Archive for the ‘Simple Science’ Category

How Many Naturally-Occurring Elements are there? Corrigendum

January 28, 2021

And in non-COVID news…

… I received an e-mail from ‘Claire’ the other day pointing out that there was an error in one of my blog articles.

I try quite hard to be ‘right’ on this blog, so despite her politeness, I was distressed to hear this.

The error was in an article written on 15th February 2010 – yes, more than 10 years ago – entitled: Just How Many Naturally Occurring Elements are there?

Reading it again after all these years I was pleased with it. The gist of the article is that there is not a clear answer to the question.

It turns out that the nuclei of the atoms of some elements are so radioactively unstable that even though they do exist on Earth naturally, at any one time there are only handful of atoms of the substance in existence.

These elements seemed to be in a different category from, say, carbon (which has some stable isotopes) or uranium (which has no stable isotopes). But some of the isotopes of uranium have very long half-lives: 238U has a half-life 4.468 billion years – roughly the length of time that the Earth has existed.

So of all the 238U has which was donated to the Earth at its formation – very roughly half of it has decayed (warming the Earth in the process) and half of it is still left.

So I had no problem saying that 238U was ‘naturally-occurring’, but that it was a moot point whether Francium, of which there are just a few atoms in existence on Earth at one time, could really be said to be ‘naturally-occurring’.

So in the article I stated that I had stopped giving an exact number for the number of ‘naturally-occurring’ elements – I just say it is ‘about 100’ – and then discuss the details should anyone ask for them.

What was my error?

In the article I stated that Bismuth – atomic number 83 – is the heaviest element which has at least one stable isotopes. For elements with larger atomic numbers than Bismuth, every isotope is radioactively unstable.

What Claire told me was that in fact the one apparently stable isotope of bismuth (209Bi, the one which occurs naturally) had been found to be unstable against alpha decay, but with an exceedingly long half-life. The discovery had been announced in Nature in 2003: link

Click image for a larger version. Link to Nature here

What I want to comment on here is the length of the half-life: The authors estimated the half life of 209Bi was:

  • 1.9 (± 0.2) x 1019 years.
  • 19 billion billion years

This is an extraordinarily long time. For comparison the estimated age of the Universe – the time since the Big Bang – is estimated to be about:

  • 1.4 x 1010 years.
  • 14 billion years

Imagining that 1 kilogram of pure 209Bi was gifted to the Earth when it was formed roughly…

  • 0.4 x 1010 years.
  • 4 billion years

…ago. Then since that time less than 1 in a billion atoms (0.15 micrograms) of the 209Bi would have decayed.

We might expect a single nuclear decay in 1 kilogram of pure 209Bi every 5 minutes.

How could one measure such a decay? The authors used a transparent crystal of Bismuth Germanate (Bi4Ge3O12) which scintillates when a radioactive particle – such as an alpha particle passes through it. In this case, the crystal would ‘self-scintillate’.

But the background rate of scintillation due to other sources of radiation is much higher than the count due to the decay of the 209Bi.

To improve the discrimination against the background the authors cooled the crystal down to just 0.1 K. At this very low temperature its heat capacity becomes a tiny fraction of its heat capacity at room temperature, and the energy of even a single radioactive decay can be detected with a thermometer!

Combining light detection and heat detection (scintillating bolometry) helps to discriminate against spurious events.

And my point was…?

For all practical purposes 209Bi is stable. Anything with a half-life a billion times longer than the age of the Universe is at least stable-ish!

But Claire’s e-mail caused me to reflect that the apparently binary distinction between ‘stable’ and ‘unstable’ is not as obvious as I had assumed.

By this extraordinary measurement, the authors have reminded me that instead of saying that something is ‘stable’ we should really state that it may be stable, but that if it decays, its rate of decay is beyond our current limit of detectability.

So for example, we know that neutrons – outside a nucleus – decay with a radioactive half-life of just 10.2 minutes. But what about protons? Are they really unconditionally stable?

People have searched for the decay of the proton and established that protons may be stable, but if they do decay, their half-life is greater than 1.7 x 1034 years – or more than a million, billion, billion times the age of the Universe.

So now we know.

Rocket Science

January 14, 2021

One of my lockdown pleasures has been watching SpaceX launches.

I find the fact that they are broadcast live inspiring. And the fact they will (and do) stop launches even at T-1 second shows that they do not operate on a ‘let’s hope it works’ basis. It speaks to me of confidence built on the application of measurement science and real engineering prowess.

Aside from the thrill of the launch  and the beautiful views, one of the brilliant features of these launches is that the screen view gives lots of details about the rocket: specifically it gives time, altitude and speed.

When coupled with a little (public) knowledge about the rocket one can get to really understand the launch. One can ask and answer questions such as:

  • What is the acceleration during launch?
  • What is the rate of fuel use?
  • What is Max Q?

Let me explain.

Rocket Science#1: Looking at the data

To do my study I watched the video above starting at launch, about 19 minutes 56 seconds into the video. I then repeatedly paused it – at first every second or so – and wrote down the time, altitude (km) and speed (km/h) in my notebook. Later I wrote down data for every kilometre or so in altitude, then later every 10 seconds or so.

In all I captured around 112 readings, and then entered them into a spreadsheet (Link). This made it easy to convert the  speeds to metres per second.

Then I plotted graphs of the data to see how they looked: overall I was quite pleased.

Click for a larger image. Speed (m/s) of Falcon 9 versus time after launch (s) during the Turksat 5A launch.

The velocity graph clearly showed the stage separation. In fact looking in detail, one can see the Main Engine Cut Off (MECO), after which the rocket slows down for stage separation, and then the Second Engine Start (SES) after which the rocket’s second stage accelerates again.

Click for a larger image. Detail from graph above showing the speed (m/s) of Falcon 9 versus time (s) after launch. After MECO the rocket is flying upwards without power and so slows down. After stage separation, the second stage then accelerates again.

It is also interesting that acceleration – the slope of the speed-versus-time graph – increases up to stage separation, then falls and then rises again.

The first stage acceleration increases because the thrust of the rocket is almost constant – but its mass is decreasing at an astonishing 2.5 tonnes per second as it burns its fuel!

After stage separation, the second stage mass is much lower, but there is only one rocket engine!

Then I plotted a graph of altitude versus time.

Click for a larger image. Altitude (km) of Falcon 9 versus time after launch (s) during the Turksat 5A launch.

The interesting thing about this graph is that much of the second stage is devoted to increasing the speed of the second stage at almost constant altitude – roughly 164 km above the Earth. It’s not pushing the spacecraft higher and higher – but faster and faster.

About 30 minutes into the flight the second stage engine re-started, speeding up again and raising the altitude further to put the spacecraft on a trajectory towards a geostationary orbit at 35,786 km.

Rocket Science#2: Analysing the data for acceleration

To estimate the acceleration I subtracted each measurement of speed from the previous measurement of speed and then divided by the time between the two readings. This gives acceleration in units of metres per second, but I thought it would be more meaningful to plot the acceleration as a multiple of the strength of Earth’s gravitational field g (9.81 m/s/s).

The data as I calculated them had spikes in because the small time differences between speed measurements (of the order of a second) were not very accurately recorded. So I smoothed the data by averaging 5 data points together.

Click for a larger image. Smoothed Acceleration (measured in multiples of Earth gravity g) of Falcon 9 versus time after launch (s) during the Turksat 5A launch. Also shown as blue dotted line is a ‘theoretical’ estimate for the acceleration assuming it used up fuel as a uniform rate.

