I made some crude measurements with probe type cooking thermometer. If I would record continuously it would be more meaningful. This is just a concept.
I measured 5 cases:
#1 – cowboy camping – it was clear but protected by trees – calm – air temp was 31.5F, surface of sleeping bag was 35.5. The surface of the sleeping bag was 4F warmer than the air because of the surface layer of air right next to the sleeping bag.
#2 – cowboy camping – clear – about 50% protected by trees – calm – air 47.7, surface 43.7. The surface of the sleeping bag was 4F colder than the air because of radiative heat loss.
#3 – tent (silpoly mid with open door) – cloudy – calm – air outside 32, air just above sleeping bag 38, surface 42. The air inside the tent was 6F warmer than the outside air even though the tent door was wide open. The surface of the sleeping bag was another 4F warmer because of the air layer.
#4 – tent – clear about 50% protected by trees – windy – air outside 41.5, air inside 43, surface 44.7. The air inside tent was 1.5F warmer than outside air and the surface was 1.7F warmer than the inside air.
#5 – tent – clear about 50% protected – calm – air outside 33, air inside 40, surface 38.5. The air inside the tent was 7F warmer than the outside air and the surface was 1.5F colder than the inside air (a little radiative heat loss happening).
One over-all conclusion is if it’s calm and clear, if I sleep in the tent instead of cowboy camping, I can have the same comfort if it’s 10.5F colder. The tent lowers the effective lower comfort rating of my sleeping bag by 10.5F. In #2 the surface of my sleeping bag is 4F colder than the outside air. In #5 the surface of my sleeping bag is 6.5F warmer than the outside air.
Another over-all conclusion is that if I’m protected by trees or clouds, the tent adds 6F of warmth. In #1 the surface of my sleeping bag is 4F warmer than the air. In #3 the surface of my sleeping bag is 10F warmer than the outside air.  The tent doesn’t add as much warmth if it’s cloudy or protected by trees, as if it’s clear.
Another conclusion is that when it’s windy, most of the advantage of the tent is “blown away”. I didn’t have a night of windy cowboy camping so can’t compare. In #4 the surface of my sleeping bag is 3.2F warmer than outside air.
Based on Stephen’s data, I think a DCF tent would not add as much warmth as a polyester or nylon tent. The inside air in the tent would be colder because of radiative heat loss because the DCF doesn’t absorb IR. And the surface of the sleeping bag would be colder than the air inside the tent because of radiative heat loss. Maybe 5F colder? Maybe 10F colder?
One could calculate how much extra down one would need to make up the less warmth, and compare the weight of that to the weight saved from using DCF.
I was only in 50% clear places. Ridges and trees blocked half of the clear night sky. If I was on a mountain top or a wide plane I could get 100% clear and the temperature differences would be bigger.
One could continuously measure the air temperature outside the tent, inside the tent, and surface of sleeping bag, and wind speed and get better data.
If you know the temperature of the surface of the sleeping bag, then it’s just conduction down to your body. It doesn’t matter if it’s clear, windy, or whatever. (assuming the sleeping bag cover impedes wind enough).
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