Once cabin pressure exceeds roughly twice the outside (vacuum) pressure, gas escaping a breach reaches the speed of sound in the hole and the flow "chokes" — the outflow rate depends only on the upstream (cabin) pressure, not on how empty space already is. That makes the mass leaving the cabin proportional to the pressure still inside it, which turns depressurization into a clean exponential decay: bigger breach or smaller cabin, faster decay.
ṁ = Cd·A·P·√(γ/RT)·(2/(γ+1))^((γ+1)/(2(γ-1)))
P(t) = P₀·exp(−t/τ), τ = V / (Cd·A·K·R·T)
Meanwhile the crew's remaining useful consciousness isn't a fixed countdown — it's a dose. Each instant spent at a given cabin pressure consumes a fraction of the time-of-useful-consciousness (TUC) budget available at that pressure, so as pressure keeps falling the budget burns faster. This sim integrates that dose every frame from published aerospace-physiology TUC-vs-cabin-altitude data, so a slow leak barely dents it while a violent rupture can exhaust it in single-digit seconds.
- Breach diameter — sets orifice area A; doubling diameter quadruples area and roughly quarters the decay time constant.
- Cabin volume — more air mass to vent through the same hole, so decay is slower for the same breach.
- Distance / egress speed — the race the crew is actually running: reach the safe module's hatch before the consciousness dose reaches 100%.
Real-world relevance: this choked-orifice model is exactly what NASA and Soyuz decompression-timeline planning uses to size warning margins and mask-donning drills — the difference between a slow leak crew can calmly patch and a rupture that leaves seconds to act.