Spring Rate/Motion Ratio Calculator

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MeCalledEvan
No not quite.

I will try to digest this some more, but I think that you're over-thinking this (which sounds strange coming from me). Assuming no bushing squish, etc, such that the geometry is constant, the suspension can only move up and down (albeit often in an arc, but as I just said above, this has only tiny effects on the motion ratio). All of those extra, lateral forces that you're talking about become additional vertical forces with regard to the suspension. So, yes, they will have effects on the amount of roll for a given lateral g (mostly via the roll-center height), but they won't change the motio ratio. They are merely additional forces acting on the outboard end of the suspension, which, after being leveraged by the motion ratio, become additional forces acting on the spring.



Edited 1 time(s). Last edit at 10/21/2013 02:23PM by Iowa999.

once again somebody droning on in an argument with only themself.
Misunderstand something simple in the early phase, write papragraphs off into the desert...
Yeah well I think we need MORE VIOLINS in school.

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John Vanlandingham
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Fuck off.

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Iowa999
Fuck off.

No professor, you shut up and learn..You aren't a rally guy, this is a rally forum not a forum for girly-men autocrossers which is what you are..
so you want to learn?
Shut up. You learn with your eyes and ears, Prof, not your mouth.

---

John Vanlandingham
Sleezattle, WA, USA

Vive le Prole-le-ralliat

www.rallyrace.net/jvab
CALL +1 206 431-9696
Remember! Pacific Standard Time
is 3 hours behind Eastern Standard Time.

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MeCalledEvan

No not quite. Here I will use Paint to create a very simplistic 2D representation and explain.

So, the tire contact patch is going to always be subject to 3 forces and 3 moments (when the vehicle is in motion and the tire is in contact with the ground). For the sake of simplicity, we are going to ignore all but two of the forces, and focus a little on FY (Lateral force) and mostly on FZ (Normal force). These forces are constrained by the control arms/trailing arms/swingarms/struts/whatever. A component of each force will (nearly) always go into each suspension arm.

In looking at my lovely diagram, you can see that in droop, the Lateral and Normal forces are partly going into the spring/damper, but also a component of each force is also going into the lower control arm (LCA). This will effectively increase your ride rate, and stiffen your suspension, because now you are partly using your control arm and chassis rigidity as a spring in vertical wheel motions. In a perfect world, your control arm and chassis have an infinite spring rate. So lets do some math:

Mmmmmm....since there is no possible vertical motion in the suspension from the Fy force only, then the spring can't directly enter into resisting Fy forces. As the Iowa guy says, any Fy forces that result in force on the springs are doing so because they are acting at the tire patch in a vector path that is not through the roll center; this imparts a rolling movement in the car (hmm... guess that's why it's called a roll center hunh?) which imparts more or less pressure on the springs. The springs and the anti-roll bars are both contributing to managing the rolling forces.

So the spring's rate is acting on 2 separate motions (pure vertical and pure rolling) and thus effects both. The arm ratio forces the spring rate to changed by the square of the ratio for vertical movement. (Jumps and landings, etc.) But any such ratios usually are different for the spring's effect on the roll 'spring rate'.

Ideally the anti-roll bar's anti-roll rate would be a lot higher than the spring rate in effecting roll forces, so that the coil spring rate would be a relatively trivial part in the anti-roll forces, and they could be changed without effecting the roll rate too much. But that is not always true; for a simple leaf spring live axle, the leaf springs are often the only roll spring force there. And at the opposite extreme, if you had one spring in the middle only then there would be no roll rate contribution from the spring at all. (This has been done at the local circle track, BTW, and probably at many tracks!)

As far as the wheel versus ball joint in measuring the arm ratio, they see the same vertical motion and thus the same rate. So just calculate it at the ball joint.

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starion887
So the spring's rate is acting on 2 separate motions (pure vertical and pure rolling) and thus effects both. The arm ratio forces the spring rate to changed by the square of the ratio for vertical movement. (Jumps and landings, etc.) But any such ratios usually are different for the spring's effect on the roll 'spring rate'.

