# Units

A friend pointed out just recently: we usually measure a car’s fuel efficiency in Miles per Gallon. But some would like us to switch to the more logical Gallons per Mile (or 10,000 miles, to make the numbers more convenient, or whatever), which would be the fuel consumption. But that, technically, is an area, so for example a car which gets 55ish mpg actually has a fuel consumption of 0.051 mm^2 (ht: A/S).

1. #1 Traciatim
2010/07/30

In Canada we have switched to L/100km and I find it counter intuitive that the lower the value the better the rating. It’s probably just me being used to using the American MPG for so many years though.

2. #2 Jérôme ^
2010/07/30

And this area even has a physical meaning. It is the cross-section of the pipeline that needs to be filled with fuel along the road, so that cars can work on it.

More seriously, using L/10^5 m has the advantage that it helps making good judgment calls about reducing fuel intake for cars. (And miles and gallons are another reason why Americans look so medieval to the civilized world…).

3. #3 Chris' Wills
2010/07/30

mpg at 62mph (km/l at 100km/h) are sensible measures for humans who want to go from A to B.

If you want to travel 500km how many litres of petrol will you need = direct cost to you (simply divide distance by km/l and you have your answer).
Plus, of course, a buggeration factor to allow for the fact that you’ll be driving at 140/160km/h not 100km/h.

Gallons per mile can work in a similar way (just multiply instead of divide), but most people don’t think that way especially when you have fractions.

As a measure of efficacy (it isn’t efficiency as they have units, efficiency should be a dimensionless number) either will do.

For marketing/advertising mpg or km/l beat gpm or l/km, bigger is always better.

4. #4 Ketil Tveiten
2010/07/30

Distance per volume of fuel (e.g. mpg, km/l) is a useful number when it’s post-nuclear-apocalypse and you need to know if you’ll reach Thunderdome with than one can of gas you found under some rubble.

Volume of fuel per unit of distance (e.g. gpm, l/km) is useful in the real world, when you want to know how much it’s going to cost you to have a car. You usually will drive about the same amount/distance each week, so l/km translates directly into money/time, which is useful for making the household budget.

So, in summary: mpg is good if you’re Mad Max, for everyone else, gpm is the only useful measure.

5. #5 Ketil Tveiten
2010/07/30

Also, I don’t see that an inverse area (mpg) is any more intuitive than an area (gpm).

6. #6 carrot eater
2010/07/30

None of them are areas, but I think that instead of replacing miles/gallon, we should simply add two things:

cost/mile: if what you care is operating cost, at current prices. this becomes a necessary comparison when there are multiple fuels to choose from.

units CO2/mile: if that’s what you care about

7. #7 Eli Rabett
2010/07/30

The folk on the mainland used L/100 km.

8. #8 Russell
2010/07/30

Well, it’s not really an area because the gallons in this case are a convenient substitute for “BTUs, hydrocarbon variety.” With small changes, your car can run on propane or methane, and their volumes are quite different, especially since the last is carried around as a gas.

Jérôme, let me know the next time you board a plane that uses kilometers for navigation. As far as I can tell, the whole world has committed itself to nautical miles, and to the traditional compass. Even France has returned to it, despite a short but aborted attempt to metricize the compass, replacing the 360 degrees, each divided into 60 minutes, with 400 grads, each divided into 100 metric minutes. Which is how the kilometer was defined.

So yeah, the US should drop the statute mile. In its place, we should move all road signage to what the entire world uses for navigation: the nautical mile. ;-)

9. #9 Hank Roberts
2010/07/30

I understand the rest of the world also has different definitions for other units of measure — gallon, ton, conservative, ….

10. #10 Tony Sidaway
2010/07/30

By coincidence I happened to be watching some American television programme this morning, probably Countdown or Rachel Maddow because MSNBC seems to be the only American TV news channel broadcast from the planet I actually live on. There was a piece about a competition to produce usable cars that have low fuel consumption, and they discussed how the issue of alternative fuels was handled. Essentially they went for MPG equivalent, though not much detail was provided on how the equivalence was handled. Did anybody else hear about this?

I’m sorry to be so vague about this, but I’m out now and I can’t watch flash-based television streams on my telephone.

11. #11 Phil Hays
2010/07/30

I suggest grains per fathom. The only units that real men use. ;-)

[There was an old saying in the Met Office in the old days that the (old) ocean model would run on fathoms per fortnight if it could -W]

12. #12 Tony Sidaway
2010/07/30

Ah yes, grains. When the Mythbusters people started talking about firearm shell payload in terms of grains, I was quite surprised. They have no problem talking about 9 mm caliber pistols so the use of archaic measures seemed unnecessarily obscure. Fortunately the British version had a helpful commentary that translated the grains into grammes.

