The room is modelled as one well-mixed air volume. Each occupant exhales CO₂ at a steady metabolic rate G (set by the Activity level control); the HVAC system replaces air at a fresh-air rate Q proportional to occupancy. The concentration C obeys a first-order mass balance:
V · dC/dt = N · G · 10⁶ − Q · (C − C_out)
V = room volume (L) N = occupants
G = per-person CO₂ output (L/s), set by activity level
Q = N · q (q = fresh-air rate, L/s/person)
C_out = outdoor ambient CO₂ (ppm), adjustable
Solved forward with a sub-stepped Euler integration, C relaxes exponentially toward the steady state C_out + N·G·10⁶ / Q — substituting Q = N·q shows occupancy N cancels out of that ratio, so raising the per-person fresh-air rate is what actually caps the ceiling, not just adding more vents for more people. The simulation runs at 30× real time so the multi-minute approach to equilibrium is visible in seconds.
The cognitive-performance index is a piecewise curve reflecting the broad pattern reported in indoor-air-quality decision-making studies (e.g. Satish et al. 2012, Harvard "CogFx" 2015/2016): performance is essentially flat below ~600 ppm, drifts down through 1,000–2,500 ppm, and drops sharply above ~3,500 ppm as CO₂ itself (not just a proxy for other pollutants) measurably impairs strategic thinking and information usage.
- Occupancy — more people, more CO₂ generated per second.
- Fresh-air rate — ASHRAE 62.1 recommends roughly 2.5–10 L/s per person for offices; below ~5 the steady state usually exceeds 1,000 ppm.
- Room volume — a bigger air buffer slows how fast concentration changes, but doesn't change the eventual steady state.
- Activity level — harder breathing raises per-person CO₂ output G, pushing the steady state higher for the same ventilation.
- Outdoor CO₂ — the floor the room can never go below; urban/rural ambient varies roughly 400–500 ppm.
- Open a window — temporarily multiplies the fresh-air rate for 30 simulated seconds, showing how fast a burst of ventilation pulls CO₂ back down.