Which formula gives the geographic range R_geo?

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Multiple Choice

Which formula gives the geographic range R_geo?

Geographic range is the maximum line-of-sight distance over the Earth's curvature, and each height contributes its own horizon distance. The distance to the horizon from a height h (in feet) is about 1.17 times the square root of h, so for an observer’s eye height and the light’s height you get d_eye = 1.17 sqrt(Height of Eye) and d_light = 1.17 sqrt(Height of Light). The total visible range is the sum of these two horizons: R_geo = 1.17 sqrt(Height of Eye) + 1.17 sqrt(Height of Light). Other forms don’t match the geometry: adding heights directly ignores curvature; taking the square root of their sum misrepresents how each height independently determines its horizon distance; and dropping or misplacing the 1.17 factor alters the correct constant.

Geographic range is the maximum line-of-sight distance over the Earth's curvature, and each height contributes its own horizon distance. The distance to the horizon from a height h (in feet) is about 1.17 times the square root of h, so for an observer’s eye height and the light’s height you get d_eye = 1.17 sqrt(Height of Eye) and d_light = 1.17 sqrt(Height of Light). The total visible range is the sum of these two horizons: R_geo = 1.17 sqrt(Height of Eye) + 1.17 sqrt(Height of Light).

Other forms don’t match the geometry: adding heights directly ignores curvature; taking the square root of their sum misrepresents how each height independently determines its horizon distance; and dropping or misplacing the 1.17 factor alters the correct constant.

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