Short Notes for Levelling & Contouring | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

 Page 1


 ? Levelling and trigonometric levelling
 ? Tacheometry
 ? Contouring
CHAPTER HIGHLIGHTS
LeveLLing anD Trigonometric 
LeveLLing
Introduction
Levelling is a branch of surveying which works with the 
objective of fi nding or establishing the elevation of points. 
This chapter deals with measurements in a vertical plane.
Object of Levelling
 1. To fi nd the elevations of given points with respect to 
a given or assumed datum—to enable works to be 
designed.
 2. To establish points at a given elevation or at diff erent 
elevations with respect to a given or assumed datum—
to set out all kinds of engineering works.
Fundamental De? nitions
 • Level surface: is defi ned as a curved surface which at 
each point is perpendicular to the direction of gravity at the 
point. The surface of a still water is a truly level surface. 
Any surface parallel to the mean spheroidal surface of the 
earth is, therefore, a level surface.
 • Level line: It is a line lying on the level surface. It is 
therefore, normal to the plumb line at all points.
 • Horizontal plane: It is a plane tangential to the level sur-
face at that point and is therefore perpendicular to the 
plumb line through the point.
 • Horizontal line: It is a straight line tangential to the level 
line at a point and it is also perpendicular to the plumb 
line.
 • Vertical line: It is line normal to the level line at a 
point. It is commonly considered to be the line defined 
by a plumb line.
 • Datum: It is any surface to which elevations are referred. 
Mean sea level aff ords a convenient datum all over the 
world.
 • Elevation: Vertical distance above or below an arbitrarily 
assumed level surface or datum.
 • Vertical angle: It is an angle between two intersecting 
lines in a vertical plane.
 • Mean sea level: A verage height of the sea for all stages of 
the tides. It is derived by averaging the hourly tide heights 
over a long period of 19 years.
 • Bench mark: It is a relatively permanent point of ref-
erence whose elevation with respect to some assumed 
datum is known and used as a starting point for leveling 
or as a point upon which to close as a check.
Methods of Levelling
Three methods of leveling are used for determining diff er-
ence in elevation.
 1. Barometric levelling: makes use of the phenomenon 
that diff erence in elevation between two points 
is proportional to the diff erence in atmospheric 
pressures at these points.
Levelling and Contouring
Part III_Unit 12_Chapter 04.indd   1 5/31/2017   4:56:36 PM
Page 2


 ? Levelling and trigonometric levelling
 ? Tacheometry
 ? Contouring
CHAPTER HIGHLIGHTS
LeveLLing anD Trigonometric 
LeveLLing
Introduction
Levelling is a branch of surveying which works with the 
objective of fi nding or establishing the elevation of points. 
This chapter deals with measurements in a vertical plane.
Object of Levelling
 1. To fi nd the elevations of given points with respect to 
a given or assumed datum—to enable works to be 
designed.
 2. To establish points at a given elevation or at diff erent 
elevations with respect to a given or assumed datum—
to set out all kinds of engineering works.
Fundamental De? nitions
 • Level surface: is defi ned as a curved surface which at 
each point is perpendicular to the direction of gravity at the 
point. The surface of a still water is a truly level surface. 
Any surface parallel to the mean spheroidal surface of the 
earth is, therefore, a level surface.
 • Level line: It is a line lying on the level surface. It is 
therefore, normal to the plumb line at all points.
 • Horizontal plane: It is a plane tangential to the level sur-
face at that point and is therefore perpendicular to the 
plumb line through the point.
 • Horizontal line: It is a straight line tangential to the level 
line at a point and it is also perpendicular to the plumb 
line.
 • Vertical line: It is line normal to the level line at a 
point. It is commonly considered to be the line defined 
by a plumb line.
 • Datum: It is any surface to which elevations are referred. 
Mean sea level aff ords a convenient datum all over the 
world.
 • Elevation: Vertical distance above or below an arbitrarily 
assumed level surface or datum.
 • Vertical angle: It is an angle between two intersecting 
lines in a vertical plane.
 • Mean sea level: A verage height of the sea for all stages of 
the tides. It is derived by averaging the hourly tide heights 
over a long period of 19 years.
 • Bench mark: It is a relatively permanent point of ref-
erence whose elevation with respect to some assumed 
datum is known and used as a starting point for leveling 
or as a point upon which to close as a check.
Methods of Levelling
Three methods of leveling are used for determining diff er-
ence in elevation.
 1. Barometric levelling: makes use of the phenomenon 
that diff erence in elevation between two points 
is proportional to the diff erence in atmospheric 
pressures at these points.
Levelling and Contouring
Part III_Unit 12_Chapter 04.indd   1 5/31/2017   4:56:36 PM
    
