Archive for the ‘Uncategorized’ Category

Happy Christmas and Best Wishes for 2022

December 18, 2021

Click image for a larger version

Friends, it’s the end of the year and there is still so much to write about. But for the next couple of weeks, it won’t be me doing the writing.

I feel the need for a break and so I will be hunkering down in Podesta Towers and dreaming of spring sunshine on my solar panels.

My aim is to stay warm, catch up on some other projects, and try to avoid catching Omicron!

I wish you all the best for the Christmas Season and a splendidly low-carbon 2022.

Journey from the Centre of the Sun

August 15, 2021

Click image for a larger version. Some of the stages in the energy conversions and transfers that allows me to have hot water in the mornings without any carbon dioxide emissions. Simple heh?

Friends, just the other day I wrote about how my heat pump produced hot water each day.

The way in which the heat pump extracts heat from the air is ingenious in the extreme.

But as I reflected on it, I realised that this ingenuity occurred in the middle of a long series of energy transformations taking – very roughly – 170,000 years.

Please allow me to explain.

#1 Where does the energy come from?

The source of nearly* all the energy humans exploit on Earth is sunlight.

Using sunlight and carbon dioxide plants produce oxygen (thank you) and carbohydrates. This so-called ‘photosynthesis‘ captures energy from the sunlight in the form of re-arranged chemical bonds within carbohydrate molecules.

When we use animals for work – horsepower and ox-power – the energy the animals use is derived from the carbohydrate molecules in their food.

When we burn plants – primarily wood – for heat, the energy released is from the reverse of the reaction that created the carbohydrate molecules. And so, the carbon dioxide which was captured when the plant grew, is released. But since burned wood is generally only a few decades old – burning plants can be (almost) neutral in the production of carbon dioxide.

Fossil fuels are all derived from plants, and the energy of the captured sunlight has been ‘distilled’ over thousands of years by a variety of physical processes into coal, oil and gas. Unfortunately, burning fossil fuels also releases carbon dioxide, but not carbon dioxide that was recently captured. It releases carbon dioxide that was captured eons ago.

Burning fossil fuels is still the main way in which we make electricity – so electrical energy is in some sense the energy of ancient sunlight. How charming.

#2 Where does the energy of sunlight come from?

That the Sun is hot has been obvious to all humans since the dawn of time.

But the source of its immense heat was a mystery until just about 100 years ago when it was suggested that hydrogen nuclei (a.k.a. protons) might ‘fuse’ together to make helium nuclei, and release energy.

Segueing past a few decades of research and speculation, we now know for sure that nuclear fusion deep within the Sun is indeed the source of the energy that makes the Sun hot.

The environment deep within the Sun is extraordinary, with a temperature of roughly 15 million degrees Celsius.

The hot dense gas emits electromagnetic radiation – γ-rays, X-rays, ultra violet and visible light – in all directions. The nuclei and electrons in the Sun are a plasma – which is opaque to radiation. So the radiation is constantly absorbed, causing local heating, and then being re-emitted by the nuclei and electrons in the various layers of the Sun.

Because the Sun is so vast and so opaque – it takes roughly 170,000 years for the energy to travel from the core of the Sun to the surface of the Sun. Just so you know it was not a typo: I did indeed say 170,000 years.

Eventually the energy reaches the outer layers of the Sun which are at a tepid 5,500 °C (ish). The glow of this hot plasma sends visible light out in all directions and after roughly 8 minutes, a tiny fraction of it reaches Earth.

#3 My hot water: a summary

Click image for a larger version. Some of the stages in the energy conversions and transfers that allows me to have hot water in the mornings without any carbon dioxide emissions. Simple heh?

So where does the energy that heats my hot water come from? The letters in the bullet points below refer to the diagram above.

