Climbing Fall API

Rock-climbing fall maths as an API, computed locally and deterministically — the safety numbers behind a lead fall, from the harshness of the catch to whether you hit the deck. The fall-factor endpoint gives the fall factor, distance fallen ÷ rope paid out, from 0 to a maximum of 2: it, not the absolute distance, decides how hard the catch is, so 4 metres on 2 metres of rope is a brutal factor-2 onto the anchor while the same fall on 10 metres of rope is a mild 0.4. The impact-force endpoint gives the peak force the rope transmits from the spring model F = mg + √((mg)² + 2·mg·k·f), where k is the rope modulus (~20 kN for a dynamic single rope) and f the fall factor — so an 80 kg climber on a factor-1 fall feels about 6.4 kN, and the top runner sees roughly 1.66× that from the pulley effect. The ground-fall endpoint adds it up: total drop = twice the height above the last piece, plus slack, plus the rope's stretch, and tells you whether that clears the ground or a ledge. Everything is computed locally and deterministically, so it is instant and private. Ideal for climbing apps, gym and guiding tools, route-planning and education sites, and gear calculators. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 compute endpoints. Educational estimates — not a substitute for instruction and judgement.