Mathematicians Solve the Mystery of Traffic Jams 629
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 (Score:5, Informative)
Traffic Waves (Score:4, Informative)
I read about this once (Score:2, Informative)
Re:Old news (Score:2, Informative)
Re:Old news (Score:5, Informative)
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Re:Old news (Score:5, Informative)
Read the actual article at the link below (PDF) (Score:2, Informative)
Re:Cover Job (Score:5, Informative)
Re:Arrgh! (Score:2, Informative)
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 (Score:5, Informative)
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.
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 (Score:3, Informative)
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 (Score:5, Informative)
Re:Old news (Score:3, Informative)
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).
MartRe:Cover Job (Score:3, Informative)