You missed it. What I'm saying is that for the same amount of roll reaction force on the outside tires with a track increase of 2.5%, lateral g's (or V^2/r) also go up by 2.5%. Obviously, track width isn't part of the v^2/r equation. The track width increase plays into the roll reaction. Again, 2.5% more track width => 2.5% more g's for the same amount of weight transfer. But this only equates to sqrt(1.025) or +1.2% greater cornering *speed*.

However, this is an oversimplified model, assuming that the cornering limit is solely dictated by normal force on the outside tire. since grip vs. normal force is also nonlinear, it ain't as simple as that...

 

Long/short, changes in track width on the order of a few percent won't be detectable by seat of the pants or through the wheel in terms of outright grip gained, which will be very small. But change in scrub radius on the order of 10s of mm absolutely WILL be noticeable at the helm. *That* is where any change in feel of the car will come from.

 

Thinking about it a bit more, the theoretical 1.2% gain in cornering speed for a 2.5% gain in track width would be overstating it, actual grip benefit will be less than this.

Say a car has a 1600mm track width, c.g. height at 450mm, weighs 1000kg (50/50), and can take an 80m radius corner at 100km/h. That's 0.983g.
Assuming equal front and rear roll stiffness distribution for simplicity, that puts 500kg + .983*1000kg*(450mm/1600mm) = 776.5 kg on the outside tires (and 223.5 kg on the insides). Total lateral grip is 1000kg * .983 = 983kgforce

Increase track width by 40mm, and now lateral acceleration required for the same lateral weight transfer also goes up by 40mm/1600mm or +2.5%. .983g * 1.025 = 1.0076g.

Velocity for this new acceleration around the same 80m radius turn is sqrt[(1.0076g*9.81m/s^2)*80m] = 28.12m/s = 101.2km/h

But the total lateral grip required is now 1.0076*1000kg = 1008 kg, which is 25kg more than the maximum that the same tires with the same weight transfer produced in the earlier case. The tires cannot now magically produce more grip at the same exact load levels, so in reality the car will not be able to go that fast before reaching the limit of adhesion.

At some speed between 100km/h and 101.2km/h, the 40mm wider-track setup will hit its maximum cornering speed and g's. There will be an improvement over the baseline case because the outside tires will be loaded less and will be producing more lateral grip per normal force than in the first case.

 

So is it safe to say that it'll take significant width changes to see substantial performance gains or losses?

Adding or subtracting 40+mm is on the brink of requiring extensive body work to make things fit. At that point, the ROI probably isn't worth it.

 

I doubt the ROI is ever "worth it". However, a 3% increase in cornering speeds over a 2 min track could be as much as 2-4 secs. That would make a difference between winning and losing. In that light, worth every penny.

 

+3% increase in speed *everywhere* on a 2 minute track is 3.5 seconds. 3% increase in cornering speed could be on the order of 1.5-2 seconds (a LOT). But to get +3% would require *more* than a 6% increase in track width. We're talking offsets less than +20mm.

For +40mm increase in track width, we're talking 1% *max* increase in cornering speed, and it will surely be quite a bit less, probably more on the order of half a percent. Certainly less than a second at most tracks, probably more on the order of .5 sec.

Whether or not it's worth it depends. In most showroom stock classes, you're not allowed to change wheel size, and offset has to be within 5mm (or was it 1/4"?) of stock, and you can't modify the body anyway, so the question doesn't really apply (many successful showroom stock efforts have just run stock wheels).

If you're in a class that allows any wheels but requires stock bodywork and disallows tires sticking out beyond the profile of the bodywork, increasing track width via lower-offset wheels or spacers will pretty quickly require you to give up tire width. Getting the maximum tire width under the fenders is going to drive your offset selection, as tire width will give greater lap time benefit than small percentage increases in track width which only give even smaller percentage increases in cornering speed.

If you're in a class that allows body modifications, then you'll probably want to maximize overall width from outside left tires to outside right tires to the maximum extent allowed by the rules. But this doesn't necessarily mean maximizing track width, as again, tire width will play a role, and the wider track width you run, the narrower tires you'll have to run.

Worth noting that going from +55/+65 offsets to +45 all around (about the limit that you can get 255s all around on and not be obviously sticking out beyond bodywork) is a 20mm increase in track up front, and 40mm in back, less than the +40 all around we've been considering).

 

Nice writeup Zdan. I guess the differences have to be done in aggregate to appreciate the sum effect and every little bit counts.

I really hope I can do a +18 offset setup further down the line. Would probably feel quite different from the current setup.

 

ZDan/c32b- Since you guys definitely sound like you know what your talking about.......Have you taken into consideration the wheel-hub bearing load differences?

It was my understanding that if you widened the track of your car from the original engineered geometry, you run the risk of augmenting the load on the wheel-hub bearings.

....Any concerns about ruining bearings with extreme offsets?

 

Heh. I had 1.5" or 2" (can't remember) spacers on the front of a Fiat 850 years ago. Ran 'em on the street and autocrossed with old Firestone road race tires - until the right front spindle gave up the ghost, no doubt due to the extra leverage...

 

Good thread great info, I have replaced my rims with 45+ offset. Knowing the stock front offset is 55+ I recognized I will gain 10 mm only which is 1 extra cm. I am an instructor at the track so I have had my share feeling the car and I can tell you that 1 cm in the front or 2 in the rear will not make much of a difference and you will not feel it.

However, I replaced my rims with 9 inch all around with 255 tires, this changes everything. This means I have gained 42mm per side in the front. It means I have gained almost 9 CM in width in the front and let me tell you; that you will feel. I have also gained 8 cm in the back (both sides)
I suspect from engineering perspective that the lighter the object is the more you will feel notice these changes.