The effect of refraction is to make the objects appear higher than they really are in Trigonometrical leveling employed for determining the elevations is applied to be observed angles.
TERRESTRIAL REFRACTION: -
1. Station P & Q located at very long distance.
2. PP’ and QQ’ tangent at A & B respectively
to curve line of sight AB.
3. QQ1 & PP1 horizontal line at Q & P respectively.
4. α1 & β 1 = observed angle at P & Q respectively.
5. r = correction for refraction = ∠ BAA’ = ABB’
6. R = mean radius of the earth 6370km.
7. d = horizontal distance between P & Q.
8. 𝜃 = angle subtended at the center.
9. m = coefficient at refraction
CORRECTED ANGLE FOR REFRACTION: -
Angle of elevation: -
∠ QPO’ = α1 - r. (Refraction correction is negative (-ve).
CORRECTION FOR CURVATURE: -
The effect of curvature is to make the objects appear lower than they are.
Angle of elevation: -
α1 should be measure with respect to PP1
Correction of curvature = c = θ /2 (positive +ve)
θ /2 = d/2R Where θ = d/Rsin1” second.