Two houses of equal area but different shape

Architects designing custom homes often seem to go overboard on the complexity of the shape, seemingly unaware of the impacts on construction cost and operational cost. Let’s look at the walls of two custom homes of equal floor area but different shape.

Both homes are 5400 square feet on one level, nice sprawling ranch homes for a well-to-do business person. The first thought is that the house is too big, and it is, but this not an unusual size in the area of custom homes. It’s still well within Part 9 of the Ontario Building Code, which deals with houses and other small buildings.

House A was designed with a highly irregular shape to add “architectural interest”. It follows the room layout and offers more views of the local scenery. From the plans we count 56 corners.  This is not unusual for this size of house. If you walked around the perimeter of house A with a tape measure it would be 600 feet.

House B was designed by a home designer-builder who doesn’t know a lick about heat loss either, but didn’t want to do all the design work of a complicated home, especially the roof, and wanted a simple L-shape so that it would be faster to construct. House B has a perimeter of 370 feet and just 6 corners.

Assume the walls are 9 feet high. Let’s also assume an insulation R-value of R-20 for the walls and R-2.00 for windows. In reality the effective R-value for house A will be lower because of the extra wood framing material used to create the more complicated shape, but let’s hold as many things constant as we can for this exercise. Also assume that the windows are 40% of the wall area. Each of the two homes will be built in Toronto, which has 6426 heating degree days (in degrees Fahrenheit).

The way to calculate heat loss for a year is with the equation heat = 1/R * area * heating degree days * 24 hours per day.

When this is all multiplied out, the energy lost during the heating season is 192 million BTU’s for house A and 118 million BTU’s for house B.

Let’s put some dollars to that. Converting to kilowatt-hours the amount of heat is 56140 kWh for house A and 34620 kWh for house B.  For simplicity’s sake let’s say you’re paying $0.10 per kilowatt-hour after taking into account the distribution fee, debt retirement charge, taxes, and so on, and you decide to use electric baseboard heat that consumes 10% more energy than actually required, because of delays in responding to the thermostat’s call for heat. The annual heating cost of just the walls and windows is $6,175 for house A and $3,808 for house B.

That’s an added cost of of $2,367 per year, every year, for having a complicated shape instead of a simpler one. The same floor area, same wall insulation, and same window quality. If you prefer the environmental route, that’s 4.6 more metric tonnes of CO2 per year, about the emissions of an average passenger vehicle.

What about equipment costs? If it was heated with a furnace or hot water boiler the capacity of the equipment would need to be correspondingly larger and thus more expensive. That wouldn’t be too much—but move to a geothermal system and look out! It could be $12,000 more in ground loop installation costs and larger equipment.

I’ve only looked at conductive heat loss. The most diligent builder is going to have a great deal of difficulty providing a continuous air barrier with a more complicated housing plan. If the builder managed to pay very close attention to detail, even if the normalized leakage area (expressed in square inches of hole per square foot of wall) were the same between the two houses, the equivalent leakage area would be proportionally larger. Given that infiltration commonly accounts for 30% of heat loss, the impact is significant.

Then there’s the foundation required to support the wall. Ben Polley of Evolve Builders Group in Guelph, Ontario, tells me that in his estimation, every corner of a foundation wall adds the equivalent of 5 linear feet to the cost due to formwork and labour. Assuming 10 inch thick walls, 7 feet high and $80 per cubic yard of poured foundation wall, it would cost $15,210 for the house A wall foundation and $6,913 for the house B wall foundation, a capital cost increase of $8,297.

Don’t even get me started on the complicated roof design that goes on these complicated houses. Ask your local roof framer.

The take away from this evaluation is that “corners cost energy” and “corners cost money”. Lots of money.