1. Some of the recent posts on this thread are pleasing, but most are disappointing.
~o0o~

Particularly pleasing is that Tim keeps trying to get back to the topic of...
Posted by Tim:
... talking about horizontal migration of the pitch/roll centres. I.e. lateral roll centre migration and longitudinal pitch centre migration. They seem to be a pretty useless construct to me...
Also that both Tim and Geoff are supporting their views with numbers and calculations, which are easily verified or disproved by any interested reader, unlike the usual racer's anecdotes of "We gave it an extra half-turn of xxx, and gained 2 seconds!". Thank you both very much for that.
~o0o~

Claude,

Particularly disappointing is that you keep trying to avoid the very straightforward questions I asked you back on page 3. Is a R/PC that has migrated horizontally 200,000 km, and is at an altitude of 2,000 km, in a GOOD or BAD place? And WHY?
~o0o~

And much more that is disappointing.

1. There still seems to be a lot of confusion between FORCES and MOTIONS. The above R/PCs are found by a kinematic analysis of the suspension linkage (ie. by finding the "n-lines", or "force-lines"). But this is done for the purpose of calculating the control-arm forces acting from-ground-through-wheelprint, and these forces' subsequent affects on the car body. VERY IMPORTANTLY, these R/PCs in NO WAY WHATSOEVER (!!!!!) characterise the instantaneous MOTION of the car. The car moves about a "centre" (in 2-D), or a "motion screw" (in 3-D) that is totally unrelated to these "kinematic/force-based" R/PCs. If you do not understand that, then you must go back to Square One.

2. Claude, you do not appear to understand the above point.
Posted by Claude:
I do not have an issue to have a roll center going through the ground...except that at that time the lateral roll center migration will be difficult to control. But.... as Geoff remarks infinite left or infinite right, it is still a huge inertia so if you look at the transient behavior the effect is small if not negligible. Similarly I do not have a problem with a roll center crossing a tire (well.... I am a bit less sure about that) but I do have a problem when the front roll center goes towards one side of the car and the rear one towards another.
Why the problem shown in bold? I suspect you are confusing "places where forces are combined", with a "motion axis". Is that why you often refer to these as "roll or pitch axes"? If so, then you must really learn more about the dynamics of bodies.

3.
Posted by Claude:
Many people look at roll centers ... as the intersection of "forces lines" but they ignored the Huygens (or parallel axis) theorem which will influence the rotational acceleration of both suspended and non suspended masses.
This is PURE CODSWALLOP!!! It does seem to confirm your misunderstanding above (ie. points 1 & 2). To restate the obvious, the car does not rotate about your "roll or pitch axes" (ie. the line that passes through the R/PCs). To assume this, and then want to invoke the "parallel axis theorem" to analyse the Dynamics, is sheer nonsense. As is much else in that post...

4.
Posted by Claude:
Roll center is primarily about transient: ....
...
That means that the lateral movement of the roll center influences the suspended mass inertia, its stability, its response and the roll frequency, the need of roll damping.
More bulldust of the above nature...

5.
Posted by Claude:
Believe me when I teach in India or South America or Asia to young students ... I can't rush to jacking forces in the first 3 day seminar; If I do I lose 90 % of the audience....
Simple then complicated, not the other way around.
Claude, you are teaching an unnecessarily complicated form of VOODOO and BLACK-MAGIC, with a large amount of BULLDUST rolled in. Much of what you are teaching above has no connection with reality. So the more the students learn, the harder everthing is for them to understand. So then you tell them..
- And at a certain time you need to stop the intellectual...gymnastics and go testing.
This is simply your excuse for not knowing what you are talking about. Your theoretical Voodoo-Bulldust is no predictor of car behaviour, so you have to "go testing". Enough practical trail-and-error will find the solution to any problem. But if you want to speed things up by using "theory", then old fashioned Newtonian Mechanics is much simpler, and infinitely more accurate, than the rubbish you are teaching. Jacking forces can be explained on Day One, in a very simple way. Please read the "Jacking Force" thread, and if you have difficulty with it, then ask for clarification!

