1. Civil Engineering Department Government Engineering College Rajkot

2. Trigonometric Levelling
Submitted To : Prof. A. K. Gojiya Submitted By : Group C2

3. Members of Group C2 Javia Parth(130200106021)
Makvana Anil( )
Kachela Raj( )
Maradia Mit( )
Kaklotar Tejas( )
Marvaniya Dhaval( )
Kambodi Dipesh( )
Marvaniya Milan( )
Katariya Darshan( )
Mer Yogesh( )
Kher Jaydip( )
Nakrani Arpit( )
Khokhariya Jenil( )
Patel Pallav( )
Khunt Sagar( )
Patel Sagar( )
Koladiya Jaydeep( )
Barad Rajesh( )
Kothari Shrenik( )

4. Index Introduction Height and Distances Base of the Object Accessible
Base of the Object is Not Accessible
Base of the Object Inaccessible
Determination of Height
Direct Levelling on Steep Ground
Indirect Leveling

5. Introduction
Levelling is a method of determining the relative heights of various points. In direct levelling, the difference of elevations is determined using a levelling instrument. Trigonometric levelling is an indirect method of levelling in which the relative heights of various points are determined from the vertical angles measured with a theodolite and the horizontal distances measured with a tape. The height of an object above the plane of collimation from the observation. Thus, trigonometric levelling is an indirect method of levelling in which the different in elevation of the points is determined from the observation vertical angles and measured distance.

6. Height and Distances
When the distances between the stations is not large, the distances between the stations measured on the surface of earth or computed trigonometrically may be assumed as a plane distance and the amount of correction due to curvature of the earth surface, is ignored. Depending upon the field conditions and the measurements that can be made with the instruments available, the following three cases are involved: Case 1 Base of the object is accessible Case 2 Base of the object inaccessible and instrument stations and the elevated object are in the same vertical plane. Case 3 Base of the object inaccessible and instrument stations and the elevated object are not in the same vertical plane.

7. Base of the Object Accessible
Let it be assumed that the horizontal distance between the instrument and the object can be measured accurately. Let us considered a high object, such as a chimney. let as assume that the base Q of a chimney is assible and the horizontal distance D between the instrument station P and Q can be measured using a tap.

8. Let D=horizontal distance between P and Q
h=reading on the leveling staff held vertically on bench mark with line of sight horizontal
α= angle of elevation for top R
H.I.=height of instrument above ground
R be the top of chimney whose elevation is required
R.L. of instrument axis =R.L. of B.M.+ h, where h is staff reading on the staff held vertically on the B.M.
If the line of collimation intersects the chimney at R’,the distance OR’ is equal to horizontal distance D.
In triangle ORR’,
RR’=Dtan α H=Dtan α
There for the R.L. of the top of the chimney is given by
R.L. of R=R.L. of B.M.+h+Dtan α
If the R.L. of the instrument stations P is given, the R.L. of the instrument axis can be determine as.
R.L of instrument axis =R.L. of P+H.I. where H.I. is height of the instrument .

9. Similarly , if the observation is made from R. we get , PP1 = Dtan α
The true different in elevation is PP2.
Hence we conclude that if the combine correction for curvature and refraction is to be applied linearly , its sign is proactively for the angle of elevation and negative for angle od depression.
As in leveling , the combined correction for curvature and reflection in linear measurement is given by
C = D2
Where D is in kilometers
Thus , R.L. of R = R.L. of B.M. + h+ Dtan α+C

10. Base of the Object is Not Accessible

11. Base of the Object Inaccessible
When the instrument is shifted to the nearby place and the observations are taken from the same level of the line of sight: 
In such case we have to take the two angular observations of the vertical angles. The instrument is shifted to a nearby place of known distance, and then with the known distance between these two and the angular observations from these two stations, we can find the vertical difference in distance between the line of sight of the instrument and the top point of the object.

12. Determination of Height

13. Direct Levelling on Steep Ground
If the ground is quite steep the method of indirect levelling can be used with advantage. The following procedure can be used to determine the difference of elevations between P and R

14. Steps Set up the instrument at a convenient station O1 on the line PR
Make the line of collimation roughly parallel to the slope of the ground clamp the telescope
Take a back sight PP’ on the staff held at P. also measure the vertical angle α1 to P’ determine R.L. of P + PP’
Take a foresight QQ’ on the staff held at the turning point Q, without changing the vertical angle α1 . Measure the slope
Distance PQ between P and Q
R.L. of Q = RL of P’ + PQ sin α1 – QQ’

15. Shift the instrument to the station O2 midway between Q and R
Shift the instrument to the station O2 midway between Q and R. make the lien of collimation roughly parallel to the slope of the grounds clamp the telescope
Take a back sight QQ’’ on the staff held at the turning point Q measure the vertical angle α2
R.L of R = R.L. of Q + QQ’’
Take a foresight RR’ on the staff held at the point R without changing the vertical angle α2 measure the sloping distance QR
R.L. of R = R.L. OF Q’’ + QR sinα2 – RR’
Thus R.L. of R = (R.L. of P + PP’ +PQ SIN α1 –QQ’) + QQ’’ +(QR sin α2-RR’)

16. Indirect Leveling
Trigonometric or indirect levelling is the process of levelling in which elevation of points are computed from the vertical angles and horizontal distance measure in the field just as length of any side in any triangle can be computed from proper trigonometric relation.
In a modified from stadia levelling commonly used in mapping both the different in elevation and horizontal distance between the point are directly computed from measure vertical angle and staff reading.

17. Types of Indirect Levelling
On A Rough Terrain
On A Steep Slope

18. Indirect Leveling On A Rough Terrain
On a rough terrain, indirect levelling can be used to determine the difference of elevations of two points which are quite apart.
Let difference of elevation of two points P and Q is required..

22. Limitations
Indirect levelling is not as accurate as direct levelling with a levelling instrument. This method is used in rough country.
If backsight and foresight distances are approximately equal, the effectof curvature and refraction is eliminated.

23. Indirect Levelling On A Steep Slope
If the ground is quite steep, the method of indirect levelling can be used with advantage.
The following procedure can be used to determine the difference of elevations and between P and R.

24. Steps:

26. Thank You