One last shot at the tire problem! The term friction is applied to a multitude
of sins. The slip mechanism for blocks of wood and care tires are entirely
different and so their behavior are also quite different. I believe that
friction between blocks is due to interlocking asperities. When rigid blocks
are forced to slide they ride up on all the asperities at once and then
ride on the tips. With this mechanism is expected that mu static > mu dynamic.
However, for tires the rubber wraps itself around the sand grains in the
pavement and the slip comes from shearing the rubber. Furthermore, the tire
tread is not rigid so the stress are not necessarily uniform and it does not
all have to slip at once. In fact as a shearing force is applied "frictional"
forces will rise until some portion of the tire begins to slip. As more force
is applied frictional forces continue to rise as more of the tread reaches the
maximum shear stress. Only when the entire tread area reaches maximum shear
strength, at which point the whole tire is sliding, has the maximum frictional
force been reached. The lab test of a piece of tire does not show this
effect because it is not carrying enough weight. It simply slides as a rigid
block, much like a block of wood. As I suggested earlier, to model a tire
you need very soft rubber under a very high load. To perform a representative
lab experiment all the variables must be scaled, including the elastic constant
s of the rubber.
I've had enough of KY heat and humidity and I'm out of here for about a month.
Plan A is to Kayak in the Gulf of Maine and observe the wonderful tidal
resonances first hand. No need to strugle with 23 term equations. I'll just
pick up a tide chart!
When I get back I'll try some tire simulations with a force probe. I think
a big chunk of metal with art gum eraser feet, or feet cut from the sticky
rubber on climbing shoes might work. Lots of weight on small feet, so they
are highly distorted.
If you will grant me two points: 1. for a coasting car, the faster it goes
around a corner the greater the frictional force and 2. when tires squeal they
are slipping, then try this experiment. Coast through a turn at progressively
higher speeds until your tires start to squeal. Observe that at higher speeds
you get more squeal. Now since higher speed implys more force and squeal
implys slip it seems clear that the greatest frictional forces are achieved
under conditions of slip! Just be careful. A friend of mine tried this
experiment, spun his car 180 degrees and rolled backwards into a tree.
Also avoid wet roads. A neighbor of mine lost the curve in front of my
house one night in the rain and my tree took the whole front off his new
Corvette.