We had a member report using rings, similar to those shown, successfully on her pool last year. You can search for her posts if you like.
The 21,000 BTUH claim is almost certainly greatly exaggerated. As best I could determine, daily *peak* insolation values for the area west of San Francisco is not likely to exceed 600 watt-hrs/m^2. That translates to 60 watt-hrs/ft^2 or 200 BTUH/ft^2. For the 5' rings sold by InTheSwim have about 78 square feet of area, for a maximum possible gain of about 16,000 BTUH.
But, when you allow for reflectance, re-radiation, non-optimal tilt, etc . . . you'll never get 16K BTUH in heat from a single ring.
Also, if you use your pool every day, someone will likely get pretty tired of removing and then replacing them.
But, if
+ you use your pool intermittently;
+ are conscientious about maintenance tasks
+ lose heat to evaporative heat loss (probably -- I assume the air is quite dry)
then, you may like them.
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