Foundations — Environmental testing — thermal vacuum (TVAC), vibration, acoustic, EMC - EMI

This page assumes you know nothing. Every letter in the parent note — $\sigma$, $\epsilon$, $T^4$, ${\omega }_n$, $\zeta$, $Q$, $\text{Tr}$, $g_{rms}$, PSD, dB, Torr — is built here from the ground up. If a symbol appears in the parent, it is defined below before you are asked to trust it.

Part A — Numbers that describe "how hot"

Temperature $T$ and the Kelvin scale

The picture: imagine a bag of tiny bouncing balls. Cold = balls barely move; hot = balls slam around wildly. Kelvin counts from "no motion at all".

To convert from the Celsius you know: $T_{\text{K}}=T_{{}^{\circ }\text{C}}+273.15$

So room temperature $20{}^{\circ }\text{C}=293\text{ K}$, and space's background is about $3$ K — almost totally still.

Figure s01 shows two thermometers side by side — Celsius on the left, Kelvin on the right — with coloured dots for absolute zero, water's freezing point, room temperature, and a TVAC hot soak. Follow any horizontal arrow: the physical point is identical, only the number on the scale shifts by $273.15$. Notice absolute zero sits at $-273.15$ on the Celsius rod but at $0$ on the Kelvin rod — that is the whole reason we prefer Kelvin.

Part B — How heat moves (and why vacuum changes it)

There are exactly three ways heat travels. You must know all three to see why space is special — and, as promised, each gets a symbol and a law, not just a word.

Figure s02 draws a red hot block with all three exits: a blue arrow showing conduction along a solid bar to the left, green arrows of rising warm air (convection) — labelled "GONE in vacuum" — and a yellow wavy infrared arrow (radiation) to the right that survives even with no air.

Part C — Building the radiation formula symbol by symbol

The parent's headline formula is $q=\sigma \epsilon T^4$. Let's earn each piece.

Area $A$

$A$ is just how much surface is doing the radiating, in square metres (${\text{m}}^2$). Bigger radiating surface → more heat escapes, exactly as a bigger window lets out more light.

Emissivity $\epsilon$ (Greek letter "epsilon")

Picture two identical hot plates: a matte-black one throwing off strong infrared, a shiny one barely glowing. Same temperature, very different $\epsilon$.

Absorptivity $\alpha$ (Greek "alpha")

The twin of $\epsilon$: $\alpha$ is the fraction of incoming light a surface soaks up (the rest bounces off). Sunlight hitting a solar panel is governed by $\alpha$; heat leaving it is governed by $\epsilon$.

The Stefan–Boltzmann constant $\sigma$ (Greek "sigma")

Why the fourth power, $T^4$?

Figure s03 plots $q=\sigma \epsilon T^4$ against temperature. Two blue dashed markers at $300$ K and $350$ K let you read the height jump straight off the curve — the green label shows the $\approx 1.85\times$ increase for only a $50$ K rise. The steepness is the fourth power made visible.

Now the whole formula reads in plain words:

Part D — Pressure and the meaning of "vacuum"

Picture a room crowded with people (760 Torr) slowly emptying until only one person wanders per city block ($10^{-5}$ Torr).

Part E — Shaking: the vibration symbols

Mass $m$, stiffness $k$, damping $c$

Figure s04 (left panel) is the schematic: a yellow mass $m$ hangs from a blue spring $k$ and a green damper $c$ fixed to the ceiling, with a red double-arrow marking its displacement $x(t)$. The right panel is the payoff — a plot you should study next.

The dots in $\ddot{x}$ and $\dot{x}$ mean rates of change over time: $\dot{x}$ = velocity (how fast it moves), $\ddot{x}$ = acceleration (how fast the velocity changes). We need these because Newton's law connects force to acceleration.

Natural frequency ${\omega }_n$ and $f_n$

Damping ratio $\zeta$ and quality factor $Q$

Resonance and transmissibility $\text{Tr}$

PSD, g²/Hz, and $g_{rms}$

Decibels (dB) for sound and slopes

Part F — Electromagnetic noise (EMC/EMI symbols)

How these foundations feed the topic

These feed directly into the parent topic, and connect outward to Spacecraft Thermal Control Systems, Launch Vehicle Dynamics, Structural Mechanics, Electromagnetic Wave Propagation, Reliability Engineering, and Quality Assurance in Aerospace.

Equipment checklist

Test yourself — can you state each without peeking?