Leveling Curvature-and-Refraction Correction
The correction the leveling and slope-reduction tiles say they skip: with K the sight distance in thousands of feet, curvature raises 0.0239 K^2 ft and refraction bends back 0.0033 K^2, leaving a net 0.0206 K^2 ft subtracted from the far rod. A 2,000 ft sight is 0.0824 ft. Balanced backsight/foresight cancel it; a long or unbalanced sight and reciprocal/trig leveling do not. Assumes refraction k ~ 0.14; the project procedure governs.
Formula and source
h_cr = 0.0206 K^2 ft, K = sight distance in thousands of feet (curvature 0.0239 K^2 minus refraction 0.0033 K^2); equivalently 0.574 M^2 with M in miles. Subtracted from the far rod reading.
Standard leveling curvature-and-refraction correction as compiled in the standard surveying references (Ghilani, Elementary Surveying), by name.
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