Question bank — Thermal protection systems — ablators (PICA, SLA), metallic tiles, RCC

True. Since ${\dot{q}}_{\text{conv}}\propto 1/\sqrt{R_n}$, a large nose radius $R_n$ lowers the flux, and it also stands the shock off so most heat dumps into the air, not the wall.

True. The black char of an ablator and the black-coated tile both glow and re-radiate; the difference is that the ablator also removes heat by phase change and blowing, while the tile relies on radiation plus insulation alone.

False. At very high flux the equilibrium wall temperature $T_w=(\dot{q}/\epsilon \sigma {)}^{1/4}$ climbs past the melting point of any solid; only ablation's phase change and blowing can dump that energy, so PICA survives where tiles vaporize.

False. Most of it heats the air (shock layer plus wake); only a small convective and radiative fraction reaches the wall — that fraction is what the TPS manages.

True. From $T_w=(\dot{q}/\epsilon \sigma {)}^{1/4}$, a larger $\epsilon$ in the denominator lowers $T_w$; this is why the tiles carry a black high-emissivity coating rather than staying white silica.

False. They are the hottest — smallest nose radius $R_n$ means highest $\dot{q}$ — so they need the highest-temperature reusable material, carbon–carbon rated above 1600 °C.

True. From $\dot{s}=({\dot{q}}_{\text{net}}-\epsilon \sigma T_w^4)/({\rho }_{\text{abl}}{Q}^{\ast })$, a larger $Q^{\ast }$ sits in the denominator, so the recession rate $\dot{s}$ drops and less material is consumed.

False. Radiative heating from glowing shock gas becomes important only above roughly 10 km/s; a ~7.8 km/s LEO reentry is dominated by convective heating, where ${\dot{q}}_{\text{conv}}\propto v^3$.

The error inverts the physics: a small $R_n$ gives a thin shock hugging the wall and maximum heating ($\dot{q}\propto 1/\sqrt{R_n}$). Blunt bodies are cooler, which is why capsules are round.

Thickness depends on the total heat load $Q=\int \dot{q}dt$, not just the peak flux. A short spike and a long moderate soak can hit the same peak $\dot{q}$ but demand very different material thickness.

It scales as $v^3$, not $v^2$: energy per mass gives one $v^2$, and the mass flux delivering that energy to the wall gives another $v$, so $v^2\times v=v^3$.

Re-radiation ($\epsilon \sigma T_w^4$) is only one of three mechanisms and often the smallest at high flux; the dominant sinks are pyrolysis/phase change ($\dot{m}{Q}^{\ast }$) and the blowing that blocks the boundary layer.

They work by having near-zero conductivity (≈94% air) so heat can't reach the back, plus high emissivity to re-radiate — not by storing heat. That's why a glowing tile can be held by its edges seconds after the furnace.

Mars entry is comparatively moderate flux, so cheaper SLA-561V is matched to it; PICA is reserved for the highest-flux cases like deep-space and lunar return where $\dot{q}\propto v^3$ is enormous.

The shield doesn't destroy energy but redirects it: blowing pushes hot gas away into the wake, and ablated mass carries its absorbed energy off the vehicle entirely, so that energy never enters the structure at all.

A blunt nose spreads the flow and thickens the boundary layer, which insulates the wall, and it stands the shock off so heat is dumped into the air — both captured by the $1/\sqrt{R_n}$ factor.

The outgassing (transpiration) physically pushes the hot shock-layer gas away from the wall, thickening the insulating layer and blocking convective heat before it can conduct into the surface.

Low density means a lighter shield for a given thickness, and since deep-space return has huge $\dot{q}\propto v^3$, you need a high-$Q^{\ast }$ material that also doesn't punish the mass budget — PICA gives both.

A high $\epsilon$ maximizes the re-radiated power $\epsilon \sigma T_w^4$ for a given temperature, which lowers the equilibrium wall temperature and lets the material survive.

RCC is heavy, expensive, and oxidizes; over most of the vehicle the flux is low enough that light silica tiles or ablators are far more mass- and cost-efficient, so RCC is reserved for the extreme leading-edge hot spots.

It is roughly four times the energy needed to boil a kilogram of steel, so even a small fraction reaching the structure unmanaged would vaporize unprotected metal.

It is zero — the flow is brought to rest there — yet this is the point of highest heating, because all that kinetic energy has become thermal energy in the compressed gas right at the wall.

The numerator ${\dot{q}}_{\text{net}}-\epsilon \sigma T_w^4\to 0$, so recession $\dot{s}\to 0$: radiation alone carries the load and the ablator essentially stops eroding.

Since $T_w=(\dot{q}/\epsilon \sigma {)}^{1/4}$, a smaller $\epsilon$ raises the wall temperature — a local hot spot that can exceed the material limit, echoing why coating integrity is safety-critical.

It vanishes, since ${\dot{q}}_{\text{conv}}\propto v^3\to 0$; the heating problem is confined to the high-speed portion of the trajectory, not the final subsonic descent.

It exposes the underlying structure to the peak flux with no protection, which is exactly the failure mode of the Space Shuttle Columbia Accident — a reminder that the smallest-$R_n$ spot has the least margin.

The longer one, because total heat load $Q=\int \dot{q}dt$ is larger even at equal peak flux, and thickness/mass tracks $Q$, not just the peak.