6.
Posted by Claude:
[Quoting Tim->] "What is important to look at, in my opinion, are the force line slopes as the car rolls." You are absolutely right. In steady state. What about transient? What about the effect of suspended and non-suspended masses inertias around their respective instant centers?
Once again, this seems to relate to your complete misunderstanding of Point 1 above. Claude, you must go back to Square One. In this case Square One is Newton's First Law, aka Galileo's Law of Inertia. Anyone who does not have a strong appreciation of the cause-effect relationship in this Law (actually, a "postulate", or "axiom") will never understand Vehicle Dynamics. Or, for that matter, any Dynamics.
~o0o~

Bottom line, all of this stuff is easily understood through the methods of very old-fashioned Mechanics. No "complete system of second order differential equations" is needed! (I think Claude suggested that, but I couldn't find the quote...). In fact, no "cogitatio caeca" (= "thinking blind", = analysis via algebraic equations) is needed!!! I still haven't got around to browsing my copy of Den Hartog's "Mechanics", written in 1930s? and recently bought off the Interweb for \$3.99, but I am sure all that you need is in there.

Z

2. This is a great thread and discussion between three engineers I've had the pleasure of meeting in person (Tim, Claude and Geoff) and one I haven't in Z.

I have to say in Z's favour that his graphical explanation of jacking forces on the thread he mentioned is brilliant. It really opened my eyes and the fact that it can be explained so elegantly and visually means it would be better to start here than roll centres.

I can also understand how Z can rub people up the wrong way. Of course his prerogative but Claude is right to point out that teaching is about more than drilling facts into people. Inspiring the class matters, and Claude is a master at this.

Good debate as ever, but as Geoff pointed out it's just us old boys a lot of the time :-)

3. Originally Posted by Claude Rouelle
Tim,

Excellent.

We do agree much more than we disagree.

1. Were you able to figure out all this the first or second year of engineering school or FSAE? Believe me when I teach in India or South America or Asia to young students who discover race car, race car engineering, and simply how a car works I can't rush to jacking forces in the first 3 day seminar; If I do I lose 90 % of the audience. They would be overwhelmed and discouraged. Z can say that the teaching is going down the drain (he could be right but what I do not doubt is about the hunger of the students to learn, wherever they are from) but I can't change the reality of their starting point. Simple then complicated, not the other way around. I go though more details and in our professional workshop and/or our university courses. At OptimumG we have created the transient version of the "magic number" (anti roll stiffness distribution percentage) where dampers, inertia and tire deflection, tire forces and moving non linear kinematic (with or without compliances) are taken into account. I have tried to present this in a 3 day seminar to young students who discover VD ...that is the time where you start to see the guys yawning, checking their SMS or going to the bathroom. Nobody wins at that time.
Good question. The actual mechanisms behind roll centres only clicked for me a couples years ago. I was having a discussion with someone about K&C data and they mentioned the usefulness of looking at Fz vs Fy during a lateral compliance test and it suddenly hit me like a truck. I thought f*** me, how did I not notice this before. This being:
1. The Fz vs Fy IS the anti roll (geometric load transfer) effect produced by ICs being above the ground.
2. In fact the dFz IS actually the jacking force and that is what is giving the anti roll effect. Turns out jacking forces they actually aren't evil at all.
3. Exactly the same mechanism is working longitudinally and is known as anti dive, squat, lift, raise

The pre-requisite being that I had previously proven to myself mathematically the the front/side view IC's are a valid construct and can (within limits) in fact work as an instantaneous "pin joint" between the body and hub. The geometric roll centre does no such thing.

I think the reason it took so long to sink in is that I had to unlearn everything I had read and heard about geometric roll centres in the 5 years before hand.

While we are on the point of education, I'd like to share my experience where I have been in the position in the last couple of years where I had to teach a couple of people (yes literally only 2) how suspensions work in a very short time period. They were engineers, but knew absolutely nothing about vehicle engineering. I spent about 1 hour explaining things like this:
1. I explained to them the concept of the (front/side view) instant centre (not a roll centre) and how it is just an application of four bar linkage theory.
2. I suggested to them to look at the front view kinematics as 2 instant centres which pin the wheel/hub to the chassis. I draw a swing arm axle on the page to start the discussion.
3. I tell them to imagine a cornering force at each wheel. At this point its blindingly obvious that the cornering forces are creating torques about the ICs such that the outside wheel is being shoved into rebound and the inside wheel into bump.
4. Explain to them that load transfer (Ay x CGh) is doing the opposite (outside in bump inside in rebound)
5. At this point they realise themselves that the lateral forces at the contact patches combined with the ICs above the ground work to counteract the rolling moment induced by load transfer.

