#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

Archimedes buoyancy and flotation maths as an API, computed locally and deterministically. The buoyancy endpoint computes the buoyant force on a submerged or floating body, Fb = ρ_fluid·g·V_displaced — the upthrust equals the weight of the displaced fluid — from a displaced volume and a fluid (water, seawater, oil, mercury and more, or a custom density), and also gives the mass of displaced fluid; it solves the volume from a known force too. The float endpoint decides whether an object floats, sinks or is neutrally buoyant by comparing its density (given directly, from a built-in material, or as mass divided by volume) with the fluid density, and for a floating object returns the fraction submerged f = ρ_object/ρ_fluid (so 90 % of an iceberg sits below the waterline), or for a sinking object its apparent (underwater) weight. The payload endpoint sizes flotation: the displaced volume needed to float a given load, V = W/(ρ_fluid·g), or the maximum extra payload a floating body of a given volume and density can carry before it submerges, Wmax = (ρ_fluid − ρ_body)·V·g. Everything is computed locally and deterministically, so it is instant and private. Ideal for naval-architecture and marine tools, diving, ROV and ballast apps, raft and pontoon design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is buoyancy and flotation; for pressure at depth and hydrostatic force on a wall use a hydrostatics API.

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