27 replies to this topic

[gruntguru]

What is the influence of tyre compliance on roll centre height? Geometric calculations of RCH assume rigid wheels and tyres. Does the addition of compliant tyres cause the roll centre to move? From a simplistic perspective, with rigid wheels the application of a lateral force at the RC will produce zero body roll. With compliant tyres and a positive RCH there will be some body roll. Does this mean the RCH has moved down due to the addition of the tyres?

[gordmac]

Not terribly sure but in the construction used to find the roll centre is it assumed the tyre is a rigid link hinged to the ground? You might want to read an IMECHE paper "the roll-centre concept in vehicle handling dynamics" by J C Dixon.

[Johan Lekas]

What is the influence of tyre compliance on roll centre height? Geometric calculations of RCH assume rigid wheels and tyres. Does the addition of compliant tyres cause the roll centre to move? From a simplistic perspective, with rigid wheels the application of a lateral force at the RC will produce zero body roll. With compliant tyres and a positive RCH there will be some body roll. Does this mean the RCH has moved down due to the addition of the tyres?

The RCH is related to the tire contact patch and the suspension linkages that connects it to the body, so if the tires are compliant this will move around, and so will the RCH

I think Mark Ortiz has written some good stuff on RC. Here is a Link to a zip file with all his Chassis Newsletters up to sept 2009.
EDIT: All newsletters up to current also here with descriptions http://www.eviltwinm...om/?page_id=204

Newsletters about RC:
May/June 2009 (The anti controversy)
August 2004 (Roll center migration, some more)
December 2004 (Roll center below ground)
February 2006 (Roll axis inclination)
September 2006 (Roll center in trailing arm front suspension, More on roll axis and related analytical concepts. )
May 2007 (Roll axis for live-rear-axle road/hillclimb car, Roll axis of the axle)
December 2004 (Roll moments from longitudinal anti.)

Edited by Johan Lekas, 16 September 2010 - 10:26.

[gruntguru]

The RCH is related to the tire contact patch and the suspension linkages that connects it to the body, so if the tires are compliant this will move around, and so will the RCH

Yes but what about the static situation with zero roll and RCH not at ground level. Apply a transverse load at the RCH. With rigid tyres the body does not roll. With compliant tyres the body starts to roll (albeit with no suspension movement). This is not a case of movement of the RCH.

Thanks for the link.

[meb58]

gruntguru,

Would we simply expect to see RC move in sync with trie sidewall deflection? I know we're having a discussion in the P34 thread about sidewall stiffness...isn't sidewall stiffness, and perhaps air pressure, relative to RC movement assuming the suspension is 'locked' to the body?

I guess we can also assume that if the tires and suspension are 'locked' but that the bushings are not, then the bushings contribute to RC migration as well. Kind of makes me think a car is at some level a fluid pice in movement.

Edited by meb58, 10 September 2010 - 13:42.

[Johan Lekas]

...static situation with zero roll and RCH not at ground level. Apply a transverse load at the RCH.... with no suspension movement). This is not a case of movement of the RCH.

OK, I think I see what you mean. The definition of the RCH is that a transverse force there does not give suspension movement/roll, but still the car rolls. But even if it is the tire compliance causing the roll, the RCH can/will move since the geometry between the contact patch and the (not moving) suspension will change compared to the rigid wheel case
Is this a problem? I guess the tire compliance has to be taken into account when calculating roll and RCH

[Sisyphus]

The issue of tire compliance has bugged me for a long time with respect to roll center and other computations of suspension programs. Compliance cannot be ignored because as the load transfers the tire compliance will allow the centers of the ball joints in the uprights to move vertically. So, if your suspension program doesn't have tire compliance as an input then it isn't accurate. At least not as accurate as it could be.

You need a few extra lines of programming to iterate on the true position of the ball joints but it's not rocket science.

[gruntguru]

maybe a quick read here, will give some new aspects to think about the problem.
http://fsae1000.blog...e-paginate=true

So it seems the answer to my question is "the difference between force-based RC and geometric RC".

I suppose as a first approximation (considering the tyres' response to vertical forces only) you could say the adjustment to RCH follows this formula (roughly derived and not checked):

RCH(force-based?) = RCH(geom') - (wheel-rate x CGH/tyre-rate)

Interesting to note. As tyre-rate approaches infinity the force-based RCH approaches the geometric RCH as expected. As wheel rate approaches infinity the force-based RCH approaches minus infinity. This reflects the infinite moment required to produce an amount of roll (in an infinitely stiff suspension) equal to the roll caused by vertical tyre deflection.

