Diesel and petrol costs compared with other fuels

Before comparing running costs of different types of car, it is worth thinking about the cost of petrol and diesel compared with electricity, and indeed other fuels. This post is the first part of a series. We begin by considering the raw costs of fuel. Next we consider the efficiency with which we can use those fuels, which affects the the real cost of use. The third part looks how taxes affect the real costs.

Before making a comparison, it’s useful to remind ourselves of the units we are using. Lift an apple up a metre and you’ve done about a joule of work. Do that 3.6 million times and you’ve done 3,600,000 joules of work; that’s 1 kilowatt hour (kWh), the standard unit for supplying gas and electricity to the home.

Here is a direct comparison of the costs to the consumer of electricity, petrol and diesel.

We are comparing all the fuels by the price per kilowatt-hour, even though we don’t buy petrol and diesel by the kilowatt-hour.

What is there to remark on? Perhaps that the different fuel costs per kWh are broadly similar and there is no obvious reason, from this information, leading us to think that electric cars should be cheap to run.

We buy petrol and diesel in litres rather than kWh and we know that diesel fuel is a significantly more expensive than petrol, and yet the cost per kilowatt-hour for the two fuels is similar. It’s not hard to see that diesel fuel contains more energy per litre.

Let’s follow the numbers.

Petrol
A litre of petrol has an energy content 9.4 kWh per litre and petrol currently costs 116.4p per litre. So the price per kWh is 116.4/9.4 = 12.4p per kWh.

Diesel
A litre of diesel has an energy content of 10.3 kWh and costs 120.6p. So the price per kWh is 120.6/10.3 = 11.7p per kWh. We can see one reason why diesel cars cheaper to run than petrol cars: diesel, despite being 4% more expensive, is about 6% cheaper per kWh.

Electricity
Buying electricity from the electricity supply at home, we pay about 17 p per kWh. Some electricity tariffs supply electricity more cheaply at night and charge a bit more per day (20p) and less (10p) for the 7 hours overnight, averaging the same 17p per kWh.

Public electric charging stations
Electric cars are in their infancy. Charging at home is a recent step. But public charging stations are even more of an innovation. The prices of the services they provide will no doubt change over time but at the moment it can be much more expensive to charge your car from a station ‘on the road’. Ionity fast chargers charge 69p per kWh, with other providers charging more than twice what you would pay at home. If these costs become applied generally, electricity is certainly not a cheap fuel. On the other hand Lidl charges 23p p/kWh at the moment, a reasonable mark-up for the cost of providing the service. Tesco is free but one can’t see that lasting.

You can stop here if you like
The rest of this post is concerned with following the numbers through for a wide variety of fuels, not all of them for transport. I’ve put it here because I think it’s fun to collate all the fuel information and also so that later on I can branch off into considering domestic heating. You might like to have a quick look at the summary table a bit further down before departing.

Road LPG
LPG stands for liquefied petroleum gas, It liquefies under modest pressures and so can be stored in tanks and used for domestic and commercial heating and for vehicle propulsion.
LPG has an energy content of 7.2 kWh per litre and at a current price of about 65p per litre, that’s 65/7.2 = 9p per kWh.

Heating LPG
Here we find our first consideration of the effect of tax on prices. LPG for heating has much less tax on it than LPG for transport. That brings its costs down to a typical 36 p per litre and with the energy stored being 7.2 kWh/litre, that equates to 36/7.2 = 5 p per kWh.

Red Diesel
Red diesel is a tax-free version of road diesel, used for purposes like powering agricultural vehicles or heating. It is ordinary road diesel that has a red dye to colour it to check it is not used for taxable purposes. Red diesel has the same energy content as road diesel at 10.3 kWh per kWh but the reduced tax means that it costs only about 60p per litre. So the price per kWh is 60/10.3 = 5.8p per kWh.

Gas
Gas costs about 3p per kWh at the moment. That’s because the oil price is very low due to the covid crisis. My own view, for reasons that I might address eventually, is that the ‘right’ price for gas is 5p per kWh.

Summary of fuel costs
I’ve decided to summarise the fuel costs at this point before you get too bored with repeated calculations. The remaining calculations and some comments on the fuels follow the table.

Heating oil
10.85 kWh per litre and 41p per litre, which gives 41/10.85 = 3.8p per kWh.

Solid fuel
House Coal is £267 per tonne (1000 kg) or 26.7p per kg. Its calorific value is about 7 kWh/kg. So the cost per kWh is 26.7/7 = 3.8p per kWh.
Anthracite is 40p/kg with a calorific value of 9.2 kWh/kg, giving a cost of 40/9.2 = 4.34 p/kWh.
Blaze Smokeless house fuel is 33.5 p/kg, with a calorific value of 5 kWh/kg giving a cost of 33.5/5 = 6.7 p/kWh.
Like all fuels in which there is direct negotiation with the supplier, solid fuels prices depend on your ability to haggle and the time of the year at which you are buying. You can buy smokeless fuel for 28p/kg in the summer, much less than its winter price.

Wood pellets
£265 for 1150 kg, which is 23p/kg. Calorific value around 4.9 kWh/kg, which gives 23/4.9 = 4.7 p/kg.
My own view is that wood pellets are not, in general, a renewable source of energy. Wood sawdust should be used to make materials like MDF (medium density fibreboard) which is used instead of wood in many products. Those who use them believing that the have some benefit in ‘saving the planet’ should think twice. Burning pellets of wood results in more living trees being cut down and therefore encourages the destruction of the natural environment.

