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From: leichter@yale-com.UUCP
Newsgroups: net.physics,net.auto
Subject: Re: physical laws of freeway traffic?
Message-ID: <1623@yale-com.UUCP>
Date: Wed, 15-Jun-83 21:14:42 EDT
Article-I.D.: yale-com.1623
Posted: Wed Jun 15 21:14:42 1983
Date-Received: Thu, 16-Jun-83 13:54:30 EDT
References: 5941ux.284
Lines: 35

Traffic engineers do a great deal of analysis of "the physics of traffic".
I know nothing about the details, but fundamentally they view traffic in
terms of generally quite turbulent fluid flow.  I think the bunching up
you see is often essentially a series of standing waves.  (This is obvious
in certain cases, e.g. when there is an accident that slows traffic down -
change in impedence, if you will.  You see everyone slow down, then speed
up - and the effect persists long after the original cause is gone.  It
only breaks up when the traffic flow gets light enough - average inter-car
distance is large enough - so that the standing wave can be disipated.  (In
heavy traffic, when the cars ahead of you brake, you must brake, too; hence
those behind you brake, etc.)  The breakup of the wave undoubtedly looks
like the high-frequency limit for sound transmission in a gas when you set
it up mathematically,

For a very basic discussion, see The Amateur Scientist column in the March
Scientific American.

Now, for those who like HARD problems (this is from an old American Mathe-
matical Monthly, if I remember right):  Cars A and B, at time t=0, are at
rest with B just behind A.  Starting at t=0, Car A begins moving with a
constant acceleration.  Car B follows behind A as closely as possible,
subject to the constraint that it must be, say, k "car lengths" behind A
per mph of its own speed.  (I.e. it maintains a separation linearly proportional to

its speed.  Problem:  express Car B's

speed (or positio)as a reasonable function of time.



					-- Jerry

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