Leveling Curvature-and-Refraction Correction
The curvature-and-refraction correction on a long level sight.
Example
You enter
- Sight distance (ft) 2000
You get
- Combined correction (subtract from far rod) 0.0824 ft
- Curvature component 0.0956 ft
Checked against published worked examples from: Ghilani, Elementary Surveying (leveling reduction).
Details, formula, and sources
ScopeWith 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 or tableh_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.
Source and editionStandard leveling curvature-and-refraction correction as compiled in the standard surveying references (Ghilani, Elementary Surveying), by name.
Free accessThe 0.0206 K^2 (ft) / 0.574 M^2 (mi) correction is a public surveying result in any elementary-surveying reference.
What governsEstimate. AHJ and licensed professional govern.
API field namessight_distance_ft, correction_ft, curvature_ft
- Coefficient 0.0206 K^2 ft (K in thousands of feet); = curvature 0.0239 minus refraction 0.0033surveying references
- Refraction assumes the standard refraction coefficient k ~ 0.14standard atmosphere
- Balanced sights cancels with equal backsight/foresight distances in differential levelingleveling practice