Getting Called Out

Okay, I confess – one of the reasons I’m making time to blog this morning, even though I am due at one of my many jobs in a little while, is that I got called out by my esteemed coblogger a couple days back, in a post about fuel efficiency and the political benefits to be had from having some super-efficient cars on the market.  Shane says

The people buying and driving those 15 mpg SUVs are looking at the mileage they could get in a car (say 25-28 mpg) and figuring that 10-12 mpg isn’t really that big a deal. And they’d be right, since that 10 mpg, would take them half way to the most effiencient car available. But what if the really efficient cars were getting 50+ mpg or more? Then those same 10 mpg would still mean they’d need to double their effiency to reach the top of the scale. Suddenly, 10 mpg doesn’t seem like too much.

Okay, first, a basic mathematics lesson for those who didn’t quite get the point from Shane’s post.

For a more detailed rundown, you should check out Science Geek Girl.  You can also see my comments there.  But the nub of the argument is contained in this graph I stole from SGG (or, more accurately, SGG’s dad): 

Basically, at the low end of MPG, every 1 MPG increase yields quite a bit of savings, as represented by the steep slope of that portion of the graph.  However, as you pass 20 or so, it begins to level off, and by the time you get to 50, it’s nearly flat.  This makes sense, in a simple way – if the person getting 10 MPG is spending $400 to go 1000 miles, they can save $200 by doubling their mileage.  Alternatively, the person getting 40 MPG is only spending $100 to go 1000 miles, so they could never save $200, no matter how efficient the car they drove.

It’s a problem of perception and unit usage, something we see all the time in physics.  The fact is, MPG is a bad unit to use when describing fuel efficiency.  Here’s a conversion plot between MPG and Gallons Per Thousand Miles, or GPTM.

MPGI like GPTM quite a bit more, because, unlike MPG, it is bounded on the high-efficiency end, not the low-efficiency end.  By which I mean, a car can’t get less than 0 MPG, and to our minds, the difference between 1 MPG and 10 MPG is, well, small.  But 10 MPG is (duh) 10 times more efficient than 1 MPG.  This fact is much-better reflected using the GPTM unit, since the 1 MPG car has a rating of 1000 GPTM, while the 10 MPG car is 100.   GPTM is bounded at high-efficiency – you can’t go below 0 GPTM, but you only get near that with ultra-efficient cars, whereas the less efficient your vehicle, the higher your GPTM, with no upper bound below infinity.

Similarly, in the realm of the familiar levels of mileage, if you take a 10 MPG monster SUV and move over to a cheap 30 MPG sedan, you go from 100 GPTM to 33 GPTM, which sounds like it makes a big difference, in the way that my esteemed coblogger would like it to, so people who are only looking for big differences in numbers will, in fact, see them in the place where they make the most improvement.

I’m sure the car companies prefer GPM, since it’s confusing to the consumer in just the way described, but that’s no reason we ought to do things that way!  Let this be considered a clarion call for a unit shift to GPTM!

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