'Voorhees Law' Explains Why the Slower Car Often Catches up
jelizondo writes:
Phys.org has an interesting report on the reason the slower car many times catches up:
Many drivers will know the feeling: you pull ahead of the slower car you've been stuck behind and cruise the open road ahead at your own, faster speed. By the time you reach the next stop light, you're sure that you've left the slower car far behind you-but to your surprise, you see that same car cruise up right behind you in the mirror. Horror buffs might even recall scenes from "Friday the 13th," where masked villain Jason Voorhees always catches up to his sprinting victims-despite himself walking at a leisurely pace.In a new study published in Royal Society Open Science, Conor Boland at Dublin City University shows that this unsettlingly common phenomenon can be explained with simple mathematics. His model reveals precisely when and why a slower vehicle catches up after being overtaken, offering fresh insights into how individual vehicles interact with traffic signals.
In simple terms, if two objects move along the same path at different constant speeds, we expect them to reach any given point at different times. So far, however, traffic models haven't yet accounted for what happens when an overtaking event collides with the random timing of a traffic signal.
Rather than describing the average flow of many vehicles, Boland focused on pairwise interactions between just two cars. His approach treats the traffic signal as a random event: at the moment the overtaking driver gains a time advantage, there is no way of knowing how far the signal sits through its red-green cycle.
Using a straightforward probability framework, and assuming the driver arrives at the signal at a random point in its red-green cycle, Boland derived a formula for the probability that the slower car catches up at the next red light.
This probability turns out to depend on just three quantities: the time advantage gained by overtaking; the total length of the signal's red-green cycle; and the fraction of that cycle spent on red.
If a driver's time advantage is large relative to the red-light fraction of the cycle, the slower car almost certainly won't reappear. But as that advantage shrinks, as it often does during brief, more risky overtakes on busy roads, the catch-up probability climbs significantly. This could finally explain what Boland has dubbed the "Voorhees law of traffic."
On a psychological level, the model could also help to explain why we remember catch-up moments so vividly. In proving that catch-up events are statistically common, the Voorhees law shows that the frequency of the jarring reappearances of slower cars isn't just in your head.
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