Energy loss and temperature demand degreedays

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Since energy is power x time, you can write the energy lost by conduction through an area in a short duration as energy loss = area x U x (AT x duration), and the energy lost by ventilation as

Both these energy losses have the form

Something x (AT x duration),

Maximum England and Wales Sweden


(W/m2/K) 1985 1991 2002 1975 2001




Windows, doors



Figure E.3. U-values required by British and Swedish building regulations.

where the "Something" is measured in watts per °C. As day turns to night, and seasons pass, the temperature difference AT changes; we can think of a long period as being chopped into lots of small durations, during each of which the temperature difference is roughly constant. From duration to duration, the temperature difference changes, but the Somethings don't change. When predicting a space's total energy loss due to conduction and ventilation over a long period we thus need to multiply two things:

1. the sum of all the Somethings (adding area x U for all walls, roofs, floors, doors, and windows, and for the volume); and

2. the sum of all the Temperature difference x duration factors (for all the durations).

The first factor is a property of the building measured in watts per °C. I'll call this the leakiness of the building. (This leakiness is sometimes called the building's heat-loss coefficient.) The second factor is a property of the weather; it's often expressed as a number of "degree-days," since temperature difference is measured in degrees, and days are a convenient unit for thinking about durations. For example, if your house interior is at 18 °C, and the outside temperature is 8 °C for a week, then we say that that temperature (°C)

temperature (°C)

3188 degree-days of heating Feb Mar Apr May Jun Jul temperature (°C)

91 degree-days of cooling

3188 degree-days of heating Feb Mar Apr May Jun Jul

Aug Sep Oct Nov Dec

Aug Sep Oct Nov Dec temperature (°C)

2265 degree-days of heating Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Figure E.4. The temperature demand in Cambridge, 2006, visualized as an area on a graph of daily average temperatures. (a) Thermostat set to 20 °C, including cooling in summer; (b) winter thermostat set to 17 °C.

week contributed 10 x 7 = 70 degree-days to the (AT x duration) sum. I'll call the sum of all the (AT x duration) factors the temperature demand of a period.

energy lost = leakiness x temperature demand.

We can reduce our energy loss by reducing the leakiness of the building, or by reducing our temperature demand, or both. The next two sections look more closely at these two factors, using a house in Cambridge as a case-study.

There is a third factor we must also discuss. The lost energy is replenished by the building's heating system, and by other sources of energy such as the occupants, their gadgets, their cookers, and the sun. Focussing on the heating system, the energy delivered by the heating is not the same as the energy consumed by the heating. They are related by the coefficient of performance of the heating system.

energy consumed = energy delivered/coefficient of performance.

For a condensing boiler burning natural gas, for example, the coefficient of performance is 90%, because 10% of the energy is lost up the chimney.

To summarise, we can reduce the energy consumption of a building in three ways:

1. by reducing temperature demand;

2. by reducing leakiness; or

3. by increasing the coefficient of performance.

We now quantify the potential of these options. (A fourth option - increasing the building's incidental heat gains, especially from the sun - may also be useful, but I won't address it here.)

temperature demand (degree-days per year)

4000 3500 3000 2500 2000 1500 1000 500

temperature demand (degree-days per year)

4000 3500 3000 2500 2000 1500 1000 500






14 15 16 17 18 19 20 21 22 23 24 25 thermostat setting (degrees C)

14 15 16 17 18 19 20 21 22 23 24 25 thermostat setting (degrees C)

Figure E.5. Temperature demand in Cambridge, in degree-days per year, as a function of thermostat setting ( °C). Reducing the winter thermostat from 20 °C to 17 °C reduces the temperature demand of heating by 30%, from 3188 to 2265 degree-days. Raising the summer thermostat from 20 °C to 23 ° C reduces the temperature demand of cooling by 82%, from 91 to 16 degree-days.

Temperature demand

We can visualize the temperature demand nicely on a graph of external temperature versus time (figure E.4). For a building held at a temperature of 20 0C, the total temperature demand is the area between the horizontal line at 20 0C and the external temperature. In figure E.4a, we see that, for one year in Cambridge, holding the temperature at 20 0 C year-round had a temperature demand of 3188 degree-days of heating and 91 degree-days of cooling. These pictures allow us easily to assess the effect of turning down the thermostat and living without air-conditioning. Turning the winter thermostat down to 17 0 C, the temperature demand for heating drops from 3188 degree-days to 2265 degree-days (figure E.4b), which corresponds to a 30% reduction in heating demand. Turning the thermostat down to 15 0C reduces the temperature demand from 3188 to 1748 degree days, a 45% reduction.

