> miles-per-gallon (or litres-per-km) [1].

The UK is metric except for distance and beer.

So the disgusting ‘miles-per-litre’ is presumably needed too.

Also the UK gallon is different from the US gallon. And the same applies to all the other non-metric fluid measurements such as pints and fluid ounces. Historically the UK gallon was used throughout the former British Empire (Australia, Canada, India, Ireland, Malaysia, New Zealand, South Africa, etc). By contrast, almost nobody ever officially used the US gallon except for the US (and a small handful of highly US-influenced countries such as Liberia).

Each standardised on a different gallon. Prior to that, gallons depended on that you were measuring.

One, a beer gallon, the other a wine gallon. The US still also has 'dry gallons' for things like pints of blueberries.

Meaning the ideal (cursed) unit of fuel consumption has units of 1/m^2

Well, if you want to be pedantic, it's litres-of-fuel per km-driven. That doesn't cancel as nicely, if you don't drop the annotations.

Arguably, we should probably use kg-of-fuel (or mol) instead of litres-of-fuel anyway.

"litres-of-fuel per km-driven" (Volume/Distance) is still fully reductible to an area: litres is still a volume (1 cubic decimeter) and km is still a distance (1x10⁴ dm) Maybe you meant that the other way around? Distance/Volume (as in Miles/gallon) is an Area⁻¹ (Distance⁻²), which is more difficult to imagine in space.

Now, Kg is a measure of mass (or weight, depending on who you are asking), which throws density into the equation, which is proportional to the temperature, which will vary according to where and when the driving takes place. But since the time and place, and hence the temperature is (allegedly) defined when the fuel consumption was tested, the density is a constant, and as such you can leave it out from the relation.

Mass = V*ρ

(I know, I am being pedantic² :)

If you car was fueled by a fixed pipe which it travelled along, consuming all the fuel in the sections of the pipe that it moved past but no more, what would the cross section of the pipe be?

That's looking suspiciously like integration.

If a car gets 50 mpg (UK gallons), the fuel consumption is equivalent to a circular string of diameter 0.27 mm.

> Now, Kg is a measure of mass (or weight, depending on who you are asking), which throws density into the equation, [...]

It's the other way round: chemically how much energy you get from burning your fuel is almost completely a function of mass, not of volume. (And in fact, you aren't burning liquid fuel either, in many engines the fuel gets vaporised before you burn it, thus expanding greatly in volume but keeping the same mass.)

> [...] which throws density into the equation, which is proportional to the temperature [...]

For an ideal gas, sure. But not for liquid fuels.

> "litres-of-fuel per km-driven" (Volume/Distance) is still fully reductible to an area: litres is still a volume (1 cubic decimeter) and km is still a distance (1x10⁴ dm) Maybe you meant that the other way around? Distance/Volume (as in Miles/gallon) is an Area⁻¹ (Distance⁻²), which is more difficult to imagine in space.

I don't think that the reciprocal is a problem. No, what I mean is that you can't cancel fuel with driving. Litres-of-fuel is a different unit than distance-driven ^ 3. Similar to how torque and energy are different physical quantities that you can't cancel willy-nilly, despite their units looking similar.

You might find a physical interpretation for an adventurous cancelling, and that's fine. But that's because you are looking behind the raw unadorned units at the physics, and basing your decision on that.

Units are a very stripped down look at physics. So units working out are necessary for cancelling to make sense, but not sufficient.