# Solar Fraction

The water comes into our house at 50F, and we want the hot water to be at least 110F.  On our system, the solar system heats the water incoming water as hot as it can, and then a propane tankless heater heats it up to the required 110F if its not there.

So, if the solar system is able to heat the storage tank water all the way up to 110F or more, it is providing 100% of the heating, and the tankless heater does not come on.  I call this a 100% solar fraction (solar energy provides 100% of the heating).

If the solar system is only able to warm the incoming water up to (say) 80F, this is half way from 50F to 110F, and I call this a 50% Solar Fraction.

To perform the Solar Fraction calculation for a day, I look at the tank temperature in the early evening (when we use most of our hot water), and do the calculation for that temperature.  For example, if the storage tank temperature is 105F at 6pm, then the solar fraction for that day is:

SF = (105F - 50F) / (110F - 50F) = 0.917

At the end the month, I calculate the Solar Fraction for the month as the average of all the days in that month.  At the end of the year, I calculated the Solar Fraction for the year as the average of all of the monthly Solar Fractions.

## Other Factors:

### Heat Exchanger Losses:

For any kind of normal demand, the heat exchanger that we use on the system is 100% efficient, so the output temperature of the heat exchanger is equal to the storage tank temperature.  This is because the heat exchanger itself holds about 10 gallons of water that starts out heated all the way up to storage tank temperature.  For a very large draw there would be some drop in temperature, but we essentially never have this situation, so I do not account for it.  The heat exchanger has so much surface area, that it does quite well even on draws over 10 gallons.

### Pump Energy:

Our system uses a small pump to circulate water through the collector, and this should really be accounted for in the Solar Fraction calculation, since it is an energy use that is chargeable to the collection process.  I have not accounted for this, but in our case it is pretty small because our pump only draws 13 watts.

As a rough estimate of how much this would effect Solar Fraction,

If we assume that on an average day our pump runs 4 hours, then the pump energy is

Pump Energy per day = (4 hours)(13 watts) = 52 watt-hours per day

If the system provides 24 gallons hot water over that day (our average use), then the useful solar energy provided by the system is:

Energy Required to Heat Water per Day = (24 gallon)(8.3 lb/gal)(110F-50F)(1 BTU/lb-F) = 11952 BTU/day, or 3,500 watt-hours/day

So, pump energy is about (52/3500) = 1.5% of the useful solar energy output, and accounting for pump energy use would lower the Solar Fraction by about 1.5%.

Using a PV powered pump would eliminate this energy use.

### Other Rating Systems:

The SRCC rates solar water heating systems using a Solar Energy Factor (SEF), which is defined as:

SEF = (41,045 BTU/day) / (Qaux + Qpar)

Where 41,045 BTU is (I think) their view of the amount of energy needed to heat water for a typical family of 4 for a day.

Qaux is the energy that is used by the backup water heater for the day,

Qpar is the energy used by pumps and controllers.

I guess this makes sense from some point of view -- I think it may be good if you are comparing a solar heating system to a conventional water heater, because the water heater industry uses a similar measure for regular water heating systems.

For my purpose, which is to determine how well is solar water heating system I built doing in meeting my families hot water demands, it makes little sense.

One thing I don't understand at all is that the solar heating system is penalized if a low efficiency backup heater is used -- to me, the backup heater is a completely independent decision, and the effects of a good or bad backup heater should be a separate subject.

I also don't understand rating each system against a fixed hot water demand when in fact every household has its own unique demand.  It seems like this could lead to bad decisions if your demand is more or less than the 41K BTU they use.

The upshot is that there is no real way to compare the Solar Fraction I calculate to the SRCC SEF numbers -- you will have to view them as two independent ways of looking at solar water heating systems.

Gary October 5, 2009, September 13, 2010