Home Contact Sitemap
Sun Volt

Sun Volt Solar Blog

earth, the final frontier

Clean Energy, Clean Environment

We are at a cross roads in human history, we can choose to continue on as we have been, or we can make a change to improve our future and quite possibly the future for several generations to come. We are here to promote energy independence, a better environment with a higher return on investment for your hard earned money. It is what I believe in, it is why I am in the solar business.

Formulas for Solar Hot Water Systems

09 Apr 08 | Solar Hot Water

Something that I get asked quite often is “How do you know this will make enough hot water?” That is a very good question and there are several rules of thumb regarding the size of Solar Domestic Hot Water (SDHW) systems. A properly sized SDHW system will provide between 70-80% of the annual hot water. While it would be nice to provide 100 percent, this is not a realistic goal in the Northeast because of the limited daylight hours during December and January.

General rules of thumb are:

  1. Allow 20 gallons per day of use for the first two people
  2. Allow 15 gallons per day of use for each additional person

So the basic house with four people would need 70 gallons of hot water per day. The closest conventional water heater sized to that use is 80 gallons, therefore an 80 gallon SDHW system would be appropriate for that household.

Solar Collector surface area is based on the size of the solar storage tank. Again, these are rules of thumb that have been tried and tested since the 1970’s for SDHW systems:

  • Northern New England: 1Ft2/0.75 gallons
  • Northeast, New England, Mid Atlantic and Northwest: 1ft2/1.0 gallons
  • Midwest and Mountain States: 1Ft2/1.25 to 1.5 gallons
  • Southeast, Sunbelt and Hawaii: 1Ft2/1.5 to 2 gallons
  • Sunbelt desert areas: 1Ft2/1.75 to 2.25 gallons

Calculating Energy to heat water

If you are not interested in rules of thumb, here is how to calculate the actual energy required for any SDHW system. First, use the Hot Water Formulas and Calculations to determine how much hot water will be used. That use needs to be converted to a unit of energy. In the US, we use BTU, while the rest of the world uses Joule as a measurement of energy.

The basic formula is:

Energy (BTU)= Vgal x 8.345 x (Texpected - Tin) x eff

Where:
Vgal is the volume of water in gallons
Texpected is the expected hot water temperature
Tin is the temperature of the cold water supply
Eff is the system losses

The temperature for both the cold water supply and the expected hot water need to be know to calculate (Texpected - Tin). This is called the Δ T (delta T), or change in temperature. For example, the incoming water supply from a well is 45 degrees F. The expected hot water temperature is 125 degrees, this leads to a Δ T of 125 degrees - 45 degrees = 80 degrees.

From the above rules of thumb, or the Hot Water Formulas and Calculations, the example household is using 70 gallons of hot water per day.

A gallon of water weighs 8.345 pounds. It takes 1 BTU to warm 1 pound of water 1 degree Fahrenheit.

Therefore, 70 gallons of water x 8.345 pounds is 584.15 pounds of water. To 584.15 pounds x 80 degrees F = 46,732 BTU, plus efficiency losses and system losses. Efficiency losses in a SDHW system are in the solar collector glazing transmissivity, heat exchangers, pumps, etc. Generally they run around 10 to 15 percent. System losses are stand by tank loss, piping loss, etc. Generally they run about 10 percent.

Therefore, the entire solar collector array will need to collect 125 percent of the required BTUs noted above, or 46,732 BTU x 1.25 = 58,415 BTU per day.

