|MadSci Network: Physics|
Reference: Hibbeler, RC "Engineering Mechanics: Statics", Tenth Edition p424-427 For a vehicle which has the brakes disengaged and the clutch out, the things which will resist motion are friction within the axles and any parts which the axles touch, air resistance, and rolling resistance. I think that since you're traveling at relatively low speeds on this conveyor belt, you can neglect air resistance for the most part. Air resistance is a function of the speed of the object on the conveyor, and it would also act to slow the conveyor belt itself if the plane is not slipping or rolling, and these are complex things to deal with which are not really causing that much of a change to begin with, so just neglect air resistance. So, I think you should focus on the friction acting on the axles, and the rolling resistance. Friction within the axles is denoted as "mu" (looks like a u), and for your case with wheels, the moment (or torque) required to overcome this friction is R*r*u, where R is the radius of your tire, r is the radius of the axle, and u is "mu", the friction on the axle. Once you exceed this torque, however, the frictional force does not increase, so running the conveyor belt faster will not increase your speed. However, if you do not exceed this torque, the plane will not roll at all (assuming that the tires do not slip on the conveyor). Rolling resistance also comes into play. Since the tires deform, there are forces which are required to deform the tires (force of deformation), and also a force which is caused by the tire expanding back into shape (force of restoration). However, the force of deformation is always greater (yes, always) than the force of restoration, so this causes a resistance to motion. The force acts horizontally (that is, tangent to the surface and tangent to the bottom of the tire), and the force required to overcome it is approximately W*a/r where W is the weight of the plane, a is the horizontal distance between where the tire first deforms and the center of the tire, and r is the natural outer radius of the tire. Once this required force is exceeded, however, the resistance does not increase. It acts just like friction in that it will match any force up to the required force to overcome it, but will not increase past that required force. Do not forget that for an object with multiple tires/wheels, you must treat each wheel individually due to the fact that there are different weights supported by those tires/wheels... However, since these frictions are constant, try to get a general idea of how big these forces are for the plane you are trying to build. The one that will be the determining factor is the larger one. If the rolling resistance is really high, even if the axles are frictionless, the wheels still will not roll. If there is no rolling resistance, but the friction in the axles is really high, the wheels will not roll. Find the larger of the two frictions, find (or approximate) a set value, and then use that as a constant number within the program. If the force caused by the conveyor belt is less than this number, there will be no rolling of the plane's wheels. If the force is greater than this number, the force put out by these resistances will still not exceed that number. Note that F=m*a and T=f*d. So, when you're trying to figure out how fast the plane will accelerate, you must take the force (resistance) and the mass of the plane into account. If you have a rolling resistance, the required TORQUE is f*d (that's the force times the radius of the wheel, in this case). Torque is not simply force, so do not forget that! Also, technically, the friction the axles would be higher when the wheels are not rolling than when they are rolling. So, up until the wheels roll, you have a high resistance, but once the wheels roll, the friction force actually drops, and the force output by that friction is actually lower. You may want to take this into account in your program! I hope this helps you out!
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