Effects of tire Diameter on Roll Centers / Roll Stiffness

That makes good sense, you could write the roll center height (at zero roll for symmetric suspension, or the Force Application Point for an asymmetric case) as

H = (T/2)*tan(theta)
where T is the track width and theta is the angle formed by a line through the contact patch and the instantaneous center.

On our strut suspensions at least, a low but above-ground roll center implies instant centers relatively far away and with height higher than the roll center. So when you put the smaller diameter tires on that lower the car 0.5", the virtual swing arm angle (relative to wheel center) doesn't change, but the instant center height goes down by 0.5". But 0.5" is a relatively small portion of the total instant center height, and the roll center will fall in roughly the same proportion as the instant center. Meaning, not much. In your case based on the numbers you show, the instant center must have been roughly 20" off the ground, so you dropped it by 0.5", only a 2.5% reduction. The limit case seems weird to think of but nonetheless true: if the roll center is exactly at the road surface, it won't move when you change tire diameter (because the virtual swing arm is infinitely long so theta is always zero).

Its a nice illustration of something I've also been appreciating more myself lately as I work through the suspension geometry concepts - the suspension has to be tuned for a particular wheel/tire combination. Almost any change (with the possible exception of a small swaybar stiffness adjustment) has a cascade of side effects that are sometimes surprising.

I think there is a limit case where the roll center would drop by the same amount as the tire radius - if the instant center was at the same point as the roll center. Of course that would be a really wacky strut suspension that would never really exist, I mention it just to point out that my reasoning applies mostly to the case of our typical geometries and might not be universally applicable.

Tyler R said:

Hi, I know this is an old forum post, but I was looking at the suspension geometry correction kit for my Mr2 Turbo. I also do FSAE and help design the suspension geometry.

You were talking about having the roll center at the CG being the optimum handling setup due to less roll, but have you analyzed the jacking forces? The closer the roll center is to the CG the more the jacking force your car takes. Carroll Smith explains that it is best to have your roll center at the ground. This eliminates jacking forces. The roll will be greater, but the car will be faster due to less forces acting directly on the suspension components being translated directly into the chassis.

I am just a student looking to learn.
Thank You

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I think what I meant was that co-locating the CG and the roll center would eliminate body roll. I did say improve handling as well, and you are right, that was an over-simplification of the subject. It would certainly be a lie for me to claim my understanding of this subject hasn't evolved over time! I will admit that jacking forces are something I have not looked into too much.

That said, I have definitely found that raising the roll centers somewhat has some positive effects. I think a lot of this actually comes from getting the roll center to an area where it is more stable. One thing I found in my analysis was that the roll center rarely stays where you put it, and this effect gets much worse as you lower the car and the roll center drops below ground. It gets into a region where small amounts of body roll cause large changes in the roll center location, which I would expect to cause some feelings of instability. Raising it back above ground and closer to the stock location also causes it to move around a lot less. Now, a lot of this is just theory, but the improvements I and many others have felt from geometry correction I think back it up.

All that said, It's been a long time since I have really worked my geometry model or researched the geometry aspect of suspension!

Alex W said:

I think what I meant was that co-locating the CG and the roll center would eliminate body roll. I did say improve handling as well, and you are right, that was an over-simplification of the subject. It would certainly be a lie for me to claim my understanding of this subject hasn't evolved over time! I will admit that jacking forces are something I have not looked into too much.

That said, I have definitely found that raising the roll centers somewhat has some positive effects. I think a lot of this actually comes from getting the roll center to an area where it is more stable. One thing I found in my analysis was that the roll center rarely stays where you put it, and this effect gets much worse as you lower the car and the roll center drops below ground. It gets into a region where small amounts of body roll cause large changes in the roll center location, which I would expect to cause some feelings of instability. Raising it back above ground and closer to the stock location also causes it to move around a lot less. Now, a lot of this is just theory, but the improvements I and many others have felt from geometry correction I think back it up.

All that said, It's been a long time since I have really worked my geometry model or researched the geometry aspect of suspension!

Click to expand...

Thank you for getting back to me! I understand the correction now.

A roll center will always be more stable closer to the CG. This will result in less roll and more stability. The downside is the jacking force, as the moment is significantly increased. The roll center being an inch above the ground is pretty close to getting it on the ground and negates most of the jacking force. I am very curious to see what the suspension would be like optimized with the roll center on the ground. Dynamically the roll center should dip below the ground and jacking forces will be countered. I believe this is part of why the roll center moves in opposite directions when the car is lowered and the roll center is dropped below ground. Its the effect of negative jacking force. When the RC is on the ground, the jacking forces can be completely negated. Keeping the roll centers in similar places front and rear will result in a much more predictable car, but if they were both on the ground the car would have less force to overcome and ultimately more grip.

Thank you for responding and answering my questions! I have been looking to start modifying my Mr2 Turbo and when I look for research done on the cars suspension I cant find anything but your analysis. It's good analysis as well you produce a great kit! I was wondering if I could modify it in some way to test my theory and get the roll center on the ground while maintaining a good dynamic camber curve. Is there anything I can do to get it where I would like?

Thank you again!