Re: torsens and slip

[audidudi@mindspring.com (Jeffrey J. Goggin)]

>as i said more than a month ago, i can certainly conceptualise the torsen
>inappropriately allocating torque to a [virtual] axle which is sliding (has
>lost longditudinal speed).  in this case, both the viscous and torsen diffs
>will be fooled.

Hmmm ... I must have missed this one.  ;^)

>in this situation the locked centre, because it insists on equal rotational
speeds will be better.  by >deninition, this is cornering on the ragged edge.

Not necessarily...

>my understanding of the theory is offset somewhat by my experience of
oversteer in low cf conditions in my >cars where control is easier than the
above would seem to suggest, particulalry as the torsen will correct >when
longitudional speed is applied to the slower [sliding] axle (ie.
accelerate).  also as i have shown, the >other 'ragged edge' scenario,
inside wheel lift, is better with the torsen and vcd, than the locked centre as
>more torque goes to the end where it is needed,

Be careful here ... "can be supported" is a much better choice of words than
"needed."  (I also wonder whether wheel lift is truly possible with a Torsen
center diff but that's a topic for another discussion...)

>while the unlocked centre will be much worse because it has no bias ratio
to limit the damage (this is the
>famed genration 1 quattro spider bite, btdt).

BTDT as well ... no argument here.

>anyway, the point of this note is that i've been thinking about the slip
angle thing, and keep coming back to >the importance of wheels/tyres and
chassis design to this equation.

Whoa ... before you start adding more variables into the equation, let's go
back and look at what happens when the Torsen center diff starts shuffling
torque between the front and rear of the car.  More torque sent to one end
of the car also means the slip angle MUST increase to maintain the existing
front-to-rear balance; the end of the car that lost torque likewise
experiences a decrease in slip angle.  This point is non-negotiable; it's
easily derived from the Torsen paper's description of how it operates and
was confirmed by the paper's author.

The fact that a change in slip angle _doesn't_ necessarily result in a
change in grip at the tire -- as you've pointed out further on, lateral grip
v. slip angle plateaus over some range -- means you can have several slip
angles yielding the same amount of grip.  The Torsen, however, doesn't know
this ... being "dumb," it responds only to the _delta_ in resistance to
rotation between the two driveshafts and it has no way of telling whether
one driveshaft's resistance is increasing or the other's decreasing; for
traction purposes (i.e., longitudinal acceleration), it doesn't matter as
the two scenarios are effectively one and the same.  The same doesn't hold
true for lateral grip (i.e., lateral acceleration), however, as the delta in
driveshaft resistance to rotation might also be caused by a relative
difference in slip angles between the front and rear ends of the car.  This
is precisely how the Torsen can be -- dare I say, IS? -- "fooled" into
incorrectly distributing torque between them whenever a car equipped with
one in the center diff position goes around a corner... 

>for street tyres and applications (by definition), a *wide* spread of slip
angle will occur with *very >similar* tyre co-efficients of friction (cof).
[picture the cof on the y-axis and the degree of slip on the >x-axis.  the
line will rise steeply until a certain cof and then plateau over a spread of
slip angles until >tailing off, as tracton is lost.] this will mean that the
front and rear *can* exhibit *different* slip angles >*without* any
meaningful change in the tyres perception of grip (their co-efficient of
friction).

Agreed ... except that the Torsen will automatically reallocate torque based
on changes in slip angle without any regard to the amount of grip that is or
isn't available at the front or rear tires.  THIS IS THE PROBLEM!  It's just
a "dumb gear-jamming friction device" and when used in a center diff
application, it CAN'T tell the difference between a driveshaft that offers
more/less resistance to rotation due to a change in the amount of traction
available at one end of the car or because the wheels have adopted a
larger/smaller slip angle!  The two situations are markedly different and
the desired response from the Torsen is completely the opposite yet they are
both capable of generating an input signal with EXACTLY the same delta,
which is all that the Torsen is capable of sensing.  It's dumb, DUMB,
D-U-M-B... 

>in this case the vehicle will track accurately and faithfully *despite*
adopting understeer (front slip angle >greater than the rear), or oversteer
(rear slip angle greater than the front).

I disagree ... in my book, "the vehicle will track accurately and
faithfully" can only mean neutral-steer and _not_ understeer or oversteer.  

>an awd vehicle operating in these conditions will track accurately and be
able to be balanced on the >throttle.

Again, I disagree ... modulating the throttle in a Torsen-equipped car
alters the front-to-rear torque split, which in turn alters a whole host of
other parameters.  This is how a minor problem can quickly become a much
larger problem ... everything the driver does to correct is either amplified
or quashed and the vicious cycle of correction/counter-correction -- aka
"spider bite" -- begins.  

>if, however, due to the choice of tyres, i select tyres which have a much
higher co-efficient of friction (aka >racing tyres), the relationship of cof
and slip angle is different in that the cof/slip angle graph will rise
>steeply, plateau over a relatively narrow slip angle range, and then tail
off sharply. in this situation, the >cof will change significantly over a
narrow range of slip and the vehicle dynamics will be affected.  a torsen
>in these circumstances may well perceive different cof's from the front and
rear axles, and treat this as >traction.  as will a vcd.

While this is true, bringing it up at this point only complicates the
discussion unnecessarily.  The Torsen is fully capable of perceiving
differences when they exist.  It's also fully capable of perceiving them
when they don't -- it's DUMB, remember? -- and this is how problems arise
when it's used as a center diff in an AWD car.

>factors affecting this would clearly be the types of tyres used (their
cof/slip relationship - the use of >racing tyres with much more sensitive
cof/slip angle reltionships), the suspension of the car (and chassis
>dynamics) which clearly affect the *actual* cof (rather than the
theoretical), and the way in which the
>car is being driven (ie. the driver operating at the edge of the cof
envelope).  other factors which could >also "push the envelope" here would
be the use of different wheel/tyre sizes front/rear.

True enough but these factors really determine only when the "bite" occurs
and the extent of it.  I think you might find a "band-aid" for the problem
by playing around in this regard but not an out-and-out cure.  I also think
this is probably a good time to remind everybody that the Torsen DOES have
some GOOD qualities although I'm intentionally not bringing them up here
because I don't want to confuse anyone ... further.  :^)

>for a better discription of this affect, carrol smith's book "tune to win"
has been very useful for me.

I recommend it as well ... if you're mathematically inclined, however, I
also recommend Milliken & Milliken's "Racecar Vehicle Dynamics" as a useful
reference. 

* * * * * * * * * * *

Dave, on a personal note, it's clear to me from your comments above that you
still don't have a firm grasp on how the Torsen works ... for now, just keep
it simple and don't complicate matters by trying to allow for all sorts of
other variables, such as tires and chassis dynamics.  It really IS a DUMB
device and I think you are trying to give it more credit than it's due.
Frankly, it's only because it IS such a dumb device that we are even having
this discussion in the first place ... if it truly worked perfectly, no one
would have ever given it a second thought!  :^)  
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   / |      _| o    | \       _| o  Jeffrey Goggin
  /__| | | / | | __ |  | | | / | |  audidudi@mindspring.com
 /   | |_| \_| |    |_/  |_| \_| |  http://www.mindspring.com/~audidudi/
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