[Bldg-sim] U-Factor/R-Value Formula

[Cramer Silkworth]

Matthew,

First, a warning: This may spark a debate about what R-value *really* is and how it's calculated (ie, the thermodynamic definition versus a contractor's definition). This is just my understanding of it. If anyone else can explain it better, please do so.

Anyhow, it sounds like you're wondering what the "real-world" R-value of your model's envelope is. As far as I know, with these numbers you can calculate only the conductive resistance simply by dividing the thickness by the conductivity (and, technically, also by 1 sqft though it has no effect on the numerical result, just the units). That is, Rcond=L/(kA), where L=thickness, k=conductivity, and A=area. This is the definition of conductive thermal resistance found in any thermodynamics textbook. However, manufacture-rated R-values are calculated by a test according to ASTM, which includes radiant and convective effects and a certain temperature gradient (conductivity itself actually varies with temperature), so 'real' values would be a bit different.

U-value and R-values are inverses of each other: U=1/R and R=1/U. 

Theoretically you can combine the conductive resistance with "resistances" for radiation and convection, if you assume certain surface temperatures, emissitivities, windspeeds, and all that fun stuff (such as what I'm guessing the ASTM test specifies). Then, the total R-value is simply the sum of all these. I think building simulation tools often assume a certain "windspeed", etc, and factor in the additional heat loss accordingly.

I hope that helps, and is mostly right...

-Cramer
J. Cramer Silkworth 
silkworth at transsolar.com 
+49 0711-67976-182 
Transsolar Energietechnik GmbH 
http://www.transsolar.com 
Stuttgart - Munich - New York 

Climate Engineering: Technologies for energy-efficiency and user comfort in buildings.
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Partners: Dipl.Ing. Matthias Schuler, Dipl.Ing. Thomas Auer, Dipl.Phys. Stefan Holst 




-----Original Message-----
From: bldg-sim-bounces at lists.onebuilding.org [mailto:bldg-sim-bounces at lists.onebuilding.org] On Behalf Of Matthew Higgins
Sent: Monday, February 04, 2008 9:46 PM
To: bldg-sim at lists.onebuilding.org
Subject: [Bldg-sim] U-Factor/R-Value Formula

Does anyone have a formula to calculate either U-Factor or R-Value using the eQuest material properties of the following?

Conductivity = (Btu/h-ft-°F)

Density =  (lb/ft^3 )

Specific Heat = (Btu/lb-°F)

And thickness.

--
Matthew Higgins, LEED AP
Technical Specialist
Environmental Dynamics, Inc.
Architecture and Sustainability Consulting Services
505.242.2851


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