As I mentioned in my previous post using accurate heating and cooling loads to size your geothermal system is very important. In this post I’ll show you how to calculate them yourself so you can compare your results with what your potential contractors come up with. I’m going to try to make this as concise as possible but you have to understand it takes over 100 pages to explain this in ASHRAE’s (American Society of Heating, Refrigeration, and Air-Conditioning Engineers) Fundamental book. The calculations are very easy though once you have all of the information gathered.
Step 1: Determine the U-values of Your Home
Today home owners are more aware than ever about energy efficiency. I’m sure you’ve all heard of R-values on things like windows & insulation. Well in the HVAC (heating, ventilating, and air-conditioning) industry we use U-values which are just the inverse of an R-value.
U-value = 1/R-value
R-values are the thermal resistance of a material so the higher the R-value the better. Looking at the equation above you can see that means the lower the U-value the better. Collect as much information about your home’s R-values. If you don’t have any info on a certain material google it and just use an average value. Or better yet go get your hands on an ASHRAE Fundamentals book. Check your local library or buy an older version for cheap online (they are updated every 4 years but anything from 1990 on will work).
For exterior walls you’ll have to calculate an overall thermal resistance using the R-values for each material that makes up the wall. But don’t just go ahead and add everything up you have to account for the studs in the wall! Here’s an example of a typical 2×4 exterior wall:
|
Stud R-value |
Cavity R-value |
| Outside Air Film, 15 mph wind |
0.17 |
0.17 |
| Vinyl Siding, un-insulated |
0.61 |
0.61 |
| Rigid Foam Insulation, 2” |
10.0 |
10.0 |
| Plywood, 0.5” |
0.62 |
0.62 |
| Wood Stud, 2×4 nominal |
4.38 |
- |
| Batt Insulation, 3.5” |
- |
13.0 |
| Gypsum, 0.5” |
0.45 |
0.45 |
| Inside Air Film, still air |
0.68 |
0.68 |
| Total: |
16.91 |
25.53 |
If the studs are 16” on center then the stud R-value accounts for roughly 25% of the wall and the cavity R-value accounts for the other 75%. So to get the overall thermal resistance:
Wall R-value = (0.25 x 16.91) + (0.75 x 25.53) = 23.375
Wall U-value = 1/23.375 = 0.0428 [Btu/h*sf*degF]
Other common building material R-values:
- Lapped cement board, 0.25” = 0.21
- Hardboard siding, 0.44” = 0.67
- Insulated vinyl siding, 0.375” = 1.82
- Particleboard, medium density, 0.5” = 0.53
- Batt insulation, 3.5” = 13-15
- Batt insulation, 5.5” = 19-21
- Expanded polystyrene = 5/inch
- Loose fill insulation, 3.5-5” = 11
- Spray applied polyurethane foam = 5.9/inch
- Spray applied cellulosic fiber = 3.2/inch
To find your window’s U-values your best bet is to get them from the manufacturer but if that isn’t an option you can use general values. Here are a few average U-values for vertical oriented operable windows:
- Aluminum frame with thermal break, single pane = 1.2
- Aluminum frame with thermal break, insulated, double pane = 0.88
- Aluminum clad wood, single pane = 0.60
- Aluminum clad wood, insulated, double pane = 0.55
- Wood/vinyl, single pane = 0.55
- Wood/vinyl, insulated, double pane = 0.49
- Insulated fiberglass, single pane = 0.37
- Insulated fiberglass, insulated, double pane = 0.32
A few door U-values:
- Solid wood door = 0.40
- Steel door with urethane foam without thermal break = 0.38
- Steel door with polystyrene core without thermal break = 0.29
- Steel door with polystyrene core with thermal break = 0.20
- Steel door with urethane foam with thermal break = 0.20
Next you’ll need to calculate your attic/roof U-value. You could go through and try to calculate an overall R-value of the drywall, trusses, and insulation. But because in most homes there is a significant amount of air beyond those layers you can skip that step and just use the insulation and drywall values.