For a F1 car with tyre rate similar or less than wheel rate, the RC is effectively below the ground. This probably doesn't say much about the geometry of the suspension, merely that given the very still suspension, the effective roll centre would need to be very low to account for the amount of roll experienced.

Edited by gruntguru, 12 September 2010 - 03:45.

[Johan Lekas]

I think, that this is in part a reprint of the section in Dixons book. I hope it helps the matter at hand.

http://www.neohio-sc...ynamics2007.pdf

I think it's interesting to read what Mark Ortiz has to say about roll centers, and force based roll centers
In the May-June 2009 Newsletter (see link in my earlier post) he goes through this thoroughly and also comments on Mitchells Force based roll centers. A quote from the above newsletter:

In particular, it is incorrect to suppose that forces at the contact patches act along the force lines or force planes of the suspension geometry, and therefore exert moments about the center of mass according to their vertical or perpendicular distance from the center of mass. This misconception stems from a misunderstanding of what the force lines and planes represent.
The car is not a body floating in space, acted upon by angular forces in the force planes. Nor is it an airplane with four wings or control surfaces each exerting a lift and a drag force. It is a body with a center of mass above the ground plane, supported through compliant suspension at four points in the ground plane, accelerated in the x and y directions by forces in the ground plane. These forces do not act on the car as a whole along the force planes; they act on the car as a whole along the ground plane. The ground-plane forces induce support forces within the car, in the suspension systems, according to the slopes of the force planes. These induced forces create moments within the vehicle that may oppose or exaggerate the suspension displacements in roll and pitch, and can alter the distribution of tire normal forces.
This may seem merely a rhetorical distinction, but it's not. In particular, the anti-roll and anti-pitch moments do not depend on the proximity of the force plane to the center of mass. Rather, they depend only on the spacing of the wheels, the magnitude of the ground-plane forces, and the slopes of the force planes. The anti-roll and anti-pitch moments do not depend in any direct way on where the center of mass is.

[cheapracer]

What is the influence of tyre compliance on roll centre height? Geometric calculations of RCH assume rigid wheels and tyres. Does the addition of compliant tyres cause the roll centre to move? From a simplistic perspective, with rigid wheels the application of a lateral force at the RC will produce zero body roll. With compliant tyres and a positive RCH there will be some body roll. Does this mean the RCH has moved down due to the addition of the tyres?

Yes and no.

In your lateral example it's likely the RC is still central and the inner tyre may well have risen as much as the outside tyre has compressed - status quo, but in a true dynamic cornering situation where the RC has most likely migrated towards the outside of the car then the RC will be a bit lower than most software show.

[gruntguru]

In your lateral example it's likely the RC is still central and the inner tyre may well have risen as much as the outside tyre has compressed - status quo, but in a true dynamic cornering situation where the RC has most likely migrated towards the outside of the car then the RC will be a bit lower than most software show.

Not quite what I was asking. Quoting from post #4 "the static situation with zero roll and RCH not at ground level. Apply a transverse load at the RCH. With rigid tyres the body does not roll. With compliant tyres the body starts to roll (albeit with no suspension movement)."

By definition a lateral force applied at the roll centre produces no roll - correct if the tyres are rigid. With compliant tyres, the moment produced by the same lateral force (provided the RC is above ground level) will cause body roll, with (as you say) tyres on one side compressing and tyres on the other side extending.

[gordmac]

I think the SAE definition talks about applying the force to the sprung mass and the roll is suspension. By that definition the tyres are excluded.

[meb58]

gruntguru,

Wouldn't you expect a greater roll moment from an RC location at ground level or below? Or does this location preclude tyre inviolvement?

[gruntguru]

Wouldn't you expect a greater roll moment from an RC location at ground level or below? Or does this location preclude tyre inviolvement?

I only excluded the ground level case for my example of applying a lateral force at the RC. It doesn't work if the RC is at ground level. As far as cornering forces and roll moments go the apparent RC is given by the formula:

RCH(apparent) = RCH(geom') - (wheel-rate x CGH/tyre-rate)

Edited by gruntguru, 15 September 2010 - 22:55.

