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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

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 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.

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

"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

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.

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

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.

Read More at: Pinewood Derby Times Volume 9, Issue 5

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