Protons for Breakfast

Friends, here is a new song about heat pumps! It’s nonsense! But I hope you enjoy it nonetheless.

Heat Pump It Up

I hear you’re looking for something to keep you warm at night
I hear you’re looking for something to keep you warm at night
I’ve got a heat pump it’ll make you feel all right

CHORUS
I’m going to heat pump you up
I’m going to heat pump you up
I’m going to heat pump you
I’m going to heat pump you
I’m going to heat pump you up
I’m going to heat pump you
Keep you warm all night

Running slow and steady, I’ll make sure you’re satisfied,
Running slow and steady, I’ll make sure you’re satisfied,
I’m MCS compliant and Heat Geek qualified

Under-floor heating or radiators – you choose.
Under-floor heating or radiators – you choose.
We’ll give you Your Energy Your Way, you’ll kick those winter blues!

CHORUS

You say my heat pump looks too big for the space you’ve got
You say my heat pump looks too big for the space you’ve got
Well, I will squeeze it in and make sure it really hits the spot.

I’m an Urban Plumber and I know heat pumps inside out
I’m an Urban Plumber and I know heat pumps inside out
I’ll pump you up so sweetly, I’m going to make you scream and shout!

CHORUS

Friends, we are just reaching the time of year when we will begin to use our air conditioning system. Of course this use should ideally all be covered by our solar PV generation, but I just wondered precisely how well they actually matched each other.

The graph below shows weekly averages of air conditioning (AC) use (kWh/day) and solar PV generation (kWh/day) for the last three years. The consumption and generation are measured once a week by reading the relevant check meters. The simple message is that PV and AC go very well together.

Click on image for a larger version. The graph shows solar PV generation (averaged weekly) over the last 3 years in orange. The red dotted line shows smoothed data. Also shown in light blue is the consumption by the air conditioning system.

The AC system is a Daikin Mini-split with 2 indoor units similar to the one illustrated below.

Click on image for a larger version. The Daikin AC system we have installed (link). Each indoor unit can remove heat at a rate of over 1 kW.

We have one cooling unit in our bedroom (ensuring cool nights in summer) and one in the upper landing (which cools the whole of the house – but just a little bit). The system really adds to our quality of life and I regret not having installed at least one more indoor unit downstairs.

The PV system consists of two separate systems each connected to their own Solis 3.6 kW inverter.

System#1 

• 12 panels installed in November 2020
• 6 × 340 W-peak roof panels facing 20° south of West.
• 6 × 340 W-peak roof panels facing 20° south of West.

System#2 

• 8 panels installed in November 2022
• 5 × 390 W-peak roof panels facing 20° north of East.
• 3 × 390 W-peak roof panels on a flat roof ’tilted’ to the South East.

Click on image for a larger version. Aerial view of the roofs of Podesta Towers.

Nominally the system has an peak output of 7.2 kW-peak. But because of the different orientations, the peak generation from each string of panels occurs at a different time, and the actual peak generation is around 5 kW.

Seasonal and Daily demand

The seasonal cooling demand is well-matched to the seasonal generation, but in hot weather, demand for cooling continues right through the night, long after the sun has set.

Typically on hot summer days, the battery is full at around 8 p.m. when generation from the west-facing panels stops. At these times the AC is generally not operating at full power, perhaps removing 500 W of heat. If the coefficient of performance (COP) of the system is ~3, then the electrical consumption is around 250 W which is only a modest drain on the battery.

Click on image for a larger version. An AC unit is more properly described as an air-to-air heat pump. If it operates with a coefficient of performance (COP) of 3, then 500 W of electricity can remove heat from inside a dwelling at a rate of 1 kW.

Summary

We installed the AC system as a luxury – but there have been times in the last few summers when it has felt like a necessity.

When I planned the installation of the heat pump, I did consider using an air-to-air system for winter heating of the entire house – and finding some other way to heat the hot water. But at the time I felt too unsure of how things worked to risk it. But it would not have been a bad idea.

Click on image for a larger version. A younger slimmer me back in March 2021 with my newly-installed Tesla Powerwall 2.

Friends, just over 5 years ago in March 2021 my Tesla Powerwall 2 was installed. Within a day or two the battery charged itself from my 4 kW-peak solar PV and my house went off grid: it felt magical and I wrote about it a lot back then:

• After a day or two
• After a week
• After a month

Click for larger view. Re-published from my “Week One” article in 2021. After the battery was installed, we quickly went “off-grid” for the summer.

Since then I have written about the slow degradation of the battery which is disappointing to experience, but which is just part of how batteries work. However, day-to-day, the battery remains a thing of wonder – enabling us to go off-grid in summer and operate the heat pump at very low cost in winter.

Click on image for a larger version. Cumulative consumption of electricity from the grid through each year from January 2022 to April 2026. Between early May and late September we consume very little grid electricity. In 2024 I experimented with a different way of operating the battery – but it wasn’t a good idea!

In this article I just thought I would summarise how the Powerwall is performing half-way through its guarantee period.

Round Trip Efficiency

Round Trip Efficiency is an important parameter for a battery – but one that few people take time to measure. It answers the question:

If I charge the battery using 1 kWh of electricity, and then discharge the battery, how much of that energy is returned as discharged electrical energy?

The answer varies depending on the rates of charging and discharging, the temperature of the battery, the existing state-of-charge of the battery and how long the energy is stored for – amongst other things. At the moment the best one can hope for is around 90% i.e. roughly 5% loss on charging and 5% loss on discharging. The losses end up as heat.

The graph below shows the cumulative charging and discharging of the battery since March 2021. Fitting trend lines to the data we see that on average we put 3.34 MWh of electricity into the battery each year – but only extract 88% of that i.e. 2.93 MWh/year.

Click on image for a larger version. The graph shows cumulative charging and discharging of the battery month-by-month since installation.

Plotting the charging and discharging data month-by-month shows up seasonal variations with the summer being a bit worse than the winter: I’m not sure why.

Click on image for a larger version. Graph showing the the monthly averages of the amount of electricity charged per day into the Powerwall 2 and discharged per day from the Powerwall 2 since installation. The battery is used more in the winter than the  summer but the decline in winter peak capacity is clear.

Click on image for a larger version. Graph showing the monthly round trip efficiency of the Powerwall 2 since installation. The red curve shows the average of the cumulative round trip efficiency.

I have not seen any other evaluations of Round Trip Efficiency but I am reasonably satisfied with the cumulative figure of 88%.