 2. Trigonometric levelling (indirect levelling): It is the 
process of leveling in which the elevations of points 
are computed from the vertical angles and horizontal 
distances measured in the field. In a modified form 
called ‘stadia levelling’ is commonly used in 
mapping.
 3. Spirit levelling (direct leveling) A spirit level and 
sighting device (telescope) are combined and vertical 
distances are measured by observing on graduated 
rods placed on the points. It is the most precise 
method of determining elevations and the one most 
commonly used by engineers.
Levelling Instruments
Level
It is to provide a horizontal line of sight. It consists of four 
parts.
 1. A telescope to provide line of sight.
 2. A level tube to make the line of sight horizontal.
 3. A levelling head (tribrach and trivet stage) to bring 
the bubble in its centre of run.
 4. A tripod to support the instrument.
  Chief types of levels are:
Dumpy Level
 • This name originated from the fact that formerly this 
level was equipped with an inverting eye-piece and hence 
was shorter than wye level of the same magnifying power.
 • Levelling head generally consists of two parallel plates 
with 3 or 4 foot screws. The upper plate is known as 
tribrach and the lower plate is known as trivet.
Advantages of dump level over wye level:
 1. Simpler construction with fewer movable parts.
 2. Fewer adjustments to be made.
 3. Longer life of the adjustments.
Wye or Y Level
 • In dumpy level, telescope is fixed to the spindle and bub-
ble tube must be of reversible type. While in wye level, 
the telescope is carried in two vertical ‘wye’ supports and 
bubble tube may be attached either to the telescope or to 
the stage carrying the wyes.
 • Advantage of wye level over dumpy level is that the 
adjustments can be tested with greater rapidity and ease.
Reversible Level Combines the features of both the dumpy 
and wye level. For testing and making the adjustments, 
telescope can be taken out and reversed end for end.
Tilting Level The line of sight and the vertical axis need 
not be exactly perpendicular to each other. This feature 
helps in quick levelling.
 • This is mainly designed for precise levelling work.
 • Its advantage is that it can be done more quickly, but it is 
not so apparent when many readings are taken from one 
instrument setting.
Levelling Staff
It is a rectangular rod having graduations. It is used to estab-
lish a horizontal line of sight and to determine the amount 
by which the station is above or below the line of sight.
 1. Solid staff
 2. Folding staff
 3. Telescopic staff
Each metre is sub divided into 200 divisions, the thickness 
of graduations being 5 mm and painted in alternate black 
and white with 5 mm thickness each.
Surveying Telescope
 • This telescope employs two convex lenses. One nearest to 
object is called objective and other near to eye is called 
the eye-piece.
 • Object glass provides a real inverted image infront of eye-
piece, while the eye-piece magnifies the image to produce 
an inverted virtual image.
Line of Sight or Line of Collimation
 • It is a line which passes through the optical centre of the 
objective and intersection of cross hairs and eye-piece.
 • The telescope in which the focusing is done by the exter-
nal movement of either objective or eye-piece is known as 
external focusing telescope and the one in which focus-
ing is done internally with a negative lens is known as 
internal focusing telescope.
Parallax
If the image formed by objective lens is not in the same 
plane with cross-hairs, any movement of the eye is likely to 
cause an apparent movement of the image with respect to 
the cross-hairs. This is called parallax.
Essential Parts of the Telescope
 1. Objective.
 2. Eye-piece.
 3. Diaphragm.
 4. Body and focusing device.
Objective It is a compound lens called achromatic lens. It 
consists of front double convex lens made of crown glass 
and back concave-convex lens made of flint glass. It nearly 
eliminates spherical and chromatic aberrations.
Eye-piece
 • Ramsden eye-piece is commonly used which is composed 
of plano-convex lenses of equal focal length placed at a 
distance of 
2
3
f.
Part III_Unit 12_Chapter 04.indd   2 5/31/2017   4:56:37 PM
Page 3


 ? Levelling and trigonometric levelling
 ? Tacheometry
 ? Contouring
CHAPTER HIGHLIGHTS
LeveLLing anD Trigonometric 
LeveLLing
Introduction
Levelling is a branch of surveying which works with the 
objective of fi nding or establishing the elevation of points. 
This chapter deals with measurements in a vertical plane.
Object of Levelling
 1. To fi nd the elevations of given points with respect to 
a given or assumed datum—to enable works to be 
designed.
 2. To establish points at a given elevation or at diff erent 
elevations with respect to a given or assumed datum—
to set out all kinds of engineering works.
Fundamental De? nitions
 • Level surface: is defi ned as a curved surface which at 
each point is perpendicular to the direction of gravity at the 
point. The surface of a still water is a truly level surface. 
Any surface parallel to the mean spheroidal surface of the 
earth is, therefore, a level surface.
 • Level line: It is a line lying on the level surface. It is 
therefore, normal to the plumb line at all points.
 • Horizontal plane: It is a plane tangential to the level sur-
face at that point and is therefore perpendicular to the 
plumb line through the point.
 • Horizontal line: It is a straight line tangential to the level 
line at a point and it is also perpendicular to the plumb 
line.
 • Vertical line: It is line normal to the level line at a 
point. It is commonly considered to be the line defined 
by a plumb line.
 • Datum: It is any surface to which elevations are referred. 
Mean sea level aff ords a convenient datum all over the 
world.
 • Elevation: Vertical distance above or below an arbitrarily 
assumed level surface or datum.
 • Vertical angle: It is an angle between two intersecting 
lines in a vertical plane.
 • Mean sea level: A verage height of the sea for all stages of 
the tides. It is derived by averaging the hourly tide heights 
over a long period of 19 years.
 • Bench mark: It is a relatively permanent point of ref-
erence whose elevation with respect to some assumed 
datum is known and used as a starting point for leveling 
or as a point upon which to close as a check.
Methods of Levelling
Three methods of leveling are used for determining diff er-
ence in elevation.
 1. Barometric levelling: makes use of the phenomenon 
that diff erence in elevation between two points 
is proportional to the diff erence in atmospheric 
pressures at these points.
Levelling and Contouring
Part III_Unit 12_Chapter 04.indd   1 5/31/2017   4:56:36 PM
    