Logs
Kiln dried Ash logs, £350 for 750 kg = 47p/kg. Calorific value 5.5 kWh/kg, giving 47/5.5 = 8.5 p/kWh.

Manufactured heat logs
Wickes; £6.50 for 9.5 kg, a pack of 12. That’s 68p/kg. There is no given figure for the calorific value of this product but the forest research reference below indicates that the calorific values of all woods is about 5 kWh/kg. So these Heat Logs cost 68/5 = 13.7 p/kWh. They are an expensive form of heating, particularly when we take into account efficiency in the next post on this subject.

Sources of information
Figures for this post date from January 2020
http://www.monikie.org.uk/fuel-calorific-values.htm/
https://homefuelsdirect.co.uk/
https://www.nextgreencar.com/car-tax/fuel-duty/
https://www.directstoves.com/resources/guide-to-solid-fuels/
https://www.forestresearch.gov.uk/documents/1958/FR_BEC_Wood_as_Fuel_Technical_Supplement_2010.pdf
https://www.whatcar.com/news/electric-vehicle-charging-%E2%80%93-what-does-it-really-cost/n16833
https://www.thisismoney.co.uk/money/cars/article-8046323/Charging-electric-car-using-public-chargers-cost-10-TIMES-home.html

Lost poem – Elgar

This poem, about Elgar, is a memory from childhood. It’s quirky and amusing.

I’ve googled it, etc, with no luck. So I stick it here wondering if a search engine will pick it up and a fellow seeker will find that he isn’t a lone seeker.

Try to imagine if you can
That Elgar was a handyman,
And when not writing tunes and airs
Was very fond of making chairs,
And he derived such merriment
From chemical experiment.

Another thing you’d often see
Was Elgar chopping down a tree,
And once he made a double bass
Out of an ancient packing case.
I think this fact sticks out a mile:
Elgar was very versatile.

Hot water timing – a waste of effort.

Summary
It goes against our nature to be told there is nothing one can do about something but sometimes logic drives us to that conclusion. Energy saving heating controls are sometimes like that. Some controls are worthwhile: others are not. Despite apparently well-qualified sources saying the contrary, if one has a modern hot water cylinder heated by oil or gas, it saves almost no energy to have the hot water timed, rather than have it turned on continuously.

Analysis
Here is the energy label from typical recent hot water cylinder.

This label shows that the cylinder has a volume of 150 litres and loses heat at the rate of 60 watts (60 joules per second).

Calculating the energy loss
Losing energy at 60 joules per second means 60 x 3600 = 216,000 J per hour.
Overnight (from 10 pm to 6 am) or during the day (from 8am to 4 pm) are 8-hour stretchs, so during that time the total energy loss is 8 x 216,000 joules = 1,728,000 joules = 1.78 MJ. That’s 1.78/3.6 kWh, about half a kilowatt hour, ie about 3 p if you heat your hot water by gas.

So, every morning, or every evening, if the hot water has been turned off for 8 hours, the boiler uses 3 p worth of fuel just to top up the losses during the day. That’s 6 p per day, or £22 per year. Is there the possibility of saving some of that energy wasted?

As the tank loses energy it cools down
The tank contents are 150 litres (150 kg) of water. We can calculate how much its temperature falls.
Energy = mass x specific heat capacity x temperature change.
1,728,000 joules = 150 kg x 4200 J/kg K x temperature change
temperature change = (1,728,000)/(150 x 4200) = 2.74 °C (Physicists label that 2.47 K)

If the hot water is turned off, the temperature drops a small amount.
If your controls turn the hot water off for an 8-hour period, your hot water drops in temperature by about 3 °C, say from a set temperature of 65 °C down to 62 °C. That means its average temperature is 63.5 °C.
The first effect of the heating system when the time turns the hot water system back on is to heat the water back up to 65 °C. That’s where the 3 p worth of energy is used.

If the hot water is left on, the temperature doesn’t fall
If you leave your heating switched on, the hot water stays at 65 °C. Whenever the thermostat senses that the temperature dropping, it turns the heating system on to top it back up. So instead of having to reheat the water when the system turns back on, it is continually topping up the energy loss – by an amount pretty much the same as the 3-p-worth which it needs if it switches the hot water off.

But surely you save some energy by turning off?
If you keep the hot water on, it is at a steady 65 °C, that is steadily 45 °C above the 20 °C surrounding room.
If your controls turn the hot water off for an 8-hour period, the tank temperature drops from 65 °C down to 62 °C, an average of 43.5 °C above the surroundings. This is not very different from leaving the hot water on and therefore the heat loss is pretty similar.

If, when switched off, the temperature above the surroundings has dropped in the proportion 43.5/45 compared with leaving the hot water turned on. The energy loss, and the cost of the energy loss, has dropped in the same proportions.

So the heat losses during switched-off times go from £22 a year to = £22 x 43.5/45 = £21.27 a year. That means that the reheating costs drop by 83p a year.

If you have oil or gas central heating and you control your hot water heating and turn it off for periods during the day, you might save £1 a year, a trivial saving against the convenience of hot water at any time or the simplifications of your heating control system.

In fact the savings are even less
So far we’ve assumed that all the ‘losses’ from the hot water cylinder are waste. This is not always the case. At times of year when a house is being heated, energy ‘lost’ from the boiler is useful in heating the house. If the house is being heated by gas, a 60 W loss from the hot water tank is worth as much as about a 20 W heating from the gas boiler during the heating season, so the potential savings of switching off drop to about 70p a year. If you are heating by on-peak electricity, the 60 W ‘lost’ is just as good as 60 W produced by your electrical heating, so the savings are about 42 p per year.