Capacity

The capacity of battery is an important parameter for a battery – but one that few people take time to measure. It answers the question:

If I charge my battery to 100% and discharge it to 0%, how much electricity (in kWh) is discharged?

I have charted the slow decline in the capacity of the Powerwall in a series of articles. The last article I wrote on this subject has links to the previous articles, and noted that Tesla had recently changed the software that controls the battery in way which was likely to extend the life of the battery (good) by reducing my ability to charge it fully! (not good).

Click on image for a larger version. Data gathered from winter days in which the Powerwall discharged from practically full to empty. The blue dots show all the data, and the pink circles around the  dots show days on which there was no solar re-charge. The large black circles show the seasonal average

The Powerwall guarantee states that it will retain 80% of its capacity (i.e. 13.5 kWh × 80% = 10.8 kWh) after 10 years. Based on the data above I think it will be close to that that in 2031.

However, even a 10 kWh battery is actually a useful size so it is not obvious that 10 years represents the useful lifetime of the system.

Is Electricity from the Powerwall Free?

No.

In the summer the proximate cost of electricity is zero – electricity is generated by the solar PV during the day and used to charge the battery – and the battery discharges overnight. But it’s not really free.

We should really take account of the cost of the capital tied up in the slowly-degrading battery. If we take the cost of the battery (~£10,000) and divide it by the number of kWh it will supply over its lifetime (say 30 MWh or 30,000 kWh) one comes up with a cost of about £0.33 per kWh.

So, far from being free, every kWh of electricity delivered by the battery is actually quite expensive! One might consider the battery cost as the pre-purchase of a large amount of electricity.

If the battery lasts longer and delivers more than 30 MWh then the allocated cost per kWh also comes down, but for my particular battery system the figure will be in that ballpark. For battery systems purchased now the cost is definitely lower and for some systems it might be approaching £0.10 per kWh.

I am comfortable with these relatively poor financial returns. When I installed the battery it was not clear to me that it would work at all! But in terms of reducing carbon dioxide emissions, the battery is big help.

• We use no grid electricity in the summer – and hence there are no proximate emissions. Of course we still benefit from the mere presence of the grid – enabling our society to function and acting as a back-up. This is one reason why I am happy to pay standing charges – I am still benefiting from the grid even when I am not personally using electricity from it.
• In the winter the battery allows us to operate the heat pump at low marginal cost – and the heat pump is the lowest carbon way to heat the house.

Financialistas would argue that instead of buying the battery I could have invested the money and used the interest to pay the electricity bills. But Carbonistas would point out that that would have done nothing to reduce carbon dioxide emissions.

When the battery eventually reaches its end of life, I am modestly confident that the materials will be able to be recovered, and that new battery systems will be better in almost every way. And cheaper.

Click on image for a larger version. the site of an appalling gas explosion in South London in 2022. (link)

Friends, I asked Google “Are gas explosions in the UK common?“. Google told me:

“Gas explosions in the UK are rare, despite high-profile media reports, because of stringent safety regulations for the 23 million domestic gas connections. While serious incidents do occur, usually caused by leaks or unserviced appliances, they are not considered common occurrences relative to the total number of homes, though there have been roughly 12 fatalities in residential explosions in recent years.” (Link)

Another source (link) suggests there are typically “over 25” significant explosions per year.

So twelve fatalities over the last few years and 25 serious explosions per year – including appalling events such as the one pictured at the head of the article. Additionally one in six homes contain unsafe gas appliances (link) and poisoning by carbon monoxide is likely much more common than is acknowledged (link).

The National Institute for Health and Care Excellence (NICE) state that (link):

• Carbon monoxide poisoning is an under-diagnosed problem.
• The signs and symptoms of low-level carbon monoxide toxicity are often non-specific and simulate other common conditions, such as flu-like illness, food poisoning, or depression. As a result, carbon monoxide poisoning may be misdiagnosed.
• There are ~ 4,000 attendances at accident and emergency departments in England each year for treatment of carbon monoxide poison
• There are ~ 440 hospital admissions per year in England due to carbon monoxide poisoning.
• In England and Wales, approximately 40 deaths are reported each year due to carbon monoxide poisoning.
• Poisonings in residential locations, due to faulty piped gas appliances with inadequate ventilation were the place, source, and underlying reason for most accidental, non-fire related, carbon monoxide poisoning fatalities in England and Wales (1998 to 2019).

What should be an appropriate response?

Imagine if all these consequences were caused by something else? Let’s call it X. Imagine that X caused 25 explosions per year resulting in several deaths and 10 hospital attendances per day from poisoning resulting in 40 deaths per year.

Now imagine further that widespread use of X additionally created a persistent environmental harm, and reliance on X represented a grave national security issue.

Would we just shrug our shoulders? Would we pretend that this wasn’t an issue? At a very minimum we would say that regulations were not working and seek to phase out or ban X. And we would view companies seeking to promote use of X as evil and scandalous corporations looking to line their pockets while ignoring the deaths and harm their product caused.

Friends: the use of gas for heating and cooking should be phased out at the earliest opportunity. In the future we will look back and consider the fact that we once burned gas in our homes as sign of how utterly primitive we once were. It is long past time that we moved on.

Friends, Climate Sensitivity (CS) is the technical term for the answer to the question:

“If we double the concentration of atmospheric carbon dioxide, by how much will the surface temperature of the Earth change?”

It’s a question to which we would all like to know the answer. But, perhaps surprisingly, the answer remains uncertain.

One aspect of the uncertainty arises from the question of how long we wait after making the change before measuring the warming. For example, if we changed the heating setting in a house we would understand that it might take a few hours, or perhaps a day or two before a new stable temperature was reached.

One component of the heating of the Earth arises from the carbon dioxide in the atmosphere. If we could – miraculously – keep the level of carbon dioxide stable at its current level, then scientists are reasonably confident that the Earth would equilibrate at a new temperature, around 1.5 °C above the industrial value. This would take typically a few years – perhaps a decade. But there is a caveat.

The climate system is big, involving almost inconceivable amounts of water and ice. So, for example, ice sheets and glaciers can’t be formed or destroyed in a single year or even a single decade: they take centuries or millennia to adjust their extents to match changed climates. So if we stabilised carbon dioxide concentrations at their current level, global temperatures would likely stabilise within a few years – but there could possibly be a long tail of very slow responses to our new changed climate.

Two Components of Climate Sensitivity

Estimating Climate sensitivity is not easy. What drives global warming is an imbalance between the rate at which solar radiation reaches the Earth from the  Sun, and rate at which infrared radiation is radiated into space. As shown in the graphic below, when the rates of heating and cooling are equal, then Earth’s temperature is stable.