 2. Trigonometric levelling (indirect levelling): It is the 
process of leveling in which the elevations of points 
are computed from the vertical angles and horizontal 
distances measured in the field. In a modified form 
called ‘stadia levelling’ is commonly used in 
mapping.
 3. Spirit levelling (direct leveling) A spirit level and 
sighting device (telescope) are combined and vertical 
distances are measured by observing on graduated 
rods placed on the points. It is the most precise 
method of determining elevations and the one most 
commonly used by engineers.
Levelling Instruments
Level
It is to provide a horizontal line of sight. It consists of four 
parts.
 1. A telescope to provide line of sight.
 2. A level tube to make the line of sight horizontal.
 3. A levelling head (tribrach and trivet stage) to bring 
the bubble in its centre of run.
 4. A tripod to support the instrument.
  Chief types of levels are:
Dumpy Level
 • This name originated from the fact that formerly this 
level was equipped with an inverting eye-piece and hence 
was shorter than wye level of the same magnifying power.
 • Levelling head generally consists of two parallel plates 
with 3 or 4 foot screws. The upper plate is known as 
tribrach and the lower plate is known as trivet.
Advantages of dump level over wye level:
 1. Simpler construction with fewer movable parts.
 2. Fewer adjustments to be made.
 3. Longer life of the adjustments.
Wye or Y Level
 • In dumpy level, telescope is fixed to the spindle and bub-
ble tube must be of reversible type. While in wye level, 
the telescope is carried in two vertical ‘wye’ supports and 
bubble tube may be attached either to the telescope or to 
the stage carrying the wyes.
 • Advantage of wye level over dumpy level is that the 
adjustments can be tested with greater rapidity and ease.
Reversible Level Combines the features of both the dumpy 
and wye level. For testing and making the adjustments, 
telescope can be taken out and reversed end for end.
Tilting Level The line of sight and the vertical axis need 
not be exactly perpendicular to each other. This feature 
helps in quick levelling.
 • This is mainly designed for precise levelling work.
 • Its advantage is that it can be done more quickly, but it is 
not so apparent when many readings are taken from one 
instrument setting.
Levelling Staff
It is a rectangular rod having graduations. It is used to estab-
lish a horizontal line of sight and to determine the amount 
by which the station is above or below the line of sight.
 1. Solid staff
 2. Folding staff
 3. Telescopic staff
Each metre is sub divided into 200 divisions, the thickness 
of graduations being 5 mm and painted in alternate black 
and white with 5 mm thickness each.
Surveying Telescope
 • This telescope employs two convex lenses. One nearest to 
object is called objective and other near to eye is called 
the eye-piece.
 • Object glass provides a real inverted image infront of eye-
piece, while the eye-piece magnifies the image to produce 
an inverted virtual image.
Line of Sight or Line of Collimation
 • It is a line which passes through the optical centre of the 
objective and intersection of cross hairs and eye-piece.
 • The telescope in which the focusing is done by the exter-
nal movement of either objective or eye-piece is known as 
external focusing telescope and the one in which focus-
ing is done internally with a negative lens is known as 
internal focusing telescope.
Parallax
If the image formed by objective lens is not in the same 
plane with cross-hairs, any movement of the eye is likely to 
cause an apparent movement of the image with respect to 
the cross-hairs. This is called parallax.
Essential Parts of the Telescope
 1. Objective.
 2. Eye-piece.
 3. Diaphragm.
 4. Body and focusing device.
Objective It is a compound lens called achromatic lens. It 
consists of front double convex lens made of crown glass 
and back concave-convex lens made of flint glass. It nearly 
eliminates spherical and chromatic aberrations.
Eye-piece
 • Ramsden eye-piece is commonly used which is composed 
of plano-convex lenses of equal focal length placed at a 
distance of 
2
3
f.
Part III_Unit 12_Chapter 04.indd   2 5/31/2017   4:56:37 PM
      
 • Huygen’s eye-piece composed of plano-convex lenses of 
different focal length placed at a distance of two-third of 
focal length of the larger.
2
3
f
Huygen’s eye-piece
2
3
f
Ramsden eye-piece
Diaphragm It consists of cross-hairs. Horizontal hair 
is used to read the staff and the two vertical hairs enable 
the surveyor to see if the staff is vertical laterally. In stadia 
tacheometry, two more horizontal hairs called stadia hairs 
are provided.
Optical Defects of a Single Lens
Aberrations is the deviation of rays of light.
 1. Spherical aberration: The defect or imperfection 
arising from the form of curvature of the lens in 
which the rays are all not collected exactly at one 
point is called spherical aberration.
 2. Chromatic aberrations:  A beam of light after 
passing through a single lens, is distributed along 
the axis in a series of focal points in which violet ray 
is refracted most and the red is refracted least. This 
defect is called chromatic aberration.
 • The elimination of aberrations is only one of the 
requirements in the design of a telescope.
 • Other possible defects which are of little importance 
are coma, astigmation, curvature, distortion, etc.
Temporary Adjustments of a Level 
or Telescope
 1. Setting up the level
 2. Levelling up with the help of foot screws
 3. Elimination of parallax by two steps:
 (a) Focusing the eye-piece (for distinct vision of 
cross hairs)
 (b) Focusing the objective (for clear image of staff)
Terms and Abbreviations
 1. Station: It is that point where the level rod is held.
 2. Height of instrument (HI): It is the elevation of 
plane of sight with respect to assumed datum.
 3. Back sight (BS): Sight taken on a rod held at a point 
of known elevation. It is also known as a plus sight 
as the back sight reading is always added to the level 
of the datum to get the height of the plane of sight.
 4. Fore sight (FS): Reading taken on a rod held at a 
point of unknown elevation. It is also known as minus 
sight, as the fore sight reading is always subtracted 
from HI to get elevation of the point.
 5. Turning point (TP): is a point on which both minus 
sight and plus sight are taken on a line of direct levels.
 6. Intermediate station (IS): Intermediate point 
between two turning points on which only one sight 
(minus sight) is taken to determine the elevation of 
the station.
Steps in Leveling
 1. To find the amount by which the line of sight is above 
the bench mark.
 2. To know the amount by which the next point is below 
or above the line of sight.
 • Height of instrument, HI = Elevation of BM + BS 
(at BM)
 • Elevation of a point = HI – FS (at that point)
Booking and Reducing Levels
Collimation or Height of Instrument Method
 • Height of the instrument (HI) is calculated for each set-
tling of the instrument.
 • Reduced levels (RL’s) of other stations are calculated 
based on height of the instrument.
 • Generally used for fly leveling or to establish BMs.
 • This method is not suitable when there are intermediate 
points.
Check: SBS - SFS = Last RL - First RL
Rise and Fall Method
 • Difference of level between consecutive points is found 
by comparing the staff readings.
 • Higher staff reading indicates fall and lesser indicates 
rise.
 • Generally used in contour survey.
 • Used when a number of Intermediate station readings are 
required and provides a complete check for intermediate 
sights.
Check: SBS – SFS = S Rise - S Fall 
= Last RL – First RL
Use of Inverted Staff
When the point, whose elevation is much above the line of 
sight (For example, projection from the face of a building, 
underside of beams, girders, arches, etc.) the staff is placed 
inverted with its zero end touching the point. The reading on 
the staff is taken in the usual manner. Such an observation 
Part III_Unit 12_Chapter 04.indd   3 5/31/2017   4:56:37 PM
Page 4


