Archive for the ‘Personal’ Category

A Bright Future?

May 3, 2021

Click for a larger Image of the book covers.

Friends, a few weeks ago I reviewed two books about our collective energy future: Decarbonising Electricity Made Simple and Taming the Sun.

Summarising heavily

  • Decarbonising Electricity Made Simple
    • A detailed look at how the UK can attain very low carbon intensity electricity – perhaps less than 50 gCO2/kWh in 2030 – by just doing more of what we are already doing
  • Taming the Sun
    • A look at the role of solar power globally, addressing the fact that every ‘market’ will reach the point where super-cheap solar electricity is so abundant that nothing else will compete – during the day. But because of the lack of storage, solar will never be a sufficient answer.

This weekend I read A Bright Future by Joshua Goldstein and Staffan Qvist. The strapline is “How some countries have solved climate change and the rest can follow”.

Their answer is simple:

Start building nuclear power stations now and don’t stop for the next 50 years.

The authors point out

  • The astonishing safety record of nuclear power which is in direct contrast to the coal industry in which thousands of people die annually – and which releases more radioactivity and toxic compounds than nuclear power stations ever have.
  • The enormity of the climate peril into which we are collectively entering.
  • The scale of output which is achievable with nuclear power stations – generating capacity can potentially be added much faster than renewable generation.
  • The reliability of nuclear power and they contrast this with the variability of wind and solar generation.

And while I could disagree with the authors on several details, the basic correctness of their assertion is undeniable.

  • In the UK if we had one or two more nuclear power stations our climate goals would be dramatically easier to meet.
  • Globally, there are currently 450 nuclear power stations undramatically providing emission-free electricity. If there were 10 times this number our collective climate emergency would be easier to address.

And while it would be an understatement to say that nuclear power is without controversy – it seems to me that a massive investment in nuclear power plants worldwide would be a good move.

But it is not going to happen.

I am sure the authors know that their arguments are futile.

Although I personally would welcome a nuclear power plant in Teddington, most people would not.

Similarly most people in Anytown, Anywhere would not welcome a nuclear power station.

But as the authors point out – correctly – there is no renewable energy technology that match the characteristics of nuclear power.

And we need every possible low-carbon generating source to address humanity’s needs

Despite the authors’ positivity, I have never felt more depressed after reading a book than this.

 

Retirement: One year on…

May 2, 2021

Click for a larger version. Clouds and blossoms. Sometimes I think to myself, it’s a wonderful world…

Friends, it is now one year (and a day or so) since I retired from NPL. And it’s been an… interesting year.

Please allow me a few moments of reflection.

NPL

It took months for the poison that flows through that institution to leave my system.

I wrote about it a bit, (here and here and here and here) but writing about the inanity of management systems and the poisonous individuals that colonise them is such a negative activity I felt obliged to just leave that all behind.

I did worry that I might miss the physics, but in fact I am doing much more physics now at home than I was at NPL.

In the same way that Neo could read the code in The Matrix, so I see the world. As I walk into Teddington for a cup of coffee each morning, I see in the blossoms and the clouds, multiple unfolding physical principles creating a world of beauty and wonder.

I literally catch my breath at the intricate complexity of it every day.

Pandemic

I have written a lot about the pandemic in the last year, but as I reflect on the year, I am genuinely lost for words.

Some of my articles on the subject now seem especially prescient. See for example this 1st January 2021 article which predicted the daily death toll in May 2021 would be roughly 75 people per day.

Click for larger view. Prediction of the daily death toll on 1st May 2021 – it’s a little pessimistic but not far off given that the UK’s vaccine rollout had barely begun.

And recent news stories that our Prime Minister said he would rather see “bodies piled high than have another lock down” finally explains why we did not lock down in October 2020. Read my article from 26th September 2020 here.

If these reports are correct, then the number of deaths personally ascribable to the Prime Minister’s actions is now way more than the 19,000 I estimated previously.

While I myself would not want to occupy such a job, I can’t imagine the depravity of someone who could make, and then fail to acknowledge such a catastrophic error.

Carbon dioxide

Retirement (and the tax-free lump sum from my pension) has allowed me to make headway on reducing my household’s carbon dioxide emissions.