These calculations give us a ballpark indication of the benefit of turning down thermostats, but will give an exact prediction only if we take into account two details: first, buildings naturally absorb energy from the sun, boosting the inside above the outside temperature, even without any heating; and second, the occupants and their gadget companions emit heat, so further cutting down the artificial heating requirements. The temperature demand of a location, as conventionally expressed in degree-days, is a bit of an unwieldy thing. I find it hard to remember numbers like "3500 degree-days." And academics may find the degree-day a distressing unit, since they already have another meaning for degree days (one involving dressing up in gowns and mortar boards). We can make this quantity more meaningful and perhaps easier to work with by dividing it by 365, the number of days in the year, obtaining the temperature demand in "degree-days per day," or, if you prefer, in plain "degrees." Figure E.6 shows this replotted temperature demand. Expressed this way, the temperature demand is simply the average temperature difference between inside and outside. The highlighted temperature demands are: 8.7 0C, for a thermostat setting of 20 0C; 6.2 0C, for a setting of 17 0C; and 4.8 0C, for a setting of 15 0C.

Leakiness - example: my house

My house is a three-bedroom semi-detached house built about 1940 (figure E.7). By 2006, its kitchen had been slightly extended, and most of the windows were double-glazed. The front door and back door were both still single-glazed.

My estimate of the leakiness in 2006 is built up as shown in table E.8. The total leakiness of the house was 322 W/0C (or 7.7kWh/d/°C), with conductive leakiness accounting for 72% and ventilation leakiness for 28% of the total. The conductive leakiness is roughly equally divided into three parts: windows; walls; and floor and ceiling.








i i

14 15 16 17 18 19 20 21 22 23 24 25 thermostat setting (degrees C)

14 15 16 17 18 19 20 21 22 23 24 25 thermostat setting (degrees C)

Figure E.6. The temperature demand in Cambridge, 2006, replotted in units of degree-days per day, also known as degrees. In these units, the temperature demand is just the average of the temperature difference between inside and outside.

Figure E.7. My house.

Conductive leakiness







Horizontal surfaces

Pitched roof




Flat roof








Vertical surfaces

Extension walls




Main walls




Thin wall (5in)




Single-glazed doors and windows




Double-glazed windows




Total conductive leakiness


Ventilation leakiness volume





per hour)


Bedrooms 80



Kitchen 36



Hall 27



Other rooms 77



Total ventilation leakiness 90

Total ventilation leakiness 90

Table E.8. Breakdown of my house's conductive leakiness, and its ventilation leakiness, pre-2006. I've treated the central wall of the semi-detached house as a perfect insulating wall, but this may be wrong if the gap between the adjacent houses is actually well-ventilated.

I've highlighted the parameters that I altered after 2006, in modifications to be described shortly.

To compare the leakinesses of two buildings that have different floor areas, we can divide the leakiness by the floor area; this gives the heat-loss parameter of the building, which is measured in W/°C/m2. The heat-loss parameter of this house (total floor area 88 m2) is

Let's use these figures to estimate the house's daily energy consumption on a cold winter's day, and year-round.

On a cold day, assuming an external temperature of —1 °C and an internal temperature of 19 °C, the temperature difference is AT = 20 °C. If this difference is maintained for 6 hours per day then the energy lost per day is

If the temperature is maintained at 19 °C for 24 hours per day, the energy lost per day is


To get a year-round heat-loss figure, we can take the temperature demand of Cambridge from figure E.5. With the thermostat at 19 °C, the temperature demand in 2006 was 2866 degree-days. The average rate of heat loss, if the house is always held at 19 °C, is therefore:

7.7kWh/d/°C x 2866 degree-days/y/(365 days/y) = 61 kWh/d.

Turning the thermostat down to 17 °C, the average rate of heat loss drops to 48 kWh/d. Turning it up to a tropical 21 °C, the average rate of heat loss is 75 kWh/d.

Effects of extra insulation

During 2007,1 made the following modifications to the house:

1. Added cavity-wall insulation (which was missing in the main walls of the house) - figure 21.5.

2. Increased the insulation in the roof.

3. Added a new front door outside the old - figure 21.6.

4. Replaced the back door with a double-glazed one.

5. Double-glazed the one window that was still single-glazed.

What's the predicted change in heat loss?

The total leakiness before the changes was 322 W/°C. Adding cavity-wall insulation (new U-value 0.6) to the main walls reduces the house's leakiness by 20 W/°C. The improved loft insulation (new U-value 0.3) should reduce the leakiness by 14W/°C. The glazing modifications (new U-value 1.6-1.8) should reduce the conductive leakiness by 23W/° C, and the ventilation leakiness by something like 24 W/° C. That's a total reduction in leakiness of 25%, from roughly 320 to 240 W/°C (7.7 to 6kWh/d/°C). Table E.9 shows the predicted savings from each of the modifications.

The heat-loss parameter of this house (total floor area 88 m2) is thus hopefully reduced by about 25%, from 3.7 to 2.7W/°C/m2. (This is a long way from the 1.1 W/°C/m2 required of a "sustainable" house in the new building codes.)

- Cavity-wall insulation (applicable to two-thirds of the wall area)

- Improved roof insulation

- Reduction in conduction from double-glazing two doors and one window

- Ventilation reductions in hall and kitchen from improvements to doors and windows

4 8 kWh/d Table E.9. Break-down of the predicted reductions in heat loss from my house, on a cold winter day.

