Short Notes for Fundamental Concepts & Linear Measurements | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


Fundamental DeFinitions
and Concepts
Surveying is the art of determining the relative positions 
of points on, above or beneath the surface of the earth by 
means of direct or indirect measurements of distance, direc-
tion and elevation.
Objectives of Surveying
 1. To fi nd elevations of points with respect to a given or 
assumed datum.
 2. To establish points at given elevations for a proposed 
structure.
 3. To fi nd areas, volumes and other related quantities.
Primary Divisions of Surveying
 • Based on consideration of curvature of earth
 • Earth is an italics
 • Polar axis (12,713,800 metres) is shorter than equatorial 
axis (12,756,750 metres) by 42.95 km (0.34%).
Plane Surveying
 • Surface of earth is considered as a plane and curvature is 
neglected.
 • Level line is considered as straight and all plumb lines are 
considered parallel.
When,
 • The extent of area is < 250 sq. km.
 • The diff erence between arc of 18.2 km on surface of earth 
and the subtended chord distance is about 1 cm.
 • Diff erence between sum of angles in a plane triangle and 
those in spherical triangle is only one second (1?) for a 
triangle at the earth’s surface having an area of 195 sq. 
km.
 • Used for engineering projects on large scale such as fac-
tories, bridges, dams, etc.
Geodetic Surveying
 • Curvature of earth is considered.
 • All lines lying on surface of earth are curved lines and 
triangles are spherical triangles.
 • Deals in fi xing widely spaced control points.
 • Preferred for large scale works with high degree of 
precision.
Classifi cation of Surveying
Based on Nature or Function of Field Survey
Land Surveying
 1. Topographical survey:
 • To fi nd horizontal and vertical locations of certain 
points by linear and angular measurements.
 ? Fundamental de? nitions and concepts
 ? Linear measurements—tape and chain 
survey
 ? Chain surveying or chain triangulation
CHAPTER HIGHLIGHTS
Fundamental Concepts
and Linear Measurements
Part III_Unit 12_Chapter 01.indd   3 5/31/2017   5:00:24 PM
Page 2


Fundamental DeFinitions
and Concepts
Surveying is the art of determining the relative positions 
of points on, above or beneath the surface of the earth by 
means of direct or indirect measurements of distance, direc-
tion and elevation.
Objectives of Surveying
 1. To fi nd elevations of points with respect to a given or 
assumed datum.
 2. To establish points at given elevations for a proposed 
structure.
 3. To fi nd areas, volumes and other related quantities.
Primary Divisions of Surveying
 • Based on consideration of curvature of earth
 • Earth is an italics
 • Polar axis (12,713,800 metres) is shorter than equatorial 
axis (12,756,750 metres) by 42.95 km (0.34%).
Plane Surveying
 • Surface of earth is considered as a plane and curvature is 
neglected.
 • Level line is considered as straight and all plumb lines are 
considered parallel.
When,
 • The extent of area is < 250 sq. km.
 • The diff erence between arc of 18.2 km on surface of earth 
and the subtended chord distance is about 1 cm.
 • Diff erence between sum of angles in a plane triangle and 
those in spherical triangle is only one second (1?) for a 
triangle at the earth’s surface having an area of 195 sq. 
km.
 • Used for engineering projects on large scale such as fac-
tories, bridges, dams, etc.
Geodetic Surveying
 • Curvature of earth is considered.
 • All lines lying on surface of earth are curved lines and 
triangles are spherical triangles.
 • Deals in fi xing widely spaced control points.
 • Preferred for large scale works with high degree of 
precision.
Classifi cation of Surveying
Based on Nature or Function of Field Survey
Land Surveying
 1. Topographical survey:
 • To fi nd horizontal and vertical locations of certain 
points by linear and angular measurements.
 ? Fundamental de? nitions and concepts
 ? Linear measurements—tape and chain 
survey
 ? Chain surveying or chain triangulation
CHAPTER HIGHLIGHTS
Fundamental Concepts
and Linear Measurements
Part III_Unit 12_Chapter 01.indd   3 5/31/2017   5:00:24 PM
3.996 | Part III 
¦
 Unit 12 
¦
 Geomatics Engineering
 • Determines natural features of a country such as 
rivers, lakes, hills, woods and artificial features 
such as roads, canals, towns, etc.
 2. Cadastral survey:
 • Consists of fixing of property lines, boundaries of 
fields, municipalities and calculating land area.
 • Done by a revenue engineer.
 3. City surveying: This survey is done for the 
construction of streets, water supply systems, sewers 
and other works.
Marine (or) Hydrographic Survey Deals with bodies of 
water like water supply, harbour, and for determining mean 
sea level.
Example: Topographical survey of shores and banks of 
river.
Astronomical Survey
 • For finding the absolute location of a point or direction of 
any line on surface of the earth by taking latitude, longi-
tude, azimuth, local time, etc.
 • Observations are made in relation to sun or any fixed star.
Based on Object of Survey
 1. Engineering survey: For determining the quantities 
or data required for designing of engineering works 
such as roads and reservoirs.
 2. Military survey: Determining points of strategic 
importance.
 3. Mine survey: For exploring mineral wealth 
(underground surveys).
 4. Geological survey: For determining different strata 
in earth’ s crust.
 5. Archaeological survey: For unearthing relics of 
antiquity.
Based on Instruments Used
 1. Chain surveying: This is used when high accuracy is 
not required.
 2. Compass surveying: This is more precise than chain 
survey. Used for measuring horizontal angles along 
with linear measurements with chain or tape.
 3. Leveling: For finding difference in elevation of two 
points or elevation with respect to datum. (More 
precise than compass survey)
 4. Plane table surveying:
 • Measurement and plotting are simultaneous.
 • Less accurate, but suitable in areas with magnetic 
material effect.
 5. Theodolite survey:
 • Precise instrument for measuring horizontal and 
vertical angles.
 • Used for traverse and triangulation survey (base 
lines are located using triangulation).
 6. Tacheometric survey:
 • Not very accurate, but useful for topographic 
details.
 • It is a theodolite with stadia diaphragm having two 
horizontal cross hairs in addition to central hori-
zontal hair.
 7. Photogrammetry: Use photographs of vast areas 
and done for areas difficult to reach.
 8. EDM surveys: Use electronic method of measuring 
distances.
Principles of Surveying
 1. Location of a point by measurement from two points 
of reference.
 2. Working from whole to part:
 • First a system of control points are established and 
fixed with high precision. Minor control points 
are then established within main area with less 
precision.
 • This prevents accumulation of errors and to control 
and localize minor errors.
Plans and Maps
 • Neglecting earth’ s curved surface and using orthographic 
projections for graphical representation of any features 
(on, near or below earth’s surface) on a plane paper is 
called plan. Large scale is used for plan and only hori-
zontal distances and directions are shown.
 • The representation is called a map, if scale is small and 
vertical distances are also represented by contour lines.
Scales
 • Scale is a fixed ratio that every distance on the plan bears 
with the corresponding distance on the ground.
Scale Representation
 1. Engineers scale: 1 cm on plan represents some whole 
number on ground.
  Example: 1 cm = 10 m
 2. Representative factor (RF): It is a ratio.
RF
Distance on the Map
Distance on the Ground
=
  Example: 1 cm = 1 m?= ==
1
1
1
100
1
100
cm
m
cm
cm
RF 
 • Larger the denominator of RF, smaller is the scale 
of Map.
 • Engineers scale and RF are called numerical 
scales.
Part III_Unit 12_Chapter 01.indd   4 5/31/2017   5:00:25 PM
Page 3


