CO₂ Turds

Bob Runs the Numbers, Episode 1

Instead of thinking about your car's “miles per gallon,” consider gallons per mile.

Then tinker with unit analysis. Gallons per mile is volume per length, or

length^3 / length

That’s length^2 or area. That area is the cross-section of a “thread” of fuel along your route.

So let’s picture your car ingesting this thread of gasoline as it moves. For example, if your car gets 16 miles per gallon, that works out to a cup of gasoline extruded into a mile-long thread. If you're a hyper-miler hybrid driver, your car might get 64 miles per gallon, or two fluid ounces extruded into a mile-long (much skinnier) thread.

Gasoline is mostly carbon, which combines with atmospheric oxygen to form CO₂. (And water, and trace pollutants. But the bulk is CO₂.) A gallon of gasoline with about six pounds of carbon generates about twenty pounds of CO₂. (Each carbon atom grabs two heavier oxygen atoms from the atmosphere.) And the CO₂ takes up a lot more space than gasoline since it's a gas instead of a liquid; at sea level, each gallon of gasoline ends up being over a thousand (wow!) gallons of gaseous CO₂.

So what if we consider the “thread” of CO₂ being expelled by a car? If you think of the thread of CO₂ behind a car as a cylinder (a “CO₂ turd,” if you will) then you can find the diameter of the circular cross-section with this equation:

diameter = sqrt(5.67 / mpg)

So I can plug in 50 mpg for a Prius and end up with a virtual cylinder 0.34 inches in diameter that I can envision trailing behind me as I drive.

Or plug in 20 mpg for a station wagon and it's a cylinder 0.53 inches in diameter.

cross-sections of a couple example CO₂ turds

Not to get preachy or anything -- envisioning a morning commute with thousands of braided CO₂ turds is an exercise for the casual observer -- but just running the numbers and doing a little chemistry makes for an interesting (and, in my opinion, more intuitive) way of looking at the CO₂ impact of getting from point A to point B.