Friday, January 24, 2014

Height of Weight Vs Performance
by Randy Davis


While looking through the index of Pinewood Derby Times articles, I
realized that I had never performed a test on the performance effect
of the height of the ballast weight. What an oversight. This topic
tends to bring out the extremes. A few people have told me that they
made a wing at the maximum allowable height and put the weight right
at the top of the wing. On the other hand, a larger group of folks
say that the weight must be at the bottom of the car, maybe even
hanging down a bit. These folks won't even consider using a tungsten
canopy, as "that would make the weight too high".

I have always believed that the height of the weight has only a
trivial impact on performance. From a physics viewpoint, given two
cars with the center of gravity at the same lengthwise location, but
with one having the center of gravity low on the car (LCG), while the
other has the center of gravity high on the car (HCG), the LCG car
will fall a greater distance. Referring to Figure 1, note that because
of the starting ramp angle, the fall distance for the HCG car is
actually less than the fall distance of the LCG car. The actual
difference is based on the slope angle. But on this hypothetical
track, the HCG car falls only 96.6% of the LCG car's fall distance.


Figure 1 - Effect of Vertical Weight Position on Fall Distance

Although the LCG car will attain a higher speed, due to a pendulum
effect the HCG car will traverse the curved portion of the track
slightly faster than the LCG car. But unless the flat section of the
track is very short, the LCG car will overtake the HCG car on the flat
section.

But note that the example above is an extreme case, with the
difference in vertical CG of well over one inch. In most cases, the
difference between a high and low CG car is much less than one inch.

Well, enough of this speculation. Let's do an experiment to see what
really happens.

EXPERIMENTAL SETUP
First, we need to create a car on which the vertical COG can be
changed without affecting any other factor.


Figure 2 - Vertical COG Test Car


Figure 3 - Bottom of Car with Weight and Spacers Inset

The car in Figure 2 has a 1-3/8 inch hole drilled completely through
the car, and a medicine bottle cap with a 1-3/8 inch internal diameter
is glued over the hole. The resulting cavity can hold a 3.25 ounce
tungsten round (9/32 inch thick) and two hollow plastic spacers (same
OD and thickness), and a thin plastic shim to prevent rattling. On
the bottom of the car, the hole is covered with a removable plate
(Figure 3).

The experiment starts with the tungsten round at the bottom and the
two spacers on the top. Three heats are run with this configuration.
Then the plate is removed, the round placed between the spacers, and
the plate replaced. After three heats with this configuration, the
round is placed above the two spacers, and six heats are run. Then
the configuration is changed back to the round in the middle for three
heats, followed by the round at the bottom for the final three heats.
Thus, six heats are run for each configuration.

To minimize variance in heats, Outlaw wheels, nickel speed axles, and
Krytox 100 lube were used. Also, additional ballast weight was added
to bring the car up to five ounces.

EXPERIMENTAL RESULTS
As I stated above, I expected the difference in COG height would have
a relatively trivial affect on performance. But I was surprised to
find that the height of the COG made absolutely no difference in
performance.

2.490 Sec - Low COG Average
2.491 Sec - Middle COG Average
2.490 Sec - High COG Average
.0016 Sec - Standard Deviation

The 1 millisecond variation between the averages is within the
standard deviation, so the difference of 1 millisecond is
statistically insignificant.

CONCLUSION
What does this all mean? Well, within reason(1) don't worry about the
height of the COG. Certainly get the COG towards the back, keep your
car aerodynamically sleek, and have fun designing your dream car.

(1) In this test, the height of the COG varied by 9/16 inch without
any effect on performance. However, there could be a difference in
performance for more extreme swings in COG height.

From Pinewood Derby Times Volume 13, Issue 9

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