#lift

Traction-elevator engineering maths as an API, computed locally and deterministically — the counterweight, hoist-motor and rope-traction numbers a lift engineer or building-services designer sizes a passenger elevator with. The counterweight endpoint gives the balancing mass = the empty car plus a fraction of the rated load (the overbalance, typically 40–50 %, 45 % common), so a 1,000 kg car rated for 1,000 kg uses a 1,450 kg counterweight — the car and weight balance near half load and the machine is sized for the worst-case imbalance, not the full load. The motor-power endpoint uses that: because the counterweight cancels most of the car, the motor only lifts the out-of-balance load = rated load × (1 − overbalance), so power = that × g × speed ÷ efficiency (~65–75 % geared) — a 1,000 kg lift at 1.5 m/s needs only about 11–12 kW, half what a counterweight-less hoist would draw. The traction-ratio endpoint checks the friction grip: a traction elevator moves the ropes by friction over the sheave, so the available traction (e^(μθ), the capstan equation) must beat the T1/T2 tension ratio at both worst cases — a full car at the bottom and an empty car at the top — and it returns the governing ratio. Everything is computed locally and deterministically, so it is instant and private. Ideal for lift-design and building-services tools, vertical-transport and MEP utilities, and engineering calculators. Pure local computation — no key, no third-party service, instant. Sizing estimates — follow the lift code and maker data. 3 compute endpoints. For block-and-tackle use a pulley API; for capstan friction a capstan API.

api.oanor.com/elevator-api

Hot-air-balloon lift maths as an API, computed locally and deterministically — the thermal-lift, envelope-temperature and air-density numbers a balloon pilot, designer or physics teacher works a flight out with. The lift endpoint gives the buoyant lift from heating the air: gross lift = envelope volume × (outside air density − inside air density), the densities from the ideal-gas law — a 2,500 m³ envelope at 100 °C on a 15 °C day lifts about 698 kg gross, from which you subtract the envelope, basket, burner and fuel for the payload, and the hotter the air and colder the day the more it lifts. The required-temp endpoint inverts it: to carry a target lift the inside air must reach a particular density and so a particular temperature, with a check that it stays under the ~120 °C that nylon envelopes can take — the everyday pre-flight question of whether the balloon can lift today's crew and fuel. The air-density endpoint gives the moist-air density ρ = (P − 0.378·Pv) ÷ (R·T), and explains the counter-intuitive fact that humid air is LESS dense than dry air, slightly cutting the lift. Everything is computed locally and deterministically, so it is instant and private. Ideal for ballooning and aviation tools, STEM and physics-education apps, and buoyancy calculators. Pure local computation — no key, no third-party service, instant. Idealised dry-lift model. 3 compute endpoints. For Archimedes flotation in water use a buoyancy API; for party-balloon helium lift a balloon API.

api.oanor.com/hotairballoon-api