What about longer periods of switch-off
If you are away for a whole 24-hour day, that’s three times as long as the 8-hour periods we’ve considered. If you turned the heating off for that day away, the hot water temperature would drop by about 3 x 2.47 K, = 7.4 K, ie down from 65 °C to 57.6 °C, an average temperature of 61.3 °C, ie 41.3 K above the surroundings. This would take the heat loss down to 8.3p. So you can save 0.7 p by turning off the heating if you are aware for a day. Only if you are away for several days during which the tank temperature will drop very significantly, is it worth turning the hot water off. If you turn the tank off when you are away for a week, you will save about 60p. With the average household away for less than 4 weeks a year, turning off hot water when one is away can save at the most a couple of pounds a year.

If you have a combi boiler
Most combi boilers heat hot water on demand. With them there is no stored hot water and no ability to turn the hot water off. Some combi boilers have a small reservoir of water that is always kept hot so that the boiler delivers hot water even more quickly. One can save a small amount of energy by turning this pre-heat system off but manufacturers do not recommend it because the savings are small.

The only time is is worth controlling hot water heating
If you have off-peak water heating it is worth controlling the hot water heating. In that situation it makes sense to make sure that the heating of the hot water is done during the night. Let’s run the calculations.

In a flat occupied by 2 people, hot water consumption might be 100 litres (100 kg) of water per day. This water has to be heated from an average temperature of 10 °C to, 65 °C, an increase of 55 kelvin. The energy needed to heat this water is
mass x specific heat capacity x temperature rise
= 100 kg x 4200 joule/kg K x 45 K = 18.9 MJ = 18.9/3.6 = 5.25 kWh.

Heating this by on-peak electricity at 14.9p per kWh costs 14.9 x 5.25 = 78 p per day.

Heating this by off-peak electricity at 9.3 p per kWh costs 9.3 x 5.25 = 49 p per day.

So you can save 29 p per day, ie £106 per year, by using off-peak electricity.

Under those circumstances only is it worth controlling the time at which you heat the water.

Topping-up electrically heated hot water
Many electrically heated hot-water systems have a top-up facility by which one can turn an immersion heater on if one runs out of off-peak-heated water.

If one needs the top-up regularly, then certainly one is using more than 100 litres per day and there is value in considering a larger tank. There are savings in the order of £200 per year if one heats 200 litres of water a day with off-peak electricity rather than with on-peak.

On the other hand, if one tops up rarely, the easiest thing to do is to set the overnight heater to a high temperature and the top-heater to a lower temperature. It will rarely turn itself on and the cost of having hot water always available will be less than £10 a year if one found that one was turning the on-peak heater on less often than once a week.

There are exceptions to this analysis. If one wears hair shirts and likes to be nagged into reduced water consumption, rely on the overnight hot water running out and giving you the occasional cold shower so that you have less time in the shower and take pleasure in using less hot water and less energy.

In practice there are a number of confusing factors to this analysis. Experience shows that those households in which saving energy is a high priority are also those with drench showers that use most water…

Other reasons for switching the hot water off at night.
Sometimes the most numerate don’t like the feeling that there is nothing that one can do to effect a significant saving and they want to control the water heating whatever. Sometimes there is a light sleeper in the house disturbed by the noise of the hot water system…

Surely there is something you can do?
Modern hot water cylinders are much more effectively insulated. If your hot water cylinder is old, and by that I mean perhaps as little as 10 years old because insulation standards have increased rapidly in the last decade, it is worth considering a new hot water cylinder.

Hot water cylinder swap worthwhile?
Heat your hot water cylinder fully and measure the hot water temperature (say at the tap with a cooking thermometer). Then turn off its heating completely and measure the hot water temperature after 8 hours.
If the temperature falls by less than 5 °C in eight hours your cylinder is well-enough insulated. The greater fall than this, the more worthwhile it is swapping the cylinder. If the temperature falls by 20 °C in 8 hours, you’ll save well over a hundred pounds a year by upgrading to a modern hot water cylinder.

The green serenity prayer
As always it makes sense to change the things that matter, accept the things that don’t and have the wisdom to know the difference.

Electric cars 1 – baseline figures: electric cars vs an economical diesel

Small electric cars
Carwow recently tested 6 small electric cars. They were able to travel between 3.7 and 5.2 miles per kWh and had ranges between 113 and 229 miles. That’s a factor of 2 in the range but the battery sizes varied from 28.5 kWh to 52 kWh. Roughly, if you have twice the battery size, you can go twice as far. The best was the Renault Zoe which, with the 52 kWh battery, has a mass of about 1500 kg, or a ton and a half.

Larger electric cars
A Tesla Model S has a mass of 2350 kg (2.3 tonnes) with the largest (100 kWh) battery. Its range is claimed to be 315 miles. So the Model S is able to travel 315 miles/100 kWh = 3.15 miles per kWh.

Thought
Why do larger electric cars, with larger range, do fewer miles per kWh? The answer is simple. If you have a larger battery it’s much heavier (technically a larger mass). The Renault Zoe 52 kWh battery has a weight of 326 kg. The Tesla S 100 kWh battery has a weight of 625 kg, roughly twice that of the Renault Zoe for twice the capacity. If the battery has a larger mass then the whole car needs to have a larger mass because it needs to have larger motors to accelerate that mass, larger brakes to slow the mass down, stronger structures to support the mass, etc.

The biggest electric fuel tank on the market
So far as I am aware, the 100 kWh battery of the Tesla model S is the biggest car electrical fuel tank on the market. It has a capacity of 100 kWh.

