#aerodynamics

Kite-flying maths as an API, computed locally and deterministically — the line-pull, altitude and minimum-wind numbers a kite flyer, festival organiser or kite app works a flight out with. The line-pull endpoint gives the tension a kite puts on the line ≈ ½ × air density × wind speed² × sail area × a force coefficient (~0.8 for a typical flat or delta kite): because it rises with the square of the wind, doubling the wind quadruples the pull — a 1.5 m² kite holds about 47 N (nearly 5 kgf) at 8 m/s but four times that in a strong blow, so the line and your grip must be sized to the gusts, not the average. The altitude endpoint gives the flying height = the line let out × the sine of the line angle above the horizontal, with the downwind distance from the cosine: 100 m of line at a 45° angle reaches about 71 m up and 71 m downwind, while a heavy or under-flown kite sags to a low angle and never climbs. The min-wind endpoint gives the lightest wind that lifts off, where the aerodynamic lift just equals the weight: min wind = √(2 × mass × g ÷ (air density × area × lift coefficient)), so a 200 g, 1.5 m² kite needs only about 1.6 m/s (6 km/h) — lighter sails and bigger area drop the threshold. Everything is computed locally and deterministically, so it is instant and private. Ideal for kite-flying and festival apps, hobby and STEM-education tools, and outdoor calculators. Pure local computation — no key, no third-party service, instant. Flat-kite estimates — combine with real wind readings. 3 compute endpoints. For drag and terminal velocity use a drag API; for structural wind load a wind-load API.

api.oanor.com/kite-api

Mach-number and compressible-flow aerodynamics as an API, computed locally and deterministically. The mach endpoint computes the local speed of sound a = √(γ·R·T) (air γ = 1.4, R = 287.05 J/(kg·K)) and the Mach number M = v/a from a speed and a static temperature — given directly in °C or kelvin, or derived from a geopotential altitude through the International Standard Atmosphere (troposphere T = 288.15 − 0.0065·h up to 11 km, then the isothermal 216.65 K layer to 20 km) — and classifies the flight regime as subsonic, transonic, supersonic or hypersonic; the speed of sound is about 340.3 m/s at 15 °C and 295 m/s at 11 km. The speed endpoint inverts it, returning v = M·a in m/s, km/h and knots. The stagnation endpoint gives the isentropic total-to-static ratios T0/T = 1 + (γ−1)/2·M², P0/P = (T0/T)^(γ/(γ−1)) and ρ0/ρ = (T0/T)^(1/(γ−1)) — at Mach 2 the total pressure is about 7.82 times the static pressure — and will scale a supplied static temperature and pressure to their stagnation values. Everything is computed locally and deterministically, so it is instant and private. Ideal for aerospace, CFD, flight-simulation, wind-tunnel, UAV and aerodynamics-education app developers, compressible-flow and flight-envelope tools, and engineering software. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is compressible aerodynamics; for viscous flow and the Reynolds number use a Reynolds API and for incompressible pressure/velocity a Bernoulli API.

api.oanor.com/machnumber-api

Aerodynamic drag and terminal-velocity maths as an API, computed locally and deterministically. The drag endpoint computes the drag force on a body moving through a fluid, F_d = ½·ρ·Cd·A·v² — half the fluid density times the drag coefficient, the reference area and the velocity squared — together with the dynamic pressure ½·ρ·v², from a fluid (air, water, seawater, oil and more, or a custom density), a drag coefficient (given directly or from a built-in shape table) the area and the speed. The terminal endpoint computes the terminal velocity of a falling object, v_t = √(2·m·g/(ρ·Cd·A)) — the steady speed at which drag balances gravity — from the mass and area, or for a sphere from its diameter and material density, in metres per second, km/h and mph (a belly-down skydiver reaches about 55 m/s, 200 km/h). The shapes endpoint lists typical drag coefficients for spheres, cubes, cylinders, flat plates, streamlined bodies, skydivers, cars, parachutes and more. Everything is computed locally and deterministically, so it is instant and private. Ideal for aerodynamics and ballistics tools, skydiving, model-rocketry and motorsport apps, sphere-settling and sedimentation calculators, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is drag and terminal velocity; for vacuum projectile and SUVAT kinematics use a physics API and for pipe friction pressure drop use a Darcy-Weisbach API.

api.oanor.com/drag-api