Re: Torsens and slip angle ... final approach

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

Here's my follow-up response to him as well...

* * * * * * * * * * * * * * * *

>i have absolutely *no* problem with the behaviour you assert, as it, as you
>suggest, is part of the nature of the torsen, and readily identifible.

Finally!  :^)

>i have never questioned this behaviour, or that this is why the torsen cars
>understeer less than the generation 1 cars while cornering (talking ur-quattros
>here).  it is one of the immediate impressions while driving the ur-quattro. 
>as you say, it has to work like this.

I sense major progress here...

>but this is known and consistent behaviour.  the tighter the corner, the more
>the rotational difference, and the greater the shift, until bias ratio and you
>get more push.  or, put another way, the slower the corner, the more torque to
>the rear, and the less understeer to the front.  so experienced.  you're not
>saying this is a bad thing are you?

No, not at all ... beyond here lie dragons, though.

>ok, so now develop your "uncontrolled spider bite @7/10ths in the dry".  i'm
>all ears. :-)

Let's now approach the tight corner at speed and start braking hard ...
weight transfers forward, increasing grip at the front wheels, and away from
the back end, decreasing grip at the rear wheels.  At the same time, the
slip angle's increasing up front and transfering through the chassis to the
rear wheels, which increases similarly, only more slowly and not quite as
much.  The Torsen begins to sense a change in the resistance to rotation of
the rear driveshaft and starts transferring torque from the front wheels to
the rear.  Grip will increase further at the front and decrease further at
the rear.  By now, you've completed the first third of the corner and have
trailed off the brakes completely.  The car turned-in very crisply and you
feel it begin rotating into the corner, its inherent understeer somewhat
tamed ... so far, so good.

With the apex in sight, you begin to roll back on the throttle ... weight
starts to transfer rearward again, increasing grip at the back and
decreasing grip at the front.  Because the back end has drifted out a little
bit, you make a slight correction with the steering wheel ... on a good day,
that's it.  You clear the apex, put your foot to the floor and rocket
through the rest of the corner, smiling.  On a bad day...

Thanks to turbo lag and Audi's funky gearing, however, you give it a smidgen
too much throttle, a little too soon.  Because the car's still turning-in,
the slip angle of the front wheels is several degrees larger than the rear
wheels and more torque is being transferred to the rear wheels ... because
they're also turning and have relatively less grip available than the front
wheels, not to mention momentum from the initial rotation into the turn,
their cornering force peaks as the boost kicks in and they start losing grip
at a faster rate ... the back end starts sliding slightly and the Torsen
decides that the decreased resistance to rotation of the driveshaft means
there's more grip available there then it originally thought and transfers
even more of the now increasing amounts of torque rearward ... your butt
starts to send you a signal that the turn-in you found so satisfying a few
moments ago has maybe started to go too far.

The rear tires have started to slide and relative to the front driveshaft,
the rear driveshaft slows further still, sending a signal to the Torsen that
is interpreted to mean there's LOTs of grip to be had at the rear wheels and
to which it responds by sending even *more* torque back there, just like
it's supposed to do.  At this point, the back end finally lets go completely
and snaps sideways ... you dial-in a steering correction and if you don't go
any further than pointing the steering wheel straight ahead, the slip angle
at the front wheels will decrease to zero and the Torsen will transfer
torque forward, helping the rear tires to recover.  There's a good chance
you'll save it and end up driving over the apex once the rear tires hook up
again.

On the other hand, if you have to add opposite lock, the slip angle will
stay the same (except its sign will reverse) and you'll either get out of
the throttle completely, which spins the car, or mash your foot to the
floor, which will cause the rear tires to start spinning and signal the
Torsen to shift torque forwards.  As this happens and the car recovers, the
front end hooks up again and you have to unwind all the opposite lock you
dialed in ... because this causes the slip angle at the front wheels to
decrease, the Torsen will direct even more torque forward.  At this point,
you're approximately two-thirds the way through the corner and the torque
split is around 50/50, which means the car has started understeering again
... with luck, you keep it under control and off the grass as you exit the
corner.

The critical factor here is how much of a margin you have in the rear tires
... at speeds under some unknown threshold -- let's call it 7/10 -- there's
enough grip in reserve to keep the rear tires from peaking.  Once you're
past that point, however, all you have to do is step over the line even
slightly and the spider rears its ugly head.  Few people, even professional
racers, can walk a line this fine without stepping over it.  I think chassis
tuning can definitely help ameliorate the consequences of doing so but I
don't think they will have any significant effect on the basic mechanism
involved.  Plenty of band-aids but no cures...

As for why you haven't been bit, I can only speculate ... perhaps your 20v
motor doesn't have as much lag so you can better modulate the throttle?
Perhaps its torque characteristics aren't as peaky so the tires don't get
hit quite so hard?  Perhaps you aren't driving hard enough to use up the
grip margin of the rear tires?  Frankly, I just don't know at this point ...
but rest assured that I will figure it out eventually.  (I will leave it up
to you to determine how an open and/or locked center diff will behave in the
above scenario as I need to get some sleep ... been up for almost 21 hours now!)

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   / |      _| o    | \       _| o  Jeffrey Goggin
  /__| | | / | | __ |  | | | / | |  audidudi@mindspring.com
 /   | |_| \_| |    |_/  |_| \_| |  http://www.mindspring.com/~audidudi/
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