 ? Levelling and trigonometric levelling
 ? Tacheometry
 ? Contouring
CHAPTER HIGHLIGHTS
LeveLLing anD Trigonometric 
LeveLLing
Introduction
Levelling is a branch of surveying which works with the 
objective of fi nding or establishing the elevation of points. 
This chapter deals with measurements in a vertical plane.
Object of Levelling
 1. To fi nd the elevations of given points with respect to 
a given or assumed datum—to enable works to be 
designed.
 2. To establish points at a given elevation or at diff erent 
elevations with respect to a given or assumed datum—
to set out all kinds of engineering works.
Fundamental De? nitions
 • Level surface: is defi ned as a curved surface which at 
each point is perpendicular to the direction of gravity at the 
point. The surface of a still water is a truly level surface. 
Any surface parallel to the mean spheroidal surface of the 
earth is, therefore, a level surface.
 • Level line: It is a line lying on the level surface. It is 
therefore, normal to the plumb line at all points.
 • Horizontal plane: It is a plane tangential to the level sur-
face at that point and is therefore perpendicular to the 
plumb line through the point.
 • Horizontal line: It is a straight line tangential to the level 
line at a point and it is also perpendicular to the plumb 
line.
 • Vertical line: It is line normal to the level line at a 
point. It is commonly considered to be the line defined 
by a plumb line.
 • Datum: It is any surface to which elevations are referred. 
Mean sea level aff ords a convenient datum all over the 
world.
 • Elevation: Vertical distance above or below an arbitrarily 
assumed level surface or datum.
 • Vertical angle: It is an angle between two intersecting 
lines in a vertical plane.
 • Mean sea level: A verage height of the sea for all stages of 
the tides. It is derived by averaging the hourly tide heights 
over a long period of 19 years.
 • Bench mark: It is a relatively permanent point of ref-
erence whose elevation with respect to some assumed 
datum is known and used as a starting point for leveling 
or as a point upon which to close as a check.
Methods of Levelling
Three methods of leveling are used for determining diff er-
ence in elevation.
 1. Barometric levelling: makes use of the phenomenon 
that diff erence in elevation between two points 
is proportional to the diff erence in atmospheric 
pressures at these points.
Levelling and Contouring
Part III_Unit 12_Chapter 04.indd   1 5/31/2017   4:56:36 PM
    
 2. Trigonometric levelling (indirect levelling): It is the 
process of leveling in which the elevations of points 
are computed from the vertical angles and horizontal 
distances measured in the field. In a modified form 
called ‘stadia levelling’ is commonly used in 
mapping.
 3. Spirit levelling (direct leveling) A spirit level and 
sighting device (telescope) are combined and vertical 
distances are measured by observing on graduated 
rods placed on the points. It is the most precise 
method of determining elevations and the one most 
commonly used by engineers.
Levelling Instruments
Level
It is to provide a horizontal line of sight. It consists of four 
parts.
 1. A telescope to provide line of sight.
 2. A level tube to make the line of sight horizontal.
 3. A levelling head (tribrach and trivet stage) to bring 
the bubble in its centre of run.
 4. A tripod to support the instrument.
  Chief types of levels are:
Dumpy Level
 • This name originated from the fact that formerly this 
level was equipped with an inverting eye-piece and hence 
was shorter than wye level of the same magnifying power.
 • Levelling head generally consists of two parallel plates 
with 3 or 4 foot screws. The upper plate is known as 
tribrach and the lower plate is known as trivet.
Advantages of dump level over wye level:
 1. Simpler construction with fewer movable parts.
 2. Fewer adjustments to be made.
 3. Longer life of the adjustments.
Wye or Y Level
 • In dumpy level, telescope is fixed to the spindle and bub-
ble tube must be of reversible type. While in wye level, 
the telescope is carried in two vertical ‘wye’ supports and 
bubble tube may be attached either to the telescope or to 
the stage carrying the wyes.
 • Advantage of wye level over dumpy level is that the 
adjustments can be tested with greater rapidity and ease.
Reversible Level Combines the features of both the dumpy 
and wye level. For testing and making the adjustments, 
telescope can be taken out and reversed end for end.
Tilting Level The line of sight and the vertical axis need 
not be exactly perpendicular to each other. This feature 
helps in quick levelling.
 • This is mainly designed for precise levelling work.
 • Its advantage is that it can be done more quickly, but it is 
not so apparent when many readings are taken from one 
instrument setting.
Levelling Staff
It is a rectangular rod having graduations. It is used to estab-
lish a horizontal line of sight and to determine the amount 
by which the station is above or below the line of sight.
 1. Solid staff
 2. Folding staff
 3. Telescopic staff
Each metre is sub divided into 200 divisions, the thickness 
of graduations being 5 mm and painted in alternate black 
and white with 5 mm thickness each.
Surveying Telescope
 • This telescope employs two convex lenses. One nearest to 
object is called objective and other near to eye is called 
the eye-piece.
 • Object glass provides a real inverted image infront of eye-
piece, while the eye-piece magnifies the image to produce 
an inverted virtual image.
Line of Sight or Line of Collimation
 • It is a line which passes through the optical centre of the 
objective and intersection of cross hairs and eye-piece.
 • The telescope in which the focusing is done by the exter-
nal movement of either objective or eye-piece is known as 
external focusing telescope and the one in which focus-
ing is done internally with a negative lens is known as 
internal focusing telescope.
Parallax
If the image formed by objective lens is not in the same 
plane with cross-hairs, any movement of the eye is likely to 
cause an apparent movement of the image with respect to 
the cross-hairs. This is called parallax.
Essential Parts of the Telescope
 1. Objective.
 2. Eye-piece.
 3. Diaphragm.
 4. Body and focusing device.
Objective It is a compound lens called achromatic lens. It 
consists of front double convex lens made of crown glass 
and back concave-convex lens made of flint glass. It nearly 
eliminates spherical and chromatic aberrations.
Eye-piece
 • Ramsden eye-piece is commonly used which is composed 
of plano-convex lenses of equal focal length placed at a 
distance of 
2
3
f.
Part III_Unit 12_Chapter 04.indd   2 5/31/2017   4:56:37 PM
      
