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...

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.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...

~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 inNO 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.

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.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) butI do have a problem when the front roll center goes towards one side of the car and the rear one towards another.

3.

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...Posted by Claude:

Many people look at roll centers ... as the intersection of "forces lines" butthey ignored the Huygens (or parallel axis) theorem which will influence the rotational acceleration of both suspended and non suspended masses.

4.

More bulldust of the above nature...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.

5.

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..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.

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!- And at a certain time you need to stop the intellectual...gymnastics and go testing.

6.

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.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?

~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