The Joy of Curtains
By Dr. Robert E. Buxbaum January 18, 2013
In our northern climates most homes have high-tech, double-paned windows; they cost a fortune, and are a lot better than plain glass, but they still loose a lot of heat: far more than the equivalent area of wall. The insulation value is poor mostly because the thickness is low: a typical double pane window is only ½” thick. The glass panes have hardly any insulation value, so the majority of the insulation is a .3″ space between them filled with air, typically. The outer walls, by contrast, are typically 6” thick filled with air and glass –wool. The insulation value, we find, more-or-less parallels the thicknesses: the wall is 12 as thick as the window, and the R value is 12 as great. A good trick to improve on your home’s insulation, then, is to add a fairly thick layer of stagnant air inside the room; curtains are a good way to do this.
To see how much you can save by adding curtains, it’s nice (for me, and my mind-set mostly) to talk in terms of R values. In the northern USA, the “R” value of a typical, well-insulated outer wall is about 24. What that means is that it takes 24°F and one square foot of wall to remove 1 BTU per hour. That is, the resistance to heat loss is 24 °F.hr.ft2/BTU. The R value for a typical double pane window is about 2 in the same units, and is only 1 if you have single panes. The insulating quality of our windows is so poor that, for many homes, more heat is lost through the windows than through the rest of the wall space.
To figure out how much heat is lost through your windows take the area in square feet multiply by a typical temperature differential (50°F might be typical in Michigan), and divide by the R value of your paned windows (1 or 2) depending on whether it’s single or double paned. Since heat costs about $10/MMBTU ($10 per million BTU) for a gas heated house, you can figure out what a small, 10 ft2 window costs a typical Michigan householder as follows, assuming a single pane (R=1):
Q = Area* ∆T/R = 10 ft2 * 50°F/1 = 500 BTU/hr. Here Q is the heat lost per unit time, ∆T is the temperature difference between the window surface and the room, and A is the ara of the window surface.
Since there are 24 hours in a day, and 30.5 days in a month the dollar cost of that window is 500*24*31.5*10/1,000,000 = $3.78/month. After a few years, you’ll have paid $200 for that small window in lost heat and another $200 in air conditioning.
A cheap solution is to add curtains, shades, or plastic of some sort. These should not be placed too close to the window, or you won’t have a decent air gap, nor so far that the air will not be static in the gap. For small gaps between the window glass and your plastic or curtain, the heat transfer rate is proportional to the thermal conductivity of air, k, and inversely proportional to the air gap distance, ∂.
Q = ∆T A k /∂.
R = ∂/k.
The thermal conductivity of air, k, is about .024 BTU/ft. hr°F. We thus confirm that the the R-value for an air gap of 9/16” or 1/20 foot is about 2 in these units. Though the typical air gap between the glass is less, about .3″ there is some more stagnant air outside the glass an that counts towards the 9/16″ of stagnant air. The k value of glass or plastic is much higher than of air, so the layers of glass or plastic add almost nothing to the total heat transfer resistance.
Because the R value of glass and plastic is so low, if you cover your window with a layer of plastic sheet that touches the window, the insulation effect is basically zero. To get insulation value you want to use a gap between about ½” and 1” in thickness. If you already have a 2 paned window of R value 2, you can expect to be able to raise your insulation value to 4 by adding a plastic sheet or single curtain at 9/16” from the glass.
Sorry to say, you can’t raise this insulation value much higher than 4 by use of a single air gap that’s more than 1″ thick. When a single gap exceeds this size, the insulating value drops dramatically as gas circulation in the gap (free convection) drives heat transfer. That’s why wall insulation has fiber-glass fill. For your home, you will want something more attractive than fiberglass between you and the window pane, and typical approaches include cellular blinds or double layer drapes. These work on the same principle as the single sheet, but have extra layers that stop convection.
A federalist version of double drapes was to use a simple cloth curtain hung between ½” and ¾” from the window, with a heavier drape beyond that. The light cloth, was kept in place day and night, the heavier one was closed at night and opened in the daytime. This will reduce your heat loss substantially, and typically looks better than plastic. A roll-type window shade does about the same, but looks worse (in my opinion). You get insulation with either material, but only if you put the material at a distance where it will interfere with the free convection flow of cold air, shedding from the window.
A modern type of curtains is called a “cell.” These are folded lengths of two or more stiff cloths that are formed into honeycombs ½” to 2” apart with an air gap in between. This thickness of the cells maximizes the insulating power of the shade. Placed at the right distance from the window, the cell curtain will add 3 or more to the overall R value of the window (1/12 ft / .024 BTU/ft. hr°F = 3.5 ft2hr°F/BTU). It should be noted, though, that all this R value goes away if the cell, or curtain is set at more than about 1” from the layer of glass or plastic. At a greater thickness that this, the free convection flow of cold air between the window and the shade dominates the heat loss, and you’ll get a puddle of cold air on your floor. The insulation value of the shade will be lost to cold air shedding.
I would suggest a cellular shade that opens from the bottom only and is translucent. This provides light and privacy; a shade that is too dark will be left open. Behind this, my home has double-pane windows (when I was single the window was covered by a layer of plastic too). The see-through shade provides insulation while allowing one to see out the window (or let light in) when the shade is drawn. You want to be able to see out; that’s the reason you had a window in the first place. Very thick, insulating curtains and blinds seem like a waste to me – they are enough thicker to add any significant R-value, they block the light, and if they end up far from the window, the shedding heat loss will more than offset any small advantage from the thick cloth.
One last window insulation option that’s worth mentioning is a reflective coating on the glass (an e-coating). This is not as bad an idea as you might think, even in a cold climate as in Detroit. A surprising amount of heat tends to escape your windows in the form of radiation. That is, the heat leaves by way of invisible (infra –red) light that passes unimpeded through the double pane glass. In hot climates even more heat comes in this way, and a coating is even more useful to preserve air conditioning power. Reflective plastic coats are cheap enough and readily available, though they can be hard to apply, and are not always attractive.
You can expect to reduce the window heat loss by a factor of 3 or more using these treatments, reducing the heat loss through the small window to $1.00 or so per month, far enough that the main heat loss is through the walls. At that point, it may be worth putting your efforts elsewhere. Window treatments can save you money, make a previously uninhabitable room pleasant, and can help preserve this fair planet of ours. Enjoy.