Fundamental DeFinitions
and Concepts
Surveying is the art of determining the relative positions 
of points on, above or beneath the surface of the earth by 
means of direct or indirect measurements of distance, direc-
tion and elevation.
Objectives of Surveying
 1. To fi nd elevations of points with respect to a given or 
assumed datum.
 2. To establish points at given elevations for a proposed 
structure.
 3. To fi nd areas, volumes and other related quantities.
Primary Divisions of Surveying
 • Based on consideration of curvature of earth
 • Earth is an italics
 • Polar axis (12,713,800 metres) is shorter than equatorial 
axis (12,756,750 metres) by 42.95 km (0.34%).
Plane Surveying
 • Surface of earth is considered as a plane and curvature is 
neglected.
 • Level line is considered as straight and all plumb lines are 
considered parallel.
When,
 • The extent of area is < 250 sq. km.
 • The diff erence between arc of 18.2 km on surface of earth 
and the subtended chord distance is about 1 cm.
 • Diff erence between sum of angles in a plane triangle and 
those in spherical triangle is only one second (1?) for a 
triangle at the earth’s surface having an area of 195 sq. 
km.
 • Used for engineering projects on large scale such as fac-
tories, bridges, dams, etc.
Geodetic Surveying
 • Curvature of earth is considered.
 • All lines lying on surface of earth are curved lines and 
triangles are spherical triangles.
 • Deals in fi xing widely spaced control points.
 • Preferred for large scale works with high degree of 
precision.
Classifi cation of Surveying
Based on Nature or Function of Field Survey
Land Surveying
 1. Topographical survey:
 • To fi nd horizontal and vertical locations of certain 
points by linear and angular measurements.
 ? Fundamental de? nitions and concepts
 ? Linear measurements—tape and chain 
survey
 ? Chain surveying or chain triangulation
CHAPTER HIGHLIGHTS
Fundamental Concepts
and Linear Measurements
Part III_Unit 12_Chapter 01.indd   3 5/31/2017   5:00:24 PM
3.996 | Part III 
¦
 Unit 12 
¦
 Geomatics Engineering
 • Determines natural features of a country such as 
rivers, lakes, hills, woods and artificial features 
such as roads, canals, towns, etc.
 2. Cadastral survey:
 • Consists of fixing of property lines, boundaries of 
fields, municipalities and calculating land area.
 • Done by a revenue engineer.
 3. City surveying: This survey is done for the 
construction of streets, water supply systems, sewers 
and other works.
Marine (or) Hydrographic Survey Deals with bodies of 
water like water supply, harbour, and for determining mean 
sea level.
Example: Topographical survey of shores and banks of 
river.
Astronomical Survey
 • For finding the absolute location of a point or direction of 
any line on surface of the earth by taking latitude, longi-
tude, azimuth, local time, etc.
 • Observations are made in relation to sun or any fixed star.
Based on Object of Survey
 1. Engineering survey: For determining the quantities 
or data required for designing of engineering works 
such as roads and reservoirs.
 2. Military survey: Determining points of strategic 
importance.
 3. Mine survey: For exploring mineral wealth 
(underground surveys).
 4. Geological survey: For determining different strata 
in earth’ s crust.
 5. Archaeological survey: For unearthing relics of 
antiquity.
Based on Instruments Used
 1. Chain surveying: This is used when high accuracy is 
not required.
 2. Compass surveying: This is more precise than chain 
survey. Used for measuring horizontal angles along 
with linear measurements with chain or tape.
 3. Leveling: For finding difference in elevation of two 
points or elevation with respect to datum. (More 
precise than compass survey)
 4. Plane table surveying:
 • Measurement and plotting are simultaneous.
 • Less accurate, but suitable in areas with magnetic 
material effect.
 5. Theodolite survey:
 • Precise instrument for measuring horizontal and 
vertical angles.
 • Used for traverse and triangulation survey (base 
lines are located using triangulation).
 6. Tacheometric survey:
 • Not very accurate, but useful for topographic 
details.
 • It is a theodolite with stadia diaphragm having two 
horizontal cross hairs in addition to central hori-
zontal hair.
 7. Photogrammetry: Use photographs of vast areas 
and done for areas difficult to reach.
 8. EDM surveys: Use electronic method of measuring 
distances.
Principles of Surveying
 1. Location of a point by measurement from two points 
of reference.
 2. Working from whole to part:
 • First a system of control points are established and 
fixed with high precision. Minor control points 
are then established within main area with less 
precision.
 • This prevents accumulation of errors and to control 
and localize minor errors.
Plans and Maps
 • Neglecting earth’ s curved surface and using orthographic 
projections for graphical representation of any features 
(on, near or below earth’s surface) on a plane paper is 
called plan. Large scale is used for plan and only hori-
zontal distances and directions are shown.
 • The representation is called a map, if scale is small and 
vertical distances are also represented by contour lines.
Scales
 • Scale is a fixed ratio that every distance on the plan bears 
with the corresponding distance on the ground.
Scale Representation
 1. Engineers scale: 1 cm on plan represents some whole 
number on ground.
  Example: 1 cm = 10 m
 2. Representative factor (RF): It is a ratio.
RF
Distance on the Map
Distance on the Ground
=
  Example: 1 cm = 1 m?= ==
1
1
1
100
1
100
cm
m
cm
cm
RF 
 • Larger the denominator of RF, smaller is the scale 
of Map.
 • Engineers scale and RF are called numerical 
scales.
Part III_Unit 12_Chapter 01.indd   4 5/31/2017   5:00:25 PM
Chapter 1 
¦
 Fundamental Concepts and Linear Measurements | 3.997
 3. Graphical scale:
 • It is a line drawn on the map whose length cor-
responds to convenient units of length on ground.
 • It has the advantage of shrinking proportionately to 
map and distances are found accurately unlike in 
numerical scales. That is why these scales are used 
on all survey maps.
Types of Scales
 1. Plain scale: It is possible to measure two dimensions 
only.
  Example: Metres and decimetres
 2. Diagonal scale: It is possible to measure three 
dimensions such as metres, decimetres and 
centimetres.
 3. Chord scale: Used to measure an angle or to set-off 
an angle and are marked on a rectangular protractor 
graduated from 0°–90°.
 4. Vernier scale: The vernier is a device for measuring 
fractional part of one of the smallest divisions of the 
graduated scale.
If the graduations of the main scale are num-
bered in one direction only, it is called single 
vernier whereas if graduations are numbered in both 
the direction, it is called double vernier.
Least count (LC) of a vernier is equal to the dif-
ference between the smallest division on the main 
scale and the smallest division on the vernier scale.
 (a) Direct vernier: It increases or extends in the 
same direction as that of the main scale. Smallest 
division of vernier is smaller than smallest 
division on main scale.
n divisions of vernier = (n – 1) divisions of 
main scale
nV = (n – 1)S
v
nS
n
=
- () 1
   Where 
    S = Smallest division on main scale
    V = Smallest division of vernier
    n = Number of divisions on vernier 
LC = S – V = S –
() nS
n
S
n
-
=
1
LC
S
n
= =
1 main scale division
Divisions on vernier scale
 (b) Retrograde vernier: It is the one which extends 
or increases in opposite direction to that of the 
main scale. 
     In this, smallest division of vernier is longer 
than smallest division on the main scale.
nV = (n + 1)S
v
n
n
S =
+ ?
?
?
?
?
?
1
LC = V – S =
n
n
SS
S
n
+ ?
?
?
?
?
?
-=
1
   LC =
S
n
 