The house now has triple-glazing and external wall insulation that have reduced the heating demand (and CO2 emissions) by more than 50%.

In the next few months I will install a heat pump and air conditioning which should reduce CO2 emissions by a further factor 4±1.

And our solar panel/battery combination will keep us more-or-less off-grid all summer.

But as I seek to become a genuine Carbonaut, I am faced with some terrible questions:

  • Can I live a life without milk in my tea?
  • Is a life without bacon every once in a while a life worth living?
  • And cheese? Could a life without 12-month old Davidstowe cheddar genuinely be called ‘living’?

I am writing in jest, but the questions are deadly serious.

In the coming year I will write about this more, but already there are tonnes of carbon dioxide which have not been emitted due to my actions.

By my anticipated date of death in 2040, I hope to have avoided at least 60 tonnes of carbon dioxide emissions.

Age

I am feeling my age. I am in good health, but at 61 I am realistically in the last ‘third’ of my life.

And before the ravages of age slow me down, I realise I have a window of unknown length in which – perhaps for the first time in my life – I am genuinely free to do whatever I want to do.

What an exhilarating and terrifying challenge.

Thank you

And to all those people – genuine friends – who have communicated their support throughout this year – thank you.

My Energy Performance Certificate

April 21, 2021

Click for a larger image. My house was rated B for its EPC assessment

Friends, I am not quite sure why, but the other day I had my house assessed for an Energy Performance Certificate (EPC).

A very nice young man came to the house, measured some things, and then later, in exchange for £90, he e-mailed me a link to an on-line certificate. My house was awarded a B.

I looked online at the EPC ratings of the houses with my postcode, and pleasingly, mine was the best. 🙂

Click for a larger image. My house got the best EPC score of all the houses with my postcode!

You can search your own neighbourhood for houses with EPCs using this link

What does an EPC Assess?

The assessor categorised several aspects of the house on a 5 point scale from very good to very poor. The categories were structural (the walls, roof, floor and windows) and technical (lighting and the system for heating and hot water).

Click for a larger image. These features of the house were assessed.

And what did the EPC tell me?

The certificate estimates that the house uses:

  • 13286 kWh/year for space heating.
  • 2089 kWh/year for water heating.

which would suggest annual gas usage of around 15,300 kWh. In fact I expect June 20-to-June 21 gas usage to be less than 8,500 kWh or only 55% of the EPC estimate.

The certificate estimates that the house emits 2.5 tonnes of carbon dioxide per year. Based on actual usage:

  • 8,500 kWh/year of gas use is equivalent to 1700 kg or 1.7 tonnes of carbon dioxide.
  • 3,600 kWh/year of electrical use is equivalent to 720 kg or 0.7 tonnes of carbon dioxide.

I think the correct answer is about 2.4 tonnes.

So the EPC assessment of 2.5 tonnes appears accurate. But I can’t see how they arrived at that figure based on their estimate of 15,300 kWh of gas use: using a carbon intensity of 0.2 kg/kWhCO2 that would correspond to 3.1 tonnes.

The certificate recommended that I install extra solid wall insulation, even though every external square centimetre is already insulated!

It didn’t seem to take any account of the solar panels or battery that means we probably won’t be using electricity in the summer.

And so what is the EPC good for?

I think the EPC is a government document with an energy performance assessment that is probably loosely correlated with the thermal performance of a dwelling.

It is important that the numbers and ratings are not taken too seriously: I can’t see how they can possibly be accurate. But it probably does serve to identify the very worst performing dwellings, and prevent them being rented. Which is probably a good thing.

I am reminded of Ford Prefects assessment of Earth in the Hitchhiker’s Guide to the Galaxy. EPCs: mostly harmless.

The Wuling Hongguang: the most popular EV in China

March 28, 2021

I like to look at news websites from other countries to try to counter my Teddingtono-centric view of the world.

My favourite foreign news website is Deutche Welle – its measured tones are a pleasing counterpoint to the BBC news website. But I also find the China Daily propaganda site interesting.

