Calculating The Energy Gained From Solar Heating

We can work out the benefits of solar heating from work carried out by several government agencies. The Building Research Establishment estimates that the average household uses 170 litres of hot water daily at a temperature of 55°C. This represents a useful energy demand of about 3350kWh per year. Another BRE estimate gives the consumption per person as 50 litres per day, with a useful energy demand of 18kWh per person per week, or about 3750kWh per year for a four-person household. The BRE also reckons that a solar collector with an area of 4m2 could supply 1400kWh of useful energy per year, less than half the annual demand of a typical household. Even if the solar energy replaces on-peak electricity, which is the most expensive way to heat water, the value of the 1400kWh of electricity saved will not be very high and the saving in financial terms will not be great.

Before considering solar energy it is worth trying to reduce the demand for hot water, as this will save conventional fuel and allow a solar system eventually to make a greater proportional contribution to water heating. The obvious way to reduce the amount of energy used to heat water is to put a thick jacket of insulation round the hot water cylinder and the hot pipes. A further contribution to energy saving can be made by installing spray taps which use less water. It would also help simply to get into the habit of not washing under running taps and to mend leaking washers.

solar-water-heating-calculations

Only when you have carried out all possible schemes to reduce the need for energy is it worth considering the use of solar energy to heat water. If you do then decide to put in a solar collector you will gain more useful energy from it if you alter your habits to coincide with the course of the sun. Do the washing on sunny days when you collect lots of heat and have hot baths after a day of sunshine rather than on a day of overcast skies. By doing this you will use the solar energy to its best advantage and reduce your need for back-up fuels.

Calculating the energy gained

You may want to calculate how much energy a solar collector will give you. A 4m2 average collector, facing south and angled at 30° to the horizontal, will yield about 1400kWh of useful energy annually in the London area, and will give most of this energy in the summer. Further details are available using data from BRE computer studies based on solar radiation figures for Kew, just outside London. The results show the energy received by 1m2 of collector surface. To work out how much useful energy is collected, multiply these figures by the collector efficiency which the BRE takes to be 35 per cent over the whole year; so you multiply by 0.35.

Calculation from first principles

If you live in the North of England or somewhere else a long way from Kew you can calculate the energy collected from first principles. This is a long and tedious job, so it is only worth doing if you are really anxious to know. Because Kew is about the only place with detailed solar data, the details of the behaviour of the radiation in the following formulae are based on averages of Kew figures. For the number of hours of bright sunshine, use figures relating to your own site. We do not know if this method of calculation is accurate, but it gives a close tie-in with the BRE figures so should not be too far off the mark.

To start with you need to know the number of hours of bright sunshine per month where you live. The best place to ask is your local public library where they may have a copy of the Meteorological Office Climatological Atlas of the British Isles or perhaps some more recent figures. Failing that, a local RAF station might be able to help, or a university. If you use the Climatological Atlas you will have to use the data from the weather station nearest you.

There are two separate calculations to be made for the solar energy received by a collector, one for direct radiation (which is self-explanatory) and one for indirect radiation, which is that part of the radiation that is scattered off clouds, reflected from the ground and comes from the whole sky rather than just from the sun itself.

The formula for direct radiation

In a given month a solar collector will receive 0.698 I n sin(0+a) kWh of direct radiation per square metre.

I is the average monthly intensity of direct solar radiation on days of high radiation, measured in calories per square centimetre per minute on a surface normal to the radiation. You do not have to worry too much about that definition.

The figure of 0.698 in the formula converts the cal/cm2/min to kWh/m2.

  • Jan 0.41 Jul 0.63
  • Feb 0.49 Aug 0.71
  • March 0.62 Sep 0.63
  • April 0.65 Oct 0.57
  • May 0.76 Nov 0.46
  • June 0.77 Dec 0.41

n is the number of hours of bright sunshine in the month. 0 is the angle between the collector and the horizontal. A is the average solar altitude in the month under consideration: this is the apparent angle of the sun above the horizontal and will vary according to your latitude.

The formula for indirect radiation

The next step is to work out the indirect radiation on the collector. In a given month a collector receives 0.698 in (1 + cos 0) kWh of indirect radiation per square metre.

I is the average monthly background diffuse radiation intensity, measured in calories per square centimetre per minute on a horizontal surface.

Combining the two results

The indirect radiation is calculated for each month and the result added to the respective monthly direct radiation figure that you worked out earlier. This gives you the total number of kWh of solar radiation falling on one square metre of the collector each month. All that remains is to multiply the figure by the total area of the solar absorbing surface in the collector and then by the assumed efficiency, say 35 per cent (or 0.35) for a homemade solar panel and 30 per cent (or 0.3) for a trickling solar roof.

These efficiencies are on the pessimistic side: the solar radiation figures assume that the collector will be operating only during periods of bright sunshine when efficiencies should be higher than the BRE’s annual average figure. But it is safer to make a conservative estimate rather than a wildly optimistic one. At least the installation then has a chance of performing better than you expected. When you have multiplied your results by the collector area and the efficiency you will end up with an estimate of the useful energy that the collector will give you each month.

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