# How Much Collector Area Do I need to Heat My Home?

 I get asked this question a lot.  Its a good question, but the problem is that its tough to give a good answer.  The answer depends on many factors -- the main ones being: - The heat loss from your home -- that is, how well its insulated and how big it is. - Your local climate -- both how cold it is and how sunny it is. - The percentage of solar heating you want to achieve -- the Solar Fraction. If you live in a cold climate with not much sun in the winter and have a large and poorly insulated home, you might have to cover half the county with collectors to get a high Solar Fraction.  On the other hand, if you live in a in a good sun place (say Denver), and have a modest size and well insulated home, the collector area needed for a good Solar Fraction will be far far far less.

I have been giving people some rules of thumb to get a very rough idea how things might come out in their situation.  I've been looking for a tool that will give a better answer and is not to difficult to use.  The new collector output simulation tool offered by Andy Schroder looks to me like part of the answer.

Andy's Solar Collector Power Output simulator provides a hour by hour, year long simulation of the heat output for:  the collector you select,  in the location you live, at the tilt angle and azimuth you select, and for the output temperature that you select.  The simulator uses the efficiency curve of the collector you select along with a local weather file to simulate collector performance and report daily energy collected.

You can directly use the heat output from Andy's collector to do a rough estimate of the heating fuel you will save for the collector configuration you enter.

If you combine Andy's calculator with our Home Heat Loss calculator, you can get some idea of the fraction of solar heating that a given area of collectors will provide for your house.  That is, you can answer the question: "How much collector area do I need to heat my home?"  -- or at least take a reasonable cut at it.

In addition to the example below that shows you how to estimate how much collector area will be needed to reach a certain fraction of solar heating for your house, I also did some examples for a few places in the US, all using the same 2000 sqft pretty well insulated house here...  This might give you a quick gut feel for what solar can achieve (and what it can't).

If you don't want to go through the detailed example just below, you might summary of what is likely to be the "bottom line" for most of us...

## Overview of the Method

While this is a fairly lengthy procedure to go through, there is really no math to do -- you just have to look up some values for your area, and plug them into the short spreadsheet you can download below.

There are three basic steps

1 - Estimating your homes heat loss by month.

2 - Entering your collector area, and some basic information on your heating system.

3 - Estimating the heat output of your solar collector array.

These results of each of these steps are entered into a simple spreadsheet that then calculates the fraction of your heat that will come from solar each month, and the associated dollar saving.

## Step1 - Estimating The Monthly Heat Loss for Your House

The first step is to estimate the total heat loss for each month of the heating season for your house -- this will later be compared to the solar gain from your solar collectors to give a solar fraction.

Your house heat loss depends primarily on two things:

- How cold it is outside

- How well insulated and sealed your house is.

### Estimating Your Home's "R Value"

We will use the Home Heat Loss Calculator to make an estimate of how much of a heat leaker your house is.  We will calculate what the HVAC people call the "UA" for the your house -- this is the heat loss per degree for your entire house.  So, if the UA of your house comes out (say) 300 BTU/hr-F, this means that for every degree of temperature difference between the inside of your house and the outside, the house will be losing 300 BTU of heat in one hour.  So, if its 70F inside and 40F outside, and you have UA of 300 BTU/hr-F, then you would be losing about (70F - 40F)*(300 BTU/hr-F) = 9000 BTU per hour of heat energy.

The UA for your house depends on how big it is, how well insulated it is, and how well sealed it is.  The calculator will work you through this to get a UA number.  So, go to the Home Heat Loss Calculator, fill in the inputs for your home, and get the "UA" total for your home.  The number you want is the UA "Total", which is the sum of the losses from walls, ceilings, floors, ...

Getting together the information needed to calculate the heat loss for your house will take some time and effort, but its very helpful to know which parts of your home are resulting in the largest part of the total heat loss, so that you can address these areas with better insulation or better sealing.  There are several examples given on the Home Heat Loss calculator page that may be helpful.

Once you have the UA total for the house, enter it in the spread sheet as the "UA House" input.

### Look Up the Heating Degree Days For Your Location

To calculate the monthly heating requirement for your house, you will also need to know the number of Heating Degree Days for each month through the heating season for your area.  Heating Degree Days are basically a measure of how cold your climate is -- they are explained here...

One good place to get your HDD numbers is the BizEE Degree Days website.  To get your Heating Degree Days from this site, do this:

1- Use the "Station Search" to find a good weather source near you.   Enter your zip code, and then pick a good weather source.  For the example, I'm in zip 59715, and I use the KBZN airport as my source.

2- Check off "Heating"

3 - Check off "Fahrenheit"  if using US units, or "Centigrade" if using SI units

4 - Use a Base Temperature of 65F

5- In Breakdown, select "Average"

6 - In Period Covered, select "5 years"

7 - Click on the "Generate Degree Days"

Once the calculation has completed, click on the "Download Now" button to get your HDDs.  Your computer may offer to open the file with your spreadsheet program -- I'd take this option if offered.  Otherwise, download the file of HDDs, and then open the file with a text editor such as NotePad.