I was with you up to the last sentence. The spring has no "idea" why the wheel is moving up -- it could be a bump; it could be roll -- the spring merely resists upward movement and it does so in the same manner. In other words, the motion ratio is the motion ratio, and doesn't depend on why the suspension is moving. Or am I missing your point?

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starion887
Ideally the anti-roll bar's anti-roll rate would be a lot higher than the spring rate in effecting roll forces, so that the coil spring rate would be a relatively trivial part in the anti-roll forces, and they could be changed without effecting the roll rate too much. But that is not always true; for a simple leaf spring live axle, the leaf springs are often the only roll spring force there. And at the opposite extreme, if you had one spring in the middle only then there would be no roll rate contribution from the spring at all. (This has been done at the local circle track, BTW, and probably at many tracks!)

Well, sway-bars have twice the effect on roll as they do on single-wheel bump (which is why people who run on flat surfaces love them). But sort of like how a spring has no idea why the suspension is moving, a sway-bar doesn't know if the body is rolling due to weight-transfer or if the suspension is uneven because one wheel hit a bump. So when the surface is rough, sway-bars end up transmitting more roll to the body, which is often unwanted.

Put another way, from the point of view of the bars, draw a line from the ground under the left tire to the ground under the right tire. If this line is tilted, as it would be when you hit a bump with one wheel, what the sway-bar is trying to do is roll the car to match the uneven ground. That's not good.

(If you were saying, instead, that you want different motion ratios for the bars vs the springs, then that's almost a given on most cars and you could always change the rates of each separately, anyway.)

In any event, for tarmac, you often see cars getting more than half of their roll resistance from bars. For snow over gravel, you often see cars with no bars at all. If you can come up with a way for a computer to tighten and loosen the sway-bar bushings (or otherwise change their rates on the fly) as a function of surface, then you'd have a dream set-up ... for the ten minutes before it was banned.



Edited 1 time(s). Last edit at 10/21/2013 08:34PM by Iowa999.

Quote
starion887
Mmmmmm....since there is no possible vertical motion in the suspension from the Fy force only, then the spring can't directly enter into resisting Fy forces.

I see what you're saying, but I still completely disagree. Sure this would be the case if your suspension components were all 2-force members. But due to packaging constraints, this is almost never the case. The example I can think of where this would be true is in a double wishbone suspension, where the spring/damper only constrains vertical motion. In say a strut-type suspension, this is absolutely not true. The spring/damper package constrains lateral, longitudinal, and vertical force components. Don't believe me? Then explain to me another reason why so many rally drivers bend rods, deform rod guides and oil seals, smack damper pistons against cylinder walls, etc etc (Hint - go draw a Free Body Diagram). Still don't believe me? Go pull the top bolt out of your knuckle bracket (which will turn your strut into a 2-force member), drive around, see how it feels, and report back.

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starion887
As the Iowa guy says, any Fy forces that result in force on the springs are doing so because they are acting at the tire patch in a vector path that is not through the roll center; this imparts a rolling movement in the car (hmm... guess that's why it's called a roll center hunh?) which imparts more or less pressure on the springs. The springs and the anti-roll bars are both contributing to managing the rolling forces.

Roll centers are a very touchy and foggy subject. I have an article written by Bill Mitchell that I would be willing to share with anyone interested. I cannot attach it here because it is 17 MB, so if you want to read it, PM me with your email and I'll be happy to send it along.

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Iowa999
If you can come up with a way for a computer to tighten and loosen the sway-bar bushings (or otherwise change their rates on the fly) as a function of surface, then you'd have a dream set-up ... for the ten minutes before it was banned.

Oh so like what Williams did (in concept) in F1 in the early 90s? Worked great! Though was quickly banned, and the complexity was pretty ridiculous.

**Edited for typos.

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"The more I learn, the more I realize I don't know and have so much more to learn." - Claude Rouelle, Optimum G lecture June, 2011



Edited 1 time(s). Last edit at 10/22/2013 09:47AM by MeCalledEvan.

