The Voorhees law of traffic: when overtaken slow cars seem to always catch up at a red light | Motoring
This is a situation many drivers experience: When one driver overtakes another, they find that the slower car is right behind them when they reach the red light. Now a researcher has used mathematics to reveal why this situation was inevitable.
Dr Conor Boland, of Dublin City University, called his work “Voorhees traffic law”.
This name is a reference to the character Jason Voorhees in the American horror film series Friday the 13th.
“I always thought about him because he seems to walk everywhere… His victims are running away, they’re running but he catches them,” Boland said.
But in cars, it is not stones or tree branches that prevent the faster one from “running away”, but traffic lights.
Writing in the Royal Society Open Science journalBoland explains that if two cars traveling at different speeds encounter a traffic light, the distance between them may increase, remain the same, partially decrease, or disappear completely, depending on the color of the traffic light, its duration, the time advantage of the faster vehicle, and the total time it takes for the traffic lights to complete one lap.
Assuming that traffic lights change color according to a specific time cycle rather than a sensor, and that cars drive on a single-lane road, the results reveal that, on average, the possible gains and losses in distance between cars are exactly balanced when the probabilities of each of the four scenarios are taken into account.
This means that on average the advantage of one car over another remains the same after light as before.
The results show that the idea that the slower car will inevitably make it to the lights is an illusion.
“Repeated encounters are known to be disproportionately salient to human perception, especially when followed by an attempt to disengage or avoid,” Boland writes.
Simply put, it will probably be more memorable for a driver to see the car he overtook catch up with him again.
But the situation is different when drivers encounter a succession of independent traffic lights, as in towns and cities.
As Boland explains, here it becomes almost statistically certain that the slower car will be caught at at least one of the lights. This is because the probability that the slower car will never catch up depends on the probability of not making it at each traffic light multiplied by the probability of not making it at each traffic light; So the more light there is, the less likely it is that capture will not occur.
Boland said the results had implications for road safety, suggesting that speeding past others would not necessarily provide an advantage.
Kit Yates, professor of mathematical biology and public engagement at the University of Bath, who was not involved in the study, welcomed the study.
“It’s something I think about often as a slow driver. Was it really worth it for that car to overtake me at speed? When I catch them at the lights I smugly think, ‘No, it wasn’t.’ So it’s good for someone to sit down and model how and when this will happen,” he said.
However, Yates added that in his experience, catching up to a faster vehicle does not always happen, or is not surprising when it does.
He also noted that the study made a number of assumptions; these include cars moving at a constant speed between lights, without accelerating when the light turns green or slowing down when it turns red.
“But as the old adage goes, ‘all models are wrong, but some are useful,’ and I think that’s certainly useful in explaining why slower cars can often catch up with faster ones,” Yates said.
