Curvature and refraction correction
How much the earth's curve, less the bending of the line of sight, lowers a level sight over a distance, with the textbook coefficient for the refraction coefficient used.
Experimental: not yet fully verified. How results are checked
Curvature and refraction lower a level sight by 0 km at this distance, a coefficient of 0.0675 m/km² (k = 0.14).
- Curvature alone
- Refraction
- Coefficient
- Coefficient and its k
Provenance
- Computed by
- survey.reduction.curvature-refraction 1.0.0, core 0.1.0
- Model
- h = (1 − k)·D²/(2R), the curvature D²/(2R) less the refraction k·D²/(2R) (Ghilani & Wolf 2021, ch. 4); R = 6,371,000 m and k = 0.13 by default
- Accuracy
- Exact for the given k and R; k itself varies with the air near the ground, most at low sights and midday
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: h = (1 − k)·D²/(2R), the curvature D²/(2R) less the refraction k·D²/(2R) (Ghilani & Wolf 2021, ch. 4); R = 6,371,000 m and k = 0.13 by default
Accuracy: Exact for the given k and R; k itself varies with the air near the ground, most at low sights and midday
Worked example: A 1 km sight with k = 0.14. Source: add-survey-suite scenario: ≈ 0.0675 m with k = 0.14, ≈ 0.0683 m with k = 0.13. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Sight distance
- 1 km
- Refraction coefficient k
- 0.14
You get
- Curvature and refraction
- 0 km
- Curvature alone
- 0 km
- Refraction
- 0 km
- Coefficient
- 0.0675
- Coefficient and its k
- 0.0675 m/km² (k = 0.14)
Review: Not yet independently reviewed by a licensed surveyor.
Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Changes
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapter 4 (curvature and refraction), chapter 6 (reducing slope distances), and the total-station chapters (two-face zenith observations and index error).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.