Hi Rob,
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Ron
Since the exercise is maximizing tire grip and we have been speaking of that exercise with a 200tw DOT tire.
If I tune the suspension to obtain the best balance possible with the DOT 200tw tires but then switch to a sticky compound tire such as a Hoosier R compound in the same proportional stagger does that warrant more spring, ARB and associated shock dampening?
Yes. Of course someone can simply switch tires & run the car to its limits. But if the car if going to be optimized with 200TW tires ... and also with Hoosier R6 race slicks ... the optimum set-up will be different.
Since the increased grip of the tires would allow for higher cornering speeds the forces working on the suspension should increase. I would think this means at a minimum more bar would be needed.
You will want to make changes in 4 areas. All requiring a small degree of work, but nothing complex. I'll outline it below.
I would think you could use a similar spring package to control the pitch of the cars weight which is static but add more bar to deal with the added force from the increased cornering load.
Sway bars are not enough. Because as you increase the traction of the tires, the car will experience a higher degree of weight transfer under braking & acceleration.
Since I only really care a bout the 200tw tires for the RTTC or Goodguys type events a Hoosier R compound may actually be what I really tune for.
I'd like to understand the logic behind a slick vs street tire tune better. I'm sure others won't mind reading that little diddy either.
Sure. Here goes ...
Assuming, we start with DOT tires of 200TW ... and dialed the suspension in thoroughly until we declared it was "optimum" & we could "find no more" ... then we put on Hoosier R6 racing slicks of similar height, width, sidewall size & wheel backspacing to maintain the same front & rear track widths ... here is what we would experience with no suspension changes:
1. On corner entry braking, the front suspension will compress quicker & farther & the rear suspension will rise quicker & farther. The car will experience more weight transfer from rear to front ... and may, or may not, lock up the rear tires easier, depending on several suspension factors. The car will have excessive pitch angle, excessive loading of front tires & excessive unloading of rear tires.
2. On corner entry "turn-in" ... while still braking ... the car will react/respond quicker, turning the front end of the car into the corner quicker. The car will experience more weight transfer from inside to the outside. Body/chassis roll will increase & be excessive. The biggest amount of weight transfer increase will be from the inside rear tire to the outside front tire. The tires on the inside of the corner will be underworked & the tires on the outside of the corner will be overworked ... the front more so than the rear. The car will lose traction on the inside rear tire & become loose ... unless the driver adjusts by braking softer & earlier during "1".
3a. If the driver does not adapt ... and the car gets loose on corner entry ... one of two things will happen (neither good). Either the driver "corrects" for the skid ... by turning the steering into it ... which adds cross weight & grip. At the point the car "catches" regaining grip ... the car angle & steering angle are F#%&*@ ... so after the car "catches" it will push like a dump truck through the middle of the corner ... and probably snap loose on exit. Or, if the driver doesn't correct the steering, the car will simply spin out.
3b. So ... assuming the Driver adjusts to brake softer & earlier keeping the handling neutral on corner entry ... when the steering is "set" & on its arc for the middle of the corner ... and the driver releases the brakes ... the car will experience slightly more roll angle, which was already excessive, due to the increased grip on the slicks . What happens next is dependent on the rebound valving of the front shocks . If there is not enough, the front will rise & the rear will settle too early*, causing the inside rear tire to reengage too early* & the inside front tire to become unloaded too early* ... leading to a mid-corner push condition.
Additional shock "low speed" rebound valving will help this situation by delaying the transfer*, as will the other tuning changes I'll outline. While on track, the driver could help this situation by lengthening their braking zone. Meaning get off the brakes later ... and use slightly less braking pressure, to arrive at the same corner speed. Do not confuse this with trail braking.
4. When it's time to pick up the throttle ... mid-corner, while the car is still turning ... the car will transition weight transfer to the rear ... and increase the car's roll angle, just until the driver starts unwinding the steering wheel. This may, or may, not lead to a push condition on cornering under throttle, depending on the timing* of weight transfer from the outside front tire to the outside rear tire. If the WT happens too spoon, it will push.
5. Soon after the driver starts to roll on the throttle, they start to unwind the steering wheel progressively. This will shift the transfer weight ... just as progressively from rearward & outward to simply rearward, by the time the car is accelerating straight. Again, this may, or may, not lead to a push condition on exit under throttle, but depending on the timing* of weight transfer from the outside front tire to the inside rear tire. If the WT happens too soon, it will push.
So ... what do we do? Drink beer. 
Or, we could make these changes to optimize the set-up on the slicks:
A. Change to stiffer rate front & rear springs.
Note: If ... IF ... the front shock compression valving is adjustable enough ... we may be able to slow the rate of weight transfer from rear to front enough ... to restore the compression rate & distance to optimum ... and we may not. The "range" of the shock adjustment may simply not be enough. Frankly, going from 200TW to Hoosier R6's I doubt it. The only shock I know with that much range "might" be the JRI's.
B. Adjust your front & rear sway bars to stiffer settings ... or install bigger sway bars in the front & rear.
C. Fine tune the shock valving.
* Shock valving is the key tool for controlling the timing of events.
Fronts: Increase the rate of low speed rebound valving & fine tune the rate of compression valving to optimize the rate of front compression in dive with the new stiffer front springs.
Rears: Increase compression valving to slow the roll angle transition & help the car turn.
Note: If the car is still pushing on exit under throttle ... stiffen the high speed rebound valving on the front shocks and/or reduce the low speed rebound valving of the rear shocks a little.
D. Fine tune the car's front to rear grip balance by raising the rear roll center a little with your adjustable track bar or Watt's link.
How much change to achieve optimum? You won't know until you test. Just like you won't know what optimum is with the 200TW tires until you test also. 
A experienced tuner like myself can get you in the ball park, but when you start pushing a car to its limits ... that when you truly find out what the car wants.
Important note: Lazy racers want to make one big change, and that is not optimum .. far from it. The only way to keep the car "happy" & truly optimized is making small to moderate changes in all these areas I've outlined.
Sometimes true optimum requires small amounts in other areas too, such as brake bias, track width (think thin wheel spacers) toe/ackerman, slight changes in ride height and/or rake, etc.
Make sense? Got questions ?
.