Archive for June, 2021

COVID 19: Wave#3

June 29, 2021

Click for a larger image. Logarithmic graph showing positive caseshospital admissions and deaths since the start of the pandemic. The blue arrows show the dates of ‘opening’ events. See text for further details. The red and blue dotted – – – lines show similarities and differences between the start of Wave#3 and Wave#2.

Friends, do you remember the good old days when the control of deadly infectious diseases was considered a matter of public health? Sadly, we are not living in those times.

25 days ago

On 4th June I wrote:

“I am reluctantly concluding that – as they did last summer – the government are about to screw things up.

I don’t think [Wave#3] can kill ‘hundreds of thousands’, but it could easily kill ‘thousands‘ and cause serious illness in many more.

I estimated that

by the end of June we would exceed 10,000 new cases per day and approach 40,000 per day at the end of the school term“.

I then pointed out that aside from more death and serious illness and we would be rolling the variant dice. I then concluded:

“the recommendations [on what to do] were … obvious, but that writing them down was pointless, because the Government just doesn’t care!


Today (29th June) my spreadsheet tells me that the weekly averaged figure for new cases is 17,877 rather than 10,000. And it looks like at the end of the school term (~20th July) the figure could approach 100,000 positive cases per day rather than 40,000.

Currently cases are rising as rapidly as they did last summer which indicates that the virus is spreading easily in the non-vaccinated population.

The data on hospital admissions do not yet show a strong rise. But if we reach 100,000 positive cases per day it seems inconceivable that there will not be a significant extra burden on the health service.

The death rate is currently 17 people per day and rising at the same rate as it did last summer. The vulnerable population is probably not large enough to allow rates of 1000 deaths per day as in Wave#2. But it could plausibly reach 100 per day – i.e. 3000 deaths per month.

So should we abandon all restrictions on July 19th?

The normal death rate in the UK is about 1% of the population per year, or roughly 1700 people per day.

So death rates from COVID-19 of 10 or 20 people per day are not a great societal strain in themselves.

But being an infectious disease, COVID-19 has the capability to increase exponentially in prevalence and cause harm – sometimes in unforeseen ways.

Vaccination of 66% of the total population (1 dose) has limited the harm which can be done, but the virus is currently spreading freely amongst the 33% of the population (around 20 million people) who are unvaccinated. That is a lot of people.

I think removing restrictions in July will make almost no difference to the growth rate of viral prevalence, because I don’t think current restrictions are having very much effect. I could be wrong.

For me the question is whether there should be extra restrictions now because we are unsure of the harm to which are committing ourselves.

The government’s proposal that their policies are irreversible is truly Cnutian, implying that somehow they have dominion over the virus. I wonder if it knows.


I think we should take action now to avoid death rates of 100 people per day i.e. 3000 people per month, together with an unknown burden of long-term ill health.

In two months, vaccination levels could reach 90% and this point – when the viral prevalence was decreasing rather than increasing – would be a suitable point to remove restrictions.

Damaged as we all are by the pandemic, and impoverished as many people and businesses have been, I think think keeping mask-wearing and social distancing for a couple more months would be reasonable.

Allowing unrestricted mixing in the UK will create a viral breeding ground which could easily create new variants which could potentially allow viral escape from the vaccine. This is something we have seen often enough to know that it is not just a theoretical possibility.

And while 66% vaccination may reduce harm in the UK, there are many countries with a lower vaccination rate. For those countries it would be madness to allow unrestricted travel from the UK while the viral prevalence was approaching the same levels seen at the height of Wave#2.

But I know the government are not listening to me, or sadly their advisors. Individually they appear to be utterly venal, incompetent and corrupt, and collectively they appear to be in hock to a group of right-wing ideologues who are in denial about the harms caused by the virus. Despair is always an option.

The World Set Free

June 26, 2021

I recently re-readThe World Set Free” by H.G. Wells, a book which has a decent claim to being the most influential work of fiction of the 20th Century.

Written in 1913, a central theme of the book is that access to energy is central to the advance of global civilisation.

In the prologue, he imagines early humans wandering over the Earth and not realising that, first coal, and then later nuclear fuel, was literally under their feet.

Rendering of the gigantic planned SunCable solar farm. Copyright SunCable.

I had revisited the text because I realised that Wells had ignored the energy in the sunlight falling on the Earth, of which we require just 0.01% to power our advanced civilisation.

And so now, we can simply collect the largesse of energy that falls on the Earth everyday.

