In our northern climate, how quickly a structure loses heat is dependent on three factors, the first is transmission heat loss which includes the difference between inside and outside temperatures, called the delta T, and the resistance to heat flow, or R-value of the building assemblies. The second factor is natural air exchanges or air exchange heat loss. We’ve talked a lot about natural air exchanges, remember the 10% to 40% of heating costs is due to air exchanges. The third factor is radiation heat loss, primarily heat loss through glass or windows. Remember the discussion about the Laws of Thermodynamics, which I talked about here. Today, we are going to discuss R-values and the transmission heat loss. I’m going to apologize in advance, this posting is a little math heavy.

According to Wikipedia;

*The R-value is a measure of how well an object, per unit of its exposed area, resists the conductive flow of heat, the greater the R-value, the greater the resistance, and so the better the thermal insulating properties of the object.*

I think everyone associates R-Value with insulation. Most building products, including wood, drywall, and even concrete have at least some insulating value. The most commonly used insulation is fiberglass batts with listed R-values of R-11 and R-13 for 2 x 4 wall cavity and R-19 and R-21 for 2 x 6 wall cavities. Other fiberglass batt thicknesses and R-values are also available.

By the way, as of 2015, the new northern Minnesota code requirement for wall insulation is R-21.

Let’s look closer at R-21, what does that mean? R-21 is the resistance to conductive heat loss. The higher the “R” number, the more resistance. We need this information to determine heating requirements for a building. There is a simple formula to determine how much heat, in British Thermal Units, can move through the insulation. (Read about BTU’s here). The formula is the difference between inside and outside temperatures divided by the R-value times the surface area, it looks like;

**(T2 – T1 / R-value)** **x surface area**

Using an outdoor temperature of -5 degrees, (the actual design temperature for my part of northern Minnesota is -17), indoor temperature of 65 degrees, R-21 batt insulation and 100 square feet of wall area, the equation is; (-5 – 65 / 21) x 100 which equals 333.3 BTU’s per hour of heat loss per 100 square feet of wall area.

Changing to R-11 insulation for the same equation, the heat load rises to 636 BTU’s per hour. Now you see why 2 x 6 exterior walls are common in a northern climate, nearly half the heat loss of a 2 x 4 wall. Both examples only uses the R-value of the batt insulation but the entire wall assembly must be accounted for when determining heat loss. Let’s look at a typical code minimum wall assembly. In a layered wall, all R-values are added together. My example, starting from the exterior: wood siding at R-.8, OSB sheeting at R-.8, insulation at R-21, and drywall at R-.45. The R-value of the wall has risen to R-23.05, which will reduce the heat loss to 303.6 BTU’s per hour. This calculation is also not accurate because it only includes the wall cavity with the insulation. The 2 x 6 wood framing must also be included. To calculate different R-values within an assembly, such as fiberglass insulation **and** wood framing inside a wall cavity, we must convert the R-value to a U-value.

According to Wikipedia;

*The U-factor or U-value is the overall heat transfer coefficient that describes how well a building element conducts heat or the rate of transfer of heat through one square foot of a structure divided by the difference in temperature across the structure.*

What do you know, sounds the same as R-value. A U-value is the inverse of an R-value and the formula is** 1/R-value = U-value**. If the R-value is 2, the U-value is .5. If the R-value is 4, the U-value is .25. See the relationship?

An interesting side note about U-values, before 1945, all resistance to heat flow numbers were labeled in U-value. The labeling was confusing to people who associated higher numbers as better, so the R-value was invented, by the way, I’m not old enough to remember that!

It is also possible to convert a U-value to R-value using a similar formula. ** 1/U-value = R-value. ** All windows are listed in U-value, a common window might have a U-.32 which means it’s R-value is 3.125. Might be a good idea to spend a little more money on good windows.