Comparing electric car figures with a modern diesel car
Let’s compare the Tesla battery with the modest 47 litre fuel tank from my own medium-sized Renault Megane.
Diesel fuel has energy of 10 kWh per litre. So the the 47 litre tank has an energy capacity of 470 kWh. That sounds great until you realise that the efficiency of a diesel engine is about 30% compared with the near 100% efficiency of electrical motors. So let’s multiply by 30% (0.3) to work out the effective capacity of the Renault Megane fuel tank.
30% x 470 kWh = 141 kWh.
Gosh, that’s interesting. A medium-sized diesel car has nearly 50% more energy capacity than the largest electric car.
Moreover, since diesel has a density of about 0.8 kg per litre, the mass of the diesel tank plus the fuel will be about 47 kg for its energy capacity of 141 kWh, compared with the Tesla battery’s mass of 625 kg for an energy capacity of 100 kWh.
Diesel tank: 3 kWh/kg.
Electric battery: 0.16 kWh/kg.
The diesel fuel tank stores nearly 20 times as much per kilogram than the electric battery. In fact, for reasons I may tackle on a later post, the difference is even bigger than this.

Diesel car fuel consumption
The 2016 Renault Megane diesel is quiet, comfortable and has good economy figures.
It has a mass of 1500 kg, about the same smaller electric Zoe. (The Zoe’s mass is larger because the battery has a large mass.) Over around 8364 miles of mostly long-distance driving, it averaged 56 mpg with an average speed of about 30 mph. That’s a slower speed, and more accelerating and braking than the cars in the Carwow test.
8364 miles at 56 mpg is 8364/56 = 149.4 gallons for those 8364 miles.
Since there are 4.55 litres per gallon, that is 149.4 x 4.55 = 680 litre.
Each litre has 10 kWh of energy but diesel engines are only 30 % efficient, so we get 3 kWh of useful work out of each litre of diesel.
Total amount of useful work out = 3 kWh/litre x 680 litres = 2040 kWh for 8364 miles.
So energy needed per mile = 8364 miles/2040 kWh = 4.1 miles/kWh.
So we can see that the medium-sized Renault Megane travels as many miles per available kWh as a typical small electric car.

Broad facts worth remembering.
A small car will travel about 5 miles per kWh.
A large car will travel about 3 miles per kWh.
Medium cars, as you might imagine, are somewhere in the middle.
If you want to travel 300 miles in a large car, you need 100 kWh.
That is as simple as that.
A 50 kWh battery, powering a small car which does 5 miles/kWh, will give a range of 50 kWh x 5 miles/kWh = 250 miles, but there isn’t yet a small electrical car that will do that: the Renault Zoe, travelling at a constant speed along a motorway, only did 229 miles.

Other tests on the Megane
I did two trial runs on quiet motorways to measure fuel consumption at fixed speeds.
At 48 mph I averaged 72 mpg.
At 58 mph I averaged 58 mpg.
These figures point to the reasonableness of the overall 56 mpg figure experienced in practice.

What if?

What if coronavirus,
Creeps around unstoppably,
In aerosols too fine for masks to impede
And, like many a disease before it,
Is already so widespread
That, despite all our efforts,
It will take its toll
Whatever we do?

What if our many billions,
Poured out in lockdown
With no regard for wiser means,
Have had not the slightest effect,
Save for an impoverishment
That leads us to borrow more
From nations who hold in contempt
All we once regarded as dear?

What if men and women,
Entranced by man’s achievements,
With ne’er a thought for God,
Have grown oblivious to the powers of nature,
And, having been told so often
That we have rights to all and sundry,
Forget that the source is not government fiat
But fair winds and the sweat of man’s brow?

What if we are governed
By a godlessness
That, unlike the real Canute,
Knows not the limits of man’s power
But assures us that viruses can be beaten
And, were it politically expedient,
Would equally tell us
That the sea could be held back?

Canute the Great was king of Denmark, England and Norway. He was one of the first Scandinavian kings to accept Christianity. Medieval historian Norman Cantor called ‘the most effective king in Anglo-Saxon history‘, which corelates with the story of him demonstrating to his flattering courtiers that he had no power over the waves.

The story reminds one of Psalm 2:

Why do the nations conspire
    and the peoples plot in vain?
The kings of the earth rise up
    and the rulers band together
    against the Lord and against his anointed, saying,
“Let us break their chains
    and throw off their shackles.”

The One enthroned in heaven laughs;
    the Lord scoffs at them.
He rebukes them in his anger
    and terrifies them in his wrath, saying,
“I have installed my king
    on Zion, my holy mountain.”

I will proclaim the Lord’s decree:

He said to me, “You are my son;
    today I have become your father.
Ask me,
    and I will make the nations your inheritance,
    the ends of the earth your possession.
You will break them with a rod of iron;
    you will dash them to pieces like pottery.”

Therefore, you kings, be wise;
    be warned, you rulers of the earth.
Serve the Lord with fear
    and celebrate his rule with trembling.
Kiss his son, or he will be angry
    and your way will lead to your destruction,
for his wrath can flare up in a moment.
    Blessed are all who take refuge in him.

Abandoning mechanical disk drives

A fast mechanical hard drive, connected by a USB 3.0 connection to a laptop, conveys data at around 90 MB/s. Multiplying by 60 that’s 5400 MB/minute, ie around 200 minutes for 1 TB.

It is reasonable (at least in 2020) to say that man can survive on 1 TB, unless one is actively engaged in copious video editing, hence the many online storage systems that offer 1 TB as the entry level. If one does a complete backup monthly, not a daft thing to do, that means hanging around for 200 minutes, ie 3 or 4 hours, for a backup every month.

