We forgot to insulate…

While renovating a house, we completely redid its roof. To save space inside (below the roof), we opted to insulate above the rafters (a process known as sarking).

We chose 20 cm of Steico wood wool insulation, giving us a pretty good U-value of $0.134 \frac{W}{m².K}$ (R-value of 7.56).

However, we also wanted to insulate between the rafters. Since they measure 10 cm × 10 cm, it would be a shame not to use that space to reduce heating costs. We planned to add another 10 cm of Métisse insulation (basically shredded unwanted clothes).

But when the ceiling drywall was put on, we (or more specifically the contractors ¹) forgot to install the ceiling insulation.

At first glance, that looks really bad. We had planned for 30 cm of insulation, and leaving out 10 cm means losing about a third of what we intended.

Should we insulate more?

So we started looking for ways to fill the empty wall slopes after the fact. It turns out polystyrene beads flow really nicely, and they seemed like a good option for us.

For 40 m², the cost would be 670 €. But is it worth it to add that missing third?

Using the excellent ubakus.de tool, we calculated the roof’s U-value with and without the extra insulation.

We found that the existing roof (only with the 20 cm of wood wool) has a U-value of $0.189 \frac{W}{m².K}$. Adding polystyrene beads would reduce it to $0.134 \frac{W}{m².K}$.

The next step is to figure out the yearly heating cost lost through the roof.

The U-value is a useful measure: it represents the power that flows through a surface for a given temperature difference. The yearly heating season is around 200 days (October to April). During this time, the average outside temperature is about 7 °C ², while the inside is kept at 20 °C. For our 40 m² roof, the total annual heat loss is:

• $\frac{0.189W}{m^2 \cdot K} \times 40m^2 \times (20K - 7K) \times 200 \text{days} = 471 \text{kWh}$ for the existing roof
• $\frac{0.134W}{m^2 \cdot K} \times 40m^2 \times (20K - 7K) \times 200 \text{days} = 334 \text{kWh}$ with the added insulation

So insulating those last 10 cm would save us 137 kWh per year.

How much is that? With electric radiators, the cost would be: $137 \text{kWh} \times 0.2 \frac{\text{€}}{\text{kWh}} = 27 \text{€}$ per year.

But since we’re using a heat pump with a COP of at least 3, that annual €27 loss is really only about €7 ³.

So yeah, not worth it. At all.

The magic of insulation

Insulation is magical in the sense that the first centimeters are far more effective than the later ones.

There are two units (inverses of each other) for insulation: U-value and R-value. $U = \frac{1}{R}$.

The R-value is useful because it can be added up directly (a quick way to see if you’ve hit your target). But energy loss is divided by the R-value (or multiplied by the U-value).

This creates an asymptotic curve: the first centimeters reduce heat loss dramatically, while each additional layer matters less and less.