miles (per gallon) to go before understanding fuel economy

The rocket scientist just bought a new car.  He claims he was thinking about trading in his old Pontiac Aztek well before I bought my new car, but even if we were thinking about the need for new cars at the same time, I guarantee we had distinctly different thought processes in deciding what kind of cars to buy.  I have a much more aerodynamic dog than he does (hound dog vs. golden retriever), so a convertible made a lot better sense for me than for him. (Sorry, Katie…) 

One obvious consideration in buying a car is fuel economy.  Fuel economy is the figure of merit for everything from advertising to the "Cash for Clunkers" program.  C for C only allowed you to trade in cars with an EPA fuel efficiency rating of 18 mpg or less.  If you had a Toyota Camry and you wanted to get a new Prius, you were on your own.

So which is better:  going from a car that gets 34 miles per gallon (mpg) to one that gets 50 mpg, or changing from a car that gets 18 mpg to one that gets 28 mpg? For the precise among you, let's define
'better' to mean saving you the most money in fuel costs.  So the first one is
better, right?  You've got a 16 mpg improvement vs. a 10 mpg
improvement.

Not so fast.  Let's say you drive 18,000 miles each year.  The amount of gas you need to drive 18,000 miles if you get 18 miles per gallon of gas is 18,000 miles/18 miles per gallon = 1,000 gallon.

Miles per gallon	Gallons of gas needed for 18,000 miles
18	1,000
28	643
34	529
50	360

If I change from a car that gets 18 mpg to one that gets 28 mpg, I save 1000-643 = 369 gallons of gas.  If I change from 34 mpg to 50 mpg, I save 529-360 = 169 gallons of gas.  Sort of counter intuitive, huh?  That's what Richard P. Larrick and Jack B. Soll of Duke University found in a study in which they asked people to rank order five pair of proposed mpg changes in order of "their benefit to the environment (i.e. which new car would reduce gas consumption the most compared to the original car?)"  Sixty percent of the respondents rank ordered the changes according to the difference in mpg.

If you plot (as the authors did in their paper) the amount of gas used for a fixed driving distance vs. the miles per gallon your car gets, the plot is definitely not linear. I've made a similar plot for three different driving distances – 10,000 miles, 15,000 miles and 20,000 miles and indicated on the graph where the two mileage differences I compared above are located.

This is an example of linear reasoning being applied to a case in which it doesn't apply.  In some countries, the figure of merit is a quantity like how many gallons you need to drive 1000 miles.  (Actually, the quantity is liters per 1000 kilometers since just about everyone in the civilized world except us uses the metric system.)  I calculated the gpm (gallons per mile) in the table below and you can compare the fuel efficiency much more easily.  

Miles per gallon	Gallons per 1000 miles
18	55.5
28	35.7
34	29.4
50	20.0

Larrick and Sole argue that gallons per mile and not miles per gallon should be used to help people understand energy efficiency, but I would argue we need to take it one step further.  I used to like to ask my graduate students the following question:  "What one skill do you want your students to have when then enter the intro course in your discipline in college?" 

For me, the answer is the ability to really read graphs.  That's a little bit of a cheat for an answer because there's a lot of math tied up in understanding graphs.  But a graph gives you so much more information than a number does.  In this case, we're really not interested in just a number:  we're interested in the slopes between the sets of points — or (dare I say) the derivatives of the curves. On the graph below, I've identified the slopes between 15 mpg and 20 mpg and between 35 mpg and 40 mpg with dark lines.  The lines are a lot steeper for the low-mpg interval than for the high-mpg interval, even though we're looking at a 5-mpg difference in both cases.

Another important thing to notice is that how much you drive in a year makes a pretty significant difference.  This graph tells me that the more miles you drive, the more important it is for you to improve the fuel economy of your car.  The little old lady with the Mercedes who only takes it out on a Sunday for church is not making too much of a dent in the petroleum stores.  The person who drives from Allen to downtown Dallas five days a week, 50 weeks a year really needs to worry about fuel economy.

The final thing I would hope people notice from the graph is the total amount of fuel.  Changing from a 10 mpg to a 12 mpg vehicle definitely saves fuel; however, you're still using a lot more fuel than if you went to a 15 mpg or 30 mpg vehicle.

Of course, there's a caveat – there always is.  Although the study focused on environmental impact in terms of fuel used, don't forget that there can be significant differences in terms of emissions.  In fact, the two best things you can do with your current car to help the environment are to make sure your car is tuned up so that if combusts the fuel efficiently, and maintain the right tire pressure.

My hopes for getting students to learn how to use and digest information from graphs is probably doomed for disappointment.  People want the easy solution:  just give me one number I can base my decision on.  Just as No Child Left Behind has reduced school performance to standardized test scores, and all universities care about anymore is how many students are enrolled and whether the students think the professors are entertaining – never mind what they learn, the average person wants things to be laid out.  I'm with Einstein:  Everything should be made as simple as possible.  But no simpler. 

Maybe we need a test before you're allowed to buy a new car.  On second thought, that would probably kill the Big Three faster than they've been able to do it themselves.