Correction Due to Slope | Taping Corrections | Surveying
In surveying, tape correction(s) refer(s) to correcting measurements for the effect of slope angle, expansion or contraction due to temperature, and the tape's sag, which varies with the applied tension. Not correcting for these effects gives rise to systematic errors, i.e. effects which act in a predictable manner and therefore can be corrected by mathematical methods.
When distances are measured along the slope, the equivalent horizontal distance may be determined by applying a slope correction.
The vertical slope angle of the length measured must be measured. Thus,
For gentle slopes (less than 20%)
𝐶_ℎ=ℎ^2/2𝑠
For steep slopes (between 20% and 30%)
𝐶_ℎ=ℎ^2/2𝑠+ℎ^4/(8𝑠^3 )
For very steep slopes (greater than 30%)
𝐶_ℎ=𝑠(1−cos𝜃 )
Where:
C_h is the correction of measured slope distance due to slope;
𝜃 is the angle between the measured slope line and horizontal line;
s is the measured slope distance.
d is the horizontal distance.
The correction C_h is subtracted from s to obtain the equivalent horizontal distance on the slope line:
d = s - C_h