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Re: Torque Sensing Differentials - math corrections, conclusions stay

To: the Quattro List
From:  Flunking the math dude

Better me correct my homework than getting lambasted, or taking any more than
I have.  You guys are quick.  The numbers I used on Page 7 of the technical
papers were inputed in error.  I used Td = (Trg - T2), instead of the correct
Td = (T1 - T2), which effectively doubled the BR, for those who care to know),
so I offer apologies to Dave E., he had the 70% BR correct at 2.31.  Thanks to
Jeff G. for finding my math errors.  Guess that's why he tracks numbers for a
living.  The conclusions don't change, only the BR.  Thanks for the interest,
here's my corrected post.

All this talk of torsen, you guys are confusing me and my calculator... :)

In a message dated 98-03-01 08:30:17 EST, I write:

<< Subj:	Torque Sensing Differentials
 Date:	98-03-01 08:30:17 EST
 To:	quattro@coimbra.ans.net
 Specific to the Torsen posts:
 (Please bear with me, for length, I have jumped already, and extrapolated
'wheel/axle' references to driveshaft - i.e the article is written assuming a
side to side Torsen, not front to rear)
 Dave E:
I have found that audi claims 75/25/25/75 which is a 3:1 BR, not 2.31:1.  For
Reference, a 50/50 diff has a 1:1 BR.  A 60/40/40/60 has a 1.5:1 BR
>From an audi center torsen chassis perspective, that means you can have
<<**3.0**>> times the torque of the front going to the rear OR <<**3.0**>>
times the torque of the rear going to the front, ALL IN THE SAME TURN.  Why I
claim the bite is there.  For a rwd or fwd torsen (this articles example) you
don't change the inherent chassis character, you're just increasing the
traction of that rwd/fwd character.

You can't talk of a static split or Locking Effect without talking about Bias
Ratio.  If you reduce the Locking Effect (to say 60/40/60), that means you
REDUCE your Bias Ratio, look on page 8 (Bias Ratio = the amount of torque of
the higher traction wheel supports *  torque supported by the lower traction
wheel.  So, let's compare a 75/25/25/75 torsen to a 60/40/40/60 torsen.  The
bias ratio of the 75 is <<**3:1**>>, the bias ratio of the 60 is
<<**1.5:1**>>.  What does that mean?  The 75 torsen is able to give <**3.0**>>
times the torque to the slower driveshaft (vs. the slipping one), the 60
torsen is only able to give <<**1.5**>> times the torque (vs the slipping
driveshaft).  So, as you narrow the torsen scope, so goes your traction
benefits of that change.  For reference, a 50/50 split center is a <<**1:1**>>
bias ratio. 

For maximum Torsen Locking in terms of absolute traction, you want the widest
range.  Why?  Cuz it gives the highest available Collective torque transfer to
the driveshaft with the most traction (that is the SLOWEST rotation, btw). As
you get higher in locking effect, the gains in Bias Ratio are much higher for
smaller gains in Locking Effect.  This can be simply stated in terms of
absolute traction:  A higher Locking Effect Range gives maximum traction
ability in a given center differential application.

