Fuel efficiency calculations

Some maths to try and understand the comparative fuel efficiency of vehicles using petrol, diesel and electricity as their fuel. For example, is a 3 mile per kWh electric car more or less fuel efficient than a 80 mile per gallon diesel car? (Spoiler: more)

First we need to understand the energy content of the fuels in question. According to the UK Government there is 9.6kWh of energy in a litre of petrol and 10.9kWh in a litre of diesel. We can then work out the miles per kWh by dividing the miles per gallon figure by 43.5 for petrol cars, and by 49.5 for diesel cars.

So a 50 mpg diesel car is doing roughly 1 mile per kWh. And a 22 mpg petrol car is achieving 0.5 miles per kWh. Almost all electric cars can manage at least 2.5 miles per kWh, so a diesel car would have to do 123.75 mpg to be using its fuel as efficiently as that, and for a petrol car it would be 108.75 mpg. Electric motorbikes can usually achieve twice the fuel efficiency of an electric car, so those figures would be double.

Why is this? Optimistically only about 35% of the actual energy in diesel and petrol is converted into motion, the rest is mainly wasted as heat from combustion of the fuel. Meanwhile electric motors generally turn over 90% of their fuel into motion, with the batteries wasting energy as heat at the extremes of their performance envelope.

Raw fuel efficiency is one aspect, but fuel cost is equally important, i.e. £ per mile. Right now in our part of the UK the cost of petrol is about £1.20 per litre, and diesel about £1.24 per litre. Electricity can cost up to £0.30 per kWh from a commercial fast charger, or as little as £0.045 per kWh on an EV-friendly domestic energy tariff.

To work out the £ per mile we simply divide £5.45 by the fuel efficiency of a petrol car, or divide £5.63 by the fuel efficiency of a diesel car. So our 50 mpg diesel car costs £0.113 per mile, and the 22 mpg petrol car costs £0.248. The electric car calculation is the same, divide the cost of a kWh, say £0.30, by the fuel efficiency, say 2.5 miles per kWh, and in this case get £0.12 per mile.

Purely on fuel costs, a 50 mpg car filled with £1.24 per litre diesel is cheaper to run than a 2.5 mile per kWh electric car charged with £0.30 electricity.

However, charge the electric car overnight at home at £0.045 per kWh and the £ per mile drops to 1.8 pence per mile. Almost a tenth of the £ per mile of the diesel car. And the electric motorbike mentioned above is going to easily cost less than a penny per mile to run.

Finally, if the electricity you charge your car or motorbike with has come from the solar PV panels on your rooftop, then the pure fuel cost is zero...

Electric Vehicles

There's been a lot of press recently, created by the UK government's policy to prohibit the sale of new petrol and diesel cars from 2040, about the inability of the country's power infrastructure to support a nation's worth of electric cars. Putting aside for one moment that it will likely be sometime between 2050 and 2060 before the last of the new petrol or diesel cars sold in 2040 are no longer in regular use, we still have at least 23 years to come up with a reliable power infrastructure to support widespread EV adoption. Personally I don't think this is a major issue, especially when there's a deadline to galvanise efforts. Also, given that we already have the solutions, in my opinion it is just a case of implementing them at scale.

The first thing to consider is the generation of sufficient electricity for all these additional EVs. Some analysts have calculated that there is a need for handful of new nuclear power stations to cope with the extra demand for electricity. This is based on an assumption of a high peak load when everyone tries to charge their cars simultaneously. Whereas, if every car had a sibling storage battery from which the car was charged, the challenge becomes charging the storage batteries rather than the cars. This is significantly easier, as the storage batteries are always connected, and a simple load balancing algorithm would spread the load on the grid. Ensure that the storage battery has twice the capacity of the EV battery, and you can charge the storage battery at any time of the day or night. This technology already exists, under the banner of Demand Side Management, so if every household across the country had a storage battery tomorrow, the grid would continue to work just fine.

For sure millions of EVs will require more electrical power than is currently generated. And localised micro power generation is a potential solution for this additional power. Even in the northern latitudes of the UK during winter there is solar energy to be obtained from roof top PV panels. When the likes of Ikea can sell you PV panels and a storage battery for a few thousand pounds, you can be sure this is a mature, proven technology. There is still a major need for a country-wide power grid though, as solar and other renewable energies are not evenly distributed. But considering the vast storage battery capacity now available from the paragraph above, the contribution of renewable energy can now be significantly higher than fossil or nuclear. In theory, with sufficient storage capacity, there is no reason why all the country's energy cannot come from renewable sources.

But where are all these batteries going to come from? Are there sufficient rare-earth metals to produce them. This is another bit of scare mongering that has made the mainstream media, perpetuated by journalists that can't even fact check on Wikipedia. For starters rare-earth metals are not rare, as in scarce, but are rare, as in not found conveniently in seams of ore. This does make them more expensive to extract, but also makes them easier to find, because they are pretty much everywhere. Secondly, rare-earth metals aren't widely used in batteries, so there's no need to extract large quantities of these plentiful metals to build batteries. Rare-earth metals are used in electric motors though. But the good thing about that is that electric motors are about the simplest mechanical system you can build, and are extremely reliable. Essentially the electric motor in today's EV is maintenance free for life.

So far my thoughts have been based on the state of current technology. Imagine the world 23 years ago, and now think forward 23 years, noting that the rate of technological development is accelerating. Electric motors and EVs will be more efficient, requiring less energy. Batteries will have higher energy density and charge faster. Micro generation of solar energy will be widespread, as will macro generation from wind, wave and tidal sources. If anything, having stored energy distributed widely around the country will given us a more resilient and robust power infrastructure, not the frail brown-out prone grid the mainstream media portrays.