 • Huygen’s eye-piece composed of plano-convex lenses of 
different focal length placed at a distance of two-third of 
focal length of the larger.
2
3
f
Huygen’s eye-piece
2
3
f
Ramsden eye-piece
Diaphragm It consists of cross-hairs. Horizontal hair 
is used to read the staff and the two vertical hairs enable 
the surveyor to see if the staff is vertical laterally. In stadia 
tacheometry, two more horizontal hairs called stadia hairs 
are provided.
Optical Defects of a Single Lens
Aberrations is the deviation of rays of light.
 1. Spherical aberration: The defect or imperfection 
arising from the form of curvature of the lens in 
which the rays are all not collected exactly at one 
point is called spherical aberration.
 2. Chromatic aberrations:  A beam of light after 
passing through a single lens, is distributed along 
the axis in a series of focal points in which violet ray 
is refracted most and the red is refracted least. This 
defect is called chromatic aberration.
 • The elimination of aberrations is only one of the 
requirements in the design of a telescope.
 • Other possible defects which are of little importance 
are coma, astigmation, curvature, distortion, etc.
Temporary Adjustments of a Level 
or Telescope
 1. Setting up the level
 2. Levelling up with the help of foot screws
 3. Elimination of parallax by two steps:
 (a) Focusing the eye-piece (for distinct vision of 
cross hairs)
 (b) Focusing the objective (for clear image of staff)
Terms and Abbreviations
 1. Station: It is that point where the level rod is held.
 2. Height of instrument (HI): It is the elevation of 
plane of sight with respect to assumed datum.
 3. Back sight (BS): Sight taken on a rod held at a point 
of known elevation. It is also known as a plus sight 
as the back sight reading is always added to the level 
of the datum to get the height of the plane of sight.
 4. Fore sight (FS): Reading taken on a rod held at a 
point of unknown elevation. It is also known as minus 
sight, as the fore sight reading is always subtracted 
from HI to get elevation of the point.
 5. Turning point (TP): is a point on which both minus 
sight and plus sight are taken on a line of direct levels.
 6. Intermediate station (IS): Intermediate point 
between two turning points on which only one sight 
(minus sight) is taken to determine the elevation of 
the station.
Steps in Leveling
 1. To find the amount by which the line of sight is above 
the bench mark.
 2. To know the amount by which the next point is below 
or above the line of sight.
 • Height of instrument, HI = Elevation of BM + BS 
(at BM)
 • Elevation of a point = HI – FS (at that point)
Booking and Reducing Levels
Collimation or Height of Instrument Method
 • Height of the instrument (HI) is calculated for each set-
tling of the instrument.
 • Reduced levels (RL’s) of other stations are calculated 
based on height of the instrument.
 • Generally used for fly leveling or to establish BMs.
 • This method is not suitable when there are intermediate 
points.
Check: SBS - SFS = Last RL - First RL
Rise and Fall Method
 • Difference of level between consecutive points is found 
by comparing the staff readings.
 • Higher staff reading indicates fall and lesser indicates 
rise.
 • Generally used in contour survey.
 • Used when a number of Intermediate station readings are 
required and provides a complete check for intermediate 
sights.
Check: SBS – SFS = S Rise - S Fall 
= Last RL – First RL
Use of Inverted Staff
When the point, whose elevation is much above the line of 
sight (For example, projection from the face of a building, 
underside of beams, girders, arches, etc.) the staff is placed 
inverted with its zero end touching the point. The reading on 
the staff is taken in the usual manner. Such an observation 
Part III_Unit 12_Chapter 04.indd   3 5/31/2017   4:56:37 PM
    
