|Grand Prix Racing -||The Science of Fast Pinewood Cars|
Yes, a Grand Prix car can "pop a wheelie"! Is it a good idea? That's what most of this page is about. How can a wheelie be accomplished and can any benefit come of it?
Wheelie popping is one form of car body rotation. It can also be one way to lift two wheels off the track. In popping a wheelie, some energy is lost to car body rotation and some is made available for speed since it can be done in such a way that the front wheels never touch the track. On the other hand, the extra weight of the front wheels is carried on the rear axles so that rear axle friction must increase some. But we also know that the front axle friction that would have been produced if the front wheels were on the track is less than the extra now forced on the rear axles, except possibly on the transition. Air resistance might also be increased as more of the car is exposed to direct air flow. Another problem, though, is that a wheelie that lifts the front too high will effectively shorten your car at the finish line. In the worst case, a vertical wheelie, your car is shortened a bit more than six inches! So, if it can be controlled, the possible benefits look good.
A wheelie is produced when the forces acting on your car lift its nose off the track. The forces that are available to act are gravity and air resistance. Others that you may enjoy working with, if legal by your rules, are electricity, magnetism, chemical reactions, etc., these would be mounted on your car and activated in clever ways.
To use gravity is easy. You just get the weight centered behind the rear axle. If you want to produce a wheelie at a certain angle do this: position the center of your weight behind and below the rear axle so the angle formed by a line from the center of mass through the rear axle and a line from the rear axle to the front axle is the angle you want plus 90 degrees. You can put the weight above the rear axle and further behind it, but that wheelie would always make your rear bumper rub the lane median, even if it only occurs on the flat.
The trick is making it happen! There is not much room to concentrate the weight below the rear axle, 0.59 inches for your wheel radius minus 0.375 inches for clearance = 0.215 inches, less than a quarter of an inch. Behind the rear axle there can be more space, if a small wheelie angle is desired. We'll find out how small below.
Air resistance is another possible way to lift the nose. The nose itself must be designed to direct the air downward strongly enough to over power the gravitational force, so the center of mass must be positioned to allow the effect. Unfortunately, the front wheels must touch the track until the critical speed is achieved to lift the nose.
A sustained wheelie is one that is held from the start of a race to the end. If not held all the way down, the front wheels will spin up on the track to maximum speed on the ramp before popping up on the flat or on the flat after doing a wheelie on the ramp. The only other alternative is radical bobbing on the ramp or flat, which can occur when the conditions for a wheelie are borderline.
Only a sustained wheelie can yield all the benefits of a wheelie, if it is even possible. Otherwise, if it is not possible to have a sustained wheelie, the crowd would most certainly applaud the ability to launch into a wheelie on the ramp or pop one on the flat or just bob the nose up and down. None of these behaviors will likely win the race, but perhaps a few friends. The judges may not be happy since your car may try to smash across the finish line gate 3 inches above the track.
Without discussing if it is possible, we can simulate these behaviors and see if there is a reasonable payoff for thinking about this design choice.
A wheelie with an angle equal to or less than the ramp angle and the center of mass below the rear axle will begin on the start and flatten out when the transition angle is equal to the wheelie angle. If the center of mass is above the rear axle, and the wheelie angle is less than the ramp angle, then the wheelie won't begin until the transition, but the rear bumper will rub the lane median. So a sustained wheelie requires an angle greater than the ramp angle and a center of mass below the rear axle. For an AWANA track the ramp angle is about 21.2 degrees. The weight must be placed at more than an angle of 21.2 + 90 = 111.2 degrees from horizontal below the rear axle. Suppose we can get it to be just -0.05 inches below the rear axle. Then the center of mass must be less than, -0.05/tan(111.2) = -0.02 inches behind the rear axle. Of course, these distances would be very difficult to measure.
For a wheelie on the ramp only, we target an angle less than 111.2 degrees and get the center of mass to live -0.05 inches below and -0.01 inches behind the rear axle. This allows more room to fit the weight in the rear without the threat of the bumper dragging on the lane median, but makes the wheels spin up.
We can compare race times of cars that wheelie using the model derived in this manual. The results are the same as lifting two wheels.
But can it be done well - without the rear bumper hitting the lane median or the car veering to one side and jumping off the track?
Let's see how dense a material would be needed to weight a car enough for a sustained wheelie and for a wheelie on the ramp only. Then, we could determine what materials we could use to build such a car.
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|Grand Prix Racing -||The Science of Fast Pinewood Cars|
|Copyright © 1997, 2004 by Michael Lastufka, All rights reserved worldwide.|