SOLVED EXAMPLES
Example 1
Find the LC of the vernier scale in a theodolite, if 59 
divisions on main scale are equal to 60 division on vernier 
scale and the smallest reading on main scale is 10'.
(A) 10? (B) 15?
(C) 20? (D) 30?
Solution
LC =
S
n
n = Number of divisions on the vernier = 60
S = Smallest division on main scale = 10 '
LC =
10
60
'
= 10? (i.e., 10 seconds)
Hence, the correct answer is option (A).
 (c) Error due to use of wrong scale:
Correct length = 
RF of wrong scale
RF of correct scale
Measure length
?
?
?
?
?
?
×
Correct area = 
RF of wrong scale
RF of correct scale
Calculated are
2
?
?
?
?
?
?
× a a
Example 2
A surveyor measured the distance between two points on 
the plan drawn to a scale of 1 cm = 50 m and the result was 
500 m. Later, however, he discovered that he used a scale 
of 1 cm = 25 m. Find the true distance between the points.
(A) 250 m (B) 500 m
(C) 750 m (D) 1000 m
Solution
Measured length = 500 m
RF of wrong scale used 
Part III_Unit 12_Chapter 01.indd   5 5/31/2017   5:00:26 PM
Page 4


Fundamental DeFinitions
and Concepts
Surveying is the art of determining the relative positions 
of points on, above or beneath the surface of the earth by 
means of direct or indirect measurements of distance, direc-
tion and elevation.
Objectives of Surveying
 1. To fi nd elevations of points with respect to a given or 
assumed datum.
 2. To establish points at given elevations for a proposed 
structure.
 3. To fi nd areas, volumes and other related quantities.
Primary Divisions of Surveying
 • Based on consideration of curvature of earth
 • Earth is an italics
 • Polar axis (12,713,800 metres) is shorter than equatorial 
axis (12,756,750 metres) by 42.95 km (0.34%).
Plane Surveying
 • Surface of earth is considered as a plane and curvature is 
neglected.
 • Level line is considered as straight and all plumb lines are 
considered parallel.
When,
 • The extent of area is < 250 sq. km.
 • The diff erence between arc of 18.2 km on surface of earth 
and the subtended chord distance is about 1 cm.
 • Diff erence between sum of angles in a plane triangle and 
those in spherical triangle is only one second (1?) for a 
triangle at the earth’s surface having an area of 195 sq. 
km.
 • Used for engineering projects on large scale such as fac-
tories, bridges, dams, etc.
Geodetic Surveying
 • Curvature of earth is considered.
 • All lines lying on surface of earth are curved lines and 
triangles are spherical triangles.
 • Deals in fi xing widely spaced control points.
 • Preferred for large scale works with high degree of 
precision.
Classifi cation of Surveying
Based on Nature or Function of Field Survey
Land Surveying
 1. Topographical survey:
 • To fi nd horizontal and vertical locations of certain 
points by linear and angular measurements.
 ? Fundamental de? nitions and concepts
 ? Linear measurements—tape and chain 
survey
 ? Chain surveying or chain triangulation
CHAPTER HIGHLIGHTS
Fundamental Concepts
and Linear Measurements
Part III_Unit 12_Chapter 01.indd   3 5/31/2017   5:00:24 PM
3.996 | Part III 
¦
 Unit 12 
¦
 Geomatics Engineering
 • Determines natural features of a country such as 
rivers, lakes, hills, woods and artificial features 
such as roads, canals, towns, etc.
 2. Cadastral survey:
 • Consists of fixing of property lines, boundaries of 
fields, municipalities and calculating land area.
 • Done by a revenue engineer.
 3. City surveying: This survey is done for the 
construction of streets, water supply systems, sewers 
and other works.
Marine (or) Hydrographic Survey Deals with bodies of 
water like water supply, harbour, and for determining mean 
sea level.
Example: Topographical survey of shores and banks of 
river.
Astronomical Survey
 • For finding the absolute location of a point or direction of 
any line on surface of the earth by taking latitude, longi-
tude, azimuth, local time, etc.
 • Observations are made in relation to sun or any fixed star.
Based on Object of Survey
 1. Engineering survey: For determining the quantities 
or data required for designing of engineering works 
such as roads and reservoirs.
 2. Military survey: Determining points of strategic 
importance.
 3. Mine survey: For exploring mineral wealth 
(underground surveys).
 4. Geological survey: For determining different strata 
in earth’ s crust.
 5. Archaeological survey: For unearthing relics of 
antiquity.
Based on Instruments Used