is entered in the level page book with a minus sign for 
convenience. The levels of the points (using inverted staff) 
can be obtained by simply adding the staff readings to the 
height of the instrument.
SOLVED EXAMPLES
Example 1
A back sight reading on BM = 100 m was 2.67 m. The 
inverted staff reading to the bottom of a girder was 1.5 m.
The RL of the bottom of girder is 
(A) 101.17 m (B) 98.83 m
(C) 104.17 m (D) 95.83 m
Solution
Height of the instrument (HI) 
= BM + BS
= 100 + 2.67
= 102.67 m
RL of bottom of girder = HI – FS 
But as the FS is inverted reading FS 
= –1.5 m
RL = 102.67 – (–1.5)
= 104.17 m
Hence, the correct answer is option (C).
Balancing Back Sights and Fore Sights
 • By placing the instrument approximately between two 
successive staff stations in fly leveling the errors due to 
curvature and refraction may be eliminated called balanc-
ing of sights and no correction for the inclination of the 
line of sight is necessary.
 • HI method is more rapid, less tedious and simple and is 
more suitable where it is required to take a number of 
readings from the same instrument setting. 
 • Rise and fall method though tedious provide a full check 
in calculations for all sights. 
Curvature and Refraction
 1. Correction for curvature (C
c
)—negative: Because 
of the curvature of the earth, the staff reading is 
more and object appears to be lower than it really is. 
Therefore correction is negative.
   Correction for curvature,
C
c
 = 
d
R
2
2
(–ve)
  Where 
    d = Horizontal distance between station and the 
point along line of sight 
   R = Radius of earth, 6370 km (in same unit as d)
		 	 ? C
c
 = 0.07849d
2
 metres (d in km) 
 2. Correction for refraction (C
r
)—positive:
 • Refraction curve is irregular because of varying 
atmospheric conditions, but for average conditions 
it is assumed to have a diameter about 7 (diameter 
of earth).
C
r
 = 
1
72
2
d
R
?
?
?
?
?
?
(+ve)
									= 0.01121d
2
 meters (d in km) 
 3. Combined correction due to curvature and 
refraction (C):
C
d
R
d
R
C
d
R
dd
=-
=
?
?
?
?
?
22
2
2
2
1
72
6
72
0 06728 .( metres  in km)
 4. Distance to the visible horizon (d): This takes both 
curvature and refraction into account 
d
C
=
0 06728 .
 km
  Where, C = Combined correction in metres
A d P
B
C
O
Example 2
Find the combined correction for curvature and refraction 
for distance of 2.1 km (in metres).
(A) 0.296 (B) 0.049
(C) 0.112 (D) 0.483
Solution
C = 0.06728d
2
 metres 
    = 0.06728 (2.1)
2
C = 0.296 m
Hence, the correct answer is option (A).
Example 3
The observer standing on the deck of a ship just sees a light 
house. The top of the light house is 52 metres above the sea 
Part III_Unit 12_Chapter 04.indd   4 5/31/2017   4:56:37 PM
Page 5


 ? Levelling and trigonometric levelling
 ? Tacheometry
 ? Contouring
CHAPTER HIGHLIGHTS
LeveLLing anD Trigonometric 
LeveLLing
Introduction
Levelling is a branch of surveying which works with the 
objective of fi nding or establishing the elevation of points. 
This chapter deals with measurements in a vertical plane.
Object of Levelling
 1. To fi nd the elevations of given points with respect to 
a given or assumed datum—to enable works to be 
designed.
 2. To establish points at a given elevation or at diff erent 
elevations with respect to a given or assumed datum—
to set out all kinds of engineering works.
Fundamental De? nitions
 • Level surface: is defi ned as a curved surface which at 
each point is perpendicular to the direction of gravity at the 
point. The surface of a still water is a truly level surface. 
Any surface parallel to the mean spheroidal surface of the 
earth is, therefore, a level surface.
 • Level line: It is a line lying on the level surface. It is 
therefore, normal to the plumb line at all points.
 • Horizontal plane: It is a plane tangential to the level sur-
face at that point and is therefore perpendicular to the 
plumb line through the point.
 • Horizontal line: It is a straight line tangential to the level 
line at a point and it is also perpendicular to the plumb 
line.
 • Vertical line: It is line normal to the level line at a 
point. It is commonly considered to be the line defined 
by a plumb line.
 • Datum: It is any surface to which elevations are referred. 
Mean sea level aff ords a convenient datum all over the 
world.
 • Elevation: Vertical distance above or below an arbitrarily 
assumed level surface or datum.
 • Vertical angle: It is an angle between two intersecting 
lines in a vertical plane.
 • Mean sea level: A verage height of the sea for all stages of 
the tides. It is derived by averaging the hourly tide heights 
over a long period of 19 years.
 • Bench mark: It is a relatively permanent point of ref-
erence whose elevation with respect to some assumed 
datum is known and used as a starting point for leveling 
or as a point upon which to close as a check.
Methods of Levelling
Three methods of leveling are used for determining diff er-
ence in elevation.
 1. Barometric levelling: makes use of the phenomenon 
that diff erence in elevation between two points 
is proportional to the diff erence in atmospheric 
pressures at these points.
Levelling and Contouring
Part III_Unit 12_Chapter 04.indd   1 5/31/2017   4:56:36 PM
    
