torsen tech 101

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

orin, eric, others - it is time for me to front up on the technical side of
things in the torsen debate.

by way of background, about 12 months ago i got pissed of with the "60
minutes" tone of the spider debate (and the name calling) and the lack of
fundamental understanding of differentials which lead to all sort of claims.
so i resolved to figure it all out.  i have emailed, written and wheedled my
way around various people and organisations to assemble what is probably one
of the finest collections of useless information about differentials, awd
systems, and traction control systems on the planet.  and i have promised
myself that i would, one day, get my life back.  that time has come...

anyway, for the record, most information in the public domain of the torsen
is incomplete.  it is not that it is inaccurate, but simply that people read
what they want to in it (not naming names of course).  while summaries (such
as eliot lim's) are accurate, they are also incomplete.

earlier this year when scott claimed that the locked diff couldn't
proportion torque, i twigged that perhaps this was the cause of the problem.
scott and jeff believed then that the locker can't do things that it can,
and conversely that the torsen can do things that it can't.  anyway, i
digress.

while attempting to understand scotts position and what his "undersanding"
of the torsen actually was, it is now clear that the issue is simply that
scott and other do not understand how either the torsen or the locker
operates.

the major misunderstanding in this debate the assumption that the torsen
"distributes torque", and that the locker doesn't.

that is incorrect.

both distribute torque in exactly the same manner.  the only input to the
equation is (as phil has pointed out), the tractive force at either axle.
they are both dumb devices.  if one gets fooled by slip angles, then they
both do.

when cornering within the bias ratio of torque distribution the torsen diff
is *locked*.  you may need to re-read that statement.

let me say it again in a different form.  the torsen operates as a bevel
differential until relative slip between the axles occurs.  this causes the
differential to *lock*.  until torque distribution across the diff reaches
the bias ratio.  which is usually 3:1 (25:75) in audi applications, but can
also be 4:1 (80:20) depending upon the design.

with the diff locked (within the bias ratio), it is *exactly* the same as
the locker.  exactly the same.  both shift torque rearwards depending upon
relative slip when cornering.  the only difference is that the torsen starts
of as an open diff (50:50 torque split) on corner entry.  which means less
understeer than the locker which has a static torque distriution which
mirrors the weight distribution of the car (60:40).

the other difference in operation is what happens when the torsen hits the
bias ratio.  while the locker will continue to shift torque rearwards, at
this point the torsen diff *unlocks* and allows relative axle speed
differences.  at this point it is acting as an open differential again, but
it is operating at the bias ratio (fixed torque split, variable axle
speeds).  which it maintains (allowing wheel spin) as long as required.
this is the torsen 4-wheel drift which we know and love.

if you understand these points, you will understand that the issues that
scott, jeff and othes have with the device are in fact, not technicaly
possible with a torsen.  it is as simple as that.  the "bite" has to be due
to other issues.  the "alignment" thread (pre and post personal attacks)
gives clear evidence of this causing similar handling (bite) traits on both
torsen and non-torsen cars.  which makes it quite clear really.

i hope that this has cleared up the theory and establihed a technical
baseline for further discussions.  i am happy to expand on these points if
anyone wishes.

i have found that following are the essential reading on the subject and
would recommend them for those interested in further study:
1) "comparison of the dynamics of conventional and worm gear differentials"
freeman
2) "the influence of a torsen on the handling of awd vehicles", heibing
3) "traction and handling synergy of a torsen", platteau
4) "the new torsen ii technology", egnaczak
5) "car suspension and design, chapter 10: 4wd", daniels

dave
'95 rs2
'90 ur-q
'89 mb 2.3-16

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

Date: Wed, 20 Oct 1999 00:49:38 -0700 (PDT)
From: Orin Eman <orin@wolfenet.com>
Subject: Re: Torsen theory for Gary

> Now, this whole arguement depends on several factors:
> (1) Does the torsen in fact redistribute torque to the rear wheels
>     when powering through a turn?

True.  Since this hasn't been quoted yet, here is an extract from
the infamous SAE 885140:

[40m radius turn, acceleration of 4 m/s^2, high-grip (uG approx 0.9)]

"...the front wheels follow a wider radius than the rear wheels on the
circular course, so that 0.2% of forced slip occurs _between_ the
two axles, which reduces the wheel slip under traction at the front
wheels, and reduces the slip at the rear wheels.  This results in the
tractive forces being redistributed towards the rear wheels, so that
the tractive force distribution is 38/62%.  The extent of this
redistribution decreases with increasing cornering radii and road speeds.
With small cornering radii and low speeds the extent of torque
redistribution can increase to the torque split limit of 25/75%.
[Orin: that shudder from the rear you feel in parking lot turns.]
On a high grip surface, the torque limit split is reached at
a radius of about 15 meters."

So, yes, absolutely, you can get 75% torque rear due to cornering alone.

> (2) Assuming #1 is true, how much does the rearward torque shift
>     affect the attitude of the car?  (i.e. large or only small affect)

Good question.  This is the question that needs addressing.
Phil says aligment is crucial.   Tires matter too.