be kept from at least two permanent
objects or stations whose position have already
been well defined.

The purpose of working from whole to part is
to localise the errors and
to control the accumulation of errors.
This is being achieved by establishing a heirarchy of networks
of control points( Stations having known position)

Operations in Surveying
Operations in surveying consists of :
Planning
Field Observation
Office Works
Setting out Works

Planning
To decide
the methods to be adopted for surveying;
the resources (instruments & personnel) to be used;
the control points/ stations to be used ( those already available and/ or to set
up).
The planning operation needs a-priori field visit and this is known as
reconnaissance.
Field Observation
It involves
Collection of field data by making necessary measurements;
Recording of observed data in a systematic manner.
Before starting any field observation, the permanent adjustments of
all the instruments need to be checked thoroughly by trained personnel and if
required, it must be adjusted.

Office Work
It involves
Processing, analysing and calculation of observed data;
Preparation of necessary data (for making plan or map of the area);
Making of a plan or map of the area;
Computation of relevant field parameters as per design for setting out
engineering works at site.
Setting out Works
To locate and establish different parameters / dimensions at the site as
per design for further engineering works.

What is a Scale ?
• Scale of a map or a drawing is actually the
proportion between the distance on the map or
drawing to the corresponding distance on the ground.
• Thus if on a map it is written 1 cm = 10 m
• It means that 1 cm on the drawing is actually 10 m on
the ground.

CONVENTIONAL SYMBOLS AND SIGNS

CHAIN SURVEYING
Chain survey is the simplest method of surveying.
In chain survey, only measurements are taken in the field,
and the rest work, such as plotting calculation etc. are done in
the office.
Here only linear measurements are made i.e. no angular
measurements are made.
This is most suitably adapted to small plane areas with very
few details.
If carefully done, it gives quite accurate results.

Chain
A chain is mainly used in chain surveying to measure the distances.
A chain may be metric or non-metric.
Generally a chain consists of 100 or 150 links each 300 mm or 200
mm length.
The link is made of galvanized mild steel wire 4 mm to 6mm
diameter.
The ends of each link are bent into a loop and connected together by
means of three oval rings.
The ends of the chain are provided with handles for dragging the
chain on the ground, each wire with a swivel joint so that the chain
can be turned without twisting.
The length of the chain is measured from the outside of one handle
to the outside of another handle.

Types of chains
• Metric chains
– Metric chains of length 20m, 30m, 50m and 100m are
used now-a-days for measuring the distances in metres
and its fractions.
• Non-Metric chains
– The following are the non metric chains in which the
unit of measurement is foot.
• a) Engineers chain It is 100 feet long and consists of 100
links, each of 1 foot length.
• b) Gunter’s chain or surveyor’s chain It is 66 feet in length,
consists of 100 links each being 0.66 foot long
• c) Revenue chain It is 33 feet long and consists of 16 links. It
is used in cadastral survey

Steel band or Band chain
• It is made of steel ribbon 16 mm wide and is
available in 20 and 30m lengths.
• It is wound on an open steel cross in a closed case.

Tapes
Tapes are used for measuring the distances
in precise work.
Following are the various types of
tapes.
a)Cloth or linen tape It is made of woven
linen strip 5 mm to 15 mm wide and
varnished. It is easily affected by damp.
b) Metallic tape It is made of linen strip
inserted with metallic wires.
c) Steel tape It is made of thin steel strip
and is available in 10, 20, 30 and 50 metre
lengths. It is widely used for measurements.
d) Invar tape It is made of an alloy of
steel and nickel. It is used for the work of
highest precision.

Arrows
Arrows are made of good
quality hardened steel wire of 4
mm diameter.
The arrows are made 400 mm
in length, are pointed at one
and the other end is bent into a
loop or circle.

Ranging rods
• Ranging rods are used to range some
intermediate points in the survey
line.
• The length of the ranging rod is
either 2m or 3m.
• They are shod at bottom with a
heavy iron point.
• Ranging rods are divided into equal
parts 0.2m long and they are painted
alternately black and white or red
and white or red, white and black.
• When they are at considerable
distance, red and white or white and
yellow flags about 25 cm square
should be fastened at the top.

• Cross staff
– The simplest instrument used for
setting out a right angle. The
common forms of cross staff are:
Open cross staff, French cross staff,
Adjustable cross staff.
• Pegs
– These are rods made from hard
timber and tapered at one end,
generally 25mm or 30mm square
and 150mm long wooden pegs are
used to mark the position of the
stations on the ground.

• Plumb Bob
– It is a solid cone attached to a thread. It is used
when measuring distances along slopes to transfer
points to the ground.

