# Effective R Value of Common Wall Construction Methods

Quote of the Day

I’ve finally stopped getting dumber.

— Epitaph on the headstone in Budapest of Paul Erdös, one of the world’s most prolific producers of mathematics.

## Introduction

Figure 1: My Current Cabin. It is being torn down next year. I will not miss it.

I have contracted with a firm to build an insulated, steel-sided, garage at my lake site in Northern Minnesota, which they will complete building sometime in December. Next summer, I have a contractor starting construction of a new cabin about 50 meters from the garage. The new cabin will replace my old cabin (Figure 1), which is an old hunting shack that was built back in the 1930s. Because the winters are hard in this part of the country, I have become interested in the insulation value of different types of wall construction. My contractor has his preferred approach (2x6 conventional framing), and I am curious as to how it compares with other framing methods.

In this post, I will put together a simple model for computing the R-value of different types of wall construction. This analysis will provide me a quantitative basis for understanding which methods are the most economically sound.

For those who are interested, I have included my Mathcad source and its PDF here.

## Background

### Definitions

Thermal Conductivity ([κ] = W/m-K)
Thermal conductivity is the property of a material to conduct heat. Heat transfer occurs at a lower rate through materials of low thermal conductivity than through materials of high thermal conductivity. The thermal conductivity of a material usually depends on its temperature – this means that thermal analysis is non-linear in general. It is analogous to electrical conductivity.
Thermal Resistivity ([Rλ]=m-K/W)
The reciprocal of thermal conductivity.
R-value aka Thermal Insulance ([R]=m2K/W or ft2·°F·hr/Btu)
It is the thermal resistance of a unit area of a material. This is the most common way for the insulation properties of building materials to be specified.
Thermal Resistance (Rθ=K/W)
Thermal resistance relates the change in temperature across a material to the heat flow through the material. We define thermal resistance as ${{R}_{\theta }}\triangleq \frac{{\Delta T}}{Q}$.
Thermal resistances combine just like electrical resistances. This means that you can model the thermal resistance of composite structure using series and parallel thermal resistances.
You can relate thermal resistance to R-value using the formula $Q=\frac{{\Delta T}}{{{{R}_{\theta }}}}=\Delta T\cdot \frac{A}{R}$, where Q is the heat flow through a specific piece of material, A is the area of the surface with an R-value of R,.
Thermal Bridging
Thermal bridging occurs when relatively conductive material allows an easy pathway for heat flow around a thermal barrier, like insulation. In electronics, we call the comparable phenomena leakage. The most common form of thermal bridging occurs when wall studs and headers allow heat to flow around insulated wall cavities. I really did not understand the importance of thermal bridging until I used an infrared camera to photograph one of my walls. You could clearly see the framing members (Figure 2). The dark areas indicate lower temperature, which means leakage of heat.

Figure 2: Thermal Photograph of a Stud-Framed Wall and Ceiling in My Montana Condo.

Framing Factor
The percentage of the outer surface of a home with a thermal bridge of framing material between the indoor and the outdoor.

### Wall Construction Methods

Building Sciences Corporation has an excellent discussion on the differences between conventional framing and advanced framing, and I strongly encourage you to visit their site.

There are two main types of residential framing today:

• Conventional framing
Also called platform framing, it started in the 1930s as a way to reduce the fire risk associated with balloon framing.
This approach to framing has been coming on strong since 2000. It uses various techniques to reduce both thermal bridging and the amount of wood used.

#### Conventional Framing

Virtually all homes today are built using conventional framing, which has been the standard since the 1930s and is nicely illustrated in by Figure 3. For the studs that surround the heated rooms, insulation usually fills the gaps between the studs. Conventional framing has the advantages of being simple and using inexpensive materials, but it has the disadvantage of having many paths for heat to flow around insulation through thermal bridging. This makes it expensive to heat or cool.

Figure 3: Example of Traditional Framing. (Source)

Advanced framing methods have two purposes: (a) more efficient use of materials, and (b) more thermally efficient, which it accomplishes by reducing the amount of framing material that will act as a thermal bridge. Figure 4 provides a good example of some of the techniques used with advanced framing.

Figure 4: Example of Advanced Framing Techniques. (Source)

### Computing Wall Component R Values

Figure 5 shows my wall construction model. The variables are all associated with wall construction, i.e. on-center stud separation or pitch, and the wall thickness (τ).

Figure 5: Wall Construction Model.

Figure 6 shows how I defined my R value units and the R values I used for specific components (Source).

Figure 6: R Values Used in this Post.

## Analysis

Figure 7 shows my calculations for the R value of a home as a function of (1) the stud pitch, (2) conventional vs advanced framing, and (3) 2x4 versus 2x6 studs. Both the stud pitch and framing type are handled by way of a parameter called the framing factor (FF). My FF values came from this document. The stud width is represented by the variable τ.

Figure 7: Table of R Values.

## Conclusion

Here is a larger version of the table to make it easier to read.

Figure 8: Table of R Values By Construction Method.

There are several conclusions that I can draw from my table:

• Switching from a 16" stud pitch to a 24" stud pitch makes little thermal difference (~0.7R) , but it will reduce the amount of framing material I need.
• Switching from conventional framing to advanced framing makes little thermal difference (<1R).
• Using 2x6 studs instead of 2x4 studs makes a big difference (~5R).
• Moving from conventionally framed 2x4s with a 16" pitch to advanced framed 2x6s with a 24" pitch gives me 6.7R of additional insulation value – this is a big deal.

There are additional things I can do to improve the R value of my construction practices, like adding a layer of insulation. These changes can easily be added to my model.

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