The Limits of High Gas Mileage

posted in: Design, Global View | 0

In making policy and predicting market strategy, and the doomer in me says, in preparation for collapse, we need to know what the absolute limits are on personal transportation efficiency. That is, the limits which no amount of engineering can pass.

Here is a post on an interesting blog, that captures the rough data for limits to efficiency for highway driving on gasoline. Unfortunately, most of the comments are not interesting, and miss the point of how these limits are absolute. The actual values produced depend on how fast and how slippery and how efficient you think engines can be.

Partial quoting from Do The Math:

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!

Putting these together, a tragically un-aerodynamic car would see a drain of energy of Edrag=½(ρAD)v², where the term in parentheses is the mass of the air involved. A real car has better aerodynamic performance than a piece of plywood, so we include a term called the drag coefficient, cD, and the energy expended on fighting air for the journey becomes Edrag=½cDρADv². The drag coefficient for cars ranges from 0.25 for a Prius to numbers like 0.5–0.6 for SUVs and pickup trucks. Loads of sedans come in around cD=0.3, so we’ll use that number for the present analysis.

A more practical set of limits given our behavioral and aesthetic preferences might be A=2.5 m², cD=0.2, and 30% engine efficiency. This puts us at 84 MPG. Not a bad place to be, but shy of the magic 100 MPG. And even this is not a snap: note that we are nowhere close to this mark at present.

How does the Prius today get a fuel economy in the low 50′s? The drag coefficient is on the low side, at 0.25. The area is small-ish—I estimate 2.5 m², and the big trick is that the engine can be optimized for freeway speeds since the battery can assist acceleration at lower speeds. Traditional cars sacrifice freeway efficiency for the get-up-and-go performance that is so important in test drives. If I use 25% engine efficiency with the aforementioned values, I get 56 MPG.

We have so far neglected rolling resistance (mainly from tires) in this analysis, primarily to keep things simple while capturing the dominant contributor to fuel economy at freeway speeds. At a rolling friction coefficient of 0.01, a 1 ton car (1000 kg; 10,000 Newtons) requires 100 Newtons of force to push along—independent of velocity. This effect alone (e.g., driving in a vacuum) would result in a limit of 160 MPG at a 20% engine efficiency. At 30 m/s (67 m.p.h.) in air, factoring in rolling resistance: … and our “realistic” 84 MPG car now gets 63 MPG.


So you can plug whatever figures you like into the equation. You can factor in transmissions and differentials and air conditioning and lighting. But the important point is, barring fantastic efficiency improvements to ICEs, don’t hold your breath, some number between 60 and 100 mpg is probably the best fleet average we will ever achieve in consumer vehicles at highway speeds.

The limit would be higher for small unusual vehicles like a single-seat recumbent faired motorcycle, and there are impractical vehicles like the solar racers and electrathons that have low drag.

As a sidebar aircraft get much worse mileage due to increased speeds. Flying magazine says some famously efficient 4 place Mooneys get around 18 mpg and smaller slower planes a little bit better. Long distance powered sailplanes can get very high mpgs.

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