Useful attic R-values:
- Gypsum, 0.5” = 0.45
- Gypsum, 0.625” = 0.56
- Batt insulation, 3.5” = 13-15
- Batt insulation, 5.5” = 19-21
- Batt insulation, 6-7.5” = 22
- Batt insulation, 8.25-10” = 30
- Batt insulation, 10-13” = 38
- Loose fill cellulosic insulation = 3.4 per inch
- Loose fill mineral fiber insulation, 3.75-5” = 11
- Loose fill mineral fiber insulation, 6.5-8.75” = 19
- Loose fill mineral fiber insulation, 7.5-10” = 22
- Loose fill mineral fiber insulation, 10.25-13.75” = 30
*Remember to convert them to a U-value.*
Partitions also need to be considered. Partitions are any vertical wall between a conditioned space and an unconditioned space (or less conditioned space). Interior walls between garages, crawl spaces, or unconditioned mechanical rooms are all good examples. To calculate the U-value of a partitioned wall use the same method I showed you for calculating exterior wall U-values.
Finally, you need to calculate the U-value for your basement walls and floor. Below grade walls transfer heat differently than exterior walls. Heat transfer occurs in a circular motion between your walls and the surface of the ground. The farther down the wall you go the less heat loss you have.
Different soils will have different conductivities but an average soil is 9.6 Btu*in/h*sf*degF. Using that conductivity heat loss for below grade concrete walls is as follows:
| Feet below ground |
Un-insulated |
R-4.2 |
R-8.3 |
R-12.5 |
| 0-1 |
0.41 |
0.15 |
0.09 |
0.07 |
| 1-2 |
0.22 |
0.12 |
0.08 |
0.06 |
| 2-3 |
0.16 |
0.09 |
0.07 |
0.05 |
| 3-4 |
0.12 |
0.08 |
0.06 |
0.05 |
| 4-5 |
0.10 |
0.07 |
0.05 |
0.04 |
| 5-6 |
0.08 |
0.06 |
0.05 |
0.04 |
| 6-7 |
0.07 |
0.05 |
0.04 |
0.04 |
| Total |
1.15 |
0.624 |
0.445 |
0.348 |
So for an un-insulated basement wall that is 7 feet below the ground each linear foot of wall will have a U-value of 1.15. For basement floors use the following table to determine your U-value:
| Depth of Floor Below Grade [ft] |
Shortest Width of House [ft] |
|
20’ |
26’ |
32’ |
| 5 |
0.032 |
0.0275 |
0.023 |
| 6 |
0.030 |
0.026 |
0.022 |
| 7 |
0.029 |
0.0245 |
0.021 |
If your house is wider than 32 feet just interpolate the U-values to the size you need.
Step 2: Calculate your areas
Now that you have the hard part out of the way you need to go around and measure your house. If you can create a spreadsheet for this it will make your future calculations easier. Add a row for each room in your home and put the area type (ie. wall, window, door, etc.) in separate columns at the top. You will need the areas of your walls, windows, doors, & partitions as well as the floor area of each room and the linear foot of your basement walls. Keep track of which direction (north, northeast, east, etc.) your windows and above-grade exterior walls are facing by creating separate columns for each direction. Make sure that you subtract your window areas from the overall wall area so you aren’t accounting for that space twice. When you have the overall floor area calculated (in square feet) multiply that by your wall height to determine the volume of air each room can hold (in cubic feet). This will be used later in the air changes per hour calculation.
Click to Enlarge
Step 3: Determine your design temperatures
To do a heating or cooling load calculation you need t o figure out what your “design day” is. A design day is basically a worst case scenario. For your heating calculation it is the coldest day of the year and for your cooling calculation it is the hottest day of the year. Your local contractor should be able to tell you what design temperatures they use for your area otherwise get your hands on an ASHRAE Fundamentals book like I mentioned above. You also need to determine what temperatures you want to keep your house at in the summer and in the winter. I’m going to show you how to calculate the heating load first so you can just enter the winter temperatures for now. Next you will need to come up with a temperature for the spaces on the other side of your partitions. The only partition we have in our home is our garage wall. Typically a garage temperature would be close to the outside design day temperature but half of our garage was converted to a workshop so they have supply air registers in the space. Even though we have them closed completely they leak air into the space and keep it milder than outside (which we plan to change in some of our future renovations). So I used a partition temperature of 30 degF. Finally, you need to find out what the average ground temperature is in your area. ASHRAE uses this diagram of the ground temperature:
For Wisconsin I used a ground temperature of 23 degF. Insert these temperatures at the top of your spreadsheet and use them to calculate three delta Ts. Equations as follow:
- Heating Delta T = Room Design Temp – Outside Heating Design Day Temp
- Partition Delta T = Room Design Temp – Partition Temp
- Ground Delta T = Room Design Temp – Ground Temp
Keep all of these temperatures at the top of your spreadsheet so we can reference them in our calculations.