  • Nuclear fusion (A) around 170,000 years ago created energy from the fusion of hydrogen nuclei that were themselves created in the primordial ‘big bang’.
  • This energy travelled through the Sun’s layers as a variety of forms of electromagnetic radiation – γ-rays, X-rays, ultra violet and visible light – until it reached the outer layers when the radiation could travel uninterrupted into space (A, B).
  • A tiny tiny fraction of this radiation was intercepted by solar panels on my roof, which converted some of the visible light into an electrical current (B, C, D).
  • This electrical energy was stored in a battery by electrically forcing ions of lithium metal (shown in the figure as red dots) to cluster together against their desire to diffuse away from one another (E).
  • This energy was then released at night by allowing ions of lithium metal to diffuse away from one another (F), forcing electrons around an external inverter circuit that created AC currents to power a motor in a compressor (G) and electronics which ran the heat pump.
  • The heat pump then chilled a refrigerant (G) that extracted heat from molecules in the air that had also been heated by sunlight over the preceding few days.
  • This energy was transferred as heat to water flowing in a circuit through the heat pump (G).
  • And then this energy was further transferred as heat to fresh water in a hot water tank (H).

And then finally (I) a few hours later, this energy was transferred to the outer layers in my face and hands where transient receptor proteins in thermoreceptors in my skin sent signals to my brain that caused me to realise the water coming from the tap into the sink was ‘just right’.

Simple heh?

* Nearly?

Humans do exploit one source of energy which did not originate in the fusion of nuclei within the Sun: nuclear power.

Nuclear power exploits energy released by splitting the nuclei of heavy atoms that were created – as I understand it – during the last few destructive moments of a previous generation of stars.

These elements – uranium primarily – were then deposited on the primordial Earth as it formed at the same time as the Sun was ‘born’.


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.




The Cat Sat on the Mat

March 14, 2021

While walking though Teddington the other day I saw tender sight which brought a smile to my eyes.

A man was mending his very old car – an Austin Maxi – and had tools and components laid out around the car.

And just by the car was a small mat on which his cat was very contentedly sat.

I commented to him that it was very considerate of him to put down a mat for the cat.

He smiled.

Then he told me that the mat was there to cover a drain so that he didn’t accidentally lose any parts. And the cat was sitting there opportunistically rather than by invitation.


Correlation does not imply causation

It had seemed so obvious that the man had placed the mat down for the cat. I had immediately intuited his state of mind and fondness for his cat.

In order to have fully appreciated what was happening, I would have needed to:

  • Imagine into being a drain – for which I had no evidence – it was completely covered.
  • And then understand that it would be sensible to cover the drain if working near it – a mat would be ideal.
  • And finally understand that cats will sit on mats unbidden.

And so I was reminded that even the simplest and most apparently obvious things are sometimes not what they seem.


See also these links suggested by astute commenter Dave Burton

In the bleak midwinter

January 19, 2021

So here we are in the bleak mid-winter – the place that everyone with External Wall Insulation loves to be.

As I remain-at-home-to-protect-the-NHS-and-save-lives I have spent a great deal of time staring at the following graph which shows the impact of the triple-glazing and External Wall Insulation.

Click for a larger vsrsion. Plotted in blue against the left-hand axis, the average daily consumption of gas (kWh per day) This is shown against the left-hand axis. Plotted in green against the right -hand axis is the average difference of the outside temperature from 19 °C (°C).

The graph shows two quantities plotted versus the number of days since the start of 2019.

  • In blue, I have plotted the average daily consumption of gas (kWh per day)
    • This is shown against the left-hand axis
  • In green, I have plotted the average difference of the outside temperature from 19 °C (°C)
    • This is shown against the right-hand axis

The dotted red line shows the weather now (circled in green) is colder than it was at this time two years ago.

However the amount of gas (circled in blue) that I am using to maintain the temperature of the house is now about half what was then: just over 50 kWh per day now versus just over 100 kWh per day then.

The carbon dioxide emissions associated with heating the house look set to be about 1.25 tonnes this winter – still a terrible figure – but much lower than 3 tonnes emitted in the winter of 2018/2019.

To go further we need to ditch the gas boiler and switch to a heat pump. Hopefully we will achieve this in the summer and then we can reasonably hope that next winter we will lower the carbon dioxide emissions associated with heating the house to about 0.4 tonnes – just 13% of what it was in 2018/2019.



Rocket Science

January 14, 2021

One of my lockdown pleasures has been watching SpaceX launches.

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

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

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

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

Let me explain.

