## The Insulation Sweet Spot

How much insulation is enough? If I double the R value, does that mean I halve my heating and cooling loads? Unfortunately it’s just not that simple, increased insulation has diminishing returns in reduced heat transfer. To explain this, first, let’s start with carefully defining R Value. It’s a measure of resistance to heat transfer and can be stated as follows:

Using the above formula gives the R value in SI units which we will work in for the rest of this article. To convert to US Imperial units, you need to times the R_{SI} by 5.678. Now lets use the above formula and apply it to an example of a wall. We want to calculate the heat transfer value, which will then give us the heating/cooling energy requirement for our heating/air-conditioning system and from that we’ll be able to work out the cost. The formula now looks like this:

The assumptions we are using are below, some of these are inflated to accentuate the potential savings:

- Area of external wall: 100m2
- Temperature difference between internal thermostat set point and external temperature: 15 Degrees C (quite a difference, either hot climate trying to cool or cool to cold climate trying to heat)
- Coefficient of Performance (COP) of Heating or Cooling Device: 2.5 (relatively poor)
- Assume that we are paying $0.25c for every kWh of delivered energy to the building
- 24 hour average occupancy, so continual maintenance of desired temperature.

We’ll start with a single brick wall (R_{SI} Value of 0.106) and then slowly increase the insulation to determine how much money we can save. Here’s how much the heat transfer reduces as R value increases:

As you can see, the reduction in heat transfer is huge, at least initially. In fact nearly 80% of the heat transfer is stopped with just R_{SI}0.5 insulation. As you increase the R Value further the savings in heat transfer drop off significantly:

- R
_{SI}0.5 to R_{SI}1.0: 11% extra heat saving - R
_{SI}1.0 to R_{SI}2.0: 6% extra heat saving - R
_{SI}2.0 to R_{SI}3.0: 2% extra heat saving - R
_{SI}3.0 to R_{SI}4.0: 1% Extra heat saving

So what about the effect to costs? See the following graph for the details on the heating and cooling cost savings for our conceptual building:

Once again, we see a very big drop off in savings as R Value increases. And these savings are potentially inflated, if the average internal temperature to external temperature difference was halved to 7.5 degrees C, we’d see these values halve also.

There is obviously a sweet spot somewhere between R_{SI}1 and R_{SI}4, probably around the R_{SI}2.5 mark. Of course, this depends on the insulation costs, the cost of the structure to house the insulation and the design life of the building. For example, going from R_{SI}2 to R_{SI}4.0 may only require a small increase in insulation costs, but if the wall framing need to be increased in width by an inch, this could be quite costly.

The other important consideration here is that this is all based on theory. What is actually going to happen in an average building is probably going to further lessen the impact that your wall insulation has on your heating and cooling costs. For example, if you poked five small 100 x 50mm holes in the insulation of our conceptual house, depending on drafts etc, you’d probably reduce R_{SI}3.5 walls insulated walls to the equivalent of R_{SI}3.0.

In windy climates or pressurised buildings, this could be a lot worse. Similarly there are likely a lot of other easy wins to increase the actual performance of your house that don’t relate to your wall insulation, for example:

- Glazing type (R Value)
- Glazing area (lots of windows usually means lots of heat transfer)
- Floor insulation (appropriate in cooler climates)
- Floor ground coupling (appropriate in warmer climates)
- Efficiency of your air-conditioning and heating system
- Cost and carbon intensity of your energy supply source (eg gas verse electricity)

I hope this helps explain the R Value sweet spot.

For the control freaks out there who want to know exactly where that is for their particular building/climate/energy mix etc, get in touch!