Antenna Height Planner

Fresnel zone — a radio path needs an ellipsoid of clear space around the sight line, not just an unobstructed straight line. Its radius at any point is 17.32·√(d₁·d₂/(f·d)) metres. Keep 60% of it clear and the link behaves close to free space; lose more and diffraction loss climbs quickly.

Earth bulge — the ground rises d₁·d₂/(12.75·k) metres above the chord, with k = 4/3 for standard atmospheric refraction. Over a few kilometres that is small; what matters far more is that a low antenna starts with almost no clearance to give away.

The tightest point is scanned, not assumed — with unequal antenna heights the worst clearance is near the lower end, not mid-path. Checking mid-path alone flatters the answer badly: for a 30 m gateway to a 2 m sensor over 8 km it reports 57% clearance where the true minimum along the path is 28%.

Range — the same field-calibrated model as the coverage calculator, capped by the radio horizon 4.12·(√h₁+√h₂) and by the furthest we have measured this class of link.

Device height is capped at 10 m — Okumura-Hata's mobile-antenna correction is linear in height and only fitted over 1–10 m. Extrapolated to a sensor on a 20 m pole it hands out roughly 45 dB of free gain, which reads as a twentyfold range increase and is pure artefact. Above 10 m the range figure holds flat; treat it as a floor, not a ceiling.

Smooth-earth geometry. Real terrain, buildings and trees will be worse — confirm with a site survey before committing to a mast.