Trigonometric Leveling

1. When the distance D can be measured:

h/D = tanѲ

h = D tanѲ

R.L. of top = R.L. of point A + Height of Instrument (HI) + h

If the distance D is much greater, then we consider the effect of curvature ‘c’

Corrected length, h’ = h – c

R.L. of top = R.L. of point A + Height of Instrument (HI) + h’

2. When the distance D can’t be measured:

TanѲ1 = V/(B+D)

V = B tanѲ1 + D tanѲ1 …………………..(i)

TanѲ2 = V/D

V = D tanѲ2 ………………………………….(ii)

from eqn. (i) and (ii)

we get, D tanѲ2 = B tanѲ1 + D tanѲ1

D tanѲ2 – D tanѲ1 = B tanѲ1

D (tanѲ2 – tanѲ1) = B tanѲ1

Thus, D = B tanѲ1 / (tanѲ2 – tanѲ1)

Also, V = B tanѲ1 tanѲ2 / (tanѲ2 – tanѲ1)

Therefore, R.L. of point P = R.L. of B.M. + B.S. (Back Side) + V + Correction (only applicable if large distance).