This is an independent 2D companion, not a flattened 3D scene: it solves the same choked-flow gas dynamics and draws the result as two purpose-built 2D views instead of a 3D particle cabin. Outside a breached hull is near-vacuum, so the pressure ratio across the hole stays far below air's critical ratio (0.528) for the whole event — the escaping gas is choked at the hole throughout. The choked-flow mass rate through an orifice of area A is:
ṁ = Cd·A·P·√(γ/(Rs·T)) · (2/(γ+1))^((γ+1)/(2(γ-1)))
γ = 1.4 (air), Rs = 287 J/(kg·K), T ≈ 293 K (isothermal cabin)
Cd = discharge coefficient (0.5 jagged tear → 1.0 clean-cut hole)
Combining this with the ideal gas law P = mRsT/V and dm/dt = −ṁ gives a first-order exponential decay for cabin pressure, integrated live here with a clamped Δt and plotted directly on the right-hand graph:
dP/dt = −λP, λ = Cd·A·Rs·T/V · √(γ/(Rs·T))·(2/(γ+1))^((γ+1)/(2(γ-1)))
P(t) = P₀·e^(−λt)
Falling cabin pressure is converted to an equivalent altitude with the ISA barometric formula, then mapped through published hypoxia physiology data to estimate Time of Useful Consciousness (TUC) — how long a crew member can act purposefully before donning a suit becomes impossible. The dashed line on the graph marks that moment. TUC collapses from tens of minutes to single-digit seconds as equivalent altitude climbs past ~30,000 ft, which is why a large sudden breach is unsurvivable without an already-sealed suit.
- Breach diameter — hole size; area grows with the square of diameter, so a 10× larger hole vents roughly 100× faster.
- Cabin volume — more air reserve slows the pressure drop for the same hole.
- Starting pressure — spacecraft have flown anywhere from 34 kPa (Apollo, pure O₂) to 101.3 kPa (ISS, Earth-like mix).
- Discharge coefficient — a jagged micrometeoroid puncture chokes flow more than a clean structural failure of the same nominal size.