I call it a propaganda site rather than a news site because that’s what it is. It never contains anything which could be construed as negative about China and only contains negative stories about the West. However much the Chinese Communist Party would like to pretend otherwise, China is not a normal country.

Nonetheless, one can learn a great deal by seeing how they portray things. And their articles can also help to place a Teddingtono-centric view into a wider perspective. They rarely have stories about Teddington.

Electric Vehicles

Electric Vehicles (EVs) are the future of transportation. And China is the world’s largest market for EVs.

But as I understand it, in Beijing at least, one cannot simply buy a car. Instead, one enters into a lottery where the prize is permission to buy a car. The chance of winning permission to buy a car with an Internal Combustion Engine (ICE) is incredibly low, but the chance of winning permission to buy an EV is much higher.

With that in mind, an article caught my eye in the China Daily lauding the achievements the Wuling Hongguang Mini EV.

A mini-sized model from Chinese brand Wuling, the Hong Guang Mini EV, toppled Tesla’s Model 3 as the world’s best-selling electric car in January, with deliveries exceeding 36,000 in the month, more than those of the Model 3 and Model Y combined.

The BBC reported on this too.

Image Courtesy of Wikipedia

The car is very basic – its battery (9.2 kWh or 13.8 kWh) is typically just 20% the size of the batteries in EV’s on sale in the UK. Its range (~120 km or 170 km) is small, but perfectly adequate for a day of city driving. But its most shocking statistic is its cost: $4,200.

In contrast, the Tesla models it displaced as best sellers cost more than $30,000.

Why is this important?

The very existence of any car at that price has to be a manifestation of engineering fundamentals. In this case EVs are technically simpler to make than conventional cars.

So why are EVs in the UK (and Europe and the US) currently so expensive?

Well I don’t know, but I would guess it is a classical supply and demand situation – with supply severely limited. One bottleneck is the rate at which batteries can be made. Logically existing manufacturers want to put the limited numbers of batteries available into expensive cars. But that shortage won’t last for ever and the price of batteries is falling year on year.

And – batteries excepted – the simplicity of manufacture and assembly of the cars is such that China Daily asserts:

… Wuling does not see itself as a car manufacturer anymore. It aspires to become a creative, popular and boundary-free lifestyle brand.

The reason I am writing this is because it struck me that the Wuling Hongguang looked like it might be the 21st Century equivalent of The Mini. A cheap unpretentious way to get about.

If a basic EV similar to the Hongguang were sold in the UK for (say) £5,000 to £10,000, I think it would be wildly popular. And I suspect that time is coming.

As other people have speculated, the death of the ICE car may come sooner than anyone expects.

Battery Day. One week on…

March 24, 2021

Click for larger view. The graph shows daily electricity drawn from the grid (kWh). Before the solar panels were installed average usage was 10.9 kWh/day. After the solar panels were installed this fell by a couple of kWh/day. After an increase over Christmas when our son returned, we were back to normal. In the last month the solar electricity generated on the lengthening days have reduced the electricity drawn from the grid. Since the battery was installed a week ago, we have not drawn any electricity from the grid.

Wow. 

My wife and I have both been slightly gob-smacked by the Tesla Powerwall.

Since installation last week, without changing our daily habits, we have been off-grid, using only electricity which has been generated on our own roof.

In all likelihood, we will probably be substantially off-grid for the next six months.

The combination of the solar panels and the battery is transformational.

Solar Panels

Click for larger view. The graph shows daily electricity generated by the solar panels (kWh/day) since installation in November 2020. The solid green line shows my guess for what to expect and the yellow dots show the expected monthly average based on an EU website with historical data. The green dots show actual monthly averages and the pink line shows a 5-day running average.

Broadly, as the graph above shows, things are proceeding as I had foreseen.

Battery

We are currently using the battery in its default mode. In this mode it does not try to predict tomorrow’s sunshine ‘harvest’ and does not top-itself-up with night-rate electricity.

This seems to be fine with our relatively low usage and the increasing solar generation as we head into summer.

We will need to change mode to include off-peak top-ups when we head into winter, and possibly even in the summer after we scrap our gas boiler and install a heat pump for our domestic hot water requirements. But for now, it seems to work very straightforwardly.