Principle of Chain Surveying
• The principle of chain surveying is to divide
the area to be surveyed into a network of
connected triangles as a triangle is the only
simple figure that can be plotted from the
lengths of its sides measured in the field.
• Since triangulation forms the principle of
chain surveying, the chain survey is also
sometimes called as chain triangulation.
• If the area to be surveyed is triangular in
shape and if the lengths and sequence of its
three sides are recorded, the plan of the area
can be easily drawn.

Equipment Required in Chain Surveying
The equipment required in chain surveying includes the following:
(i) A chain with a set of ten arrows.
(ii) A metallic tape 20 m or 30 m in length.
(iii) About one dozen ranging rods (the actual number depends upon the extent of
survey).
(iv) An offset rod.
(v) An optical square or a cross-staff.
(vi) A plumb-bob.
(vii) About 2 dozen pegs (the actual number depends upon the extent of survey).
(viii) A mallet or a hammer.
(ix) A field-book and a good pencil.
(x) Sundries such as chalk, nails, field-glass, etc.

Chain survey steps
1. Reconnaissance
The preliminary inspection of the area to be surveyed is called reconnaissance.
The surveyor inspects the area to be surveyed, survey or prepares index sketch or key
plan.
Walk the whole area and thoroughly examine the ground, note the position of
boundaries, road, and river etc., various difficulties to chain lines, select stations, and
prepare neat sketches called index sketches or key plan.
2. Marking stations
Stations are marked with ranging rod, or wooden peg, driving a nail or spikes if
hard surface, or embedding stone with a cross mark.
3. Reference sketches
After marking the station should be referenced i.e. located by measurement called
ties taken from 3 permanent points which are easily identified such as corner of building.
4. Running survey line
After the preliminary work, chaining is started from base line and carried
throughout all the line of the framework continuously. So chain is laid and kept lying, offset
are taken to locate the nearby details. Make ranging wherever necessary. Measure the change
and offset and enter in the field book.

Chain Survey is Suitable when
Ground is fairly level and simple
Plans are required on large scale e.g. fields
When area is small in extent
Chain Surveying is Not Suitable
For Large Areas
When too many details are required
Wooded countries
Undulating areas

Procedure for Measurement of an Area by Chain
Triangulation
PROCEDURE:
Let ABCDE be the given field whose area is
to be measured, fix the pegs at A, B, C, D &
E.
Divide area into three triangles ADE, ABD
and BCD by joining AD and BD.
Measure the lengths AB, BC , CD, DE, EA,
AD and BD.
Calculate the area of the triangles.
The sum of the areas of the three triangles is
the area of the given field.

Survey Station
• Survey stations are of two kinds:
Main Stations
Subsidiary or tie
Main Stations:
Main stations are the end of the lines, which
command the boundaries of the survey, and the lines
joining the main stations re called the main survey line or
the chain lines.
Subsidiary or the tie stations:
Subsidiary or the tie stations are the point selected
on the main survey lines, where it is necessary to locate
the interior detail such as fences, hedges, building etc.

Tie or subsidiary lines:
A tie line joints two fixed points on the main survey
lines. It helps to checking the accuracy of surveying and to
locate the interior details. The position of each tie line should
be close to some features, such as paths, building etc.
Base Lines:
It is main and longest line, which passes approximately
through the center of the field. All the other measurements to
show the details of the work are taken with respect of this line.
Check Line:
A check line also termed as a proof line is a line joining
the apex of a triangle to some fixed points on any two sides of
a triangle. A check line is measured to check the accuracy of
the framework. The length of a check line, as measured on the
ground should agree with its length on the plan.

Offsets:
• These are the lateral measurements from the base line to
fix the positions of the different objects of the work with
respect to base line.
• These are generally set at right angle offsets. It can also be
drawn with the help of a tape. There are two kinds of
offsets:
– Perpendicular offsets
– Oblique offsets
• The measurements are taken at right angle to the survey
line called perpendicular or right angled offsets.
• The measurements which are not made at right angles to
the survey line are called oblique offsets or tie line offsets.

