Atmosphere — International Standard Atmosphere (ISA): the barometric formula in the troposphere (1.98 °C / 1000 ft lapse) and the isothermal layer above the tropopause (~36,089 ft).
Blood oxygen — alveolar gas equation P_AO₂ = 0.2095·(P − 47) − P_CO₂/0.8 feeding the Severinghaus SpO₂ curve. CO₂ falls with altitude, tuned to acute-exposure data (~87% @ 10k, ~72% @ 18k, ~50% @ 25k ft).
Density altitude — PA = elev + (29.92 − altimeter)·1000, then DA = PA + 120·(OAT − ISA temp).
Horsepower — Gagg–Ferrar relation HP ≈ rated·(1.132σ − 0.132), σ = density ratio at your density altitude; turbos hold rated power to a critical altitude.
Power curve — parabolic drag polar C_D = C_D0 + C_L²/(πAR·e); power required = drag × TAS. The region of reversed command is the band from stall up to the minimum-power speed. Drag values are representative estimates and V-speeds (Vs, Va, Vno, Vne) are typical published figures — check your POH; the climb readout is idealized (constant ~80% prop efficiency) and optimistic at low speed.
Cabin altitude — cabin_P = min(sea level, ambient + ΔP) inverted to an altitude; ΔP is each aircraft's published max pressure differential.
Data sources — bundled ~110 airports (offline elevation) plus aviationweather.gov METAR for live temp/altimeter (via a same-origin proxy once hosted), falling back to open-meteo.com current weather by coordinates for fields without a METAR.
References — FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25) and Airplane Flying Handbook (FAA-H-8083-3) for density altitude, the FAR 91.211 oxygen rules, and the power curve / region of reversed command; J.D. Anderson, Introduction to Flight (parabolic drag polar, power-required = drag × TAS); the alveolar gas equation and Severinghaus SpO₂ relation, with acute-exposure SaO₂ figures from high-altitude physiology literature (e.g. J.B. West). Power-curve V-speeds and the narrow trainer reversed-command band cross-checked against Van's Air Force, GoFly, and Boldmethod.
Educational models for healthy unacclimatized adults at acute exposure. Real SpO₂ varies with fitness, acclimatization, and individual physiology. Not for medical or operational flight-planning use.