The Snow Shelter Balance: Inside Temperature, Wall Thickness, and the Ventilation a Sleeper Can Afford

A snow shelter is warmed only by its occupants, and it must exchange air with the outside to keep carbon dioxide down; both facts can be put into one steady-state balance. This study models a hemispherical shelter of inner radius 1.1 m with a snow wall of stated thickness, snow conductivity stated by density, a sleeping metabolic heat of 75 W per person, and the fresh-air flow required to hold carbon dioxide at a stated limit of 3000 ppm, which is 4.65 m³/h per sleeper and which carries away heat at 1.679 W/K per sleeper. For two sleepers, a 0.45 m wall, and snow of density 300 kg/m³, the equilibrium inside temperature is −27.2 °C when it is −40 °C outside, −17.2 °C at −30 °C outside, −7.2 °C at −20 °C outside, and would reach 0 °C (with a computed uncapped value of +2.8 °C, the surplus going to melt the wall) at −10 °C outside. Thickening the wall from 0.30 m to 0.60 m raises the inside temperature by only 3.2 K, because the floor and the ventilation together lose as much heat as the wall. At −20 °C outside, the inside reaches 0 °C at 4.02 sleepers; at −30 °C it would need 10.14 sleepers, more than the shelter can hold, and at −40 °C 42.46, because each added sleeper brings 75 W of heat but also a ventilation loss that grows with the temperature difference. Sealing the shelter to save heat does not work: with two sleepers the carbon dioxide limit is reached in a computed 18.0 minutes. In thick, low-density walls with several sleepers, ventilation is the largest single loss — 60.6 percent of all loss for four sleepers behind a 0.60 m wall of low-density snow — and it, not conduction, sets the warmest temperature the shelter can reach. The sizing rule is: build the wall near 0.45 m, spend remaining effort on floor insulation and a small, controllable vent, and size occupancy to the coldest expected night rather than expecting extra occupants to warm a very cold shelter to 0 °C.