Tuesday, July 15, 2008

Several More Thoughts: On The Road Ed.

[EDIT AND UPDATE: I have been shown a copy of the paper, and Larrick and Soll, referenced below, have conducted a serious study evaluating people's perceptions in making economic choices, rather more than the glib suggestions I made in an earlier draft of this post. As well, they received no external funding for the research.]

Among my many sins, I live my life as a dirty hypocrite of an exurban commuter. I get up earlier than I have to in order to turn eight hours into nine and a half by way of the Subaru, all so I can sink my extra cash into landscaping. (If I lived in the urban center, I'd probably have sunk it into questionable private schools instead, or maybe not) The ironic part is that I actually work in another suburb, and this distant shithole is still as close as I can afford to live, if I want to shack up my kids decently. I'm stuck with this fool's bargain for at least another couple years (at which point my suburban home will in all likelihood become unsellable). Thank god I got that PhD.

With an extra workday vaporized on the highway every week, at least I have some time to think (although not too deeply or I'll end up in a ditch). Unsurprisingly, a lot of that shallow reverie goes to politics and music. The rest goes to thinking, again unsurprisingly, about the reviled act of driving. I didn't quite have five.

1. Gonna write me up...
Everybody has seen this stupid graph by now, that shows automobile gas mileage as a function of speed, and topping out at a miserly 60 mph or so, it conveniently highlights the "don't speed" mantra of the obnoxious do-gooders of the world. I'm happy with the economic responsibility, but find the paternalistic safety business to be antithetical, and it's in my interest to disown this graph. What kind of vehicle are we talking about here? What engine? What conditions (on a treadmill)? In short, why the hell don't they design cars so that the fuel economy peaks at speeds people actually want to drive. And for that matter, even if Yuppie McDouchebag in his Magnum ought to be driving that souped-up hearse (I mean really, look at the ugly bastard) at 60, I, in my conscientious little econo-rocket, want to be exempted.

To make a car go, you need to overcome the forces arrayed against it, which in the case of the automobile include the rolling resistance, the air resistance, and the inefficiencies of the engine. The first two items both increase with velocity, and since I know dick-all about rolling resistance, and suspect there's little to be done about it, I want to concentrate on the airflow, which is significant. The drag force increases with the square of velocity (twice as fast means four times as much force to overcome), and the amount of power required to compensate it varies with v3 (and it needs eight times as much juice to do it). Now, you can engineer the proportionality constant, such that you're only squaring and cubing smallish numbers at highway speeds (and more on that in a minute), and this keeps many aeronautical engineers gainfully employed even today, but still, this dependence, the shape of the curve, is the unavoidable obstacle to automotive physics, at least for vehicles of the accustomed shape.

To help consider what it would take to make a car cruise at 70 mph and still be near its peak mileage efficiency, I constructed a handy, and necessarily qualitative, plot. The black line is the source of my complaint, the data from the previous figure inverted, because I want my scale to be energy (or as I'm now reading it, power integrated over some standard trip, which ends up equivalent to gallons per mile) instead of mpg. The total energy required to move the car will be what's needed to power the wheels, as well as to overcome the air resistance (shown by the red curve, and labeled as described above; it is proportional to the cube of the velocity; adding the rolling resistance will steepen this curve). In the limit of a perfectly efficient motor, these resistances are the only thing I'll need to compensate for, and my operating curve would be the same as the red line. The black curve becomes inefficient at low speeds because of the designs used in real-world vehicles. Engineers have no doubt played millions of games with gearing and combustion design and so forth to get a pretty decent gpm over a pretty wide stretch, but if I want that to extend out to span 70 mph, I still need to add more power overall (all of us know this from occasionally driving better cars, or pushing our own). Considering that my goal here is to use less fuel, finding a hotter 70 is kind of pointless. You still have to overcome that extra drag as you speed up, which takes more energy.

Experiments with my Subaru have verified all this, by the way, and to my regret. I suppose that the first step to meet growing global fuel prices will be the return of the shitbox compact, cars that feel like you're flying even when you're only going 50.

