That 37% difference between innermost and outermost tread was to illustrate to you that it's the camber curve that's softening effective spring rate at the wheel on cornering, not the swinging path of the spindle assmebly that you seem to think of by the following quote. "We have a doube wishbone suspension so the virtual center of rotation is very far from the wheel". In-wheel double wishbone suspension generates much steeper camber curve than the most commonly used MacPherson strut suspension and therefore in-wheel double wishbone has a closer virtual center (in your term) and has a bigger effect of softening effective spring rate at the wheel on cornering. Plus there's a common misconception that effective spring rate at the wheel is proportional to the motion ratio and therefore a little change in leverage doesn't matter. Effective spring rate at the wheel is NOT proportional to the motion ratio, but to the SQUARE of motion ratio. The 37% number is to illustrate how significant is leverage just from camber curve ALONE, not to directly refer to an offset change.

You can have motion ratio of a control arm due to mechanical leverage. You can have motion ratio of a shock absorber due to non-perpendicular geometry to the a-arm. You can have motion ratio on a spindle due to camber curve. It's clear that when I say motion ratio in my context, it refers to the overall motion ratio of the amount of spring compression for the corresponding vertical movement of a particular point on the tread. It's the overall motion ratio that determines the effective spring rate at that particular point on the tread. What's not clear about it?

And I'll say it again here that I've been saying all along that you may not notice any change in handling balance with the usual mild offset change on the S. I've been trying to illustrate the "extreme case" like my miata where the race tires stick out 2 full inches than stock in response to OP's point of "read on some forums and some mags".

 

So you're saying that the effective change in the length of the lever arm from the virtual (or "instant", if you don't like "virtual") center to the new location of the applied force has nothing to do with the wheel rate?

Is it possible we're thinking of the same thing but explaining it in different ways? Obviously this linkage and its instant center is directly related to the fact that it causes increased negative camber as it is compressed.

Agreed. But that center is always moving as the suspension moves, and IS far inboard. It must be inboard of the inner pivot points. So even though it may be closer than a McPherson strut system, it is still far from the hub compared to the offset changes we're talking about, so the effect is not large. Let's assume it's two feet from the hub at nominal ride height. The change in your lever arm is less than an inch (offset, etc.) over 24". This is yielding a little over 3% change in leverage.

What's not clear about it is that your calculations above are based on tread width, which had nothing to do with the topic at hand. Why not just use numbers relevant to the thread? Then maybe your calculations would support your final statement and I think that would have been less confusing.

 

That's of course not what I mean. I'm not exactly sure what you mean but don't assume what I say and then call BS. My statement you quoted says there's 37% DIFFERENCE in wheel rate between the innermost and outermost tread. That means for every inch the innermost tread rises up, there's 17% more upward movement on the outermost tread. And this 17% difference comes from just camber curve alone (as you can see from my previous calculations using 1-deg-per-inch), regardless of how your shock absorber is attached to the lower arm or how the spindle assembly move up/down in an arc or what type of suspension you have. As long as you get the same 1-deg-per-inch of camber curve and 9.5" of tread width, the 17% difference in motion ratio and 37% difference in wheel weight are there regardless. This is targeted at your statement of "We have a double-wishbone suspension so the virtual center of rotation is very far from the wheel". I think what you misssed here is the word DIFFERENCE. I'm not saying the absolute motion ratio on the outermost tread depends on camber curve alone. I'm saying the DIFFERENCE in motion ratio on the outermost tread COMPARE TO the innermost tread depends on camber curve alone.

Secondly, assuming you refer "rotation" in that statement to the -ve camber gain, then the steeper the camber curve the closer this virtual center of rotation. Double-wishbone suspension has much steeper camber curve than the more common MacPherson strut suspension. So because we have a double-wishbone suspension, the virtual center of rotation should be closer not farther.

The length of this "linkage" (see assumption above) exactly reflects the camber curve and like I said it's camber curve alone that generates the 37% difference in wheel rate.

It doesn't matter how this center moves. See this is what you seem to think how the spindle assembly move up/down affecting the virtual centre of -ve camber gain and thus wheel-rate-softening effect. That's what triggered me to clarify. The spindle assembly can move up/down in any wierd arc (generating different roll centre height) all it wants and yet it's ONLY the camber curve (or virtual center as you describe) that makes the DIFFERENCE in wheel rate between innermost and outermost tread (i.e. wheel-rate softening effect) because the same wierd arc affects both innermost tread and outermost tread. We're talking about DIFFERENCE, not absolute motion-ratio. Why do we talk about difference instead of absolute motion-ratio then? Because we're talking about how camber curve "soften" wheel-rate, not "how camber curve affects wheel-rate".

Like I've been saying all along, you most likely won't notice the difference on the mild offset change in the S. My initial reply with the extreme case of my miata was to respond to OP's point of "read on some forums and some mags". It's not misconception like you said earlier. It happens in extreme cases, especially when front/rear camber curves are vastly different.

My original question to you of "what's not clear" refered to your statement "I'm also a little confused by your use of the term motion ratio". Anyway...

Like I said all along, you most likely won't notice the difference on the mild offset change in the S. There's no need to throw in numbers to support that. Again, like I've mentioned before, the numbers I threw in was to tell you the importance of camber curve alone on softening wheel weight while cornering (because of 2nd-order relationship). And because camber curves in some cars can be dramatically different front and back, in some extreme case increasing wheel offset dramatically even with same amount front and back CAN throw off handling balance, especially when you take into account of weight jacking I mentioned earlier which has a much bigger effect. It's not common misconception.

 

Cool.

I should elaborate on why I said "common misconception." I said that because I've seen people explain, many times, the leverage change as if it were a pure swing-arm suspension. You know, like in the old VW bug. I was just trying to say that the effect would be less than that of that type of suspension.

I still think we're saying the same thing, but different ways. Anyway, I think we've beaten it to death. I'll have to dig out my old suspension book to see for myself if I'm FOS or not.

Cheers.

 

It's all cool.

Ah, now I know why you said what you did! Compare to swing axle, yes the spindle in a double-wishbone suspension doesn't rotate as quick a rate to the lower a-arm (as in VW swing-arm suspension) and therefore double-wishbone may not generate as much camber curve as VW swing-arm (depending on VW swing-arm length). So compare to VW swing arm, then yes the double-wishbone suspension may have farther virtual centre than VW swing-arm. I never thought one would compare double-wishbone suspension to VW swing-arm.

I guess we are talking the same thing in different ways then. So no, you're not FOS.

 

Here is a (last?) drawing I would like to share.
It shows a cross section of the frontend of the car during hard righthand cornering with max + (top) and max - (bottom) offset.
The "tyres" are made of non deforming stuff.
The one and only thing that doesnt change during cornering is the road itself (duh) so I started to draw that line first.
Even with lots of neg. camber curve the INSIDE of both wheels stay in contact with the road.
If you put the two drawings on top of eachother you will see that the max - offset (the bottom drawing) brings the car closer to the ground.
In real life tyres are not made of solid rubber so things will be different again.
More body roll for one.
Thats what I ment with sidewall stiffness having an effect on handeling/balance/cornering too.

The proof of the pudding is in the eating.
lets eat

 

Like I said before, it's impractical to have dynamic -ve camber on the outside tire on hard-cornering.

 

Very interessting and usefull thread!

Thnaks!