Space agriculture - 2D habitat air balance

Crew respiration and wheat photosynthesis share one cabin atmosphere: how much crop keeps the air breathable.

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The science

Photosynthesis and respiration are the crew's air supply

Net photosynthesis 6 CO2 + 6 H2O + light → C6H12O6 + 6 O2 evolves one mole of O2 per mole of CO2 fixed. A crew member consumes about 0.84 kg O2 and exhales about 1.0 kg CO2 per day (respiratory quotient about 0.87). Canopy gross photosynthesis here is a saturating light response P = Pm(1 - exp(-α I f / Pm)) where f = 1 - exp(-k LAI) is the Beer-Lambert light interception and Pm rises with CO2 and falls away from the optimum temperature.

Closed-loop bookkeeping

Cabin air is a well-mixed ideal gas, n = PV/RT. Fixed carbon becomes dry biomass (CH2O, 30 g/mol); plant respiration returns CO2. The page tracks carbon in air plus biomass and checks conservation. LED power follows from a photon efficacy of about 2.5 µmol/J.

Honest simplifications: generic wheat-like canopy with illustrative constants, no nutrient or water limitation, no growth stages, constant harvest rule (dry matter above 900 g/m2 is cut back), crew rates are averages, and trace gases, humidity, thermal control and power supply are not modelled. Literature estimates of the crop area needed per person range roughly from 20 to 50 m2 depending on light and CO2.

What to try
  • "Crew only (no plants)": CO2 climbs steadily and the CO2 controller (scrubber) caps it, while O2 falls.
  • "Too little crop": plant O2 stays below the crew demand (bottom-right graph) so cabin O2 drifts down.
  • Raise LED PPFD or CO2 setpoint: the same crops make more oxygen but use more LED power.
  • Read the "Area for crew O2" readout and set the crop area near it.
Cabin oxygen
Biomass and canopy LAI
Plant net O2 vs crew demand