It's frustratingly hard to make a really big dent in the leakiness of an already-built house! As we saw a moment ago, a much easier way of achieving a big dent in heat loss is to turn the thermostat down. Turning down from 20 to 17 °C gave a reduction in heat loss of 30%.

Combining these two actions - the physical modifications and the turning-down of the thermostat - this model predicts that heat loss should be reduced by nearly 50%. Since some heat is generated in a house by sunshine, gadgets, and humans, the reduction in gas consumption should be more than 50%.

I made all these changes to my house and monitored my meters every week. I can confirm that my heating bill indeed went down by more than 50%. As figure 21.4 showed, my gas consumption has gone down from 40 kWh/d to 13 kWh/d - a reduction of 67%.

Leakiness reduction by internal wall-coverings

Can you reduce your walls' leakiness by covering the inside of the wall with insulation? The answer is yes, but there may be two complications. First, the thickness of internal covering is bigger than you might expect. To transform an existing nine-inch solid brick wall (U-value 2.2W/m2/K) into a decent 0.30W/m2/K wall, roughly 6 cm of insulated lining board is required. [65h3cb] Second, condensation may form on the hidden surface of such internal insulation layers, leading to damp problems.

If you're not looking for such a big reduction in wall leakiness, you can get by with a thinner internal covering. For example, you can buy 1.8-cm-thick insulated wallboards with a U-value of 1.7W/m2/K. With these over the existing wall, the U-value would be reduced from 2.2W/m2/K to:

Definitely a worthwhile reduction. Air-exchange

Once a building is really well insulated, the principal loss of heat will be through ventilation (air changes) rather than through conduction. The heat loss through ventilation can be reduced by transferring the heat from the outgoing air to the incoming air. Remarkably, a great deal of this heat can indeed be transferred without any additional energy being required. The trick is to use a nose, as discovered by natural selection. A nose warms incoming air by cooling down outgoing air. There's a temperature gradient along the nose; the walls of a nose are coldest near the nostrils. The longer your nose, the better it works as a counter-current heat exchanger. In nature's noses, the direction of the air-flow usually alternates. Another way to organize a nose is to have two air-passages, one for in-flow and one for out-flow, separate from the point of view of air, but tightly coupled with each other so that heat can easily flow between the two passages. This is how the noses work in buildings. It's conventional to call these noses heat-exchangers.

An energy-efficient house

In 1984, an energy consultant, Alan Foster, built an energy-efficient house near Cambridge; he kindly gave me his thorough measurements. The house is a timber-framed bungalow based on a Scandinavian "Heatkeeper Serrekunda" design (figure E.10), with a floor area of 140 m2, composed of three bedrooms, a study, two bathrooms, a living room, a kitchen, and a lobby. The wooden outside walls were supplied in kit form by a Scottish company, and the main parts of the house took only a few days to build.

The walls are 30 cm thick and have a U-value of 0.28W/m2/0C. From the inside out, they consist of 13 mm of plasterboard, 27 mm airspace, a vapour barrier, 8 mm of plywood, 90 mm of rockwool, 12 mm of bitumen-impregnated fibreboard, 50 mm cavity, and 103 mm of brick. The ceiling construction is similar with 100-200 mm of rockwool insulation. The ceiling has a U-value of 0.27W/m2/0C, and the floor, 0.22W/m2/0C. The windows are double-glazed (U-value 2 W/m2/0C), with the inner panes' outer surfaces specially coated to reduce radiation. The windows are arranged to give substantial solar gain, contributing about 30% of the house's space-heating.

The house is well sealed, every door and window lined with neoprene gaskets. The house is heated by warm air pumped through floor grilles; in winter, pumps remove used air from several rooms, exhausting it to the outside, and they take in air from the loft space. The incoming air and outgoing air pass through a heat exchanger (figure E.11), which saves 60% of the heat in the extracted air. The heat exchanger is a passive device, using no energy: it's like a big metal nose, warming the incoming air with the outgoing air. On a cold winter's day, the outside air temperature was —8 0C, the temperature in the loft's air intake was 0 0C, and the air coming out of the heat exchanger was at +8 0C.

For the first decade, the heat was supplied entirely by electric heaters, heating a 150-gallon heat store during the overnight economy period. More recently a gas supply was brought to the house, and the space heating is now obtained from a condensing boiler.

The heat loss through conduction and ventilation is 4.2kWh/d/°C. The heat loss parameter (the leakiness per square metre of floor area) is 1.25 W/m2/0C (cf. my house's 2.7 W/0C/m2).

With the house occupied by two people, the average space-heating consumption, with the thermostat set at 19 or 20 0 C during the day, was 8100 kWh per year, or 22 kWh/ d; the total energy consumption for all purposes was about 15 000 kWh per year, or 40kWh/d. Expressed as an aver

Figure E.10. The Heatkeeper Serrekunda.
Figure E.11. The Heatkeeper's heat-exchanger.

age power per unit area, that's 6.6 W/m2.

Figure E.12 compares the power consumption per unit area of this Heatkeeper house with my house (before and after my efficiency push) and with the European average. My house's post-efficiency-push consumption is close to that of the Heatkeeper, thanks to the adoption of lower thermostat settings.

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