 1. Chain surveying: This is used when high accuracy is 
not required.
 2. Compass surveying: This is more precise than chain 
survey. Used for measuring horizontal angles along 
with linear measurements with chain or tape.
 3. Leveling: For finding difference in elevation of two 
points or elevation with respect to datum. (More 
precise than compass survey)
 4. Plane table surveying:
 • Measurement and plotting are simultaneous.
 • Less accurate, but suitable in areas with magnetic 
material effect.
 5. Theodolite survey:
 • Precise instrument for measuring horizontal and 
vertical angles.
 • Used for traverse and triangulation survey (base 
lines are located using triangulation).
 6. Tacheometric survey:
 • Not very accurate, but useful for topographic 
details.
 • It is a theodolite with stadia diaphragm having two 
horizontal cross hairs in addition to central hori-
zontal hair.
 7. Photogrammetry: Use photographs of vast areas 
and done for areas difficult to reach.
 8. EDM surveys: Use electronic method of measuring 
distances.
Principles of Surveying
 1. Location of a point by measurement from two points 
of reference.
 2. Working from whole to part:
 • First a system of control points are established and 
fixed with high precision. Minor control points 
are then established within main area with less 
precision.
 • This prevents accumulation of errors and to control 
and localize minor errors.
Plans and Maps
 • Neglecting earth’ s curved surface and using orthographic 
projections for graphical representation of any features 
(on, near or below earth’s surface) on a plane paper is 
called plan. Large scale is used for plan and only hori-
zontal distances and directions are shown.
 • The representation is called a map, if scale is small and 
vertical distances are also represented by contour lines.
Scales
 • Scale is a fixed ratio that every distance on the plan bears 
with the corresponding distance on the ground.
Scale Representation
 1. Engineers scale: 1 cm on plan represents some whole 
number on ground.
  Example: 1 cm = 10 m
 2. Representative factor (RF): It is a ratio.
RF
Distance on the Map
Distance on the Ground
=
  Example: 1 cm = 1 m?= ==
1
1
1
100
1
100
cm
m
cm
cm
RF 
 • Larger the denominator of RF, smaller is the scale 
of Map.
 • Engineers scale and RF are called numerical 
scales.
Part III_Unit 12_Chapter 01.indd   4 5/31/2017   5:00:25 PM
Chapter 1 
¦
 Fundamental Concepts and Linear Measurements | 3.997
 3. Graphical scale:
 • It is a line drawn on the map whose length cor-
responds to convenient units of length on ground.
 • It has the advantage of shrinking proportionately to 
map and distances are found accurately unlike in 
numerical scales. That is why these scales are used 
on all survey maps.
Types of Scales
 1. Plain scale: It is possible to measure two dimensions 
only.
  Example: Metres and decimetres
 2. Diagonal scale: It is possible to measure three 
dimensions such as metres, decimetres and 
centimetres.
 3. Chord scale: Used to measure an angle or to set-off 
an angle and are marked on a rectangular protractor 
graduated from 0°–90°.
 4. Vernier scale: The vernier is a device for measuring 
fractional part of one of the smallest divisions of the 
graduated scale.
If the graduations of the main scale are num-
bered in one direction only, it is called single 
vernier whereas if graduations are numbered in both 
the direction, it is called double vernier.
Least count (LC) of a vernier is equal to the dif-
ference between the smallest division on the main 
scale and the smallest division on the vernier scale.
 (a) Direct vernier: It increases or extends in the 
same direction as that of the main scale. Smallest 
division of vernier is smaller than smallest 
division on main scale.
n divisions of vernier = (n – 1) divisions of 
main scale
nV = (n – 1)S
v
nS
n
=
- () 1
   Where 
    S = Smallest division on main scale
    V = Smallest division of vernier
    n = Number of divisions on vernier 
LC = S – V = S –
() nS
n
S
n
-
=
1
LC
S
n
= =
1 main scale division
Divisions on vernier scale
 (b) Retrograde vernier: It is the one which extends 
or increases in opposite direction to that of the 
main scale. 
     In this, smallest division of vernier is longer 
than smallest division on the main scale.
nV = (n + 1)S
v
n
n
S =
+ ?
?
?
?
?
?
1
LC = V – S =
n
n
SS
S
n
+ ?
?
?
?
?
?
-=
1
   LC =
S
n
 
