Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!linus!wivax!decvax!yale-com!leichter 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 decvax!yale-comix!leichter leichter@yale