Automating R-value Calculations

When designing a roof with tapered insulation that meets energy code, it’s often assumed that the thinnest part of the roof (near the drains) meets the minimum R-value requirements for the entire assembly. This is a conservative assumption, and one which usually results in excessive thickness for a roof’s target insulation value.

Since the roof increases in thickness further from the drains, the actual R-value of the assembly needs to account for these variations in depth. Here’s a common technique for calculating R-value for a tapered insulation roof as defined in the Washington State Energy Code (1322):

When calculating compliance using U-factors, area-weighted averaging is allowed. Where insulation is tapered (e.g. roofs), separate assembly U-factors shall be calculated for each four-foot section of tapered insulation.

In the past, these calculations were a time intensive process, but proved to be worthwhile for yielding a thinner, more efficient, and cost effective roof. We’ve developed a way of streamlining this process into a tool we can quickly use on any project. The file calculates average thickness of the roof along a 4’x4′ grid. These thickness values are then used to calculate the total R-value of the roof assembly.

Our test project here was an office building in Seattle, with an R-39 roof assembly (based on energy models for code and performance to date). As the basis for design, the insulation material we used was Johns Manville Tapered ENRGY3, which is R6 per 1″. When we factored the values for tapered insulation, we noticed that we could reduce the roof thickness by 2″. In doing so we were able to provide some relief to the building height, eliminate a complicated roof step detail at the roof terrace, and save roughly $15,000 by removing the excess material.

The thermal assembly plans we use for code compliance remain the same, but the top of roof dimensions will lower in section. We document this with a tapered roof insulation plan (below), which is generated by the same tool we used for the calculations. After a couple minutes of formatting, we have a sheet documenting the now super efficient roof assembly.

Update (12/14/2012):  In the process above, we were calculating the average thickness of the entire roof and using that value to calculate the R-Value for the assembly.  However this roof does not meet the conditions for R-Value averaging and instead requires U-Value averaging, which results in a different final R-Value.  This was a quick fix in the Grasshopper definition, and when rechecking the numbers required to reach the target R-39 Roof, we are able to remove 1.5″ from the original roof assembly, rather than the full 2″ as described above. Thanks to ARUP for their help with this.