Step 4: Calculate your heating loads
In your spreadsheet create columns for each of the following: wall, window, door, roof, partition, basement wall, basement floor, infiltration, and total. Above each column name put the corresponding U-value you calculated earlier for each of the construction types. Above the infiltration column put your air changes per hour (ACH) rate from the table below:
Use your design day temperatures for the winter and summer outdoor temperatures and take a good guess on your homes tightness. I used a medium tightness for our home so our winter air changes per hour is 0.91 and our summer air changes per hour is 0.48. For now just enter the winter air changes per hour over the infiltration since we’re starting with the heating calculations.
Now onto the actual heating load calculations. For each room enter the corresponding equations:
- Window = (Sum of window areas) x Window U-value x Heating Delta T
- Wall = (Sum of wall areas) x Wall U-value x Heating Delta T
- Door = Door area x Door U-value x Heating Delta T
- Roof = Floor area for rooms with roofs x Roof U-value x Heating Delta T
- Partition = Partition area x Partition U-value x Partition Heating Delta T
- Basement Wall = Basement wall linear feet x Basement wall U-value sum x Ground Delta T
- Basement Floor = Floor area for basement rooms x Basement floor U-value x Ground Delta T
- Infiltration = (Room volume x winter air changes per hour/60) x 0.018 x Heating Delta T
- Total = Sum of the equations above for each room
Now all you need to do is add up the total column to find out the overall heating load of your house. You finally have your answer! I do need to not e that this total is a sum of each individual room peak so it might be slightly higher than it will actually be. But for our house my hand calculated heating load was 71,652 Btuh whereas the computer generated heating load was 70,720 Btuh. So that’s pretty accurate if you ask me!
Click to Enlarge
In cold climates like we have here in Wisconsin residential units are sized to handle the heating loads but in warmer climates where the cooling loads are higher they are sized base on cooling loads. So let’s go on to calculate your cooling load.
Step 5: Calculate your cooling loads
Cooling loads are more difficult to calculate because you have to take into account your latent load (humidity) too. For residential calculations ASHRAE has come up with some generalized numbers to do cooling calculations by hand. The accuracy of the calculations is reduced but there isn’t many other alternatives.
For walls ASHRAE uses cooling load temperature differences (CLTDs) and for windows they use glass load factors (GLFs). Both are dependent on the wall/window direction. Use the tables below to find a CLTD for your walls, roof, and partitions and a GLF for your windows :
Put these CLTDs and GLFs at the top of your spreadsheet. Then add the summer temperature (room design, cooling design day, & summer partition) as well as the delta T’s calculated from them (cooling delta T & summer partition delta T). You can assume the ground temperature is the same but you will need a new ground delta T using the cooling design day temp. Next you’ll need to determine your summer air changes per hour using the table below:
Now all you need to do us enter in the following equations for each room:
- Window = (Sum of north window areas) x North GLF + (Sum of east window areas) x East GLF + etc.
- Wall = (Sum of north wall areas) x North CLTD x Wall U-value + (Sum of east wall areas) x East CLTD + etc.
- Door = Same equation and CLTD as walls
- Roof = Floor area x Roof CLTD x Roof U-value
- Partition = Partition area x Partition CLTD x Partition U-value
- Basement Wall = Basement wall linear feet x Basement wall U-value sum x Summer Ground Delta T
- Basement Floor = Floor area for basement rooms x Basement floor U-value x Summer Ground Delta T
- Infiltration = (Room volume x summer air changes per hour/60) x 1.1 x Cooling Delta T
- Total = Sum of the equations above for each room
Click to Enlarge
For my cooling loads I came up with 41,000 Btuh but my computer generated calculations came up with 26,000 Btuh. So those generalized numbers obviously overestimate the cooling loads!
And that ends the longest post I’ve ever written! Wasn’t that fun? I hope that was helpful. Leave a comment if you have any questions.
To see the entire Going Geothermal mini series click here:
[Figure & Table Source: ASHRAE Fundamentals Handbook 1997]
