Q. How Significant is Thermal Bridging through Studs and Rafters?
A. We believe there is a significant advantage to reducing the thermal bridging associated with rafters and studs. One of the advantages of open-cell foam is the ability to virtually fill the rafter bay and eliminate much of the exposed wood surface (closed-cell foam is often cost prohibitive with this approach). Rafters and studs are relatively poor insulators and will contribute to heat loss, convection currents, and a decrease in comfort. Basic temperature gradient calculations can determine the expected temperature of the rafter at any given point (see below). During the winter, the temperature of the rafter will gradually increase towards the interior surface since the r-value of the rafter is the greatest at that point. Therefore, eliminating thermal bridging of the rafter is least important at the interior surface, but increases with importance as you progress towards the exterior sheathing.
For example, filling a 14” rafter cavity with only 6” of closed-cell foam will leave nearly 8” of rafter surface exposed on each side. Additionally, filling the cavity with 4” of closed-cell foam and the remainder with 10” of fiberglass will not fully eliminate the effects of thermal bridging. This is because fiberglass is air-permeable and will not suppress convection currents. There is a misconception that the primary benefit of spray foam is stopping air leakage – this is only a fraction of the benefit. Spray foam inhibits convention currents – maintaining constant R-value and preventing air-movement within the cavity. Nevertheless, spray foam significantly outperforms fiberglass even in an air-tight building assembly because of its ability to suppress convection currents, maintain r-value and limit conduction. This is precisely why modern Energy Star refrigerators filled with foam use half the energy of older models filled with higher r-value fiberglass. Similarly, by nearly filling a cavity completely with foam, we are mimicking the benefits of SIPs (structural insulated panels) – little thermal bridging, no convection currents, constant R-value.
The diagram and calculations below exhibit the temperature gradient of a 2×14” rafter to demonstrate the heat loss and thermal bridging effects of a rafter at any given point:
The chart above demonstrates the temperature of the 14” rafter at various intervals assuming a 72°F interior temperature and a 20°F exterior temperature. The rafter surface area influences heat transfer in the same manner as radiator fins. The more surface area exposed the more thermal bridging taking place. If the rafter were completely exposed, the average temperature of the rafter would be 46.5°F. If the rafter were filled with 4” of foam, the remaining 10” of exposed rafter would yield an average temperature of 53.2°F. Conversely, if the rafter were filled with 12” of foam, the average temperature of the exposed rafter would now be 66.61°F, thus eliminating the majority of the radiator effect.
With a few more calculations, you can extrapolate the total BTU heat loss associated with the total exposed rafter surfaces. These calculations are limited to the conduction mode of heat transfer; they do not take into consideration the heat transfer through convection and radiation which will further add to heat loss from the exposed rafter area.