STADIA TACHEOMETRY DETERMINATION OF HORIZONTAL DISTANCE AND DIFFERNCE IN ELEVATION BETWEEN TWO STATIONS

Aim: To determine the horizontal distance and the differnce in elevation between two stations by the principles of statia tacheometry.

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 an arbitrarily selected station P from where the staff stations A and B can be sighted without any obstruction and the instrument is levelled using the foot screws.
3. The theodolite is set on the face right mode and the vernier A on the face right mode and the vernier A on the horizontal circle is initially set at 0°00’00” and the staff station A is sighted.
4. The central vertical cross hair is made to bisect the staff station A and the central horizontal cross hair is made tangential to 2.0 m mark on the staff station.
5. The horizontal and vertical angles are recorded by reading the horizontal and vertical circles respectively.
6. The stadia hair readings for the staff station A are also observed and recorded.
7. The theodolite is swing to the right and the staff station B is sighted.
8. The central vertical cross hair is made to bisect the staff station B and the central horizontal cross hair is made tangential to 2.0 m mark on the staff station B.
9. The horizontal and vertical angle are recorded by reading the horizontal and vertical circle respectively.
10. The stadia hair readings for the staff station B are also observed and recorded.
11. The observations are closed on the first staff station A.
12. The vernier A is then initially set  90°00’00” and the horizontal and vertical angles and the stadia hair readings are observed for both the staff stations A and B are recorded by repeating the above procedure.
13. The theodolite is then set on the face left mode and the horizontal and vertical angles and the stadia hair reading are observed for both the staff station A and B are recorded by repeating the above procedure for the initial settings of 180°00’00” and 270°00’00” on vernier A. The staff stations are sighted in the same sequence as above but by swinging the theodolite to the left.
14. The average of the horizontal angles subtended by the line AB at the instrument station P and the vertical angles are found.
15. The average vertical angles and the staff intercepts are substituted in the relevant expression for horizontal distance for inclined line of sight and vertically held staff and the horizontal distances of the staff stations A and B from the instrument station P are determined by the principles of stadia tacheometry.

16. From the mean value of the horizontal angle APB and the horizontal distance PA and PB, the horizontal distance AB is determined by the cos rule.
17. The difference in elevation between the two staff stations A and B is determined using the horizontal distance and the vertical angles in the relevant trignimetric expression. 

Tabulation

Inst At

Sighted To

Horizontal Circle Reading -Vernier

Included Angle

Average Included Angle

Vertical Circle Reading - Vernier

Average Vertical Angle

Stadia Hair Reading

A

B

Mean

C

D

Mean

Top

Middle

Bottom

P

APB

Angle A Angle B

Formula

PA = KS_ACOS²(Angle A) + C COS (Angle B)

PB = KS_BCOS²(Angle A) + C COS (Angle B)

Horizontal Distance between AB can be obtained by using Cosine rule

AB² = PA² + PB² – 2PA x PB Cos APB

h1= 2- PAtan (Angle A)

h2= 2- PBtan (Angle B)

Difference in elevation between A and B = h2- h1

 

Result : Thus the horizontal distance and the difference in elevation between two stations A and B are as the mean values.

                                 i.            Horizontal distance AB =

                               ii.            Difference in elevation between A and B =