SOLVED EXAMPLES
Example 1
Find the LC of the vernier scale in a theodolite, if 59 
divisions on main scale are equal to 60 division on vernier 
scale and the smallest reading on main scale is 10'.
(A) 10? (B) 15?
(C) 20? (D) 30?
Solution
LC =
S
n
n = Number of divisions on the vernier = 60
S = Smallest division on main scale = 10 '
LC =
10
60
'
= 10? (i.e., 10 seconds)
Hence, the correct answer is option (A).
 (c) Error due to use of wrong scale:
Correct length = 
RF of wrong scale
RF of correct scale
Measure length
?
?
?
?
?
?
×
Correct area = 
RF of wrong scale
RF of correct scale
Calculated are
2
?
?
?
?
?
?
× a a
Example 2
A surveyor measured the distance between two points on 
the plan drawn to a scale of 1 cm = 50 m and the result was 
500 m. Later, however, he discovered that he used a scale 
of 1 cm = 25 m. Find the true distance between the points.
(A) 250 m (B) 500 m
(C) 750 m (D) 1000 m
Solution
Measured length = 500 m
RF of wrong scale used 
Part III_Unit 12_Chapter 01.indd   5 5/31/2017   5:00:26 PM
3.998 | Part III 
¦
 Unit 12 
¦
 Geomatics Engineering
=
×
=
1
25 100
1
2500
RF of correct scale =
1
50 100
1
5000 ×
=
\ Correct length 
=
?
?
?
?
?
?
×
RF of wrong scale
RF of correct scale
Measured lenght t
=
?
?
?
?
?
?
?
?
?
?
?
?
×
1
2500
1
5000
500
 = 1000 m.
Hence, the correct answer is option (D).
 (d) Error due to shrinkage:
  
Shrinkage factor/Ratio =
Shrunk length
Actual length
  Similarly,
  
Shrunk scale = Shrinkage factor × Original scale
Shrunk RF = Shrinkage factor × Original RF
  
Correct distance
Measured distance
Shrinkage factor
Correct 
=
a area
Measured area
Shrinkage factor
=
()
2
Example 3
The plan of an old survey drawn to a scale of 1 cm = 10 m, 
15 cm (shrunk and a line) long now measured 12 cm only 
and an area on the plot measured 95 sq. cm. Find the true 
area of the survey.
(A) 12974 m
2
 (B) 13635 m
2
(C) 14844 m
2
 (D) 15629 m
2
Solution
True RF
cm
m
==
×
=
1
10
1
10 100
1
1000
Shrinkage factor = =
12
15
4
5
Original area on plan 
=
Measured area
(Shrinkage factor)
2
=
?
?
?
?
?
?
95
4
5
2
= 148.44 cm
2
True area of the survey 
=
Original Area on plan
(Correct RF)
2
=
?
?
?
?
?
?
148 44
1
1000
2
.
= 148.44 × 10
6
 cm
2
= 14844 sq. m
Or,
Scale of plan 1 cm = 10 m
Area of the survey = 148.44 × (10)
2
 
