Mathematicians Solve the Mystery of Traffic Jams

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."

Old news

[Hatta]

This has been known [amasci.com] for years.

Traffic Waves

[Phroggy]

Does this mean now there's math to support this [amasci.com]?

I read about this once

[Neil Blender]

20 fucking years ago.

Re:Old news

[Gregb05]

I actually remember reading this from a series of books called Imponderables [imponderables.com], years ago.

Re:Old news

[orclevegam]

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.

Re:Old news

[jonbryce]

On the M25 and M42, two of the busiest roads in the country, the variable speed signs have revenue cameras attached to them, so anyone who disobeys them gets fined.

Re:Old news

[bcattwoo]

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.

Read the actual article at the link below (PDF)

[JasonSpradlin82]

The article referenced was actually published in the September 2006 edition of the Proceedings of the Royal Society A: http://journals.royalsociety.org/content/h107x295723j3734/fulltext.pdf [royalsociety.org]

Re:Cover Job

[jargon82]

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 [slashdot.org]

Re:Arrgh!

[GNU(slash)Nickname]

The trouble with automated systems is that they assume ideal conditions. Anyone who's experienced at driving on ice and in deep snow will tell you how much fun it is to have your ABS take over and spin you around a couple times (or crawl up the side of the plowed-snow bank along the road), when left to your own devices you'd have geared down (yes, auto trannies CAN do that), likely not used the brakes at all, and slowed *safely*.

WTF? That makes no sense at all. ABS is an Antilock Braking System, not Automatic. It modulates the brakes when it detects wheel lock, it doesn't apply them under any conditions.

If you don't touch the brakes at all, the ABS does nothing. Much less "take over and spin you around a couple times".

Re:Old news

[Just Some Guy]

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

Ummm, no [tirerack.com]. 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 [audi.co.za] 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.

Watch the movie

[RonTheHurler]

This was shown in a time-lapse sequence in a movie called Koyaniskatsi (or some spelling similar to that)
Produced about 20 or 30 years ago.

Cool movie.

If anyone can find it or confirm the proper spelling, I'd appreciate an update.

Re:Old news

[bcattwoo]

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.

Re:Old news

[mvdwege]

Try a motorbike.

My Moto Guzzi 1000 SP III is useless below 30 km/h in second gear. First gear works, but just barely, to trundle along at constant throttle, unfortunately the power/weight ratio is such that the least throttle movement translates into huge jerks. And my experience is that this is typical for Guzzi motorbikes, they have very tall first gears, and a correspondingly higher speed in second, and even though they're V-twins (usually thought of as sedate low-rev trundlers), they're useless below 2000 revs.

And this is not even a very powerful bike, only 72hp (240 kg dry weight). Japanese bikes tend to have shorter firsts, but even they suffer from jerkiness, made worse because they are usually higher-powered.

I have to ride the clutch if I want to keep moving in a jam. Thankfully this is usually unnecessary, as filtering is legal here in the Netherlands. Guess why I ride a big-arse touring bike for my daily commute? It's rather fun to comfortably filter through two lanes of almost-stopped traffic at a sedate 2200 revs in 2, which is about the aforementioned 30 km/h. Only concessions I have to make is taking 5 minutes at both ends of my commute to get in and out of my suit, and a reduced carrying capacity (even my hardbags and luggage rack can't compete with a car backseat or a boot).

Mart

Re:Cover Job

[Shag]

And they're two and a half years behind Philip Ball's "Critical Mass" which won the Aventis Prize for science books [newscientist.com] that year. Of course, CM dealt with a lot more than traffic jams - but they were in there. (In fact, from the new story's summary, it sounds like the researchers may have read it.)