Effects of tire Diameter on Roll Centers / Roll Stiffness - MR2 Owners Club Message Board
 
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post #1 of 13 (permalink) Old February 10th, 2009, 00:57 Thread Starter
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Effects of tire Diameter on Roll Centers / Roll Stiffness

I have been playing arround in Optimum K again, just trying different things and trying to learn a bit more while I'm at it. I discovered something interesting, quite by accident.

I had loaded up a theoretical model of the MR2 at stock 91 ride height, but based off the tire setup on my car, which is 245/40-17 rear, 225/45-16 front. I was looking at the roll center heights, and found that the front was about 2.6" off the ground and the rear was about 3.6" off the ground. I then got to thinking, what if the higher rear roll center is caused by the taller rear tire. I remodeled it for a rear tire with a 1" smaller diameter, dropping the entire car .5" in the rear. This lowered the rear roll center by LESS THAN .1".

So the CG dropped by a half an inch, but the roll center only dropped by a tenth. Remember, if you bring your CG and your roll center closer together you reduce body roll. At first I was baffled by this, but then I remembered that part of the calculation of roll centers involves the tires contact patch. If you bring the contact patch closer to the CG without changing the suspension geometry you bring the roll center and the CG closer together.

Now, practically applying this may be difficult, since its tough to upgrade tires on our cars without increasing diameter (due to limited selections), but its something to keep consider.

Last edited by Alex W; October 13th, 2014 at 21:11.
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post #2 of 13 (permalink) Old June 20th, 2009, 01:38
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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.
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post #3 of 13 (permalink) Old December 2nd, 2009, 09:21
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Very interesting so since I don't have your program Alex W what is the cg compared to roll center on the stock tires at stock height compared to your detailed setup? I would think that getting closer would increase positive handling values and decrease autocross times right?
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post #4 of 13 (permalink) Old December 6th, 2009, 19:43 Thread Starter
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Well, I have no idea where the CG is actually located on the MR2, so I can't really quantify any of this, but you are correct that, at least in theory, bringing the roll center and the CG closer together should reduce body roll / improve handling. This is what people THINK they are doing when they lower the car, unfortunately the roll center drops way faster than the CG.
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post #5 of 13 (permalink) Old December 10th, 2009, 11:54
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So what you're really saying is that using smaller diameter tires causes the CG to drop by half the diameter change, but the roll center height doesn't drop nearly as much. In other words, you can use a smaller tire to lower the mass centroid axis and decrease the roll moment at one axle without increasing roll stiffness or jacking.

And at the same time you're probably reducing unsprung weight. Sounds like win-win-win to me. What is the downside that I'm missing?

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post #6 of 13 (permalink) Old December 10th, 2009, 12:35 Thread Starter
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Biggest downside is probalby lack of tire selection. Its very difficult to get sticky, and especially wider sticky tires on an MR2 without increasing the diameter vs stock.
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post #7 of 13 (permalink) Old December 10th, 2009, 12:52
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Not so much for the Mk I owners

Personally, rather than get a big street tire, I'll buy a small R-compound or other aggressive tire for my fun driving and an all-season for DD'ing. Mk I's can fit a 13-inch wheel which opens up the tire options when talking about really aggressive compounds. Plus the decrease in unsprung and rotating mass is a huge benefit. I'm planning on getting some 13s sooner or later for some fun tires. Something like a a 225/45/13 or 215/50/13, which will take almost a full inch off of Mk I ride height and weighs several lbs less than a stock 185/60/14 RT615, for example.

But I guess that brings up the debate of whether you want a lot of grip for a DD or not. If you do, you'll have to pay for it with much more expensive and shorter-lasting tires. Personally, driving on the street is just about having fun and I don't need huge grip to have fun.

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post #8 of 13 (permalink) Old December 10th, 2009, 20:05 Thread Starter
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Quote:
Originally Posted by bentheswift
Not so much for the Mk I owners

Personally, rather than get a big street tire, I'll buy a small R-compound or other aggressive tire for my fun driving and an all-season for DD'ing. Mk I's can fit a 13-inch wheel which opens up the tire options when talking about really aggressive compounds. Plus the decrease in unsprung and rotating mass is a huge benefit. I'm planning on getting some 13s sooner or later for some fun tires. Something like a a 225/45/13 or 215/50/13, which will take almost a full inch off of Mk I ride height and weighs several lbs less than a stock 185/60/14 RT615, for example.

But I guess that brings up the debate of whether you want a lot of grip for a DD or not. If you do, you'll have to pay for it with much more expensive and shorter-lasting tires. Personally, driving on the street is just about having fun and I don't need huge grip to have fun.

Yeah, thats very true. If you can get down into a 13" or so race tire that still has super short sidewalls (see these a lot of some prepared cars for autocross) thats where you can really take advantage of this effect. Another benefit is the gearing, smaller tires = more torque.
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post #9 of 13 (permalink) Old January 3rd, 2018, 19:53
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Jacking forces vs. Roll

Quote:
Originally Posted by Alex W View Post
Well, I have no idea where the CG is actually located on the MR2, so I can't really quantify any of this, but you are correct that, at least in theory, bringing the roll center and the CG closer together should reduce body roll / improve handling. This is what people THINK they are doing when they lower the car, unfortunately the roll center drops way faster than the CG.
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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post #10 of 13 (permalink) Old January 4th, 2018, 08:35 Thread Starter
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Quote:
Originally Posted by Tyler R View Post
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
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!


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post #11 of 13 (permalink) Old January 10th, 2018, 19:20
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Quote:
Originally Posted by Alex W View Post
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!
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!
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post #12 of 13 (permalink) Old January 16th, 2018, 12:19 Thread Starter
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I was looking at my model a little yesterday, and even with my geometry kit, at my current ride height it looks like my roll centers are fairly close to ground level. Slightly above, but not by much. I will have to re-visit the model to say with any more accuracy than that. At any rate, it wouldn't be hard to adjust the ride height to put them at ground level, if that was your goal. So, modification to the kit probably wouldn't be required, just ride height adjustment.


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post #13 of 13 (permalink) Old January 16th, 2018, 12:20 Thread Starter
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Quote:
Originally Posted by Tyler R View Post
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?
I was looking at my model a little yesterday, and even with my geometry kit, at my current ride height it looks like my roll centers are fairly close to ground level. Slightly above, but not by much. I will have to re-visit the model to say with any more accuracy than that. At any rate, it wouldn't be hard to adjust the ride height to put them at ground level, if that was your goal. So, modification to the kit probably wouldn't be required, just ride height adjustment.


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