Diminishing Insulation Returns

2010 March 10
by Otto

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?

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:

[table: insulation cost/benefit analysis]

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.

5 Responses leave one →
  1. Tim Miller permalink
    January 31, 2011

    Howdy, nice home photos. I’m restoring a 108 year old grand home and still planning the super insulation of the walls. Been intrigued about staggered double stud walls – 10″ filled with cellulose. In reading about your use of foam, a question came to mind. What type of sub siding did you use? And why?
    did you use double or tripple glazed windows?
    Sincerely
    Tim Miller

  2. Otto permalink*
    February 1, 2011

    Staggered-stud walls are great, but if you’re restoring an old home suddenly thickening the walls might be strange. You should always keep in mind the character of your house when you start renovating. How thick are current walls? You might find that the foam gives you the same R value as a thicker cellulose wall. The other key benefit of foam is that it really cuts down on air infiltration, which is a huge source of heat loss, especially in older homes. Cellulose will also settle over time, creating a gap at the top of the wall.

    Regarding windows, you need to balance cost, R-value, and your home’s character. If your windows have real character (old wavy glass, beautiful double-hung frame detailing etc), you might find that a combination of reducing air infiltration in walls & ceilings, combined perhaps with custom-made storm windows, might give you the improvements you need without compromising the character of the house.

    If the windows truly need to be replaced, I still urge you to consider the character of the house. Despite a slight performance weakness, double-hung windows might still be good. While fiberglass is probably the best frame option, wood or aluminum-clad wood might fit the house better.

    Beyond all that, the better the R-value of the window the better. Triple-glaze is great, but it also makes for a heavier window. The third pane of glass adds virtually no insulating value by itself; the benefit comes from creating an additional air pocket. So you might also want to consider a double-paned window that has a thin polyester film suspended in the middle. Much lighter and essentially the same R-value. Also consider argon or krypton gas filling, as well as low-e coating.

  3. Tim Miller permalink
    February 3, 2011

    Howdy Otto, thanks for the advice. But you didn’t answer my question about the sub siding. I was wondering if your home has OSB or plywood or the more futuristic pink Ownings insulation board for sub siding…
    My old home has 7′ tall 3′ wide single pain 108 year old windows and they will be replaced by much smaller& efficient windows. The homes Character is a minor issue , my opinion worshiping it = forking out huge energy costs to heat and cool it. It is surprising how little difference thicker walls make. The house has some that are 1′ wide already but these are hollow. What a heat bill it use to have. The thick walls over-sized window sills allows for interesting decor options too…

    The sustainability of cellulose verses foam appeals to me as does the huge difference in cost. Settling of the insulation is either due to poor workmanship and myth.

  4. Otto permalink*
    February 3, 2011

    I’m not sure what you mean by “sub siding.” My walls are 12″ SIPs, so on top of those is just house wrap and then the siding. If you are wondering whether you should put a solid skin of insulation around the outside of the house, I strongly encourage that.

    I can’t comment on your home’s character as I’ve never seen it, but I would say that thicker walls probably make a bigger difference than you think. Uninsulated walls not only have really low R values but probably huge air infiltration. Why do you say it is surprising how little difference that makes? Have you tested it? Of course, doing both is the best, but I’m just looking for best bang for the buck here.

    If your windows are facing south, even poorly insulated windows can have a net heat gain due to the solar gain during the day.

    Cellulose certainly is much more sustainable. And if you have enough volume in the walls you can do a fantastic job with it. The one thing I would recommend is reducing infiltration. Easily 30-50% of your entire heating bill is probably due to draft conditions.

    Best of luck with this project! It sounds like you’re asking all the right questions.

  5. Tim Miller permalink
    February 4, 2011

    Hi Otto. Thanks, Sips likely OSB… I almost forget about Sips , so much foam is being spray applied and the pink insulation board by Owens 4 by8′ sheets can be used instead of sub siding wall underlayment,.

    I think all windows are the largest net heat gain & loss in any insulated wall. But am likely to install thermal shades to reduce heat loss in cold months. to supplement energy efficient windows. Over hanging pergolas and trees will be the summer buffer.

    Another benefit of the cellulose is its reduction of air infiltration an fire retardant and insect resistance . Plus i’m creating rain screen exterior walls to for their many benefits. Again thanks for your information. Tim

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