= 14844 m
2
.
Hence, the correct answer is option (C).
Linear Measurements—Tape  
and Chain Survey
Introduction
For any surveying, basic measurements are linear measures. 
Different methods are used for measuring lengths depend-
ing on the importance of work, location and degree of preci-
sion required.
 1. Direct measurement—Chain and tape
 2. Measurements by optical means
 3. Electro-magnetic methods (EDM)
Direct measurements are done by passometer, pedometer, 
odometer, speedometer, pacing and chaining.
Different Types of Chains
 • Chains are formed of straight links of galvanised mild 
steel.
 • The length of a link is the distance between the centers of 
two consecutive middle rings.
 • Length of chain is measured from outside of one handle 
to the outside of other handle.
 • Metric chains: 
(a) 20 m chain (100 links)
(b) 30 m chain (150 links)
 • Gunter’ s/surveyor’ s chain:
(a) 66 ft (100 links)
(b) Adopted for land measurement.
 • Engineer’ s chain—100 ft (100 links)
 • Revenue chain—33 ft (16 links)
(a) Used for measuring fields in Cadastral survey.
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Page 5


Fundamental DeFinitions
and Concepts
Surveying is the art of determining the relative positions 
of points on, above or beneath the surface of the earth by 
means of direct or indirect measurements of distance, direc-
tion and elevation.
Objectives of Surveying
 1. To fi nd elevations of points with respect to a given or 
assumed datum.
 2. To establish points at given elevations for a proposed 
structure.
 3. To fi nd areas, volumes and other related quantities.
Primary Divisions of Surveying
 • Based on consideration of curvature of earth
 • Earth is an italics
 • Polar axis (12,713,800 metres) is shorter than equatorial 
axis (12,756,750 metres) by 42.95 km (0.34%).
Plane Surveying
 • Surface of earth is considered as a plane and curvature is 
neglected.
 • Level line is considered as straight and all plumb lines are 
considered parallel.
When,
 • The extent of area is < 250 sq. km.
 • The diff erence between arc of 18.2 km on surface of earth 
and the subtended chord distance is about 1 cm.
 • Diff erence between sum of angles in a plane triangle and 
those in spherical triangle is only one second (1?) for a 
triangle at the earth’s surface having an area of 195 sq. 
km.
 • Used for engineering projects on large scale such as fac-
tories, bridges, dams, etc.
Geodetic Surveying
 • Curvature of earth is considered.
 • All lines lying on surface of earth are curved lines and 
triangles are spherical triangles.
 • Deals in fi xing widely spaced control points.
 • Preferred for large scale works with high degree of 
precision.
Classifi cation of Surveying
Based on Nature or Function of Field Survey
Land Surveying
 1. Topographical survey:
 • To fi nd horizontal and vertical locations of certain 
points by linear and angular measurements.
 ? Fundamental de? nitions and concepts
 ? Linear measurements—tape and chain 
survey
 ? Chain surveying or chain triangulation
CHAPTER HIGHLIGHTS
Fundamental Concepts
and Linear Measurements
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 • Determines natural features of a country such as 
rivers, lakes, hills, woods and artificial features 
such as roads, canals, towns, etc.
 2. Cadastral survey:
 • Consists of fixing of property lines, boundaries of 
fields, municipalities and calculating land area.
 • Done by a revenue engineer.
 3. City surveying: This survey is done for the 
construction of streets, water supply systems, sewers 
and other works.
Marine (or) Hydrographic Survey Deals with bodies of 
water like water supply, harbour, and for determining mean 
sea level.
Example: Topographical survey of shores and banks of 
river.
Astronomical Survey
 • For finding the absolute location of a point or direction of 
any line on surface of the earth by taking latitude, longi-
tude, azimuth, local time, etc.
 • Observations are made in relation to sun or any fixed star.
Based on Object of Survey
 1. Engineering survey: For determining the quantities 
or data required for designing of engineering works 
such as roads and reservoirs.
 2. Military survey: Determining points of strategic 
importance.
 3. Mine survey: For exploring mineral wealth 
(underground surveys).
 4. Geological survey: For determining different strata 
in earth’ s crust.
 5. Archaeological survey: For unearthing relics of 
antiquity.
Based on Instruments Used
 1. Chain surveying: This is used when high accuracy is 
not required.
 2. Compass surveying: This is more precise than chain 
survey. Used for measuring horizontal angles along 
with linear measurements with chain or tape.
 3. Leveling: For finding difference in elevation of two 
points or elevation with respect to datum. (More 
precise than compass survey)
 4. Plane table surveying:
 • Measurement and plotting are simultaneous.
 • Less accurate, but suitable in areas with magnetic 
material effect.
 5. Theodolite survey:
 • Precise instrument for measuring horizontal and 
vertical angles.
 • Used for traverse and triangulation survey (base 
lines are located using triangulation).
 6. Tacheometric survey:
 • Not very accurate, but useful for topographic 
details.
 • It is a theodolite with stadia diaphragm having two 
horizontal cross hairs in addition to central hori-
zontal hair.
 7. Photogrammetry: Use photographs of vast areas 
and done for areas difficult to reach.
 8. EDM surveys: Use electronic method of measuring 
distances.
Principles of Surveying
 1. Location of a point by measurement from two points 
of reference.
 2. Working from whole to part:
 • First a system of control points are established and 
fixed with high precision. Minor control points 
are then established within main area with less 
precision.
 • This prevents accumulation of errors and to control 
and localize minor errors.
Plans and Maps
 • Neglecting earth’ s curved surface and using orthographic 
projections for graphical representation of any features 
(on, near or below earth’s surface) on a plane paper is 
called plan. Large scale is used for plan and only hori-
zontal distances and directions are shown.
 • The representation is called a map, if scale is small and 
vertical distances are also represented by contour lines.
Scales
 • Scale is a fixed ratio that every distance on the plan bears 
with the corresponding distance on the ground.
Scale Representation
 1. Engineers scale: 1 cm on plan represents some whole 
number on ground.
  Example: 1 cm = 10 m
 2. Representative factor (RF): It is a ratio.
RF
Distance on the Map
Distance on the Ground
=
  Example: 1 cm = 1 m?= ==
1
1
1
100
1
100
cm
m
cm
cm
RF 
 • Larger the denominator of RF, smaller is the scale 
of Map.
 • Engineers scale and RF are called numerical 
scales.
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Chapter 1 
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 Fundamental Concepts and Linear Measurements | 3.997
 3. Graphical scale:
 • It is a line drawn on the map whose length cor-
responds to convenient units of length on ground.
 • It has the advantage of shrinking proportionately to 
map and distances are found accurately unlike in 
numerical scales. That is why these scales are used 
on all survey maps.
Types of Scales
 1. Plain scale: It is possible to measure two dimensions 
only.
  Example: Metres and decimetres
 2. Diagonal scale: It is possible to measure three 
dimensions such as metres, decimetres and 
centimetres.
 3. Chord scale: Used to measure an angle or to set-off 
an angle and are marked on a rectangular protractor 
graduated from 0°–90°.
 4. Vernier scale: The vernier is a device for measuring 
fractional part of one of the smallest divisions of the 
graduated scale.
If the graduations of the main scale are num-
bered in one direction only, it is called single 
vernier whereas if graduations are numbered in both 
the direction, it is called double vernier.
Least count (LC) of a vernier is equal to the dif-
ference between the smallest division on the main 
scale and the smallest division on the vernier scale.
 (a) Direct vernier: It increases or extends in the 
same direction as that of the main scale. Smallest 
division of vernier is smaller than smallest 
division on main scale.
n divisions of vernier = (n – 1) divisions of 
main scale
nV = (n – 1)S
v
nS
n
=
- () 1
   Where 
    S = Smallest division on main scale
    V = Smallest division of vernier
    n = Number of divisions on vernier 
LC = S – V = S –
() nS
n
S
n
-
=
1
LC
S
n
= =
1 main scale division
Divisions on vernier scale
 (b) Retrograde vernier: It is the one which extends 
or increases in opposite direction to that of the 
main scale. 
     In this, smallest division of vernier is longer 
than smallest division on the main scale.
nV = (n + 1)S
v
n
n
S =
+ ?
?
?
?
?
?
1
LC = V – S =
n
n
SS
S
n
+ ?
?
?
?
?
?
-=
1
   LC =
S
n
 