 2. Trigonometric levelling (indirect levelling): It is the 
process of leveling in which the elevations of points 
are computed from the vertical angles and horizontal 
distances measured in the field. In a modified form 
called ‘stadia levelling’ is commonly used in 
mapping.
 3. Spirit levelling (direct leveling) A spirit level and 
sighting device (telescope) are combined and vertical 
distances are measured by observing on graduated 
rods placed on the points. It is the most precise 
method of determining elevations and the one most 
commonly used by engineers.
Levelling Instruments
Level
It is to provide a horizontal line of sight. It consists of four 
parts.
 1. A telescope to provide line of sight.
 2. A level tube to make the line of sight horizontal.
 3. A levelling head (tribrach and trivet stage) to bring 
the bubble in its centre of run.
 4. A tripod to support the instrument.
  Chief types of levels are:
Dumpy Level
 • This name originated from the fact that formerly this 
level was equipped with an inverting eye-piece and hence 
was shorter than wye level of the same magnifying power.
 • Levelling head generally consists of two parallel plates 
with 3 or 4 foot screws. The upper plate is known as 
tribrach and the lower plate is known as trivet.
Advantages of dump level over wye level:
 1. Simpler construction with fewer movable parts.
 2. Fewer adjustments to be made.
 3. Longer life of the adjustments.
Wye or Y Level
 • In dumpy level, telescope is fixed to the spindle and bub-
ble tube must be of reversible type. While in wye level, 
the telescope is carried in two vertical ‘wye’ supports and 
bubble tube may be attached either to the telescope or to 
the stage carrying the wyes.
 • Advantage of wye level over dumpy level is that the 
adjustments can be tested with greater rapidity and ease.
Reversible Level Combines the features of both the dumpy 
and wye level. For testing and making the adjustments, 
telescope can be taken out and reversed end for end.
Tilting Level The line of sight and the vertical axis need 
not be exactly perpendicular to each other. This feature 
helps in quick levelling.
 • This is mainly designed for precise levelling work.
 • Its advantage is that it can be done more quickly, but it is 
not so apparent when many readings are taken from one 
instrument setting.
Levelling Staff
It is a rectangular rod having graduations. It is used to estab-
lish a horizontal line of sight and to determine the amount 
by which the station is above or below the line of sight.
 1. Solid staff
 2. Folding staff
 3. Telescopic staff
Each metre is sub divided into 200 divisions, the thickness 
of graduations being 5 mm and painted in alternate black 
and white with 5 mm thickness each.
Surveying Telescope
 • This telescope employs two convex lenses. One nearest to 
object is called objective and other near to eye is called 
the eye-piece.
 • Object glass provides a real inverted image infront of eye-
piece, while the eye-piece magnifies the image to produce 
an inverted virtual image.
Line of Sight or Line of Collimation
 • It is a line which passes through the optical centre of the 
objective and intersection of cross hairs and eye-piece.
 • The telescope in which the focusing is done by the exter-
nal movement of either objective or eye-piece is known as 
external focusing telescope and the one in which focus-
ing is done internally with a negative lens is known as 
internal focusing telescope.
Parallax
If the image formed by objective lens is not in the same 
plane with cross-hairs, any movement of the eye is likely to 
cause an apparent movement of the image with respect to 
the cross-hairs. This is called parallax.
Essential Parts of the Telescope
 1. Objective.
 2. Eye-piece.
 3. Diaphragm.
 4. Body and focusing device.
Objective It is a compound lens called achromatic lens. It 
consists of front double convex lens made of crown glass 
and back concave-convex lens made of flint glass. It nearly 
eliminates spherical and chromatic aberrations.
Eye-piece
 • Ramsden eye-piece is commonly used which is composed 
of plano-convex lenses of equal focal length placed at a 
distance of 
2
3
f.
Part III_Unit 12_Chapter 04.indd   2 5/31/2017   4:56:37 PM
      
 • Huygen’s eye-piece composed of plano-convex lenses of 
different focal length placed at a distance of two-third of 
focal length of the larger.
2
3
f
Huygen’s eye-piece
2
3
f
Ramsden eye-piece
Diaphragm It consists of cross-hairs. Horizontal hair 
is used to read the staff and the two vertical hairs enable 
the surveyor to see if the staff is vertical laterally. In stadia 
tacheometry, two more horizontal hairs called stadia hairs 
are provided.
Optical Defects of a Single Lens
Aberrations is the deviation of rays of light.
 1. Spherical aberration: The defect or imperfection 
arising from the form of curvature of the lens in 
which the rays are all not collected exactly at one 
point is called spherical aberration.
 2. Chromatic aberrations:  A beam of light after 
passing through a single lens, is distributed along 
the axis in a series of focal points in which violet ray 
is refracted most and the red is refracted least. This 
defect is called chromatic aberration.
 • The elimination of aberrations is only one of the 
requirements in the design of a telescope.
 • Other possible defects which are of little importance 
are coma, astigmation, curvature, distortion, etc.
Temporary Adjustments of a Level 
or Telescope
 1. Setting up the level
 2. Levelling up with the help of foot screws
 3. Elimination of parallax by two steps:
 (a) Focusing the eye-piece (for distinct vision of 
cross hairs)
 (b) Focusing the objective (for clear image of staff)
Terms and Abbreviations
 1. Station: It is that point where the level rod is held.
 2. Height of instrument (HI): It is the elevation of 
plane of sight with respect to assumed datum.
 3. Back sight (BS): Sight taken on a rod held at a point 
of known elevation. It is also known as a plus sight 
as the back sight reading is always added to the level 
of the datum to get the height of the plane of sight.
 4. Fore sight (FS): Reading taken on a rod held at a 
point of unknown elevation. It is also known as minus 
sight, as the fore sight reading is always subtracted 
from HI to get elevation of the point.
 5. Turning point (TP): is a point on which both minus 
sight and plus sight are taken on a line of direct levels.
 6. Intermediate station (IS): Intermediate point 
between two turning points on which only one sight 
(minus sight) is taken to determine the elevation of 
the station.
Steps in Leveling
 1. To find the amount by which the line of sight is above 
the bench mark.
 2. To know the amount by which the next point is below 
or above the line of sight.
 • Height of instrument, HI = Elevation of BM + BS 
(at BM)
 • Elevation of a point = HI – FS (at that point)
Booking and Reducing Levels
Collimation or Height of Instrument Method
 • Height of the instrument (HI) is calculated for each set-
tling of the instrument.
 • Reduced levels (RL’s) of other stations are calculated 
based on height of the instrument.
 • Generally used for fly leveling or to establish BMs.
 • This method is not suitable when there are intermediate 
points.
Check: SBS - SFS = Last RL - First RL
Rise and Fall Method
 • Difference of level between consecutive points is found 
by comparing the staff readings.
 • Higher staff reading indicates fall and lesser indicates 
rise.
 • Generally used in contour survey.
 • Used when a number of Intermediate station readings are 
required and provides a complete check for intermediate 
sights.
Check: SBS – SFS = S Rise - S Fall 
= Last RL – First RL
Use of Inverted Staff
When the point, whose elevation is much above the line of 
sight (For example, projection from the face of a building, 
underside of beams, girders, arches, etc.) the staff is placed 
inverted with its zero end touching the point. The reading on 
the staff is taken in the usual manner. Such an observation 
Part III_Unit 12_Chapter 04.indd   3 5/31/2017   4:56:37 PM
    