But it is unfair to criticise a futurist for what they omitted – getting anything right at all about the future is hard.

But re-reading the book I realised that Wells’ imagined vision of the future has been – I think – profoundly influential. Let me explain.

The Most Influential Book of the Twentieth Century?

The book initially follows a scientist (Holsten) who uncovers the secret of what he calls “induced radio-activity” – allowing the controlled release of nuclear energy.

And eventually a world of atomic-powered planes and automobiles follows.

But the political institutions of the world remained archaic and unsuited to the possibilities of this new world.

And in a stand-off broadly following the divisions of the actual World Wars, he foresees a global war fought with atomic weapons – a phrase which I think he must have invented.

Fictional Atomic Bombs

Of course in 1913, atomic bombs did not exist. H G Wells envisaged them as follows.

“…the bomb-thrower lifted the big atomic bomb from the box and steadied it against the side [of the plane]. It was black sphere roughly two feet in diameter. Between its handles was a little celluloid stud, and to this he bent his head until his lips touched it. Then he had to bite in order to let air in upon the inducive. Sure of its accessibility, he craned his neck over the side of the aeroplane and judged his pace and distance. Then very quickly he bent forward, bit the stud, and hoisted the bomb over the side.

“Never before in the history of warfare had there been a continuing explosive… Those used by the allies were lumps of pure Carolinum, painted on the outside with un-oxidised cydonator inducive enclosed hermetically in a case of membranium. A little celluloid stud between the handles by which the bomb was lifted was arranged so as to be easily torn off and admit air to the inducive which at once became active and set up the radioactivity in the outer layer of the Carolinum sphere. This liberated fresh inducive and so in a few minutes the whole bomb was a blazing continual explosion.

Carolinum belonged to the beta group of Hyslop’s so-called ‘suspended degenerator’ elements, [and] once its degenerative process had been induced, continued a furious radiation of energy and nothing could arrest it. Of all of Hyslop’s artificial elements, Carolinum was the most heavily stored with energy and the most dangerous to make and handle. To this day it remains the most potent degenerator known. What earlier 20th Century chemists called its half-period was seventeen days; that is to say, it poured out half the huge store of energy in its great molecules in the space of seventeen days, the next seventeen days’ emission was half of that first period’s outpouring and so on…. to this day, the battle-fields and bomb fields of that frantic time in human history are sprinkled with radiant matter, and so centres of inconvenient rays

“A moment or so after its explosion began, [the bomb] was still mainly an inert sphere exploding superficially, a big inanimate nucleus wrapped in flame and thunder. Those that were thrown from aeroplanes fell in this state, they reached the ground mainly solid, and, melting soil and rock in their progress bored into the earth. There, as more and more of the Carolinum became active, the bomb spread itself out into a monstrous cavern of fiery energy at the base of what became very speedily a miniature active volcano. The Carolinum, unable to disperse, freely drove onto and mixed up with the boiling confusion of molten soil and superheated steam, and so remained spinning furiously and maintaining an eruption that lasted for years or months or weeks according the size of the bomb…

“Once launched the bomb was absolutely unapproachable and uncontrollable until its forces were nearly exhausted, and from the crater that burst open above it, puffs of heavy incandescent vapour and fragments of viciously punitive rock and mud, saturated with Carolinum, and each a centre of scorching and blistering energy, were flung high and far.

“Such was the crowning triumph of military science, the ultimate explosive that was to give the ‘decisive touch’ to war…

Actual Atomic Bombs

Of course almost every detail of the account above is wrong.

But qualitatively, it is spot on: a single weapon which could utterly destroy a city not just at the time of its detonation, but have effects which would persist for decades afterwards: the “ultimate explosive”

And critically, the book was read by Leo Szilard, a man with a truly packed Wikipedia page!

On September 12, 1933, having only recently fled Germany for England, Szilard was irritated by a Times article by Rutherford, who dismissed the possibility of releasing useful amounts of nuclear energy.

And later that day, while crossing Southampton Row in London, it came to him how one could practically release nuclear energy by making a nuclear chain reaction. He patented his idea and assigned the patent to the UK Admiralty to maintain its secrecy.

In the following years he was influential in urging the US to create a programme to develop nuclear weapons before the Germans, and so he came to be present in Chicago when Fermi first realised Szilard’s chain reaction on December 2nd 1943.

On seeing his invention work, he did not rejoice. He recalls…

“There was a crowd there and when it dispersed, Fermi and I stayed there alone. Enrico Fermi and I remained. I shook hands with Fermi and I said that I thought this day would go down as a black day in the history of mankind.

