Little gaps in insulation can let a lot of heat escape.

And I can prove it: q(Btuh) = U X A X ∆T! See, end of post. All done, fini.

OK, that's not fair let's look at some pictures.

This is a small gap in insulation. It is about 1 square foot out of an area of 75 square feet. The insulation is R19 and for the sake of argument we will say that it really is working as R19 The metal top of the fan box is close enough to zero that I will use that. So it would seem reasonable to say that the average R value is 18.75 [(19 X 74)/75].  That's hardly any difference, 18.75 Vs 19? Nothin!

Except that's wrong. Q(Btuh) = U X A X ∆T. "Q" is the total energy flow(measured in British Thermal Units per hour), "U" is the rate of heat transmission (in Btuh/square foot). "A" is the total area and "∆T" (Delta T) is the temperature difference across the surface in degrees Fahrenheit. "U" by the way is the the measure of the rate of heat flow. We just lost R though, where did that go?

Engineers and scientists measure the rate at which things happen. R value is how much that rate slows. Getting from "U" to "R" is easy, divide 1 by either and you get the other. R 2 = U 0.5. R 3 = U 0.33. R is handy as a marketing tool, the higher the number the better. That's pretty easy to understand. Also you can add R values, which you can't do with U.

So with our exposed fan above how do we figure the actual R value of the total area? Here's the formula: U(avg) = [(U1A1) + (U2A2) + (U3A3) .../ A(total). (BTW, does anybody know how to get proper math formulas with sub characters out of HTML?)

In the example above we have R 19 at U 0.0526316 and R 0 at OOPS, can't divide by 0, lets call the fan R 0.5 = U 2. We have 74 square ft times 0.053 = 3.922 plus 1 square foot times 2 = 2 which adds up to 5.922 which we divide by total area (75) and end up with an overall U value of 0.07896 which equals R 12.66. That is a big difference for missing one square foot of insulation.

Of course there are those joists in there, 16 inches on center, which have an R value of about 5.5, this is going to make things worse. I won't run the whole formula but in a simple framing system like this about 10% of the area is joists, so 7.4 square feet. Now we have 65.6 square feet at R 19, 7.4 at R 5.5 and 1 at 1/2. Result? R 10.9 at most.

See how fast it slips away? What if things were worse?
 

That's a big hole. I didn't calculate the effect because I knew it was coming out. The owners were afraid to run it so it just sat there as a hole in the insulation. It leaked a lot of air too.

Sometimes it just looks like a wall (or an electrical box) until you use the IR imager. Even if you can't see it the effect is still there. What can look like an innocent little gap is really robbing you blind.

Want another way to look at it? Let's start with an R 40 attic.  Lose one percent of your insulation, lose more than 25% of your R value. Lose eight percent and you only have 25% left. Makes you want to hurry into your attic and neaten your insulation doesn't it? Well, do a good job and don't forget about the attic hatch.