## Friday, December 18, 2009

### Hypothetical Maximum Gas Milage

My car gets between 32 and 24 miles per gallon, depending on how I drive it. Gas milage is a big deal these days, since the price of gas usually goes up, most notably that time in 2008 when it went to \$4+ per gallon in most of the US. The entire country was having an apoplexy even though much of the world willingly (or unwillingly) pays more. But it was a reminder that 8MPG big cars like SUV had significant downsides.
I often compute my miles per gallon when I fill the tank. A sudden drop is often sign that I need to refill the tires, change the air filter, or get a tuneup. But I'm left wondering, what's the hypothetical maximum for gas milage, especially when I see commercials bragging about cars whose gas milage is worse than the cheap car I own for myself. (They get 22-24 MPG and brag, several times in the commercial, about how great that is. What?)
I have to make some assumptions. A gallon of gas has 1.3*10^8J of chemical energy in it. Energy can be used to impart acceleration, depending on weight. Let me assume that the car can't be any lighter than mine, since my car is a compact car, the smallest type that Americans are typically willing to drive. (Europe and Japan have some smaller light-duty cars, because gasoline tends to be mind-bogglingly expensive there. That and space is limited.) My car weighs 800kg. Doing the math, I'm left with 162500 m^2/s^2, and left to convert this to a linear distance based on typical driving habits. I can divide by standard city acceleration patterns, which would have units of m/s^2, and be left with meters, which I can convert to miles (the MPG). A study of new york buses suggested that their acceleration was typically 2.77 m/s^2. Mine may be greater, but this seems like a reasonable figure for driving in a city. This gives me 58664.26 meters, or 36.5 MPG.
36.5MPG would, according to this, be the absolute maximum possible efficiency of a car weighing similar to mine. Achieving this level of efficiency would involve an impossible 100% efficient motor, and many other physics contrivances not practical in the real world. Better gas mileage would involve a lighter car, electric hybrid engine (to shift some of the energy to more efficient electric motors), or some other such complete re-design.