I was quite aware of the dangers. Not because I am so wise but because I have read a book written by H. G. Wells called The World Set Free. He wrote this before the First World War and described in it the development of atomic bombs, and the war fought by atomic bombs. So I was aware of these things.

But I was also aware of the fact that something had to be done if the Germans get the bomb before we have it. They had knowledge. They had the people to do it and would have forced us to surrender if we didn’t have bombs also.

We had no choice, or we thought we had no choice.

Was the book really influential?

Of course I don’t know.

But it is striking to me that by merely imagining that such terrible weapons might one day exist, and feasibly imagining the circumstances and results of their use, H.G. Wells placed this idea firmly into Szilard’s mind.

And Szilard was a man who – with good reason – feared what the German regime of the time would do with such weapons.

And so when recalling the first sustained and controlled release of atomic energy in Chicago, he immediately recalled H.G. Wells vision of a war fought with atomic bombs.


“The World Set Free” is fascinating to read, but it is not – in my totally unqualified opinion – a great work of literature.

The characters are mainly implausible, and the peaceful and rational world government Wells envisages would follow nuclear devastation might be better characterised by George Orwell. (Scientific American contrast Orwell and Wells’ ideas about science and society in an interesting essay here.)

By contrast, some of the plot twists are strikingly plausible. I was struck in particular when – after the declaration of World Government from a conference in Brissago in Switzerland – one single monarch held out.

In what might now be called “a rogue state”, a conniving ruler – “a Fox” – sought to conceal some “weapons of mass destruction”. After an attempted pre-emptive strike on the World Government was foiled, an international force searched the rogue state, grounding its aeroplanes, and a search eventually unearthed a stash of atomic bombs hidden under a haybarn.

Perhaps George Bush had been reading “The World Set Free” too!



How we experience climate change

June 24, 2021

One of the challenges of communicating around the topic of Climate Change is that it is simultaneously:

  • A profound threat to humanity.
  • Not currently obvious to residents of many parts of the world.

Worlds which are 2 °C or even 3 °C warmer will be changed in ways which are – in places – utterly disastrous for humankind, and which – in my opinion – threaten our advanced civilisation.

I am ‘all in’ for doing what we can do to minimise the harm to which we have already committed ourseves and our children.

But although evidence for climate change is ubiquitous to people who look for it, for people living in the UK, it can also be easy to overlook. Nobody has direct awareness of changes of annual average temperature of 0.02 °C a year.

Nonetheless, older people – a group of which I count myself a junior member – are aware that things have changed over their lifetime.

We have a sense that the frequency and intensity of extreme weather – events which catch our attention – has changed. For example many people think:

  • “There isn’t as much cold weather as there used to be.” Or
  • “There are more nights when it doesn’t cool down than there used to be”. Or
  • “There are more hot days than there used to be”.

A new page from the Met Officethe Global Climate Extremes Dashboard – highlights the nature of these changes.

How we experience climate change

The Met Office page shows an analysis of global historical data, rather just UK data. But the categories of analysis match my own qualitative sense of what is changing in the UK.

The authors chart the following:

  • The increasing number of warm days per year.
  • The decreasing number of cold nights per year.
  • The increasing length of periods of warm weather.
  • The increasing temperature of the hottest days.
  • The increasing rainfall on the wettest days.
  • The increasing tendency for rain to fall in intense events.

As an example, the figure below shows the increasing number of warm days each year. A warm day is defined as being in the top 10% of temperatures from the period 1961 to 1990.

Click for a larger version. The plot shows the change in the number of warm days per year – days when the maximum temperature exceeds the 90th percentile of the distribution for the period 1961-1990 – expressed as a difference from the 1961-1990 average. Over my lifetime (so far) the number of hot days in each year has increased by more than 20 days per year. Figure copied from the Met Office Site.

The Met Office Page and the paper on which it is based are significant and valuable for three reasons.

Firstly it highlights how we as individuals experience climate change. Without specifically counting hot days or measuring temperatures, over periods of a few decades people notice that ‘things are different’ without being aware of changes in the underlying average.

Secondly, it highlights the insidious nature of climate change. These analyses show that we are heading towards dramatic changes, but at a rate which it is hard for people to perceive directly over just a year or two.

Finally, from a metrological perspective, these analyses are robust against almost all systematic biases in the underlying data set. These analyses typically don’t even rely on instruments being calibrated!