A fast 1TB USB solid state disk will operate many times faster than a mechanical hard drive. This one, from Sandisk, costs £150 and promises 1000 MB/s. In practice a typical laptop USB port will limit that to 400 MB/s. This is still five times as fast as a mechanical hard drive. It means completing a full backup in half an hour.

So moving from mechanical hard disks to fast solid-state-disks can save a couple of hours hanging around time per month.

If one regards one’s labour, or one’s free time, as worth as little as £5 per hour, swapping from a mechanical hard drive to SSD could save one 2 hours of hanging around per month, £10 per month, £120 per year…not far of the price of the fast SSD saved in a year. If one is in a commercial environment, the time value of money means that it is even more worthwhile to make the move to solid state storage.

Covid-19 and its overall effect on England and Wales death rate.

Covid-19 has affected death rates in obvious ways: it has been a direct cause of death; it has occurred alongside other illnesses, resulting in some earlier deaths as a consequence; its disruptive presence throughout the health service has resulted in early deaths for some who have been denied life-saving treatment, or have been reluctant to seek treatment, for other conditions. As 2020 comes to a close, we can see the overall effect of covid over getting on for a whole year and its overall impact on the death rate for England and Wales.

This graph shows the erratic nature of the weekly death figures. There are big spikes down at Christmas (and other holidays) when deaths are reported late and up just after New Year when the deaths over Christmas are added in. But this graph already shows some interesting figures.

The death rate for over 65s is about 4%. That means that 1 in 25 over-65s die within a year on average. But since there are about 11 million people over 65, that is about 440,000 over-65s deaths per year.

The death rate for under-65s is about 0.2%. We can see that that it has varied little as a result of covid. On average 1 in 500 under 65s die every year. And since there are nearly 50 million under-65s, that means that there are about 100,000 under-65s deaths per year.

The average total death rate for England and Wales is the 440,000 over-65s plus the 100,000 under-65s, giving a total annual death rate of about 540,000.

If we average the weekly death rate over a 4-week period, we see more of the underlying pattern.

This shows that the death rate for over 65s varies quite a lot over the year, hitting a peak sometimes over 6% in the winter, dropping to below 4% in summer. This year we had a very high peak of over 8% in March but that was followed by particularly low death rate in August. Some of those who died in the April covid peak did not live to die at their expected time of August. This provokes the question as to what extent the reduced deaths of August compensated for the increased deaths in May. To find out the extent of this balance, we average over a longer period of 4 months.

The 4-month average shows that 2020 is only a slightly unusual year. For the over-65s, the death rate rose to a high of 5.6%, while falling to an unusual low of 3.6% in September.

Certainly covid was instrumental in the particularly high death rate in April but there was another contributory factor: winter 2018-19 was a year in which there were relatively few flu deaths. This means that the vulnerable who would normally have died in that winter were still around in the peak of the 2019-20 season and among those who succumbed to covid.

We still see the particularly low death rate of 3.6% in September, a consequence of the vulnerable dying in April and not being around to contribute to the September statistics.

Monthly figures are not available for years before 2010. But whole year figures are available from 2006 and are shown here.

As can be seen, the 2020 death rate is entirely normal in the historical context, having an overall death rate for over 65s of 4.5%, slightly more than the peak of 4.4% in 2015 but less than the 4.8% figures from 2006 to 2008

Calculating total excess deaths
On the basis of previous years we predict how many deaths we would expect in a given year and compare it with the actual number of deaths. These figures we have been dealing with enable us to make a prediction for death rates for 2020.

If we confine our calculations to the recent low death-rate years, the average death rates for under-65s from 2013 week 52 to 2019 week 51 are as follows:
Under-65s – 0.169%
Over-65s – 4.321%

Using the figures below for the numbers in the two cohorts, this gives predicted deaths for 2020 of
Under-65s – 83,376
Over-65s – 459,545
Total – 562,922 (The extra 1 being a consequence of rounding issues.)

In fact the total deaths in England and Wales for 52 weeks from 2019 week 52 to 2020 week 51 has been 600,058. This is an excess death figure of 37,136. However, if we compare 2020 with 2006-8, we find that 2020 has had 27,491 fewer deaths pro rata than these years.

Even if the excess mortality in 2020 is close to 37,000, that includes deaths from all causes, including the knock-on excess deaths from all other diseases where treatment has been disrupted by attention to covid. (Many of us know perhaps more individuals who have had life-saving treatment disrupted than individuals who have died of covid.)

Bearing in mind that there have been suggestions that excess deaths for cancer may be, at a minimum, in the order of 10,000, it seems likely that the excess deaths due to covid will be well under 30,000. This is in stark contrast to the figure published for covid deaths in England and Wales of 65,795 (as on 31/12/2020).

As can be seen from the graph below about excess winter deaths, seasonal deaths commonly vary by over 20,000 from one year to another. In which case, even were the 37,000 excess deaths this year all due to covid, that would not be far out from the range of swings that habitually occur from year to year – see the graph below.

Survivability – the chance of surviving the year
So far we have calculated in terms of death rates, the chance of dying in a year. But a different, and possibly more relevant, perspective is to consider the chance of surviving the year, a more useful way of seeing the impact of covid on our lives.

For those of us over 65, over the 6 years from 2013 to 2019, the death rate was 4.3%, meaning that our chance of survival was 95.7%. 2019 was a particularly good year in which survivability of over-65s was 95.9%. In 2020, with a death rate of 4.5%, survival rate has been 95.5%.

Here we can see how survivability has changed over the last fifteen years.

