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Mathematicians Solve the Mystery of Traffic Jams

Posted by Zonk on from the next-they'll-use-geometry-on-the-mystery-of-the-haunted-amusement-park dept.

mlimber writes "Do you ever find yourself in a traffic jam, thinking, 'Man, there must be a bad accident up ahead,' but as you plod along you see no evidence of any crash? Some mathematicians have solved the mystery by developing a mathematical model that shows how one driver hitting the brakes a little too hard can cascade into a backup miles behind. The mathematicians' future research will investigate how automatic braking systems may alleviate the problem."

7 of 629 comments (clear)

  1. Old news by Hatta · · Score: 5, Informative

    This has been known for years.

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    1. Re:Old news by orclevegam · · Score: 5, Informative

      It is kind of like the Slinky effect, where you send a pulse down it and it rebounds. Car stops ahead and the cars behind begin breaking, and this begins a chain reaction... I'd love to catch this in the act at night and film the tail-lights lighting up in sequence. The term you're looking for is standing wave. The problem isn't actually the breaking, it's everyone not giving enough room between themselves and the person ahead of them to absorb small slowdowns. The time between when you slow down and accelerate back up to speed needs to be factored in. If the people coming into the jam are entering faster than people can accelerate out of the jam, it will either remain static or become worse.
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    2. Re:Old news by bcattwoo · · Score: 4, Informative

      I wonder why this isn't taught in driver's ed. Meh. I imagine they also teach you to use your signal, not speed, not tailgate, not run red lights, not drink and drive, stop at stop signs, and a million other rules and good driving practices that people ignore.
    3. Re:Old news by Just+Some+Guy · · Score: 4, Informative

      My tires are 60R15, so the tire has a diameter of 15in/0.6=63cm, and a perimeter of ~200cm.

      Ummm, no. You left out the width of your tire (Google guesses you meant 205/60R15). So the sidewall is 60% as tall as the width, or 123mm. The 15" rims are 381mm, plus 123mm*2 = 62.7cm outside tire diameter. Almost the same number but your formula was completely wrong.

      For my car, a '99 A3, the first gear ratio is 1.833:1. [...] The minimum clutch-less speed is 0.2*463*60=5.6km/h.

      Huh? You're just making that up now, aren't you. Let's try that again.

      Another Google guess gives it a transmission ratio of 2.714 in first gear, times a final drive ratio of 4.875, for a net ratio of 13.231:1. At base revs, your car is going (850rev/min) / 13.231 * (62.7 * 3.142 cm/rev) * (60min/h) * (1km/100000cm) = 7.6km/h.

      The same formula using top revs in 4th gear (0.742 ratio) gives approximately the correct top speed of your car, so I'm pretty sure my formula is right. Since the article is about cars and math, we might as well use correct math when discussing them.

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    4. Re:Old news by bcattwoo · · Score: 4, Informative

      The clutch is more or less is two plates that are brought into contact to transfer power from the rotating engine to stationary transmission (assuming you are stopped). When you engage the clutch, the plates are initially moving at different speeds causing friction and wear. When you "ride the clutch" you keep the clutch in this wearing state longer/more often and as a result end up replacing your clutch sooner than later.

  2. Traffic Waves by Phroggy · · Score: 3, Informative

    Does this mean now there's math to support this?

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  3. Re:Cover Job by jargon82 · · Score: 5, Informative

    They are also behind LAST years mathematicians. Although by a bit shy of a year. http://science.slashdot.org/article.pl?sid=06/12/27/0350218