is entered in the level page book with a minus sign for 
convenience. The levels of the points (using inverted staff) 
can be obtained by simply adding the staff readings to the 
height of the instrument.
SOLVED EXAMPLES
Example 1
A back sight reading on BM = 100 m was 2.67 m. The 
inverted staff reading to the bottom of a girder was 1.5 m.
The RL of the bottom of girder is 
(A) 101.17 m (B) 98.83 m
(C) 104.17 m (D) 95.83 m
Solution
Height of the instrument (HI) 
= BM + BS
= 100 + 2.67
= 102.67 m
RL of bottom of girder = HI – FS 
But as the FS is inverted reading FS 
= –1.5 m
RL = 102.67 – (–1.5)
= 104.17 m
Hence, the correct answer is option (C).
Balancing Back Sights and Fore Sights
 • By placing the instrument approximately between two 
successive staff stations in fly leveling the errors due to 
curvature and refraction may be eliminated called balanc-
ing of sights and no correction for the inclination of the 
line of sight is necessary.
 • HI method is more rapid, less tedious and simple and is 
more suitable where it is required to take a number of 
readings from the same instrument setting. 
 • Rise and fall method though tedious provide a full check 
in calculations for all sights. 
Curvature and Refraction
 1. Correction for curvature (C
c
)—negative: Because 
of the curvature of the earth, the staff reading is 
more and object appears to be lower than it really is. 
Therefore correction is negative.
   Correction for curvature,
C
c
 = 
d
R
2
2
(–ve)
  Where 
    d = Horizontal distance between station and the 
point along line of sight 
   R = Radius of earth, 6370 km (in same unit as d)
		 	 ? C
c
 = 0.07849d
2
 metres (d in km) 
 2. Correction for refraction (C
r
)—positive:
 • Refraction curve is irregular because of varying 
atmospheric conditions, but for average conditions 
it is assumed to have a diameter about 7 (diameter 
of earth).
C
r
 = 
1
72
2
d
R
?
?
?
?
?
?
(+ve)
									= 0.01121d
2
 meters (d in km) 
 3. Combined correction due to curvature and 
refraction (C):
C
d
R
d
R
C
d
R
dd
=-
=
?
?
?
?
?
22
2
2
2
1
72
6
72
0 06728 .( metres  in km)
 4. Distance to the visible horizon (d): This takes both 
curvature and refraction into account 
d
C
=
0 06728 .
 km
  Where, C = Combined correction in metres
A d P
B
C
O
Example 2
Find the combined correction for curvature and refraction 
for distance of 2.1 km (in metres).
(A) 0.296 (B) 0.049
(C) 0.112 (D) 0.483
Solution
C = 0.06728d
2
 metres 
    = 0.06728 (2.1)
2
C = 0.296 m
Hence, the correct answer is option (A).
Example 3
The observer standing on the deck of a ship just sees a light 
house. The top of the light house is 52 metres above the sea 
Part III_Unit 12_Chapter 04.indd   4 5/31/2017   4:56:37 PM
      
level and the height of the observers’ eye is 5 metres above 
the sea level. Find the distance of the observer from the light 
house.
(A) 26.9 km (B) 36.42 km
(C) 41.6 km (D) 45.32 km
Solution
Let A be position of top of light house at 52 m above ground 
and B be position of observers’ eye at 5 m above ground.
C
1
 = 52 m C
2
 = 5 m
We know d = 
C
0 06728 .
km
d
1
 =
52
0 06728 .
				= 27.8 km 
d
2
 = 
5
0 06728 .
= 8.62 km 
\ Distance between A and B 
= d
1
 + d
2
= 36.42 km.
Hence, the correct answer is option (B).
d
1
 
d
2
 
A O 
B  
C'
A'
B'
O'
Types of Levelling
Differential Levelling
 • The direct leveling which is used to determine the eleva-
tion or difference in elevation of points at some distance 
apart regardless of their horizontal positions is called dif-
ferential leveling.
 • It is also known as fly leveling 
Reciprocal Levelling
When it is necessary to carry levelling across a river or any 
instance requiring a long sight between two points so situ-
ated that no place for the level can be found from which 
lengths of FS and BS will be even approximately equal, spe-
cial method, i.e., reciprocal levelling must be used to obtain 
accuracy. 
This method eliminates:
 1. Error in instrument adjustment.
 2. Combined effect of earth’ s curvature and refraction of 
the atmosphere.
 3. Variations in the average refraction.
The true difference in elevation (H) is equal to the mean of 
the two apparent differences in elevation, obtained by recip-
rocal observations.
Horizontal line
Horizontal line
Level line
Level line
Line of sight
Line of sight
River
River
A
A
ha
B
e hb
h
1
a
h
1
b
B
Reciprocal levelling
 •
Hh hh h
ab a b
=- +-
() {}
1
2
11
()
  Where
  h
a
, h
b
 = Staff readings at A and B when staff is close 
to A
  h
1
a
, h
1
b
 = Staff readings at A and B when staff is 
close to B
 •
Hh hh h
ab a b
=- +- ()
{}
1
2
11
()
 • Total error, eh hh h
ab a b
=- -- ()
{}
1
2
11
()
Total error includes line of collimation error, curvature 
error and refraction error, e = e
col
 + e
cur
 - e
ref 
.
Example 4
Two points A and B are 1720 m apart across a wide river. 
The following reciprocal levels are taken with one level:
Level
Readings on
A B
A 3.165 3.810
B 0.810 2.365
Calculate the true difference of level between A and B
(A) 1.9 m (B) 1.5 m
(C) 1.1 m (D) 0.9 m
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