So, audi marketing went for traction, NOT handling.  Reread that statement.
For those Gen I folks that never locked the center, audi increased your
TRACTION 'potential' <<**3**>> fold on the Gen II Torsen Center.
 Regarding your abs argument.  That is true to a certain extent, but it is
less than a VC, and many other types, because these others freewheel (go to
open diff), not a percentage as the Torsen does.   However, until we gain some
consensus on acceleration, I'd rather leave the braking part out of the torsen
argument.  Let's talk about torque split on acceleration, not braking or
coasting for now.
Looking at a 57/43 static split, I ask, ok what is the "range".  As long as
you have a range, my claim is A) you have a potential bite if you have
57/43/xx (where xx is larger than 51) and B) you lose the "traction" gains vs
other lockers as you reduce the range, and C) you reduce the ability to rely
on a "simple" abs system as you decrease the range (read, changing bias on an
older car, may or may not enable you do use your abs).  So did audi in the S4
use 57/43/25/75 or  57/43/43/57?  Or did they use 57/43/43/57?  (I argue the
latter) Either way, you assign that to the Bias Ratio, it DECREASES, and you
have added only another variable to your torsen equation, and you really
haven't reduced the chassis dynamics while turning.  And as you narrow the
range, the gains over a fixed diff become minimal, and BR Decreases in terms
of Traction. In terms of chassis dynamics, I say that becomes nil.  Does EDL
change absolute Traction?  I bet a bunch of BR is does.  So did audi.
 Or, do we find that the 57/43/xx keeps the chassis dynamics at understeer all
the time?  I don't know, but my optimism wanes some thinking of the setup.  I
guess it would depend on whether we are 'shimming' or 'helixing' all available
 In terms of slip angle what is happening?  Well, a car that tracks
differently in a turn needs a certain amount of driveshaft freedom,
specifically to audis awd, a car in a turn needs to have one driveshaft spin
faster than the other.  A main reason why you don't have a 100% locking
differential in a Torsen.  At that 25% speed differential, the torsen will
become, well, a torsen.  That is to say, on <acceleration> (don't confuse this
with engine coasting or braking) the driveshafts can be moving at a different
speed to each other, beyond 25% they will lock.  The definition of a 75%
locker, either driveshaft can spin 25% faster than the other.  But if you get
enough wheel slip, the torsen will lock the slipping driveshaft to the non
slipping one.  When that wheel slip is really high, i.e. a WOT spool up, the
rears lose traction the rear driveshaft spins faster than the front, and
torque transfers forward.  You can feel this effect in a straight line, the
Torsen hunt, just pull away from a stop in a straight line in the snow, with
just medium gas.  You can actually feel the torsen working back and forth.  In
a turn it does this too, only now, that hunt is more dramatic.  Why?  Because
the slip angle of the tires in terms of track +/- traction exceed the 25% slip
of the torsen.  So ALL the torque goes front to rear, immediately.
 So, I look at fixed split torsens and ask, "What makes them better than a
50/50 fixed diff?"  In terms of chassis, what gains are made with a 60/40/xx
Torsen vs. a 60/40 fixed diff, torsen or otherwise?  I see why torsen centers
have limited uses in racing.   Look at the Bias Ratio.   Any gains in using
them?  I suppose a 70/30 to 51/49 might have use, wonder what all the elusive
racing torsens used? For any split higher than that 50/50, my argument is for
that small gain in BR, you lose big in terms of chassis dynamics,
specifically, going from pushing RWD style (oversteer) to pulling FWD style
(understeer) in the same turn.   
 Mr. Hines:
 1)  you are correct, a torsen is immediate.  A gain, to some (tho understand,
the latest and greatest of the VC can take less than one revolution vs your
1/4 rev).  For theoretical absolute traction in a straight line (read: it
assumes NO chassis dynamics, only maximum traction for a given torque).  No so
for those who might be turning in the snow/gravel/(wot)tarmac, slowing the
rear wheels with a slide, regardless of throttle, you will always have maximum
torque rear, until you begin to "modulate" or power up to the point of
slipping the rear faster than the fronts, then things will change (see your
point 2a).
 3)  Nominal split has a range.  Otherwise it is NOT a torsen, by definition
it's a locking differential.  Torque sensing means torque transfer, if you
have a 50/50 split you aren't transferring any torque.  You are gaining
Collective torque the drive axles can support only.  The same thing a 50/50
locking center diff is doing  (reread this on page 3)
 Maybe some clarification on the difference between a locked 50/50 center
diff, a locked 50/50 torsen diff, a 50/50 VC center diff, a 50/50 clutch
center diff, 50/50 magnet, 50/50 sheer, and a fixed 50/50 no Center diff is in
order.  A locked 50/50 split center diff is the same as a torsen 50/50 and ALL
the others in terms (Collective) torque when they reach maximum f/r slip, the
only difference is slip angle and freewheel ability.  A fixed 50/50 no diff,
means that you have 50/50 torque regardless of torque or no torque, slip angle
or no,  driveshafts will spin the same speed ALL the time.  The reason audi
eliminated the 50/50 Gen I locker center and ran a fixed 50/50 split (no
diff), is that they are the same thing if you never unlock the Gen I.
 So, let's understand that changing a Torsen center to be more rear biased,
may or may not bring you the gains you think, they certainly aren't monumental
over a Gen I setup.  The best way to summarize this torque issue:
" *To Gain torque (vs. a slipping axle/driveshaft) you transfer it from
somewhere.  You transfer it FROM somewhere, you will transfer it back
somewhere too. In terms of TRACTION that torque transfer in a center diff
(75/25/25/75) will transfer <<**3.0 BR**>> between the FRONT AND REAR DIFFS, a
huge variable in terms of HP applied to a rwd to fwd character in the same
 Your chassis may or may not accept that caveat, in terms of a torsen center,
I found there is a point that giving back can sting ya.  It's inate in the
chassis dynamics and the Torsen dynamics in every audi with Gen II + Gen III
lockers (Torsen Center, Locking Rear and Torsen Center, Torsen Rear
 CJ Miller et.al.:
 The article on that web page has a couple of issues that need to be really
addressed.  1), you first have to look at the "axle" characteristics explained
in terms of center driveshaft, which changes how you achieve some of the
characteristics.  2, the claims of "proprietary" things, like exactly what
change in  helix, what change in shim, what the exact slip (freewheel) is for
any given setup.  This leaves a lot of unknowns as far as exactly what is in
our audis.  I'm not convinced that information will become a known.  3)
Torque in a Center Diff, doesn't necessarily translate to TRACTION, since
before you get TRACTION, you have ANOTHER 2 differentials.  A variable that is
specifically NOT addressed in this article.  It speaks of differentials in
terms of being the diff driving the wheels.