Below are comparisons of how much conventional fuel would be used to heat the water in the example household:

  1. Electricity has 3,413 BTU per kWh. Electric hot water systems are 100 percent efficient, but have standby losses. Therefore (46,732 BTU x 1.10)/3,413 = 15 kWh per day. At $0.175 per kWh utility company rates, that equals $2.625 per day
  2. Propane has 91,600 BTU per gallon. Propane hot water systems are about 65 percent efficient and have stand by losses. Therefore (46,732 BTU x 1.55)/91,600 = 0.80 gallons of propane per day. At $3.05 per gallon, that equals $2.41 per day
  3. Natural gas has 100,000 BTU per Therm (Therm is 1 CCF or 100 cubic feet). Natural gas hot water systems are about 65 percent efficient and have stand by losses. Therefore (46,732 BTU x 1.55)/ 100,000 = 0.73 CCF per day. At 1.60 per Therm, that is $1.15 per day
  4. Heating oil (#2 distillate) has 140,000 BTU per gallon. Oil fired hot water systems are generally 80 to 85 percent efficient and may or may not have standby losses. Therefore (46,732 BTU x 1.2)/ 140,000 = 0.40 gallons per day. At $3.97 per gallon, that is $1.59 per day.

Calculating size of solar array based on energy needed

Here is where things get a bit complex. Every location has a different amount of Insolation which is the amount of solar radiation received on a given surface. The NREL (National Renewable Energy Lab) has a program called PVWATTS which can give very specific data on a month by month basis. This is important for sizing of solar thermal space heating systems. Usually this data is given in units of kWh/Meter2 per day. That is acceptable because that can be converted to BTU/Ft2 per day by multiplying kWh/M2 by 317. Each kWh equals 3,413 BTU, A M2 equals 10.76391 Ft2. Therefore 3,413 BTU/10.76391 = 317.

I like to pick a moderate month, such as April or September, and size the SDHW system to meet 100 percent of the load in that month. I often find that this is the best compromise for the New York region as it will give more hot water than needed during the summer months, and less during the winter.

The example household requires 58,415 BTU per day from the solar system. According to the PVWATTS program, a solar collector tilted at latitude for the month of April will receive 4.63 kWh/M2 per day. Convert to BTU per Ft2, 4.63 kWh/M2 x 317 = 1,579 BTU/Ft2, therefore 58,415 BTU/1,579 BTU/Ft2= 37 Ft2.

That would be a perfect world theoretical solar collector and it is a good median figure. Like many things, there are other considerations:

  1. The efficiency of the collector absorber plate coating
  2. The efficiency of the Heat Transfer Fluid (HTF)
  3. The incident angle of the sun on the surface of the collector in both the horizontal and vertical axis
  4. The ambient temperature of the collector
  5. The internal temperature of the collector and the HTF

At this point, the equation becomes a calculus problem and a somewhat complex one at that. The general idea is to increase size to overcome the collector losses. Field work indicates that in the Northeast, doubling the theoretical size works well. This equates to about a 50% loss over the theoretical model noted above. This is how the above noted rules of thumb on collector size vs. storage tank size are formed.

1. Absorber plate coating also called “Black Chrome.” Solar selective coating has come a long way since the 1970’s. Basically, it is a type of paint that accepts and converts more energy, in the form of visible, infrared and UV light, from the sun and converts it to heat without radiating it back into the atmosphere. These are highly specialized products and are not normally available to the general public.

2. Heat Transfer Fluid or HTF. HTF removes the heat from the absorber plate and transfers it to a heat storage tank. It can be water, antifreeze, oil, etc. Water is the best HTF as far as efficiency is concerned, but can present freezing problems.

3. Sun incident angles on the collector surfaces. A solar collector is at it’s optimum when the sun is 90 degrees from the surface. The further away the sun is from perpendicular, the less dense the energy is that is striking the surface.

4. The solar collectors have operating categories based on the ambient temperature (Ta) that the collector is in vs the water temperature within the collector (Ti). This is known as the Ti-Ta. In the summer time when the Ti-Ta is 36 or less degrees Fahrenheit, the collector is operating as a Category C unit. In the winter time when the Ti-Ta can be 90, 100 degrees or even greater, the collector is operating as a Category D unit.

Related posts:

  1. Solar Domestic Hot Water Systems
  2. Does solar hot water work in cold climates?
  3. Hot Water Formulas and Calculations
  4. Solar Thermal Systems
  5. Solar Domestic Hot Water for my house

Tags: ,

09 Apr 08 | Solar Hot Water
« Solar power backup for Critical Household Systems
Congress passes Clean Energy Tax credits »


Leave a Reply