The joint trends of increasing frequency and magnitude of warm extremes and decreasing frequency and magnitude of cool extremes, is a particularly striking signal of trouble in the decades to come.


Back Down to Earth

June 22, 2021

Friends, at the end the last article I wrote:

The combination of 12 solar panels and a Tesla Powerwall battery has been sufficient for us to be practically off-grid for the last 3 months. And that will probably continue for another 3 months. feels astonishing to be sustaining a good quality of life powered entirely by the Sun.

As we approach the summer solstice, I feel like I have reached apogee in a solar-powered rocket, and I am briefly floating weightless.

A week of miserable weather has brought me firmly back down to Earth.

After 87 days drawing no electricity from the grid, as the chart below shows, we have had to re-connect.

Click for a larger version. The graph shows daily electricity drawn from the grid (kWh) since November last year. After the battery installation, this fell to almost zero. Also shown is daily electricity used from the battery and solar panels (kWh). This has risen recently because electricity is now being used for air conditioning, cooking and domestic hot water.

We have now switched the mode of operating the battery so that it charges itself at night using off-peak electricity.

Solar Statistics: Summer Solstice Review

The summer solstice is probably a good point to review the performance of the solar panels installed last November 2020.

The £4200 system consists of 12 Q-Cells Duo BLK-G8 panels tilted at 40°. Six panels facing 25° East of South and six facing 65° West of South. A fuller description can be found here.

Click for a larger version. The graph shows daily solar generation (kWh) versus day of the year along with a 5-day running average. Also shown are two estimates for expected generation (kWh)alongside typical daily consumption.

The last 5 days have seen very poor generation. Last Friday 18th June, generation was just 2.3 kWh – more typical of mid-winter than mid-summer! And a battery with 13.5 kWh capacity is not big enough to see us through this dip.

Click for a larger version. The graph shows cumulative solar generation (kWh) versus day of the year along with a cumulative exports (kWh). Also shown are lines showing the estimated annual and semi-annual generation as specified by the installer.

Total generation so far this year is 1780 kWh – very close to 50% of the installer’s annual estimate.

The system has exported 590 kWh, my benevolent contribution to the grid, and I have used around 1200 kWh saving me around £250 compared to the situation without solar panels and batteries. If the panel’s performance is similar in the second half of the year, this would give a modest 3.5% return on my investment.

Carbon dioxide emissions 

Some fraction of this generation will have displaced gas generation which would have given rise to 0.45 kgCO2 per kWh, and some fraction will have displaced a typical generating mix which would have given rise to roughly 0.2 kgCO2 per kWh.

So depending on the assumptions made, my electricity generation has probably avoided emissions of between 350 kg and 800 kg of carbon dioxide so far this year, and will probably have avoided between 0.7 and 1.6 tonnes of CO2 by the end of the year.

The bigger plan 

The installation last week of the Air Source Heat Pump, a Vaillant Arotherm plus 5 kW model, together with a domestic hot water cylinder, marks the end of my investments in reducing carbon dioxide emissions from the house.

The ‘magic’ of the heat pump is that it uses 1 kWh of electrical energy to extract typically 2 kWh of thermal energy from the air, yielding around 3 kWh of heating.

This is central to reducing my carbon dioxide emissions. It has allowed me to replace the polluting gas boiler.

To compare carbon dioxide emissions with what what would have happened if I had made no changes, I have made a month-by-month estimate of household carbon dioxide emissions over the next 20 years.

These calculations are still preliminary, but the figure below shows their general form. It charts the anticipated carbon dioxide emissions if I had done nothing, alongside the anticipated carbon dioxide emissions in my plan.

Click for a larger graph. This chart shows month-by-month calculations of anticipated household carbon dioxide emissions based my current plan, or the do nothing alternative.

The green line shows an initial rise due to the 10.5 tonnes of carbon dioxide emitted during the manufacture of:

  • External Wall Insulation Boards (1.6 tonnes)
  • External Wall Mortar (1.0 tonnes)
  • Argon Triple Glazing (1.9 tonnes)
  • Solar Panels (1.6 tonnes)
  • Battery (1.4 tonnes)
  • Heat Pump (1.5 tonnes)
  • Air Conditioning (1.5 tonnes)

The green line then shows a much lower slope. The calculations indicate a break-even in terms of carbon dioxide by the end of 2023, and the non-emission of around 60 tonnes of carbon dioxide by 2040 when compared with the ‘do nothing‘ alternative.