I have – obviously – been analysing  the data and I will write about that in due course. But here I will just note two curiosities that make the analysis slightly tricky.

The first is that the battery itself consumes electricity, but the amount of power it uses is not declared. Using some secondary indicators I estimate that – as installed at the moment – it appears to be drawing about 50 W i.e. 1.2 kWh a day.

Click for larger view. On the App screen, energy flows between the grid, our home, the solar panels and the battery all appear equivalent.

A second curiosity  is that – as reported by the App – it looks like the energy flows in all directions are all equivalent. But this is not the case

  • For example, when the app reports 1 kW flowing into the battery for one hour one might expect the battery’s state of charge to increase by 1 kWh. But because of the conversion losses, the battery probably only stores about 0.95 kWh.
  • Similarly, on discharge, if the app reports drawing 1 kW from the battery for one hour one might expect the battery’s state of charge to decrease by 1 kWh. But because of the conversion losses, the state of charge probably falls by about 1.05 kWh.

The actual state of charge of the battery is indicated as a percentage on the app, but this data is not exported.

Altogether this makes, the state of charge of the battery – how many kWh of electricity are stored in it – quite tricky to estimate. But I am working on it.

Overall

Overall, I have the sensation of floating.

The thought that the combination of a battery and some solar panels is enough to disconnect from the grid for the next six months is truly transformational. Both from a carbon emission perspective, and from a financial perspective.

Wow!

Click for larger view. The graph shows daily electricity drawn from the grid (kWh). Before the solar panels were installed average usage was 10.9 kWh/day. After the solar panels were installed this fell by a couple of kWh/day. After an increase over Christmas when our son returned, we were back to normal. In the last month the solar electricity generated on the lengthening days have reduced the electricity drawn from the grid. Since the battery was installed a week ago, we have not drawn any electricity from the grid.

Battery Day: First Results

March 20, 2021

Me and my new Tesla. This unit contains 13.5 kWh of battery storage along with a climate control system to optimise battery life. We have placed it in the porch so that (when visits are allowed again) everyone who visits will know about it!

Last September, Tesla held their ‘Battery Day‘ during which they unveiled their road map towards cheaper, better, batteries.

Not to be outdone, last Monday VW held their own ‘Battery Day‘ during which they unveiled their road map towards cheaper, better, batteries.

And last Thursday was my own battery day, when Stuart and Jozsef from The Little Green Energy Company came and installed a Tesla Powerwall 2 at Podesta Towers in Teddington. I was (and still am) ridiculously excited.

I am still evaluating it – obviously – but here are a couple of notes.

How it works

The system has two components. An intelligent ‘gateway’ that monitors loads and supplies, and a climate-controlled battery storage unit.

Click for a larger version. The left-hand graphic shows how AC power enters our house, and how DC power generated by solar panels is linked to the grid. When the Solar PV is sufficient ,power is exported to the grid. The right-hand graphic shows how the TESLA ‘gateway’ device monitors the solar PV, domestic loads and battery status and intelligently decides what to do.

The gateway (and the battery) are electrically situated between the electricity meter and all the loads and power sources in the house. So all energy enters or leaves the battery module as AC (alternating current) power.

But its internal batteries must be supplied with DC (direct current).

This makes it ideal for storing power from the AC grid, but less than ideal for storing the DC current generated by solar PV panels.

One might have expected that a device designed to store solar power might intrinsically operate using DC and indeed, some battery systems – positioned between the solar PV and the inverter – do this.

So the choice to place the Powerwall™ where it is, is a compromise between the extra functionality this location offers – it can back up the entire house – and the inefficiency of storing solar PV which is first converted to AC by the inverter, and then re-converted back to DC by the Powerwall. The support document states that the conversion from AC to DC and back to AC has 90% round-trip efficiency.

The photograph below shows the gateway installed under the stairs in our house.

Click for a larger version. The Tesla ‘Gateway’ installed in our house. The unit is positioned in between the electricity meter and all the domestic loads. The black conduit leads under the floor to the battery which is installed in the porch.

