When a vehicle moves through air faster than the air can get out of the way, the flow is brought to rest at the nose (the "stagnation point") and its kinetic energy converts to heat. The higher the Mach number, the hotter that stagnation point gets — this is aerodynamic heating, the reason hypersonic vehicles need exotic materials that subsonic aircraft never touch.
Stagnation temperature:
T_stag = T_air · (1 + (γ−1)/2 · M²)
γ = 1.4 (air), T_air in kelvin, M = Mach number
Examples (T_air ≈ 216 K, 11 km):
M 0.85 (airliner) → T_stag ≈ 250 K ≈ −23°C (barely above ambient)
M 3.3 (SR-71) → T_stag ≈ 686 K ≈ 413°C (real skin ≈ 315°C, recovery factor r ≈ 0.85–0.9)
M 8 (X-43A) → T_stag ≈ 2981 K ≈ 2708°C (needs UHTC / ablative shielding)
Material temperature ceilings:
Al-Li alloys ≤ 180°C (fuselage skin, low weight)
Ti-6Al-4V ≤ 600°C (compressor blades, SR-71 airframe)
Ni superalloy + TBC ≤ 1100°C (turbine blades, thermal-barrier coating)
CMC / C-C composite ≤ 2000°C (combustor liners, re-entry nose caps)
UHTC (ZrB₂, HfB₂, HfC) > 2000°C (hypersonic leading edges)
- Mach number — sets free-stream speed; heating grows with M², so doubling speed roughly quadruples the stagnation-temperature rise.
- Ambient conditions — the baseline air temperature the aircraft flies through; cruise altitude starts colder, so the same Mach number reaches a lower peak than at ground level.
- Heat map / Material zones — toggles the fuselage tiles between a continuous temperature gradient and discrete bands showing which real material would be required at each point.
- The nose carries the full stagnation-heating spike (cos² fall-off, a simplified modified-Newtonian law); the cylindrical body only sees a low skin-friction baseline, matching why nose caps and leading edges use the most exotic materials while the fuselage skin stays comparatively ordinary.