Diminishing Insulation Returns

When I had our house foamed, the spray foam people told me I was an idiot for getting more than 4 inches of foam. Anything more than that was simply a waste of money.

The local brand of closed-cell polyurethane spray foam is Corbond. On their website they have a graph that looks like this:

More Insulation Is Clearly Useless. Or is it?

In an accompanying table of data, they state that the first inch of insulation reduces 72% of the heat loss. By the time you have four inches, adding a fifth inch reduces additional heat loss by only 1%. That inch of foam costs as much as the first inch (and insulates just as well), but is 72 times less effective. So was I an idiot for adding 12 inches of foam to my house? Maybe. Read on.

My initial thought was that everything about insulation is diminishing returns. Let’s say you built a house but didn’t put a roof on it. If you stretch a plastic sheet across the top, you’ll probably reduce heat loss by about 90%. If you replace the plastic sheet with a real wood roof, you’ll probably reduce heat loss by another 90% (for a total of 99% reduction). That means that ten dollars of plastic sheeting gives you 90% heat loss reduction. A ten thousand dollar roof gives you only a tenth of the additional heat loss reduction. So  why would anyone put on an actual roof–and then spend another several thousand dollars insulating it (to reduce heat loss to 99.9%, an additional reduction of only 0.9%)?

The problem with looking at insulation this way is what I call a frame of reference error. Did you ever see the Charles and Ray Eames movie “Powers of Ten” in science class in school? (If not, I highly recommend it: www.powersof10.com.) You zoom from intergalactic spaces down to the earth, spend only a few seconds in a ‘normal’ frame of reference – a park picnic in Chicago – and then dive into an atomic scale. The only reason the picnic appears to be the fulcrum between enormous and tiny is because that’s the frame of reference we understand. If we were atoms – or galaxies – then the tipping point between big and small would be shifted.

What does this have to do with insulation? Consider this: that Corbond graph showing insulation effectiveness would look exactly the same (aside from the numbers) if it went in 1/10 inch increments or in 10 inch increments. The first 1/10 of an inch is a lot more effective than subsequent fractions of an inch. The same holds when comparing increments of 10 inches.

So the only reason we think of those additional inches as being a waste of money is because we’re measuring on the scale of inches.

So how much insulation should we use?

The financially-minded title of this post, “diminishing insulation returns,” implies the answer. We need to look at the point where the incremental insulation costs more than the cost of the energy saved over the lifetime of the insulation. It really doesn’t matter whether the inch of insulation saves you 72% of your heat loss or 1% of your heat loss. It matters whether the absolute savings outweighs the absolute cost.

Here, of course, the calculation becomes fairly complex. Some largely unknowable considerations:

1. What’s the “lifetime” of the insulation? 30 years? 50 years? 100 years?

2. How will energy costs change over that time period?

3. What’s the net present value of those energy costs (ie what will the inflation rate be over the lifetime of the insulation)?

I would suggest that a conservative place to start would be to assume a 30-year lifetime, no change in inflation-adjusted energy prices, and ignoring the time value of money.

The guy who did the calculation of my house energy efficiency (Called a HERS rating – Google it), Matt Primki in Billings, provided me the following information: 1 square foot of R-1 insulation costs $1 to heat for a year in Bozeman (using $8/decatherm natural gas in a 8000 Heating Degree Day climate). Using that data and combining it with the cost and R-value of a specific insulation type, it’s easy to calculate the ideal amount of insulation. Using a 6.2 r-value/inch (typical closed-cell foam) at $0.65 per board foot (what my local guy charges; one board foot is a 12-inch square one inch thick), here is the calculation:

With these parameters, the 4th inch of insulation becomes partially uneconomic. Varying the parameters moves the “economically ideal” amount of insulation, although by less than I would have thought. Triple the price of energy, and you should use 6″ of insulation. Quintuple the price and you should use 7″. Triple the price of energy and assume a lifetime of 60 years, and the formula recommends 8″.

I was really surprised to see how little the recommended total insulation changed. I also learned that, from a strictly financial point of view, I potentially overinsulated my house in some places.

There is one important caveat if you’re using this approach to plan your insulation. As your house approaches Passive House standards (ie becomes so well insulated that a traditional heating system is no longer needed), the calculation changes dramatically. As you deduct the cost of the heating system, the cost of insulation effectively drops dramatically and the cost/benefit scale shifts.