Estimating the expected thermal performance of my house

//trigger warning// This article is long and dull. It’s about estimating the thermal performance of my home. //trigger warning//

Friends, I have used two kinds of analysis to enable me to plan the thermal improvement of my house.

• The first analysis involves measuring the thermal performance of the house:
  • I have explained how to do this previously (link) using weekly gas-meter readings and local weather data.
  • This allows me to see whether any changes I make have affected anything.
• The second analysis involves modelling the thermal performance I should expect from my house.
  • This allows me to anticipate the likely costs and benefits of a range of possible changes.
  • That’s what this article is about.

Both these steps are important.

Thermal Model

My basic thermal model of my house assumes that heat flows from the inside of the house to outside through the ‘building envelope’ This term describes all the building elements that separate the inside of the ‘envelope’ (where I live!) from the outside.

In this article I will consider these elements under 4 categories

1. Windows & doors
2. Walls & Roof
3. Floors
4. Air flow

The basic assumption in the model is that the amount of heat flowing through each ‘building element’ is proportional to:

• Its area (measured in metres squared, m^2)
• The temperature difference between the inside and outside (measured in °C)

This ignores other important factors such as whether it is windy or rainy, or the action of the Sun in heating the house. These are limitations of the model.

The thermal performance of building elements is most commonly specified by a U-value which states how many watts of heat will flow through the one square metre of the element when there is a temperature difference of 1 °C between its internal and external surfaces.

So to model the house:

• I made a list of all the ways in which heat can leave the interior of the house:
  • i.e. all the building elements involved in the envelope of the house: windows, doors, walls floors, etc
• I measured the physical size of each building element.
• I used educated guesswork (link) to estimate the thermal performance (U-value) of each building element
  • The values I used are in the table below.

• I then multiplied the area (m^2) of each building element by the U-value (W/m^2/°C) to get the amount of heat transmitted through that element per degree of temperature difference (W/°C)
• I then added up all the transmission values (W/°C).

You can download the spreadsheet that I used here (Thermal Model of House [Excel format]) in case it helps you with your own calculations.

Let’s start with the windows and doors.

1. Windows & doors

The table below (click it to see an enlarged version) shows:

• A label for each window (or door) so I don’t get confused
• It’s basic dimensions from which I calculate the area of each item
• A categorisation into one of 4 types of window: Single-glazed, 25 year-old double glazing, modern double glazing, and triple glazing.
• The U-value associated with that type of window
• The transmission through the window is the product of its U-value and its area.
  • I have colour-coded the transmission column to highlight the worst performing windows.
• Finally, I added up the transmissions to give a total transmission through all the windows and doors of 79.1 W/°C.

Please don’t be fooled by my use of a single decimal place – the uncertainty in this estimate is around 10%.

Thus my guess is that when the temperature outside falls 10 °C below the internal temperature, heat will flow out through the windows and doors at a rate of 10 °C x 79.1 W/°C. = 791 watts

The table above refers to the situation in 2018. Last year (2019) I replaced several windows and this year (2020) I will replace one more door and the remaining poor quality windows.

Replacing a building element its area remains the same so I can estimate the new transmission from the area and the new U-value, and so estimate the impact of the changes I have made.

The table below shows my estimate of the effect of these changes in 2019 and 2020:

When the changes are made this year, the transmission through the windows will be around 30 W/°C down from the roughly 80 W/°C back in 2018.

We’ll see how this compares with the overall heat loss from the house at the end of the article.

I have retained the back door for sentimental reasons even though it does not perform well thermally. That is because the house is for the people I love, and sentimental attachment to particular architectural features is a common problem when upgrading buildings.

• Thermal perfection is worth nothing without domestic harmony.

2. Walls & Roof

My house is a 1930’s end-of-terrace house which has been extended several times over the last 50 years. Construction techniques have changed a good deal over that time and so there is considerable uncertainty about exactly how some walls are constructed.

My estimates are summarised in the table below (click it to see an enlarged version). It shows:

• A label for each roof or wall element.
• It’s basic dimensions from which I calculate the area of each item.
  • I then subtract the area of any windows or doors to get the net area.
• A categorisation into one of 4 types of wall: Solid Brick, Cavity Wall, Insulated Cavity wall, Externally-Insulated Wall.
• The roof (labelled ‘loft’) is extraordinarily well-insulated with approximately 200 mm of Celotex insulation.
• The U-value associated with that type of wall
• The transmission through the element is the product of its U-value and its area.
  • I have colour-coded the transmission column to highlight the worst performing walls.
• Finally, I added up the transmissions to give a total transmission through all the windows and doors of 148.7 W/°C.

The uncertainty in this estimate is probably around 10%.

Thus my guess is that when the temperature outside falls 10 °C below the internal temperature, heat will flow out through the walls and roof at a rate of 10 °C x 148.7 W/°C. = 1487 watts

Note that I haven’t included the wall between my house and my neighbour’s house. This is because I think the temperature difference between our two houses is likely to be small and so I have assumed there will be negligible heat flow.

The table above refers to the situation in 2018. This year (2020) I will clad most of the external walls with External Wall Insulation (EWI).

