## Getting your Force Based Roll Center's

Here are our CFD links and discussions about aerodynamics, suspension, driver safety and tyres. Please stick to F1 on this forum.
First things first I guess. In order to calculate my FBRC Im going to need an actual corning force. So tired data being a premium, lets use a simple eqtn I found in C.S. tune to win, where Cornering force = (friction Force) x (weight over f or r axle). I know he uses a graph of coefficient of friction vs. normal load but, im poor and can't afford something like tire testing.

My second question is this, I read mitchells article about the FBRC/FAP. My understanding is that you go about finding your roll center the same way you always did using the kinematic, but the important bit is the the Force Application Point(s) which is basically any point or two that intersects the vertical c.g. axis.

Yet, Paul Haney (in his book) goes about finding the roll center using the classical method of instant centers, and applies the lateral and vertical forces at the RC.

I understand that the kinematic RC has some weak points 1 being that the methods used to find it are based on rigid bodies, yet we know that nothing in the real world is absolutely rigid. And unfortunately my dynamics book doesn't have a section on non-rigid four-bar link problems.

So can anyone shed some light? That fact that you can not find the derivation of the FBRC in any kind of literature sort of scares me into thinking that a) not very many people understand it and b) it is extremely complex to derive, given that people are only explaining concepts rather than showing how to find it.

Tom im awaiting your reply as I feel you will more than likely know how to solve this.
fastback33

Joined: 29 Aug 2007

You make an important observation in that people take varying approaches to engineering problems - in this case be it kinematic or "force based" roll centers. Bear in mind, neither of them is necessarily right, wrong, or better than the other. They're all just an approximation... some better suited for certain situations than others.

To be honest, effects of tire lateral stiffness might just as, or more significant than the different between kinematic and force centers. As a further admission, I've never seen a good work-through of the difference between the two in a practical example showing level of significance. Ultimately when you're to the point of having to worry about the difference between the two, using a multi-body simulation code automatically takes care of all that - tires and compliances included!

My only words of advice are to pretty much ignore the conclusions that people come up with that have no true basis - no matter who it is. If you want to understand something, prove it out yourself. This may be a good case for it. Draw out some scenarios, 'do the math', and let us know what you come up with.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

In all honesty, I would think Paul haney's assumption is probably the most correct, here's why.

early in your(our) engineering career you take statics, dynamics and, strengths. In dynamics you learn about instantaneous center's and how to find them. This is applicable to cars thanks in part to four bar linkage problems. Which results in you being able to find your instant center. Here is the problem(s) I have with the kinematic roll center. It's this imaginary point that supposed creates a moment with the center of gravity. How can an imaginary point without any physical connection to the car or suspension create forces?

If the forces were applied at the instant center, that might make more sense to me. The only proof I have that this exists is jacking forces, and the supposed moment arm the rc and cg have with each other. Which are the only reason i'm bothering with this concept.

So, I have been drawing up differing scenarios with a symmetric case and asymmetric the problem I struggle with is how to connect an imaginary point with an actual force? Put simply, I view FBRC's as a tiny bit more involved statics problem with an instant center. I used techniques which we are taught in our beginning engineering courses. I have thought of posting them up, but there isnt really anything profound within the proof especially if I can't find a roll center.

Haney is correct because he takes all of these concepts based on engineering principles and applies them to cars. Hell, even in RCVD you see the milliken brothers use the kinematic concept. (granted it is aged a bit)
fastback33

Joined: 29 Aug 2007

There must be a "roll center point" in some car, since the car must be turning around some point.

As an approximation you can use the Kinematic Roll center, which atually is a 4linkage instant center applied twice.(this I read from somewhere I don't remember)

The first 4 links are: two wishbones, chassis, hub/upright.
Oh well, I found it, better read it yourself :p

Vehicle Dynamics

All these ideas are mostly valid to know how will your suspension react, but not how much.

I still don't know why there's SO much interest in trying to know where is the real roll center. As if doing so would grant you that you can design your car and be utterly fast.

As JT said, you still need to know about tires. Probably the best solution would be to enter all your data in a multibody physics simulator and watch the parameters there.
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Caito

Joined: 16 Jun 2009
Location: Argentina

Well for one, Bill and Doug Milliken are father and son, not brothers

I'll say it again, kinematic centers are just an approximation and an easy tool for gauging the coupling of forces. You are correct, they are imaginary points and not actual physical entities. But if they're easier to calculate and close enough to the "real" solution, why not use them?

