Grand Prix Racing - The Science of Fast Pinewood Cars

# Does wheel weight matter?

Have you ever been tempted to buy those heavy-looking wheels in the hobby stores to try on your car? Here's where we'll see why it's not a good idea! I've heard rumors about university studies that claim weighted wheels help pinewood cars to win, but I have personally concluded that if there really were such studies they were made with much larger cars! Perhaps they used soapbox derby cars, the kind that contestants ride down a hill. People seem to confuse the two derbies.

When considering weighted wheels, weight from the car body is "moved" to the wheels to keep the weight to the competition limit. Heavy wheels rest on the track, so they don't contribute to axle friction. They don't increase tread friction either, since weight that was pushing through the axles is now pushing directly on the track. But since the car body weighs less, there is a decrease in axle friction. But, the wheel's moment of inertia increases with the added weight. That slows acceleration and reduces the possible maximum speed as energy is stored in the wheel.

So the question is, "Where is the "break even" point between increased moment of inertia and reduced friction?". If there is one, another question becomes important, "Can a car be built on the other side of the break even point to take advantage of it?".

## Considerations

Changing both the weight of the car body and the wheels affects almost every force on the car except tread friction and air resistance. Here is a list of some of the factors to consider:

1. The "flywheel effect"
2. Increased moment of inertia
3. Reduced body weight
4. Reduced axle friction

First, let's look at the factor most people think is the one that makes adding weight to the wheels worth while.

## The Fly Wheel Effect

The "fly wheel effect" became popular in the seventies as a way to help battery powered cars conserve energy for acceleration on the road. It is a transfer of the linear kinetic energy of the car to the rotational kinetic energy of a heavy revolving disk, the fly wheel, and back again. But it does not occur without energy loss. If much of the vehicle's energy is converted to rotational kinetic energy so the fly wheel is spinning fast when the vehicle stops at a traffic light, then the energy can be returned to the vehicle by gears to drive the wheels and speed up the car when the light changes to green.

Pinewood cars aren't designed to work that way. They aren't made to slow down then speed up. There is no mechanism to collect and return the rotational energy. Wheels don't make good fly wheels since they must slow down when the car does.

## Rotational Inertia

A heavy wheel stores more kinetic energy than a lighter one. It takes longer to spin it up and longer to spin it down. That's why cars with heavy wheels are slower getting to the bottom of the ramp. As we already know, a slower can win a race. The reason they win is different. Some people think that cars with heavy wheels keep the "slower" speed for a longer distance. So, overall the car's average speed is faster. In order for this theory to work, we need to find where the heavy wheeled car is supposed to pass the lighter one.

If we iqnore the benefit of shifting weight to the wheels, that is less friction, we can readily see that the heavy wheeled car can never be expected to win! We'll examine the effect of the reduced friction in the next section.

Using the model of a car with axles, that is no air resistance to make things simpler, we can see the effect on the coasting distance, yc. The inertial mass, M, of the car is an apparent mass. As the wheels spin, the car acts as if it were heavier than it really is. It's the inertia of slower spinning up and spinning down that makes the car act like one with more mass or inertia.

coasting distance, yc = Mv02/2Df

speed at the bottom of the ramp, v0 = \[2Lr(-mgsinO-Dr)/M]

so, yc = 2Lr(-mgsinO-Dr)/2Df after substituting for v02.

The coasting distance increases only because of lower friction on the ramp, Dr, and flat, Df, since the inertial mass, M, cancelled out. So two cars with the same friction coefficients, but different weight wheels will coast the same distance. There is no advantage in only having heavier wheels!

## Reduced Friction

You can see from the expression for coasting distance, yc, that if one car had less friction, it would indeed coast farther; the numerator increases and the denominator decreases. One expects that the decrease in friction would help speed the car up too. It does, but the heavy wheels fight the extra acceleration so that in general, it is still a slower car.

In that analysis, we found that for every bit of gain from less body weight, the moment of inertia is increased so much that the gain is wiped out and then some. In fact, it turned out, that it doesn't matter how much weight is shifted, but how much space it ocupies on the wheel that is critical! The wheel simply has to be big enough so that it is possible to have some room to put the weight. Grand Prix wheels can not be more than 3.5 inches in radius to be legal. It would take wheels just over 45 inches in radius, weighing the same as the small ones!

No ring of any mass can be shifted to the wheels to speed up a Grand Prix car!

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