This is a 2D phase-space view of the same cabin-atmosphere control loop as the 3D particle-cloud version — instead of watching individual O₂ and N₂ molecules drift through a habitat, you watch the station's state itself move through a 2-D plane whose axes are the two numbers that actually decide crew safety:
x = P_total = P_O2 + P_N2 (Dalton's law)
y = P_O2 (ideal gas law per species)
Every safe or unsafe condition is a region of this plane, not a single number: the green rectangle is the intersection of the safe total-pressure band and the safe ppO₂ band; orange strips above/below it are fire-risk and hypoxia; blue strips left/right are under- and over-pressurization. The bright dot is the station's current state, and the fading trail behind it is its recent history — a leak drags the trail left and down, and the controller fights back by pushing it right and up.
Underneath, the physics is identical to the 3D version: gas is tracked as two independent masses converted to partial pressure, a hull breach loses gas by molecular effusion, and a deadband controller draws on finite N₂/O₂ tanks to correct total pressure and ppO₂ independently. Effusion's mass rate scales as √(molar mass) — the heavier O₂ molecule carries more mass out through the hole per escape than the lighter N₂ does, even though N₂ escapes in slightly larger mole counts (the classic Graham's-law statement, which is about mole/number rate, not mass rate):
ṁ_i = P_i · A_hole · √(M_i / (2π·R·T)) (Hertz–Knudsen effusion, mass form)
The strip chart below the phase plot plays the same trajectory out against time, so you can read both "where is the station right now" and "how did it get there."
- Leak hole diameter — sets the effusion area of the breach; the trail's leftward/downward pull scales with hole area, not linearly with diameter.
- Crew size — each astronaut metabolizes O₂ at a steady real-world rate (~0.84 kg/day), a slow drift the controller must also cover even with no leak.
- Controller response gain — scales both valves' maximum makeup flow; too low and the trail escapes the safe rectangle into a hazard strip before the controller can pull it back.
- Simulate Puncture — snaps the leak to a large hole instantly, so you can watch the state point jump and the controller correct it in real time.
Real-world relevance: this is the same pressure-vs-composition control problem ISS and other crewed spacecraft solve continuously — total cabin pressure held near 101.3 kPa with ppO₂ kept in a narrow band that is neither hypoxic nor a fire hazard.