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

This page builds the toolbox. The parent note throws around symbols like $v$, $\rho$, $\sigma$, $Q^{\ast }$, and phrases like "stagnation point" and "$\sigma T^4$". If any of those looked like magic runes, this page turns them into pictures. We go in order, so each idea leans on the one before.

1. Speed $v$ — how fast, in a straight line

The picture: an arrow along the flight path. The length of the arrow is the speed. A longer arrow means more distance covered each tick of the clock.

Why the topic needs it: every heating formula depends on $v$ — and dangerously so. As we build up to the convective heating law in section 6, we will see the heat scale as $v^3$, meaning doubling the speed multiplies the heating eightfold.

2. Kinetic energy and specific energy $e_k$

Why the $\frac{1}{2}{v}^2$ and not just $v$? Because energy is what it takes to stop the motion, and stopping something twice as fast costs four times as much work — the $v^2$ captures that. Try it: pushing against a wall twice as hard over twice the distance is four times the effort.

The picture: imagine slicing the vehicle into 1-kg cubes. Each cube carries the same $e_k$. This lets us talk about heating "per kg of shield" without knowing the total mass.

Worked number (matches the parent): at $v=7800$ m/s, $e_k=\frac{1}{2}(7800{)}^2=3.042\times 10^7\text{J/kg}\approx 30\text{MJ/kg}.$ The prefix M (mega) means one million, so $30$ MJ $=3.0\times 10^7$ J. That is the "terrifying" number: about four times the energy needed to boil away a kilogram of steel.

See Specific Impulse and Energy Budgets for where this "per kilogram" bookkeeping comes from.

3. Density $\rho$ — how much air is packed in

The picture: a box one metre on each side. Count the air molecules inside it and weigh them — that weight is $\rho$. A crowded box = high density; a nearly empty box = low density.

Why the topic needs it: the heat the vehicle feels depends on how much hot gas is thrown at it each second, and that is set by $\rho$. As we will see in section 6, the convective heating combines $\rho$ and $v$ into a product $\rho v^3$ that peaks at a middle altitude — high up there is too little air ($\rho$ small), low down the vehicle has already slowed ($v$ small). We meet that product properly once its formula is on the table.

4. Nose radius $R_n$ — how "round" the front is

The picture: below, a fat rounded nose (large $R_n$) versus a pointy nose (small $R_n$), each with the biggest circle that fits.

Why the topic needs it: the stagnation-point heating scales as $1/\sqrt{R_n}$ — a bigger, blunter nose lowers heating. We explain why in section 6, right after the convective-flux symbol is defined. This single fact explains why reentry capsules are round bowls, not arrows. Details live in Blunt Body Aerodynamics.

5. The bow shock and the stagnation point

The picture: a curved shock standing off the nose like a bow-wave in front of a boat. Between the shock and the wall is the glowing shock layer. The centreline hits the wall at the stagnation point.

More in Bow Shock and Stagnation Point and Reentry Aerothermodynamics.

6. Convective heat flux ${\dot{q}}_{\text{conv}}$ — heat carried into the wall

The picture: shine a heat lamp on a stamp-sized patch of the shield. $\dot{q}$ is how brightly that patch is being cooked; ${\dot{q}}_{\text{conv}}$ is the share of that cooking done by hot gas scrubbing against the surface.

7. Temperature $T$, radiative flux ${\dot{q}}_{\text{rad}}$, and the exponent-four law

Why the fourth power $T^4$ and not just $T$? Because radiated power grows ferociously with temperature — this is measured, not chosen, and captured by the Stefan–Boltzmann law. It is the reason a glowing tile can dump enormous heat back out: doubling $T$ multiplies the radiated heat by $2^4=16$.

The picture: the same tile at rising temperature glows dull red, orange, then white — and the arrows of escaping light thicken far faster than the temperature climbs.

The full story is in Radiative Heat Transfer and Stefan–Boltzmann Law.

8. The ablator symbols: $\dot{m}$, $Q^{\ast }$, $\dot{s}$, ${\rho }_{\text{abl}}$

The picture: the char surface peeling back like a slowly melting candle; $\dot{s}$ is the speed the surface retreats, $\dot{m}$ is the mass of "smoke" it releases.

How the pieces feed the topic

Every box carries a symbol you now own, spelled the same way as in the text: ${\dot{q}}_{\text{conv}}$ is "q_conv", ${\dot{q}}_{\text{rad}}$ is "q_rad", and $\dot{m}$ is "m dot". The parent note's formulas are just these boxes wired together.

Equipment checklist

Cover the right side and answer each before revealing: