Download Trigonometric Levelling

Civil Engineering Department
Government Engineering College
Rajkot
Trigonometric Levelling
Submitted To :
Prof. A. K. Gojiya
Submitted By :
Group C2
Members of Group C2
•
Javia Parth(130200106021)
•
Makvana Anil(130200106033)
•
Kachela Raj(130200106023)
•
Maradia Mit(130200106035)
•
Kaklotar Tejas(130200106024)
•
Marvaniya Dhaval(130200106036)
•
Kambodi Dipesh(130200106026)
•
Marvaniya Milan(130200106037)
•
Katariya Darshan(130200106027)
•
Mer Yogesh(130200106038)
•
Kher Jaydip(130200106028)
•
Nakrani Arpit(130200106039)
•
Khokhariya Jenil(130200106029)
•
Patel Pallav(130200106041)
•
Khunt Sagar(130200106030)
•
Patel Sagar(130200106042)
•
Koladiya Jaydeep(130200106031)
•
Barad Rajesh(140203106002)
•
Kothari Shrenik(130200106032)
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
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.
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.
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.

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

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 .
H=Dtan α

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 = 0.06735D2
Where D is in kilometers

Thus , R.L. of R = R.L. of B.M. + h+
Dtan α+C
Base of the Object is Not Accessible
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.
Determination of Height
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
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’

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’)
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.
Types of Indirect Levelling
Indirect Levelling
On A Rough Terrain
On A Steep Slope
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..



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.
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.
Steps:

