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Fuck you guys for making me dig up my thermodynamics textbook. The following will deal with heat loss through your backside.
Thermal cunduction can be simplified to
q/A=ΔT*k / R
q being heat transfer, A being area, ΔT being temperature difference in Kelvin, k being the thermal conductivity of the heat sink and R being the insulation value of the insulator.
If we assume a ΔT of 40 (37C body, -3C ground), a k 1.5 (dry earth) or 4 (granite) and an R of 4 (3.9 for the pad, 0.1 for the compressed sleeping bag insulation), q/A will be 15 J/s/m2 for dry earth and 40 for granite. If you lay on snow you should calculate the insulating properties of the snow and add that to the R of you pad. Snow has around 1 R-value/inch, making the formula
q/A=(ΔT*k)/(R+s)
s being the thickness of the snow in inches.
The average human body radiates about 90 J/s of energy while asleep A person that is 2 meters tall and has an average width of 0.5 meters has a base contact surface of 1 m2. Assume the insulation on top brings the heat loss through the top in equilibrium with half the total radiated heat. Therefore q/A must be less than 45 J/s/m2, or the person must either decrease his contact surface by curling up, increase his heat output by increasing his metabolism or shivering of bring a thicker sleeping bag. This calculation ignores heat loss through convection, which leads us to...
