Heat loss simplified

As soon as heat is turned loose, it tries to warm everything it comes in contact with. Sadly, if it is minus 20 C outside, heat released inside will do everything it can to escape confinement, like a dog I had once. To keep a house warm, new heat has to be released to replace the heat that got away.

Keep it inside

If there is a temperature difference between the inside and outside of a building heat travelling by conduction moves from the hotter side to the colder side. Slowing the travel of heat, heat loss, through the walls ceilings and floors in contact with exterior, the building envelope, is the main strategy for keeping the heat inside buildings.

The other significant source of heat loss in buildings is ventilation heat loss, which sounds like a bad thing, but is essential. A house needs fresh air for the health of the people inside as well as most of the stuff the house is made of. Heat is lost when the warm air leaving the house is replaced by colder air from outside.

Heat loss (or gain) through the building envelope is determined by;
The temperature difference of the exposed walls, ceiling or floor between the inside and outside.
The area of the exposed walls, windows, doors, ceilings under unheated space or floors over unheated space or soil.
The resistance to heat flow of the different materials used for exposed walls, ceiling or floors.
The volume of air flowing out of the house replaced by outside air with a different temperature.

Heat loss in homes happens where the outside meets the inside

The typical Edmonton single family house has a heated full basement, partly below grade (ground level) and partly above grade. Below grade walls and floors are exposed to soil temperatures, which will almost always be different from air temperatures, heat also flows differently from house exterior to soil than house exterior to air.

Walls above grade have penetrations, such as windows and doors that have a higher heat loss than the rest of the wall.

Ceilings that separate the inside from the outside are below an unheated ventilated attic.

A single family house in Edmonton will almost certainly be stick framed. Stick framing is softwood lumber cut to standard dimensions, 2 by 4, 6, 8, etc. spaced at standard dimensions such as 16 inches or 12, 24 etc..

Stick framed walls, floors and ceilings are mostly empty space separated by wood 1 5/8 (38 mm) wide on the wall ceiling or floor face, a 2 by 4 wall is 3 5/8 (92 mm) long in the direction of heat flow. Framing is covered or clad using materials seldom more than an inch (25.4 mm) thick. The exposed 2 by 4 wall (building envelope wall) will be somewhere around 6 inches (150 mm) total thickness in the direction of heat flow depending on the materials used on both sides of the framing.

Builders in cold climates experimented with filling the hollow spaces of framed exterior walls with insulation in the early 20th century. Building scientists systematically tested the materials used for framing resistance to heat flow. This resulted in R values, resistance to heat flow for building materials and insulation using imperial measurement, RSI when metric measurements are used.

R ratings for walls are calculated by adding all the Rs for each layer of material of the wall in the direction of heat flow. R ratings are based on the resistance of the material and the distance heat has to travel, increasing the distance directly increases the R. If one inch of a type of wood has an R of 1.1, two inches will have an R of 2.2.

The R of each layer in the direction of heat flow is added, in this case, half inch drywall, R 0.4, 2X4 16′ center framing with fiberglass insulation batts, R 10.4, 3/8″ plywood or OSB sheathing R 0.4, and siding. There is also resistance where heat is transferred to or or from the air surrounding each side of the wall. When added, the total R for this wall will be between R 12 and R 13.

The framed wall is made from softwood with an R of 1.1 per inch and the spaces between the framing which can be filled with insulation. The R for the framing is established using the percentage area of framing R and insulation R to estimate a combined R for the assembled wall.

Wall R is calculated using the ratio of framing R to insulation R

Once the R of an assembly, wall, ceiling, window, door or floor has been established heat flow can be estimated by multiplying area, the difference in temperature, by 1/R, also known as U. If a 1000 square foot R 13 exterior wall has a temperature of 68 degrees F on the inside and the temperature on the outside of the wall is -2 degrees F, the estimated heat loss will be,
1000 sq. feet*70 degrees F * 1/13 (U 0.077) = 5385 BTU/hr. heat loss. In metric when outdoor temperature is -19 C and indoor is 18 C, 100 square meters * 37 degrees C (19+18) * 1/ RSI 2.3 (USI 0.43) = 1591 Watts heat loss. (For delta T or temperature difference, below zero numbers are positive, -2 F outside, and 68 inside = delta T 70 F. -19 C outside and 18 inside = delta T 37 C)

Window and door manufacturers do their own R calculations more or less the same way as walls. A modern window is combination of different materials, some might be hollow or filled with heavy gases. The manufacturer supplies the buyer with the U rating, which can be found on the product label or their website. Canadian product labels use USI, the metric standard. If U is 1/R then R is 1/U, if you are curious about the R of windows, just divide U into one, ie, 1/U 0.3 is R 3.3. 1/ USI 1.1 = RSI 0.9.

