Institute for Quantum Information and Matter, a National Science Foundation Physics Frontiers Center

How many miles per gallon?

Thoughts while watching the Olympics …

My car gets about 30 miles per gallon of gasoline. Miles per gallon has the dimensions of inverse length squared, and the reciprocal of 30 miles per gallon is roughly the area of a circle whose diameter is 0.3 mm, or about 1/100 of an inch.

That means that when I drive my car, the fuel I consume has the same volume as a thin thread stretched along the road over the distance I travel, with a thickness just a few times the width of a human hair.*

That skinny little thread of gasoline is enough to keep my car going! Thinking about it reinforces one’s appreciation for the internal combustion engine.

Okay, let’s compare with another admirable machine — the human athlete. How many calories a runner burns depends on the runner’s weight, pace, and other things, but a typical male runner burns between 100 and 150 kilocalories per mile. Over a 26 mile marathon, that comes to about 3500 kcal, roughly equivalent to a pound of fat.

The human stomach holds about a gallon. I don’t recommend this, but if the marathon runner goes to McDonald’s after the race and scarfs down a few Big Macs, orders of fries, and Cokes, he’ll fill his stomach with about as many calories as he burned during his run.

So the marathon runner also gets about 30 miles per gallon. A skinny little thread of fuel, about 0.3 mm thick, is enough to keep you and me going, too!  Is that a universal constant of Nature?

Wait ’til I tell my car!

* I heard this nugget from Charlie Bennett, who, appropriately, told it to me while we were sharing a taxicab.

2017-01-13T10:06:05+00:00 August 10th, 2012|Reflections, The expert's corner|17 Comments

1. John August 10, 2012 at 3:12 pm - Reply

Professional marathon runners aren’t typical runners, though. They’re going faster, which should be harder, but they’re able to do so because they are more efficient. I’d guess 75-80 kilocalories per mile might be closer. Quibbling here.

• preskill August 10, 2012 at 3:48 pm - Reply

Thanks. In that case, hold the fries.

2. David Meyer August 10, 2012 at 4:03 pm - Reply

Not exactly a universal constant—on a bicycle a human is somewhere between 5 and 10 times as efficient, depending on speed and mass.

3. John Sidles August 10, 2012 at 5:01 pm - Reply

That’s a wonderful Fermi problem!

A natural follow-on question is this: If everyone on Earth jumped in a car, and drove 30 miles per hour, what would be the diameter of the equivalent gasoline thread, and how long would it take the continued combustion of this thread to double the CO2 level of the earth’s atmosphere?

This is a wonderfully edifying/terrifying calculation to carry through, immediately before reading arXiv:1110.1365v3.

Yes, a planet with \$latex mathcal{O}10^{10}\$ people living on it is in a mighty serious situation. And yes too, QC/QIT/QSE does have considerable to do with getting into it and getting out of it.

4. rrtucci August 10, 2012 at 7:02 pm - Reply

1kcal = 10^23 ev
If breaking a bond yields 10ev, runners and cars such at efficiency

5. rrtucci August 10, 2012 at 7:08 pm - Reply

Oops I posted prematurely.
I meant
1kcal = 10^23 ev
If breaking a bond yields 10ev, runners and cars are pretty inefficient by some standards: they have to break 100 kcal/mile = 10^24 bonds/mile

6. rrtucci August 10, 2012 at 7:10 pm - Reply

More exactly
4 kcal = 10^23 ev

7. rrtucci August 10, 2012 at 7:15 pm - Reply

I should have said creating bonds, not breaking bonds

8. preskill August 10, 2012 at 7:39 pm - Reply

Right. A gallon of gasoline has a lot more calories than a gallon of whole milk (more by better than a factor of 10). But we can’t drink the gasoline.

9. rrtucci August 10, 2012 at 7:44 pm - Reply

By the way,
1 mile is about 1/4 million angstrom = 25,000 nm.
1 Bohr radius is 1/2 angstrom.
So those runners are creating 10^18 bonds per Bohr radius of distance traveled. Pretty pityful

• rrtucci August 10, 2012 at 8:20 pm - Reply

This is totally wrong. Sorry.1 mile is not 1/4 million angstrom. I mis-remembered

• rrtucci August 10, 2012 at 8:31 pm - Reply

The correct conversion is
1 mile = 1.6X10^13 angstrom = 3.2 X 10^13 Bohr radii
so maybe its more like 10^11 bonds created per Bohr radius traveled

10. shaunmaguire August 10, 2012 at 10:34 pm - Reply

I already see Lagrangian Coherent Structures while driving. Now I’m also going to visualize a little thread coming out of my car’s arse (exhaust pipe?)!

[url=http://www.economist.com/node/14843793][The Economist’s popular explanation of Lagrangian Coherent Structures][/url]. The late Jerry Marsden introduced me to these.

• preskill August 11, 2012 at 8:15 am - Reply

Or, when you’re running, out of yours!

11. John Sidles August 11, 2012 at 2:02 pm - Reply

In graduate school my then-girlfriend (and future) wife was production manager for the Bulletin of the Atomic Scientists, and through her I acquired a considerable measure of respect for that fine journal, which expressed a certain gravitas with regard to the relation of physicists to the broader society. Given the concern that even non-physicists are expressing with regard to CO2-driven climate instability, it might be no bad thing if Quantum Frontiers were to imbibe some of that same broad-ranging gravitas. The present topic of energy efficiency is well-suited as a starting point.