2. When a blunt object meets an irresistible force.
You may have noticed my careful qualifier "of this shape." That proportionality constant on the drag, at least the part of it we can change, is called the drag area (CdA), the product of the dimensionless drag coefficient and the area of the vehicles front-facing outline.

The graph at the right is a plot of the drag coefficient vs. Reynolds number (basically a dimensionless velocity). For auto travel, the Reynolds number is about 5x106 (the extreme right of the plot). At this point, the drag coefficient is pretty constant, and remains so even as you keep speeding up. (Again, this is just the proportionality constant, the force still increases as you speed up, always.) This corresponds to the presence of a turbulent boundary layer, the air is moving randomly near the surface of the vehicle and doing a good job of shifting momentum around. At low speeds (low Reynolds numbers), the drag coefficient increases. Here, the boundary layer is laminar (flows smoothly over the surface), and skin friction matters a lot more. Interestingly, there is a minimum in the drag coefficient, for most shapes, at Reynolds numbers of about 3x105, which corresponds to a normal car moving at about 6 mph. This minimum varies with shape a little though, and you can also make an object appear faster (in this dimensionless sort of analysis) by making it smaller. It's hard to imagine tweaking the "effective" speed by a factor of ten, but if you could design for that sweet spot...that would be pretty cool. (Studying transitional flow is hard, by the way.)

I had a professor once that argued in office hours that if a typical racehorse could go just a little bit faster, it'd break through that transitional flow wall, and dominate the track. (He hated me, he hated all of us.)

3. Always with the tradeoff.
Hey, did you like the way I inverted mpg up there to get a more useful measure of my car's performance? When you're counting your pennies, it's more useful to consider how much it costs getting from one place to another, the measure of which is gallons (proportional to dollars) per mile, and not the usual mpg. It's something to consider when comparing mileage improvements too. Economically, an increase in gas mileage from 10 to 20 mpg (0.1 down to 0.05 gpm, a savings of 0.05 gpm) is a lot more significant than an improvement from 40 to 50 mpg (0.025 to 0.02, a savings of 0.005 gpm), which, I guess, is good to know. It sounds like the sort of interesting but not earth-shattering observation that's good fodder for newspaper or magazine columns, but two authors have have taken it a little further. (Since you probably don't have a subscription to Science either, where their article appears, you can read here how Larrick and Soll tackle "the mpg illusion.") These two just got published in a premiere journal for what looks like a unit conversion, but it's more a psychological study and a policy question about how people underestimate the cost of car ownership. The price of a car for a few more high-end mpgs is a cost loser over the vehicle's lifetime, and a better consumer choice, and better policy choice, is to improve mileage of lower-performing vehicles. For American policy, I'll add, it suggests we'd be better off mandating minimum mileage standards rather than average ones.

4. I don't want a pickle, I just want...a ZAP!
Back to aerodynamics, it should be noted that the more obvious way to decrease the drag area is (duh) to decrease the area. This is one reason motorcycles get far better mileage than cars (decreasing weight helps a lot too). Bikes mean you don't have to stop for traffic jams, either.

But if you're a maniac like me, the combination of two wheels and 60 miles per hour is a death sentence, and even normal people prefer not to trek around on one of these guys in the winter, when it's raining, etc. One obvious solution to a less painful commute is to drive vehicles which trade off the lightness, speed, and economy of a motorcycle with the relative safety of an automobile. Lightweight one-person vehicles could take us pretty far in dealing with an oil crunch, and let poor bastards like me keep on with their miserable suburban existences. I'm thinking a motorcycle with a roof and a radio here--and a rollbar. We've done the Escort already, and the need to pretend the thing was a real car remains unclear. I say fuck the hatchback, the back seat no one could occupy anyway, the spare, the passenger side, and two of the four soda-straw cylinders, and get me from here to there at cost.

As of yesterday, all idle googling revealed to me on this front was Toyota's glorified Segway--an obvious death trap under the conditions I'd really need a car for (that is, too far to bike), and some similarly misguided efforts that looked like terrestrial jet-skis. But it turns out that I can no longer call myself prescient and wise: these are scheduled for next year, one-seaters, and they look absolutely badass.


Damn. I want one too.

1 comment:

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Thanks