It’s disappointing to be back ‘on grid’ for a few days, but overall the solar panels are performing pretty much as anticipated, already avoiding the emissions of hundreds of kilograms of carbon dioxide.

And they are just one part of the plan. The installation of the Air Source Heat Pump is the last part of the plan, and I will now monitor the house to see if my expectations are fulfilled.


June 16, 2021

Friends, I am experiencing a sensation akin to weightlessness.

It is the feeling of living a good life without consuming electricity or gas from the grid.


The combination of 12 solar panels and a Tesla Powerwall battery has been sufficient for us to be practically off-grid for the last 3 months. And that will probably continue for another 3 months.

Click for a larger version. The graph shows daily electricity drawn from the grid (kWh) since November last year. After the battery installation, this fell to almost zero. Also shown is daily electricity used from the battery and solar panels (kWh). This has risen recently because electricity is now being used for air conditioning, cooking and domestic hot water.

Household use of electricity has gone up in recent days as we have used electricity for water heating and air conditioning. But we have plenty to spare at the moment.

We have exported around 580 kWh so far this year, displacing mainly gas-powered generation. So in addition to not emitting any carbon dioxide from our own home, we have reduced emissions from other people’s homes by around 200 kg.


Last week we had the gas boiler removed and so since then we have only been using gas for cooking.

But on some days, the cooking load has been light and all we need to do is cook a bit of rice which can be done easily on a single ring induction heater (similar to this).

And so on those days, we have drawn no gas from the network.


At the moment it is just for a few days at a time. But it feels astonishing to be sustaining a good quality of life powered entirely by the Sun.

In fact, because of the air conditioning, I am probably cooler (thermally, not style-wise) than you.

As we approach the summer solstice, I feel like I have reached apogee in a solar-powered rocket, and I am briefly floating weightless.

Boiler Killer Strikes Again

June 12, 2021

Teddington: 10 June 2021:

Vaillant Ecotec, 10, a hardworking combination boiler, was today found dead in the garden of his family home in Teddington, West London. His torso was found in the front garden, with body parts gruesomely strewn across the grass. This grizzly discovery marks the fifteenth unexplained death of a boiler in Teddington this year.

We understand that he had been in good working order just recently, and his death has left other household appliances in a state of shock.

Bosch Fridge Freezer, 8, was lost for words. “He put in a fine performance over the winter, emitting almost 1.5 tonnes of carbon dioxide. You really couldn’t ask for a better boiler. And now it’s summer and he had been hoping for a bit of rest, just heating water for the odd shower. I can’t believe he’s gone.”

Early reports suggest that the slaying was pre-meditated and the killer was probably operating on a so-called ‘contract’. An Air Source Heat Pump was seen in the back garden just before the incident, and a Police spokesman confirmed that they considered that sighting was significant.

Heat Pumps#1

June 10, 2021

Installation of an air source heat pump (ASHP) in my own house is sadly on hold while the installers await delivery of a part. So I thought I would take this opportunity to update you with one or two things I have learned about how real-world heat pumps operate.

What is a heat pump?

I am preparing an article about how heat pumps work internally, but considering only their operational behaviour, they work like the device illustrated below.

Click for a larger version.

  • Powered by electricity, they extract heat from the air.
  • Cold water enters the the heat pump.
  • Warm water flows out.

The engineered ‘miracle’ of a heat pump is that 1 kWh of electrical energy can extract between 2 kWh and 4 kWh of heat energy from the air.

It might seem that nothing could be simpler or more wonderful? But the engineering reality behind the ‘miracle’ requires that the heat pump be operated carefully.

The problem

The key problem is that heat pumps require a high flow of water through them in order to enable efficient operation of the heat exchangers which extract heat from the air. Typical flows are in the range 20 to 40 litres per minute of water.

For my 5 kW heat pump, this can warm such a flow of water by only 2 or 3 °C. So how can such a device heat water to 55 °C?

Domestic Hot Water

When the heat pump is configured to heat domestic hot water – for sinks and bathrooms – then the circuit looks like the figure below.

Click for a larger version. Schematic diagram of how a heat pump heats domestic hot water. See text for further details.

In DHW-mode, the water in the heat pump circuit is passed through a steel tube wound inside an insulated water storage cylinder. This acts as a heat-exchanger between the water in the heat pump circuit, and the water in the cylinder.

But remember, the ‘hot’ water in the heat pump circuit is just a degree or two warmer than the returning ‘cold water. So how can this ever heat the domestic water to 55 °C.