Theory is great, but...
1- with car on levelish ground and tires at "hot" pressures, measure height of something "inboard" near the corner of the car in question (like the height of the top of the fender) and record it, then measure the height of something "outboard" (like the center of the wheel or similar) and record it.
2- jack the car up and put it on jack stands and remove the chassis spring in question. Re-measure the "inboard" height, reinstall the wheel, and either with a good hydraulic jack or other means, get the wheel to the same RELATIVE height to the inboard height I.e. if the car is now 12.75" higher than original measurement, then wheel will be 12.75" higher too. The wheel is now at "ride height" with the car in the air and no spring installed.
3- As accurately and repeatably as possible (I'm anal so I use digital caliper or similar) measure the gap where the spring used to be, and record.
4- place 1/8" shim under tire, and re-measure spring gap, and record
5- repeat, repeat, etc up and down as much as you want and record it .
6- do math: divide each wheel movement increment (0.125" in my example) by the corresponding change in spring length and you will have the actual motion ratio at the tire (where you actually care about it) for each position of the corner. You can see if its rising rate, falling rate, and its a real number, not simulated or calculated. Yes there are lots of other factors that go into a cars' resistance to roll, heave, etc, but most folks don't have the means to accurately measure or calculate any of it, or know what to meaningfully do with any of the information. Most importantly- test, test, test, drive all you can, make changes and record the changes and what you felt, drive more, and drive a bit more just be-fuckin-cause that's why we do this after all.

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ericlangbein
Yes there are lots of other factors that go into a cars' resistance to roll, heave, etc, but most folks don't have the means to accurately measure or calculate any of it, or know what to meaningfully do with any of the information. Most importantly- test, test, test, drive all you can, make changes and record the changes and what you felt, drive more, and drive a bit more just be-fuckin-cause that's why we do this after all.

Amen.
You can run numbers until your head spins and still end up with garbage and no seat time. The most valuable thing you can do is try it out and see how it works for you.

Thanks for bringing this full circle Eric.

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"The more I learn, the more I realize I don't know and have so much more to learn." - Claude Rouelle, Optimum G lecture June, 2011

The only counter-quibble I have to the idea of just trying it to see if it works is the problem of local minima. When everything is considered at once, it's a (highly) non-linear system, so this could be a serious problem. As a simple example, as you raise almost any car above its original ride-height, the roll centers shoot up. This might shift the trade-off for swaybars (that I brought up above) against having these things, because you are now resisting the roll due to lateral acceleration much more by the geometry; but it also might not shift the goal away from swaybars because now you are transferring more weight. Even more, on most cars, the front and rear roll centers move up and down at different rates, which would change the need for bars and/or springs at the two ends differently. A tweak-and-test approach might take much too long to find a new best combination. A little math to get a reasonable new starting point could easily be worth it. Just knowing that playing with ride height is simultaneously increasing weight transfer, but also countering roll via the heightened roll centers, is, IMO, useful, as well.

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Iowa999
A little math to get a reasonable new starting point could easily be worth it. Just knowing that playing with ride height is simultaneously increasing weight transfer, but also countering roll via the heightened roll centers, is, IMO, useful, as well.

Sure you are definitely correct, but then your challenge becomes being able to apply that math to the real world. If you have the means to collect and analyze quantitative data via accelerometers/linear pots/etc etc, your argument is 100% valid.

But if you're going by more qualitative methods, like driver feel, which almost everyone is stuck doing due to lack of resources, you then have to factor in an additional number of very complex variables. Driving style would be a good example of one of these variables.

At the end of the day, without some extensive data acquisition, all of the pretty numbers from the little bit of math you calculated are just that- pretty numbers that you can toss around in your brain. That effort would be more valuable if it were spent tooling around in your car doing what real people have to do: test and tweak.

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"The more I learn, the more I realize I don't know and have so much more to learn." - Claude Rouelle, Optimum G lecture June, 2011



Edited 1 time(s). Last edit at 10/24/2013 12:48PM by MeCalledEvan.