A recent study published in Royal Society Open Science sheds light on a common driving experience—when a slower car seems to catch up after being overtaken.
The research, led by Conor Boland from Dublin City University, uses a mathematical model to explain how traffic signals play a crucial role in this phenomenon.
How Two Cars Interact on the Road
The study focuses on a simple scenario involving two vehicles traveling at different constant speeds. Normally, one would expect the faster car to remain ahead after overtaking. However, the model shows that this is not always the case.
Because traffic lights operate on timing cycles that drivers cannot predict, a faster driver may encounter a red light soon after overtaking. This creates an opportunity for the slower vehicle to catch up.
Why Traffic Lights Matter
According to the study, the likelihood of a slower car catching up depends on three main factors:
- The time advantage gained during overtaking
- The total duration of the traffic signal cycle
- The proportion of time the signal remains red
If the faster car is forced to stop at a red light, the slower vehicle can reduce the gap despite moving at a lower speed.
Introducing the “Voorhees Law of Traffic”
The research introduces the concept of the “Voorhees law of traffic,” inspired by Jason Voorhees, a character known for unexpectedly catching up to faster-moving targets.
This idea suggests that when the time advantage gained by overtaking is small, the chances of being caught up increase significantly. On the other hand, a larger lead reduces this probability.
Effect of Multiple Traffic Signals
The study also highlights that the chances of this catch-up effect increase when multiple traffic lights are involved. On longer urban routes with several signals, the probability of at least one such event becomes much higher—explaining why many drivers experience this situation frequently.
Wider Implications
Beyond explaining a familiar driving scenario, the findings could help improve traffic flow models by factoring in how vehicles interact with traffic signals. The study also suggests that these events are statistically common, which may be why they stand out so clearly in drivers’ memories.