You should see a list showing the number of HDD's for each month of the year.  There is also a "% estimated" column, which basically indicates the quality of the data -- it the % Estimated is high, then you might want to go back and pick another weather source.

Take a look at the numbers, and decide how many months you want to include in your heating season.  I would eliminate any mid summer months in which you know you would never run the furnace, but I would keep the spring and fall months in which you do run the furnace sometimes -- these are typically months is which solar fractions are highest.

Now enter the HDD's for your heating season months in the spreadsheet as shown just below.  Enter the HDD's in the column labeled "HDD" (light blue background).  For the months you consider outside your heating season, enter zeros.

Now that you have entered the UA value and your Heating Degree Day estimates for each month, you should now see reasonably accurate monthly heat loss numbers for your house in the "Heat Loss" column.

## Step 2 -- Heating Plant Inputs

Enter your inputs for the blue cells in this part of the spreadsheet:

 UA house 250 BTU/hr-F (the house heat loss per degree F from Home Heat Loss Calculator Collector area 240 sqft Fuel Energy/unit 92000 Enter the energy per unit of fuel you use in BTU -- e.g. Propane = 92,000 BTU/gal, Electricity = 3412 BTU/gal, Nat Gas = 100000 BTU/t Fuel price/unit \$2.20 Enter the price you pay per unit of fuel -- e.g. we pay about \$2.20 per gallon of propane, and about \$0.10 per KWH of electricity) Heating Efficency 0.75 Enter the overall efficiency of your propane, gas or electric heating system

- UA House -- enter the UA for the house if you have not already.

- Collector area -- enter the total area of the collector you plan to install in the "Collector Area" cell.

The collector area should include the area of all the active collectors you plan to install.

I would also include the collector area the area of any south facing windows that meet these criteria:

- The windows receive sunlight for a substantial part of the day (eg from 9am to 3pm).

- The glass used in the windows has a  medium to high SHGC (Solar Heat Gain Coefficient).

This approach basically allows the passive solar gain of the south facing windows to be included in the solar heat gain.  South facing windows with a high to medium SHGC are generally as efficient (or even more efficient) than dedicated active collectors.

So, as an example, if you plan to use four 4 by 10 ft collectors (160 sqft), and you have 100 sqft of south facing windows that meet the criteria listed above, you would enter 260 sqft in the "Collector Area" cell of the spreadsheet.

- Fuel Energy/unit -- enter the fuel energy per Unit of fuel for the fuel you use.

For propane, this is 92,000 BTU per gallon
For Electricity, this 3412 BTU per KWH

For Natural Gas, this 100,000 BTU per therm

- Fuel price/unit -- enter the price you pay for each unit of fuel -- e.g. we pay about \$2.20 per gallon of propane

- Heating Efficiency -- enter the efficiency of your heating plant.
This is likely to be lower (worse) than the quoted efficiency for your furnace due to duct losses etc.

## Step 3 - Estimate Collector Heat Output

Using Andy's Solar Collector Power Output simulator enter inputs to reflect your situation.

Here is an example for:

- Billings, Montana

- Single glazed, selective surface flat plate collector (represented by a Heliodyne Gobi 410)

- Using an average collector inlet temperature of 45C (113F) with a 5C (9F) temperature rise through the collector.

- Collector aimed due south and tilted to 70 degrees for good winter performance (note 1)

- Average over 10 days (this makes it easier to read the monthly averages needed below)

- Check the output per square meter rather than per collector.

This is the simulation output:

I added end of month vertical lines to make it easier to read off the average monthly values.

As an example of how to read the chart, the chart tells you that  for day 180 into the year, the heat output from 1 sq meter (10.8 sqft) of collector varies from a low of about 1.25 KWH for the day to a high of about 2.35 KWH for the day, with a median output of about 1.75 KWH for the day.  So, if you had (say) 10 square meters of collector, then you have a 50% probability of seeing about 18 KWH a day of heat output to the storage tank.

Now eyeball estimate the average daily output for each month of the year.  The small black dots indicate my guesses at average daily output for each month -- eg just over 1.0 for January.

Enter the average monthly values in the spreadsheet column labeled "Andy Output".   For months that you consider to be fully outside of the heating season (as discussed above), enter zero.

 Note that if you are used to working with spreadsheets, you can download Andy's simulation output as a CSV file that your spreadsheet software can read.  You can then add an equation for each month that calculates the average daily output for that month. But, this is not at all critical -- the eyeball estimates will work fine for this kind of rough estimate.

These average daily outputs will be used to estimate the output for each month and to compare that to your home heat loss for the same month giving you the fraction of heat that comes from solar.

