Terrestrial curvature
Computation of the influence of terrestrial curvature and refraction.
For a distance (D) of 349 km (width of Switzerland east to west), the apparent height difference due to terrestrial curvature (E) and refraction (R) would be -8318 m.
The illustrated example shows the commonly known effect of the apparently disappearing ship on the horizon of a large lake with increasing distance from the point of observation.
| D [km] | E [m] | E-R [m] | Remark |
|---|
| 1 | 0.08 | 0.07 | |
| 10 | 7.8 | 6.8 | |
| 100 | 780 | 680 | |
| 221 | 3834 | 3335 | Switzerland: N-S |
| 349 | 9560 | 8318 | Switzerland: E-W |
Formula
E = D*D / 2r
E-R = 0.87 * D*D / 2r
The value of 6370 km was used for the earth's radius.
The value of 0.87 is obtained from 1 minus the refraction coefficient (~0.13).
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GeodesyLast updated: 19.01.2009