SOLVED EXAMPLES
Example 1
Find the LC of the vernier scale in a theodolite, if 59 
divisions on main scale are equal to 60 division on vernier 
scale and the smallest reading on main scale is 10'.
(A) 10? (B) 15?
(C) 20? (D) 30?
Solution
LC =
S
n
n = Number of divisions on the vernier = 60
S = Smallest division on main scale = 10 '
LC =
10
60
'
= 10? (i.e., 10 seconds)
Hence, the correct answer is option (A).
 (c) Error due to use of wrong scale:
Correct length = 
RF of wrong scale
RF of correct scale
Measure length
?
?
?
?
?
?
×
Correct area = 
RF of wrong scale
RF of correct scale
Calculated are
2
?
?
?
?
?
?
× a a
Example 2
A surveyor measured the distance between two points on 
the plan drawn to a scale of 1 cm = 50 m and the result was 
500 m. Later, however, he discovered that he used a scale 
of 1 cm = 25 m. Find the true distance between the points.
(A) 250 m (B) 500 m
(C) 750 m (D) 1000 m
Solution
Measured length = 500 m
RF of wrong scale used 
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=
×
=
1
25 100
1
2500
RF of correct scale =
1
50 100
1
5000 ×
=
\ Correct length 
=
?
?
?
?
?
?
×
RF of wrong scale
RF of correct scale
Measured lenght t
=
?
?
?
?
?
?
?
?
?
?
?
?
×
1
2500
1
5000
500
 = 1000 m.
Hence, the correct answer is option (D).
 (d) Error due to shrinkage:
  
Shrinkage factor/Ratio =
Shrunk length
Actual length
  Similarly,
  
Shrunk scale = Shrinkage factor × Original scale
Shrunk RF = Shrinkage factor × Original RF
  