Rocket Science#1: Looking at the data

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

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

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

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

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

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

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

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

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

Then I plotted a graph of altitude versus time.

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

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

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

Rocket Science#2: Analysing the data for acceleration

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

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

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

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

I then wondered if I could explain that behaviour.

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

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

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

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

Rocket Science#3: Maximum aerodynamic pressure

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

And then there’s the satellites themselves to study!

Good luck with your investigations!


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


Everything is Rubbish!

December 22, 2020

All the factories in all the world are just making rubbish. All that differs is the speed and path of the trajectory from Factory to Dump.

Friends, when I say that “Everything is Rubbish“, this is not the moaning of a 60-year old man dissatisfied with new-fangled ways.

This is the insight of a 60-year old man who has seen with perfect clarity that, with very few exceptions, every object one ever ‘owns’ is really just ‘leased’ as it makes its way from a factory to a dump.


Recently I have been sorting my way through a loft filled with the detritus of bringing up two children, along with a few items of memorabilia from earlier in my own life.

And the following thought is irrepressible:

If anyone else looked at this they would call it junk“.

And in a related theme, a couple of close friends have recently been charged with sorting the belongings of a deceased parent.

And items which were one preciously hoarded as treasures, are revealed in the cold light of a parent’s absence to have negative monetary value: they are impossible even to give away.

And in a further related theme, I tried to play a VHS-Video Cassette the other day – and the player would not play. [PAUSE for younger readers to laugh at this folly].

I looked inside and poked around – they really are ingenious! – but to no avail. This package of metal and components is now junk. And so are all the 100 or so video cassettes. In their day I probably paid £1000 for them. Now, all the subtlety and artistry that went into their creation is worth nothing.

What has lasted?

I do have a small number of items which have lasted longer than the average.

  • I have a couple of photographs of my parents’ wedding – these are 68 years old and still in excellent condition.
  • Most days I still use the calculator that I bought in 1978 before I went to University. And I have a few books from that era too.
  • And I still regularly listen to music through  a pair of Wharfedale Denton loudspeakers. These were a present from my father for my 18th birthday in 1978. I recall that he could not believe that a pair of loudspeakers could conceivably cost £55 – but if were he alive today he would be pleased at their longevity.

But even for these items, it is not that they will last forever, but simply that the arc of their trajectory from factory to dump is slightly longer.

Why do I mention this?

Because the truth has struck me hard in the last few weeks.

  • All the factories in the world are really Rubbish Factories

All that differs is the category of rubbish and the arc of its path from Factory to Dump.

I know I am not the first person to mention this.

And I know that my own life is not a good exemplar of a life which minimises the amount of rubbish generated.

But it just struck me as being deeply, deeply true.






It didn’t have to be this way.

December 21, 2020

If the Government had followed advice and had a lockdown in October which had the same effect as the Lockdown#2 did in November. Then by mid-November 6000 fewer people would have died. Click for a larger image.

Friends. Let me ask you to imagine an alternative reality.

In this reality, our government would have taken the advice of SAGE and instituted Lockdown#2 in October instead of November. It is not a crazy idea that a government should accept the advice of the people it has asked to advise it. Here are some news stories from 13th October 2020.

If they had taken that advice, where would would be now?

Let’s assume that:

  • Events would have evolved along a similar path to what actually happened one month later when we entered Lockdown#2. And that…
  • After the end of Lockdown, things continued as they actually continued.

Based on these assumptions

  • I calculate that in Mid-November 6000 fewer people would have died than had actually died at that point.

Additionally, the death rate would have still been below 100 people per day. At that low rate, there would have been an extended window in which Track Trace and Isolate might conceivably have been made to work.

What would have happened after this is harder to say. Every European country has seen a resurgence in the virus, and so I guess we would have too.

Here are two possibilities.

  • If we had managed to control the virus at low levels, then compared with the situation now, 19,000 people would be alive and we would be able to have Christmas celebrations.
  • If the virus had taken off exactly as it actually did in October – but just delayed by 6 weeks, then the number of people saved would only have been about 13,000.