Click on image for a larger version. The surface temperature of the Earth is determined by a balance between rate at which sunlight warms the  Earth, and the rate at which the Earth radiates that heat (as infrared radiation) into space. When the two rates are equal, the Earth’s temperature will be stable.

Conceptually there are at least two steps in the calculation of Climate Sensitivity:

• By much does a change in the concentration of carbon dioxide affect the radiant energy balance (or imbalance)?
• By much does a change in radiant energy balance (or imbalance) affect Earth’s surface temperature?

Currently, the imbalance (as measured by satellites) is a few watts per square metre and growing. This imbalance sounds small but evaluated across the Earth’s 500 million square kilometres it is immense.

Click on image for a larger version. Figure from a paper by Mauritsen et al (Earth’s Energy Imbalance More Than Doubled in Recent Decades) discussing measurements of Earth’s energy imbalance. The graph shows the measured change in energy imbalance estimated from satellite measurements. The grey bars indicate years in which there have been El Niño events.

In order to estimate Climate Sensitivity we need to additionally estimate by how much Earth’s temperature will change in response to the radiation imbalance.

So far, the surface temperature of the Earth has increased by roughly 1.5 °C compared to the pre-industrial era. So doing some simple mathematics one can say that if a 50% increase in carbon dioxide concentrations has resulted in 1.5 °C of warming then the climate sensitivity might be very roughly double that – in the region of 3 °C/doubling.

Historic estimates of Climate Sensitivity

The first quantitative estimate of Climate Sensitivity was made by Arrhenius in 1896. He estimated that if the concentration of carbon dioxide in the atmosphere doubled from 300 parts per million to 600 parts per million, then the Earth’s surface temperature would increase by approximately 5.5 °C.

Click on image for a larger version.  Graphical representation of calculations by Arrhenius in 1896.

In 1937, Callender addressed the same problem and thought the sensitivity would be lower – perhaps just 2 °C – for a doubling of the concentration of carbon dioxide.

Currently, the International Panel on Climate Change estimates that Climate Sensitivity is about 3.0 °C and is “…likely in the range 2.5°C to 4.0°C, and very likely between 2.0°C and 5.0°C…”.

So over the 130 years since Arrhenius’s original estimate, our calculations have increased in complexity by many orders of magnitude but it seems that early estimates were more or less in the right ball park.

A recent posting by Professor Ed Hawkins reviewed how predictions of Earth’s temperature rise made 15 years ago were doing. The posting is technically complex, but overall the predictions made 15 years ago appear to have slightly underestimated the warming i.e. the climate appears to have warmed slightly more than anticipated. But more or less, the estimates of Climate Sensitivity appear to be about right, at least when considered on a time scale of a decade or so.

Click on image for a larger version. Two figures pasted together from an article by Professor Ed Hawkins. He looked at how the predictions for global temperature made in 2013 (upper graph A) compared with the actual change in global temperature (lower graph B). Actual temperatures appear to be at the upper end of the predicted range.

Equilibrium Climate Sensitivity.

But as a I mentioned earlier, the key question is really over what period should we evaluate Climate Sensitivity (CS)?

What drives climate change is an imbalance between the rate at which solar radiation reaches the Earth, and rate at which infrared radiation is radiated into space. Only when these two quantities are in balance will the Climate System and Earth’s temperature begin to stabilise.

And that means that even if we stop emitting now and the atmospheric concentration of carbon dioxide stabilises, then as my hero James Hansen argues, – in contrast with the IPCC – we still have global warming “in the pipeline”. He argues that this has not been taken account of in the IPCC estimates and – looking at paleo-climate data from recent inter-glacial periods – he suggests that the Equilibrium Climate Sensitivity is around 4.8 °C for a doubling of carbon dioxide concentration – at the very upper end of the IPPC estimate.

We have currently increased carbon dioxide concentration in the atmosphere by 50% and it’s hard to see how – even in the most optimistic perspective – we will avoid doubling carbon dioxide concentrations to around 600 ppm some time in the latter half of this century.

If the equilibrium climate sensitivity really is 4.8 °C, then we are condemning our children and grandchildren to live in a world which is unimaginably different from the world in which we live now. Sea level rise – although slow – will make the destruction of London and other major coastal cities inevitable. It will take a few hundred years, but there will be nothing our children can do to stop it.

This may seem like hyperbole, but it is not. At the peak of the previous ice age around 20,000 years ago, Earth’s average temperature was just 5 °C lower than the pre-industrial value, and sea levels were lower than they are currently by 140 metres. A world which is 4.8 °C warmer than now would likely have no ice sheets or glaciers and sea level would be likely be around 60 metres higher than now. This rise would not happen overnight. It would take centuries extending into millennia: but it would be inevitable.

Inevitable? Yes. We have no way of lowering carbon dioxide concentrations in the atmosphere. I wrote previously about what a scheme to reduce concentrations by 1 billion tonnes a year (around 3% of current annual emissions) might look like: it was at the very edge of the conceivable. And even if we did manage to lower carbon dioxide concentrations, it is not clear that the Climate system would re-stabilise as we would hope.

Another recent article looked at geological estimates of the relationship between atmospheric carbon dioxide and global temperature over much longer timescales than considered by Hansen. These estimates are very hard to make and subject to considerable uncertainty. Nonetheless, the analysis suggests that very long term Climate Sensitivity of Earth is closer to 9 °C for a doubling of carbon dioxide concentration.

How to react?

Friends, I wish I knew. In honesty I find it disheartening and want to look away. I want to focus on a world in which solar power and heat pumps can save the day.

Perhaps I am suffering from climate over–sensitivity, but the prospect – or even the risk of the prospect – of committing our children and grandchildren to an Earth warmed by 3.0 °C, or  4.8 °C or – heaven forbid – by 9 °C is sickening to me: these are civilisation-ending outcomes. I just can’t understand why so few people are as affected by this as I am.

===============

P.S. Doubling?

You may be curious about why climate sensitivity is expressed in this way. Why don’t we just specify how many degrees Celsius of warming arise from each additional ppm of carbon dioxide concentration?

The answer is that in a simple analysis, the amount of warming per ppm of carbon dioxide changes depending on how much carbon dioxide there already is. But doubling the concentration of carbon dioxide has roughly the same effect independent of the original concentration – you can see this in the graph of Arrhenius’s calculation above. So for example, we might expect that doubling carbon dioxide concentration from 150 ppm to 300 ppm would have the same effect as doubling carbon dioxide concentration from 300 ppm to 600 ppm.

