Trigonometric levelling with the curvature and refraction correction
A single long total-station shot is reduced to an elevation, carrying instrument and target heights and the combined correction for earth curvature and atmospheric refraction.
Apply· about 18 minutes by hand· 6 steps
Given
A total station is set over control station STA 14, whose elevation is 1,286.31 ft (US survey feet). The height of the horizontal axis above the mark is 5.42 ft.
A prism is set over point P. The height of the prism center above the mark at P is 6.15 ft.
Observed slope distance from instrument to prism = 6,480.22 ft.
Observed zenith angle = 87°14′35″. Angles are read to 1″.
Combined curvature and refraction correction, in feet, is 0.0206 times the square of the horizontal distance expressed in thousands of feet.
Elevations are reported to 0.01 ft.
Required
The horizontal distance and the vertical component of the observed line.
The combined curvature and refraction correction.
The elevation of point P.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
Premium
The worked solution is part of Premium
This problem is 6 steps of computation, with the arithmetic shown at every stage and an independent check at the end. Several problems from every category are free to read in full so you can judge the format first.
Every calculator, the whole reference library and all the guides are free to use forever - the practice bank, the full problem library and the printable job paperwork are the paid upgrade.