With over-65s survival rate consistently a little above 95% we can see that the effect of covid has been really very small. We can stop worrying and regard 2020 as a normal year.

Since first publishing this, the Office for National Statistics has crunched the figures. Their figures are for the 12 months to the end of November 2020. Here is the graph for age-standardised-mortality.

As you can see, this graph is pretty much identical in shape to my own graph on death rates above. Again it shows that 2020 is not a particularly exceptional year.

The BBC, in their publication of the ONS statistics, were very naughty. They focused on the excess deaths in 2020 being greater than any other year since the Second World War. Well, since the population (at 68 million compared with 47 million during WW2) and the proportion of over-65s (18% as opposed to 10%) are greater in 2020 in any other year, of course we should expect the death rates to be greater.

Statistical notes
These figures are produced by taking the ONS published weekly death rate figures, multiplying them by 52 to give an annual death rate figure and dividing them by the numbers in the two cohorts (0-64 and 65+).

Numbers in the two cohorts are calculated from published UK population figures, reduced by 11.3% decreasing to 11.0% from 2010 to 2020 to account for those in Scotland and Northern Ireland.

Percentage of over-65s in the UK population is derived from the sources below, interpolating between fixed point data where necessary. Here are the figures used.

https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/weeklyprovisionalfiguresondeathsregisteredinenglandandwales

https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/weeklyprovisionalfiguresondeathsregisteredinenglandandwales

https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/ageing/articles/whatdoesthe2011censustellusaboutolderpeople/2013-09-06#:~:text=In%202011%2C%209.2%20million%20residents,from%202001%20with%208.3%20million.

https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/827518/Recent_trends_in_mortality_in_England.pdf

https://www.thelancet.com/journals/lanonc/article/PIIS1470-2045(20)30388-0/fulltext

https://www.univadis.co.uk/viewarticle/uk-covid-19-daily-up-to-35-000-excess-cancer-deaths-predicted-724669

https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/datasets/deathsregisteredinenglandandwalesseriesdrreferencetables

Multiple bank accounts

For a long time I was a believer in a single, well-checked bank account. I realised now that I’d never checked most of my spending. I had a rough idea how much it was because I noticed whenever I took out £100 or so from the bank and how long it had been since I last withdrew cash. At any instant I could see how much cash I’d spent by how much was left in my wallet. But I never checked small amounts like the 49p for cable clips, or the £1.50 for a pasty, because I never checked individual receipts for cash payments.

I always had a rough idea how much cash I spent which I checked by matching 4 or 5 cash withdrawal slips with the bank statement, at the same time checking the dozen or so big items which were not cash, and my total cash spending from the cash withdrawal

Then the world changed as the number of card payments from my ‘single, well-checked bank account’ steadily rose. Come bank statement checking time, I found it was a nightmare with so many bits of paper. The big items were being disguised by a large number of small items, like 49p for some cable clips or £1.50 for a pasty. Bank account checking, which had been easy, became difficult. That coincided with a suggestion from a family member that multiple bank accounts were worth considering and eventually I was converted. I now have four main bank accounts:

Income
Bills
Savings
Day-to-day

Income account
All my income goes into my Income account. From that account there are three standing orders to my other three accounts. It takes seconds to check my Income account statement because just my income goes in and three standing orders come out.

Bills account
I have a Bills spreadsheet (Google docs) which lists all my regular bills, including estimated amounts for things that I know will happen. It’s something like this:

The spreadsheet tells me that my regular bills are something around £650 a month and there is a standing order from my Income account to my Bills account of £700 a month. It’s easy to check my Bills account because there is the single income from my Income account and a number of payments, all of which I am expecting and included on the spreadsheet. As the years go on, I add more and more things to the Bills spreadsheet which gradually gets clearer as a predictor of the regular outgoings.

Savings account
There is a standing order from my Income account straight into my Savings account, of an amount I have decided to save every month. (In fact there is another standing order into the Savings account of £150, the car replacement cost and the family holiday cost. Those amounts, too, accumulate in my savings account and, come new car time and holiday time, those bills are paid from my savings account.) Checking my savings account is easy. There are the two standing orders, one from Income and one from Bills, and that’s it until I spend on holiday or car.

Day-to-day
The third payment from my Income account is to the Day-to-day account. From that I pay food, car fuel, meals out, any hobby expenditure, paint for the house, furniture, books, magazines, Amazon expenditure, Ebay, optician charges…plus cable clips and pasties. In other words, all the other expenditure. My credit card comes out of this account as well. So all my expenditure is summarised by the Bills account or the Day-to-day account, through which all my expenditure is paid.
My day-to-day account is a Starling account, though Monzo is just as good. Starling is an electronic banking account that is very easy to use and check. It is my wallet and gets filled up by the standing order at the beginning of the month. At any stage of the month I can look at it and see how much I have spent and how much I have left.
Do I check the Day-to-day account? No I don’t. It’s like I used to treat my wallet. I only look at the totals. But it’s better than my wallet because I can look back at the expenditure over the month and instantly see the patterns in my expenditure. Starling provides me with monthly summaries categorising my expenditure as well as the detail if I want it.

The consequence of all the above is that I check Income, Bills and Saving monthly. But it only takes seconds, because they are so easy to check. I check Day-to-day quite often but briefly, seeing how long it is until the end of the month and how much I have left. As for the nightmare of monthly checking of my bank statements, that has gone completely. Life is so much easier and clearer.
Is this OCD? Possibly. But actually it is appropriate OCD. Appropriate OCD makes life easier, reducing the time doing things that one doesn’t want to do, leaving more time for the things that one does want to do.