13. #13 Thomas
2010/07/30

A fun question: take a well trafficked road and calculate how thick layer of petrol would build up on it each day if all cars just dumped the fuel instead of burning it. It gives a perspective on the size of the problem, especially when you consider that in gas form it takes up ~1000 as much space.

14. #14 Nick Barnes
2010/07/30

40 mpg is about 17 picoacres.

15. #15 peter
2010/07/30

I think a better one is gallons per hour.
for a given engine, which is designed to run at a particular nominal speed, it’s much more accurate. also why mileage in town goes down. you’re not moving, but the engine’s still burning.

16. #16 Paul Kelly
2010/07/30

Tony,

You were watching Rachel Maddow. The competition talked about was The X Prize for cars sponsored by Progressive Auto Insurance. Find out more at the official website.

17. #17 Paul Kelly
2010/07/30

When the wife and I travel the important calculation is miles per argument.

18. #18 Zeke Hausfather
2010/07/30

The tendency to use “increase fuel economy x mpg” as a standalone unit doesn’t help either. Increasing from 10 to 15 mpg is quite a bit different in terms of fuel consumption then increasing from 30 to 35 mpg. The former has a 7-fold larger impact than the latter.

19. #19 Geoff Wexler
2010/07/30

How about using climate forcing per unit distance? The SI unit of a watt/m^3 would be huge, but I’m sure that David MacKay who is the great inventor of original and manageable units would solve that problem. Otherwise just multiply by 10^[-3n].

20. #20 David B. Benson
2010/07/30

http://en.wikipedia.org/wiki/Mile#Roman_mile

Then everybody has to change signage and whatnot.

21. #22 bellisaurius
2010/07/31

I was tearing my hair out over the fact mpg is an area issue (I just never thought about it) when I suddenly had a “hey dummy” moment, the relevant measure is miles per lb mass (although since gas is pumped at a fairly consistent temperature and pressure, they’re essentially the same). Shame we don’t use that though, it will make gases a little less confusing later.

2010/07/31

L/100k is a much, much better measure. (Though old fuddy-duddies like me tend to do the instant translation to mpg in some circumstances.)

Since I’ve been using a fuel additive to improve consumption, I just find it a lot easier to say that I’m now using 2L per 100k less than I used to. Much easier to work out the cash difference with the fuel priced per L and the cost per L of the additive easily added in.

23. #24 Kooiti Masuda
2010/08/01

In Japan people talk about “nenpi” (literally “fuel cost”) in the unit of km/L. Japanese Wikipedia remarks that “tei-nenpi” (low fuel consumption) corresponds to high values of “nenpi”.

24. #25 davidp
2010/08/03

The area dimensioned measures (L/100km, g/mi) add and average meaningfully. To answer the question “What is the average milage of these two cars” requires much more calculation in mpg than in g/mi.

25. #26 Nosmo
2010/08/03

I prefer inverse square picofarads instead of miles per gallon, and mhos instead of miles per hour.

yes Capacitance really is a distance, and Conductivity is a velocity (which is why RC is a time). It is more obvious in cgs then mks units.

26. #27 Bob in Chico
2010/08/05

A Car Talk (the NPR show) puzzler back in 2006 highlights the perils of using mpg instead of L/110km or g/mi. The puzzler reads:

“You drive a gas-guzzling SUV that gets a whopping 10 miles per gallon. Your sleek and efficient spouse drives a sleek and efficient hybrid that gets 100 miles per gallon.

Now, let’s assume that both of you drive the same distance each year. Your spouse sees an ad for a new, super-duper hybrid that gets 200 miles per gallon. She is lobbying to trade in her old, wasteful 100-mile per gallon hybrid for the new 200-mpg model; her thinking being that getting this new hybrid to replace the old one will really improve the average miles per gallon of your household.

On the horns of a dilemma, you seek out the one person you trust with questions automotive: your mechanic, Crusty!

“What can I do,” you ask, “to improve our household’s miles per gallon without buying this new hybrid?”

Crusty says, “Well, if we tune up your old SUV, and inflate the tires correctly, and remove that four inches of accumulated bird poop on the roof, I’m pretty sure we can get you all the way up to 11 miles per gallon.” Your heart sinks.

What should you do? That’s the question. Under which scenario would your household see the biggest improvement in miles per gallon: by getting the new hybrid, or by tuning up the old SUV?”

Of course, the correct answer, which is counter-intuitive, is that tuning up the SUV gives the biggest improvement in mpg.

If g/mi had been stated in posing the puzzler, the answer is obvious.