ept 11 & 12 trigonometric-levelling

8/18/2019 Ept 11 & 12 Trigonometric-Levelling

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KITSW-Civil Engineering Department

EXPERIMENT – 11

SINGLE PLANE METHODAIM: Determination of elevation of the object

Apparatus: Theodolite, tripod, levelling sta, plumb bob, measurement tape.

Theory:

TRIGINOMETRIC LEVELLING

This is an indirect method of levelling. In this method the dierence in elevation of the points is determined from the

observed vertical angles and measured distances. The vertical angles are measured with a transit theodolite and The distances are measured directl !plane surveing" or computed

trigonometricall !geodetic surve". Trigonometric levelling is commonl used in topographical wor# to $nd out the

elevation of the top of buildings, chimnes, church spires, and so on. Also, it can be used to its advantage in di%cult terrains such as mountaineous

areas. Depending upon the $eld conditions and the measurements that can be made with

the instruments available, there can be innumerable cases.

Assuming the instrument stations and the object to be in the same vertical plane, thefollowing two cases arise.

Determination of elevation of object when the bae i inacceible ! theIntr"ment #tation an$ the Elevate$ Object are in the #ame Vertical %lane

If the hori&ontal distance between the instrument and the object cannot bemeasured due to obstacles etc., two instrument stations are used so that the are inthe same vertical plane as the elevated object. 'ig. (

%roce$"re)" *et up the theodolite at +) and level it accuratel with respect to the altitude

bubble.(" Direct the telescope towards +( and bisect it accuratel. lamp both the plates.

-ead the vertical angle θ)." Transit the telescope so that the line of sight is reversed. Mar# the second

instrument station +( on the ground. Measure the distance +)+( accuratel. -epeatsteps !(" and !" for both face observations. The mean values should be adopted.

/" 0ith the vertical vernier set to &ero reading, and the altitude bubble in the centreof its run, ta#e the reading on the sta #ept at nearb 1.M.

2" *hift the instrument to +( and set up the theodolite there. Measure the vertical

angle θ( to ' with both face observations.0ith the vertical vernier set to &ero reading, and the altitude bubble in the centre of itsrun, ta#e the reading on the sta #ept at the nearb 1.M

3 Instrument axes at same level

3 Instrument axes at diferent level


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Intr"ment a&e at ame level

In 'ig. (,

4et h 5 'A6

θ) 5 angle of elevation from +) to '

θ( 5 angle of elevation from +( to '

* 5 sta reading on 1.M., ta#en from both +)6 and +(6, the reading being the same inboth the cases.

d 5 hori&ontal distance between the two instrument stations.

D 5 hori&ontal distance between +) and '

'rom triangle O1’A’F, h 5 D tan θ) 77777777777777777777777777 !i"

'rom triangle O2’A’F, h 5 !D 8 d" tan θ( 7777777777777777777 !ii"

'rom 9s. !i" and !ii"

D tan θ) 5 !D 8 d" tan θ(

or D !tan θ) 7 tan θ(" 5 d tan θ(

or D 5d tan 2

(tan 1 - tan 2)

;ence, h 5 D tan θ) 5 d tan 2 tan 1(tan 1 - tan 2 )

-.4. of ' 5 -.4. of 1.M. 8 * 8 h


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Intr"ment a&e at $i'erent level

Depending upon the terrain, three cases arise:

A. Instrument axis at O2 higher that that at O1 ()i*+ ,-

h) 7 h( 5 A6A< 5 *( = *) 5 *

'rom triangle +)6A


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B. Instrument axis at O1 higher than that at O2 ()i*+ .-

h( = h) 5 *) = *( 5 *

'rom triangle +)6A


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Instrument -.4 > -eading on ?ertical ;ori&ontal -.4 o f

*tation 1.M sta #ept at angle distance the

1.M. !@" between object

instrument

station and

object

-esult:

The reduced level of the given object is :


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E/%ERIMENT ! 01

DO23LE %L4NE MET5OD

AIM: Determination of elevation of the object when base is inaccessible.

Apparatus: Theodolite, tripod, levelling sta, plumb bob, measurement tape.

Determination of elevation of object when the bae i inacceible ! theIntr"ment #tation an$ the Elevate$ Object are not in the #ame Vertical%lane

4et B and - be the two instrument stations not in the same vertical plane as that of C. The procedure is as follows:

)" *et the instrument at B and level it accuratel with respect to the altitude bubble.Measure the angle of elevation θ) to C.

(" *ight to the point - with reading on hori&ontal circle as &ero and measure theangle -BC) , i.e, the hori&ontal angle α at B.

" Ta#e a bac#sight s on the sta held at 1.M.

/" *hift the instrument to - and measure θ( and β there.

In 'ig. ,

AC6 5 hori&ontal line through A

C6 5 vertical projection of C

Thus, ACC6 is a vertical plane

*imilarl, 1CC< is a vertical plane

C< 5 vertical projection of C on a hori&ontal line through 1

B-C) 5 hori&ontal plane

C) 5 vertical projection of C

- 5 vertical projection of 1 on a hori&ontal plane passing through B


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α and β 5 hori&ontal angles

θ) and θ( 5 vertical angles measured at A and 1 respectivel.

'rom triangle ACC6 , CC6 5 h) 5 D tan θ) 777777777777777 !)"

'rom triangle B-C) , ∠BC)- 5 )EF° 7 !α 8 β" 5 π 7 !α 8 β"

'rom the sine rule,PQ1

sin β 5

RQ1

sin α 5

RP

sin [π – (α + β)] 5

d

sin (α + β)

∴ BC) 5 D) 5d sin β

sin (α + β) 777777777777777777 !("

and -C) 6 D( 6d sin α

sin (α + β) 777777777777777777777 !"

*ubstituting the value of D in !)", we get

h) 5 D) tan θ) 5d sin β tan 1

sin (α + β)

∴ -.4. of C 5 -.4. of 1.M. 8 s 8 h)

As a chec#, h( 5 D( tan θ( 5d sin α tan 2

sin (α + β)

If a reading on 1.M. is ta#en from 1, the -.4. of C can be #nown b adding h( to -.4. of1.

+bservation table :

Instrument -.4 > -eading on ?ertical ;ori&ontal -.4 o f

*tation 1.M sta #ept at angle distance the

1.M. !@" between object

instrument

station and

object

-esult:

The reduced level of the given object is :

ept 11 & 12 trigonometric-levelling

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