Correct distance
Measured distance
Shrinkage factor
Correct 
=
a area
Measured area
Shrinkage factor
=
()
2
Example 3
The plan of an old survey drawn to a scale of 1 cm = 10 m, 
15 cm (shrunk and a line) long now measured 12 cm only 
and an area on the plot measured 95 sq. cm. Find the true 
area of the survey.
(A) 12974 m
2
 (B) 13635 m
2
(C) 14844 m
2
 (D) 15629 m
2
Solution
True RF
cm
m
==
×
=
1
10
1
10 100
1
1000
Shrinkage factor = =
12
15
4
5
Original area on plan 
=
Measured area
(Shrinkage factor)
2
=
?
?
?
?
?
?
95
4
5
2
= 148.44 cm
2
True area of the survey 
=
Original Area on plan
(Correct RF)
2
=
?
?
?
?
?
?
148 44
1
1000
2
.
= 148.44 × 10
6
 cm
2
= 14844 sq. m
Or,
Scale of plan 1 cm = 10 m
Area of the survey = 148.44 × (10)
2
 
= 14844 m
2
.
Hence, the correct answer is option (C).
Linear Measurements—Tape  
and Chain Survey
Introduction
For any surveying, basic measurements are linear measures. 
Different methods are used for measuring lengths depend-
ing on the importance of work, location and degree of preci-
sion required.
 1. Direct measurement—Chain and tape
 2. Measurements by optical means
 3. Electro-magnetic methods (EDM)
Direct measurements are done by passometer, pedometer, 
odometer, speedometer, pacing and chaining.
Different Types of Chains
 • Chains are formed of straight links of galvanised mild 
steel.
 • The length of a link is the distance between the centers of 
two consecutive middle rings.
 • Length of chain is measured from outside of one handle 
to the outside of other handle.
 • Metric chains: 
(a) 20 m chain (100 links)
(b) 30 m chain (150 links)
 • Gunter’ s/surveyor’ s chain:
(a) 66 ft (100 links)
(b) Adopted for land measurement.
 • Engineer’ s chain—100 ft (100 links)
 • Revenue chain—33 ft (16 links)
(a) Used for measuring fields in Cadastral survey.
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Chapter 1 
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 Fundamental Concepts and Linear Measurements | 3.999
 • Steel band/band chain 
(a) More accurate than chain
(b) Made of blue steel—20 m and 30 m chains
T apes
Tapes are used for more accurate measurements.
Cloth or Linen Tape
Used for rough and subsidiary measurements such as 
offsets. It is rarely used because of the following reasons:
 1. Easily affected by moisture or dampness and thus 
shrinks.
 2. Length gets altered by stretching.
 3. Likely to twist and tangle.
 4. It is not strong.
Metallic Tape
These tapes are light and flexible and are not easily 
broken and useful in cross-sectioning and in some methods 
of topography where small errors can be neglected.
Steel Tape
 • Superior to cloth or metallic tape and is more accurately 
graduated.
 • It is very delicate instrument and very light, therefore 
cannot withstand rough usage.
Invar Tape
 • Used for linear measurements of very high degree of pre-
cision such as base lines and are measured rapidly.
 • It is made of alloy of nickel (36%) and steel.
 • Coefficient of thermal expansion =
1
10
 of that of steel  
=
1
10
() a
s
Where, a s
 = 12.5 × 10
-6
/°C (for steel)
 • Greater disadvantage is that it is subjected to creep and its 
coefficient of thermal expansion goes on changing and it 
is costly, easily bent and damaged.
Instruments used for Chaining
Arrows/marking pins: Usually 10 arrows with one chain 
are used. It is 40 cm long and 4 mm diameter. (IS code)
Wooden pegs: Used to mark the positions of the stations or 
terminal points of a survey line. They are 15 cm long and 
2.5–3 sq. cm cross-section.
Ranging rods: Used for ranging intermediate points in sur-
vey line. They are either 2 m or 3 m.
Ranging poles: These are 4–8 m and 6–10 cm diameter 
similar to ranging rods but used in case of very long lines.
Offset rod: Measures rough offsets and are 3 m long.
Butt rod: Measures offsets and is used by architects and 
surveyors.
Plasterer’s laths: Ranging a line—setting intermediate 
point 
1
2
 to 1 m long.
Whites: Similar to laths-pieces of sharpened thin sticks.
Plumb bob: Used for centering the instruments, transfer 
points on to the ground, make poles vertical and transfer 
points from line ranger to the ground.
Line ranger: It consists of either two plane mirrors or two 
right angled isosceles prisms used for ranging.
Ranging Out Survey Lines
If the length of survey line exceeds the length of the chain, 
some intermediate points have to be established in line with 
the two terminal points.
The two methods of ranging are:
 1. Direct ranging: When two ends of survey lines are 
inter visible.
 2. Indirect/reciprocal ranging: When both the ends of 
a survey line are not inter visible due to high inter 
veining ground.
Error Due to Incorrect Chain
 • If chain is too long, measured distance is less and there-
fore error is negative and correction is positive.
 • If chain is too short, measured distance is more and there-
fore error is positive and correction is negative.
  Let L, L' = Correct and incorrect length of chain/tape 
respectively.
    l, l' = True and measured length of line respectively
 1. Correction to measured length:
  True length of line = Measured length ×
' L
L
ll
L
L
= '
'
?
?
?
?
?
?
 2. Correction to area:
  True area = Measured area ×
'
?
?
?
?
?
?
L
L
2
AA
L
L
= '×
'
?
?
?
?
?
?
2
  A, A' = True and measured area of the ground.
 3. Correction to volume:
  True V olume = Measured volume ×
'
?
?
?
?
?
?
L
L
3
VV
L
L
= '
'
?
?
?
?
?
?
3
  V and V ' = True and measured volumes.
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