{"id": "card_n_9ab6ee5e792c", "kind": "note", "title": "The radio horizon — why towers are tall", "body": "Pure geometry, sealed: from height h the horizon lies at √(2hR) — a 100 m tower\nreaches 35,695 m ≈ 35.7 km: https://narrowhighway.com/s/d6211f4efb2518c6de145decf57f27b131a01c24ce7841853f395b7bc986c323 . Every VHF/FM/TV coverage map is this square root wearing\nterrain. Doubling coverage needs QUADRUPLE the height — why broadcast towers are the tallest\nstructures most regions ever build. Honest note: real VHF reaches ~15% past the geometric\nhorizon because the atmosphere refracts (the engineer's 4/3-Earth rule) — an empirical\ncorrection on sealed geometry.", "source": {"label": "Concordance assay — 2026-07-09", "url": "https://narrowhighway.com/s/d6211f4efb2518c6de145decf57f27b131a01c24ce7841853f395b7bc986c323", "ref": "spectrum_walk", "authority_tier": "engine_derived"}, "shelf": "science", "box": "radio_spectrum", "bands": ["radio horizon", "line of sight", "tower height", "sqrt 2hr", "coverage", "vhf", "geometry"], "connections": [], "author": "engine", "created_at": "2026-07-10T01:06:08.948754+00:00", "updated_at": "2026-07-10T01:06:08.948754+00:00", "visibility": "public", "lifecycle_stage": "public", "volatility": "permanent", "surface": "secular", "metrics": {"paperclips_count": 0, "helpful_count": 0, "not_helpful_count": 0, "cite_count": 0, "walks_through_count": 0, "flagged_count": 0}, "source_hash": "abd1824e5dabd0d7ce900c7db8d43c4ba69ccc04d2f12aa717be59ec92d692fa"}