Calculation of the energy used to maintain set indoor conditions

The calculator makes very basic computations of heat loss through the walls, and through air exchange. It also calculates the energy needed to maintain the indoor relative humidity by evaporating or condensing water. Heating energy is offset by waste heat from lighting and equipment.

This calculator is a learning aid; it should not be used to check the energy rating on your house.

Some characteristics of the building must be given to the calculator:

• The surface to volume ratio is the area of external wall and ceiling divided by the room volume. It is typically around 1 for a room of moderate size.
• The U-value is the thermal transmittance of the external surface, in W/m².K The value is around 1 for a typical house but can reduce to 0.3 for specialised buildings such as cold stores.
• The air changes per hour vary from 0.03 for a modern, large, windowless building with good sealing of joints and openings, to around 2 for a typical house. For busy public rooms the air change rate can be 5 or more, to sweep out carbon dioxide and other gases.
• The energy used for equipment and lighting within the building will offset the heating energy needed. For a museum exhibition room a value of 30 kWh/m³ per year is reasonable if fluorescent tubes and LEDs are largely used; much more energy is used by the distressingly common tangle of dimmed and screened tungsten halogen spot lamps. For a museum store, or a country church, use zero.

The graphical display

The graph may not display in ancient browsers, but works in Firefox, Opera, Chrome and Safari. It shows the inside and outside climate in thin traces and superimposes three bold energy traces for the total energy used to maintain the indoor climate, the heating/cooling energy and the humidification/dehumidification energy.

Limitations of these calculations

The heating calculation takes the temperature difference between inside and outside and calculates the heat flow according to the U-value and the area of outside surface for each cubic metre of volume. It adds to this the heat exchanged in the air moving in and out of the building. Finally, the heating energy is offset by heat generated within the building for other purposes.

The humidity calculation takes the difference in water vapour concentration between indoors and outdoors. This is multiplied by the cubic metres of air exchanged during the month. This weight difference is assumed to be compensated by evaporation or condensation of water, requiring the latent heat for the phase change, in either direction.

These calculations assume perfect efficiency of the apparatus used to achieve the climate. The calculation does not take account of buffering of the humidity by absorbent materials, which if sufficiently abundant can moderate the relative humidity over several months, without using energy. In the same way, temperature buffering by a massive floor slab laid directly on the ground can also reduce the energy needed for temperature regulation over several months.

Because of these unquantified complications, the calculation makes several simplifications. The calculator is intended to allow you to explore the magnitude of energy savings that can be made by tinkering with various aspects of the building and its climate specification. Much more detailed calculations are needed for the proper design process, to optimise re-use of waste heat, to incorporate ground source heat exchangers, variable fresh air ventilation and many other improvements to energy efficiency.

To include these refinements, and to compute an accurate U-value, there are several enormously complicated programs available to building design engineers.

Here are some examples of playing with the simple variables which can be adjusted with this calculator.

Tim Padfield, December 2010