If the Government had followed advice and had a lockdown in October which had the same effect as the Lockdown#2 did in November. Then to date – 20th December 2020 – somewhere between either 13,000 (red curve) or 19,000 (blue curve) fewer people would have died. Click for a larger image.

Why do I mention this?

This is not complex mathematics.

And while there are uncertainties in this calculation, the number of lives which might have been saved is on the order of 10,000 – no matter how you make the calculation.

The understanding that when a virus is in a period of exponential growth, acting earlier saves lives and livelihoods, is well-known to anyone with even the slightest knowledge of this field.

Even I recognised the trend and recommended a series of planned Lockdowns on 26th September 2020

It seems clear to me that the government must have known what was happening and yet they deliberately chose the path they did knowing full well that thousands of their own compatriots would die.

This is a despicable behaviour and ought to elicit the resignation of the Prime Minister.

Image Stolen from Red Molotov

COVID-19: Day 352: The Second Wave will be deadlier than the First

December 18, 2020


Friends: Despite good news on vaccines, the corona virus outlook over the coming month is bleak.

This week the rates of positive tests and  hospital admissions have continued to increase.

Today (Day 353) the seven day rates of positive tests and hospital admissions are higher, and rising faster, than before Lockdown#2 started on Day 310.

Sadly, the second wave is proving more deadly than the first.

  • I have estimated the switchover from First to Second wave as taking place on 16th August (Day 228) – close to date of minimum hospital admissions.
  • If admissions continue at the current value (7-day average of 1700 admissions per day) up to the end of the year – a near certainty –  then the cumulative admissions for the second wave will be equal to the total admissions for the first wave (135,000) later in December.
  • If deaths continue at the current value (7-day average of 430 deaths per day), then the cumulative deaths for the second wave will equal the 41,000 deaths for the first wave sometime in late January 2021.

And of course, the second wave is not over.

Recent data for the number of daily positive tests and their 7-day retrospective average together with an earlier optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily hospital admissions and their 7-day retrospective average together with an earlier optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Recent data for the number of daily deaths and their 7-day retrospective average together with an earlier optimistic projection shown as a dotted line. Details of the curves shown below are given later in the article. Click for a larger version.

Data#1. Prevalence

Since late April the ONS prevalence survey has been randomly testing people in England each week to look for the virus. They then collate their data into fortnightly periods to increase the sensitivity of their tests. Details of their full results are described methodically in this ‘bulletin‘.

Data from Table 1d of the ONS spreadsheet: Click for a larger version.

The number of people tested and the number of positive tests are given in their table above. ONS estimate that at the end of the measurement period on 12 th December 2020 on average 1.1 % of the UK population were actively infected, up from the previous weeks estimate of 0.9%.

The raw count of positive tests was:

  • 1,672 from 159,052 people tested in the two weeks to 12th December,
  • 1,992 from 184,538 people tested in the preceding two weeks, and
  • 2,096 from 163,077 people tested in the two weeks preceding that.

The data in the table above are graphed below.

ONS Estimated prevalence of COVID-19 in England extracted from Table 1 d Click for a larger version.

Note these estimates come from random survey tests (so-called Pillar 4 tests), not clinical tests.

I have shown two curves on the graph above.

  • The black dotted line (– – –) is the same curve I have plotted for the previous thirteen weeks. (Link)
  • It is a fit to the 3 black data points and shows what we might expect if viral prevalence were doubling every 15 days.
  • The blue continuous curve is the ONS model for what is ‘really happening’.
    • I cannot explain how this estimate lies consistently below the data on which the model is based. Clearly there is something I have still not understood. I did ask ONS but they did not reply.

Data#2. Tests and Deaths

The graph below shows three quantities on the same logarithmic scale:

  • the number of positive tests per day
  • the number of people newly admitted to hospital each day
  • the number of deaths per day.

The data were downloaded from the government’s ‘dashboard’ site.

  • Positive tests refer to Pillar 1 (hospital) and Pillar 2 (community) tests combined – not the Pillar 4 tests from the ONS survey.
  • The deaths refer to deaths within 28 days of a test.
  • Hospital admissions for the UK nations combined.

All curves are 7-day retrospective rolling averages of the data since July. This week I have extend the time frame to look into the first four months of 2021.