The trick is having a smart heat-pump controller and low losses in the connecting pipework.

The heat pump controller first sets the heat pump operating parameters to warm the water returning from the DHW by a few degrees.

As the DHW tank warms, the returning water also warms, and the controller slowly adjusts the operation of the heat pump to increase the temperature of the water it supplies to the DHW tank. Eventually the controller detects when the water in the DHW tank has reached its set temperature.

So for example, if the outside temperature is 10 °C, and the water returning from the DHW tank is initially at 20 °C, then:

  • Initially the controller configures the heat pump to heat the flowing water to (say) 22 °C. Pumping heat from air at 10 °C to water at 22 °C can be done much more efficiently than pumping heat from 10 °C to 55 °C.
  • At first the temperature of the water returning from the DHW tank will be only slightly above 20 °C. But as heat is transferred to the DHW tank the temperature of the water returning from the DHW tank increases.
  • In response to this increase in the temperature of the returning water, the controller re-configures the heat pump to an incrementally higher temperature.

By adopting this clever strategy:

  • The first part of the heating can be done with higher efficiency – perhaps resulting in 4 units of heating for each unit of electrical work.
  • The later part of the heating is less efficient and might only results in 3 units of heating for each unit of electrical work.
  • So overall – depending on the maximum temperature required – the so-called coefficient of performance (COP) is usually somewhere between 3 and 4.

Space Heating 

When the heat pump is configured for room heating – so called ‘space heating’ in the lingo – then the circuit looks like the figure below.

Click for a larger version. Schematic diagram of how a heat pump heats radiators. See text for further details.

I was surprised to find that in this mode of operation the water from the heat pump is not passed directly through the system of radiators.

Instead, most of the water passes through a short section of tubing called a ‘low loss header’ and goes straight back to the heat pump. This allows the heat pump to operate at high flow rates.

The water used in the radiators is drawn from the top of the ‘low loss header’ and returns – cooler – to the top of the ‘low loss header’.

However there is almost no pressure difference between the top and bottom of the ‘low loss header’ – and so very little water would naturally flow through the radiators. So a hydraulic pump is used to push water through the radiators.

The cooled water from the radiators now mixes with the main flow at the bottom of the ‘low loss header’ and returns to the heat pump.

Click for a larger version. Schematic illustration of a ‘low loss header’ See text for further details.

So for example, if the heat pump is supplying 20 litres per minute of water at 55 °C to the ‘low loss header’:

  • The hydraulic pump draws perhaps 4 litres per minute of water at 55 °C leaving 16 litres per minute to flow straight through the header.
  • The return water from the radiators is cooled to (say) 45 °C.
    • From this one can calculate that the radiators have provided heating of 2.8 kW.
  • So at the bottom of the ‘low loss header’ there is a mixture of:
    • 16 litres per minute of water at 55 °C
    • 4 litres per minute of water at 45°C
    • When mixed together this makes 20 litres per minute of water at approximately 53 °C which is returned to the heat pump.

At first I was puzzled by this arrangement, but then I realised it was clever trick.

  • It allows the heat pump to operate at high flow rates and yet heat water only over small temperature differences.
  • And it allows the radiators to operate with lower flows and bigger temperature drops.

For those with experience of electronics, it is analogous to the ‘impedance matching’ effect of a transformer.

It’s complicated…  

Things are more complicated than these diagrams would suggest.

Firstly, the heat pump can only operate in one mode at a time.

So the heat pump controller changes modes by operating a valve to direct the water from the heat pump either to the DHW storage tank or the radiators.

Secondly, there are numerous features incorporated for reasons of safety or maintainability.

Some of these guard against the effects of thermal expansion of the water, some guard against the (low risk) of Legionella infection, and some are filters or energy monitoring components.

But I hope the explanations above come close to getting to the gist of heat pump operation.

I have lots more to say about heat pumps: so stay tuned!

Estimating Rates of Air Change in Homes

June 6, 2021

Air flow in modern homes

Modern homes are built with low air leakage rates and then mechanically ventilated to keep the air ‘fresh’. To prevent heat losses associated with this air exchange, the outgoing ‘stale’ air is flowed through a heat exchanger to warm the incoming ‘fresh’ air.

However this Mechanical Ventilation with Heat Recovery (MVHR) is not suitable for many older homes – such as mine – which are too leaky.

My home has gaps between floorboards on the ground floor and the air can flow in and out easily through the underfloor void.

