Maths has a point-to-point to prove on speed

By Burkard Polster and Marty Ross

The Age, 22 July 2008

Did you know that speed enforcement dates back to 1903? The problems started in New York State, where incorrigible hoons would speed along at 40 miles per hour – too fast to be caught by the bicycled policemen.

The police responded with an ingenious “point-to-point” system of enforcement. It consisted of three fake tree trunks placed at 1 mile intervals. Each trunk concealed a policeman equipped with a stopwatch and telephone. This setup allowed the first two policemen to calculate the time a car took to travel the mile between their trunks. If the car’s average speed was over the limit, the third policeman could then jump out and book the driver.

The system worked, but the drawbacks are obvious. First of all, employing three officers to sit all day in trees is humorous but wasteful. And, using humans means the system is subject to human error.

However, the point-to-point system is fundamentally simple and reliable. And, on a toll road such as the new EastLink Motorway, it would be very easy to automate. Each time you pass a tollgate, a computer registers your license plate and the exact time that it sees you: just like the officers in their tree trunks. And, of course the computer could then do the simple arithmetic to check whether you’ve been speeding, and then issue your ticket automatically. Such splendid service!

Intriguingly, the computer would not know exactly when the speed limit was broken. The high average guarantees that the driver has been speeding at some moment without actually pinpointing when. This also means the point-to-point system can fail to detect speeding, if the driver slows down sufficiently before the next camera. But why would a speedster bother?

Let’s look at an example. Suppose the tollgates are 5 km apart and the speed limit is 100 km/h. So, traveling exactly at the speed limit the trip will take you 1/20 of an hour, or 3 minutes. Now, suppose instead you decide to speed at 120 km/h for the first minute. Then you will have traveled 2 km in this minute, leaving 2 minutes to travel the remaining 3 km. That means that for the next 2 minutes you’ll have to be traveling at 90 km/h whilst cars are racing past you. Great fun.

According to the Victorian Department of Justice, there are no firm plans to implement the point-to-point system on EastLink. Instead, motorists can look forward to a traditional battery of fixed radar guns. Unlike the point-to-point system, radar guns can be beaten, if for instance a clever GPS system warns you when you are approaching them.

But the point-to-point system may still have its day. Since 2005, the Victoria Police has been trialing the system on small stretches of the Hume Highway. This trial misses perhaps the most important point: if the coverage is not comprehensive then a speedster will be tempted to misbehave along the blind stretches. So, implemented in this way the point-to-point system has the same drawback as using radar guns. But the simple mathematical logic of the point-to-point system may still shine through, convincing the authorities of the system’s value.