Heat leaking through the insulation boils liquid hydrogen into vapor. The vapor accumulates in the ullage (empty headspace) and its pressure follows the ideal gas law:
boil-off rate = Q_effective / L
Q_effective = heat influx × (1 − insulation efficiency)
P = m_vapor × R_specific × T_vapor / V_ullage
When pressure crosses the relief valve's set point, the valve opens and vents vapor at a rate proportional to the overpressure, pulling the pressure back down — the same proportional-relief behavior used on real cryogenic tanks. Lateral acceleration from a maneuver tilts and sloshes the liquid surface, modeled as a damped pendulum driven by the g-load:
vent rate = k × max(0, P − P_set)
slosh angle'' = −ω0²·angle − damping·angle' + forcing·g_lateral
Better insulation and lower heat influx slow boil-off and keep pressure closer to nominal; a high heat influx with poor insulation drives fast pressure buildup, frequent venting, and faster fuel loss — exactly the trade-off cryogenic tank designers balance between insulation mass and propellant boil-off.