House Design Geometry

How the shape and size of a heated volume of air effects the energy use of that heated volume

The ultimate objective of heating the air inside any R-2000 Home is to do using as little energy as is cost effectively possible. If you can rearrange the design of your 1,600 sq. ft. bungalow to still maintain 1,600 sq. ft. of usable floor area in a way that will use less heating energy, that becomes a major design consideration. These design options need to be addressed with equal weight to the number of bedrooms, square footage, living room layout, etc.

To illustrate the point, we'll use a simple example of heating one cubic foot of air. If a heat source was placed within the cube of air to keep it warm while it was cold around its exterior surface, it would lose heat equally in all directions. All other things being equal, the amount of heat it would lose is directly proportional to its exposed surface area.

The greater the surface area, the higher the heat loss. Our one cubic foot of heated air has six square feet of surface area to conduct heat loss through. Therefor, for every cubic foot of heated air, this design has six square feet of exterior surface - 1:6.

If we double the dimensions of our cube of heated air, it becomes a square containing eight cubic feet of heated air with 24 square feet of exterior surface area. A more energy efficient design, because now for every cubic foot of heated air, there are only three square feet of surface area through which to lose heat - 1:3.

Suppose we think that our larger shape containing eight cubic feet of heated air is not architecturally interesting and we decide to change its shape to give it more "curb appeal". By changing the design, we are still left with the same heated volume of air but the surface area has increased from 24 to 32 square feet. Our design becomes less energy efficient, as now for every cubic foot of heated air there are four square feet of surface area - 1:4.