treediff, Clinton, and driving around curves
Thu, 10 Jun 1999 21:33:06 -0700
my handwaving argument goes as follows:
Tire friction is isotropic. It doesn't matter if accelerations are due to
braking, acceleration, or turning; all that matters is that the resultant is
small enough to avoid skidding. In order to make the most of our tires, then,
we wish to keep the magnitude of acceleration constant and close to the
frictional limit, resulting in a circular locus for desired accelerations.
Negotiating the curve involves smoothly transitioning from braking into to
accelerating out of the curve, and we do so by swinging the acceleration
vector around either the left or right arc of the friction circle.
I believe this results in an ideal hyperbolic path through a curve, which is
close enough to the traditional outside-inside-outside line for handwaving.
The big factor ignored in my analysis, and yours, is that of weight transfer.
All these accelerations will lighten, and hence reduce grip from, the set of
tires towards which they are directed. This is why people pay attention to
their suspension. This is also why hitting the brakes in a turn is a poor
idea: sudden brake inputs load the fronts, unload the rears, and you get
oversteer, with the results you described.
Grand Prix motorcycles are even more complicated: not only do they deal with
weight transfer issues, but when they are heeled over, the effective gear
ratio changes due to the change in distance between the axle and contact patch.
Grand Prix show jumping horses are more complicated yet: they are very
non-isotropic in the accelerations they can apply, they can actively transfer
weight, and not only are their contact patches time-dependent, but they also
come in two stable enantiomers (and a few more unstable ones). Oh, and they
also have to deal with major accelerations in that third dimension.