I'm a big proponent of the notion... use as simple a model as you possibly can, that gives you enough resolution to answer the problem at hand.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

You know it is funny. at the beginning of my whole vehicle dynamics hobby, I wanted all of the concepts and hated the math. Now that I've been in it a couple years, I want a little bit of concept and then all math. The mathematics are the ONLY way to actually understand what is happening. Other than RCVD i wish there were more math based books, that go into simulation and possibly a multibody systems approach using matlab or something.

I appreciate the insight guys!
fastback33

Joined: 29 Aug 2007

fastback33 wrote:Other than RCVD i wish there were more math based books, that go into simulation and possibly a multibody systems approach

If only...
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

In my experience, kinematic roll centers are directionally correct at best and completely dangerous at worst. Roll-center analysis invariably implies the creation of a 'pin joint' at the roll center location, where forces are transmitted between the sprung and unsprung bodies; this aspect of RCs is true of kinematically determined roll-centers and force-based methods (Mitchell, Ortiz, etc). Force-based roll center's advantage over its kinematic cousin is that distribution of lateral tire load is accounted for. Creation of a singular joint is especially suspicious for independent suspensions. The notion of a "roll moment arm" between the CG and roll center is a nice thought, but is a gross oversimplification.

However, regarding independent suspension, the instant center is a much more valid approximation of a pin joint and is a much better location to apply suspension forces. So a better option for the original poster is to determine a jacking coefficient at each corner independently (using instant centers), which is based in mechanical statics. The concept can be visualized in a Free Body Diagram. Without tire data, you may be unwilling to assume a distribution of tire force, in which case you will stop at the jacking coefficients.

As an aside, it is important not to confuse the "roll center" you read about in Carrol Smith books with a modal center located between the trackwidth, which is derived from a 2 DoF (roll & heave) modal analysis of a vehicle. It is a more common engineering exercise to investigate modal analysis in the pitch plane, but it is equally valid in the roll plane.
GSpeedR

Joined: 14 Jul 2011

GSpeedR wrote:In my experience, kinematic roll centers are directionally correct at best and completely dangerous at worst. Roll-center analysis invariably implies the creation of a 'pin joint' at the roll center location, where forces are transmitted between the sprung and unsprung bodies; this aspect of RCs is true of kinematically determined roll-centers and force-based methods (Mitchell, Ortiz, etc). Force-based roll center's advantage over its kinematic cousin is that distribution of lateral tire load is accounted for. Creation of a singular joint is especially suspicious for independent suspensions. The notion of a "roll moment arm" between the CG and roll center is a nice thought, but is a gross oversimplification.

However, regarding independent suspension, the instant center is a much more valid approximation of a pin joint and is a much better location to apply suspension forces. So a better option for the original poster is to determine a jacking coefficient at each corner independently (using instant centers), which is based in mechanical statics. The concept can be visualized in a Free Body Diagram. Without tire data, you may be unwilling to assume a distribution of tire force, in which case you will stop at the jacking coefficients.

As an aside, it is important not to confuse the "roll center" you read about in Carrol Smith books with a modal center located between the trackwidth, which is derived from a 2 DoF (roll & heave) modal analysis of a vehicle. It is a more common engineering exercise to investigate modal analysis in the pitch plane, but it is equally valid in the roll plane.

I've toyed with the idea of what I think you stated, where you apply your contact patch loads at the instant center. I've never done it that way only merely played with it in my head, which I assume you are then able to generate your jacking forces no? This is what bothers me about that, wouldn't you then after finding jacking forces be able to calculate your tire load distribution which is basically what finding your FBRC is giving you also? Thus the whole concept of doing the instant center method twice would be pointless and we wouldn't even need a roll center...

And not sure what you're on about with the modal center idea?
fastback33

Joined: 29 Aug 2007

Now I'll admit, if Ortiz and friends have some stuff written on the specific topic - I haven't read it. I only know what I've seen in practice.

In my mind, I picture the "roll" center as a point that defines the jacking coefficient of the left and right side of the suspension simultaneously; jacking coefficients which are (in theory, not practice) independent of tire lateral forces. However, by applying varying amounts of lateral force on either tire there will varying amounts of both direct load transfer and a net jacking force.

