DETERMINATION OF HORIZONTAL DISTANCE AND ELEVATION

Aim:To determine the horizontal distance between two given stations of which one is in accessible and its elevation.

Instrument and Accesories Required:

            Theodolite, Tripod Stand, Levelling Staff, Pegs, Arrows, etc.

Side View

Top View

Procedure:

1. The theodolite is mounted on the tripod stand.
2. The theodolite is centered over one of the given stations P from where the other given inaccessible station R and the staff station G can be sighted without any obstruction. The instrument is levelled using the foot screws and the altitude bubble is brought to the centre of its run.
3. Station R is sighted through the telescope.
4. The central vertical cross hair is made to bisect the station R and the central horizontal cross hair is made tangential to the top most point of the station R.
5. The vertical circle is read and the vertical angle is recorded.
6. The theodolite is then turned and the staff station G is sighted.
7. The line of sight is made horizontal by setting both the verniers C and D on the vertical circle at 0°00’00” and the staff reading on station G is observed and recorded.
8. Another instrument station Q is selected 20 m away from P and in line with station P and R on the same vertical plane by reversing the line of sight at P.
9. The theodolite is shifted and the centered over the station Q. The instrument is levelled using the foot screws and the altitude bubble is brought to the centre of its run.
10. Station R is sighted again through the telescope.
11. The vertical angle is read and the vertical angle is recorded by repeating the above procedure.
12. The theodolite is then turned and the staff station G is sighted.
13. The staff reading on G is observed and recorded after making the line of sight horizontal following the above procedure.
14. The horizontal distance between the two given stations P and R and the elevation of station R are determined from relevant trignometric expressions.

Tabulation

Inst At	Sighted To	Vertical Circle Reading					Remark
		Vernier C	Vernier D	Mean
				°	‘	“
P	R
Q	R

Formulas

S=S1-S2 =h2-h1

h1= D tan(Angle P)

h2= (D+ 20) tan (Angle Q)

(D+ 20) tan (Angle Q) -  D tan(Angle P) = S1-S2

(D+ 20) tan (Angle Q) -  D tan(Angle P) = S

D(tan(Angle Q) – tan( Angle P)) = S – (20tan (Angle Q))

D = S – (20tan (Angle Q)) / (tan(Angle Q) – tan( Angle P))

Result: Thus the horizontal distance between the two given stations and the elevation of the given stations are determined

1. Horizontal Distance PR =
2. Elevation of R =