Other accounts
For a while, bank accounts have been free. So, if a different type of expenditure arises, it’s been easy to have another account for that expenditure. Even where there is a charge (Starling charges £2 a month for extra accounts) it can be worth having additional accounts if you can’t get a free one from a different bank. House renovations: get a house renovation account. Pay for everything with a card from that account and instantly you can see how much has been spent on the whole project. If it’s easier, and to avoid confusion, it’s possible to have separate car and holiday accounts to keep them separate from general savings. Husband and wife ‘pocket money’, separate from general household expenditure, can also go in separate accounts.
Other forms of income – share dividends, self-employed work etc – can also each have their own account. That way, come tax return time, all the information is in one account.

Power tools – battery vs mains

Here is a very rough comparison of the costs of mains and 18V power tools. The comparisons are between Einhell, Makita, deWalt, Milwaukee and Bosch. The comparisons are rough and ready, using the cheapest available items in each category in Screwfix, Toolstation and Wickes online as sources for the prices. There was no attempt to match specifications, for instance by ensuring that all were brushless, etc. Milwaukee corded tools are not included because they do not seem to be generally.

Don’t compare directly the Total, excluding battery, column for corded and cordless, because the former does not have an impact driver included.
The brands are in price order with Einhell by far the cheapest and Bosch most expensive.

Thoughts:
1. There is not an awful lot of difference between the main brands, particularly since I noticed that the Bosch cordless tools are particularly highly specified, which accounts for some of the price premium over the others. A friend whose judgement I trust says that the Milwaukee quality is better than Makita.
2. The cordless premium is calculated by subtracting the corded prices in the corded column from those in the cordless. As can be seen, the cordless premium is relatively low (around 10% when one takes into account the previously mentioned high specifications of Bosch cordless). So, once one has the batteries and charger, one might as well go cordless.
3. All brands have one or two cheap offers which bundle a couple of batteries and a charger, making the transition to cordless less than the prices above indicate.
4. Makita LXT was launched in 2005 and is still their major brand. So the technology is mature and obsolescence of currently purchased tools unlikely to be a problem.
5. Makita is a market leader and it may be that its ubiquity stimulates competition which tends to drive the price down.

Relevant reviews

https://www.pyracantha.co.uk/top-6-best-impact-driver-reviews/

On Trustpilot, Einhell seems to get poor reviews, whereas Einhell UK gets good ones. Bizarre. Toolstation has variable reviews of Einhell. Wickes has generally good reviews of the brand.
https://uk.trustpilot.com/review/einhell.co.uk
https://uk.trustpilot.com/review/www.einhell.com

Makita seems to have chuck problems. See for instance:
https://www.screwfix.com/p/makita-m8101k-710w-electric-percussion-drill-240v/3043r

Other random thoughts
Mainstream manufacturers are also producing 10.8 V or 12 V tools in addition to 18 V. I suppose that ‘small and light’ must be the aim. At the same time there is a tendency to move to higher voltages for beefier tools, sometimes double 18 V and sometimes treble. So the battery market seems to be getting more diverse rather than more standardised.


Container ships…

…and the business of transporting manufactured goods across the world.

Seeing this video of the container ship Maersk Essex, I couldn’t resist trying to count how many containers she seemed to be carrying.

At the rear we see the stack is 19 containers wide and probably 10 containers high (guessing on how deep they go into the body of the ship) and it seems that the ship is about 20 containers long. That’s 19 x 10 x 20 = 3800 containers altogether. These containers are 40 ft long, twice the standard unit for calculating container loads, which is the TEU (Twenty-foot Equivalent Unit), so our calculation would seem to show that the capacity of the ship is 7600 TEU.

In fact our calculation is a significant underestimate. As this photo shows, containers are stacked well inside the hull of container ships.

The website marinetraffic.com gives more details of the MAERSK ESSEX. She was was built in 2011 and is sailing under the flag of Denmark. Her carrying capacity is 13,100 TEU and her current draught is reported to be 12.5 meters. Her length overall (LOA) is 366.44 meters and her width is 48.26 meters. At the time that I am writing, 24 November 2020, marinetraffic.com says she is on her way from Los Angeles and due to arrive at Yokohama on 2 December.

Consider the Maersk Essex to be fully loaded. That’s 366 x 48 x 12.5 m³ = 220,000 cubic metres and since each cubic metre of water has a mass of 1 metric tonne (1t), the total mass of water displaced is 220,000 t.

In fact the ship is not uniform and rectangular so in this case we have overestimated the displacement. In fact her Gross Tonnage is 141,000t.

Panamax and New Panamax ships

The Maersk Essex is an interesting size. She is just within the size for the new, wider, deeper Panama canal, which opened in 2016. The new canal sections increased the size of ships from 5000 TEU to 13,000 TEU, these sizes of ship being referred to as Panamax and New Panamax respectively.

There are significantly larger container ships. The HMM Algeciras built in 2020 is 400 m long and 61 m wide. It has a gross tonnage of 228,283t and a container capacity of 23,964 TEU. Ships like this which are larger than will fit through the Panama Canal are called post-Panamax or super-Panamax.

Suez canal

The Suez Canal now allows ships up to 400 m long with a beam of 50 m and a draft of 20.1 m. This is larger than New Panamax, leading to a maximum ship size of 160,000 tonnes, and a container load of around 14,500 TEU. In fact the Suez Canal has no locks and so there is no engineering limit on ship length, despite the regulation limit of 400 m.

