PPT: Levelling & Contouring | Geomatics Engineering (Surveying) - Civil Engineering (CE) PDF Download

 Page 1


Levelling & Contouring
Welcome to this comprehensive presentation on Levelling and Contouring, 
two fundamental concepts in surveying and civil engineering. Throughout 
these slides, we'll explore the key definitions, methods, and calculations 
essential for accurate land measurement and topographical 
representation.
We'll begin with basic levelling concepts, examine arithmetic checks and 
reciprocal levelling, then move to corrections for curvature and refraction, 
and finally cover contouring techniques. This knowledge forms the 
foundation for all types of construction and infrastructure projects.
Page 2


Levelling & Contouring
Welcome to this comprehensive presentation on Levelling and Contouring, 
two fundamental concepts in surveying and civil engineering. Throughout 
these slides, we'll explore the key definitions, methods, and calculations 
essential for accurate land measurement and topographical 
representation.
We'll begin with basic levelling concepts, examine arithmetic checks and 
reciprocal levelling, then move to corrections for curvature and refraction, 
and finally cover contouring techniques. This knowledge forms the 
foundation for all types of construction and infrastructure projects.
Levelling Fundamentals
Reduced Level
The elevation of a point with respect to either Mean Sea Level (MSL) or with respect to 
a fixed point of known height is called reduced level.
Bench Mark
A relatively permanent point of reference whose elevation with respect to some 
assumed datum is known. Used as a starting point for leveling or as a check point.
Sight Types
Back sight: First reading taken after setting up the instrument (plus sight). Fore sight: 
Last reading taken from an instrument station (minus sight). Intermediate sight: All 
readings between back and fore sights.
Height of Instrument
The Reduced Level (RL) of line of sight of the instrument set up at different stations. 
H.I = R.L + B.S and R.L = H.I 3 F.S
Page 3


Levelling & Contouring
Welcome to this comprehensive presentation on Levelling and Contouring, 
two fundamental concepts in surveying and civil engineering. Throughout 
these slides, we'll explore the key definitions, methods, and calculations 
essential for accurate land measurement and topographical 
representation.
We'll begin with basic levelling concepts, examine arithmetic checks and 
reciprocal levelling, then move to corrections for curvature and refraction, 
and finally cover contouring techniques. This knowledge forms the 
foundation for all types of construction and infrastructure projects.
Levelling Fundamentals
Reduced Level
The elevation of a point with respect to either Mean Sea Level (MSL) or with respect to 
a fixed point of known height is called reduced level.
Bench Mark
A relatively permanent point of reference whose elevation with respect to some 
assumed datum is known. Used as a starting point for leveling or as a check point.
Sight Types
Back sight: First reading taken after setting up the instrument (plus sight). Fore sight: 
Last reading taken from an instrument station (minus sight). Intermediate sight: All 
readings between back and fore sights.
Height of Instrument
The Reduced Level (RL) of line of sight of the instrument set up at different stations. 
H.I = R.L + B.S and R.L = H.I 3 F.S
Arithmetic Checks in Levelling
Rise and Fall Method
The sum of back sights minus the sum of fore sights equals 
the sum of rises minus the sum of falls, which equals the last 
reduced level minus the first reduced level.
3B.S - 3F.S = 3Rise - 3Fall = Last R.L 3 First R.L
Height of Instrument Method
The sum of back sights minus the sum of fore sights equals 
the last reduced level minus the first reduced level.
3B.S - 3F.S = Last R.L 3 First R.L
Reciprocal Levelling
Used when it's difficult to set up the instrument midway 
between two points. Accounts for two types of errors: X (error 
due to inclined line of sight) and e (error due to curvature and 
refraction).
Page 4


Levelling & Contouring
Welcome to this comprehensive presentation on Levelling and Contouring, 
two fundamental concepts in surveying and civil engineering. Throughout 
these slides, we'll explore the key definitions, methods, and calculations 
essential for accurate land measurement and topographical 
representation.
We'll begin with basic levelling concepts, examine arithmetic checks and 
reciprocal levelling, then move to corrections for curvature and refraction, 
and finally cover contouring techniques. This knowledge forms the 
foundation for all types of construction and infrastructure projects.
Levelling Fundamentals
Reduced Level
The elevation of a point with respect to either Mean Sea Level (MSL) or with respect to 
a fixed point of known height is called reduced level.
Bench Mark
A relatively permanent point of reference whose elevation with respect to some 
assumed datum is known. Used as a starting point for leveling or as a check point.
Sight Types
Back sight: First reading taken after setting up the instrument (plus sight). Fore sight: 
Last reading taken from an instrument station (minus sight). Intermediate sight: All 
readings between back and fore sights.
Height of Instrument
The Reduced Level (RL) of line of sight of the instrument set up at different stations. 
H.I = R.L + B.S and R.L = H.I 3 F.S
Arithmetic Checks in Levelling
Rise and Fall Method
The sum of back sights minus the sum of fore sights equals 
the sum of rises minus the sum of falls, which equals the last 
reduced level minus the first reduced level.
3B.S - 3F.S = 3Rise - 3Fall = Last R.L 3 First R.L
Height of Instrument Method
The sum of back sights minus the sum of fore sights equals 
the last reduced level minus the first reduced level.
3B.S - 3F.S = Last R.L 3 First R.L
Reciprocal Levelling
Used when it's difficult to set up the instrument midway 
between two points. Accounts for two types of errors: X (error 
due to inclined line of sight) and e (error due to curvature and 
refraction).
Reciprocal Levelling Procedure
1 Instrument at Point A
Take readings on staff at point A (hA) and on staff at point B 
(hB). The difference represents the apparent height difference 
plus any errors.
2 Instrument at Point B
Take readings on staff at point A (h'A) and on staff at point B 
(h'B). If the instrument is correct, then hA 3 hB = h'A 3 h'B.
3 Calculate True Readings
The true difference in reduced level between points A and B 
can be calculated by accounting for the systematic errors in 
the measurements.
4 Verify Results
The reciprocal levelling method provides a check on the 
accuracy of the measurements and helps eliminate systematic 
errors.
Page 5


Levelling & Contouring
Welcome to this comprehensive presentation on Levelling and Contouring, 
two fundamental concepts in surveying and civil engineering. Throughout 
these slides, we'll explore the key definitions, methods, and calculations 
essential for accurate land measurement and topographical 
representation.
We'll begin with basic levelling concepts, examine arithmetic checks and 
reciprocal levelling, then move to corrections for curvature and refraction, 
and finally cover contouring techniques. This knowledge forms the 
foundation for all types of construction and infrastructure projects.
Levelling Fundamentals
Reduced Level
The elevation of a point with respect to either Mean Sea Level (MSL) or with respect to 
a fixed point of known height is called reduced level.
Bench Mark
A relatively permanent point of reference whose elevation with respect to some 
assumed datum is known. Used as a starting point for leveling or as a check point.
Sight Types
Back sight: First reading taken after setting up the instrument (plus sight). Fore sight: 
Last reading taken from an instrument station (minus sight). Intermediate sight: All 
readings between back and fore sights.
Height of Instrument
The Reduced Level (RL) of line of sight of the instrument set up at different stations. 
H.I = R.L + B.S and R.L = H.I 3 F.S
Arithmetic Checks in Levelling
Rise and Fall Method
The sum of back sights minus the sum of fore sights equals 
the sum of rises minus the sum of falls, which equals the last 
reduced level minus the first reduced level.
3B.S - 3F.S = 3Rise - 3Fall = Last R.L 3 First R.L
Height of Instrument Method
The sum of back sights minus the sum of fore sights equals 
the last reduced level minus the first reduced level.
3B.S - 3F.S = Last R.L 3 First R.L
Reciprocal Levelling
Used when it's difficult to set up the instrument midway 
between two points. Accounts for two types of errors: X (error 
due to inclined line of sight) and e (error due to curvature and 
refraction).
Reciprocal Levelling Procedure
1 Instrument at Point A
Take readings on staff at point A (hA) and on staff at point B 
(hB). The difference represents the apparent height difference 
plus any errors.
2 Instrument at Point B
Take readings on staff at point A (h'A) and on staff at point B 
(h'B). If the instrument is correct, then hA 3 hB = h'A 3 h'B.
3 Calculate True Readings
The true difference in reduced level between points A and B 
can be calculated by accounting for the systematic errors in 
the measurements.
4 Verify Results
The reciprocal levelling method provides a check on the 
accuracy of the measurements and helps eliminate systematic 
errors.
Corrections for Curvature and 
Refraction
Curvature Correction 
(CC)
CC = -(d²/2R) where d is the 
horizontal distance between 
points and R is the radius of 
earth (6370 km). Simplified: CC 
= -0.07849d² meters (d in 
kilometers).
Refraction Correction 
(CR)
CR = +(1/7)CC, accounting for 
the bending of light rays 
through the atmosphere. This 
partially offsets the curvature 
error.
Combined Correction 
(C)
C = -0.06728d² meters (d in 
kilometers). This formula 
combines both curvature and 
refraction effects for practical 
applications.
Visible Horizon
The distance to the visible 
horizon can be calculated as d 
= 3.8553:c km, where c is the 
height in meters above the 
reference surface.