This completes the inputs, and the spreadsheet should now look like the one just below, but with your inputs and outputs.

 How Much Collector Area Do I Need To Heat My House? Enter inputs for your house and collector in the blue cells UA house 250 BTU/hr-F (the house heat loss per degree F from Home Heat Loss Calculator Collector area 240 sqft Fuel Energy/unit 92000 Enter the energy per unit of fuel you use in BTU -- e.g. Propane = 92,000 BTU/gal, Electricity = 3412 BTU/gal, Nat Gas = 100000 BTU/Therm) Fuel price/unit \$2.20 Enter the price you pay per unit of fuel -- e.g. we pay about \$2.20 per gallon of propane, and about \$0.10 per KWH of electricity) Heating Efficency 0.75 Enter the overall efficiency of your propane, gas or electric heating system HDD Heat Used Andy Output(1) Solar Heat Out Usable Solar Heat Solar Fraction Fuel Saving (F-day) (BTU/mo) (KWH/sqm-day) (BTU/mo) (BTU/mo) (dollars) Jan 1303 7,818,000 1.3 3,017,527 3,017,527 0.39 \$96.21 Feb 1027 6,162,000 1.6 3,713,880 3,713,880 0.60 \$118.41 Mar 924 5,544,000 1.7 3,945,997 3,945,997 0.71 \$125.81 Apr 666 3,996,000 1.6 3,713,880 3,713,880 0.93 \$118.41 May 0 0 0 0 0 0.00 \$0.00 Jun 0 0 0 0 0 0.00 \$0.00 Jul 0 0 0 0 0 0.00 \$0.00 Aug 0 0 0 0 0 0.00 \$0.00 Sep 0 0 0 0 0 0.00 \$0.00 Oct 653 3,918,000 2.2 5,106,584 3,918,000 1.00 \$124.92 Nov 967 5,802,000 1.2 2,785,410 2,785,410 0.48 \$88.81 Dec 1422 8,532,000 1 2,321,175 2,321,175 0.27 \$74.01 Year Total 6962 41,772,000 24,604,452 0.59 \$746.59 Notes: (1) The monthly heat output from the collector as calculated by Andy's Collector Power Output simulation

So, now you have for each month and for the full year:

- The heat you use each month

- The heat that your solar heating system provides for each month

- The fraction of your heating that solar supplies

- Your estimated dollar saving in fuel.

You now you have a rough idea how much of your heating demand this solar collector array will meet.   From here, you can start playing around with different strategies for improving things -- would you be better off adding more collector area, or more attic insulation, or better windows, etc.   This is the real value of this exercise -- it gives you a basis for making intelligent decisions about where to spend your energy saving dollar.

## The "Bottom Line" Message For Most of Us

One other thing I should mention that might be appealing to people who don't want to go through all this stuff.  For the situation in which 1) you are retrofitting solar to an existing house with typical to pretty good insulation, and 2) you live in a cold to moderately cold climate.  Then, the answer as to how much collector you should have is almost always:  "Add as much collector area as you have space for and budget for."  That is, with typical house insulation and infiltration levels in coldish climates its almost impossible to add so much collector area that you will go over your heating needs.  Homes with VERY good insulation, or homes in more moderate climates, or homes in very sunny areas, or homes owned by people with big collector budgets may be a different story, but for most of us, the "add as much collector as you can" ground rule works pretty well.

Notes:

- There are many approximations and sources of error in this method -- some of the most obvious ones:

- The simulation uses a fixed temperature for the collector, when in fact the collector temperature varies throughout the day -- other approximations in the simulation are covered on Andy's website.

- The Home Heat Loss Calculator has a whole raft of approximations which are explained on the calculator page.

- The simulation does not include any of the interaction between the heat storage system and the collectors -- it basically assumes that if the collectors can provide the heat, you will have a way to store it and use it later.

- The losses from the system components outside the collectors (primarily storage) are not included.  These should be fairly small on a well insulated system, but can be large if the system is not carefully designed.

- The simulation (I believe) does not fully account for the beneficial effects of reflected light off a snow field on steeply tilted or vertical collectors -- this can be a significant bonus, and the nice thing is that it adds to collection without increasing heat loss (as increasing collector area would).

- Nothing in the method accounts for passive solar gains from south facing windows.  If you have windows with a good SHGC and have some means to insulate them from night heat loss, these windows can be very effective collectors.  You should include them in your collector area as discussed above.

Still, I think this method is a world better than the rules of thumb I used to use, and should give a fairly good idea how a well designed system should perform.

- I should say that Andy represents and sells a particular brand of solar collector (a very interesting design).  But, the simulation offers a wide variety of collectors, and, as far as I can tell, Andy treats them all fairly.
My thanks to Andy for providing this very helpful tool.

Gary April 14, 2010