Learn to Build A Winner (Cont'd)

The Problem

The Pinewood Derby Car problem is defined by the rules for building and racing derby cars and the racing environment. They determine which principles of physics affect the Car's performance. Therefore, it is appropriate that we first identify those rules and conditions. Variations will be presented where possible.

The Track.
Track construction suggestions are supplied in the Cub Scout Leader How-To Book, No. LM33831.
1. The length of the Track is about 32 feet. The distance from start to finish lines is about 28 feet. Some tracks are longer than this, up to 50 or 60 feet, if the racing surface is particularly fast.
2. The Lanes of the Track consist of strips of wood about 0.250 (1/4) inch (but less than 3/8 inch) thick and about 1.625 (1 5/8) inches wide affixed to the race track. The Car straddles this strip.
3. The starting line is about 4 feet higher than the finish line.
4. The modern Track profile slopes from about 30 degrees at the start line changing gradually to 0 degrees about 12 feet from the start line. Some profile variations are shown on the next page. (Some tracks add "humps" at various places down the track.)
5. The Track may consist of two or more lanes. (One or more lanes, if the competition is "against the clock.")
6. Race cars are held at the starting line by a starting device which allows all cars to be released at the same time.
7. Race results (order of finish) may be judged by eye or by a variety of electronics.
Fig 1. Track styles
The Car.
In the following statements, there are some "is"s and some "may be"s. The distinction is that "is" means that it is usually this way, in my experience. "May be" means that there appears to be variation among the various rules that I have read. In any case, your specific, local rules take precedence. (Get them, read them, understand them!) The list of rules here is for purposes of discussion in this paper.
1. The Car must rest freely on its wheels in the bottom of a prescribed rectanguloid (box).
  - Length is limited, usually to 7 inches or less.
  - Width is limited, usually to about 2.75 inches or less.
  - Height may be limited.
2. The weight of the Car is limited, usually to 5 ounces or less.
3. The weight of the wheels, axles, and wood may be supplemented, provided that the additional weights are securely affixed (glue or nails) to the Car. The type of weight may be limited.
4. Movable parts, other than the wheels, are usually prohibited.
5. Axle location and installation may be limited.
  - Front wheels must be totally behind the nose.
  - Usage of the original axle slots may be required.
  - Retention of the original wheelbase may be required.
  - Retention of the original axle slot relationship to the front of the car may be required.
6. The Car must roll on wheels and axles as provided in the "official kit", usually the "Official Grand Prix Pinewood Derby Kit".
  - Wheels must turn around the axles provided in the kit.
  - Bearings, bushings, sleeves and washers are usually prohibited.
  - All four wheels may be required to contact the track.
7. Removal of significant amounts of mass from the wheels is usually prohibited.
8. Modifying the contour of the wheel tread is usually prohibited. This may prohibit rounding and grooving the tread, to produce less track contact.
9. The Car must be free wheeling with no starting devices.
10. Any form of spring is usually prohibited.
11. Only dry lubricants may be used. Fouling the track must be avoided.
12. Subterfuges, such as magnets (to spoof finish line electronic sensors) or adhesive (to cause the starting mechanism to pull the car at the start), are prohibited.