#buoyancy

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

Matemáticas de flotabilidad y flotación de Arquímedes como una API, calculadas local y determinísticamente. El endpoint de flotabilidad calcula la fuerza de flotación sobre un cuerpo sumergido o flotante, Fb = ρ_fluido·g·V_desplazado — el empuje hacia arriba es igual al peso del fluido desplazado — a partir de un volumen desplazado y un fluido (agua, agua de mar, aceite, mercurio y más, o una densidad personalizada), y también da la masa del fluido desplazado; resuelve el volumen a partir de una fuerza conocida también. El endpoint de flotación decide si un objeto flota, se hunde o es neutro comparando su densidad (dada directamente, de un material incorporado, o como masa dividida por volumen) con la densidad del fluido, y para un objeto flotante devuelve la fracción sumergida f = ρ_objeto/ρ_fluido (así que el 90 % de un iceberg está bajo la línea de flotación), o para un objeto que se hunde su peso aparente (bajo el agua). El endpoint de carga dimensiona la flotación: el volumen desplazado necesario para flotar una carga dada, V = W/(ρ_fluido·g), o la carga máxima adicional que un cuerpo flotante de un volumen y densidad dados puede llevar antes de sumergirse, Wmax = (ρ_fluido − ρ_cuerpo)·V·g. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de arquitectura naval y marinas, buceo, aplicaciones de ROV y lastre, diseño de balsas y pontones, y educación en física. Cálculo puramente local — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esto es flotabilidad y flotación; para presión a profundidad y fuerza hidrostática en una pared, use una API de hidrostática.

api.oanor.com/buoyancy-api

Fluid-statics maths as an API, computed locally and deterministically. The pressure endpoint computes the pressure at a depth in a fluid — the gauge pressure ρ·g·h and the absolute pressure (gauge plus atmospheric) — in pascals, kilopascals, bar, psi and atmospheres, for water, seawater, oil, mercury and more, or a custom density; depths accept metres, feet or centimetres, which makes it handy for diving (about 10 m of seawater adds one atmosphere). The force endpoint computes the resultant hydrostatic force on a submerged vertical rectangular surface — an aquarium wall, a tank side, a dam face or a flood gate — as F = ρ·g·h_c·A from its width and the top and bottom depths, and gives the depth of the centre of pressure, which sits below the centroid. The buoyancy endpoint applies Archimedes' principle, F_b = ρ_fluid·g·V, to give the buoyant force and the displaced mass, and — if you supply the object's density or mass — tells you whether it floats or sinks and what fraction sits below the waterline. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil and marine engineering tools, diving and aquarium apps, tank and dam design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is fluid statics; for pump power and head use a pump API and for pipe flow rate use a pipe-flow API.

api.oanor.com/hydrostatic-api