Levelling may be defined as the art of determining the relative heights or elevations of points or objects on the earth’s surface. It deals with measurements in a vertical plane.

Levelling is done for following purpose:
  • To prepare contour map for fixing sites for reservoirs, dams, barrages, etc. and fix the alignment of roads, railways, irrigation canals, and so on.
  • To determine the altitudes of different important points on a hill or to know the reduced levels of different points on or below the surface of the earth.
  • To prepare the longitudinal section and cross sections of a project i.e. roads railways, irrigation canals etc. in order to determine the volume of the earth work.
  • To prepare layout map for water supply, sanitary or drainage schemes.
Instrument use for levelling:



 Thedolite
 Dumpy Level
 Levelling Staff
 Measuring Tape

        

Common Definitions of Terms used in Levelling:

      Bench Mark (BM): It is a fixed reference point of know elevation. These are very important marks. They serve as reference points for finding the RL ( Reduced Level ) of new points or for conducting levelling operations in projects involving in roads, railways etc. There are four kind of bench marks

·  G. T. S. (Greater Trigonometrically Survey) Bench Marks: They are the bench marks established with very high precision at intervals all over the country by the survey of India department, and their positions and elevations above the standard datum (mean sea level at Karachi) are given in the catalogue published by that department. They are also known as G.T.S. maps.

·  Permanent Bench Marks: These are fixed points or marks established by different government departments like PWD, Railways, Irrigation, etc. The Reduced Levels (RL) of these points are determined with reference to the GTS bench marks and are kept on permanent points like the plinth of building, parapet of a bridge or culvert,  and so on. Sometimes they are kept on underground pillars.

·   Arbitrary Bench Marks: They are the reference points whose elevations are arbitrarily assumed. They are used in small levelling operations.

·  Temporary Bench Marks: When the bench marks are established temporarily at the end of a day’s work, they are said to be temporary bench marks. They are generally made on the root of tree, the parapet of a nearby culvert, a furlong post, or on similar place.


Back sight reading (B.S.): This is first staff reading taken in any setup of the instrument after the levelling has been perfectly done. This reading is always taken on a point of known Reduce Level i.e. on a bench-mark or change point.

Foresight reading (F.S.): It is the last staff reading in any set up of the instrument, and indicates the shifting of the instrument.

Intermediate sight (I.S.): It is any other staff reading between the BS (back sight) FS (foresight) in the same setup of the instrument.

Change point (C.P.): This point indicates the shifting of the instrument. At this point, an FS (foresight) is taken from one setting and a BS (back sight) from next setting. Any stable and well defined object such as a boundary stone, curb stone, rail, rock etc is used as change point.

Height of Instrument (H. I.): When the levelling instrument is properly leveled, the RL (reduced level) of the line of collimation is known as the height of the instrument. This is obtained by adding the BS (back sight) reading the RL (reduced level) of the BM (benchmark) or CP (change point) on which the staff reading was taken.

Type of Levelling:

Simple levelling : When the difference of level between two points is determind by setting the levelling instrument midway between the two points, the process is called simple levelling. 



Suppose A and B are two points whose difference of level is to to be determined. The level is set up at O exactly mid-way between A and B. After proper temporary adjustment the staff reading on A and B are taken. The difference of these readings gives the difference of level A and B. Let the respective readings on A and B be 2.340 and 3.135 m. The difference between these readings gives the difference of level between A and B, which is equal to 3.135 – 2.340 = 0.795 m.
If the R.L. ( Reduce Level ) of A is 100, the R.L. ( Reduce Level ) of B may be found thus :
H.I. ( Height Of Instrument ) at O = 100 + 2.340 = 102.340.

R.L. ( Reduce Level ) at B = 102.340 – 3.135 = 99.205.

Differential Levelling : Differential levelling is used in order to find the difference in elevation between two points when I) the points are a greate distance apart. II) The differences of elevation between the points is large. III) There are obstacles between the points.
This method is also know as compound levelling or continuous levelling. In this method the level is set up at several suitable positions and staff reading are taken at all of these. 


Suppose it is required to know the differences of level between A and B. The level is setup at points O1,O2,O3 etc. After temporary adjustment staff reading are taken at every setup. The points C1,C2 and C3 are known as change points. Then the difference of level between A and B is found out. If the difference is positive, A is lowe than B. If it is negative, A is higher than B.
Knowing the R.L. ( Reduce Level ) of A, that of B can be calculated.

