|MadSci Network: Physics|
I think I can help you a bit on this one. We are going to assume that for each case, you store the same amount of potential energy in the elastic band independent of all other design characteristics. We are also going to assume that friction in the drive axle is the same for each case. The primary goal is speed, correct? If it is some sort of a race, then you will want to get from A to B in the shortest amount of time. This means that you will want to maximize the amount of energy put into translational motion (that is, the forward motion of this car). There are three things you'll need to look at, then: traction, weight, and gear ratio. Traction is of the utmost importance. If the wheels do not slip, you are, in the ideal case, not transmitting any energy into the ground as heat due to friction. Of course, you still will end up having some friction because your wheels will be a bit toe-in or toe-out. Your rear wheels should have a soft, grippy surface such as rubber to eliminate slipping. Your front wheels should be made out of a slicker material, because if they are out of alignment by a bit, you want as little transmission of friction to the ground as possible. Concerning weight, you want your wheels to be as light as possible. The front wheels should be small, thin, and as light as possible. As long as the front axles is well-greased, we can assume that there is no friction in the axle, so rotational speed is not the big issue. Rotational momentum, however, IS an issue, since we want to translate energy into the translation of the car, not into the spinning of the wheels. Your rear wheels should be as light as possible, also, but they may need some width to help them hold traction off the starting line. Do not go overboard on the width, or your wheel weight will slow your car down. Rotational kinetic energy is 1/2 * I * w^2 (I is the moment of inertia and w^2 is the rotational speed in radians). If you increase your weight on a wheel that is the same size, you will increase the moment of inertia, and thus decrease your rotational speed. Concerning size, the front wheels should have a pretty small radius for weight and rotational mass purposes. The rear wheels should primarily be based on the gear ratio between the cylinder the elastic band is attached to and the wheels themselves. If the band is still unwinding after the finish line, you did not get to convert that additional potential energy in the elastic band into kinetic energy. This would mean that your wheels were too large. Also, the larger the wheel, the lower the torque being transmitted, so your acceleration will be terrible. If your wheel is too small, you will transmit so much torque that the wheel will spin. Also, with a very small wheel, at the maximum rotational speed achievable, you may not be going very fast. Concerning the specific design process for the rear wheels: The rim material should probably be a light plastic. These wheels will not be under much actual stress, so they do not need to be very strong, just very very light. Concerning gear ratio, try making the wheel about the right size so that your elastic band just finishes unwinding at the finish line. This should allow you to reach a maximum speed, use all available energy stored in the elastic band, and minimize slipping due to overtorque. You might do some tests with a wheel slightly smaller than this, also, but do not exceed this size. Once you've got a few potential wheels chosen, use the grippiest rubber you can find for the contact surface. Do not use a material that deforms very much, though...too much wheel deformation causes rolling resistance that will slow your car significantly. Hope this helps you out, Joel Reference: Hibbeler, RC. "Engineering Mechanics: Statics, Tenth Edition" Friction: pg 379-382 Rolling Resistance: pg 426 Moments (Torque): pg 121-147
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