Radio / Radar Horizon
Line-of-sight distance from antenna heights, with standard refraction.
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The engineering
Radio waves bend slightly earthward in the standard atmosphere, so the radio horizon runs ~15% past the visual one — the famous 4/3-earth-radius trick makes the rays straight again by inflating the planet.
10 m of mast buys 13 km; height is the cheapest amplifier there is. Ducting weather can wildly exceed this — that's the anomaly, not the design number.
Where this math comes from
Marconi's 1901 transatlantic shot 'over the horizon' set off two decades of confusion (the ionosphere, it turned out, was cheating for him). For VHF and up, the honest limit is geometry plus refraction — Schelleng, Burrows, and Ferrell's 1933 Bell paper introduced the effective-earth-radius model that became the 4/3 rule.
Every coverage map, radar fence, and repeater-site argument since is this square-root law with real estate attached.
- 1901Guglielmo MarconiOver-the-horizon mystery starts propagation science.
- 1933Schelleng, Burrows & FerrellEffective-earth-radius (4/3) refraction model.
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