Seasonal pv/solar pool heating

Thomas’ calculations are correct as far as raw heat gain. I came up with about 0.42 degrees F per day or 23.7 days for a 10 degree heat gain, based upon 3 panels and ZERO losses.
However, we cannot ignore the losses. So these numbers are pretty meaningless.

Here in Northern California, most people use their pools between  3-6 months a year and we find that a typical installation runs between 50-70 percent of the pool area. (the spread in those numbers really depends on the number of months and/or exactly where in N. Calif. it is. We have a bunch of micro climates)

Assuming that your pool is about 15x30 or about 450 sq. ft and in ground, those numbers would indicate that you could need somewhere in the range of 7-10 panels to provide supplemental heat. This assumes a desired water temp of 80 degrees F. 
(For Florida, where many people are trying to use their pools year round, I understand the recommendation is about 100 percent of the pool area.)

As far as a pool cover, most of the numbers are calculated based upon the use of a cover when night time temps drop more than 15 degrees F below your desired water temperature.  So, if the desired temp is 80, it is a pool cover when the nighttime low falls below 65 degrees F.  OR, you need to increase the heat input.

Doing another back of the envelope type calculation, I came up with about 14 panels to achieve and hold an 10 degree heat rise (to an 80 degree temperature) w/o a cover.  So, would you want to buy an extra 4-7 panels to avoid using a cover ? Maybe discussing a motorized cover (or other easy cover/uncover method) might help.

But, so far, our calculations are based on a lot of assumptions.  You need to be more specific about your needs, either here, or with a professional in your area (best choice).  What is the surface area of your pool, is it in ground or above ground, what is the typical water temp, how much heat gain are you actually looking for, during what months etc. What is the horsepower and gpm of your current pool pump and how many hours a day are you currently running it ?

I don’t want to sound all doom and gloom.  I have run into situations where with a large enough pool pump being run enough hours, installing couple of valves and  a few hundred feet of 1.5 or 2 inch black plastic pipe, provided enough heat gain to satisfy the wants and needs of the owner.  Some people are not after an 80 degree pool, they just want something to take the edge off.