Friends, the other day I was reminded of the poem Sometimes by Sheenagh Pugh. It begins…

Sometimes things don’t go, after all, from bad to worse.

It’s a lovely poem and I have reproduced it in full at the end of this article. As Sheenagh Pugh herself makes clear, it is not about the good fortune that happens sometimes by random chance. She comments:

I think most people read it wrong. When read carefully, it says sometimes things go right, but not that often, and usually only when people make some kind of effort in that direction. So it isn’t blithely and unreasonably optimistic.

I try not to be blithely and unreasonably optimistic, but I think it’s important to acknowledge when something good happens.

The occasion that put me in mind of the poem was a public meeting held by Richmond Council as they launched their “Smarter Homes Hub“. It’s difficult to know quite how all the Council’s plans will pan out, and as I’ll explain below, there are still plenty of problems. But it felt like something had changed for the better.

Smarter Homes Hub

The Council is in an odd position. It can declare a Climate Emergency and state that it wants the borough to be carbon neutral by 2043, but it has no power to compel its residents – who emit most of the carbon – to do anything. And it has very little money to incentivise them either. But it does retain the power to stop people acting.

So in my opinion the best thing that the Council can do is to reduce the uncertainty and trepidation that residents experience when they consider retrofitting. Richmond Council’s attempt at this is a “Smarter Homes Hub” – a web page and booklet that brings links to relevant resources in one place.

Below is an extract from the graphical interface on the opening page of The Hub.

Click on image for a larger version.

I won’t go into every category but I would like to look at just a few of the topics:

• Heat Pumps
• Solar Panels
• Ecofurb
• Retrofit Stories.

Heat Pumps

I was disappointed with this section. It says many sensible things but to me still lacks clarity and positivity.

Coincidentally, a friend sent me this Politico article which bemoans how hard it is to get a heat pump installed. The article is interesting because (a) I found the author’s complaints very familiar, (b) it mentions this blog (calling it “obscure but useful“) and (c) because it highlights the political significance of improving the  experience of having a heat pump installed. This is an area where the council can play a role.

For example, on stage at the launch event, a  member of the planning team stated that (if I recall correctly) for 99% of houses (not flats) in the borough, a heat pump would be a “permitted development” requiring no council permission or consultation. Why doesn’t the text begin with that assertion? Here’s some possible text.

Installing a heat pump is probably the most significant step most people can take to reduce emissions of carbon dioxide and the council support the installation of heat pumps in every home in the borough.

The council is aware that people have worried about planning permission, but our planning team have determined that for 99% of houses in the borough, installation of up to two heat pumps (!) is a permitted development i.e. the  council doesn’t need to be involved. Your installer will sort out the details for you.

The remaining 1% of houses are probably “listed” and they too can have a heat pump, but understandably there may be restrictions about placement. The Council will work with residents to find a solution.

Instead one finds bland text and when one looks up the linked planning page one finds the usual long of list of conditions all of which strike fear and doubt into the heart of civilians. They gratuitously describe the garden of a home as its “curtilage”. Really? Use of this kind of arcane terminology communicates to readers that they are venturing into a land where ordinary English is not spoken and where their ordinary appreciations do not matter.

As the Politico article makes clear, installing a heat pump is not as straightforward as it should be even for the keen and willing. And the Council need to replace the fear, uncertainty, and doubt in the minds of potential installers with unequivocal reassurance, certainty, and support.

Solar Panels

I was disappointed with this section too. As with heat pumps the text is worthy and full of details but lacks a key message. For example, one does not find out until the very end of the very long web page that the Council is offering a £500 subsidy towards the installation of Solar Panels! Here’s a suggestion for revised text.

If your house has roofs facing East, West or South then solar panels offer the opportunity to generate free electricity, maintenance free, for 25 years. A typical South facing installation will generate around 4,000 kWh per year while East or West facing systems will generate only around 3,000 kWh/year but they will do so at times when home owners are more likely to be able to make direct use of the energy themselves and when the grid electricity prices are higher.

The Council fully support the installation of solar panels on all homes in the borough and will offer a £500 subsidy for the installation through their trusted solar installer Make my House Green. Google Maps makes most surveys simple, so why not contact Make My House Green right now and see if your home is suitable. 

(Edit 19/3/2026: The underlined text was added at the  suggestion of a reader: see comments for more details.

EcoFurb

This is a genuinely interesting development. EcoFurb offer a service which will survey homes and advise on a full range of possible retrofit options. It addresses one of the most profound difficulties for people trying to retrofit their own homes: where to start? Friends, I have a PhD in Physics and experience in processing data, but even I found the process daunting. I can quite see that people will be willing to begin changing their home but just be paralysed by indecision.

Ecofurb offer an on-line analysis tool which I think looks up MCS records of past work and any EPCs to make a guess at a what a home might need. When I used it, the tool was a bit a hit and miss, but even so I think it’s a great idea because it suggests specific installations and estimates costs. Having a cost estimate in advance helps people to gauge their expectations.

Ecofurb also offer a full survey which I guess costs several hundred pounds, but which offers more tailored options. They also offer advice on installers another difficulty that stymies people eager to get work done.

I will certainly be suggesting people take a look at this service, and I hope it will prove to be as good as it seems.

Retrofit Stories.

For me, the most welcome section of the site was the retrofit stories section. I had written about some of these residents previously and but the Council have made videos that portray them and their choices in a powerfully positive light. Yes, it’s propaganda. But it’s pro-paganda in the face of a tidal wave of “neg-aganda” about the misery of life with a heat pump.

I’ve linked to the videos at the end of the  article. I believe that when people see people like themselves living happily in homes like theirs, it plants within them a seed of idea that change for the better is possible

So briefly, I am allowing myself the indulgence of hoping that things at the Council will not, after all, go from bad to worse.

‘Sometimes’ by Sheenagh Pugh

Sometimes things don’t go, after all,
from bad to worse. Some years, muscadel
faces down frost; green thrives; the crops don’t fail.
Sometimes a man aims high, and all goes well.

A people sometimes will step back from war,
elect an honest man, decide they care
enough, that they can’t leave some stranger poor.
Some men become what they were born for.

Sometimes our best intentions do not go
amiss; sometimes we do as we meant to.
The sun will sometimes melt a field of sorrow
that seemed hard frozen; may it happen for you.

