06 · Coming home

Heat

½ mv² at 7.8 km/s is ~30 MJ/kg, dumped into air in minutes. A blunt body parks most of it in a shockwave. Heating climbs roughly with v³.

In English

Coming home, all that kinetic energy becomes air heat in minutes. A blunt capsule lets the shockwave eat it. A sharp nose takes it in the face. Faster than LEO (Moon, Mars) is much worse because heat ~ v³.

Try this: Leave 7.8 km/s. Switch blunt vs sharp. Then drag toward 11 km/s.
Keep this: Blunt bodies survive. Heating scales roughly with v³.

Lab · ½ mv² has to go somewhere

LEO is not “falling slowly.” It is 7.8 km/s of kinetic energy per kilogram — about 8 kWh, dumped into air in minutes. A blunt body parks most of that in a shockwave. A sharp nose eats it.

Speed 7.80 km/s

Energy: 30.4 MJ/kg
Heat index ~v³: 1.00 × LEO
On the skin: 10%

Suborbital. Still hot. Not orbit.

Stagnation heating ~ ρ^0.5 v^3 (Sutton–Graves). Energy to dump is ½ v². Blunt bodies make a detached shock that the vehicle does not swallow. Sharp is for cruise missiles, not LEO entry.

Skip reentry and lifting bodies trade heat rate against time. The lab’s “on the skin” fraction is a cartoon of that shock split, not a TPS sizing tool.