To seal my home to modern standards would require re-building the entire ground floor – adding insulation as one worked. One would then add MVHR to the newly-sealed house. This would be very disruptive, and so I have instead chosen to remain married.

So in my old house and many like it, heat losses from air flow are highly uncertain.

Wouldn’t it be great if there were some way to measure air flow in older homes which was cheap and convenient!


Air flow through a building is commonly characterised by the number of air changes per hour – ACPH. But how can this be measured if one doesn’t know where the air is coming in or going out?

This building wiki suggests:

Tracer gas measurement can be used to determine the average air change rate for naturally’-‘ventilated spaces’ and to measure infiltration (air tightness)’. To do this, a detectable, non-toxic gas is released into the space and the reduction in its concentration within the internal atmosphere is monitored over a given time period.’

By ‘tracer gas measurement’ the wiki means that a gas is released into the air at a known rate, and its concentration measured versus time. If the rate of production of tracer gas is known, then the final stable concentration allows one to work out the number of air changes per hour (ACPH).

  • If the number of ACPH is small, the final concentration will be high.
  • If the number of ACPH is high, the final concentration will be low.

What this wiki frustratingly fails to point out is that carbon dioxide is an ideal tracer gas and has been used for years for this purpose.

This essential fact is pointed out in the first paragraph of an outstandingly clear and authoritative paper from Andrew Persily and Lillian de Jonge.

Carbon dioxide generation rates for building occupants Persily A, de Jonge L. Indoor Air. 2017;27:868–879. . It’s also available with alternate formatting here.

The first line of the abstract is:

Indoor carbon dioxide (CO2) concentrations have been used for decades to characterize building ventilation and indoor air quality.

This surprised me because in all my reading about this subject in the UK I have never seen it mentioned. But then, in the first line of the paper itself, Persily and de Jonge point out just how old the idea is:

Indoor CO2 concentrations have been prominent in discussions of building ventilation and indoor air quality (IAQ) since the 18th century when Lavoisier suggested that CO2 build-up rather than oxygen depletion was responsible for “bad air” indoors.

The gist of their paper is a thorough review and examination of the factors which affect the rates at which human beings emit carbon dioxide. I won’t deprive you of the pleasure of reading the paper but factors discussed include:

  • The ratios of fat, protein and carbohydrate in people’s diet.
  • Age, gender and ethnicity.
  • Body size and mass.
  • Levels of activity.

The paper is very readable and I recommend it in the highest terms.

A worked example: my bedroom.

At night my wife and I sleep in a room which is about 7 m long, 3.5 m wide and 2.2 m high. So it has a volume of 7 x 3.5 x 2.2 = 54 cubic metres, or 54,000 litres.

There are no obvious draughts and I had no idea how many air changes per hour there were.

But overnight, the concentration of carbon dioxide rises from about 450 parts per million (ppm) characteristic of fresh air, and stabilises around 1930 ppm.

I can work out the number of air changes per hour ACPH using the formula below.

In this formula:

  • The room volume in litres
    • In my case 54,000 litres
  • c is the measured stable CO2 concentration in ppm
    • In my case 1930 ppm
  • c0 is the concentration of CO2 in ‘fresh’ air in ppm
    • In my case around 450 ppm
  • 10-6 is the scientific way of saying “divide by a million”
    • 1/1,000,000
  • CO2 production rate is what Persily and de Jonge’s paper tells us:
    • For sleeping males over the age of 11, the answer is within 10% of 12.7 litres per hour.
    • For sleeping females over the age of 11, the answer is within 10% of 10.2 litres per hour.
    • So our joint CO2 production rate is about 23 litres per hour

Putting all those numbers in the formula……we find the rate of change of air is around 0.29 ACPH – with the answer probably being within 10% of that value.

Some other factors.

Persily and de Jonge’s paper is extraordinarily thorough and tackles some of the tricky problems about using this technique for estimating air flow in buildings.

Firstly, there is the question of the level of activity of the people in a particular space. The metabolic rate is generally measured in units of mets with 1 met being roughly the metabolic activity during sleep. Very roughly it corresponds to around 58 watts.

The paper has extensive tables showing the CO2 production rate in litres per second for different levels of activity of different sexes at different ages. (Remember to multiply these numbers by 3600 to convert them into CO2 production rate in litres per hour before using them in the formula above.)

Secondly, there is the wider question of which volume of air is relevant. My bedroom represents a small volume with well understood rates of CO2 production.

