nklr contact patch velocity

[Chris Krok]

> > Consider the source. I think this is from the same genius who claimed that > rolling motorcycle tires have zero velocity relative to the pavement. While > it may be true if one assumes perfect conditions, no tire or tread flex, > clean and perfect pavement, etc., it doesn't take much imagination to see > that a tire contact patch could easily deform and move relative to the > pavement as the tire rolls.

I'm not the original posting genius, but I'm afraid that this is true, without the assumptions. Remember, the coefficient of static friction is much higher than that of dynamic/sliding friction. (Non-engineers: put a book on a table and push it. Notice that it takes a certain amount of force to start it moving, but less force to keep it moving at a constant speed. Also note the difference between this "break free" force and any acceleration force.) If your contact patch was moving relative to the pavement, in any direction, then the (lower) sliding friction would be in effect. If you took a turn, you'd wipe out. Also, your brakes stop you faster when they are not locked up. That's how ABS works. As soon as it detects lockup, it frees the brakes, so the wheel can begin turning, regaining its "zero velocity" contact patch and hence its traction before reapplying. Also note that if you are driving a car and go into a skid, you turn the wheels in the direction of the skid. The purpose is again to get the wheels turning and regain traction. In a more extreme case, watch drag racing. Before lining up, they do a burnout to warm up the tires and make them stickier. When they launch, consider that if the tires broke free, they would just sit there and smoke, considering the amount of power they are putting down. Someone also took high-speed films of top fuel dragster wheels on launch. Tons of wrinkle, but the bottom stays still. If that's not enough, watch the Goodyear "Aquatread" commercial, where they show a tire going through water, shot through glass on the underside. Also, if you plot the trajectory of a point on the wheel, you will see that it takes a "bouncing" path. There is a cusp where it hits the ground, where it undergoes a 180 degree change in velocity direction. (In fact, this is on the cover of my calc text.) Therefore, it must pass through zero velocity. Of course, this is perpendicular to the pavement, but if you want assumptions, how about a bike going straight, with symmetric tires? (which they all are.) The centerline of the tire has no reason to "slide" to either side due to symmetry, so it is at zero velocity. I am reluctant to refer to this as a "slap," though, as the tire is a continuum, and the motion of the tire itself is better described as a wave. (i.e., in tire-fixed coordinates.) Granted, with tires like knobbies, the outer knobs will roll in as the tire flattens. However, I guarantee you that the center of the patch is stationary. Chris -- Dr. J. Christopher Krok Project Engineer, Adaptive Wall Wind Tunnel Graduate Aeronautical Laboratories, California Institute of Technology MS 205-45 Phone: 626.395.4794 Pasadena, CA 91125 Fax: 626.449.2677