Other pinch points around the world

Malaccamax, about 300,000 tonnes is a term used for the largest ships that can get through the shallow 25 m deep Strait of Malacca between Sumatra (of Indonesia) and Malaysia. Seawaymax, only 28,500 tonnes, describes the largest ships that can travel through the canal locks of the St Lawrence Seaway.

Standard container sizes

What we often refer to as a Shipping Container is technically an ISO Intermodal Container, designed for transporting goods in ships, lorries and trains without the goods being individually loaded or unloaded. The ‘standard’ ISO size is 20 feet (6.1 m) long x 8 feet (2.43 m) wide x 8 feet 6 inches (2.59 m) high. This is technically 1 TEU. Most containers are twice as long as that and a 40 ft container is obviously 2 TEU.

Hi-cube

Hi-cube containers are taller than standard containers at 9 ft 6 in (2.89 m). Hi-cube containers look distinctly taller than they are wide. By the end of 2013, half the word’s maritime fleet was in 40 ft hi-cube containers.

Other container sizes

In 2003 the EU commenced a process of defining the European Intermodal Loading Unit (EILU). The size of this container has yet to be defined, some 17 years after its proposal. It will be longer than 45 feet and, at 2.5 m about 10 cm wider than ISO containers. It will be difficult to fit it in with existing container ships. As can be imagined, the maritime freight organisations think it’s not a good idea.

From ship to rail and the problems of loading gauge

The size of freight allowable on trains is determined by what is called the loading gauge. European railways have loading gauges which are large and the transport of hi-cube ISO containers on such trains is no problem. Most of the British railway system is constructed to a loading gage called W6a. This is too small for the carriage of ISO containers.
W10 loading gauge allows standard wagons to carry ISO hi-cube containers. W12 allows room for these containers to have refrigeration packs as well. All new rail structures are built to W12 loading gauge.
There is a steady programme to enlarge UK railways to W10 and W12 loading gauge on the main rail freight routes so that containers can be offloaded from ships and then loaded directly onto rail lines for transport around the country but, as this map shows, only a small proportion of UK railways can carry the containers in which most goods are shipped.

https://www.networkrail.co.uk/wp-content/uploads/2019/03/Enhanced-W10-loading-gauge-map-of-the-network.pdf

How much does it cost to ship a container?

The website freightos.com gave me a price of $5,500 (£4,100) for the cost of transporting a 40 ft hi-cube container from Hong Kong to Felixstowe UK on 5 January 2021. The shipping time quoted was 31-37 days.

Ports.com tells me that this journey, via the Suez Canal, is 11,047 nautical miles and at a speed of 13 knots will take 35.4 days.

http://ports.com/sea-route/port-of-hong-kong,hong-kong/port-of-felixstowe,united-kingdom/

How much fuel is used to bring our container to the UK?

As the following link shows, 13 knots is a particularly slow speed. A normal speed is over 20 knots. I’m going to use this figure to read off a fuel consumption for a contain ship carrying our container.

The graph says that a ship of 10,000 TEU will consume about 180 t per day. To calculate the worst case scenario, I am going to assume that the ship still takes 35 days to travel from Hong Kong to Felixstowe.

So total fuel used is 180 tonne/day x 35 days = 6300 tonnes.

The ship has a capacity of 10,000 TEU, and since our container is 2 TEU, there are about 5000 containers on the ship.

The amount of fuel used to transport our 2-TEU container is 6300/5000 = 1.2 tonnes. These tonnes we are using are metric tonnes, giving the confusing symbol mt in all the fuel tables. Current prices are $369 (£277) per tonne. That means that the fuel cost of getting our container from Hong Kong to the UK is 1.2 tonnes x £277/tonne = £332.

Bearing in mind that fuel prices were about three times as high three years ago, the fuel cost then could have been as high as £1000 and perhaps we would have paid extra because of that, perhaps an extra £900, making the total cost £5000.

In normal (non-covid) times, to get our container from Hong Kong to the UK would be about £5000, of which £1000 is the fuel cost.

What can we fit into a 40 ft hi-cube container?

An ISO container is 6.2 m x 2.43 m x 2.89 m externally. We need to make allowances for the thickness of the walls which I am going to suggest are each 0.125 m thick.

So the internal dimensions of the ISO container are 5.95 m x 2.18 x 2.64 m = 34 m³. This is 34,000 litres.

A shoe box for men’s shoes is 34.5 cm x 22.5 cm x 13 cm = 10,091 cm³ = 10 litres. We can fit 3500 shoe boxes into a hi-cube container but that is if they are sent in the box. If they are bagged and packed more efficiently, over 5000 pairs of shoes will fit into a hi-cube container.

Since it costs £5000 to bring 5000 pairs of shoes to the UK, that’s £1 per pair of shoes on transport cost of which 20p is fuel cost.

What’s in it for the ship owner?

In March 2010, the average price for a 10,000 TEU ship was about £90 million. That’s about £130 million in today’s prices.

As we’ve seen, the ship can transport 5000 containers, each size 2 TEU, from Hong Kong to the UK for a cost of £5000 each. But for each container it needs fuel worth about £1000, so the income generated by the trip is £4000 for each container x 5000 containers = £20 million.

The trip takes around 35 days, so the ship can do 10 such trips per year. If each is as profitable, that is net receipts of £200 million per year.

In rough figures, buy a ship for £130 millon. Earn £200 million a year carting things around the seas of the world with a profit margin of say 10%. So you earn £20 million a year and pay off the ship after 6 or 7 years. This is obviously a rough guess at the sizes of the figures involved.

Container ships are on average the newest ships at sea with an average age of 9 years. This is because so many have been built in the last couple of decades with the rapid expansion of world trade.