And boom, they understand suspensions better than most people in the industry. In about one hour, the basics are in their head and I didn't mention the word roll centre once. Yes there are some simplifications but each step can be completely explained with a free body diagram.

Conversely, when I first read about geometric roll centres, It required a leap of faith because I didn't understand how drawing all of these lines nails down the point that the body rolls about. But I thought that its so complicated that it must be right. I ran with it for years but it never sat well with me.

Ironically I still use the geometric roll centres and my own spreadsheet (which is doing the classic LLTD calcs) to do baseline setups. Its not a bad tool for steady state setup, especially for road cars where you have more similar cornering forces left and right since you are well under the limit. I think the classic roll centre theory is a decent approximation for this job and the cost in computational time and man hours is practically zero. When you consider that the springs you choose will eventually be overridden by the driver's subjective feedback, there no point wasting a lot of time calculating the spring rate in any more detail than you need.

Originally Posted by Claude Rouelle
2. Look at a Nascar or a Grand Am or a good GT car or an LMP1 and observe the front splitter left and right ride height pretty good consistency despite the braking, acceleration, banking, aero effect of speed, lateral G, tire deformation etc... They are not on bump stops most of the time; that I know so. Their "pitch axis" is like an "hinge" quite often parallel to the ground which helps them to keep the best possible downforce. They then play with the rear static ride height, rear springs, the whole car kinematics dampers and ARB, inertias etc to give their car the attitude and therefore the aerobalance they want. For a race car performance or a passenger car crash avoidance (active safety) it is all about transient. Everything else are just pictures of a film that we stop so that that we can understand the steady state behavior. But we forget to move the film back to its real speed
I believe all of that. I just don't believe it has anything to do with a geometric roll centre which is the current discussion point.

In terms of controlling the roll motion have a read of this SAE paper and consider this:
• When the outside damper is hard on the bumpstop. The outside wheel vertical movement becomes zero while the inside still moves. Your roll centre (as in the roll motion axis) is now the contact patch of the outside wheel.
• Now consider the point just as the bumpstop starts to engage. The outside wheel rate is increasing and its movement is diminishing. The inside wheel continues to move into rebound unrestricted. The motion roll axes is then somewhere in betrween the CL and the outside wheel is it not?
• Now forget the bumpstops and realise the a simple rising rate suspension is going to have this same effect.

Then ask how is it in any way valid to transfer your body roll inertia to the geometric roll centre with the parallel axis theorem???

4. Excellent post Tim. Thank you.

I think I had the same epiphany looking at Z's diagram of jacking forces. I now genuinely don't think geometric roll centres are a good teaching tool at all. They give a superficial understanding, which requires a lot of unlearning. Anti-roll as the angle of the n-line is much simpler and physically meaningful.

Ben

5. Yea exactly.

I'm all for simplified models, but if you need to first unlearn what you've learned in order to progress to the next step then the tool is not ok in my opinion.

6. Good question. The actual mechanisms behind roll centres only clicked for me a couples years ago. I was having a discussion with someone about K&C data and they mentioned the usefulness of looking at Fz vs Fy during a lateral compliance test and it suddenly hit me like a truck. I thought f*** me, how did I not notice this before. This being:
The Fz vs Fy IS the anti roll (geometric load transfer) effect produced by ICs being above the ground.
In fact the dFz IS actually the jacking force and that is what is giving the anti roll effect. Turns out jacking forces they actually aren't evil at all.
Exactly the same mechanism is working longitudinally and is known as anti dive, squat, lift, raise
Just remember, a K&C test is different because you have a constrained chassis. On the rig, jacking produces changes in wheel pad load. On the track, jacking produces a steady state change in suspension deflection with no net change in tire load.

However, in transent you have to get from State A to State B, so there will be a change in tire load based on the inertia of the system resisting this change in displacement.

7. Originally Posted by Buckingham
Just remember, a K&C test is different because you have a constrained chassis. On the rig, jacking produces changes in wheel pad load. On the track, jacking produces a steady state change in suspension deflection with no net change in tire load.

