Question: If your attic is going to have 50 bags of insulation blown into it, does it make much of a difference if it enters flat or lumpy?

Let’s look at an example. If the insulation goes in completely flat, let’s state we have a nice consistent R-value of 30 throughout the attic.

There are all kinds of methods it can enter lumpy, however let’s presume that 50% of the attic has lumps of R-50 insulation, and the other 50% is valleys with only R-10. We wish to discover the average R-value of this lumpy setup. It’s the same quantity of insulation, and the average of R-50 and R-10 is R-30. But, how does it really perform?

Let’s do the math!

Now, we can’t simply average the R-values. If we did that here, we’d get R-30, and we’d be wrong. The heat will take the path of least resistance, and the less resistance you give it, the more heat will stream. If you’ve studied physics, engineering, or structure science, you’ve probably seen the formula for heat flow by conduction:

Heat circulation formula building science
If we computed the amount of heat streaming through the lumps and valleys in this attic, we’d see that the R-10 half (red bar listed above) would allow method more heat to flow than the R-50 half (yellow bar listed above). In fact, the R-10 valleys, having one-third of the R-value, would permit 3 times more heat to flow than if it had R-30. The R-50 lumps would allow only 3/5 the heat flow as R-30.

Also, the total quantity of heat circulation is greater for the lumpy insulation than for the flat insulation As you can see below, the red and yellow parts together amount to a lot more heat flow than the orange (in fact 1.8 times as much).

Heat circulation through flat and lumpy insulation.
Due to the fact that the lumpy insulation allows more heat circulation, it’s got to have a worse average R-value. Clearly, the average R-value is going to be more influenced by the underinsulated part than by the over insulated part.

To find the average R-value the correct way, we first need to transform R-values to U-values. R represents resistance, as in resistance to heat circulation, so the greater the number the better when we’re talking about building materials. U-value, the heat transfer coefficient is the reciprocal of the R-value, so the lower the number, the better.

The equation for average U-value is:.

Average U-value formula, to find the average R-value of insulation.
Taking the attic as 1000 square feet overall and putting in 1/R for U, we get:.

average u-value for R-50 & R-10.
Taking the reciprocal of 0.06, we get the average R-value of about 17, which is much lower than the R-30 we had actually get by improperly balancing the R-values.

Conclusion.

As I stated above, heat takes the path of least resistance, so the amount of additional heat going through the R-10 half far exceeds the additional heat flow that’s stopped on the R-50 side. Instead of getting an R-30 average, the lumpy attic has an R-17 average.

In practical terms, this means that if you see an attic with lumpy insulation, act with a rake and smooth it out. In the example I simply exercised, you ‘d almost double the R-value without including any extra insulation!

Another common example of the flat-or-lumpy conundrum is an attic that’s completely insulated except for one little location, say the pull-down attic stairs. We can go through the exact same steps as above and show that an attic that has a uniform R-30 over 99% of the area and 1% at R-1 (the pull-down stairs) will have an average R-value of 23.

That’s right, those pull-down stairs can reduce your overall R-value by 25%. One little uninsulated location reduces the R-value dramatically.