But is a CO2 meter placed in a ground floor room measuring the characteristic concentration of the room it is in, the whole ground floor, or the entire house? Resolving questions like this may take a few experiments, such as moving the meter around.

Additionally, the amount of CO2 generated in a house over a day may not be clear. For example, the number of occupants and their level of activity may be hard to determine.

Mi casa no es tu casa

The situations encountered in your home will be different from those in my home.

Nonetheless, if you are trying to assess air flow within your home, I would recommend that you consider using carbon dioxide measurements as part of your arsenal of measurement techniques.

I use two CO2 meters and can recommend them both:

COVID 19: What have we learned? Nothing.

June 4, 2021

Click for a larger image. Logarithmic graph showing positive cases, hospital admissions and deaths since the start of the pandemic. The blue arrows show the dates of ‘opening’ events. See text for further details. The red dotted line shows cases doubling every 15 days as they did in September 2020.

Friends, so here we are, 4th June 2021, and I am reluctantly concluding that – as they did last summer – the government are about to screw things up.

The graph at the head of the page shows casesadmissions and deaths throughout the pandemic.

The situation now is strikingly similar to July last year, except that the growth rate of cases is more similar to September last year.

The statistics for admissions and deaths represent ‘ground truth’ – but when the situation is changing rapidly they lag the spread of the virus by several weeks

So to assess the spread we should look at cases. And with the best part of 1 million tests a day, mostly in asymptomatic people, we should have a reasonably good track on what is happening.

In my previous blog (s), I suggested we should not care about:

  • the absolute number of cases,
  • the population prevalence of cases,
  • or even the rate of change of cases.

What mattered was:

  • Is there the potential for the pandemic to expand into the general population and kill hundreds of thousands of people?

Last summer the answer was definitely ‘Yes’.

This summer I previously thought the answer was probably ‘No’.

Now I think that in fact the virus has run away from us – spreading through schools – and has the potential to reach to the general unvaccinated population.

And although it I don’t think it can kill ‘hundreds of thousands’, it could easily kill ‘thousands‘ and cause serious illness in many more.


First of all, please let me me warn you about statistics which state the fraction of the ‘adult’ population which have been vaccinated. Adulthood is not relevant.

It seems that unvaccinated and previously uninfected people can catch COVID and spread it, no matter how young, even if their symptoms are not strong.

As I write: 59% of the entire population, including practically all of the most vulnerable groups have received a first dose of the vaccine. Vaccination is reaching an additional 8% of the population per month.

Together with the 10% – 20% (roughly) of the population who have had the disease, we are close to herd immunity. This would be relevant if the virus were spreading randomly through the population. But it isn’t.

The virus appears to be spreading amongst exactly the fraction of the population who have not been vaccinated. This is an inevitable consequence of our choice to vaccinate the elderly first. And as social restrictions have eased, viral spread is barely hindered by social distancing.

There are three problems with this.

#1: More Death 

If we consider the population of people who could be infected to be the roughly 20 million people under 30: then with a fatality ratio of 0.01% this corresponds to a summer with a further 2000 dead people under 30. If we are lucky the number might be only a few hundred.

To me, these wholly preventable deaths seem like those who died in WW1 after the armistice: more tragic somehow than the previous 129,000 deaths.

This does not take account of the fact that vaccinated people are not invulnerable – merely less vulnerable.

#2: More Illness

Without further interventions, the current case rate appears to be growing at the same rate it did in schools last September. Cases are doubling roughly every 15 days. By the end of June they will exceed 10,000 per day and approach 40,000 per day at the end of the school term.

Aside from the deaths, this corresponds to a lot more illness – some of it chronic ‘Long COVID’.

#3: Rolling the variant dice

The larger the pool of infected people, the more chance the virus has to mutate and find variants which might escape the vaccine, or – heaven forbid – take a more dangerous form.

As far as I understand, nobody knows why elderly people are more vulnerable to COVID-19. But imagine a hypothetical COVID-21 which was more deadly to children? Is that an experiment we really want to conduct?


The latest outbreaks have not been contained locally– yet another failure of Track, Trace, and Isolate.

The vaccination program means that unlike last summer, we are unlikely to face a wave of a further 80,000 dead people.

But I am expecting a further wave of wholly unnecessary deaths – I just don’t know how large a wave to expect.

I did write out a list of recommendations for what we should do about this situation. But having edited it, and reflected on it, I realised that the recommendations were all obvious, but that writing them down was pointless, because the Government just doesn’t care!

Stay safe.




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