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How Many Lanes Are Best on a Pinewood Derby Track?

It is a simple fact that tracks with more lanes will cost more, and timers for them will also cost more.   Also, more lanes require more lane maintenance.   But what about their practicality when it comes to use?   Let’s be frank: the conditions of the various lanes on a Pinewood Derby track are not equal.   It therefore makes sense to give each Cub’s car a chance to race on each lane, and then to take the average race time for that car as it’s measured performance.   Or even use the sum of the times if you want to avoid having to divide the sum to find an average.   But make sure each car races the same number of times.   Let's look at the consequences.

If this is the approach you take, and you race each car once on each and every lane of the track, to avoid lane biases, then the number of races you’ll need to run will be approximately equal to the number of cars in the Derby.   If you run the Derby in batches, with each unique batch consisting of the same number of cars as lanes on the track, and the number of cars is exactly divisible by the number of lanes, then the number of races required will be equal to the number of cars in the Derby.   If not exactly divisible, the number of races will be increased slightly but only by the number of lanes.   Within this batching technique, it is simplest to simply permute the car positions until each car has raced once on each lane.   So, this batching approach is in fact very efficient.

If you take this same approach, but instead of batches you merely permute the cars assigned to the lanes from the entire list of entrants, starting with the first car in the first lane and ending with the last car in the last lane, then the number of races needed to allow each car to have raced once on each lane will be equal to one less than the sum of the number of cars and the number of lanes, regardless of how many cars there are.   This is very close to the same number of races as needed when running the race in batches of cars.

A difference worth noting between running as above in batches or in one giant permutation is the logistical difference and its effect on those managing cub participation and recording the timed results.   In the batch approach, there is a certain "divide and conquer" effect working to the advantage of the parents managing the Derby.   However, the giant permutation approach, which has one new car assigned to the first lane just as another has raced the last lane, provides a continuous flow of events that is perhaps easier to administer.   But with batching, any one cub only visually experiences competition with those in his same batch, whereas with a giant permutation, that cub will visually experience competition with twice as many others.

And, to answer the question posed in the title, if fairly allowing each car to race on each and every lane to avoid lane biases affecting any car’s performance, then the number of races needed to complete a race-timed derby is generally the same (plus or minus a few) regardless of the number of lanes comprising the track.   We can observe, however, that with either the batch or giant permutation technique, a cub will visually experience races against more of his fellow cubs on tracks having more lanes.

Finally, a most important differentiator, the more lanes on a track, the heavier it is.   The heavier it is, the more difficult it will be to set up, take down, transport, and store.   It is this final relationship that makes three-lane tracks so very popular.


Dr. Barclay J. Tullis, Vice President of Intelligent Automation
Ph.D., PE-Electrical, Registered Patent Agent 55690, Ham callsign W6WT
www.novelthink.com/



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