The acceleration increased as the rocket’s mass reduced reaching approximately 3.5g just before stage separation.

I then wondered if I could explain that behaviour.

  • To do that I looked up the launch mass of a Falcon 9 (Data sources at the end of the article and saw that it was 549 tonnes (549,000 kg).
  • I then looked up the mass of the second stage 150 tonnes (150,000 kg).
  • I then assumed that the mass of the first stage was almost entirely fuel and oxidiser and guessed that the mass would decrease uniformly from T = 0 to MECO at T = 156 seconds. This gave a burn rate of 2558 kg/s – over 2.5 tonnes per second!
  • I then looked up the launch thrust from the 9 rocket engines and found it was 7,600,000 newtons (7.6 MN)
  • I then calculated the ‘theoretical’ acceleration using Newton’s Second Law (a = F/m) at each time step – remembering to decrease the mass by 2.558 kilograms per second. And also remembering that the thrust has to exceed 1 x g before the rocket would leave the ground!

The theoretical line (– – –) catches the trend of the data pretty well. But one interesting feature caught my eye – a period of constant acceleration around 50 seconds into the flight.

This is caused by the Falcon 9 throttling back its engines to reduce stresses on the rocket as it experiences maximum aerodynamic pressure – so-called Max Q – around 80 seconds into flight.

Click for a larger image. Detail from the previous graph showing smoothed Acceleration (measured in multiples of Earth gravity g) of Falcon 9 versus time after launch (s) during the Turksat 5A launch. Also shown as blue dotted line is a ‘theoretical’ estimate for the acceleration assuming it used up fuel as a uniform rate. Highlighted in red are the regions around 50 seconds into flight when the engines are throttled back to reduce the speed as the craft experience maximum aerodynamic pressure (Max Q) about 80 seconds into flight.

Rocket Science#3: Maximum aerodynamic pressure

Rocket’s look like they do – rocket shaped – because they have to get through Earth’s atmosphere rapidly, pushing the air in front of them as they go.

The amount of work needed to do that is generally proportional to the three factors:

  • The cross-sectional area A of the rocket. Narrower rockets require less force to push through the air.
  • The speed of the rocket squared (v2). One factor of v arises from the fact that travelling faster requires one to move the same amount of air out of the way faster. The second factor arises because moving air more quickly out of the way is harder due to the viscosity of the air.
  • The air pressure P. The density of the air in the atmosphere falls roughly exponentially with height, reducing by approximately 63% every 8.5 km.

The work done by the rocket on the air results in so-called aerodynamic stress on the rocket. These stresses – forces – are expected to vary as the product of the above three factors: A P v2. The cross-sectional area of the rocket A is constant so in what follows I will just look at the variation of the product P v2.

As the rocket rises, the pressure falls and the speed increases. So their product P v, and functions like P v2, will naturally have a maximum value.

The importance of the maximum of the product P v2 (known as Max Q) as a point in flight, is that if the aerodynamic forces are not uniformly distributed, then the rocket trajectory can easily become unstable – and Max Q marks the point at which the danger of this is greatest.

The graph below shows the variation of pressure P with time during flight. The pressure is calculated using:

Where the ‘1000’ is the approximate pressure at the ground (in mbar), h is the altitude at a particular time, and h0 is called the scale height of the atmosphere and is typically 8.5 km.

Click for a larger image. The atmospheric pressure calculated from the altitude h versus time after launch (s) during the Turksat 5A launch.

I then calculated the product P v2, and divided by 10 million to make it plot easily.

Click for a larger image. The aerodynamic stresses calculated from the altitude and speed versus time after launch during the Turksat 5A launch.

This calculation predicts that Max Q occurs about 80 seconds into flight, long after the engines throttled down, and in good agreement with SpaceX’s more sophisticated calculation.


I love watching the Space X launches  and having analysed one of them just a little bit, I feel like understand better what is going on.

These calculations are well within the capability of advanced school students – and there are many more questions to be addressed.

  • What is the pressure at stage separation?
  • What is the altitude of Max Q?
  • The vertical velocity can be calculated by measuring the rate of change of altitude with time.
  • The horizontal velocity can be calculated from the speed and the vertical velocity.
  • How does the speed vary from one mission to another?
  • Why does the craft aim for a particular speed?

And then there’s the satellites themselves to study!

Good luck with your investigations!


And finally thanks to Jon for pointing me towards ‘Flight Club – One-Click Rocket Science‘. This site does what I have done but with a good deal more attention to detail! Highly Recommended.


Thinking about domestic batteries

January 3, 2021

My External Wall Insulation project is complete and the solar panels are installed, so I am left to simply gather data on how things are working: a retired metrologist’s work is never done!

So inevitably my mind is moving on to the ‘next thing’, which is possibly a battery, and I am left with nothing to do but write over-long articles about the possibilities.

  • [Note added on 9/1/2021: If you like this article, then try also the next article on the same subject – link – I think it is a little clearer and the spreadsheet has been improved.]

The idea of using a battery is very simple: store solar electricity and use it later! But as I tried to think about it, I found myself intermittently perplexed. This could be an age thing, or just due to my lack of familiarity with solar power installations, but it was not at all obvious to me how to operate the battery in harmony with the solar panels.

This is because energy can flow in several directions.

  • For example electricity from the solar panels could charge the battery, operate the domestic load, or be exported to the grid.
  • Similarly, the battery could charge itself from the grid, operate the domestic load or export energy to the grid.

Understanding these things matters because domestic scale batteries are not cheap.

  • A rechargeable AA battery with 5 Wh of capacity (3.3 Ah @ 1.5V) costs around £5.
  • If we scale that up to 13.5 kWh (the size of Tesla battery) then 2700 rechargeable AA batteries would cost about £13,500.
  • In fact there are some economies of scale, but the likely cost is still around £10,000.

After making several simulations I think I have a clearer idea how the scheme would work, so please allow me to explain.

Mode#1: Storing in the day.

At the moment the solar panels generate at the whim of the weather gods – and the iron diktats of celestial geometry.

In sunshine – even at mid-winter – the panels can generate at more than 2 kW and unless we are using that electricity in the house at the moment the Sun is shining, the power is exported to the grid.

Click for a larger version. Solar electricity (in kWh) generated daily since the solar panels were installed.

  • Over the last 50 winter days the panels have generated about 136 kWh
  • I have used about 60% of that, saving round 81.6 x 24.3 pence ~£19.83
  • But I have given away about 40% of the electricity I have generated.
  • I can arrange to sell that electricity to EDF, my electricity and gas supplier, for the grand price of 1.8 pence per unit i.e. the 54.4 units I have donated would be worth £0.98
  • However, if I could have stored those units and used them later I would have saved approximately £13.22.

So using a battery to store solar energy and then use it later to displace buying full-price electricity makes some financial sense. It also makes carbon sense, displacing grid electricity with low-carbon solar energy.

In winter, a battery would make the most of the meagre solar supply and in summer it would allow us to be effectively ‘off grid’ for many days at a time.

Mode#2: Storing at night.

But batteries can also be used to store electricity generated at night time – when it is cheap. EDF charges me 24.31 pence for each unit I use between 6:30 a.m. and 11:30 p.m. (‘peak’ rate) , but only 4.75 pence for each unit I use overnight (‘off peak’ rate).

