This is a pretty good method to determine how large a solar collector is needed to heat your hot tub.
The size of the collector needed to heat a hot tub depends on a lot of things: volume of the tub, how well its insulated, how good the cover is, what your climate is like, how hot you keep it, ... Its not easy to take all that into account to get a good idea what size collector you need. But, I ran across the method detailed below in "More Other Homes and Garbage" that uses the temperature drop of the hot tub over 24 hours to determine the daily heat loss for your hot tub in your climate and for the way you use it -- it seems like a good approach to me.
By the way "More Other Homes and Garbage" is a terrific book written the 80's, but full of good ideas, good analysis, and written in a style that won't put you asleep -- and, its only $8 used!
Here is the step by ste:
If you can, its best to do this test in the winter when the heat loss is higher.
If the collector area comes out quite low (say 6 sqft), I'd build a larger collector and just have some reserve in hand. If you are buying a commercial collector, you will need to just pick a size that is a reasonable match to the estimated size -- maybe the next larger size. If you are building the collector, you will want to consider standard sizes of materials -- that is, there is no point in trying to build a 26 sqft collector when standard sheet and glazing sizes would make it easier to build a 32 sqft (4 by 8) collector.
Ideally, you would do the test in the coldest part of the year in which you use the hot tub, so that the collector size is up to matching the tub heat loss in the coldest time period you use the tub. But, I would not pick an extreme cold day -- just a day that is typical of the coldest time of year you use the tub.
If you can't do the temperature drop test in the coldest part of the year in which you use the tub, then you should probably adjust the collector area upward based on the temperature difference between the hot tub and the outside air. For example, if you do the test in the spring when the hot tub temp is 104F, and the average outdoor temperature over 24 hrs is 50F, then the temperature difference is 104F - 50F = 54F. If in the winter the average outside temperature is 30F, then the temperature difference is 104F - 30F = 74F. So, you would probably want to ratio the collector area up by 74F/54F = 1.4 to get a collector area that would heat the tub on an average winter day. When estimating these temperatures, you want to use averages not extremes -- you want the 24 hour average temperature on an average day for the season you are looking -- e.g. where I am, we can get down to -40F on an extreme winter night, but our 24 hour average for the same season might be more like 25F. WeatherSpark.com is a good place to get averages.
If you don't like where you end up on the plot above (i.e. you have a large 24 hour temperature drop), consider beefing up the insulation, getting a better cover, or placing the the hot tub in a protective environment (e.g. a sunspace). Hot tubs use a lot of energy (probably more than anything else in your house), so it worth taking all the steps you can to improve their efficiency.
For some actual DIY hot tub solar heating systems, look here...
The method is from "More Other Homes and Garbage.
The hot tub heat loss can be calculated from the temperature drop of the water -- so, if the temperature drops 10F in a 300 gallon tub, the heat loss is:
Heat loss 24 hours = (300 gal)*(8.34 lb/gal)*(10F)*(1 BTU/lb-F) = 25,000 BTU
To estimate the collector area from the heat loss, the method assumes that each sqft of collector will produce 1000 BTU on a sunny day. This seems about right to me, and matches the SRCC test data for glazed flat plate collectors pretty well. For example, a Heliodyne 4 by 8 collector produces 32K BTU on a sunny day with a temperature difference of 36F...
The thing I like about this method is that by using the actual temperature drop for your hot tub where you are, it takes into account most of the many variables that would go into a fully analytical approach.
Bear in mind that in sizing the collector, a sunny day is assumed. On part cloudy or cloudy days, that may not be enough to heat the tub fully depending on the season.
Gary May 12, 2012