Stadia Tacheometry (Distance and Elevation)
The classic instrument method of reading a distance and rise off a rod interval, still used for topo checks: with K = 100, the horizontal distance H = K s cos^2(theta) and vertical V = (K s/2) sin(2 theta) from the stadia interval s and vertical angle. A 1.50 ft interval at +5 degrees gives 148.9 ft and a 13.0 ft rise; on a level sight it reduces to the bare H = 100 s with no rise. Internal-focusing instrument (C ~ 0), no curvature/refraction correction. A computational aid; the instrument's stadia constants govern.
Formula and source
H = K s cos^2(theta); V = K s cos(theta) sin(theta) = (K s/2) sin(2 theta); elevation = station_elev + HI + V - rod_center. (K = 100)
The stadia-tacheometry distance and elevation reduction with the standard interval factor K = 100, as compiled in the standard surveying references, by name.
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