Control

The system is controlled by an app which is – frankly – mesmerising. It shows how electrical power flows between:

  • the grid,
  • the battery,
  • our home, and
  • our solar panels

Click for a larger version. Screenshots from the app at various times yesterday.

There is less room to adjust the parameters of the system than I had anticipated. This appears to be because, in exchange for a guarantee that the battery will retain at least 80% capacity (10.8 kWh) after 10 years, one is required to relinquish detailed control to the Tesla Brain.

Through a built in network connection, the device is in constant touch with Tesla who monitor its performance and can detect if it is abused in some way. I am not sure how I feel about that – but then guaranteed long-term performance is certainly worth something.

One feature of this relinquishing of detailed control concerns ‘time-of-use’ tariffs. I anticipate that – especially in winter – I will need to charge the battery overnight on cheap rate electricity.

The system supports this mode of operation but is not yet operational. Apparently it needs to study the patterns of household use for 48 hours before being enabled.

When operational, one gives the system general instructions and then allows it to choose when, and by how much, to charge. There is for example no way to force the battery to charge to 100% on command.

In practice I suspect it will be fine, but at the moment it still feels a little weird.

Performance on Day#1

The simplest way to show how the Powerwall™ works is by looking at the data which the ‘App’ makes available.

The first graph shows the household demand through the day. It’s fascinating to look at this data which has 5 minute and 0.1 kW resolution. The metrologist in me would like more – but in honesty, this is enough to understand what is happening.

Click for a larger graph. See text for details.

Now we can look to see how that demand was met. Overnight, we relied mainly on the grid.

Click for a larger graph. See text for details.

The battery could have supplied this overnight electricity, but it had been set to hold a reserve of 16% of its capacity (~2 kWh) in case we required backup after a power cut. We have lowered that setting now because, thankfully, power cuts are rare in Teddington. The battery drew power from the grid overnight in two short periods to maintain this reserve.

Additionally, at the end of a sunny day in which the solar PV filled the battery, there was brief period where we returned electricity to the grid.

During the day – which was very sunny 🙂 – the household electricity demand was met by the electricity from the solar panels.

Click for a larger graph. See text for details.

Without the battery, most of this 16.91 kWh of electricity would have been sent to the grid. But now only a tiny fraction was returned to the grid, most of it being captured by the battery – see below.

Click for a larger graph. See text for details.

The graph above shows the battery maintaining its reserve charge at night, and then charging from the solar PV during the day. At peaks of household demand, the charging is paused. At around 16:00, the battery was briefly full, and shortly thereafter it began discharging to meet household demand.

As I write this at 1:00 p.m. on the day after the day shown (a rather dull day 😦 ), the battery is 56% full and charging.

The graph below shows all the above curves together.

Click for a larger graph. See text for details.

Overall

The Powerwall system is an object of wonder. It is beautifully engineered and miraculous in its simplicity.

It transforms the utility of the solar PV allowing me (rather than electricity companies) to benefit from the investments I have made.

I will post more about the performance in terms of cost, electricity and carbon dioxide when I have more data.

But for the moment I will just thank Jozsef and Stuart from The Little Green Energy Company for their professionalism and attention to detail. And ‘No’. I am not being paid to say that – quite the opposite!

Stuart and Jozsef from The Little Green Energy Company. You can’t see it, but they assure me they were both smiling. Click for a larger version

 

Sometimes I find it hard to like EDF

March 16, 2021

Click for larger version. EDF wrote to me today to say they are increasing the price of ‘night rate’ electricity by 73.7%.

Energy is a wonderful thing. But sometimes it can be hard to like the companies which sell it to us…

…especially when they increase the price of their product by 73% overnight!

As regular readers will know, since 2018 I have been working hard to reduce my household energy consumption and the concomitant carbon dioxide emissions.

My 3-step plan has been:

  1. Reduce household heating requirement with insulation and triple-glazing.
  2. Switch from gas heating to electrical heating with a heat pump.
  3. Use solar panels and a battery to generate low-emission electricity and reduce the cost of switching to electrical heating.

Part#1 is complete: winter is not yet at an end, but heating demand appears to about 50% lower.

Part#2 is underway and I hope to have a heat pump installed this summer. But electrical heating is more expensive than gas heating.

