Re: Boating with an S4

["Avram Dorfman" <dorfman@est.org>]

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.

The following are excerpts from the Gleason Torsen white paper
(http://www.sonic.net/garyg/zonc/TechnicalInformation/TorsenDifferential.htm
l):

    1) The drive axles associated with an open differential are
interconnected by a bevel gear set designed to divide equal torque between
drive axles.

    2) The maximum amount of torque conveyed by the drive axles collectively
[on an open differential] is limited to approximately twice the amount of
torque supported by the drive wheel having the least traction.

    3) The maximum amount of torque conveyed by the drive axles collectively
[with an open differential] is limited to approximately twice the amount of
torque supported by the drive wheel having the least traction.

    4) under the same conditions, a '4:1' bias ratio [i.e. Torsen]
differential is capable of delivering approximately two and one-half times
more torque to the drive axles collectively than an open differential.

So, if we add all of this up, we get the following:

    a) If an open differential is allowing wheelspin, how much torque is the
driveline conveying? Let's assume that there is 1 lb-ft worth of friction
coming from say wet ice at the slipping wheel. Then there is no more than 2
lb-ft being delivered, and 1 of it is spinning the slipping wheel. If the
car is not moving, then the remaining 1 lb-ft must not be enough.

    b) If you put a Torsen diff in the same situation, how much torque will
the new driveline convey? Well, if the open diff was conveying the 2 lb-ft,
then the 4:1 torsen driveline would convey 2.5 * 2 lb-ft, or 5 lb-ft. of
torque. 1 lb-ft to the spinning wheel, and therefor the other 4 to the
gripping wheel(s). Thus, 4:1 bias ratio. If 4 lb-ft is enough to get you
unstuck, then off you go. If it's not, then off you don't.

The torsen doesn't transmit "30% of the gripping wheels' torque to the
slipping wheel." It "allows a maximum torque difference of 30% between
driven axles." When a car is on a jack,  I can spin a wheel with my bare
hand. Furthermore, once the wheel is spinning, it keeps spinning even
without my bare hand. However much torque it takes to spin a wheel in the
air (way less than 1 lb-ft), 4 * that is just not enough to get my brother's
car up a hill, or to pull an S-4's rear wheels back up over a right-angle
cliff.

Where does the rest of the engine's potential torque go? (This is my
analysis - all of the above pretty much comes straight from the white paper)
I believe it simply goes to accelerating the spinning wheel until the engine
is spinning so fast that it can't spin any faster, which is determined by
how much gas you're giving it, and the rev limiter if you have it floored.
Either way, the engine never actually builds up to it's full torque
potential b/c something else gives long before that would happen - the wheel
spins.

Think of it this way: If you built a special driveshaft that basically had a
"torque wrench" built into it - a spring that would allow the shaft to
twist, with a little dial showing you how many lb-ft was currently being
applied to twisting it, and you floored it while you had a wheel in the air,
it would barely twist at all almost immediately, the wheel would just spin.
There would be a moment while the wheel was accelerating, that the dial
would register a little torque, but once the wheel caught up to the engine
speed dictated by the amount of gas you were delivering to the engine (i.e.
about 0.20 sec) it would read nearly zero.

-Avram