# Determining the Average R-Value of Tapered Insulation

Jonathan Ochshorn

© 2011 American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in *ASHRAE Transactions,* Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAE's prior written permission. A version of this essay was presented at the *ASHRAE Winter Conference in Las Vegas*, February, 2011.

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Tapered panels built up over flat panels create a four-way slope with internal drainage. Image courtesy Dow Building Solutions.

## Abstract

Heat loss through tapered roof insulation is generally computed using an R-value based on the average thickness of the tapered section. However, this misrepresents the actual performance of the tapered insulation, which is always less efficient than an equal volume of un-tapered insulation. For commonly-encountered slopes formed with 1-way and 4-way tapers, the true efficiency of tapered insulation (compared with an equal volume of un-tapered insulation) depends only on the ratio of high- and low-point R-values, and ranges from 100% to about 70% for R-value ratios between 1 and 10. The impact of curved heat flow trajectories on the efficiency of the tapered forms is a function of taper angle or slope, and becomes significant only at slopes much steeper than those found in typical tapered roof insulation applications. Equations are derived, and tables are presented, for the efficiency of tapered insulation considering volumetric forms typically encountered in practice. Examples illustrate how these tools can be used to accurately calculate heat loss through a roof assembly with tapered insulation.

*PDF of full paper is here*.

*Online tapered insulation R-value calculator is here.*

*Derivative article published in CSI's Construction Specifier (August 2011) is here*.

**Errata:** On page 865, immediately above the subheading "TAPERED INSULATION EXAMPLE 2," the value of 62% should be changed to 38%, so that the phrase reads: "...a value that is 38% lower than the true heat loss."

First posted May 17, 2011 | Last updated July 9, 2011