Tuesday, September 14, 2010

Cracking the Whip

Last fall I went on a mission trip to the other end of the state with a group of twenty or thirty people. We traveled in a convoy of about six or seven cars. On the way back I was driving at the rear of the convoy, and I noticed that I was frequently falling behind and having to drive ten or fifteen mph over the speed limit to catch up. At one point, the car in front of me was pulled over for speeding while trying to catch up with the preceding car, and later in the trip a tire on my car blew out in the same situation. I wasn't happy.

Being a good engineer, I put my mind to the problem to figure out why it was happening. The lead car driver swore he wasn't speeding, but the cars in the back definitely were.

The phenomenon involved is similar to cracking a whip. If the second car falls behind at all, it will have to speed up slightly to catch up with the leading car. It will start pulling ahead of the third car, which will then have to speed up even more to catch the second car. As this pattern is repeated down line, the cars in the back suddenly find themselves falling behind and having to go much faster than the average speed of the convoy in order to close the distance. It's an emergent behavior of the convoy system as individual drivers try to make decisions about driving while following the rules of the convoy :"keep the car in front of you in sight."

If the whip-cracking phenomenon is a result of the convoy rules, it can be ameliorated by changing the rules. I propose two techniques for solving the problem: an elegant solution and a practical solution.

The Elegant Solution:
Subtract half the number of cars in the convoy from the speed limit. The resulting number is the maximum speed of the leading car. Each subsequent car is allowed to drive 1 unit (mph or kph) faster than the car preceding it. If all cars follow their speed limits under all but the most extreme circumstances, each car will be able to catch up with the car in front of it (albeit slowly) while keeping the maximum speed of the last car within a reasonable range of the legal speed limit.
A convoy of 10 cars is driving on an interstate with a legal speed limit of 70 mph. The lead car drives no faster than 65, car 2 66, car 3 67, and so on so that the 10th car drives no faster than 75. The average speed of the convoy is 65 mph, and as any car falls behind they can catch up with the car ahead of them by driving 1 mph faster.

The Practical Solution:
Use cruise control! If any cars do not have cruise control, put them at the back of the convoy. Emphasize strongly to all drivers that they should set cruise control at the legal speed limit and LEAVE IT ALONE!

I haven't tested either of these methods yet, but I intend to in a few weeks as I travel with another convoy.