To determine the R.L. at the top of the elevated object by trigonometric leveling.

Object: To determine the elevation (reduced level) of an object at all the certain heights.

Instruments:

Plumbob, tripod stand, theodolite, staff rod, ranging rods, tape.

Theory:

1. Distance of an object is inaccessible, and the instrument is at the same level.

Theory: if the horizontal distance between the instrument and object cannot be measured directly due to the obstacle (hindrance), then twice the instrument is set at the two different points in such a way that the instrument axes are at the same level.

Procedure:

1. Set up the theodolite at station O_1, and its all temporary adjustment is done.
2. Set up the horizontal angle zero and rotate the theodolite towards the point O₂ in such a way that the central reading touches the selected point on the top of the selected object.
3. Clamp both the plates and read the vertical angle.
4. Set the second point behind station O1, namely O2, and repeat all the procedures that we have done at station O₁.
5. Read the vertical angle
6. Measure the distance between O₁ and O₂ with the help of tape.
7. Now that all readings are done, measure the distance between the object and the first station, O1, i.e., D, with the help of the formula given as under:

∆FO₁A’

h=DtanӨ₁

∆FO₂A’

h=(d+D)tanӨ₂

(d+D)tanӨ₂= DtanӨ₁

DtanӨ₂+ dtanӨ₂= DtanӨ₁

D= ℎ𝑡𝑎𝑛𝚹2 / ( 𝑡𝑎𝑛𝚹1−𝑡𝑎𝑛𝚹2 )

Instrument axis are not on the same level

Theory: if the horizontal distance between the instrument and object cannot be measured directly due to the obstacle (hindrance), then twice the instrument is set at the two different points in such a way that the instrument axes are not at the same level.

The instrument near the object is at the lower position.

Procedure:

1. The theodolite is set over the instrument station (O1) exactly, and all the temporary adjustments are done.
2. Set up the horizontal angle zero and rotate theodolite towards in the vertical plane to sigh the top of the selected object.
3. Clamp both the plates and read the vertical angle Ө₁.
4. Set the second point behind the station O,_1, namely O,_2, and repeat all the procedures that we done at the station O₁.
5. Read the vertical angle Ө₂
6. Now that all readings are done, measure the distance between the object and the first station, O_{1, i.e.,} D, with the help of the formula given as under:

∆FO’₁A’’:

h₁=DtanӨ₁

∆FO’₂A’:

h₂= (d+D)tanӨ₂

∆h=h₁-h₂

∆h= DtanӨ1-(d+D)tanӨ₂

∆h= DtanӨ₁-d tanӨ₂-DtanӨ₂

D= ∆ℎ+ℎ𝑡𝑎𝑛𝚹2 / 𝑡𝑎𝑛𝚹1−𝑡𝑎𝑛𝚹2

The instrument near the object is at the higher position.

Procedure:

1. The instrument is closer; the object is in a higher position.
2. The theodolite is set over the instrument station (O1) exactly, and all the temporary adjustments are done.
3. Set up the horizontal angle zero and rotate the theodolite towards in the vertical plane to sigh the top of the selected object.
4. Clamp both the plates and read the vertical angle Ө₁.
5. Set the second point behind the station O,_1, namely O_{2,, and repeat all the procedures} that we done at the station O₁.
6. Read the vertical angle Ө₂.
7. Now that all readings are done, measure the distance between the object and the first station, O_{1,, i.e.,} D.
8. By considering two triangles (∆FO’1A’’ & ∆FO’2A’), the following formula is obtained to measure D.

D= ∆ℎ−ℎ𝑡𝑎𝑛𝚹2 / 𝑡𝑎𝑛𝚹2−𝑡𝑎𝑛𝚹1

Calculation: