*I haven't double checked these numbers, but it seems to be close - my math could be off...
Typical solar insolation is around 7 kwh/sq meter in your area in the summer. Or 7k Joules per second.
Water requries 4.2k Joules per kilogram per degree C.
550 gallons is 2082 kilograms. From 66F to 80F is 16F difference or 9 degrees C.
This nets a requirement of 78,699.6k joules to heat the 550 gallon pool. Assuming a solar insolation of 7kwh/sq meter, then a 1 sq meter heater at 100% efficiency would take 11,242.8 seconds to heat the pool - or approximately 31.23 hours. Obviously this won't work because you only have ~12hrs worth of insolation, and likely a lot less 'effective' hours depending on shade/angle.
So let's assume that the height of insolation will last approximately 4 hrs, then we need 7.8 times more area. So now the solar heater has to be ~8 sq meters. But a solar heater is not 100% efficient, and will need some excess capacity in order to deal with wind, shade, etc. At 71% efficiency (a figure I found on some random solar heater page) that brings us to 11sq meters or approximately 100 sq ft.
With 10ft long conduit you'd need 10' worth of width as well - at 1/2 diameter that's 240 10' lengths of conduit, or 2400' of conduit, or $624 worth of conduit prior to hoses, connections, etc.
