## Calculating energy savings with U values – an approximation

Sooner or later, and in my experience, sooner, you get asked “*and what’s the payback for your spend on insulation?*” It’s a question that annoys me a bit because if you talk about, for example, renewing a kitchen, no one asks that same question. You can easily double the cost of a kitchen because of lifestyle choices you make. Yet applying such choices to insulation cannot be understood by most people.

Anyway, rant over for now. Let’s look at a simplified payback calculation based on underfloor insulation.

Part of this building has a simple suspended wooden floor. We have not been able to lift a floorboard to check out the exact construction, but from the little evidence we have we saw that the joists are on 400mm centres. The best guess is that the joists are 2” x 4” (50mm x 100mm) timber. Such a floor is likely to have a U value of 0.8 or so and lots of air leaks, especially when it is windy. We will come back to the air leakage in another blog post.

So how much heat is lost through the floor, and what will it cost for a year’s heating?

The U values is expressed in Watts per square metre per degree K. Hence we need to know the total area first, that’s 58 m^{2}. So the floor with its U value of 0.8 will transmit 46.4 Watts per degree K temperature difference.

The next thing we need is the temperature difference over the course of a year. This comes in the form of ‘degree day’ figures. These figures can be used in all sorts of ways and the results are subject to interpretation. I’m going to use a simple annual figure so as to avoid most of the complexity and get a decent ball park figure.

For the southern UK there are around 3,400 degree days based on a temperature of 18.5^{o}C. Domestic energy is measure in kW hours, so we need the degree hours which requires a multiplier of 24 giving a figure of 81,600 degree hours.

Applying this to our transmission figure gives us just under 3.8 kWh per year of lost warmth. At a cost of 0.13 per unit for gas heating that represents a cost of £492.

Installing 100mm of good quality insulation should reduce the U value to around 0.22. As all the other figures remain the same the cost reduces in proportion to £135, an annual saving of £350 or thereabouts.

Whilst the insulation is being done the airtightness of the floor is being assured removing the normal draughts from this area. As the draughtiness has not been measured, and it is impossible to calculate, I cannot say with any certainty what the improvement and hence savings, will be.

As a side note, calculating the effect of doubling the insulation thickness is really complicated as the joists between the insulation batts act as a thermal bridge and the actual calculation becomes very tricky using what is known as the “Combined method”. In simple terms, doubling the insulation thickness may get, at best, a further 40% reduction in heating cost, say another £150. The manufacturers of the insulation do not recommend this approach. However, if the joists turn out to be 150mm deep then it would be worth the additional thickness as its full benefit will be felt. Otherwise the effect is not known with any precision and it’s a guess.

If you are seeking a provable very low energy building then this simple approximation will not be good enough. Allowances need to be made for edge detailing of thermal bridges and the perimeter to area ratio, both of which I have ignored. To do this properly you need the assistance of a proven software package.

## References

Calculating heat loss – AECB CarbonLite Programme, Volume Two, Principles and methodologies. Page 7 illustrates the complexity of the overall U value calculation.

U value of insulation is for Celotex GA range.

U value for timber joists taken as 0.18 as they are load bearing and from the 1930s, so quite solid. (http://www2.ntu.ac.uk/nti/uwe/hi4web/insulation%20calcs/section3.htm)