## October 19, 2006

### R U Warm Yet?

We’re doing some remodeling.  Of course we want to be very energy efficient.  So two questions came up: is it worth using the best current glass for new windows and does it make sense to replace existing double-paned seventeen year old windows at the same time.

Before I could do the math, I had to relearn what R factor is all about and then learn about U factor as well.  Of course, I started with Wikipedia.  Then I had to search the web for some local data.  This post is meant to make it easier for you to do the same thing if you’re faced with the same questions.  It’s also a test in using Google spreadsheets for me and a chance to get your reaction to them.

In simple English, the R of a material is the number of square meters of that material thr0ugh which you will LOSE a watt of energy for each degree centigrade of difference between the inside and outside temperature.  Materials like glass don’t need many square meters of surface to lose lots of watts so that makes them low R.

A typical single pane of glass has a R of 1.0.  You will one watt per degree of difference between the inside and outside of your house for each square meter of single pane glass you have in the wall (worse if there are cracks around the glass through which air flows).  On the other hand, well-insulated walls in New England according to the EPA guidelines have an R as high as 28.  It takes 28 square meters of well-insulated wall to lose as much energy as one square meter of single paned glass.

At some point it occurred to someone that this measure is upside down, that we really want to know how much heat we lose per unit of area rather than how much area we need to lose heat.  That’s why U was invented.  From a mathematician’s point of view, it’s just the reciprocal of R.  A material with a U of 1.0 loses one watt per square meter per degree of temperature difference.  If the U is 0.5, the material loses only have a watt per square meter per degree.  So low U is good.

Before I could do any useful calculations, I had to un-metrify.  My tape measure doesn’t measure meters; my thermometer doesn’t measure in centigrade; and the tables I have for the efficiency of heating fuels and systems are in BTUs per hour, not watts.  Turns out that the non-metric use an R which is in square feet, BTUs/hour, and degrees Fahrenheit. One RSI (metric R) equals 5.6745 the non-metric R.  Unfortunately for those of us in non-meteric nations, U values come from the metric R.  One non-metric U (if there were such a thing) would be 5.6745 times the U value printed on windows.  I’ll hide all that ugly stuff in a spreadsheet, though.

OK.  The question is what’s it worth to have high R (low U) windows.  For simplicity, let’s think about one window which five feet high and two feet wide, ten square feet.  If it’s an old single pane window (RSI=1, Metric U=1, non-metric R =5.6745, non-metric U=.176), it will lose 1.76 BTUs per hour per degree of difference between inside and outside temperatures.

What’s that mean over a full heating season? Ah, now you need to know how many heating degree day units there are in a year where you live.  You can find that out (roughly) by looking at the NOAA tables.  They tell me that for Vermont (population-weighted average if you want to be technical), there were 8167 heating degree days altogether for the 2003/2004 season and that this was 100.7% of normal so close enough to use in my calculation.

Assuming that you keep your inside thermostat at 65 degrees (you do, don’t you?), you can multiply degree days by 24 to get degree hours for the year.  196,000 degree hours in Vermont.  Since we already know that our ten foot square single pane window is losing 1.76BTUs per degree hour, we just multiply and find that it loses about 345,000 BTUs/year.

Now we need to know what that costs.  For that we use another handy government spreadsheet which tells us that there are 138,690 BTUs in a gallon of number 2 fuel oil (also has numbers for electricity, propane etc.). It also says that an oil furnace has an efficiency of 78% so, given the typical oil furnace, you only actually get 108,178 BTUs of usable heat from each gallon you burn.

The window lost 345,000 BTUs; we divide that by 108,178 BTUs per gallon and find out that about 3 gallons of heating oil went out that window last year; less, of course, if you live in a warmer climate; more if you keep your thermostat higher.

If you had double pane window with a U of 0.40 (RSI of 2.5), you would lose only 40% as much heat and so you’d save 1.8 gallons a year.  At current energy prices, it means the payback for replacing the single pane window with double pane is about \$4.50/year.  Unless you can find windows a lot cheaper than I can, the payback period is infinite.  You’d earn a better return by putting your window replacement money in the bank and collecting the interest.  Of course I know energy prices will go up (even though they’re in freefall at the minute); but I can always reconsider and get new windows then.

The actual question we faced was whether to replace double pane windows (1.8 gallons/year) with triple pane which have an R of about 3.5 and a U of .29 (at best).  The triple pane would save us only .3 gallons of year so make absolutely no sense.

But the energy-economics are very different when putting in new windows.  Then you only have to look at the cost difference between new triple-pane, double-pane, and single pane.  And you don’t have to consider installation cost at all.  Moreover, it makes economic sense to consider likely increases in the price of energy when putting in new windows because you WON’T want to replace them later when prices go up.

A Vermonter can save 2.1 gallons/year or \$5.50 year (current prices) by choosing triple-pane over single-pane.  That would easily justify a \$50 price difference for the new windows. There isn’t nearly as much saving in triple pane over double pane - .3 gallons or \$.75/cents per year but prices will go up and you’ll be saving the planet.

Net, replacing windows with lower U windows only makes economic sense when the window is broken or very drafty.  Using low U windows in new construction makes lots of sense.