Info-to-Build-On Heat Loss Math makes common sense. by Raoul Hennin January 31, 2007

Vermont Castings "Defiant" Woodstove

We have finally gotten our cold snap in Maine this year - over the past two weeks we have hovered close to 0°F. Our houses let us know they are maintaining a ΔT from inside to outside ("Delta T" is a change in temperature). The ΔT across the building envelope creates tell-tale signs in most homes. Windows sometimes perspire. Floors develop new creaks or moans. Air moves in unexpected drafts. We get re-acquainted with the heating appliances in our homes. The recent cold weather has given me reason to celebrate a new Vermont Castings Defiant woodstove by burning wood nonstop for 12 consecutive days! Shelter Institute carries all of Vermont Castings' wonderful stoves.

I have taught the science of heat loss at Shelter Institute for many years. We schedule "Heat Loss" early in our 2-week class because it influences so many design decisions throughout the house. In four hours, Shelter Institute students learn to calculate precisely the theoretical flow of heat from inside the house to outside during the coldest hour of the coldest day of the year. In warm climates, the problem can be reversed, although humidity makes the cooling calculations admittedly more complex.

In class, we calculate overall heat loss and estimate the size of the heating system for a given house and then extrapolate, using climatic data, to arrive at a seasonal heat load and yearly cost of heating the house. We consider what would be the optimal amount of insulation, size and orientation of windows, and how much fresh air to admit. We discover that there is such a thing as too little or too much insulation, too many windows, and a house that is too tight, or too loose.

Heat Loss is somewhat unusual in the building sciences because the math appears simple. In fact, we choose simple math because it gives accurate estimates with minimal work. A house experiences heat loss in three ways: conduction, radiation, and infiltration. We do three separate calculations and sum them to arrive at the overall heat loss for the house. Today, I will discuss only the formula for conduction. For the other two, I highly recommend taking the class.

Perhaps the easiest form of heat loss to define and control is conduction. Conduction is minimized by insulation, or high R-value walls. R is for Resistance to heat loss. The simple formula for heat loss due to conduction is:

Don't get scared off by the math! This is easy and it actually sheds light on how to build the house. One BTU (British Thermal Unit) is the amount of heat energy that raises the temperature of one pound of water by one degree farenheit. The first problem we solve in class is: how many BTU's are required to make a cup of tea? (hint: a pint is a pound the world around)

The beauty of the conductive heat loss formula is that it tells us immediately that heat loss depends on 3 factors: ¹/_R-value is the amount of insulation, A is the surface area of the structure, and ΔT is the change in temperature across the building envelope. More insulation (higher R-value) means less heat loss. Bigger houses (with bigger surface Areas) will require more energy to heat. And, of course, it makes sense that the colder it is outside (the greater the ΔT), the more heat we will need inside to keep warm. The formula allows us to put numbers to our intuitive grasp of heat loss and begin to make decisions about our house.

It only takes about 15 minutes to calculate the conductive heat loss for a house by choosing an R-value from the insulation label, adding up the square footages of walls and roof, and looking up the 30-year minimum average daily temperature for the coldest day of the year. What makes this class fun, and what we spend time on in class, is building an intuitive knowledge of heat loss that enables us to design truly energy efficient, comfortable homes.

One of the finer points of heat loss emerges when we consider how humans experience the movement of heat to or from ourselves. Picture getting out of bed in the morning and stepping onto the carpeted floor, walking over to the bathroom. Who wouldn't pause a moment in anticipation of the first step onto tile? Why? The tile is exactly the same temperature as the carpet, but our experience is dramatic as one bare foot snoozes on the carpet and the other confronts conducting tile. We literally feel the tile sucking the heat out of the souls of our feet.

Comfort depends on how heat is delivered as well as the actual temperature achieved. So houses need to deliver heat in appropriate modes for optimal efficiency. In fact, if heat is delivered and conserved in comfort-oriented ways, we can reduce overall temperature and heat loss. A radiant heat system under tile in the bathroom would certainly change the morning routine. Radiant heat under carpet, however, makes less sense as the carpet insulates the living space against the heat. (i.e. We would end up heating our basement crawl space.)

The thermodynamic behavior of a house will encompass conduction, radiation, and air movement as heat moves from where there is some(inside) to where there is less (outside). Combining our calculations with a healthy and skeptical intuition, we can get a fairly accurate picture of what will happen in our new house before we build it. We can design the house systems to accommodate a range of comfort zones. This is where the fun begins as we consider the impact on our comfort of every surface, every window, every door, and each source of heat throughout the house.

And then there is Solar Gain from sunlight through the windows into the house during the day. But you will have to come to class to practice those calculations...