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More Torsen stuff - KISS of Trg

Now that the KISS theory is out the window, a look at some basic assumptions
to discussions of Trg and Tshift.  Specifically, looking at the difference
between Trg and Engine Torque.  My original motivation for this exercise was
to look for optimal shift points, but decided to add the Trg and the Tshift in
for the heck of it.  Very interesting results.

For all our prior Tshift equations here, we assumed Trg = Engine Torque.
Well, technically that is ONLY correct, when you have a Transmission Ratio
(not final drive) of 1:1.  That would be 4th gear to most audi 5spd

Torque to Drive axles (or in this case Trg) is the Product of Flywheel Torque
and Gear ratio.  A Gear Ratio is specifically a Torque multiplier.  So, if we
have 200lb/ft of torque at the flywheel and a 2.125 Gear Ratio in second gear,
Trg = 200 * 2.125 = 425 lb/ft.  So, with a 78/22/22/78 Center Torsen, the
Tshift is <(Tmax - Tmin) * .01 * torque> or simply (78 - 22) * .01 * Trg = .56
* 425 = 238lb/ft.  

Taking some of Dave E.'s power output numbers to a 20vt Urq, I find that the
Tshift is most significant in the first couple gears and less so as you
progress.  For Example:
Car = 20vtq, Stock 217hp, 5spd trans codes (3B, APL,AUM, AOA,AUL)

Trg 1st gear (@3.600) = 750lb/ft+ from 2000rpm>5500rpm
Tshift 1st gear = 400lb/ft+ 2000rpm>5500rpm
Trg Max = 821lb/ft @ 2000rpm
Tshift Max = 485 lb/ft @2000rpm

Trg 2nd gear (@2.125) = 400lb/ft+ from 2000rpm>6000rpm
Tshift 2nd gear = 225lb/ft+ from 2000rpm>6000rpm
Trg Max = 485 @ 2000rpm
Tshift Max = 271 @ 2000rpm

Trg 3rd gear (@1.360) = 235lb/ft+ from 1500>6600rpm
Tshift 3rd gear = 150lb/ft+ from 2000rpm to 5500rpm
Trg Max = 310 @ 2000rpm
Tshift Max = 174 @ 2000

*Trg 4th gear (0.967) = 220lb/ft from 2000>5500rpm
*Tshift 4th gear = 100lb/ft+ from 2000>6600rpm
*Trg Max = 220 @ 2000rpm
*Tshift Max = 123lb/ft @2000rpm
*For KISS, this is the closest to what we've been using to date*

Trg 5th gear (@.730) = 150lb/ft+ from 2000>5500rpm
Tshift 5th gear = 85lb/ft+ from 2000>5500rpm
Trg Max = 166lb/ft @ 2000rpm
Tshift Max = 93lb/ft @ 2000rpm

I just finished the program, but some interesting trends develop.  One might
say easily to shift up when you want to control Tshift.  However, I do find
that the torque flattens as you increase in gears (read less peak), so the
tshift might be argued to be more significant in the higher gears depending on
slip or traction.  

I'm not sure whether this matrix will help explain spider bites, but it does
show some significant torque that is being shifted about in that center
Torsen.  Add to that some tweeks and the significance becomes monumental.  I
put the same trans GR above on a model of Dave E's RS2 Torque curve.  Trg Max
1st Gear = 1087lb/ft @ 3000rpm, 627lb/ft second gear, and 411lb/ft in third.
That's Tshift max of 609lb/ft,359lb/ft, and 230lb/ft respectively.

Spider soup anyone?

Scott Justusson