CIVIL ENGINEERING DIFFERENT UNITS
CONVERSION FACTORS
FEET OR METERS
1 Feet = 12 inches
1 Feet = 0.3048 meter
1 Feet = 0.0929 meter square
1 Inch = 25.4 mm
1 Meter = 1,000 mm
1 Meter =3.281 feet
1 Meter = 1.094 yard
1 Meter Square = 10.764 square feet

CENTIMETER
1 Centimeter = 0.3937 inches
1 Centimeter = 0.032808 feet
2.54 Centimeter= 1 inch
30.48 Centimeters = 1 Foot
91.44 Centimeters = 1 yard
ACRE
1 Acre = 43,560 Square Feet
1 Acre = 10 square chains
1 Acre = 0.4047 Hectare
1 Acre = 100 square meters
HECTARE
1 Hectare = 10,000 Square
meter
1 Hectare = 107,639 sq ft
1 Hectare = 11959.8 sq. yards
1 Hectare = 11959.8/4840 =
2.47 acre
FOOT OR FURLONG
1 Foot = 12 inches
1 Furlong = 660 feet

MILE
1 Mile = 5280 feet
1 Mile =8 furlong
1 Mile = 80 chains
1 Mile = 1.60935 kilometers
1 Mile = 1609.2655 meters
1 Mile Square = 27,878,400
square feet
1 Mile Square = 2.59 square
hectares
YARD
1 Yard = 36 inches
1 Yard = 3 feet
1 yard = 0.9144 meters
1 Yard = 91.44 centimeter
1 Square Yard = 9 square feet

RANGING
• Method of locating or establishing
intermediate points on a straight line
between two fixed point or two survey stations
is called as ranging.
There are two methods of ranging
– Direct Method (Two ends of survey line or stations
are inter-visible)
– Indirect Method (Two ends of survey line or
stations are not inter-visible)

• DIRECT METHOD: This method is used when
two ends of survey stations or survey lines are
inter-visible.
Direct ranging can be done by 2 methods:
1) RANGING BY EYE
2) 2)RANGING BY LINE RANGER

RANGING BY EYE
Consider two pints X and Y which are
inter-visible to each other.
In this method ranging rod is fixed at
station X and Y.
Suppose if we want to locate a point Z on
ground which is in line with XY.
The surveyor stands half a metre back side
of ranging rod at X in line with XY.
Assistant then moves another ranging rod
under the guidance of surveyor in such a
way that ranging rod hold by assistant is in
the line XY at point Z betwwen X AND Y.
Similarly other points can be located by
similar way.
Surveyor has to guide assistant by using
some hand signals so that ranging rod
comes in the line.

RANGING BY LINE RANGER
• Line ranger is a light and easy to use instrument which can be used for ranging.
• It consists of 2 plane mirrors or 2 right-angled isosceles prism places one above the
another.
• Diagonals of two prism are silvered so as to reflect light.
• Lower prism is fixed while the upper prism is moveable.
• Instrument is provided with handle at bottom which gives ease to the user for using
the instrument.
• Two ranging rods are fixed at inter-visible points.
• Then surveyor moves with the line ranger.
• The point where two images coincide in line ranger is the point in line with two
fixed ranging rods.
• At this point a pebble is dropped from the handle of line ranger and point is traced on
ground.

INDIRECT RANGING or Reciprocal Ranging
• This method is used when two ends of survey stations or survey line are
not inter-visible.
• Let X and Y be the 2 stations which are not inter-visible. So to proceed in
straight line between X and Y process of indirect ranging is applied.
• Two intermediate points M1 and M2 are located in such a way
that person standing with ranging rod at M2 can see M1 and X whereas
person with ranging rod at M1 can see M2 and Y.
• Now person at M2 will guide the person at M1 to come in line with M2
and X on a new position M3.
• Now the person at M3 will guide the person at M2 to come to a new
position M4 such that M3, M4 and Y are on same line.
• Ranging rod is fixed at M3 & M4 and chaining is continued along the hill.

Set Out Right Angles and Perpendicular Lines in the
Chain Surveying
1. Setting out Right Angles: the 3-4-5 Method
• To set out right angles in the field, a measuring tape, two ranging
poles, pegs and three persons are required.
• The first person holds together, between thumb and finger, the zero
mark and the 12 metre mark of the tape. The second person holds
between thumb and finger the 3 metre mark of the tape and the
third person holds the 8 metre mark.
• When all sides of the tape are stretched, a triangle with lengths of 3
m, 4 m and 5 m is formed (see Fig.,), and the angle near person 1 is
a right angle.
• NOTE: Instead of 3 m, 4 m and 5 m a multiple can be chosen: e.g.
6 m, 8 m and 10 m or e.g. 9 m, 12 m and 15 m.