Videos

Video 1

Video 2

Video 3

Friends, as I wrote previously, Ripple went bankrupt last year. But fortunately the Kirk Hill Wind Farm which it begat, and of which I own one seventeen thousandth part (~0.006%) had already been spun out of the main venture. And so it lives on! Things have been chaotic since the demise of Ripple, but the wind farm itself has still been generating and I just thought I would note here what that means for me, personally.

Before I start going on about kilowatt hours, I would just like to record my gratitude to the people within the co-operative who have stepped up to bring order to the chaos after the collapse. They are using skills and perspectives that I lack almost completely – and I am very grateful. One result of their endeavours is that it looks like the money that the wind farm has been earning will begin flowing again eventually. But a second result of their work is that we now have access to data on generation from the wind farm over the last year. So here are some graphs…

Podesta Towers

At Podesta Towers in Teddington we use around 6,100 kWh of electricity per year for all purposes, including heating. I wrote previously that one kilowatt hour is roughly the amount of work that an adult human can do in a day. So somehow the way my wife and I live relies on a truly phenomenal amount of electrically-powered assistance.

Solar generation (over the last three years) has amounted to a staggering 5,700 kWh/year, of which about 35% is used directly in the house, around 25% is stored in the battery for later use, and around 40% is exported to the grid.

Click on image for a larger version. Cumulative solar generation during the last three years. Also shown is my expectation for 2026 which is based on data up until today and then extrapolated as the average of the previous three years as a dotted line.

So average solar generation falls about 5% short of our annual usage. Obviously, we are over-supplied in summer and under-supplied in winter. Plotting cumulative solar generation and cumulative use since the start of 2024 the data looks like this:

Click on image for a larger version. Cumulative solar generation since the start of 2024 shown alongside cumulative electricity use in our home.

The trends in consumption and production for the last two years are very similar – but 2025 was a spectacular year for solar generation.

Podesta Towers+ Kirk Hill

Wind generation peaks in winter and my hope was that the roughly 3,000 kWh/year of generation that I purchased would “fill in” the shortfall in solar generation at Podesta Towers. Generation from Kirk Hill began in April 2024 and here is how the actual generation has added to solar generation….

Click on image for a larger version. Cumulative solar generation from Podesta Towers since the start of 2024 shown alongside cumulative wind generation from Kirk Hill, wind farm.

It’s clear that 8,780 kWh/year is a lot of generation. Here’s how it compares with our cumulative consumption.

Click on image for a larger version. Cumulative solar and wind generation since the  start of 2024 shown alongside cumulative electricity use in our home.

So cumulative generation from our home-based solar and our share of the Kirk Hill wind farm is outpacing consumption. However even now, in winter, there are around 4 months in which generation does not exceed consumption.

Click on image for a larger version. Graph shows monthly averages (expressed as kWh/day) of consumption at Podesta Towers, and renewable generation (wind and solar). Wind generation only began in April 2024, and one can see that the periods of the year in which consumption exceeds generation (shaded in grey) have been reduced significantly.

Carbon dioxide emissions

Friends, unless you are just chasing money, the only point in undertaking any of these actions: installing solar or buying a fraction of a wind farm: is to reduce carbon dioxide emissions.

The graphs above show that overall, my wife and I are responsible for around 8,780 kWh/year of renewable electricity generation and consume around 6,000 kWh/year of electricity, of which around 3,000 kWh comes from the grid.

Click on image for a larger version. Graph showing cumulative consumption of electricity from the grid during the course of the year for the  last 4 years. Notice that we have low or zero grid consumption in the summer months. Over the course of a year, cumulative consumption amounts to roughly 3,000 kWh.

Using a carbon intensity figure for grid electricity (link) of 0.18 kgCO2 per kWh, our household emissions amount to around 3,000 × 0.18 = 540 kg CO2 annually. If we add together the roughly 3,000 kWh of generation from Kirk Hill and the 2,400 kWh of solar export from the roofs of Podesta Towers one arrives 5,400 kWh of export. At the same carbon intensity this amounts to around 972 kgCO2 of emissions avoided. (I could argue that the figure for emissions avoided is a considerable underestimate because it avoids emissions primarily from gas-fired power stations, but that’s an argument for another day.)

Comparing 540 kgCO2 emissions with 970 kg CO2 emissions avoided, one might be tempted to say we have negative emissions of carbon dioxide. No.

If at any point during the year one consumes electricity from the grid, then carbon dioxide is emitted into the atmosphere and *nothing* you do can remove that carbon dioxide from the atmosphere. That carbon dioxide will warm the Earth for at least the next thousand years or so. If we additionally generate renewable electricity that avoids emissions by other people, that’s great. But it still does not remove the carbon dioxide from that we emitted from the atmosphere. Accountants can balance actual emissions with avoided emissions, but physicists can’t. And the planet only sees what’s in the atmosphere.

As an analogy consider the case of a murderer: their victim is dead forever. Nothing that the murderer subsequently does can bring that person back. Even saving the life of another person will not bring the dead person back. And so it is with carbon dioxide: once emitted, carbon dioxide cannot be removed from the atmosphere. Avoiding further emissions is a valuable thing, but it still does not reverse the effect of the previous emissions.

I say this not to be negative, but to be realistic: this is the reality we face: all CO2 emissions just make things worse.

But even with all these caveats, the results I have described here are not a bad outturn for your averaged semi-detached tower in Teddington. And I honestly don’t know how to do more!

I wish you good luck in your endeavours.

Friends, back in the olden days (2012), I wrote a blog story about Brownian motion that featured a video (above) made by my colleagues at NPL. Observations of this so-called Brownian motion – when quantified – were the basis for the Nobel Prize in Physics award to Jean Perrin 100 years ago in 1926. Summarising greatly – it was part of his demonstration that atoms really existed – amongst the most profound discoveries that human beings have ever made.

Back in 2012, the experimental apparatus for observing Brownian motion required a great deal of expensive kit  and was very tricky to set up. But it turns out that in the same way that conventional photography has been transformed by digital cameras, the same has also happened to micrography – it is now much easier than it used to be.

Click on image for a larger version. My two microscopes. On the left is a simple microscope with the screen showing the dial of my watch. On the right is digital microscope with 4 different lenses showing a sliver of the stem of a carnation flower. Both microscopes can take photographs or movies with ease, or be configured as USB “webcams”.

Recently I have had a hankering – perhaps even a yearning – to do this experiment for myself. The moving particles in Brownian motion needed to be around one thousandth of millimetre in diameter (0.001 mm), or one micrometre. This is often referred to informally as “one micron”. I had no idea what sort of instrument I needed and so I bought one microscope and then another and set about seeing what I could see when I looked down them. In this article I will tell you about my adventures and share some pictures and videos.

