MPG of a Human

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On Do the Math, three previous posts have focused on transportation efficiency of gasoline cars, electric cars, and on the practicalities of solar-powered cars. What about personal-powered transport—namely, walking and biking? After stuffing myself over Thanksgiving, I am curious to know how potent human fuel can be. How many miles per gallon do we get as our own engines of transportation?

Okay, the “miles” part is straightforward. And we can handle the “per.” But what’s up with the gallon? A gallon of what? Here we have all kinds of options, as humans are flex-fuel machines. But food energy is not much different from fossil fuel energy in terms of energy density.

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A Solar-Powered Car?

If you like the sun, and you like cars, then I’m guessing you’d love to have a solar-powered car, right? This trick works well for chocolate and peanut butter, but not so well for garlic bread and strawberries. So how compatible are cars with solar energy? Do we relish the combination or spit it out? Let’s throw the two together, mix with math, and see what happens.

What Are Our Options?

Short of some solar-to-liquid-fuel breakthrough—which I dearly hope can be realized, and described near the end of a recent post—we’re talking electric cars here. This is great, since electric drive trains can be marvelously efficient (ballpark 85–90%), and immediately permit the clever scheme of regenerative braking.

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MPG for Electric Cars?

A typical efficient car in the U.S. market gets about 40 MPG (miles per gallon) running on gasoline. A hybrid car like the Prius typically gets 50–55 MPG. In a previous post, we looked at the physics that determines these numbers. As we see more and more plug-in hybrid or pure electric cars on the market, how do we characterize their mileage performance in comparison to gasoline cars? Do they get 100 MPG? Can they get to 200? What does it even mean to speak of MPG, when the “G” stands for gallons and a purely electric car does not ingest gallons?

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100 MPG on Gasoline: Could We Really?

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Since I was a teenager, I frequently heard stories that some guy had invented a car that could get 100 miles per gallon (MPG), but that powerful interests (often GM, Chevron, etc.) had bought rights to the idea and sat on it. We suckers were left to shell out major bucks for gasoline, when a solution was in hand and under wraps.

Leaving aside the notion that such a design would bring unbelievable prosperity to its holder (i.e., no real incentive to sit on it), let’s look at what physics says is possible.

We like cars because we can travel quickly from point A to point B. So let’s evaluate the energy requirements to make that journey at freeway speeds. We will use the somewhat awkward (although appropriate) speed of 67 m.p.h. because it conveniently maps to 30 meters per second. At these speeds, aerodynamic resistance is the dominant energy drain, so we will start by evaluating only this to get a lower bound on fuel efficiency, and find that we do a pretty good job! Continue reading