Setting out Perpendicular Lines: the Rope Method
• A line has to be set out perpendicular to the base line from peg (A).
Peg (A) is not on the base line.
• A long rope with a loop at both ends and a measuring tape are used.
The rope should be a few metres longer than the distance from peg
(A) to the base line.
Step 1
One loop of the rope is placed around peg (A).
Put a peg through the other loop of the rope and make a circle on the
ground while keeping the rope straight.
This circle crosses the base line twice (see Fig.a).
Pegs (B) and (C) are placed where the circle crosses the base line.
Step 2
Peg (D) is placed exactly half way in between pegs (B) and (C).
Use a measuring tape to determine the position of peg (D).
Pegs (D) and (A) form the line perpendicular to the base line and the
angle between the line CD and the base line is a right angle (see
Fig.B)

STEP-1
STEP-2

The single prismatic square
• The prism of the single prismatic
square is fitted in a metal frame with a
handle.
• Attached to the handle is a hook to
which a plumb bob can be connected
(see Fig. 23).
• The special construction of the prism
enables to see at right angles when
looking through the instrument.
• The single prismatic square or single
prism can be used to set out right
angles and perpendicular lines.

Setting out right angles Using single prismatic
square
• The prismatic square has to be placed vertically above
peg (C).
• This can be achieved by using a plumb bob.
• The instrument can be hand-held by the operator, but
even better is to install the instrument on a tripod (see
Fig)

STEP-2
• The instrument is
slowly rotated until
the image of pole A
can be seen when
looking through the
instrument (see Fig.)

• An assistant should hold pole
(D) in such a way that it can be
seen when looking through
the opening just above the
prism.
• At the indication of the
operator, pole (D) is slightly
moved so that pole (D) forms
one line (when looking
through the instrument) with
the image of pole (A) (see Fig).
• The line connecting pole (D)
and peg (C) forms a right angle
with the base line.

Setting out perpendicular lines
Using single prismatic square
• The base line is
defined by poles
(A) and (B).
• A line
perpendicular to
the base line has to
be set out from
pole (C); pole (C) is
not on the base
line.

Step-1
• The operator should stand
with the instrument on the
base line (connecting A and
B).
• To check this, the assistant,
standing behind pole (A)
(or B), makes sure that the
plumb bob, attached to the
instrument, is in line with
poles (A) and (B) (see Fig).
• The operator then rotates
the instrument until the
image of pole (A) can be
seen.

Step-2
• The operator then moves the
instrument along the base line
until he finds a position for
which (when looking through
the instrument) pole (C) is in
line with the image of pole
(A) (see Fig.).
• While searching for the right
position, the operator must
keep the instrument always in
line with poles (A) and (B).
• This is done under the
guidance of the assistant
standing behind pole (A).

Step-3
• When the correct position of
the instrument is found, peg
(D) is placed right under the
plumb bob.
• The line connecting pole (C)
and peg (D) is a line
perpendicular to the base
line (see Fig)

well-conditioned triangles
• A well conditioned triangle is a triangle in which no angle is less than 30
degrees.
• One of the way to survey the area is to divide the entire area is smaller
triangles and then take the measurement of sides of the triangles.
• Triangles are preferred because it is easy to re-construct exact triangle on
paper with only side's measurements (no angle measurement is required).
• This will not be true for higher polygons like quadrilaterals.
• A well conditioned triangle will have it's edges far enough and vertex will
be clearly identified.
• Ill-conditioned triangle can have ambiguity in vertex position and so, it can
lead to wrong measurements

Traversing
Traversing is that type of survey in which a number of
connected survey lines form the framework and the directions
and lengths of the survey lines are measured with the help of an
angle measuring instrument and tape or chain respectively.
Suitability
The closed traverse is suitable for locating the boundaries
of lakes, woods, etc and for a survey of large areas.
The open traverse is suitable for surveying a long narrow
strip of land as required for a road of the canal or the coastline

Types of Traverse Surveying
• There are two types of traverse
surveying. They are:
Closed traverse: When the
lines form a circuit which ends
at the starting point, it is known
as a closed traverse.
Open traverse: When the lines
form a circuit ends elsewhere
except starting point, it is said
to be an open traverse.

Chain Traversing
• The method in which the whole work is
done with chain and tape is called chain
traversing.
• No angle measurement is used and the
directions of the lines are fixed entirely
by linear measurements Angles fixed
by linear or tie measurements are
known as chain angles.
• The method is unsuitable for accurate
work and is generally used if an angle
measuring instruments such as a
compass, sextant or theodolite is
available.

Plotting of a Chain Survey
• Plotting means to represent on paper, to a suitable scale, the
previously surveyed objects in accordance with their shape and
size.
• Plotting is commenced after the field-work is over.

