Some data of interest to pool designers
Welp, I can now give up some data that might be of interest. I'm finding that, in fact, my planning is working out better than expected regarding heating. I'm finding that I can actually keep this small pool 6000 gallons quite warm with deadfall firewood with a little effort. For the designers in the crowd, my assessment is that the 2 inch styrofoam boards outside the concrete (cinder block) walls is probably quite important.
I'm finding that by running the fire perhaps every other day through the daylight hours will increase/maintain the water in the 70s. I've added an automotive radiator in the heating chamber, and plumbed the filtration water through there. And the heat is still not totally free. To heat, I have to run about a KW of electricity to turn the two fans and the pump. But, for me, its worked out pretty well. I'm pleased. I'm probably not all that objective, and it is a little bit of a case of special circumstances, but there's data here that might be extrapolated by competent engineering. The bottom line, a very small pool, carefully built, can be heated throughout the winter with free (trash quality) wood and for me, it seems a pretty good set of trade-offs.
BTW, I can also confirm that building a pool in the woods is a really dumb idea, and that most family pets are (to my surprise) not at all familiar with swimming.
PS The heatloss with all of the heating stuff cold for 48 hours is 1 degree F per 24 hours. Thats with 2 inch 4x8 styrofoam casually place on surface, with 1 'blue tarp laid over those, under an unheated homemade greenhouse hoophouse (very leaky). My arithmetic had predicted 1.5 degrees per day. Its been mild here, dipping into the high 30s at night and drifting up into the 50s during the day.