Hull Breach: Rapid Cabin Decompression

Breach Status

SEALED — press Open Breach

Controls

Breach diameter 50 mm

Cabin volume 100 m³

Starting pressure 101.3 kPa

Discharge coeff. Cd (hole sharpness) 0.70

Live Readouts

Cabin pressure

101.3 kPa

Elapsed time

0.0 s

Mass flow rate

0.00 kg/s

Time of useful consciousness

∞

How it works

Outside a breached hull is near-vacuum, so the pressure ratio across the hole is always far below air's critical ratio (0.528) — the escaping gas is choked at the hole for the entire event. 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 decay for cabin pressure:

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)   (exact for constant λ, integrated live here with a clamped Δt)

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. TUC collapses from tens of minutes to single-digit seconds as the 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.

Cabin air (particles) Breach point

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