Reentry heating

Why does a returning capsule glow white-hot in air far too thin for a person to breathe?

A returning capsule does its most violent burning somewhere around sixty or seventy kilometres up. At that altitude the air is roughly ten thousand times thinner than at sea level; an unpressurised human would be unconscious in seconds and, above the Armstrong limit near nineteen kilometres, their body fluids would boil at body temperature. There is essentially nothing there. And yet that nothing is enough to wrap a spacecraft in glowing gas hot enough to destroy it.

The obvious reading is that the vehicle rubs against the air and the friction heats it. Hold that thought lightly. It gets the location right and the mechanism wrong, and once the mechanism is right the whole design of a heat shield stops looking like armour and starts looking like something stranger.

Begin with the accounting rather than the physics of surfaces. A spacecraft in low orbit moves at about 7.8 kilometres a second. Half of v squared gives about 30 million joules per kilogram — roughly seven times what a kilogram of TNT releases. Coming back from the Moon at about 11 kilometres a second, the figure is nearer 60. Every kilogram of returning vehicle is carrying that much energy, and to sit on the ground it must carry none of it.

So the real question is not why the vehicle gets hot. It is: where is all that energy supposed to go?

Consider braking with rockets instead. Killing 7.8 km/s with a decent chemical engine — exhaust speed around 2.9 km/s — needs a mass ratio of e to the power 7800 over 2900, about fourteen. Some ninety-three per cent of whatever comes home would have to be propellant, which would then need lifting on the way up. The atmosphere is not one option among several. It is the only brake anyone can afford.

Now the mechanism, and here friction genuinely is the wrong word. At hypersonic speed the air cannot get out of the way; it piles up into a shock wave standing ahead of the vehicle, and the gas crossing that shock is brought almost to rest relative to the craft in a fraction of a microsecond. Its ordered motion becomes random motion, which is what temperature is. Work out the ideal-gas temperature rise from that conversion and you get tens of thousands of kelvin — absurdly high, and the real gas never reaches it, because the energy goes instead into tearing molecules apart and stripping electrons off atoms. The shock layer ends up as thousands of degrees of dissociated, partly ionised air.

That answers the puzzle in the question. Temperature is energy per molecule, not energy per cubic metre. Thin air does not mean cool air; it means few molecules, each carrying an enormous share. Thinness governs the rate at which heat is delivered, not the temperature it is delivered at.

Which turns the design problem inside out. The energy has to go somewhere, and the good place is the air. Here is the counterintuitive move that made crewed return possible: make the vehicle blunt. A slender, streamlined shape — the instinct of every aircraft designer — draws the shock in tight against the skin and pours the heat straight into the structure. A blunt body pushes a detached bow shock well out in front, so most of the heated gas is thrown sideways and swept away before it can touch anything. H. Julian Allen and A. J. Eggers worked this out at NACA around 1953, and it is why capsules look like the wrong end of a shuttlecock.

The rest is trajectory. Heating rate rises steeply with speed but also with air density, so the entry corridor is chosen so that the vehicle sheds most of its velocity high up where there is almost no air to heat, and only meets thick air once it is slow. Too shallow and it skips back out; too steep and it arrives fast in dense air, where loads and heating both spike. The thin air at peak heating is not an embarrassment for the theory — it is the whole point of the plan. Whatever heat still arrives is given something to consume: an ablative shield chars and vaporises, and the departing gas both carries energy away and blows outward into the shock layer.

Two corrections are worth making explicit. First, "friction" implies the surface doing the heating, with a rougher surface heating more. It does not work that way. The heating is done by the gas the shock has already compressed, and the vehicle is then warmed by that gas — by convection from it and, at high enough speeds, by radiation from it. On a fast lunar-return entry, radiation from the glowing shock layer becomes a serious fraction of the total load, which is exactly why an entry at 11 km/s is a different engineering problem from one at 7.8. Second, the glow is mostly not the vehicle: much of the light comes from shock-heated, ionised air, and that ionisation is also what interrupts radio contact during part of the descent.

It is fair to add that the altitudes quoted for peak heating and peak deceleration are approximate and shift with entry angle, vehicle shape and mass.

• Why entry from an interplanetary trajectory, arriving faster still, is dominated by radiation rather than convection.
• How the thin Martian atmosphere makes landing large masses harder than either orbital return to Earth or a landing on an airless Moon.

Every term the collection defines is gathered in the glossary.