Grand Prix Racing - The Science of Fast Pinewood Cars

# What is the worst source of friction?

Available potential energy conversion to kinetic energy vs. dissipation by friction; that's the main battle in the Grand Prix race. But of the many sources of friction, what is the one that must be contended with the most to produce more speed?

## Sources

First, what are the ways that energy can be dissipated - that is directed away from being converted into speed? Here the design factors that reduce the available potential energy even before the car is set on the track are not considered.

1. Aerodynamic pressure drag - a slight vacuum is created behind the car
2. Tread friction - the tread wants to skid on the track
3. Axle friction - the axle slides on the wheel bore about a tenth the track length
4. Hub friction - the axle hub rubs against the wheel center
5. Body/wheel friction - the inside edge of the wheel bode rubs the body
6. Impact on the lane median - up to 1% of the car's energy can be lost!
7. Drift - any motion across the track is wasted work
8. Heat - a small amount of heat is produced by all of these
9. Vibration - some vibration, sometimes even enough to collapse a weak track
10. Wheel vibration - a particularly bad kind of vibration
11. Wheel rotation - energy is stored in the wheels and may be returned
12. Body rotation - work is done to rotate the car body from nose down to forward

All of these prevent the available potential energy from being converted to kinetic energy. Heat and vibration result from all of these to some degree, but is probably not measurable. Inertial dissipations and drift aren't generally considered "rubbing" mechanisms (friction). So the first six are really the only true sources of friction. Of those six, only the first three are modeled dynamically in this manual. Hub and body/wheel friction can be thought of as components of axle friction. In fact, when axle friction is measured, hub and body/wheel friction is lumped in too. Friction due to lane median impact is modeled as a random event, so we can't expect accurate theoretical results for its contribution to total friction over the whole race. Estimates of this type of friction can be made by comparing theoretical times and actual race times. For those wanting to know more about friction itself, the formal name for its study is tribology.

## How much does each source of friction effect race time?

In order to make an objective statement, some conventions must be set so we can compare results for each type. That way a virtual race can be staged to illustrate the differences in performance. To compare results, we'll use the loss or split distance to some reference car with a "standard" configuration. Extending that line of thought, one would like the result to be in the realm of "how much improvement might one expect if the source of friction was significantly reduced?". So, a car with typical friction values should be used as the reference and the loss distance should be computed to show the possible improvement in the reference car's performance. In this case then, the variants would be cars where the source of friction under examination is eliminated altogether. Then, the loss distance of the reference car would be the maximum gain or advantage that can be expected by reducing the friction of the source.

## What is typical?

This is a sticky question. Even if you race on an Official AWANA track, that track might be finished differently than someone else's, the club might only allow graphite as a lubricant or the clubbers may all build bulky cars. Given the wide variety of possible "typicals" the best that can probably be done is to find some values that are not too extreme, but somewhere in the middle.

Below then, is a table of the reference car parameter values we will use. Any parameter not listed will be taken as having the value set by a rule limit or as it comes in the kit. For example, all the wheel parameters are those of the AWANA kit.

Symbol Parameter Value Units
a Aerodynamic Drag Coefficient 0.5 Scalar
u Tread Friction Coefficient (front and rear) 0.01 Scalar
n Axle Friction Coefficient (front and rear) 0.2 Scalar
CMh CM above rear axle 0.5 Inches
CMx CM in front of rear axle 1.9 Inches
N Nose 1.5 Inches
B Base 3.875 Inches
A Frontal Crosssection 2.5 in2

Using these parameters for the reference car, a virtual race was staged. The reference car raced three cars that are identical except for one parameter each. One has no aerodynamic drag. Another, no tread friction. The remaining car has no axle friction. If you are interested you can see how this race is run.

Here are the results of the race!

Friction Source Removed Race time (seconds) Advantage (inches)
None (Reference Car) 2.8999 0.0
Aerodynamic Drag 2.8717 4.22
Axle Friction 2.7968 15.45

## Discusion

It appears that axles are the source of greatest friction; more time ought to be spent on reducing it for the greatest advantage. From computer simulations we can more quickly get this kind of result rather than grinding through the list of equations. In fact, a computer can work with more digits to be more accurate. When this same race is run through a program with the same equations, each time that was computed "by hand" except the reference car's is about three thousands of a second faster than the computer simulation times. This happens because the computer keeps track of more digits for the value of k, the air mass displacement per inch of track. The time and speed equations are very sensitive to the value of k, which is a very small number since air has little mass.

With this in mind, it turns out that if the axle friction coefficient of the reference car (and the others that have it) is set to about 0.13 the advantages of having no axle friction and no tread friction are nearly equal at about 10 inches and that of no air resistance is only 4 inches or so.

Here's a race in which tread friction dominates: it's a similar virtual race as before with the axle friction coefficients set to 0.08:

Friction Source Removed Race time (seconds) Advantage (inches)
None (Reference Car) 2.8365 0.0
Aerodynamic Drag 2.8121 3.84
Axle Friction 2.7991 5.889004

By setting the axle friction coefficient to even smaller values, the tread friction becomes even more dominant. Also, as discussed in our analysis link, the inner and outer radius of the wheels helps determine this critical point between dominating axle and tread friction. These results apply specifically to AWANA kit wheels but if you race with Boy Scout kit wheels, the critical point is a bit lower, about 0.11 since they have a larger bore, thus slightly more axle drag for the same coefficient of axle friction.

The rule of thumb then for cars using either kit wheel is: if your car has an axle friction coefficient greater than about 0.12, then axle friction dominates. if your car has an axle friction coefficient less than about 0.12, then tread friction dominates.

So the type of friction it pays off most to reduce depends on how much axle friction you start with. It is also true that this critical point depends on the tread friction coefficient. Not only that, but we can determine how much of an effect a small change in axle or tread friction coefficient has on the overall wheel friction.

In fact, we can say that a small change in tread friction will be about ten times more effective in reducing drag than the same small change in axle friction.

Now that you know what the greatest source of friction is likely to be in terms of potential advantage in inches at the end of the track, how much can you really reduce it? Also, how do we know if some of the other energy wasters listed above aren't worse offenders than axle and tread friction? Stay tuned. Some of these questions can be answered by doing experiments. The research continues.

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