Data for positive casesdaily hospital admissions and daily deaths. Click for a larger version. Recent details for each quantity are given in separate graphs at the head of the article.

The graph shows the data alongside exponentially decreasing and then increasing trends shown as dotted lines.

  • The declining trends correspond to quantities halving every 21 days – the rate at which the epidemic declined during Lockdown#1.
  • The increasing trends correspond to quantities doubling every 15 days, roughly the rate at which the second wave grew.

Data#3. Details and Projections

Because we are now in the non-exponential phase of the epidemic, I have re-plotted recent data for casesadmissions and deaths on a linear scale: these can be found at the top of the article.

I have also included some projections (as dotted lines) assuming that:

  • The effects of Lockdown#2 began to show through on Day 324,
  • The declines will be as swift as in Lockdown#1 (halving every 21 days).
  • The declines will continue after the 2nd December end of Lockdown#2.
  • The decline in hospital admissions is delayed 5 days with respect to cases
  • The delay in deaths is delayed 7 days (a change from last week) with respect to hospital admissions.

The curved dotted-line projections on the linear graphs at the graphs at the top of this article are effectively the same as the straight-line projections on the combined (logarithmic) graph. Please note that:

  • These are guidelines not predictions.
  • Look to see if quantities fall faster than this, or slower than this.

It is clear that the data are no longer following the hoped-for declining trends.

Since cases lead to admissions which lead to deaths, we can use data for positive cases and  hospital admissions to predict deaths in the coming days and weeks. These projections are shown below.

Data for daily deaths. are shown as a solid black line. The yellow dotted curve (– – –) is the predicted daily death curve assuming 27% of admissions die 7 days after admission. The red dotted curve (– – –) is the predicted daily death curve assuming 2% of cases die after 17 days. Click for a larger version.

The predicted death rate based on positive cases suggested there would be a very large fall in the death rate which has not materialised. My guess is that the drop in positive cases in the last two weeks of lockdown was caused by some kind of sampling variation.

The predictions based on hospital admissions are more reliable (I think) because they are less affected by the ‘fair-sampling’ issues when anticipating deaths from positive cases.

These predictions suggest that in the coming weeks deaths will rise further – approaching 500 deaths per day in the new year.


In my opinion, it’s all a big mess: but you knew that already so I won’t dwell on it.

But with the vaccine being distributed – my 84 year-old father-in-law will receive his first shot tomorrow – we can finally look forward to a reduction in the death rate.

The UK population is about 60 million and herd immunity will not act strongly in our favour until about 60%-70% of people are immunised. So we might expect to see a natural decline in the virus without social distancing after about 40 million people have become immune.

Guessing that 1 million vaccinations per week are possible – I could not find a reliable estimate – then herd immunity will not come until the autumn.

However, there are only 12.5 million people over 60 (link) and these (along with health care workers) are amongst the first in line for the vaccine. It seems just possible that this entire cadre could be immunised by Easter (April 4th).

If that were achieved then hospital admissions and deaths should fall steadily through the early part of 2021 even as positive cases likely continue to rise: something to look forward to.

Stay safe.

Acoustic Thermometry in Ancient China

November 23, 2020

Have you ever stared into a well and tried to see the bottom? Even shining a torch down, it can be  hard to see just how far down the water is. But occasionally you can catch a reflection from the surface and appreciate the depth.

Yesterday, I recalled that sense of vertigo as I peered into the depth and darkness of the well of my own ignorance.

I was reading a paper on some weather records in China,

An Introduction to Some Historical Government Weather Records of China

Pao K. Wang and De’er Zhang

Bulletin of the American Meteorological Society Vol 69, No 7 July 1988 pp 753-758

And as the paper described some practices from the 18th Century B.C. i.e. 3800 years ago – a glint of light reflected off the surface of my ignorance and I realised just how colossally deep the well was.

  • I know almost nothing about China.

I paused, caught my breath and continued reading. Here are some of the things I learned.

Shang Dynasty

In the introduction the authors describe the earliest known weather records from the Shang Dynasty, dating as far back as the 18th Century BC. The world was a busy place back then.

