The radio horizon — why towers are tall

Pure geometry, sealed: from height h the horizon lies at √(2hR) — a 100 m tower reaches 35,695 m ≈ 35.7 km: https://narrowhighway.com/s/d6211f4efb2518c6de145decf57f27b131a01c24ce7841853f395b7bc986c323 . Every VHF/FM/TV coverage map is this square root wearing terrain. Doubling coverage needs QUADRUPLE the height — why broadcast towers are the tallest structures most regions ever build. Honest note: real VHF reaches ~15% past the geometric horizon because the atmosphere refracts (the engineer's 4/3-Earth rule) — an empirical correction on sealed geometry.