Monday, April 18, 2011

When Does It Start?

So I'm driving to work the other day, and I'm stuck behind this car whose driver has decided that today, freeways shall be traversed at the speed of 42 mph.  (In reality, I suspect this decision applies to most days, but I'm trying to be conservative here.)  And it's almost impossible to pass him, because the stream of cars passing both of us is too dense and too much faster than we are to enter safely.

Eventually, I manage, and at a relatively safe moment, I cast a quick sidelong glance at him and affirm that he's northward of 80 years old.  Now, there's a lot of talk that drivers that old should be looked at fairly hard and often to establish that they're able to drive safely, but I'm actually not thinking about that.  What I'm thinking about is, at what point did he become a 42 mph kind of driver on the freeway?  Was he always like that, or did he start out as what most of us would consider an ordinary kind of driver, and over time got slower and slower?  I mean, maybe there are places where 42 mph is considered sort of daring, and that's where he grew up.

At this point in the discussion, someone invariably pipes up and mentions that such drivers are in fact safer than those driving at some higher speed, say, 80 mph, on the assumption that 80 mph is just inherently less safe.  There's something to be said for that point of view, in that there's less time to avoid impacts if you're driving at a higher speed, and any impacts you do end up in are more dangerous.  But that's only part of the picture.

The reality of the situation is that although (in Los Angeles) the freeway traffic occupies a continuum of speeds, most of the traffic—perhaps 90 to 95 percent—falls between 60 and 80 mph.  And your risk of impact depends primarily on how often you encounter cars travelling at that range of speed.  A long time ago, in grad school, I spent a little time figuring out how often you encounter cars on the road: either passing slower cars, or being passed by faster ones.  And what I found was that the details of the speed distribution of cars matters very little.  There are only four parameters of interest: the density of cars on the road, the percentage of cars you're faster than, the average speed of those cars that you're faster than, and the average speed of those cars that are faster than you.

That means that you could pretty much figure out the rate at which both my 42 mph driving friend and the hypothetical 80 mph driver would encounter cars by simply assuming everybody else was driving 70 mph.  Our superannuated man behind the wheel would encounter cars nearly three times more often than the 80 mph driver, and encounter them at nearly three times the relative rate of speed.  To be sure, the combined energy of an actual collision would be greater for 70 mph and 80 mph than it would be for 42 mph and 70 mph, but the increased frequency of encounters and the much shorter period of time drivers would have to avoid them would, I think, more than compensate for that.

All in all, I think if you want to drive slower to be safer, you're better off driving 60 mph, or whatever the lower end of speeds is for your road of choice.

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