On average, we use around 11 kWh/day of electricity, around 9 kWh of which is used during ‘peak’ time. So if I could buy that electricity at the ‘off peak’ rate (costing 9 x 4.75 = 42.75 p), store it in a battery, and then use it the next day, then I would avoid spending 9 x 24.31 pence = £2.19.

This strategy would save me around £1.76 per day, or around £640 per year – a truly staggering amount of money!

It would also be slightly greener. The exact amount of carbon dioxide emitted for each unit of electricity – a quantity known as the carbon intensity – depends on how the electricity is generated,

  • Electricity generated from coal has a carbon intensity of around 900 gCO2/kWh
  • Electricity generated from gas has a carbon intensity of around 500 gCO2/kWh
  • Electricity generated from nuclear, solar or wind has a carbon intensity of a few 10’s of gCO2/kWh

Depending on mix of generating sources, the carbon intensity of electricity varies from hour-to-hour, day-to-day and from month-to-month.

To estimate the difference in carbon intensity between ‘peak’ and ‘off peak’ electricity is quite a palava.

  • I went to the site and downloaded the data for the carbon intensity of electricity assessed every 30 minutes for the last three years.
  • I then went through the data and found out the average carbon intensity for ‘Off Peak’ and ‘Peak’ electricity.
  • I averaged these figures monthly.

The data are graphed below.

Click for a larger version. Carbon intensity (grams of CO2 per kWh of electricity) for UK electricity evaluated each month since the start of 2018. The red curve uses data for ‘Peak Rate’ electricity and the blue curve shows data for ‘off peak’ electricity’. The black curve shows the difference between ‘peak’ and ‘off-peak’ and the dotted red line shows the average value of the difference.

The average ‘Peak Rate’ carbon intensity over the last two years is approximately 191 g CO2 per kWh, and the ‘Off-peak’ average is approximately 25 g (or 13%) lower.

I calculated that over the last year if I used 9 peak units and 2 off-peak units per day then the carbon emissions associated with my electricity use would have been 749 kg (~three quarters of a tonne) and the cost would have been £822.

If I had instead bought all those units at night, stored them in a battery, and used them the next day the carbon emissions would have been 661 kg – a saving of 88 kg and the cost would have been just £188 – a saving of £634.

Summary so far

So these two strategies involve using the battery to:

  • Store solar electricity in the day (which maximises my personal use of my personal solar electricity)
  • Store grid electricity at night (which appears to be amazingly cost effective and has about 13% lower carbon emissions)

Understanding how these two strategies can be combined had been hurting my head, but I think I have got there!

I think the operating principles I need are these:

  • Whenever solar electricity is available, use it.
  • If the solar power exceeds immediate demand,
    • If the battery is not full, store it.
    • If the battery is full, export it for whatever marginal gain may be made.
  • At night, charge the battery from the mains so that it is full before the start of the next day.

I have run a few simulations below assuming a Tesla Powerwall 2 battery with a capacity of 13.5 kWh. If you want, you can download the Excel™ spreadsheet here, or view typical outputs below.

  • Note: I hate sharing spreadsheets because as Jean Paul Satre might once have said “Hell is other people’s spreadsheets“. Please forgive me for any errors. Thanks

Battery only: No Solar

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both are zero in this graph. Both should be read against the right-hand axis.

In the first simulation the battery charges from empty using 2 kW of ‘Off Peak’ electricity and fills up just before morning. It then discharges through the day (at 0.4 kW) and is about half empty – or half full depending on your disposition – the next evening.

So the next day the battery starts charging from about 50% full and then discharges through the day and is again about 50% full at the end of the day.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both are zero in this graph. Both should be read against the right-hand axis.

So based on this simulation, it looks like a stable daily charge and discharge rate could effectively eliminate the need to use ‘Peak-Rate’ electricity.

Each night the battery would store however much electricity had been used the day before.

Battery and solar in harmony 

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and should be read against the right-hand axis.

The simulation above, shows what would happen if there were weak solar generation typical of this wintry time of year. As the solar electricity is being generated. the rate of discharge of the battery slows – is reversed briefly – and then resumes as the solar generation fades away.

A modest generation day – typical of a bright winter day or a normal spring day – is shown below.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

At its peak the solar generation reaches 2 kW – and in the middle of the day re-charges the battery to capacity. When the battery reaches capacity – the solar generation covers the domestic load and the excess electricity is exported (blue curve).

On a long summer day solar generation might reach 3.6 kW but here I assume just a 2.5 kW peak. In this scenario, the battery barely discharges and solar generation covers the domestic load and exports to the grid during the day. Only in the evening does the battery discharge.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

Battery and heat pump and solar 

The battery and the solar panels are just a part of the wider project to reduce carbon emissions which – if you have been paying attention – involves replacing my gas boiler with an air source heat pump. This uses electricity to move heat from outside into the house.

Back in the Winter of 2018/19 the gas boiler supplied up to 100 kWh/day of heating. In the slightly milder winter of 2019/20 the boiler used on average 70 kWh/day of gas for heating. This winter the External Wall Insulation and the Triple Glazing seem to have reduced this average to about 40 kWh/day – with a peak requirement around 72 kWh on the very coldest days.

Using a heat pump with a coefficient of performance of about 3, it will require 40/3 kWh= 13.3 kWh/day of electrical energy to supply these 40 kWh of heat energy. This amounts to an additional 0.55 kW running continuously.

I have simulated this situation below by increasing the load to 1.0 kW. In this case the battery will discharge a couple of hours early and we will have to buy a couple of units of full-price electricity.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

And finally we come to the reasonable worst-case scenario. Here there would be effectively no solar power (dull winter days!) and the external temperature would be around 0 °C requiring around 72 kWh of heating i.e. 3 kW of heating power. This will require 1 kW of electrical power to operate the heat pump on top of the 0.4 kW of domestic load.

Click for a larger version. The dotted (—-) red line shows the battery capacity of a Tesla Powerwall 2 and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.

In this scenario we would require about 8 hours of full price electricity @1.4 kW i.e. 11.2 kWh which@ 24.3 p/kWh would cost around £2.70. So if there were 10 of these days a year it would cost roughly £27/year.

I could avoid purchasing this full price electricity by buying two Tesla Powerwall batteries to give a capacity of 27 kWh. But spending an additional £8000 to avoid paying £27 year does not look like a sound investment.

Click for a larger version. The dotted (—-) red line shows the battery capacity of two Tesla Powerwall 2 batteries and the green curve shows the state of charge of the battery. Both should be read against the left-hand axis. The yellow curve shows the electrical power generated from the solar panels and the blue curve shows the power exported to the grid. Both should be read against the right-hand axis.


Overall, I think I now understand how a battery would integrate with the way we use energy in this house, and I think it makes sense.

Regarding money:

  • Using a battery  I would appear to be able to save many hundreds of pounds each year by purchasing off-peak electricity instead of peak electricity.

Regarding carbon:

  • Without solar panels, the switch to ‘Off Peak’ electricity should reduce annual emissions from roughly 749 kg to about 661 kg – a saving of 88 kg.
  • With solar panels we should generate roughly 3700 kWh of low carbon electricity, all of which will be used either by me or by someone else, displacing carbon-producing generation. This would be true with or without a battery. But the battery allows me to personally benefit.
    • During the summer the battery should allow me to benefit from the full amount of solar energy generated, reducing grid use (and expenditure) to almost zero.
    • During the winter, where only about 2 kWh of solar generation is available each day, it should reduce carbon emissions by about 20% compared with using ‘Off Peak’ grid electricity.
    • In the worst case – when using a heat pump to heat the house on very cold days with negligible solar power – I will need to buy full price electricity for a few hours a day.

So when I replace the gas boiler with an air-source heat pump, we will inevitably rely on the grid for some full-price electricity on the few coldest days of the year. That is why I have been so keen to reduce the amount of heating required.

Solar Power in Teddington

November 18, 2020

An Accidental Installation

Slightly to my surprise, I became the owner of a solar power installation last week.

I had planned the works on my house in this order:

  • Triple-glazing
  • External Wall Insulation (EWI)

Wait for a Winter

  • Heat pump
  • Solar Panels
  • Battery

This plan was partly rational. The largest carbon emissions are associated with heating, and so tackling those first – and evaluating their performance overwinter – was sensible.

But I was irrationally averse to getting solar panels because they felt like an indulgence – something I would “allow myself as a treat” after the hard work had been done. However, I changed my mind.

The main reason was that for the EWI work, I needed my neighbour’s permission to put scaffolding in the side passage by their building. My neighbour is an NHS clinic and it took several weeks to locate the person responsible and submit appropriate safety documentation. Although it was all perfectly pleasant – it was long-winded and not a process I wanted to repeat.

With that in mind, once the EWI scaffolding was erected, I called up a local solar power installer, Andy Powell from GreenCap Energy and asked whether he could install a system in the next two weeks using the EWI scaffolding. He visited the next day, and said that he could indeed use the scaffolding and that a 12-panel system would cost £4200. Importantly, he was able to install it the following week.

I had been thinking of all kinds of clever arrangements of panels, but it turns that if you want to put more than 12 panels on your roof, you need a special licence – which takes quite a bit of work – and time.

I reflected that if I installed the panels now, I would save roughly £1000 by using the existing EWI scaffolding. And that £4200 was much less than I had expected. So I put myself in Andy Powell’s capable hands and let him get on with it!

And there was one more piece of serendipity. At that point in the EWI work, it was possible to run the power cable from the panels to the main distribution board by running an armoured cable outside the house, buried underneath the EWI. This saved a lot of mess inside the house.

#1: The Components

The system consists of 12 solar panels, a device called an inverter, some isolation switches and generation meter.

  • The 1.7 m x 1 m panels are from Q-cells. The choice of panels available is bewildering so I just accepted Andy’s recommendation. They look beautiful and seem to work just fine.
  • Each panel generates roughly 40 V and up to 10 A amperes of DC current. They are connected in two banks to the inverter through two cables that poke through a small hole in the roof.
  • The Inverter is a SOLIS 4G 3.6 kW model. It takes the DC voltage and turns it into 220 V AC that can be used around the house or exported to the grid. There is also an add-on that enables the system to be monitored from a phone.
  • In my installation this AC current then goes back outside via an armoured cable buried in the wall  and then comes back inside under the floor, through a power meter, to the distribution board.

The gallery below shows some pictures of the process: click a picture for a larger version.

#2: The Site

Google Maps view of my home showing the shape and orientation of the available roofs. And photographs before and after the installation. Click for a larger image.

There were two roofs available for solar panels on my house – a smaller triangular roof facing 25° east of south, and a larger roof facing 65° west of south.

My initial plan was to cram as many solar panels on the south-facing roof as possible, but being triangular, the large 1.7 m x 1 m panels do not fill up the space very efficiently. I could have squeezed 7 panels on, but in the end I opted for 6 on each roof – it seemed to look a little less ugly.

To my surprise – experimentation with Easy PV software (more details later in the article) seemed to show that the orientation wouldn’t make much difference to the overall energy generated.

The path of the Sun at the summer and winter solstices and the equinoxes. In the summer when most solar energy is generated, the sun sets up to 30° north of west, and so the west-facing panels continue generating later in the day after the south facing panels are in shadow. Having panels on both roofs allows for generation for a longer fraction of the long summer days. Click for a larger version.

I think the reason is that – as Andy Powell pointed out – no panel can generate for more than 12 hours because it doesn’t work when the Sun is behind it!

But in the summer, when most solar energy is generated, the Sun is above the horizon for up to 16 hours and at the solstice it sets more than 30° north of due west.

And so the west-facing panels continue generating later in the day after the south-facing panels are in shadow. Having panels on both roofs allows for generation for a longer fraction of the long summer days.

The path of the Sun at the summer and winter solstices and the equinoxes. The yellow zone shows sun orientations at which only the south-facing panels generate. The red zone shows sun orientations at which only the west-facing panels generate. The purple zone shows sun orientations at which both sets of panels generate.

Of course it is not just the east-west position of the Sun – the so-called azimuthal angle – that affects generation – the height of the sun in the sky – its elevation – is also important.

Sites such as this one will plot maps showing the course of the Sun through the sky on any particular date from your particular location.

The blue line shows the path of the Sun through the sky on November 11th for my location at 53° latitude and 0° longitude. 180° corresponds to due South. Click for a larger version. The shaded yellow boxes indicate the azimuthal angles at which the two banks of panels generate. And the green line shows the optimum elevation of the Sun.

From the figure above we see that the Sun is low in the sky at this time of year (Doh!) – it only rises 20° above the horizon at midday – but that even at this time of year, the generation from the west-facing panels in the afternoon prolongs the useful generation time. From initial observations the power on the two banks of panels is equal at about 1 p.m.

#3: Expected Performance

Frustratingly, working out the expected performance of a solar installation is complicated. One needs to:

  • calculate the Sun path diagram for each day of the year,
  • factor in the weather,
  • consider each bank of panels separately.

Fortunately, approved installers such as Greencap can run standard calculations, or using software like Easy PV you can – after some messing about – come up with your own estimate.

Output from Easy PV software allows one to calculate how much electricity is likely to be generated by each bank of solar panels in a year.

For my installation, both estimates suggested that I should expect to generate roughly 3700 kWh of electricity each year. This figure is roughly how much electricity my house uses each year.

If I could capture each one of those generated kilowatt hours and use it to displace one that I buy from EDF  I would save more than £800/year. However, things are not so simple.

Looking around  one can find a few records (such as this one) of people’s generated power. They seem to indicate that in the UK I should expect roughly 5 times as much daily generation in the summer as in the Winter.

Putting that information together with the fact that I can expect 3700 kWh over the year I concocted a function (sine squared with an offset in case you care) to guide my expectations.

So in the summer I can expect the panels to generate perhaps 15 kWh/day – much more than I need – but in the winter the panels might only generate perhaps 3 kWh/day – much less than I need.

My guess at how many kWh per day I can expect from my solar panels. The average household consumption is shown is shown as a red dotted line (- – -). Click for a larger version.

#4: Actual Performance

I only have 10 days of data for the panels and these are plotted on the graph above and they seem broadly in line with my expectations.

I can already see the effect on my electricity usage. As can be seen on the graph below, my daily average use is 2.1 kWh below the average before the panels were installed.

Daily electricity usage (from a smart meter) before and after solar panel installation. Click for a larger version.

This may not sound much but even if the panels only ever performed at that level, this would prevent the emission of 73 kg of CO2 per year, and (@£0.24/unit) save me £175 per year. For those of you that are interested, that’s a 4.2% return on investment. But I expect the panel performance to be much better than this when averaged over the year.

But what is hard to capture in words is the sheer wonder of the installation. In bright November sunshine the panels generate more than 2 kW of electrical power – so I can boil a kettle and still see the smart meter read zero usage.

#5: What next?

For the next few weeks I intend to let the dust settle, and try to get my head around how the system is working.

But one obvious difficultly – which will become more pressing as we move into Spring – is that when the Sun shines the panels produce kilowatts of electricity whereas the house itself generally consumes just a few hundred watts.

At the moment any excess electricity is exported to the grid – my smart meter says 13 kWh so far – as a gift to the nation!

So in the next few weeks I will sign up with a company to buy this electricity. There are several companies who will buy at between £0.03 and £0.055 per kWh.

In the longer term it may well make sense to get a battery as well. But batteries are expensive, and the more I have thought about it, the main use of a battery in my situation would not be to store solar electricity, but to switch the time at which I bought electricity from the day (when electricity is carbon intensive and expensive) to the night (when electricity is cheap and generally less carbon intensive). But that is a question for another time.

External Wall Insulation: How well does it work?

November 16, 2020

Be Constructive will probably finish my External Wall Insulation (EWI) in just a day or two, but I am already trying to see its effect, even as they apply the last coats of render.

So “How well does it work?”

I won’t have a definitive answer until later in the winter, but this article describes the procedures I am using and you can look at the preliminary data and come to your own – preliminary – conclusions.

The data  

I have written about this before (here, here, here and here!) but please allow me to recap.

To work out how well the EWI is working I measure two things:

  • the difference between external and internal temperatures, and
  • the amount of gas I use each day or each week.

For the last two years I have done this weekly – even I find it too tedious to read the gas meter every day!

But a few weeks ago – in the same week as the EWI work started – I switched to using a ‘smart meter’ and this allows me to download a spreadsheet with daily gas (and electricity) consumption. So now I can work with either daily or weekly averages of gas consumption.

I can then get either the daily or weekly average temperatures from the weather station I have in my back garden. If you don’t have a weather station in your garden then you can use data from nearby stations on the Weather Underground (Link: Zoom in to find weather stations near you).

So how do I use the daily and weekly data to estimate how well the EWI is working?

Weekly data

The graphs below are complex so I will describe each element in turn.

We start with my average daily gas consumption (blue squares) since November 2018. I have averaged the data over 5 weeks to remove anomalously cold or warm weeks. This makes it easier to view the general trend of the data.

My average daily gas consumption (in kWh/day) over the last two years. Click for a larger version and see the text for details.

The data are plotted versus days since the start of 2019, and several events which I think might have affected gas consumption are shown in pink.

  • Triple Glazing of most windows.
  • Installation of a chimney sheep.
  • Triple Glazing of remaining windows.
  • External Wall Insulation (EWI).

Notice that in the summers, gas consumption falls to around 5 kWh/day due to water heating and cooking, but that increases in the winter to as high as 100 kWh/day. It is the temperature-dependent part of this consumption that I think is related to the effectiveness of the insulation in the house.

Next we have a graph of the difference between the internal temperature (nominally 19 °C) and the average weekly external temperature over the same period. This is the ‘demand’ to which the gas central heating responds. Again, I have averaged the data over 5 weeks.

This data is plotted (green circles) on the same graph as the gas data, but should be read against the right-hand axis. Plotting the data in this way shows that the gas consumption is obviously related to external temperature.

Average daily gas consumption (in kWh) over the last two years in blue plotted against the left-hand axis and the difference of the average external temperature from 19 °C in green plotted against the right-hand axis. Click for a larger version and see the text for details.

It’s clear from the similarities between the two curves that the variation in winter gas consumption is due to the external temperature. I mention this extremely obvious fact because I was personally surprised by how similar the two curves were.


My model of my house tries to predict the gas consumption based on knowledge of the weather, and a single parameter that describes all the ways that heat flows out of the house. This parameter tells me how many watts of heating power I need to keep the house 1 °C above the outside temperature. In case you are interested, the equations which summarise this are given in the figure below.

The mathematical model – in case you care. In the green background the heating power is expressed in kWh/day and in the blue background the heating power is expressed in W. Click for a larger version.

Initially I matched the model to the data using what is known in statistics as “the null hypothesis“i.e. I assume that nothing I have done has made any difference. So:

  • I adjusted the heat loss parameter of the model to match the data in the middle of the winter of 2018-2019.
  • The best fit is made by assuming I use roughly 280 W of gas heating for each °C that the external temperature fell below 19 °C. (That’s 6.7 kWh per day per °C)

The red dotted line (- – – ) shows the modelled gas consumption assuming that nothing I have done has made any difference. Click for a larger view.

With this assumption, it is clear that the model overestimates the gas consumption in subsequent winters: so it looks like the actions I took did have some effect i.e. the same demand has led to lower gas consumption. Phew.

To estimate how big an effect I modified the model so that the effectiveness of the insulation could be changed at two points: day 244 and day 657 shown as vertical pink lines in the graph below.

The red dotted line (- – – ) shows the modelled gas consumption assuming that the thermal performance of the house has improved from 280 W/°C in winter 2018/2019 to 240 W/°C in winter 2019/2020, to 134 W/°C in the current winter 2020/21 . Click for a larger view.

  • For the first section I assumed that I needed to use 280 W of gas heating for each °C that the external temperature fell below 19 °C.
  • For the second section I assumed that I needed to use only 240 W of gas heating for each °C that the external temperature fell below 19 °C – about 15% less.
  • For the final section – i.e. currently – I anticipate that I will need to use only 134 W of gas heating for each °C that the external temperature falls below 19 °C.

You can see that in the current winter (day 650 onwards) there is not yet enough data to say which value of heat loss parameter will best match the data.

Looking at previous years, the model does not match the data well in spring and summer – so I don’t feel I can definitively estimate the heat loss parameter until winter is fully upon us.

But the estimate of 134 W/°C – less than half what it was two years ago – does not (at this stage) look unreasonable.

Daily Data

I can apply the same model to the smart-meter data that I download from EDF which gives me my daily gas consumption. I can then compare this directly with the daily average temperature.

I expect this daily data to show added variability when compared to the weekly-averaged data because:

  • The ‘constant term’ – in my case roughly 200 W or 4.8 kWh per day – due to use of gas for cooking and heating water may look constant when averaged over 5 weeks. But it likely fluctuates from day-to day depending how much cooking or hot water is used.
  • In the short term, heat can be stored and released from the fabric of the building.
  • During the EWI works, there have been many days during which doors were open.

Also I must confess to a metrological faux pas in this article by using two units to describe the effectiveness of the insulation: watts (W) and kilowatt hours per day (kWh/day). Both are valid choices, but I will make penance for having used mixed units by showing graphs below in both sets of units!

With these caveats in mind, let’s look at the data.

Daily gas consumption in kWh/day (left-hand axis) and temperature demand (right-hand axis). The straight lines show weekly averages. Click for a larger version.

Daily gas consumption in terms of average power (W) (left-hand axis) and temperature demand (right-hand axis). The straight lines show weekly averages. Click for a larger version.

Notice the strong day-to-day correlation between gas consumption and average external temperature deficit.

I guess it is this strong correlation that allows gas supply companies to order the correct amount of gas in advance.

But the day-to-day data have oddities. For example, on some days the gas consumption seems anomalously low (e.g. days 298, 304 and 307), and on others anomalously high (e.g. days 294, 310).

Bearing these anomalies in mind we can divide the gas consumption data by the temperature deficit data to give the gas power per °C of ‘demand’. These graphs are shown below.

Gas power (in kWh/day) per °C of demand. The straight lines show weekly averages and the double line (===) shows the running average (±3 days). The dotted red line (– – – ) shows the level I hope to achieve. Click for a larger version.

Gas power (in W) per °C of demand. The straight lines show weekly averages and the double line (===) shows the running average (±3 days). The dotted red line (– – – ) shows the level I hope to achieve. Click for a larger version.

The daily data show too much variability to allow easy interpretation. But looking at the running average and the week-to-week data it looks like there is a trend downwards towards improved thermal performance over the course of the EWI works

However there are considerable uncertainties.

  • These data take no account of the non-thermal use of gas.
    • For example, heating 50 litres of water a day from 10 °C to 50 °C would use 2.3 kWh/day, the energy of which would substantially go down the drain
  • Similarly, at these low power levels, I should probably be taking account of:
    • The roughly 11 kWh/day of electrical power that we consume.
    • The roughly 4 kWh of heating provided by the warm bodies of myself and my wife.


So it will take time before I can definitively evaluate the effect of the EWI. But by spring 2021, I suspect that I will have stared at the data long enough that the best way to analyse the data will have become clear to me. I hope so!

The reason it matters is that next year I plan to stop using the gas boiler altogether and switch to using an air source heat pump. Before spending yet more money on that I am keen to try to anticipate the likely demand so I can pick the right model!

Meanwhile, I am positively enjoying the EWI. I don’t know if this is a psychological effect of spending large amounts of money on something – or a genuine sensation caused by a more stable temperature and – I think – reduced air leakage.

And although still clad in scaffolding, the house itself is beginning to look rather smart. I’ll be sure to post some pictures when the Be Constructive team have left.


External Wall Insulation: How it’s done.

November 11, 2020

As many of you will know, I am having External Wall Insulation (EWI) applied to my house.

As closer confidantes will confirm: I am obsessed with the project. Why? Because based on my calculations, it is the single-most effective thing one can do to an old house to improve its thermal performance and reduce carbon dioxide emissions.

And yet very few people seem to be doing it. My hope is that by simply talking about it – and by measuring how effective it really is – more people will consider it as an option.

The idea of EWI is simple – “just stick insulating materials to the outside of a house“. But the reality of doing this reliably and leaving the house weatherproof and looking good is complex.

There are some nice videos out there, such as this one below showing the Be Constructive team working on a previous house. There are more videos here. And if you want details, then check out the extensive EWIPro Complete Guide (pdf) and all the materials are available at the EWI Store.

But partly for my own satisfaction I thought I would outline each step with pictures rather than video. Also, the video shows the application of expanded polystyrene boards and the procedure for the polyurethane foam boards that I have used is a little different.

So here is my description the process. There is a gallery of photographs at the end of the article.

Step 1: Preparation

The job began by protecting all the working surfaces – the patio and the front and rear gardens – with protective plastic, and then all the windows were covered with a transparent adhesive film.

For my house, the Be Constructive team demolished an old chimney which no longer had a reason for existing, and removed almost 2 tonnes of loose render from the side wall. So much render was removed that the wall had to be roughly re-rendered before they could begin applying the EWI.

They then moved the boiler exhaust, external electrical fittings and drain pipes to take account of the fact that the house was about to grow by about 120 mm in all directions. This stuff is rather tedious – but essential.

Next came the preparation of the outside walls and the painting of a ‘stabilizing primer’. This penetrates porous surfaces and binds them, creating a surface to which adhesive can stick. This is particularly important for some building blocks which can be quite powdery.

Step 2: Boarding. Kingspan K5

Next the team installed so-called ‘starter track’. This plastic support is screwed into the wall at the level of the first layer of insulating boards – usually just above the damp proof course – and makes sure the boards are horizontal, and supports them while the adhesive mortar dries.

Different stages in the application External Wall Insulation. Click for a larger version.

Normally EWI utilises either expanded polystyrene (sometimes abbreviated as XPS or EPS) or Rockwool™, and boards made from these materials are available in a wide range of thicknesses.

However I had asked to use a board made by Kingspan called K5. I chose this because I could only put about 100 mm thickness around the house – and for a given thickness, K5 will give the best insulation.

I limited the insulation to 100 mm because that amount would still keep the walls underneath the existing ‘soffit’ under the eaves. Also – if the insulation were much deeper – I felt the windows might seem to be too recessed.

Only 100 mm thickness of Insulating Boards would fit under the eaves of my house. Click for a larger image.

For some reason, 100 mm thick boards of Kingspan K5 were not available and so the Be Constructive team glued pairs of 50 mm thick boards together to achieve the required thickness.

The ‘double’ boards were stuck to the wall using several thick blobs of adhesive mortar. Using a big blob of mortar perhaps 10 mm deep allows the outer surfaces of the boards to be made parallel even when the underlying wall is not.

In my illustrations I have deliberately drawn the boards as being not parallel. In fact the Be Constructive team actually took a lot of care into making the final surfaces vertical and smooth. This is important because it is very difficult to compensate for this after the fact.

The boards are ‘overlapped’ at corners and cut to shape around windows and other architectural features. Any gaps are filled in with expanding foam.

Insulating Boards are overlapped at corners. Click for a larger image.

Step 3: Mechanical Fixing.

Once the boards are stuck to the wall and the mortar has set, the boards are mechanically fixed in place. To achieve this a hole is drilled through the boards and into the wall. Then a plastic fixing is pushed into the hole. Finally a metal nail is hammered into the plastic fixing which locks the plastic fixing in place – like a rawlplug – and holds the boards against the wall.

Using metal nails adds a heat leak directly through the boards: each fixture increases the thermal transmittance of the board by about 3%. However there is not much that can be done about that. It would be unwise to rely solely on the mortar or just plastic fixings.

Step 4: Base Coat Layers

Now the boards are attached to the wall and functionally insulating the house. But they are neither weatherproof nor attractive.

Preparatory stages in the application of weatherproof render. Click for a larger version.

So the next step is to coat the boards with an adhesive mortar (called a ‘base coat’) in which a glass-fibre mesh is embedded. This mesh is essential to prevent cracking due to building movement.

For polystyrene insulation this is a simple process: the boards are rasped to create a smooth surface; a layer of base coat is applied; the mesh is pressed into place; and then the mortar is smoothed. This forms a surface on which the the final render can be applied.

For K5 insulation, the process is more complicated because the surface of the boards should not be abraded. So:

  • First a thin layer of the base coat is applied to boards to create a smooth surface.
  • Then a second layer of base coat is applied into which the fibre-glass mesh is pressed.
  • Finally a third layer of base coat is applied to form a surface on which the final render can be applied.

The base coat also meshes with the corner and reveal ‘beads’, and with extra fibre-glass mesh placed around the corners of windows.

Step 5: And finally

And finally we come to the point where render is applied.

The render is a mixture of stone with a specifiable particle size: 1 mm, 1.5 mm or 2 mm , together with a mortar and a silicone polymer. It can be coloured in a very wide range of colours.

Additionally, my house will have ‘faux’ bricks called ‘brick slips’ applied to match architectural details on neighbouring buildings.

I’ll be sure to post pictures when we have finished.


Anticipated general look of the front of our house after rendering. Click for a larger view.

Photo Gallery – click for a larger version

Does it work?

But does it work? Well, of course it works! It would be physically impossible for it not to work!

The question isHow well does it work?“. And specifically, “Does it work as well I anticipated in my modelling?

These are complicated questions to answer definitively – and they are especially difficult to answer quickly.

I will not have a definitive answer until later in the winter, but I will explain how I will answer the question in a follow-up article. For now I will just tease you with the answer that the data look ‘promising’.

Keep warm 🙂

The Drinking Bird

November 4, 2020

While on a Zoom call with colleagues the other day, someone mentioned that during their time at Bell Labs, they had worked opposite Miles V. Sullivan.

I did not recognise the name. Then he told us what Miles V. Sullivan had done – he had invented ‘the drinking bird’! If you have not seen one of these, it is a small glass toy shaped with a bird-like form which first stands upright, and then leans of over to sip water from a glass, a process which repeats apparently endlessly. It is a wonder to behold.

I remembered having stared at these in shop windows as a child. I had imagined that such an ingenious device must stem from antiquity – and indeed it does have ancestry. But in this implementation, Miles V. Sullivan patented it in 1945. And according to my source, used the money to fund his PhD studies.

After the Zoom call I immediately moved our son’s  Drinking Bird onto the laboratory bench kitchen table for further experiments. As I set it ‘drinking’ I was re-fascinated by the subtle interplay of multiple physical principles. And I resolved to read more about it.


There are some excellent explanations out there (e.g. this one or that one) and here is a video from ‘The Engineer Guy’.

I have added a couple of clarifying points below:

Illustration of the operation of the drinking bird in four stages. See the text for details. Click for a larger version

If one looks at the ‘bird’ one sees something like the situation in A above: a red liquid with ‘nothing’ above it. To understand the operation of the device it is important to realise that (a) the space is not ’empty’: it is filled with the vapour of the liquid and (b) the red liquid is composed of a transparent liquid with just a tiny amount of red dye.

The pressure of vapour above a liquid depends very strongly on the temperature of the liquid surface: the more energetic molecules in the liquid can sometimes leave the surface, escaping the attraction of the other molecules, and become part of a gas (called a vapour when it is in contact with its own liquid). In a closed container, the molecule will bounce around and eventually return to the liquid surface. In the steady state, as many molecules will leave the liquid, as return to it. When this state of balance is achieved the pressure is called the saturated vapour pressure.

Illustration of the molecular nature of a liquid and its vapour. Molecules are represented by blue blobs. Their direction of motion is shown for some molecules by a red arrow. Molecules in the liquid jiggle back-and-forth and if they are near the surface and by chance have sufficient energy they can escape into the vapour. The chance of escape is very temperature dependent. Molecules in the vapour occasionally rejoin the liquid. When the rates of leaving and rejoining are equal, the vapour pressure is said to be ‘saturated’.

  • If we cool the liquid surface, the average energy of molecules in the liquid falls, and the rate at which molecules escape into the vapour falls and the saturated vapour pressure falls.
  • If we cool the container, then vapour will start to condense as liquid on the cold surface.

In B I have coloured-in the space with two different shades (pink and green) to show that the two volumes of vapour are in touch with two different liquid surfaces.

In C, we now have a non-equilibrium state. The beak has been cooled, and a few small droplets of liquid will have condensed. The vapour in the neck and head is now in contact with two liquid surfaces: the liquid in the neck, and the colder liquid droplets in the beak. This situation is complicated and not stable.

  • The increased rate at which molecules are removed from the vapour as they condense in the beak lowers the pressure in the head allowing the pressure in the base to push the liquid up the tube.
  • On balance, molecules will evaporate from the liquid surface in the neck and condense in the liquid in the beak. As they condense, they release latent heat, warming the droplets in the beak and effectively transferring heat from neck to the beak. The process will continue as long as the beak is cooled by evaporation of the water on its outer surface.

The illustration in D is just to show that what I can measure is just the location of the top of the column, and not actually the height of the liquid column supported by the pressure difference.

So it’s complicated. But I found even the explanation by The Engineer Guy disappointingly qualitative.

So I thought there might be room for an explanation which involved actually measuring something! And there were two questions I wanted answered.

  • How cold does the ‘beak’ get in operation?
  • What’s the liquid inside? How can one possibly tell?

The first of these questions turned out to be easy to answer, but the second one has proved really hard.

How cold does the ‘beak’ get in operation?

To answer this question I attached a thermocouple (about £18 from Amazon: a great Christmas gift) to the felt that was glued to the bird’s beak.

Experimenting on a ‘Drinking Bird’. The picture shows a thermocouple attached to its beak with an elastic band.

I then wetted the beak and measured the temperature versus time every 10 seconds until the answer stabilised – which took around three minutes. The temperature fell by 1.8 °C.

In this first experiment the bird’s beak was still, but in operation the birds beak initially moves through the air and I wondered if this motion was significant.

To answer this I used a small USB-powered fan to move air past the beak at about 1 m/s (measured with a small hand-held anemometer). And the moving air did have a significant effect. In moving air the temperature fell much more quickly and by a larger amount: approximately 4.3 °C. I was so surprised by this large number that I repeated the experiment and obtained similar data with a change of 4.5 °C.

Remember that in order to repeat these experiments you need to completely dry the beak which generally takes about a day.

The graph below summarises the data. So still air or moving air, the answer is more than the “three tenths of a degree”  that The Engineer Guy claims about 6′ 30″ into the video. If he was making the video in very moist air or at very low temperatures, it might be possible to get such a small temperature drop. But I think its probably just a (rare) slip.

Temperature change of the wetted beak of the drinking bird versus time for still and moving air. Click for larger version.

In fact I could have looked up these answers in a table for the operation of a wet-and-dry-bulb hygrometer (psychrometer) but where would have been the fun in that! And it is an interesting feature that you may care to verify, that above a threshold air speed, the temperature of the beak doesn’t depend on air speed.

Anyway, thrilled by having ascertained the temperature difference driving the bird’s drinking habit, I turned to the second question.

What’s the liquid?

I felt fairly confident that Methylene Chloride (Chloromethane) – the liquid which The Engineer Guy asserted was in the bird – was no longer used. It is a highly corrosive chemical commonly used in paint stripper and probably not approved for use in a delicate glass toy that could be played with by children.

The Wikipedia page suggests a number of possible liquids which could be used:

  • Ethanol
  • Methanol
  • Di Ethyl Ether
  • Carbon Tetrachloride
  • Chloroform
  • Chloromethane

But how can you tell which liquid? I suspected that for a given temperature difference, the height of the liquid column was characteristic of the liquid used. So…

  • Using standard tables in Kaye and Laby I looked up the vapour pressure of the different substances at different temperatures.
  • From this I worked out the latent heat of vaporisation and calculated the vapour pressures above each liquid at 19 °C and at 20 °C.
  • The difference between the vapour pressures at these two temperatures told me the pressure forcing the liquid column upwards for 1 °C temperature difference.
  • Finally, I looked up the density of the liquids. I then used the change in the height of the liquid column as an indicator of the pressure difference.

Some Equations. Just in case you care. Click for a larger version.

So now I knew that for a given temperature difference each liquid would rise up the tube by a different characteristic distance.

  • Chloromethane: 1917 mm/°C
  • Di Ethyl Ether: 363 mm/°C
  • Methanol: 87 mm/°C
  • Chloroform: 63 mm/°C
  • Ethanol: 43 mm/°C
  • Carbon Tetrachloride: 34 mm/°C

So we can see why (in the absence of safety concerns) chloromethane would be a good choice: for a given temperature difference it would rise up the tube more than five times further that the next best liquid, di-ethyl ether, and about 20 times further the next best candidate, methanol.

Now all I had to do was to measure the height of the column as I changed the temperature difference between the base and beak.

The Experiment

I followed the ‘Golden Rule of experimental physics: Do it quick! Then, do it right. And so it became apparent very quickly that this was going to be difficult.

I won’t trouble you with all the dead ends down which I traveled over the last few weeks! Instead I will show the apparatus I arrived at and explain some of its special features.

Overview of the final experimental arrangement. Click for larger version.

An overview of the experiment is shown above, and a close up of the bird held in its bath is shown below.

Close up of the drinking bird. Click for larger version

Below is a time-lapse movie compressing the four and a half hours of the experiment into 33 thrill-packed seconds. If you press pause on the movie, you can then scroll through the movie and read off the data just like I did!

Here are some of the special features which you might not appreciate at first glance.

  1. The most important point which explanations of the drinking bird miss is that there is no air in the container. The vapour pressure is determined by the temperature of the liquid with which it is contact. When the beak is cooled, vapour condenses inside the beak to form a tiny amount of liquid. The vapour pressures above a liquid varies exponentially with temperature and this is the origin of the special sensitivity of this device.
  2. I decided to induce the temperature difference not by cooling the beak but by warming the base in a bath of water. To keep the temperature uniform I stirred it with a cappuccino frother. But the experiment went on so long that I got ‘thumb fatigue’ and couldn’t hold down the button! Hence I bought a stirrer hot-plate for a very reasonable £65, but I only used the stirrer, not the heater.
  3. My thermocouple reader only has a sensitivity of 0.1 °C and this was not sufficient resolution for this experiment. To detect smaller temperature changes I used thermistors as thermometers. For the bath I used waterproof thermistors (£5.95 for 5) and for the beak I used miniature thermistors  (£5.81 for 10). I first calibrated one against the other by tying them together in waterproof tape and immersing them in a glass of water as I heated it by intermittently adding a few cubic centimetres ofhot water.
  4. To measure the column height I printed out a scale that I could attach to the neck. This does not give me the column height directly – just a marker of where the upper end of the column is. I was interested in the rate of change of the column height rather than its absolute value. I applied a crude correction for the fact that as the upper end of the column rose, the lower end (which I couldn’t see) got lower.
  5. I applied power very gently, heating the water up with just a watt or two of electrical power resulting in the temperature changing at roughly 1 °C over two hours – or 8.3 mK per minute. The power supply was a very reasonable £69. The idea was to balance the column exquisitely so that I would be able to make it go up or down by changing the heater power. But in fact the system has hysteresis – a given bath temperature does not give rise to a unique column height. More on this later.
  6. I really should have used a better ohm meter for the thermistor on the beak, but I didn’t have one!

Finally the results. First I plotted the bath and beak temperatures as a function of time through the experiment. I did this by scrolling through the video and taking data every 5 minutes. You can see how the bath warms deliciously slowly.

Beak and Bath temperatures as a function of time. Click for a larger version

The graph below shows the same information as the graph above but now I have added in green the observed height of the liquid column – this is referenced against the right-hand axis.

The shaded regions are where the liquid column was observed to climb or fall along the neck. Readings above 90 mm corresponded to partial filling of the bird’s head and could not be accurately measured.

Finally I plotted the observed column height versus the measured temperature difference. The results of the video experiment (Experiment 4) are plotted in green below alongside results from a previous experiment where I took data on both rising and falling liquid columns.

Observed column height in centimetres versus temperature difference between the beak and the bath. Click for a larger version


The first feature of the results which surprised and frustrated me was the hysteresis – the height is not a unique function of the temperature difference.

I did not have the patience to investigate this fully, but I am pretty sure it is a real feature and not just a feature of poor experimental method. I still don’t understand precisely why it occurs, but I think it is connected with the fact that the vapour in the head is in contact with two liquid surfaces at different temperatures. The vapour pressure is therefore not well-defined and depends on the temperature of the liquid column which is different when rising or falling.

The vapour in the head is in contact with two liquid surfaces at different temperatures. Click for a larger version.

But from the measured slopes it seems the column rises roughly 285 ± 25 mm/°C. Looking at the list of likely liquids, although the uncertainty is large, I think the data rule out chloromethane (as expected).

My conclusion is that the liquid is most likely diethyl ether: flammable and dangerous, but not quite in the category of chloromethane. The difference between the expected rate of rise (363 mm/°C) and the experimentally measured rate of rise is quite large, but the disagreement is very much greater with the other candidate liquids. One could imagine that the reason why the measured sensitivity is lower than the theoretically expected one is because the vapour in the head is connected to two liquid surfaces – the cold one in the beak, and the warm one in the neck.

So…at this point you are probably thinking – will this article never end? That is certainly what I am thinking. So summarising abruptly, the drinking bird is a beautiful demonstration of subtle physics. And when I am not so busy insulating my house, I may well return to see if I can develop either a better theory, or make some better measurements.

My House: comparing models and measurements

July 28, 2020

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.

Previous articles about my house.












Estimating the expected thermal performance of my house

July 22, 2020

//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.


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.

Be Constructive!

July 5, 2020

Friends, I am very excited.

Yesterday I signed and returned the contract to have external wall insulation applied to my house. The work will start in mid-September in time for what I hope will be a really cold winter!

My calculations suggest this should reduce direct heat loss through the 133 square metres of walls on my house by a factor which might be as large as 5 – WOW!

There are still many uncertainties. For example:

  • I don’t know the extent of heat loss to the Earth through the ground floor.
  • And I am unsure about the significance of air flow in losing heat.

But by continuing my measurements through this summer and next winter I hope to gain insight that should help me plan the next steps.

Be Constructive

The company I have engaged to do this are charmingly called Be Constructive and they seemed very professional in their assessment of the work.

The work itself is conceptually easy to understand. But it has many time-consuming steps that are required in order to get a finish which will last for many years. The video below shows some of the basics of the process.

When the work is being done I will add more details but here are some of the decisions I have made.

I want the house to look visually similar before and after…

The reason for this is that I want to show that this can be done by ‘normal people’ – and not just measurement obsessives such as myself. Consequently:

  • I have resisted my son’s request to paint the whole house bright yellow.
  • I have restricted insulation to a thickness of 100 mm. I think this is thin enough that the insulation will not be immediately visually obvious.  
  • To get the best thermal performance from this thickness, I have reluctantly used a proprietary insulator – Kingspan K5. I would have preferred ‘Rock wool’ but the Be Constructive surveyor thought the thermal performance would not satisfy me! 
  • The lower part of the house – and the neighbouring houses – has exposed brickwork. This will be matched as closely as possible using ‘brick slips’ – thin ‘faux bricks’ – on top of the render. This looks incredibly tedious and I am glad not to be doing it myself!

This work is expensive. The whole job will cost around £20,000 or about £150 per square metre, rather more than the guide price (link) of £90 square metre. This increased cost per square metre is due to the improved insulation, the use of brick slips, and one or two ‘fiddly bits’. My guess is that about 40% of the cost is associated with the rendering rather than the insulation. 

But in terms of heat loss, the work is considerably more cost effective than the triple-glazing I had done previously, and should represent a big step towards making the house carbon-neutral. 

The return on investment – in terms of reduced bills – will probably be around 2%. But my rationale is moral rather than financial.

I see wasting heat and putting carbon dioxide in the atmosphere as being in the same category as leaving a sewer to spill onto the street. Given that I have the wherewithal to do something about this, I feel it would be shameful not to act.

..but I do have a large empty wall…

..and my son did want the house pained yellow… Perhaps I should get a mural like this fantastic painting of William Morris?

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