To calculate heat loss through windows, multiply the area of the complete window, frame and all, times the temperature difference and U. 100 square feet of U .30 (USI 1.72) windows have a heat loss of 2100 BTU hr. when the temperature outside is -2F or -19 C, in metric, .929 sq. meter*37*1.72=591.4 Watts/hr.

Ceilings below unheated attics are the norm for Edmonton houses. Ceilings are insulated by piling loose insulation or batts between and on top of the framing. Attics are mostly unused, so homeowners are able to pile as much insulation as they can fit over the framing as long as it does not interfere with attic ventilation of the underside of the roof, which is another topic addressed here. If the insulation has buried the framing, measure insulation depth and multiply the depth times the R per inch for the insulation type, loose fiberglass is R 3 per inch, fiberglass batt R 3.5/inch, loose Cellulose is R 4/inch, wood shavings R 2.2 per inch. Insulaton depth times R is your ceiling R, eg, 10 inches R3/inch loose fiberglass is R 30.

Ceiling area is multiplied times temperature difference between outdoors and indoors, divided by R or multiplied by U which is the same thing as dividing by R. The result is the heat loss for the temperature difference. If you are wondering why bother with R, R must be used for adding the resistance of the various layers, for ceilings, add the R of ceiling drywall, 0.5 to the insulation R, or not it will not make much difference. A 1000 square foot ceiling below an unvented attic with R 30 insulation will lose heat at 1000*70/30 = 2333 BTU/hr. if the temperature inside the attic is 2-F and inside temperature is 68F, for heat loss estimating assume ventilated attic temperatures are the same as outdoors. Metric heads who are losing it because this Canadian is flagrantly flouting international standards can find the answer to that here.

If the metric fans are back, RSI is R divided by 5.678 and when Imperialist R is multiplied by 5.678 it is mathematically transformed into World Government approved RSI.
One million BTUs are equal to 1.05 GigaJoule (GJ) very close to 1 GJ, which will come in handy later.

Below grade heat loss estimating will be based on the temperature of the soil in contact with the building envelope, which in most Edmonton cases will be a concrete foundation wall. To make things even more interesting, the foundation wall is usually partially above grade and partially below. The above grade portion is exposed to air temperature. R of an 8 inch concrete wall is about 2.2, as in not very much.

To calculate heat loss below grade a fudge factor can be used. Temperature difference will be based on the average mean annual soil temperature. For Edmonton that is 41 F, 5 C. The foundation perimeter (not the area), the difference between mean soil temperature and the desired basement temperature times the factor, 1.42 for a fully insulated concrete wall, 2.46 for an uninsulated below grade concrete wall, if they are five feet or more below grade. A basement of a house 25 feet by 40 feet has a perimeter of 130 feet, delta T is 27 F (68- 41). 130*27*1.42=4984.2 BTU/ hr for an insulated basement wall, 8,494.2 BTU hr. for an uninsulated basement wall.

For above grade heat loss, If the basement wall is fully framed and insulated with 2X4s add framed wall R to concrete R 2.2, divided into the area of above grade foundation walls times the delta T or temperature difference between outdoor air temperature and inside, the same as for framed walls.

Basement floors for Edmonton it is safe to assume are uninsulated unless you know differently, such as a slab with professionally installed in floor heating. A lowish heat loss factor is used that takes into account most of the heat lost through the slab will be at the edges, the parts of the slab that are closest to the exterior walls. The factor for an uninsulated slab six feet below grade is 0.044, which is multiplied by the slab floor area and soil basement temperature difference, the area of a 25X40 slab is 1000 sq.ft.*27*.044=1188 BTU/hr.

There are other factors that a proper heat loss estimate will take into account, such as how exposed the building is, the direction of each side of the house faces etc.. No matter how much detail is added or left out, a heat loss estimate can only be an estimate based on hypothetical values.

The purpose for all this calculating is to estimate how much energy a building needs to stay warm. Once heat loss is known heating systems can be designed. A heating design temperature is used to select equipment, for Edmonton that would be -26 F, -31 C. The design temperature is one that the local temperature will be above 99% of the time. If you are worried about that 1%, don’t be, heating equipment is chosen to deliver more than estimated heat loss design temperature. The other way that heat loss estimates can be used is to estimate any particular building’s heat loss annually using Heating Degree Days (HDD).

A heating degree day is based on daily average temperature records. If the average temperature for a day is less than 64 F or 18 C the HDD for that day is 1 HDD per degree. If the average for a particular day’s temperature in Edmonton was -1 C that day was 19 C HDD (18+1). Once each day’s HDD is recorded they can be added to give HDD per week, month or year. Edmonton’s annual HDD is usually just over 5000 C, or 9000 F HDDs. If annual HDDs are substituted for Delta T in a heat loss calculation, the result will be the total annual energy heat loss for that year. This should not be confused with energy consumption, which will be more, depending on the heating appliance’s efficiency.

Next we will look at a hypothetical house’s energy requirements for heating.