Really the question to ask is, when determining the jacking coefficient of a half suspension... how much difference is there between the "kinematic" approach of finding a-arm intersection of control arm planes and drawing that back to the tire footprint center, versus doing a statics analysis. Maybe I'll just sit down and work it out at some point this week.

As I say, all of this neglects the effects of lateral tire deflection - but that's a separate topic.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

fastback33 wrote:
I've toyed with the idea of what I think you stated, where you apply your contact patch loads at the instant center. I've never done it that way only merely played with it in my head, which I assume you are then able to generate your jacking forces no? This is what bothers me about that, wouldn't you then after finding jacking forces be able to calculate your tire load distribution which is basically what finding your FBRC is giving you also? Thus the whole concept of doing the instant center method twice would be pointless and we wouldn't even need a roll center...

And not sure what you're on about with the modal center idea?

Don't worry about the modal center stuff...some people use the term "roll center" to define a point useful in vibration analysis.

I understand why people want a roll center: they want a single number they can display on their sheet and compare with other singular metrics like roll rate. Using instant centers is fine, that's a valid kinematic analysis that's been done on linkages for a hundred years. Transferring tire loads to the instant center gives the resultant force coupling (vertical/lateral) for that individual suspension and that is what jacking is. When you take that analysis the extra steps and combine the suspensions together is where you run into problems; an independent suspension has distinct application points. If you had a lot of time and constructed a complete kinematic independent front suspension (including every arm and part) there would be no method to create a roll center. The chassis couples an independent suspension together, I don't think we need to do it beforehand. Needless to say, the sprung mass certainly doesn't roll about a point determined purely from suspension kinematics (or even from FBRC)...a vehicle with asymmetric springs should make that obvious.

The only "roll center" that makes sense is that output from an ADAMS model, which analyzes the forces about the chassis and calculates a neutral point. So basically it determines what the chassis actually rolls about at one instant in time. It is post-processed, however, it can only be determined after you've summed your forces and moments about the chassis.

I will conceded, that there have been plenty of races won with roll centers and for a purely symmetric (kinematically and setup-wise) formula style racecar, then they may be "close enough". I think simply determining jacking coefficients for each side is more valid and more informative. Others may disagree.
GSpeedR

Joined: 14 Jul 2011

Good post GSpeedR.

I've always found the force based roll centre proponents slightly loose their way when they still try and manufacture a point on the vehicle centreline.

In practice the kinematic roll centre or instant centre both give a reasonable approximation to what's going on without needing a detailed calculation.

If you have a nervous rear end on entry to slow corners and the next session's two hours away are you going to consider a lower rear RC (along with some other changes) or are you going to do a full ADAMS analysis and find the roll axis for a specific manoeuvre?

That's not to say one is better than the other, but obsessing about the precise lateral migration of the kinematic roll centre is as silly as pretending that the static kinematic RC height isn't a useful metric for all but the most asymmetric race cars.

Ben
ubrben

Joined: 28 Feb 2009

GSpeedR wrote:I think simply determining jacking coefficients for each side is more valid and more informative. Others may disagree.

I agree.. but my point is, those two jacking coefficients can equally be expressed by themselves as ratios, or as a (Y,Z) coordinate for the intersection of those two vectors (in an opposed force compliance test on a K&C rig for example).

I think a lot of this comes down to the term 'roll center' being a poor description, and even worse how much attention is paid to it. I don't particularly care about the point about which the sprung mass is rolling at a given point in time. Big deal. The force coupling is where it's at.
Grip is a four letter word.

2 is the new #1.
Jersey Tom

Joined: 29 May 2006
Location: Huntersville, NC

I agree with Tom.
"I was blessed with the ability to understand how cars move," he explains. "You know how in 'The Matrix,' he can see the matrix? When I'm driving, I see the lines."
n smikle

Joined: 12 Jun 2008

What works for me is to calculate kinematic RC (I use susprog) at three points:
1) static
2) intermediate between static and maximum roll
3) at maximum roll

For practical reasons I ignore wishbone and chassis flexibility and to calculate maximum roll I have damper sensors. Tyre deformation roll is apart.

I find it useful to know RC migration to have bettwer estimates of what happens speed and force wise through the dampers and set damper curves oriented to the stimulus I measure.

That is only for rapid assesment of the "amateurish" teams that I work for as a consultant. I would use better and more complete tools for other cases if required.
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Belatti

Joined: 10 Jul 2007
Location: Argentina

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