Is the pool shaded? In Austin, 940 Btu/ft^2 of sun falls on the ground
on an average 48.8 F January day with a 58.8 daily max temp. An R1 cover
with 80% solar transmission would make 0.8x940 = 24h(T-48.8)1ft^2/R1,
for a pool temp T = 81 F. An R2 cover with 3 layers of plastic film and
70% solar transmission would make T = 104.
An 84 F pool with a 491 ft^2 R1 cover needs about 24h(84-48.8)491/R1
= 415K Btu/day. If 1 ft^2 of 4/12 (18.4 degree) south roof collects
940cos(18.4) = 892 Btu/day of overhead sun + 1200sin(18.4) = 379 Btu
of south sun, totaling 1271, and 80% enters an 84 F collector when
it's 53.8 outdoors for 6 hours and 0.8x1271-6h(84-53.8)1ft^2/R1 = 836
Btu/day, you might heat the shaded pool with 415K/836 = 496 ft^2 of roof,
eg buy a $29 No. 412700 27' round clear vs blue pool cover from
http://www.solarcovers.com (800) 433-4701 and put their $9 411632
16'x32' cover on a roof over wires to keep it from gluing itself to
the roof when there's no water trickling over the shingles beneath it.
With RC = R1x62.33x4' = 249 hours, the pool would cool from 84 F to
48.8+(84-48.8)e^-(5x24/249) = 71 F over 5 cloudy days.
In a cloudier climate, we might heat a pool with a cover inflated with air
during the day and soap bubble foam at night that can sink to the bottom
for swimming. In Phila, 620 Btu/ft^2 falls on the ground on an an average
30 F January day. If 0.8x620 = 6h(84-30)1ft^2/R1 + 18h(84-30)1ft^2/Rv
Btu/day, the cover needs US Rv = 5.7 at night, about 2" of foam.
I can't believe you typed all that Rhetoric in there. jeeeeze.....
That's engineering, not rhetoric :-)
You are welcome.