# A Simple Metric for Vehicle Efficiency

Introducing a fuel-agnostic metric for both vehicles using an internal combustion engine and pure electric vehicles.

For quite some time the fuel efficiency of a vehicle using an internal combustion engine (ICE) has been expressed as either miles-per-gallon, *MPG*, or as *litres-per-100km*, relating a given volume of fuel to a distance travelled**¹**. For battery-electric vehicles (BEVs) two values are advertised: the energy stored in their batteries (in *kWh*) as well as the range (in miles) the vehicle is expected to travel on a fully charged battery. There is less talk of efficiency for BEVs like it did not matter; the numbers appear at first sight not even related or relatable to the ICE efficiency standards. The purpose of this story is to abstract the established efficiency metrics for vehicles into a number that could be applied equally to ICE based vehicles and BEV.

## Simple Engineering Units

For BEVs the energy storage capacity is given in kWh and their range in miles. The first step is to express both together as a ratio, ** kWh/mile**, i.e. how much energy is needed per mile travelled, or alternatively as its inverse, how many miles can be travelled with a given amount of energy,

**. For instance, a Tesla Model S advertised with both a**

*miles/kWh**57.5kWh*battery and a range of

*235miles*would yield

*4.09 miles/kWh*or

*0.24 kWh/mile*.

The same metric can be used for an ICE vehicle based on the energy density of fossil fuels: petrol with a specific energy of *46.4 MJ/kg* offers *9.5kWh/litre*; Diesel fuel with a specific energy of *45.6 MJ/kg* provides *10.722 kWh/litre* (due to its higher density). Given an imperial gallon containing *4.546 litres*, this results in the specific energy as *43.188 kWh/gallon* and *53.290kWh/gallon* for petrol and Diesel, respectively. These numbers can be used to convert the *MPG* values into ** miles/kWh** by dividing the

*MGP*value by the energy content per gallon for the fuel used. For instance, a petrol powered car with

*40 MPG*would yield

*0.93 miles/kWh*or

*1.08 kWh/mile*.

## Further Simplification

Looking at the term *kWh/mile* tells me that there is still scope for simplification, in particular since the unit *mile* is not universal. Since one mile is equivalent to *1,609.340m *and one *kWh* is equivalent to *3,600 kWs*, i.*e. 3,600 kJ*, the above metric of *kWh/mile *can be converted such that *1 kWh/mile = 3,600kJ/1,609.340m = 2.237 kJ/m. *The metric or unit chosen,** kJ/m**

*,*is simply the energy spent in

*kJ*for moving a vehicle by one meter. Conversely, one could conceive the inverse,

**, or the distance in meters the energy expenditure of**

*m/kJ**1kJ*would move the vehicle. Along that line,

*1 mile/kWh*would translate into

*0.447m/kJ*.

The reader familiar with SI units will of course notice that the unit *kJ/m* is equal to *kNm/m *or simply *kN *(with* *the meter cancelling out). That’s one of many advantageous aspects of using SI units, in addition to being based on decimal numbers.* *The reader will recognise the *Newton* as the unit for force which is actually not surprising. A certain force is needed to move a vehicle along a road over a distance at a certain speed**²**. This force multiplied by the speed results in power, and the power integrated over time (or the distance) will yield the energy spent to travel that distance.

**The bottom line**: a simple metric for the efficiency of vehicle motion is how much energy per unit distance has to be spent on average to move the vehicle along a route, the specific motion energy, ** kJ/m**. The less energy is needed, the more efficient the vehicle is. The unit

**is a fuel-agnostic indicator for motion efficiency of a vehicle using SI units only.**

*kJ/m*## Energy Efficiency Examples

Having downloaded a couple dozen samples from the Electric Vehicle Database shows the order of magnitude of the specific motion energy.

It is interesting to note that a lot of small and sensible vehicles exhibit a similar specific motion energy, around *0.55kJ/m* to *0.62kJ/m*. Not surprising, SUV style cars will require at least 50% higher motion energy values due to their weight and usually poor drag coefficient (by virtue of being boxes). The average over this small sample is about *0.64kJ/m; *note, that this is a small sample but including most popular EVs.

With the above table as a reference, similar ICE based vehicles and their MPG values downloaded from Honest John yield the following table.

The correspondence in vehicles is not 1-to-1 as not all EV models have a comparable ICE models; the average motion energy is about *2.67kJ/m*.

**The obvious question:** Why is there a gain in efficiency of about **4** between ICE based vehicles and BEVs, e.g. going from a modest ICE based family car consuming 2 kJ/m to a similar BEV consuming 0.5kJ/m? Well, that will be due to the energy efficiency of an internal combustion engine which converts only a fraction of the chemical energy contained in the fuel into actually usable mechanical energy (realistically between 20% and 30%, depending on design and fuel). The energy available at the battery can be converted into mechanical energy at a much higher efficiency, at about 90%.

The efficiency gain of 4 is of course only valid if the electricity was generated by a renewable source. If the electric energy is generated by burning fossil fuel in a power plant, its efficiency has to be taken into account, too. There might still be some overall gain as power plants are more efficient and might use excess heat (Combined Heat and Power), heat that is completely lost in the exhaust of an ICE based vehicle.

## Ceterum censeo

The energetic gain obtained with the electrification of individually owned cars is laudable, but the electrification on its own is not as far reaching as a transformation of society would be. Ideally, society would not rely on individual car ownership, at least in urban areas. Rather, human-centred urban planning allows people to walk, cycle and use public means of transport. Fewer cars is the call, and smaller cars, together with their electrification, and possibly autonomous vehicles for shared transport.

Some of that efficiency gain in the vehicle electrification is unfortunately obliterated by producing and adopting larger & heavier vehicles such as SUVs, a classic example of a rebound effect: an efficiency gain is squandered by spending more of the same resulting in the opposite of what was desired. It can only be hope that people do not succumb to Suvitis.

**Notes**

- Anglo-Saxon countries express fuel efficiency in a very pragmatic manner: given an amount of fuel at hand (or better in a container), how far can the vehicle get with that amount of fuel? It is a very tangible metric and one only needs to be able to multiply in order to work out the distance for a given amount, e.g. 4 gallons in the tank on a 40
*MPG*car results in a 160 miles range. In contrast, European countries use*litres-per-100km*which is rather an Engineering approach: what is the amount of fuel needed to travel a known and well defined distance. - The energy expenditure is proportional to the square of the speed, the vehicle mass, drag coefficient, rolling resistance, drive train losses as well as many other factors. The range will depend primarily on the speed the vehicle travelled when the test was carried out. However, the fuel efficiency will plateau at some speed, usually around 55–60 mph, and as long as the same speed profiles are used for both ICE based vehicles and BEVs, the absolute speed would not matter in a comparison.