The Microscopes

The first microscope I tried was advertised as a “Coin Microscope” with a magnification of ×1000 and cost £27. This is a perfectly pleasant item, but quite unsuited to the task at hand. The specification “×1000” is utterly meaningless. The more appropriate specification is that the field of view is 7 mm × 4 mm which can be viewed at a high resolution on the built-in screen or via photographs or movies captured on a memory card. Optimistically particles 1 micron in diameter would be visible at best as a single pixel.

The second microscope, made by AmScope, looked much more like “a proper microscope”.  It had 4 lenses with magnifications of  ×4, ×10, ×40, and ×100,  and cost around £217 (there’s a discount if you sign up to their newsletter). I was extremely impressed with the microscope. The screen was large and bright and there were basic instructions printed on the microscope body – and detailed settings available on the screen.

The specification of the  magnification was not particularly meaningful to me – what I wanted to know was the field of view. So I bought a microscope calibration slide (£9) and took some photographs on the different magnifications. I measured the full field of view to be:

• ×4 lens: 2.8 × 1.55 mm
• ×10 lens: 1.12 × 0.64 mm
• ×40 lens: 0.28 × 0.16 mm
• ×100 lens: 0.11 × 0.06 mm

The photographs below show the relative fields of view covered by the different microscopes and lenses. It is clear that the AmScope gives access to phenomena on a wholly different scale than the coin microscope.

Preparing Samples

The Reverend Brown’s original observations were made in 1827 using particles from various sources which he estimated to be between 1.3 and 6 micrometres in diameter. Some samples were pollen grains from various plants and mosses, and some were minerals, including a sample derived from a fragment of The Sphinx.

Nowadays it’s possible to purchase solutions of plastic or glass spheres that are mono-dispersed i.e. the diameters of the spheres are closely similar. But there are two cheaper alternatives: homogenised milk and graphite powder. Homogenised milk contains spherical fat globules that are reasonably uniform in size and just a few thousandth of millimetre in diameter. Graphite powder – used as a lock lubricant – contains flakes of a wide range of sizes.

It turns out that it is not so hard to observe Brownian motion using the AmScope, but sample preparation can be tricky and there are several pitfalls into which beginners to microscopy might stumble. However the use of the digital screen rather than an eye-piece is transformational in making the instrument easier to use. In case you want to have a go at this and have as little prior knowledge as me, here are my tips.

• First of all, don’t be in a hurry.
• To view anything using the AmScope, it needs to be placed on a 25 mm × 75 mm piece of glass called a microscope slide.
• To view the milk, dilute some homogenised milk by about 10:1 with water and place a tiny drop in the middle of the slide. You can try it undiluted but the images will be very “busy”
• Cover the drop with a microscope cover glass – a piece of spectacularly thin glass, 25 mm × 25 mm square. The liquid will squish out to cover the entire are of the cover glass. If any liquid squeezes out the side, you probably used too much.

• Place the slide and cover glass under the microscope on the lowest power lens (×4). Check that the microscope slide is in roughly the right place and use the x- and y- adjusting knobs to move it roughly into place.
• For looking at milk select the lighting to come from below and slowly adjust the focus until you see something that looks interesting.
• The depth of focus of all the lenses is very shallow, so it is quite possible to focus on just (a) the top of the cover glass, (b) the bottom of the cover glass, (c) the top of the microscope slide or (d) the  bottom of the microscope slide. The milk solution will be trapped in between (b) and (c).

Using graphite powder is a little trickier than using milk because the particles are very different in size and clump together, and they are not even approximately spherical, instead forming flakes. But this property allows for an interesting and in my estimation, beautiful, visualisation. One illuminates the sample from above, and then occasionally a graphite flake will be jiggled enough to twinkle – reflecting the illumination back into the lens.

To prepare the sample, I squeezed some graphite powder into water with a drop of detergent to allow the water to wet the powder. I then picked up a drop of the suspension with just a few flecks of graphite visible.

One limitation of the AmScope is that the illumination from above is not delivered through the lens, and so when using the ×40 and ×100 lenses, the lens body actually blocks out the light. Nonetheless, I like the images.

Results.

Friends, I did consider getting a bit numerical, but I am such a dilettante that instead I just made a video showing how I prepared the samples and showing what I could see. Enjoy.

Friends, if you have hankered – or even yearned – to peek at the microscopic wonders all around us then I can strongly recommend the AmScope model that I used. I also bought some pre-prepared slides with examples of natural samples such as stems of plants or parts of insects. The natural forms one observes are profoundly beautiful and humbling. Just take a look at the staggering pictures below showing a slice through the stem of a carnation.

We really do live in a world of transcendental beauty.

Other people’s YouTube videos about Brownian motion

Alom Shaha

Steve Mould

Friends, I still encounter a lot of people who think that Climate Change is not actually happening and consequently they see policies that seek to reduce the impacts of Climate Change as an unjustified imposition. Indeed many people feel extremely indignant and are outraged by policies that can be broadly described as “Net Zero”.

I have no doubt that people with these beliefs are well-intentioned – most people are. But from my point of view, this absolutist denial of reality can make it hard to find a point at which we can begin to engage in a conversation.

I have found that in the face of such an impasse, it can be helpful to re-focus attention onto the early history of humanity’s study of the Earth’s temperature. Considering only work carried out between 1800 and 1900 takes some of the political heat out of the discussion.

Previously on this channel…

I have written previously about several of the pioneering discoveries in the nineteenth Century that laid the foundation for our understanding of Earth’s Climate. Most notable are:

• Arrhenius’s 1896 paper describing his calculation of the warming effect of increasing the concentration of CO2 in Earth’s atmosphere (link).
• Langley’s work in the 1880’s to measure the  temperature of the Moon. This involved a breathtaking experimental advance – the invention of the bolometer – that allowed him to measure infrared spectra and hence calculate the absorption of infrared light by the atmosphere (link).
• Tyndall’s truly astonishing discovery in the 1850’s of the absorption of infrared light by vapours and molecular gases (link).

These advances involved a combination of improvements in experimental techniques – notability the ability to measure infrared light – and progress in our understanding of the factors affecting the temperature of the Earth.

Today I would like to revisit the work of an even earlier pioneer: John-Baptiste Joseph Fourier

Fourier: 1827

Fourier (1768 – 1830) was a genius of the first order, and his contribution to our understanding the temperature of the Earth is one of his lesser known claims to fame, possibly because he got it (sort of) wrong!

