XKCD Interesting Factoid

[ChazInMT]

I found this funny thing on the xkcd.com web site Written by Randall Munroe and it is Okay to copy into here. (XKCD Copyright Info)
My take away on this is that it is astounding that such a small amount of fuel squirts us around to where ever we're going.



I have to say—from a dimensional analysis standpoint, ”poops” is one of the strangest units I’ve ever tried to cancel in an equation. But there’s another case of odd unit cancellation, common in everyday life, which is—in a way—even weirder: Gas mileage.

In the US, we measure fuel economy in miles/gallon—which could just as easily be written as gallons/mile. (This reciprocal form has some advantages. It’s popular in Europe, where it’s expressed as liters per 100 kilometers.)

But regardless of which units you use, there’s something strange going on here. Miles are units of length, and gallons are volume—which is length³. So gallons/mile is length³/length. That’s just length².

Gas mileage is measured in square meters.

You can even plug it into Wolfram|Alpha, and it’ll tell you that 23.5 MPG is 0.1 square millimeters (roughly the area of two pixels on a computer screen).

Unit cancellation is weird.

Ok, so what’s the physical interpretation of that number? Is there one?

It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.



Here's the complete XKCD page.

[redpoint5]

Very interesting. I will be giving my fuel economy figures in terms of mm^2 from now on :P

How efficient does my car need to be to achieve tubes that are as thin as a strand of hair?

[ChazInMT]

Originally Posted by redpoint5

Very interesting. I will be giving my fuel economy figures in terms of mm^2 from now on :P

How efficient does my car need to be to achieve tubes that are as thin as a strand of hair?

According to Wikipedia, human hair can be 17 to 180 micrometers in diameter. So based on that, I figured you'd need to get between about 90 to 10,000 MPG depending on the color of, and location harvested, of the strand of hair you are using.

[Piwoslaw]

Frontal area is also measured in sq. meters, so maybe the ratio of the two numbers would mean something? Like who gets the best FE per unit of FA.
Or maybe it's a constant, an important building block of the physics of the Universe?

[Mustang Dave]

That's an interesting way of expressing fuel economy. My Mustang has a lifetime average of .07968 mm^2, or .0063" diameter - just over twice the diameter of an average human (scalp) hair.
mm^2 = (liters/100km)/100.
The amount of energy contained in petroleum hydrocarbons is quite impressive.

[niky]

I saw that comic this morning, and at first I was: "funny", then... "what?" then... oooh... that's pretty logical. This one was almost as awesome as the half-empty glass.

Originally Posted by Piwoslaw

Frontal area is also measured in sq. meters, so maybe the ratio of the two numbers would mean something? Like who gets the best FE per unit of FA.
Or maybe it's a constant, an important building block of the physics of the Universe?

It would be interesting to find out what the theoretical maximum you could get for every square meter of frontal surface area is, and if there is a linear relationship.

[Slow_s10]

That really is a pretty cool way of looking at fuel economy. Oh and thanks for killing like an hour of my time with that... because of course I had to go back and see all of the other "what if" questions that were asked. The first one was absolutely hilarious BTW.