The weather records were carved on ox bones or turtle shells by ‘diviners’.

The diviners predicted the weather based on the pattern of cracking of the bone or shell when it was burned. But – astonishingly in my view – they then later carved the actual weather on the same piece of bone or shell!

Zhou Dynasty

In the Zhou dynasty (1111 BC to 246 BC), there were no weather records as such, but people did note extreme weather events such as floods or droughts.

Crucially they recorded the dates at which rivers or lakes froze, and the dates at which particular flowers blossomed. These records have been used to indirectly infer the climate at that time.

West Han Dynasty

In a book, Huai-Nan-Zi, dating to 120 BC a passage states:

“…by hanging feather and charcoal together one can know the dryness or wetness of the air…
When it is dry, the charcoal is light. When it is wet, the charcoal is heavy.

This is clearly a description of a primitive hygrometer operating on the principle that charcoal has a very large internal surface area that can adsorb a relatively large amount of moisture when exposed to moist air. But what is the role of the feather?

Later, in the years leading to 220 AD, it is reported that local governments are required to report the amount of rainfall “…from the beginning of spring to summer, and the beginning of the fall.

There are no records of the rain gauges used, but there must surely have been a standardised procedure.

Descriptions of rain gauges appeared much later in a 1247 AD book Nine Chapters of Mathematics. This describes four techniques for determining rainfall and snowfall from which the shapes of the gauges can be determined. But sadly no actual records remain.

Later Han Dynasty

But perhaps the most fascinating instrument described is a device dating from 1086 AD for measuring the temperature of the soil at different depths.

My visualisation of an early Chinese acoustic ‘thermoscope’ for measuring soil temperature at different depths. Click for a larger version.

The instrument was called  guan (meaning ‘Reed Pipe’ or ‘Scale Tubes’) and was original used as ‘pitch pipes’ for providing standard pitches for tuning musical instruments. Their use is described as follows:

  • Tubes of different lengths – with different natural pitches – were buried so that different lengths were in the ground, but the length above ground was fixed.
  • Ashes were placed in the tube and these were supposed to rise when the tubes were exposed to the ‘proper’ ground temperature.
  • Since ground temperature varied with depth and with the time of year, the ashes would ‘fly’ out of different tubes at different dates giving an idea when a particular temperature had been achieved at a certain depth.

There is a good deal about this explanation that I don’t understand. Did people blow over the tubes? How did they know what was the ‘right’ soil condition? When the tube resonated, how did the ash ‘fly’?

But despite these questions, it is clear that the instrument was using the principle that the speed of sound in air – and hence the resonant frequency of a musical tube – changes with temperature.

This is the same principle that I used when I worked at NPL to build the world’s most accurate thermometer. And I also built several tube like thermometers not-so-dissimilar to the  guan.

But the  guan appears to have been more of a thermoscope than a thermometer i.e. it indicated certain temperature conditions but did not ascribe a number to that condition.

What’s missing?

One of the curiosities of the paper is something which is not there, and whose absence is not mentioned.

Given the centuries of development, and the early prowess of Chinese industry in the manufacture of silk and gunpowder and paper – processes for which temperature and humidity control are critical – I found it surprising that there was no mention of an equivalent to the numerical temperature scales developed in Europe.

Early temperature scales were developed in Europe by Newton and Rømer in 1701 and later perfected by Fahrenheit, Celsius and many others.

Of course reading one paper does very little to amend the vastness of my ignorance of China and its history. And there may indeed have been some kind of alternate scale. But if in fact there was no ‘indigenous’ Chinese temperature scale, this probably speaks to some key difference in the societies at that time.


So those are the drops of knowledge that fell in the deep well of my ignorance.

I enjoyed the wait as the drops fell and I listened for the splash as they reached the surface. But the level did not change very much!

  • If anyone has any information about books I should read, or sources I should consult,  I would be grateful if you could drop me a line.


Thanks to Peter G who e-mailed to highlight the work of Joseph Needham who too had asked questions about the anomaly of early Chinese discoveries and inventions, but the relative slowness of industrial innovation. The wikipedia page is fascinating in itself.

%d bloggers like this: