Pinewood Derby Stories and Photos from Maximum Velocity
Moment of Inertia Revisited
On November 29, 2006 an article was published in Pinewood Derby Times Volume 6, Issue 5 describing the results of an experiment to determine the effect of a change in the moment of inertia on pinewood derby car performance. The results of that experiment indicated that a larger moment of inertia was slightly beneficial.
Since then several people have questioned the validity of the results of that test, so the test was reran, making sure that as many variables as possible were eliminated or more tightly controlled. Today's article documents the results of the new moment of inertia experiment.
WHAT IS MOMENT OF INERTIA? The moment of inertia is a measure of resistance of an object to rotation. Thus, an object with a small moment of inertia can be more easily rotated than an object with a large moment of inertia. The letter "I" is the normal symbol for the moment of inertia, so it will be used as an abbreviation for the moment of inertia from this point on.
On a pinewood derby car, the size of "I" is determined by the placement of the ballast weight and by the amount of wood and wheel weight. If much of the wood is removed, the ballast weight is focused in one spot, and lighter wheels are used, then "I" will be relatively small. However, if much wood remains, the weight is spread out, and heavier wheels are used, then "I" will be relatively larger.
REAL-LIFE EXAMPLES OF "I" In the original article, the example of a golf putter was provided. Modern putters are weighted to maximize "I", which leads to more stable putting strokes (refer to the original article for a more detailed explanation).
Another real-life example of the effect of "I" is in figure skating. When a skater wants to spin faster, the arms and legs are pulled in close to the body. This reduces "I" resulting in a more rapid rotation.
AFFECT OF "I" ON PINEWOOD DERBY CARS "I" affects pinewood derby cars in two ways:
1. Left-Right Car Rotation - When a wheel contacts a guide rail, a certain amount of speed is lost. The amount of loss is determined by the force of the impact. If the car has a small "I" (weight concentrated at the balance point), then the impact force is relatively small. But if the car has a large "I" (weight located far from the balance point), then the impact force is greater and the speed loss is relatively greater.
2. Up-Down Car Rotation - When a pinewood derby car travels through the curve, it must rotate from the starting angle to a horizontal position. Some energy is required to make this rotation occur, and this energy can only come from the potential energy of the car. Thus, a larger "I" will rob more energy during the transition than a smaller "I".
EXPERIMENT SETUP A special car was used that allowed the weight to be either spread or focused (see Figure 1).
Figure 1 - Test Car
To maximize the change in "I", center weighting was used. In addition, the following equipment was used:
- 32 Foot Aluminum Freedom Track - 2.2 Gram Speed Wheels & Speed Axles - Weight at 5 ounces - Four wheels on ground - Alignment adjusted to rail-ride
The wheels were not removed or adjusted during the test. The only change was the positioning of the ballast weight (maximum or minimum "I"). Ten heats were run with each weight position. The high and low results were removed, the remaining times averaged.
EXPERIMENT RESULTS The results are graphed in Figure 2.
Figure 2 - Test Results
As you can see, the low "I" configuration was slightly faster than the high "I" configuration. However, the amount of difference in performance was only three milliseconds, while the standard deviation of the heats was between three and four milliseconds. So, the effect of "I" on performance was extremely small under these experimental conditions.
NOTE An interesting (at least to me) side result of the experiment was the consistency of car performance. After measuring the low "I" configuration and the high "I" configuration, the low "I" configuration was retested. Thus, the car ran 30 heats, with a standard deviation of between three and four milliseconds. These results support the value of rail-riding as an alignment technique, and the value of Krytox 100 as a lubricant.