April 1970: after the Apollo 13 oxygen-tank explosion, three astronauts crammed into the two-man Lunar Module "lifeboat" for the trip home. The LM's lithium-hydroxide (LiOH) CO2 canisters were sized for two men for two days — not three men for four. The Command Module carried plenty of spare canisters, but they were square and the LM sockets were round.
CO2 produced: dm/dt = n_crew · r_person (r ≈ 0.043 kg CO2 / person / hour, resting)
Partial pressure (ideal gas law):
P_CO2 = (m_CO2 / M_CO2) · R · T / V_cabin
M_CO2 = 44 g/mol, R = 8.314 J/(mol·K), T ≈ 294 K, V_LM ≈ 6.65 m³
mmHg = P_CO2[Pa] × 760 / 101325
Reaction: 2 LiOH + CO2 → Li2CO3 + H2O (fixed absorption capacity per canister)
Removal: dm/dt -= Σ (active, unsaturated canisters) × rate_canister
- Crew in the LM — 2 (design case) or 3 (the real April 1970 crowding); more crew means faster CO2 production.
- Mission clock speed — how many simulated minutes pass per real second, so a multi-day buildup plays out quickly.
- Mailbox adapter fix — toggles the two square Command Module canisters onto the cabin air loop through the improvised cardboard-and-tape duct (the real fix, built from a suit hose, a sock and duct tape). With it off, only the two round LM canisters can absorb CO2 — the historical bottleneck. With it on, both canister banks scrub in parallel, roughly doubling total CO2 removal throughput.
The dashed mark on the gauge is NASA's ~7.6 mmHg (1%) caution threshold; concentrations at or above 15 mmHg (2%) are treated here as the danger threshold, where headache and impaired judgement begin. The "computed" box above numerically integrates the same mass-balance equation from mission start with the fix permanently off vs. permanently on, so the two numbers are the genuine difference the historical fix bought the crew — not a scripted value.