1. Trignometric Levelling

2. Shree swami atmanand saraswati & Institute of technology
Name En.no.
Patel Jignesh
Patel Urmil
Patel Yash
Vaghani Prince
Ramani Kishan
Subject: Surveying Submited to:
Prof. Darshika Mam

3. Contents:
-Trignometric levelling -Methods of Observation 1)Direct Method 2)Reciprocal Method -Methods Of Determining The Elevation Of Point By Theodolite

4. INTRODUCTION Definition:
-“ Trigonometric levelling is the process of determining the differences of elevations of stations from observed vertical angles and known distances. ”
-The vertical angles are measured by means of theodolite.
-The horizontal distances by instrument
-Relative heights are calculated using trigonometric functions.
-If the distance between instrument station and object is small. correction for earth's curvature and refraction is not required.

6. Direct Method Reciprocal Method
- When the observation is made from one station it is called as direct method. It is also known as single observation. -When the observation are made from both sattion then it is called as reciprocal method. -It is preferred rather than direct method because uncertain refraction are eliminated.
Reciprocal Method

7. METHODS OF DETERMINING THE ELEVATION OF A POINT BY THEODOLITE:
Case 1. Base of the object accessible
Case 2. Base of the object inaccessible, Instrument stations in the vertical plane as the elevated object.
Case 3. Base of the object inaccessible, Instrument stations not in the same vertical plane as the elevated object.

8. Case 1. Base of the object accessible
A = Instrument station
B = Point to be observed
h = Elevation of B from the
instrument axis
D = Horizontal distance between A and the base of object h1 = Height of instrument (H. I.)
Bs = Reading of staff kept on B.M.
= Angle of elevation = L BAC
h = D tan 
R.L. of B = R.L. of B.M. + Bs + h
= R.L. of B.M. + Bs + D. tan 
If distance is large than add Cc & Cr
R.L. of B = R.L. of B.M. + Bs + D. tan  D2

9. Case 2. Base of the object inaccessible, Instrument stations in the vertical plane as the elevated object.
There may be two cases.
Instrument axes at the same level
Instrument axes at different levels.
1) Height of instrument axis never to the object is lower:
2) Height of instrument axis to the object is higher:

10. Instrument axes at the same level
Case 2. Base of the object inaccessible, Instrument stations in the vertical plane as the elevated object.
Instrument axes at the same level
 PAP, h= D tan 1
 PBP, h= (b+D) tan 2
D tan 1 = (b+D) tan 2
D tan 1 = b tan 2 + D tan 2
D(tan 1 - tan 2) = b tan 2
R.L of P = R.L of B.M + Bs + h

11. Instrument axes at different levels.
1) Height of instrument axis never to the object is lower:
 PAP, h1 = D tan 1
 PBP, h2 = (b+D) tan 2
hd is difference between two height
hd = h1 – h2
hd = D tan 1 - (b+D) tan 2
= D tan 1 - b tan 2 -D tan 2
hd = D(tan 1 - tan 2) - b tan 2
hd + b tan 2 = D(tan 1 - tan 2)
h1 = D tan 1

12. Instrument axes at different levels.
2) Height of instrument axis to the object is higher:
 PAP, h1 = D tan 1
 PBP, h2 = (b+D) tan 2
hd is difference between two height
hd = h2 – h1
hd = (b+D) tan 2 - D tan 1
= b tan 2 + D tan 2 - D tan 1
hd = b tan 2 + D (tan 2 - tan 1 )
hd - b tan 2 = D(tan 2 - tan 1)
- hd + b tan 2 = D(tan 1 - tan 2)
h1 = D tan 1

13. Case 3. Base of the object inaccessible, Instrument stations not in the same vertical plane as the elevated object.
Set up instrument on A
Measure 1 to P
L BAC = 
Set up instrument on B
Measure 2 to P
L ABC = 
L ACB = 180 – (  +  )
Sin Rule:
BC=
b· sin
sin{180˚ - (+ )}
AC=
b· sin
sin{180˚ - ( + 
h1 = AC tan 1
h2 = BC tan 2

14. Thank You