Intuition The one core ideaA spaceship's nose hits air hotter than lava when it falls back to Earth, so we build it from carbon held together by more carbon — a stuff that never melts, gets stronger when hot, and barely changes size when heated. The only price: raw carbon burns in air, so almost all the engineering is about keeping oxygen away from it.
Before you can read the parent note, you need to own every symbol and word it throws at you. This page builds each one from nothing: plain words → the picture → why the topic needs it. Read top to bottom; each block uses only things defined above it.
T Δ T T temperature , "how hot" something is, measured in kelvin (K). A change of 1 K is exactly the same size as a change of 1 °C — they only start counting from different zeros.
Δ T change in temperature==: final temperature minus starting temperature.
Δ T = T final − T start
The triangle symbol Δ "the change in." It does not mean multiply — it is glued to whatever follows it. So Δ T
Think of a thermometer with two marks: where it started and where it ended. Δ T gap between the two marks — the length of the red arrow in the figure below. A big Δ T
Why the topic needs it: re-entry heats the nose by roughly Δ T ≈ 1200 – 1500 how big Δ T Thermal stress and α (coefficient of expansion) .
ε ε how much longer (or shorter) something got, divided by its original length . It is a pure number (a fraction), no units.
ε = original length change in length
Take a rubber band of length L Δ L as a fraction of the whole band . Stretching a 10 cm band by 1 cm gives ε = 0.1 bigger strain — that's why we divide by the original length.
Why the topic needs it: heating makes a material want to grow — that wanting is a strain. If it can't grow, the strain gets pushed back into it as stress (next symbols). We need ε
α α how much strain you get per one degree of heating . Units: "per kelvin," written K − 1 ε t h = α Δ T ε t h thermal strain — the fractional growth caused purely by heat.
The subscript "t h thermal one (there will be a mechanical one later). Subscripts are name tags, not maths.
α α α ≈ 2 × 1 0 − 6 K − 1 Δ T α α
Why the topic needs it: small α
E E how hard you must push to strain a material . Big E E pascals (Pa), and usually gigapascals (GPa = 1 0 9
Two springs: a stiff one (high E E E
Why the topic needs it: stress σ cracks a part. We need E
Now every symbol is earned, so the parent's key formula reads itself.
this multiplication and not something else
We multiply three things because each independently makes stress worse: hotter jump (Δ T α E any of them small and stress drops. Carbon wins by having a tiny α
Definition States of matter:( s ) ( l ) ( g ) phase the substance is in: ==( s ) ( l ) ( g ) C ( s ) H 2 ( g )
Definition The reaction arrow→ heat → turns into ." Stuff on the left (reactants) becomes stuff on the right (products). Writing a temperature above the arrow, ∼ 110 0 ∘ C
Worked example Reading a real oneCH 4 ( g ) ∼ 110 0 ∘ C C ( s ) + 2 H 2 ( g ) gas , heated to about 1100 °C, turns into solid carbon plus two lots of hydrogen gas ." The small 2 H 2 grown inside the pores — see Chemical Vapour Infiltration / Deposition (CVI/CVD) .
Δ H Δ H the heat given out or taken in by a reaction . If Δ H < 0 releases heat (it's "downhill," happens eagerly) — that's why C + O 2 → CO 2 Δ H Δ
Why the topic needs it: the making of RCC (pyrolysis, CVI) and its Achilles heel (oxidation) are all chemical reactions. You must read these arrows fluently.
Common mistake "Melting" vs "subliming"Melting: solid → liquid → gas (three stages). Subliming: solid → gas directly, skipping the liquid. Carbon sublimes near 3600 °C — it never becomes a puddle. That's why you can't cast it and why it holds its shape. See Graphite structure and sublimation .
Common mistake "Hot" vs "in oxygen"High temperature and burning are different threats. Carbon survives insane temperature but oxidises (burns) in air above ~400 °C . Keep the two separate — the whole SiC-coating story exists only because of the second one. See Silicon Carbide and oxidation-resistant ceramics .
Thermal strain = alpha times dT
Thermal stress = E alpha dT
Reaction arrows and states
Pyrolysis and CVI make the matrix
Why SiC coating is needed
Why carbon holds its shape
Cover the right side and test yourself. If any line is fuzzy, re-read its section above before opening the parent note.
What does the triangle in Δ T "The change in" — final minus start; it is not multiplication.
What is strain ε Change in length divided by original length; a unitless fraction.
What does α Fractional growth per degree of heating; units K − 1
Why does small α Small α σ = E α Δ T
What does E How stiff a material is — how much stress you get per unit strain.
State Hooke's law in words. Stress equals stiffness times strain: σ = E ε
What do ( s ) ( l ) ( g ) Solid, liquid, gas — the phase of that substance.
What does Δ H < 0 It releases heat; runs eagerly (like carbon burning).
Difference between melting and subliming? Melting passes through liquid; subliming goes solid straight to gas.
Does surviving high temperature mean carbon can't burn? No — carbon still oxidises in air above ~400 °C; temperature and oxygen are separate threats.