Method Of Calculation Of Reduced Level

There are two types

        A) The collimation system or height of instrument system

        B) The rise and fall system

The collimation system or height of instrument system


The reduced level of the line of collimation is said to be the height of the instrument. In this system, the height of the line of collimation is found out by adding the backsight reading to the Reduced level (RL) of the Bench mark (BM) on which the backsight (BS) is taken. Then the reduced level (RL) of the intermediate points and the change point  (CP) are obtained by subtracting the respective staff readings from the height of instrument ( H.I).
The level is then shifted for the next setup and again the height of the line of collimation is obtained by adding the backsight reading to the Reduced level ( RL ) of the change point (which is calculated in the first setup).
So the height of the instrument is different in different setup of the level. Two adjacent planes of collimation are correlated at the change point by an Foresight (FS) reading from one setting and a Backsight (BS) reading from the  next setting.
It should be remembered that in this system the reduced level (RL) of unknown points are to be found out by deducting the staff readings from the reduced level (RL) of the height of the instrument.



The rise and fall system

In this system the difference of level between two consecutive points is determined by comparing each forward staff reading with the staff reading at the immediately preceding point.
If the forward staff reading is smaller than the immediately preceding staff reading, a rise is said to have occurred. The rise is added to the reduce level (RL) of the preceding point to get the reduce level (RL) of the forward point.
If the forward staff reading is Greater than the immediately preceding staff reading, It means there has been fall. The fall is subtracted from the reduce level (RL) of the preceding point to get the reduce level (RL) of the forward point.
        
Example :

The following consecutive readings were taken with a dumpy level along a chain line at a common interval of 15 m. The first reading was at a chainage of 165 m where the Reduce Level (RL) is 98.085. The instrument was shifted after the fourth and ninth reading.
3.150, 2.245, 1.125, 0.860, 3.125, 2.760, 1.835, 1.470, 1.965, 1.225, 2.390, 3.035 m.
Mark rules on a page of your notebook in the form of a level book page and enter on it the above readings and find the reduce level (RL) of all the points.

1 By the collimation system
Station point
Chainage
Backsight
Intermediate sight
Forsight
RL of collimation line or height of instrument (HI)
Reduced Level (RL)
Remark
1
165
3.150
-
-
101.235
98.085
2
180
-
2.245
-
-
98.990
3
195
-
1.125
-
-
100.110
4
210
3.125
-
0.860
103.500
100.375
Change Point
5
225
-
2.760
-
-
100.740
6
240
-
1.835
-
-
101.665
7
255
-
1.470
-
-
102.030
8
270
1.225
-
1.965
102.760
101.535
Change Point
9
285
-
2.390
-
-
100.370
10
300
-
-
3.035
-
99.725
Total =                   7.500
  5.860

Arithmetical Check:
                                ∑ = Back Sight (BS) ― ∑ = Fore Sight (FS)
                                                     7.500 ― 5.860 = + 1.640
                       Last Reduce level RL ― 1st Reduce level
                                           99.725 ― 99.085 = + 1.640
Example :

The following consecutive readings were taken with a dumpy level along a chain line at a common interval of 15 m. The first reading was at a chainage of 165 m where the Reduce Level (RL) is 98.085. The instrument was shifted after the fourth and ninth reading.
3.150, 2.245, 1.125, 0.860, 3.125, 2.760, 1.835, 1.470, 1.965, 1.225, 2.390, 3.035 m.
Mark rules on a page of your notebook in the form of a level book page and enter on it the above readings and find the reduce level (RL) of all the points.

2. By the rise and fall system

Station point
Chainage
Backsight
Intermediate sight
Forsight
Rise   +
Fall -
Reduced Level (RL)
Remark
1
165
3.150
-
-
-
-
98.085
2
180
-
2.245
-
0.905
98.990
3
195
-
1.125
-
1.120
100.110
4
210
3.125
-
0.860
0.265
100.375
Change Point
5
225
-
2.760
-
0.365
100.740
6
240
-
1.835
-
0.925
101.665
7
255
-
1.470
-
0.365
102.030
8
270
1.225
-
1.965
-
0.495
101.535
Change Point
9
285
-
2.390
-
-
1.165
100.370
10
300
-
-
3.035
-
0.645
99.725
Total =                    7.500                                 5.860        3.945    2.305
Arithemetical Check : 
                                  ∑ = Back Sight (BS) ― ∑ = Fore Sight (FS)
                                                     7.500 ― 5.860 = + 1.640
                                  ∑ = Rise ― ∑ = Fall
                                         3.945 – 2.305 = + 1.640
                                    Last Reduce Level (RL) – 1st Reduce Level
                                                           99.275 – 98.085 = + 1.640

Reading the Staff:

First note the red figure, then the black figure, and finally count the spaces. Record the reading.