Green Building Advisor, one of my favorite sources of good info on building science and green building, ran my Flat or Lumpy article as a guest blog yesterday. (They also gave the Energy Vanguard blog a nice review!)
With the subject of insulation and R-value fresh in my mind again, I figured now is a good time to take it a little further. In the first article, I showed how to calculate the average R-value for lumpy insulation, and I assumed in that case that an attic had 50% coverage of R-50 and 50% coverage of R-10. The result was that the average R-value was an amazingly low R-17, not the R-30 you might guess.
So, let’s extrapolate. Instead of an attic that’s 50/50, let’s look at one that’s 99% good and only 1% bad. In this case, the 1% is from the attic pull-down stairs, which typically have no insulation.
If we have 1000 square feet total of ceiling area, and we put R-38 everywhere but the 10 square feet of the attic pull-down stairs, you may be surprised when you see the answer. (For ease of calculation, I’m going to ignore the effect of the framing in the attic.)
Are you with me? We’ve got 990 sf at R-38 and 10 sf at R-1. (I’m being generous by assuming that quarter inch of luann plywood plus the air films give it a full R-1.) When you plug those numbers into the equation for average U-value and then convert to average R-value, the answer is R-28. (See the Flat or Lumpy article for details on the math – but be careful!)
No, I am not kidding! Because of that 1% of the attic that’s uninsulated, the average R-value for the whole attic drops by 27%. I told you it was amazing, didn’t I?
The reason for this is that, although the attic stairs account for only 1% of the area, the rate that heat flows through them by conduction (per square foot) is 38 times higher than in the insulated part of the attic. In other words, the amount of heat that flows through the 10 sf of attic stairs is the same as what flows through 380 sf of the insulated attic. Wow!
Also, what I’m talking about here is just the heat that flows through the solid material, not all the extra heat that leaks through the gaps around the edge of the attic stairs. Remember, the building envelope has both insulation (to limit heat flow by conduction) and an air barrier. I’m just talking about the former here.
So, what’re you going to do? Add more insulation to the rest of the attic and bring it up to R-49? Or find a way to insulate the attic stairs? The answer’s obvious, isn’t it?
My fellow blogger Sean Lintow Sr. thought it would be a good idea for me to show you the math here instead of just referring to the equation in another article, so here it is:
Photo by kerryvaughan from flickr.com, used under a Creative Commons license.