However, in transent you have to get from State A to State B, so there will be a change in tire load based on the inertia of the system resisting this change in displacement.
I don't totally agree. If you take say a front axle with an IC above the ground and a lateral force at the contact patch, you then have a jacking force Fz = Fy.tan(IC_angle). If you raise the IC, then you raise the jacking forces. If there is no corresponding change to the rear axle IC heights, then you do increase the tyre load due to an increase in load transfer on that axle.

If you instead raise both the front and rear ICs together, both the front and rear jacking forces increase but the elastic forces from the spring decrease. So in the end the total tyre loads might be unchanged but the jacking forces are definitely there and have increased.

8. For anyone getting started with vehicle dynamics the word roll center comes up in virtually any book/paper on the topic. Even SAE/ISO/DIN have definitions for what the roll center is, these definitions usually say something along the lines of: "point at which a lateral force applied to the vehicle body is reacted without causing suspension roll angle". That definition along with the name "roll center" can fool even the brightest student of vehicle dynamics (I agree with previous posters, the car doesn't roll around the geometric RC). Correct me if I'm wrong, but there is no "official" definition for n-line/jacking coefficient/ICz-ICy.

Assuming that RC isn't the way to go, why is it still used, here's my thoughts:
- It is easy to (mis-)understand for anyone getting started in the field.
- It is useful metric of a suspension's characteristics and it can be calculated no matter what suspension type/topology used (yes, the IC/n-line method would allow the same... but it's not presented in literature).
- The way it can be used in LLTD calculations are presented in many VD books.
- Vehicle dynamics/Race engineers can see the effects of moving the RC in both driver comments and logged data, allowing them to build up experience of how RC can be used as a tuning tool. These kinds of "rules of thumb" are used at most levels of racing where engineers have to make decisions based on limited data sets in short amount of time.

Now, to get a bit more technical, as Tim alluded to: If the lateral force distribution left/right is equal the RC calculation method will give you the same results as the n-line/jacking coefficient/ICz-ICy method. So if you don't have any information on how your tires generate forces and moments, you'll be guessing this. In this case, one could argue that using the RC method is the safer way to go.

Nonetheless, since I had the "epiphany" (the same one Tim and Ben mentions) a couple of years ago, I found it interesting how people seem to get the entire side-view anti-effect notion without any problems, but struggle to grasp the very same thing in front-view.

One argument that I feel is compelling against the use of RCs is the following: If we have an independent suspension, why does the position of the right side suspension affect the left side suspension? The RC position is a function of both sides and hence makes it a poor choice for analyzing independent suspensions.

Regarding the lateral movement of the RC, I would agree it is not a very useful metric. Vertical RC movement on the other hand is extremely useful for any car that sees different vertical loading (from either down force, inertial loads or just a whole bunch of groceries).

Finally, I prefer to look at the IC location (Y,Z coordinates) as opposed to the slope of the n-line. I agree that the geometric weight transfer as a function lateral tire forces only depend on the slope or ratio of ICz-ICy. But when you want to look at the non-suspended weight transfer, the height of the IC with respect to the non-suspended CG location becomes highly relevant. Additionally, when we start to look at Mx from the tire, then the ICy with respect to the contact patch location becomes highly relevant. All of these three effects will change the weight transfer and/or suspension deflection.

Moving forward, how do we better define the name of this method/approach? I think the notation: "n-line/jacking coefficient/ICz-ICy" isn't going to make it a hit...

9. Originally Posted by HenningO
Moving forward, how do we better define the name of this method/approach? I think the notation: "n-line/jacking coefficient/ICz-ICy" isn't going to make it a hit...
The Z-bomb?

10. Originally Posted by Buckingham
However, in transient you have to get from State A to State B, so there will be a change in tire load based on the inertia of the system resisting this change in displacement.
This is number one on my list of transient vehicle dynamics effects to study should I ever get the opportunity to do some multi-body dynamics modelling. Drag racers use >100% anti-squat to generate traction this way and race car turn-in should behave the same way.

Number two on the list is proving / disproving the 'stiffer front bar for more turn-in' rule of thumb.

Number 3 is characterising front low-speed compression damping for turn-in tuning.

Number 4 is working out the correct relationship between front toe, front camber and Ackermann, to avoid front tyre scrub.

Number 5 is understanding the behaviour of static margin, during turn-in, to ensure stability.

Number 6 onward are all about transient behaviour of tyres...

Regards, Ian