The plotting of a chain survey is done in the
following steps:
• (i) A suitable scale is chosen before starting the plotting work. The
scale depends upon the importance of the work and extent of survey.
• (ii) Leave a suitable margin (2 cm to 4 cm) all round the paper.
• (iii) Select a suitable position of the base line so that the map or plan
is shown to the best advantages. The base line should be plotted as
accurately as possible because the entire accuracy of the frame-work
depends upon it.
• (iv) Mark the intermediate stations on the base line and complete the
frame-work of triangles.
• (v) Check the accuracy of the plotted frame work by means of check
and tie lines. If the error is within the permissible value, then adjust
the lengths of the sides of the wrong triangles. But if the error
exceeds the permissible limits, then resurvey the wrong lines.
• (vi) For plotting the offsets, mark the changes of the points along the
chain line from where offsets were measured and then draw the
perpendicular lines with set squares and scale off lengths of the
offsets.

• The method of plotting the offset is much simplified if offset-
scale (Fig) is used for plotting them.
• In this method, the long scale is placed along the chain line
with its zero exactly at start of the line.
• The offset scale is then placed at right angles to the long scale
and is then moved along it to the required changes and the
offset lengths are marked with a pricked.

(vii) While plotting keep the field-book side by side in the same direction as
the work proceeded in the field parallel to the chain line to be plotted and then
plot the various offsets.
After plotting one line completely, transfer the offset scale along the second
line and open the filed-book page for that line, keep it in the same direction
and plot the off-sets. Similarly plot all the lines and details and complete the
plan.
(viii) After completing the plan in pencil and checking it, ink the lines and
objects and then colour them in according with the conventional signs. The
inking and colouring should be commenced from the top left hand corner of
the sheet working from left to right and downwards.
(ix) Print the title of the survey in right hand corner at the bottom or at the top
of the drawing and then draw the scale of the plan below it.
(x) Mark the north direction in any convenient blank space near the top.

ERRORS IN CHAIN SURVEYING
Erroneous length of chain or tape
Bad Ranging
Careless holding and marking
Bad Straightening
Non- Horizontality
Sag in Chain
Variation in Temperature
Variation in Pull
Personal Mistakes.

Sources of Errors in Measurement
• Depending on Sources of Origin, Errors in
measurement fall into three classes, they are
Natural Errors
Instrumental Errors
Personal Errors

Natural Errors
These are caused due to variations in nature i.e.,
variations in wind, temperature, humidity, refraction,
gravity and magnetic field of the earth
Instrumental Errors
These result from imperfection in the construction
or adjustment of surveying instruments, and movement
of their individual parts.
Personal Errors
These arise from limitations of the human senses
of sight, hearing and touch in manipulating instruments.

Kinds of Errors
Mistakes
Mistakes are errors which arise from inattention,
inexperience, carelessness and poor judgment or confusion in
the observer mind.
Systematic Errors
A systematic error or cumulative error is an error that,
under the same condition, will always be of the same size and
sign.
Accidental Errors
Accidental errors or compensating errors are those
which remain after mistakes and systematic errors have been
eliminated and are caused by a combination of reasons
beyond the ability of the observer to control.

Error in Measurement of Distance
• Depending on the nature, errors present in
the measurement of distance have been
classified into two types:
– Systematic Errors
– Random Errors

• Systematic Errors
Systematic errors (in taping) are caused
due to: non-standard length of tape, slope in
terrain, and variations in temperature during
measurement, variations in tension, sag,
incorrect alignment of the tape etc.

• Slope Correction
Let s represents the slope distance between two points A and B, h be
the difference in elevation and H the horizontal distance between the points, all
in the same units. Let q be the slope of the terrain. thus, slope correction for
measured distance s is
• Ch = H - s = (s2 - h2) - s (always subtractive)

Correction for Temperature
• If the temperature of standardization is T0 degree and
measurements are taken at a temperature of T degree, there
is an error in length of the tape, due to difference in
standardized temperature and temperature during
observation. The corresponding correction Ct is given by
C t = a L (T- T0)
• Where,
– a is the coefficient of thermal expansion of the material of the tape
and
– L is the measured distance.

Correction for Tension
• If a tape is standardized at a tension of Po and measurements
are taken at a tension of P, the correction Cp for change in
length per distance L due to difference in standarised pull and
actual pull during observation is given by
Where,
a is the cross sectional area of the tape and
E is modulus of elasticity of the material of the tape.

Correction for Sag
• When the tape sags between points of support, it takes the
form of a catenary. The correction for sag Cs is always
subtracted from observed distance and is given by
Where,
W is the total weight of tape between supports,
L is the distance between supports and
P is the applied tension.

True length, area and volume of chain
• True distance = (L’/L) x measured distance
• True area = (L’/L)^2 x measured area
• True Volume = (L’/L)^3 x measured volume
– Where, L’ = incorrect length of chain
– L = correct length of chain

Unit 1

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Unit 1