At the start of his Magnum Opus: the Analytical Theory of Heat (1822) he suggests that he hopes to do for heat what Newton did for mechanics. You can read an English Translation from 1878 here. He writes:

His writings on the temperature of the Earth are based on applying the mathematical principles established in his analytical theory – a theory that has not been replaced in the 200 years since he established it!

He began by addressing the grand problem:

In his analysis, (2004 English translation) Fourier writes that there are three processes occurring simultaneously. In the extract below I have reformatted Fourier’s text with bullet points (Liste à puces).

Let’s look at each of these three processes in turn.

The first process: “The Earth receives the rays of the Sun, which penetrate its mass and are converted there into dark heat” is exactly in line with our modern conception. Fourier uses the phrase dark heat to refer to what we would call infrared light.

He understood that when there is a balance between incoming luminous heat from the Sun and the outgoing dark heat from the Earth, then the Earth’s temperature will be stable.

Click on image for a larger version.

The second process: “the Earth also possesses heat of its own which it retains from its origin, and which dissipates continually at the surface” is also exactly in line with our modern conception. Now we know that the interior heat of the Earth is partly primordial, and partly from radioactive decay of minerals within the Earth (Link).

Click on image for a larger version.

Fourier notes that the second process can be completely neglected compared with the first. He explains that we can estimate the rate of upwelling heat by measurements of the rise of temperature as we descend below the Earth (about 30 °C/km link).

In modern terms we would say that since the thermal conductivity of rock is about 3 W/m K then the upwelling heat flow is only 0.09 watts for each square metre of surface. In contrast, solar energy reaching the Earth’s surface (averaged over a year and all latitudes ) amounts to around 240 watts for each square metre of surface i.e. thousands of times larger than the rate of upwelling heat.

Fourier did not frame his explanation as I have above, because he lacked access to basic thermophysical data. Instead he said:

Click on image for a larger version.

Fourier considered that his analytical theory of heat could be applied in any situation, but the determination of the properties of materials, such as the thermal conductivity of rock or the transparency of the atmosphere was not his job! He considered that such investigations and discoveries were the work of Natural Philosophers.

The third process that Fourier describes is “this planet receives rays of light and heat from the countless stars among which the solar system is located…  the influence of the stars, is equivalent to the presence of an immense region closed in all parts, whose constant temperature is little inferior to that which we observe in polar lands.”

Click on image for a larger version.

In other words, Fourier reasoned that since the poles receive very little sunlight, and the rate of upwelling heat from the Earth was so small, then their temperature would be established by the temperature of the space just above the poles. Fourier reckoned this was around the temperature at which mercury freezes. This assumes that the atmosphere has no “insulating” properties – and this assumption is quite wrong.

The temperature of space is quite a difficult a concept, but if it means anything at all, then the answer is dramatically colder than -40 °C, more like – 270 °C or just 2.7 °C above absolute zero (an idea with which Fourier was probably not cognisant).

So Fourier scores 2 out of 3, which is not exactly genius level. But his genius emerges from the that fact he knew his ideas were not quite right and he also knew why! He knew it was do with the atmosphere.

The role of the atmosphere

Fourier wrote:

In modern terms we might call Fourier a theoretical physicist and he is pleading for experimental physicists to measure some phenomena against which he could test his theory. We might paraphrase his words, “…if only a Natural Philosopher would discover the properties of the atmosphere, then my analytical theory would be able to calculate the impact of those discoveries…“. And then he praises the work of de Saussure – a brilliant Natural Philosopher (aka experimental physicist) with achievements in many fields.  The achievement to which he is referring here is the invention of the heliothermometer – an apparatus to measure the intensity of the Sun’s radiation.

The  apparatus consisted of a wooden box covered with several highly transparent glass panes. The bottom of the box was insulated with blackened cork so as to absorb as much sunlight as possible and de Saussure reasoned that the temperature reached would be a measure of the intensity of the Sun’s radiation.

Click on image for a larger version. Left. A modern day re-creation of de Saussure’s Heliothermometer (link). Right: illustration of de Saussure’s experiment in the Alps.

de Saussure made measurements of the intensity of sunlight at different altitudes in the Alps and concluded that in a clear sky, sunlight travelling  downwards through the atmosphere was relatively unimpeded.

Fourier would have understood this. But he suspected that the same would not be true of infrared light travelling in the opposite direction. Early experiments of which Fourier might possibly have been aware, had concluded that some substances transparent to visible light were opaque to “dark heat” – most notably water and glass. He wrote:

These sentences confirm that Fourier understood that there had to be some way in which the “transparent body” (the atmosphere) impeded the passage of dark heat (infrared light) from the Earth’s surface to “exterior space”. But as he says clearly – what that mechanism is could not “yet be exactly defined”.

Fourier was exactly correct: there was a missing part of the puzzle. Fourier described the atmosphere as a “transparent body” but he could not have known that as regards infrared light – dark heat – the atmosphere is far from transparent. In fact – like water and glass –  it is practically opaque to infrared light.

It would take another 30 years or so until Tyndall found that the atmosphere absorbs infrared radiation. And then to his jaw-dropping astonishment, discovered that the absorption was not due the 99% of the molecules that constitute the bulk of the atmosphere, but due to the trace gases: water vapour and carbon dioxide.

Summary

Friends, I love Fourier’s article. His basic understanding of the mechanism by which the Earth’s temperature is maintained was exactly correct and clearly stated. It is striking to me how he clearly understood the  fundamental role of “dark heat” – infrared light – in cooling the Earth.

It would take the invention of a new type of thermal detector – the thermopile – before experiments on the  transmission of dark heat through the atmosphere would reveal the astonishing role of trace gases in regulating the temperature of the surface of the Earth.

Friends, before you contact my family and suggest that an intervention is required, please allow me to show you just a couple more heat pump graphs, this time using data supplied by a reader.

Dan Curran campaigns for his local Council (Kingston-upon-Thames) to adopt policies that are more friendly towards heat pump installations. He also writes a blog about his retrofit adventures (link) and was kind enough to allow me to describe his retrofit journey in an article I wrote last February 2025 (link).

Dan also enthusiastically monitors the performance of his heat pump and last week he sent me some data to plot alongside my own. Here’s the data he sent me plotted alongside the data I plotted in the previous article.

Graph #1

The graph below shows:

• the heat pumped daily (kWh/day)

versus

• the electricity consumed by the heat pump (kW/day)

for both Dan’s house (grey circles) and my own (red circles). Dan’s data is averaged over one day and covers the last two years. My own data is averaged weekly and covers the last 5 years.