OK, back to calculating the heat loss for the wall assembly including the framing. Framing lumber has an R-value of about 1.25 per inch, or R-6.88 for a 2 x 6. Most framing covers between 15% and 40% of a wall assembly. For our example, we will use 20%, or 20 square feet of the 100 square foot wall. The formula for calculating a U-value in an assembly is;

**(A1 x U1) +(A2 x U2)… = weighted average of wall in U-value.**

80% of the wall has an R-value of 23.05. Converted to a U-value, 1/23.05 = .0433. .80 (80% of the wall area) x U-.0433 = U-.0344. .20(20% of the wall area) x U.145 = U-.029. U-.029 + U.0344 = U-.0634. 1/.0634 = R-15.77. The average R-value for the 100 square foot wall assembly is R-15.77, substantially lower than the R-21 insulation. Our heat loss calculation, (-5 – 65 / 21) x 100 increases to 443.9 BTU’s per hour. This heat loss will increase with the addition of windows and doors, which have a much lower R-value than walls. What I am hoping to get across is wall assembly R-values are well below what most people realize and there is an energy penalty for the wood framing in code minimum wall assemblies.

I am going to use the previous example in an energy retrofit example. We would like to reduce the transmission heat loss of the code minimum wall assembly. We have decided to add 2 inches of extruded polystyrene, or XPS, with an R-10 insulation value, to the exterior of a home. We will use the previous example’s weighted average R-value of 15.77 and the heat loss of 443.9 BTU’s. Adding 2 inches of foam to the exterior raises the insulation level to R-25.77 and lowers the heat load to 271.6 BTU’s at a temperature difference of 70 degrees. Adding 4 inches of XPS, R-20, to the exterior and the heat load drops to 195.6 BTU’s per hour.

By the way, choosing to add R-10, or 2 inches of XPS insulation to an exterior 2 x 6 wall assembly would be a code violation in zone 7, northern Minnesota. R-15 is the minimum requirement for a 2 x 6 wall. R-10 will meet code on a 2 x 4 wall assembly. We will discuss exterior insulation in a future blog.

I chose the calculations in this posting to compare the listed R-value of a product with realized R-values in construction assemblies. There are many calculations used to determine heating and cooling needs in a home. Remember, at the beginning of this post I said there were three factors in heat loss, R-value, natural air exchanges and radiation heat loss. All affect heating and cooling costs along with comfort.

Often heating and cooling contractors are not provides with the air exchange rate, and sometimes, the wall, ceiling, and foundation R-values or window and door information in a custom or design/build home. The home is constructed using a simple floor plan with little or no detailed planning. Heat loss is estimated using code minimum design numbers to calculate heating and cooling requirements for the structure, which can result in oversized heating and cooling equipment.

We rarely use hand calculations for determining heat losses of structures. Computer software makes the process much simpler, more accurate and much faster to complete.

I think we all understand that more insulation will reduce heating (and cooling) costs and improve comfort. The problem becomes the added cost of additional insulation in the construction of the home. Many times, energy upgrades are cut in a construction budget to accommodate the granite countertops and custom showers…AHG. Energy upgrades, especially when building new, will pay for themselves several times over in energy cost savings over the life of the home. How many times in the life span of the home will the countertop become out of style and be changed? Insulation typically lasts the life of the home.

I have included a chart of R-values for common building materials. Remember, R-values in a layered building assembly can simply be added together. When calculating wall assemblies with materials of different R-values within the wall, such as insulation and wood framing, you must convert the R-value to U-value.

Lastly, one of the questions I had when I was building was if there is a recommended ratio of insulation values for the roof, walls and foundation. As it turns out, a good ratio is 100% for the roof, 50% for the walls, and 25% below grade/under slab. R-60, R-30, R-15 is a good ratio for a well insulated home.

Does the r-value of fiberglass insulation and or cellulose insulation change with a higher delta and wind exposer in a wall assembly?

To my knowledge, delta-t does not have an effect or the effect is negligible on R-value. It can have an effect on rigid insulations. I recently installed expanded polystyrene (EPS) insulation on a project. The manufacturer’s listed R-values were R-4.5 per inch at 70°F and R-4.8 per inch at 50°F. A small effect. Wind moving or having air movements through insulation can have an effect. Wind washing in vented attics is a good example. We want outside air moving through vented attics, but gently. Hot or cold air moving through the fibers of the insulation will reduce it’s effectiveness. How much depends on the amount of air moving and the delta T.