The trouble with insulation

It seems obvious at first that insulating a house well is a good idea.  As my brother put it, "It's a passive heating element. You do it once and you don't have to spend time or money on it again, unlike active heating."

Insulation is great. However, it's pretty hard to insulate well enough that no fuel heat is needed (in cold climates).  Let's take a closer look:

We measure insulation in R-value, typically per inch of thickness of a material. The exact unit is sq. ft. * degF delta / BTU.  

Concrete is R-0.08.  Softwood varies, but is around R-1.4. Fiberglass batts (what the pink panther sells) is R-3.1.  That means that 38" of concrete is about as good an insulator as 1" of fiberglass batts. 

The unit is kinda backwards; what you really want to know is "how much heat will I lose through this wall?" not "how well does this wall hold back heat".  For example, a conventional studded wall with 2" x 6" studs, fiberglass batts, drywall, Tyvek, siding, and paint will have an R value around 20 (which is the code requirement for walls in a lot of places). Suppose you keep the indoors at 70 deg F, and outside it's 40 deg F.  If the wall is 8' tall and 40' long, then the total heat loss in the wall is:

    (70 - 40) * 8 * 40 / 20 = 480 BTUs lost per hour.

Imagine a 40' x 40' house with no windows or doros, and a flat roof, with all walls, roof, and floor insulated this way. Wall area is 8' * 40' * 4 (320 sq. ft.). Floor & ceiling are 40' x 40' each (3200 sq. ft.).  

    (70 - 40) * (320 + 3200) / 20 = 5280 BTUs lost per hour.

Most of our heating happens over a 5 month period here, which is 3600 hours. That's about 19 million BTUs.  A cord of firewood is 17 MBTUs. Electricity has about 3400 BTUs per kWh; at $0.10 / kWh that's $550 to heat the house through the winter. Sound good to me.

There are some "free" heat sources in the house, like cooking, body heat, and computers. Models I've seen count these for 8 degF.  (Maybe I should become a server hosting colo facility, for the free heat).

What about windows? Windows are about R-1 per pane (not per inch). That's way lower than the wall, so we should avoid windows, right? But this is a house for people, not dry goods, and people really like windows. 2-pane glass is pretty common, so R-2 for glazing is reasonable. There are some super-expensive R-11 windows, but they are xenon-filled, which leaks out over time, and they lose their insulation value. They also have coatings that reduce the amount of solar gain.

If you have a lot of windows, adding insulation to the walls won't help much: the heat isn't going out there anyway.  

You also lose a lot of heat through "air infiltration" aka "ventilation". We typically want the indoor air to circulate outside, carrying out toxins and bringing us oxygen. Old leaky houses (like the one I'm in now) replace the full volume of air about twice each hour. The tightest houses today only replace 1/3 of the air each hour, but they have to work hard to maintain air quality. For example, they may use an air-to-air heat exchanger so the outgoing air pre-warms the incoming air. I'm thinking about "earth tubes" - long PVC pipes that snake under the ground to pre-warm outside air on the way in. They're passive once built.  

Since windows and air replacement are the main sources of heat loss in a well-insulated home, adding more insulation doesn't get you much. Doubling wall/floor/ceiling insulation won't cut your heat bill in half.  I did a lot of spreadsheet modeling this stuff, and ended up with numbers like this:

1: Exterior wall heat loss (BTU / degF / hr) 23

2: Roof or ceiling loss 56

3: inviltration loss 166

4: heat lost through glass w/out insulation 150

Restricting windows also takes away the potential for free heat from the sun. Solar heat is tricky: it is most plentiful when it's least needed. Awnings and deciduous trees are good for moderating summer sun while allowing winter sun. Still, we need the heat at night more than during the day. A well-insulated house with lots of south-facing windows will definitely be hot on summer afternoons. All those windows will mean cold winter nights, too. Ack! The solution is thermal mass. It evens the heat out between day & night. My floor will be an insulated concrete slab w/ earthen tiles over, so lots of thermal mass and conductivity there.  The walls have a mortar matrix that provides more thermal mass.

Get enough thermal mass and you can even the heat out between winter and summer. We don't get enough summer heat to do that here, but it works in many places.

There are "active" solar heat systems that are pretty cool, but more complicated. One is to dig a deep pit under the house, insulate it, put a network of (internet?) tubes through it, and fill it with gravel.  In the summer, collect solar heat on the roof and pump it down to the bottom of the gravel. The heat will slowly move through the gravel, and arrive at the house in time for winter. The math on this is pretty easy.  It's a neat idea, but way too complicated & expensive for us.

You'll notice above that the surface area of the floor & ceiling are 10x the area of the walls. Roofs are also expensive.  That suggests a two-story building, which cuts the top & bottom surfaces in half while adding only a little to the wall area. 

However, there are some downsides: working up high in the air is harder, especially for us novices. The engineering of a two-story structure is more complex.  A little floor area is lost to the stairwell. Some facilities have to be duplicated between top & bottom floors, so you aren't always running up & down the stairs to pee, or to get a screwdriver.

Of course, two-story is nice in other ways, too. It provides a clear separate of public & private spaces. It's easier to put all the plumbing together, if one bathroom is on top of another.  Maybe for the next house.

Anywhere, where does all of that leave us?

- Smaller is cheaper & more efficient.

- Insulate walls well, but don't worry about it too much; most heat will go out the windows and vents.

- Caulk well, but make sure you still have fresh air.

- Use good windows. More panes are good.

- Put most of the window area on the south side of the house.

- Have enough thermal mass for the window area. More thermal mass is good, but don't break the bank.