{"openapi":"3.1.0","info":{"title":"Sea Horizon API","version":"1.0.0","description":"Sea-horizon and visibility maths as an API, computed locally and deterministically — the distance-to-horizon, geographic-range and dip numbers a mariner, coastal navigator or marine app works sightings with. The horizon endpoint gives the distance to the sea horizon ≈ 1.169·√(height of eye in feet) nautical miles, including the standard atmospheric refraction that bends the line of sight a little past the geometric edge — at 9 ft of eye height the horizon is about 3.5 nm off — together with the dip, how far below true horizontal that watery edge lies (≈ 0.97′·√h), the correction subtracted from a sextant altitude shot to the sea horizon. The geographic-range endpoint gives how far off a light or landmark first peeps over the horizon = the sum of two horizon distances, your own plus the object's: 1.169·(√h_eye + √h_object), so a 100 ft lighthouse from a 9 ft cockpit lifts above the sea at about 15 nm — purely geometric, before the light's own luminous range and the visibility. The object-height endpoint inverts it: how tall a tower, light or headland must stand to break the horizon at a target range, or how close you must be before a known landmark appears. Everything is computed locally and deterministically, so it is instant and private. Ideal for marine-navigation and chartplotter apps, coastal-pilotage and lighthouse tools, and sailing utilities. Pure local computation — no key, no third-party service, instant. Geometric/refraction model. 3 compute endpoints. 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