treediff, Clinton, and driving around curves

[Dave Long]

see <http://members.home.net/rck/phor/05-Cornering.html>

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.

-Dave

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.