>> If we assume that both cars have the same level of grip (f),
> There's where you've gotten. Available grip =~ Cf*W, where Cf =
> tire coefficent of friction, assumed constant to a first
> approximation, and W = force on the tire normal to the ground
> plane.
Well, there's where the model falls on it's face. That's the "classical
friction" model that works for most everything except the pnuematic tire.
While it's true that a tire generates more grip with increased vertical load,
that relationship is decidedly non-linear - the rate at which grip increases
with load diminishes with load, and the rate that rate changes is very much a
function of individual tire construction.
So while it's true that Car B (assuming the same tires on both cars) must have
greater grip as a function of its increased vertical load (by virtue of being
physically heavier), one cannot assume the linear relationship to hold. Car B
will not have enough grip to make the turn at v (by virtue of a smaller f) and
so must slow down - unless the slope of that rate graph is greater than one on
the average covered by the difference in car weights, in which case Car B has
*more* grip available to it, and can go faster! (which should only happen for
*very* lightweight cars, and so probably isn't applicable)
However, it appears then that if the only difference in f is the difference
caused by the non-linear increase in grip with increased vertical load, then the
only way to determine how much Car B must slow down is to get the "grip vs
vertical load" graph from the tire manufacturer - that they don't give out.
There's something intuatively wrong here. According to all this, if I drop
500lbs of lead in the car, and get enough extra power out of the engine to keep
power/weight constant, then my performance should be unchanged. In a straight
line, I'll buy that, but when twisting and turning.... there's all that extra
momentum and inertia to deal with, that's gotta bite you _somewhere_.
Maybe it's not steady-state I should be looking at - maybe it's the
transitions....
DG
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