RE: Boating with an S4

["Dave Eaton" <Dave.Eaton@clear.net.nz>]

interesting case.  the behaviour you describe is normal for a torsen.  quite
simply, with a wheel in the air, a % of torque will go to the axle without
grip, while the remainder goes to the axle with grip, but because the amount
of torque supported by the spinning wheel is low, so is the amount sent to
the "high" side.  in other words, your car should be able to drive off a
jack with a wheel in the air -folks, don't do this at home unless your
parents are with you at the time :-), but not proceed up a hill (not enough
torque).  this is the reason for the diff lock on the torsen audis.

the issue is that *any* limiting differential is only able to support a
particular (designed) torque "bias ratio" across the diff.  our house has a
driveway where this can be the case, the rr wheel hangs in the air, and the
vehicle will stop, until the rear diff lock is pressed.

manual traction control (rear diff lock) and you're away.  the latest
technology is to replace the manual lock with a brake-based traction control
system (tcs).  without tcs, or rear limited slip differential, a locker
centre or a centre with a very high tbr would be required.  then you would
have to live with the low speed manoeuvrability issues.

as another way of illustrating this issue, with a limited slip diff, if you
can *increase* the torque being sent to the "low" side of the diff by
braking that side (remember that a spinning wheel consumes little torque),
then the torque sent to the "high" side (where the traction is) is increased
and all is well.  this is of course, what a brake-based traction control
system (tcs) is for.  audi's 'ebd' exactly.  the handbrake does similar of
course.

the other way around the problem is to have a limited slip rear
differential.  the integrale had a vc centre, and a torsen rear for this
reason.

there are of course philosophical differences between the various methods of
centre limited slip differentials.  the vc is speed sensitive (ie requires
wheel spin before it operates), while the torsen seeks to eliminate wheel
spin in the 1st place.  this, btw, is why the amalgamation of a tcs and a vc
is a little difficult.

the other way of "solving" this issue, and by far the most elegant, is using
"active" differentials where the torque shift is controlled by computer and
based on the input of various sensors (wheel speed, accelerometer, g sensor
etc).  the haldex differential goes someway down this track.

however, before we all get carried away, the major concern of manufacturers
is of course for dynamic (rather than static) behaviour.  to illustrate,
take the case of a vehicle constantly accelerating in a straight line with
either an open or a torsen centre.

in the open centre diff, you have equal torque to either axle (by
definition), while the dynamic weight distribution moves rearwards (as the
vehicle accelerates).  this results in increased front slip (less weight at
the front therefore less traction but equal torque).  when this eventually
results in front wheel spin (increased longitudinal slip overcoming
traction), the torque able to be distributed by the open centre to both
axles decreases to the level able to be supported by the spinning *front*.

the difficulty with this of course is that for optimum performance, torque
should be redistributed in proportion to the wheel traction/loading (ie..
longitudinal slip), which of course varies according to the dynamic weight
distribution.

for the torsen centre diff, the front and rear wheels continue to run at the
same *speed* of rotation, and the same longitudinal slip (by definition) as
torque is re-distributed rearwards until either the limits of adhesion or
the differentials torque split range (bias ratio) are encountered.  so the
fronts don't spin.  even on wet roads, studies have shown that the torque
redistribution is well within the bias range, and goes some way towards
matching the dynamic weight distribution of the vehicle.  at the same time,
because of less torque going through the fronts, steering performance is
obviously improved over the open diff case.

this issue has caused more than a little mis-understanding.  the fact is
that the torsen is "locked" until the torque bias ratio is exceeded,
whereupon it will allow differing output shaft speeds.  this is why, for
example, you get axle windup with torsens on full lock car-park manoeuvres
(as a point of reference, with the audi torsen in the 80q, the bias ratio is
exceeded at under about 15m turning circle on a high grip surface).

the difference between the torsen and the locked centre in the straight-line
case is very little as both are governed by the keeping the same output
shaft speeds of rotation, and so both will re-distribute torque rearwards.
the difference occurs in the case where the torsen diff's bias ratio is
encountered whereupon it will limit the torque shift, and at the bias ratio,
and allow *different* output shaft speeds, while the locked centre diff will
(theoretically) shift 100% of torque, while keeping the same output shaft
speeds (by definition).

references for your further reading:
the "torsen white paper" you quote from is actually a relatively poor
reference to understand the device.  the 1995 "torsen and tcs" white paper
which i scanned and distributed last year spends much more time on the
behaviour of a torsen in a centre application, while the 1988 audi sae paper
on the influence on vehicle handling of the torsen centre is specifically on
this issue.  the sae paper "analysis of tcs augmented by lsd"  looks at
precisely the case when one side of the torsen has no traction (split-u),
and the other does, although this is also discussed in detail in the "torsen
and tcs" paper above.

hth,
dave
'95 rs2
'90 ur-q
'88 mb 2.3-16


-----Original Message-----

Date: Wed, 11 Aug 1999 14:42:38 -0400
From: "Avram Dorfman" <dorfman@est.org>
Subject: Re: Boating with an S4

Sorry for this long post - I have included excerpts from the Gleason Torsen
white paper which I feel explains this dilemma clearly; no matter how much
torque you engine can produce, the most you will ever get out of the
driveline is determine by the amount of resistance provided by the lowest
traction wheel and the bias ratio of the diff, and if it's not enough to
move you, you don't move. Open diffs have a bias ratio of 1:1. Torsens are
more than 1:1, e.g. 4:1.

No, it wasn't your post that explained it. As a refresher, my brother (sorry
for those of you who've read this before) and I took his 80q to a funny
shaped little hill that causes 1 rear wheel to go airborne when you climb
it. The torsen didn't get us anywhere - once we ran out of momentum, the car
rolled backwards with the airborne wheel spinning at 60mph until it hit the
ground again - it didn't matter how much gas we gave it. The analysis at the
time was that a torsen doesn't do squat for you unless you have *some*
resistance against the slipping wheel. Regardless of how much torque the
engine "can" generate, the entire driveline only "is" generating however
much it takes to do what you're doing. It just doesn't take much torque to
spin a wheel in the air.