Part#3 is underway: the solar panels are performing well and a battery should be installed this Thursday. The battery should allow me to use mainly my own solar electricity, or EDF off-peak electricity for most of the year.

I carried out extensive modelling of the effect of varying patterns of electricity consumption and compared different ‘tariffs’.

I had based my costings on the fact that the night rate for electricity would be about 5p/kWh and day rate would be about 25p/kWh. Of course I knew these costs could vary over time.

Nonetheless, it would be an underestimate to say that I was ‘disappointed’ when EDF wrote to me this morning to say that price of night time electricity was to rise from 4.99 p/kWh to 8.67 p/kWh…

…a 73% rise!

Like I said, sometimes it can be hard to like the companies which sell us energy.

Switch!

I am thinking about it.

But switching is, in my opinion, a distraction. It is a way of distracting us ‘fish’ from the fact that we are in a ‘barrel’ and at the mercy of the confusopolists.

 

Previous articles about the house.

2021

2020

2019

COVID-19: The risk to men

February 17, 2021

Click for a larger version. Output from the QCOVID calculator showing the risk arising from ethnicity and biological sex compared to a 61-year old woman.

Friends, you may have read recently (e.g. The Guardian) of a new tools for analysing the risks of dying from COVID-19 including many different risk factors, including ethnicity.

The tool – called QCOVID – is available for you to use here.

Media coverage generally highlighted the relative risks appropriate to different ethnic minorities.

For some reason, the media did not mention the most prevalent risk factor for dying from COVID-19: being male.

Results 

As one does, I immediately typed in my own basic statistics: I am a white male aged 61 with a BMI of 24.8. The result was this:

Click for a larger version. Output from the QCOVID calculator for someone with my vital statistics.

I took note of the absolute risk of a COVID associated death: my risk was 0.0173% over a 90-day period i.e. a risk 1 in 5,780.

I then changed the ethnicity and biological sexuality entries to the calculator across a number of categories.

Changing ‘my’ biological sexuality to female I saw that ‘my’ risk went down to 0.0077% over a 90-day period i.e. a risk 1 in 12,987.

So the additional risk factor associated with being a biological male was 2.2.

Click for a larger version. Output from the QCOVID calculator showing the risk arising from ethnicity and biological sex compared to a 61-year old woman.

I was curious as to how this compared with differences arising from ethnicity and the results relative to the ‘Me-female’ are shown in the table above.

I found the results striking.

  • For females, the additional ethnic risk factors ranged from 1.2 to 2.0. In comparison the additional risk factor of being a white male was 2.2
  • In every ethnic category, being male carried an additional risk factor varying from 2.2 to 4.6 compared to the equivalent female.

Conclusions

I did not investigate all the various categories in the QCOVID calculator, so I cannot confirm the complete generality of this result.

But from my simple investigation, I conclude that:

  • Men of any ethnicity are at least twice as likely to die from COVID-19 as women from the same ethnic background.
  • The additional risk faced by women associated with their ethnicity is less than the additional risk faced by white males associated with their sexuality.

My question is this: why has this dramatic result affecting millions of people not been reported more widely?

Update 19th February

A correspondent pointed out in the comments this excellent data source

This site shows that excess mortality amongst men occurs worldwide, but the extent of it is highly variable from one country to another.

I don’t have an explanation of this phenomenon, but it does appear to be very real, whatever its cause.

 

 

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.

Summary 

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!

Resources

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

 

Thinking about domestic batteries

January 3, 2021

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

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

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

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

This is because energy can flow in several directions.

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

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

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

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

Mode#1: Storing in the day.

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

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

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

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

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

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

Mode#2: Storing at night.

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

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

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

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

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

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

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

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

The data are graphed below.

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

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

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

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

Summary so far

So these two strategies involve using the battery to:

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

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

I think the operating principles I need are these:

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

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

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

Battery only: No Solar

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

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

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

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

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

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

Battery and solar in harmony 

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

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

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

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

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

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

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

Battery and heat pump and solar 

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

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

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

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

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

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

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

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

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

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

Summary

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

Regarding money:

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

Regarding carbon:

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

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


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