Dan’s house is only a few kilometres from my own and so we can assume that the weather has been similar. Dan’s house is larger than mine with less insulation, but he and his wife like to keep it relatively cool at around 19 °C. Last winter my house was around 21.5 °C and this winter it has been a very stable 20.0 °C. So the data are broadly, but not quite exactly, comparable.

Click on image for a larger version. The graph shows the heat pumped daily (kWh/day) versus the electricity consumed by the heat pump (kW/day) for both Dan’s house (grey circles) and my own (red circles). Dan’s data is averaged over one day and covers the last two years. My own data is averaged weekly and covers the last 5 years. The black dotted line shows the trend of data for Dan’s house for average heating power above 4 kW.

The first interesting feature to note is the initial slope of the graphs. At heating powers up to around 4 kW – which for Dan’s house corresponds to an external temperature of around 7 °C – Dan’s data clusters around the COP = 5 line. In contrast, for low heating power, data from my home typically clusters around COP = 4.

To take a specific example, to deliver 72 kWh/day of heat (average heating power 3 kW)

• Dan’s home requires roughly 14.5 kWh/day of electricity (average consumption 0.6 kW).
• My home requires roughly 24 kWh/day of electricity (average consumption 1.0 kW).

In other words to deliver exactly the same heating power, Dan’s system requires 40% less energy. That corresponds to (another) exceptional installation by Your Energy Your Way.

At the high end of heating demand Dan’s house requires around 192 kWh/day – equivalent to a continuous heating power of 8 kW. This is well within the capability of the 12 kW Samsung heat pump installed. I was genuinely surprised that such a large house – without any special insulation – could be heated by just 8 kW – corresponding to only 3 kW of electrical consumption.

Graph #2

Of course the extreme demand rarely lasts for a whole week, so I also processed Dan’s data to plot weekly averages so that it could be directly compared to my own. None of the conclusions change and I present the graph below for completeness.

Click on image for a larger version. The graph shows the heat pumped daily (kWh/day) versus the electricity consumed by the heat pump (kW/day) for both Dan’s house (grey circles) and my own (red circles). Dan’s data is averaged weekly and covers the last two years. My own data is averaged weekly and covers the last 5 years. The black dotted line shows the trend of data for Dan’s house for average heating power above 4 kW.

Summary

The data from Dan’s house is interesting to view alongside my own. They are two very different houses both with what I consider to be excellent COPs when averaged annually. This year Dan thinks his annually averaged COP (SCOP) will be close to 4.5 whereas my own is likely to be closer to 3.8. But then as I have pointed out before, COP Envy is Pointless!

Friends, I know there are people who think that I think about heat pumps way too much. And they are probably right. But the other day I thought of a new way to plot heat pump performance that was so obvious I could not think why I wasn’t doing it already.

Allow me to explain.

The idea: Energy delivered versus Energy consumed

Why wasn’t plotting I already plotting a graph showing the heat delivered as a function of the electrical energy consumed?

Click on image for a larger version. Graph showing the amount of heat produced by a heat pump versus the amount of electricity consumed. This seems like an obvious way to present heat pump performance.

On this graph, if the heating power delivered to my home was exactly equal to the electrical power – as would be the  case for an electrical heater (or indeed any electrical appliance) – then the data would cluster around the line marked “COP = 1” in the above graph.

So what do the data for my house look like when plotted this way? Over the last 5 heating seasons I have so far collected 235 weekly readings of electricity consumed and heat delivered.

Click on image for a larger version. Graph showing the amount of heat produced by my heat pump versus the amount of electricity consumed. The  graph is described in detail in the text below.

The graph is complicated so I’ll talk you through it.

• Each green dot represents the data for one week. This represents the energy consumed and the heat delivered for both space heating and production of domestic hot water. The green-dotted line is a quadratic fit to the data forced to go through the origin.
• The pink-dotted lines represent COP values from 1 to 5.
• The horizontal black-dotted lines represent different average heating powers
  • 1 kW average heat corresponds to an average external temperature of ~12 °C
  • 2 kW average heat corresponds to an average external temperature of ~7 °C
  • 3 kW average heat corresponds to an average external temperature of ~2 °C
• The vertical blue-dotted line represents an average electrical power of 1 kW
  • Shockingly, one can see that my 162 m^2 house can be heated and hot water provided using less electrical power than a typical hairdryer.

The data cluster into three regions.

• At medium heating power, the data cluster along the COP = 4 line . This represents performance in spring and autumn.
• At higher average heating power, the data move from the  COP = 4 line to the COP =3 line. This represents performance in winter.
• At the lowest heating powers the data cluster close to the COP = 2 line. This represents performance in summer.

The summer performance can be seen more clearly in the zoomed-in version of the graph below. This corresponds to the production of domestic hot water only with an average electricity consumption of less than 100 W. The stand-by consumption of the heat pump when it is not operating is about 20 W.

Click on image for a larger version. “Zoomed-in” section of the previous graph showing the behaviour of the  heat pump in summer when it is mainly producing just domestic hot water.

Replacing the radiators

I can separate the data into data taken with the original radiators (green dots) and data taken after the radiators were replaced in October 2024 (yellow dots).

The graph shows that the new radiators do make a small difference. Looking at the trend lines on the coldest days, the new radiators allow the delivery of 3 kW of heating power using approximately 22 kWh/day (i.e. 0.92 kW) of electricity rather than the 24 kWh/day (i.e. 1.0 kW) of electricity with the old radiators i.e. a saving of around 8%. This is all worth having – but probably not worth the cough thousand pounds I spent on the radiators.

Summary

Each Saturday as I read the meters, I will now add this graph to the two other ways in which I view the data.

The first is the graph of COP and heat output (kWh/day) versus time.

Click on image for a larger version. The chart plots the weekly-averaged heating power (expressed as kWh/day) in blue against the right-hand axis versus the week of the year. The text in blue shows the number of kWh of heat delivered in each heating season (measured from August to July). Also the weekly-averaged COP is shown  in red against the left-hand axis also plotted against the week of the  year. The text in red and the dotted red line shows the seasonally averaged COP (SCOP) for each heating season (measured from August to July).

The second is a graph of COP versus heat output (kWh/day).

Click on image for a larger version. The chart plots the weekly-averaged COP versus the weekly averaged heating power (expressed as kWh/day) for each of the last 5 heating seasons.

These graphs all show the same data. But somehow each one gives a slightly different insight into the engineering miracle of heat pumps.