Look at page 10 for the "unlikely" statement.  Unlikely in a side to side
Torsen, I argue.  Maybe not so front to rear, especially as you have to put
that BR thru another differential.  "Unlikely" is Dave E., Phil P, and others
who haven't been bitten.  "Likely is the ones who set up the exact set of
variables in a turn to create the bite.>>>
 A couple more ideas to think about.  Since BR is a percentage of torque that
can be transferred in relation to the driveshaft that is spinning faster, what
does this mean BR is when a tire is at a track slip angle vs a power up tire
"peeling out"?  What does this mean with all four tires on the ground vs one
or two up?   What does this mean if you have an open front diff, and a LSD
rear?  What difference would tire size make?  Any?  To S.O.c. et al.,
"Maximum at xx" isn't my reference.    All these variables affect the BR in
terms of collective torque that can go to axles.  Another discussion perhaps? 
 I suppose we could do "Torsens in Racing" threads for a long time.  Bottom
line is this, who knows for sure?  And given Torsens own technical paper, a
torsen can be made to have a plethora of locking ranges, a plethora of
unlocking ranges, if so, we can certainly see that a center torsen can be made
to oversteer only (>50/<50/<50), however, the advantages over other types of
locking diffs (or none at all) become minimal, look at the BR chart on page 8,
it is more than my claim.  What all of us in our street cars have, is far from
Desire.  It is an absolute traction device only.  For some of the rest of us,
that has a dark side in terms of chassis dynamics.
 We are a lot further than before IMO, but a long ways to go yet.  I'm not
convinced that the answers are easy.  Which is why, even understanding the
operation of the Torsen, hasn't really helped me CORRECT the chassis issues
associated with the spider phenomenon.  Not convinced at all, you can.  By the
very definition of Torsen.
 Scott Justusson
 '87 5ktqwRS2
 '86 5ktqw
 '84 Urq
Whew, not as bad as I thought.  My apologies for the addition errors.  The
conclusions, thankfully, stay the same.  It also really shows that a very
little change in BR has a big effect on the handling of a Torsen Center Diff