To calculate the new value of the “wall + cladding”, one has to add the U values using an odd formula.

So for example, if an existing solid brick wall has a U-value of 2 W/m^2/°C and it is clad with EWI with a U-value of 0.17 W/m^2/°C, then the combined U-value is given by:

The combined U-value of 0.16 W/m^2/°C is a little better than either building element by itself.

The table below shows my estimate of the effect of the changes I have planned for this year:

When the cladding is finished, I estimate the transmission through the walls will be around 28 W/°C down from the current value of roughly 150 W/°C.

We’ll see how this compares with the overall heat loss from the house at the end of the article.

3. Floor

I have found it very difficult to estimate the heat flow through the floor of the house.

For this reason I have used a U-value that is little more than a guess: U = 0.7 W/m^2/°C.

My estimates are summarised in the table below (click it to see an enlarged version). It shows the area of each room on the ground floor of the house multiplied by this guess at a U-value.

The uncertainty on this figure is difficult to assess – but is probably around 20%.

Thus my guess is that when the temperature outside falls 10 °C below the internal temperature, heat will flow out through the floor at a rate of 10 °C x 50.5 W/°C = 505 watts

Unfortunately, it isn’t easy to do anything about the heat loss through the floor without taking up the floor and insulating underneath.

If we do any work on the house in coming years, we may try to do this, but at the moment, I can’t see any easy way to improve this.

4. Air flow

Heat is also carried from the interior of the building envelope to the exterior by air flows. But air flows are difficult to measure and hence difficult to manage.

As the house is now, there are two obviously ‘draughty’ elements – both doors. I will replace one door and improve the draught-proofing on the other.

But otherwise the house feels fine and is not stuffy. So for the moment I have decided to leave the air flow as it is, and I have simply guessed that air flow transmittance is 20 W/°C – but this is really just a guess.

However I am investigating the use of a carbon dioxide monitor as a tracer for air flow. The idea is to model the rate at which the concentration of carbon dioxide in the air increases due to breathing and cooking. If the house was perfectly sealed, the carbon dioxide levels would rise indefinitely. So the limiting value of carbon dioxide depends on the rate at which air leaks from the house. I’ll write about this some other time.

Summary

Bring all this together:

• I can estimate the thermal performance of the whole house and see how it compares with my measurements.
• I can estimate the effect of the changes I intend to make to see what is worthwhile.
• I can see how far I need to go to make the house carbon-neutral.

The model indicates:

• That the total transmittance is estimated to be~ 298  W/°C in 2018 which is – within the uncertainties of my estimate – roughly what I measured (~280 W/°C).
• That the triple glazing I installed last year should have made roughly a 10% difference, reducing this figure to roughly 260 W/°C. This is also in line with my measurements.
• The effect of the external wall insulation and the additional glazing that I am installing this year should be very significant, reducing the losses to roughly half their 2018 value.

I can also assess the monetary value of the various changes:

• The triple-glazing I installed last year:
  • Cost £7200 and reduced the transmission by ~ 39 W/°C, approximately £186 for each W/°C.
  • Based on my gas bill this is a return on investment of ~1.3%.
• The triple-glazing I will install this year:
  • Will cost £3080 and reduce transmission by ~10 W/°C, approximately £288 for each W/°C.
  • Based on my gas bill this is a return on investment of ~0.8%.
• The external wall insulation I will install this year:
  • Will cost £20,000 (!) and reduce transmission by ~98 W/°C, approximately £165 for each W/°C.
  • This cost includes roughly £5000 for cosmetic features and the use of super-insulation to limit its thickness.
  • Based on my gas bill this is a return on investment of ~1.2%.

Some people would argue that these are paltry returns. Actually – the returns are not bad from a purely financial perspective, and the external wall insulation would have benefited from the new government subsidy if I had got my timing right!

Additionally, replacing windows and repairing the exterior of a house are things which need doing every 25 years or so. So I would have to spend a significant fraction of this anyway just to maintain the house.

But my motive is not financial. By undertaking these works I am preparing for the replacement of the gas boiler with an air source heat pump in 2021. This should reduce the carbon emissions required to heat the house.

• The emissions will be reduced by a factor 2 because of these improvement in the thermal performance of the house.
• The emissions will be reduced by a factor 3 because of the coefficient of the performance of the air source heat pump – it provides three units of heat for each unit of electricity used.
• Currently grid electricity used for heating emits around 20% more carbon than burning gas directly for heating. In 2019 the figures were ~ 240 g/kWh for electricity versus ~ 200 g/kWh for gas.
• So the emissions will be reduced by an overall factor of 2 x 3 x 0.8 ≈ 4.8.
• In the coming decade, the carbon emissions associated with grid electricity are expected to fall to around 100 g/kWh, further reducing the carbon emissions associated with heating the house.

But even in 2030, the carbon emissions associated with heating the house will still be roughly 0.2 tonnes per year.

The final step will be to reduce these emissions on average, by using solar panels to generate low carbon-intensity electricity in the summer to offset the electricity I use in the winter to heat the house.

A personal note

I have no idea whether this project makes sense.

I just feel personally ashamed that my house emits 2.5 tonnes of carbon dioxide each year – just keeping me and my family warm.