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Slip angles...

Since there seems to be so much misunderstanding as to what the words "slip
angle" mean and understanding this is crucial to understanding why a Torsen
center diff behaves the way it sometimes does in an AWD car, I offer the
following quotes from Chapter Two -- "The Racing Tire" -- of Carroll Smith's
1978 classic book, "Tune to Win":

"Slip is probably the most discussed and least understood of the basic tire
characteristics.  Much of the confusion stems from the term itself.  Slip
implies slide and most people seem to believe that in order for a tire to
operate in a slip mode it must be sliding.  This is not so.

"There are actually two distinct types of tire slip -- transverse and
longitudinal.  In the transverse plane slip is referred to as "slip angle"
and affects the generation of the tire's cornering forces.  In the
longitudinal plane slip is referred to as either "slip ratio" or "percentage
slip" and affects acceleration and braking."  [NOTE: For the purposes of the
Torsen thread, QSHIPQ has been referring to longitudinal slip as "traction"
in order to avoid any further confusion on this subject.]

"The slip angle of a pneumatic tire is defined as 'the angular displacement
between the plane of rotation of the wheel (the direction in which the rim
is pointing) and the path that the rolling tire will follow on the road
surface.'  This path his made up successive footprints of the contact patch
laid down as the tire rolls.  In order for the vehicle to change direction,
regardless of road speed or the radius of the curvature, each of the
vehicle's tires must assume some value of slip angle.

Further on, Smith cautions:

"It is important that we do not confuse slip angle with steering angle,
which is the angular difference between the tire's plane of rotation and the
straight ahead position."

"As we approach the maximum value the rolling contact patch is beginning to
run out of its elastic capability and some actual sliding starts.  We now
have a combination of elastic friction and sliding friction at the contact
patch.  If we increase the slip angle further, the portion of the patch
which is sliding increases while the area which is still in the elastic mode
decreases until eventually the whole thing is sliding.  At some point
between where sliding begins and where it becomes complete the coefficient
reaches its maximum value.  At any point, if we stabilize the slip angle,
the coefficient and the cornering force will also stabilize and the tire
will enter into a steady state cornering mode at that value of cornering force.

[NOTE: The fundamental problem with a Torsen center diff (at least as *I*
see it!) is that when an AWD car is cornering harder than, say, 7-8/10ths,
the front and rear slip angles can *never* be stabilized.  Higher cornering
forces require higher slip angles but since the Torsen, as a natural
byproduct of its design, can't differentiate a lateral slip angle from a
longitudinal slip ratio (i.e., "traction"), it can readily be "fooled" into
distributing torque between the front and rear wheels in precisely the wrong
way at precisely the same time when it's most critical to get it right.] 

"It is also important to realize that, although we have been talking about
generating slip angles by steering the front wheels, a slip angle is
generated every time a tire is subjected to a side load of any description.
In entering a turn the normal sequence is for the driver to initiate the
turn by steering the front wheels in the direction of the turn.  After a
very short delay the front tires develop slip angles and the vehicle starts
to turn.  The centrifugal force developed by the initiation of the turn
applies side forces through the chassis to the rear wheels which then
develop their corresponding slip angles and cornering forces and the
vehicle, after some minor hunting, steadies into the turn.

[NOTE: The Torsen "spider bite" occurs during this "hunting" period as the
car begins its transition into (or out of) the corner but before it has
stabilized ... the reason why it tends to scare the bee-jeezus out of
skilled drivers is because they are mentally prepared for the car to
stabilize but it never does.  Without knowing exactly what the car is doing
and -- more importantly, why -- it's impossible to know what corrective
actions are required.  And as if that isn't bad enough, the situation is
further complicated by the fact that a Torsen center diff has the potential
to amplify or negate almost any corrective action the driver might take by
how it allocates the available torque between the front and rear wheels...]

"Genius consists not of operating the race car at high values of tire slip
angle but of balancing the vehicle consistently at the slip angles that will
produce maximum useful total tire thrust."

[NOTE: Q.E.D.]

* * * * * * * * * * *

There are any number of other books that address these same issues but this
particular one (grammar and punctuation errors notwithstanding) is perhaps
the most literate for readers who don't have a background in engineering or
mathematics.  Highly recommended. 
    _                _
   / |      _| o    | \       _| o   Jeffrey Goggin
  /__| | | / | | __ |  | | | / | |   audidudi@mindspring.com
 /   | |_| \_| |    |_/  |_| \_| |   http://people.delphi.com/audidudi