A mathematical model of the test unit was used to determine the amount of insulation needed at various locations. The model was exercised at various Rw-values to determine the surface temperatures and heat flows, and this was translated to inches-of-insulation to give an overall accuracy of the test to 5% or less.

The heat flow through the test piece can be predicted adequately for a variety of R-values by using the commonly available convection heat flow equation:

Q = Const * Area * (T – T_surface) ^1.25

Where T can be the warm or cold face temperature

This simplified equation is not entirely appropriate because it expects a very great distance between the vertical surface and the surrounding air. However, it gave useful approximations of warm side and cool side air temperatures.

The heat flow through the wall insulation can be calculated as:

Qwall = 1/(Wall R-Value) * Wall_Area * (T-surface – T_avg_inside).

The surface temperatures that matched these two equations were found with Excel’s Goal-Seek function.

These calculations showed that the cold region on the window side of the “window frame” had to be protected by a “cold box” to retain accuracy, but insulation was adequate to reduce external heat flow in all other areas.