## My House: comparing models and measurements

I began my last article about my house by explaining that I have used both measurements and modelling to plan thermal improvements.

However, I did not answer the question:

• Does the thermal model agree with the measurements?

In this article I will compare them and show that the agreement is good enough to use the model as a basis for planning further work.

The Measurements

There are two key measurements:

• I read my gas meter roughly once a week.
• I subtract the reading from the previous week’s reading to find out how many hundreds of cubic feet of gas were consumed that week.
• I then work out how much energy this corresponds to. You can use this calculator for your own meter.
• I then work out the average rate at which the energy was used by dividing the amount of energy by the time since the last reading.
• This gives the average power used in watts (W )
• I read my weather station.
• I record the average weekly temperature.

The Model

The model is an attempt to explain the gas consumption in terms of a single number that characterises the thermal transmision from the inside to the outside of the house.

The thermal transmission is measured in watts per degree Celsius of temperature difference (W/°C).

Comparing the model and the measurements.

Previously (link) I explained how I calculated the thermal transmission through the walls of the house. And I then used this to estimate how the thermal transmission would be affected by various planned changes.

• But how do I know if those calculations are reliable?

To check this I begin with the gas consumption data for the 80 weeks or so for which I measurements. I have smoothed this data with each point being a 5 week symmetrical running average i.e. the average consumption from 2 weeks before to 2 weeks after the time for which is plotted.

Click for a larger version.

This shows that in the summer, the average rate of gas consumption is around 200 watts.

Since the space-heating is not used in the summer, I assume this 200 W is due to the use of gas for cooking and heating water for showers. I assume that this gas consumption continues unchanged through the year.

I then assume that the excess winter use is solely caused by the lower average weekly external temperature.

Mathematically I expect the gas consumption to be give by the formula:

Click for a larger version.

Next alongside the measured gas consumption we can plot what the equation above predicts would have been the gas consumption based on:

• The calculated properties of the house looked up from data sheets about building materials and windows, and dimensional measurements of the house.
• The difference between the internal and external temperatures as worked out from weather station readings.

The graph below shows the model with a transmission of 298 W/°C – the value I calculated was appropriate to the winter of 2018/2019.

Click for a larger version.

You can see that the dotted-red curve matches the experimental gas consumption data reasonably well in the cold winter months – except during the coldest winter weather (around day 25).

You can can also see that during the following winter of 2019/2020 the model predicts that there should have been substantially more gas consumption than there actually was.

• Was this due to the £7000 worth of triple-glazing I installed?

My calculations suggested that after the triple-glazing was installed the transmission should have been reduced to 260 W/°C. This curve is plotted below:

Click for a larger version.

You can see that with a transmission of 260 W/°C the model curve describes the data for the winter of 2019/2020 reasonably well.

I was pleased to see this: this is the first data I ever seen which verifies quantitatively the effect of triple-glazing.

This gives me confidence that this crude model is describing heat transmission through my house reasonably well.

That is why I feel confident that, after spending a further £3,000 on finishing the triple-glazing, and £20,000 on external-wall insulation. This will hopefully reduce the transmission to 152 W/°C. That curve is shown on the figure below.

Click for a larger version.

How good is this level of insulation?

My expectation is that after this summer’s modifications, this house – with a floor area of almost 180 square metres – will require barely more than 2 kW of winter heating.

Over a year it would require typically 8000 kWh of heating, or 44 kWh per square metre per year.

If this performance level is verified then (according OVO energy) the house will require less than the average in every European country except Portugal: the UK average is 133 kWh per square metre per year

This is still not good enough to achieve ‘passivhaus’ status (Links 1, 2)- which requires less than 15 kWh per square metre per year. Or even the ‘Passivhaus Retrofit’ standard EnerPHit (Link) which requires less than 25 kWh per square metre per year. But it would still be exceptional for an old UK house.

Other considerations

Despite the fact that the graphs above have worked out nicely, there is still considerable uncertainty about the way the house performs.

For example, I don’t really know the significance of several factors such as heat loss through air flow, and heat loss through the floors, both of which are little more than guesses. I am concerned I may have underestimated these processes in which case the effect of the external wall insulation will not be as large as I anticipate.

And I have assumed that the internal temperature was a constant 18 °C. It’s not clear whether this is the best estimate – perhaps it should be 19 °C or 20 °C?

So the fact that these modelled results look good indicates that these assumptions may be about right, or that a combination of factors have by chance made the agreement look good.

One interesting feature of the data is that while the single parameter for heat transmission describes the winter and summer data well – it does not describe the spring and autumn data well.

The model always predicts higher gas usage than actually occurs in the spring and autumn. Look for example at the data from days 250 to 320 and from 450 to 550 on the second model.

Click for a larger version.

I do not know what causes this, but it may be that in the transitional seasons, the pattern of gas usage may differ from being almost always on (in winter) or always off (in summer). I tried adding an extra parameter to describe this effect, but it didn’t add a lot to the explanatory power of the model.

In short, the model is simple and the reality is complex, but answering the question I asked at the start of this article:

• Does the thermal model agree with my measurements?

I think the answer is “Yes” – it’s good enough to guide my choices.

### 4 Responses to “My House: comparing models and measurements”

1. Edmond Hui Says:

Just a quick scan through the post- can you assume heating for showers and cooking is the same in the winter? Incoming water would be either at ambient outside ground temp or cold water tank in loft temp. Either way your gas boiler or stove doesn’t have to heat water as far to get to ‘hot’ or to 100C in the summer. The cold water being warmer in summer also means you need less hot water in the mix for your shower. Also you probably have more salads in summer and stews and roasts in winter. If I were to guestimate I’d go for 300W for cooking and hot water in winter. That makes your triple glazing look even better, right?

2. protonsforbreakfast Says:

All good points. Water temperature is typically 10 °C colder in winter, and there is a summer/winter change in cooking habits. I’ll make the change and let you know!

3. Jonathan Says:

Dear Michael,

I attended your Protons for Breakfast course when I was a young boy, since which I have become a not-so-young boy.

Firstly if I may express my gratitude for running the course all those years ago, and indeed all the other outreach activities you got involved with. I’m very pleased to have found your blog and to hear you are doing well also.

Anyway, back to protons; despite spending a significant proportion of the course tucking in to the refreshments available outside, it seems some the whole try-to-understand-things message was passed on, and I too have found myself using some of my spare time creating spreadsheets and graphs to attempt to model things (though none quite as elegant as yours I must admit).

The pride of my collection is a spreadsheet which provides insight into the efficiency of your motor vehicle based upon details of fill-ups (or I guess charge ups?) and odometer readings. I’d be more than happy to share it with you if you were at all interested.

Anyways, all the best,

J

• protonsforbreakfast Says:

J

How kind of you to write.

Regarding protons it may interest you to know that the course had written goals and the minimum goal I set was that people should think that “NPL was a nice place with good biscuits”. It seems we hit that target. The thought that the seed of curiosity took hold is a bonus!

I would be very interested in your spreadsheet. Please send it to michael at depodesta.net . I did once write something that tried to go from mileage to the amount of petrol used on each stroke – so I would be curious to see the approach you have taken.

Every best wish

Michael