[meb58]

gruntguru,

I'm not sure I understand the question...and I apologize for dragging this thread down...

Any side force applied to the car migrates through the RC first then through all other components and then eventually reaches the tire's contact patch, yes? If we assume we have a rigid suspension then there is no RC migration if the car simply slides sideways - isn't lifted up on off the inside wheels...only its static location is affected by pneumatic tires, is this the question?

If we take two identical cars with rigid suspension and add rigid tires to one and pneumatic tires to the other I might bet the the static RC location changes based soley upon the tire's flat spot; it reduced the tires circumference or diameter and this as you know inlfuences the static instant centers and roll centers...if we exert a side force onto each car, the one with rigid tire will move predictably onto the shoulder or corner of the two outside tires - if it isn't allowed to simply slide. I think, pneumatic tire present a differnt challenge and this is perhaps based upon the type of tire...but I guess I can see the rim moving over the outside sidewall and this surely affects RC, but also, RC is affecting how far the rim moves - velocity - through its leverage - linkages. I could be totally lost here...

As dumb as this may read, do we really care about RC location and migration from a practical perspective? Do we really lose 'that' much if the ideal location is somewhat secondary to other aspects of tuning...in the interests of time and money?

Still not sure I understand the question though, but always willing to learn something new for sure.

Edited by meb58, 16 September 2010 - 14:07.

[gruntguru]

I'm not sure I understand the question...and I apologize for dragging this thread down...

No apology necessary and I don't think the thread was going anywhere to be dragged down.

The question concerns vertical deflection of the tyres only - compression on one side of the car and extension on the other so forget about lateral tyre deflection. One of the key attributes of RCH is its contribution to roll. The roll couple applied to the sprung mass during cornering uses the distance from CG to the roll axis as its moment arm eg if you raise the roll centres to the point where the roll axis passes through the CG, the roll moment will be zero and the car will corner with zero roll. This assumes rigid tyres though, because the roll moment applied to the entire vehicle (sprung plus unsprung) has CGH as the moment arm so there will still be weight transfer so vertical deflection of the tyres will cause some roll of the entire vehicle.

[meb58]

...yes, yes. I have explained this phenomenon in this way, because I am visual.

I imagine and upside down grandfather clock pendulum. The big weight on top is the CofG and the point at the other end of the arm is the RC. Lower Rc and we get more leverage on on the CofG. Raise it and we get less. But in addition, and not sure how to explain this eloquently, although the short arm will act on the CofG with less force(?) it will do so quickly - meaning the tires are loaded a little more quckly in sat transient but not in steady state. A longer virtual lever arm is just the reverse.

I happen to like this picture because niether the CofG nor the RC location is fixed...the pivot or fulcrum is really some place between and this helps to illustrate how fluid body movement really can be.

Although I cannot support my thinking with anything scientific, I agree that vertical tire deflection affects RC, has to. I guess the question might be, how influential is deflection practically? Might depend upon the application?

...forgot to add gruntguru, I also think the location of the RC affects tire deflection...so a backward and forward relationship exists here in my brain. A higer RC location my cause more tire deflection than a lower RC location in the first few degrees of roll...and a lower RC location might cause less tire deflection for the first few degrees of roll. I guess that each posses a relative realtionship?

Edited by meb58, 17 September 2010 - 12:40.

[cheapracer]

if you raise the roll centres to the point where the roll axis passes through the CG, the roll moment will be zero and the car will corner with zero roll. This assumes rigid tyres though, because the roll moment applied to the entire vehicle (sprung plus unsprung) has CGH as the moment arm so there will still be weight transfer so vertical deflection of the tyres will cause some roll of the entire vehicle.

That may be so on some software but most understand that simply isn't going to happen in the real world even with rigid tyres.

And the reason is simply enough, cars have the RC that you are refering to and have 4 other roll points being the contact patch of the tyres. Karts or anything suspensionless obviously only have the latter.

Your lateral load connection point to the wheel, being in the middle, wants to trip over the tyres contact patch on the ground and regardless of how low the CG and/or where the RC is, given enough traction and lateral force the car will fall over this point eventually.

Go and handbrake turn a car into a gutter/kerb for a practical demonstration of this point.

[gruntguru]

That may be so on some software but most understand that simply isn't going to happen in the real world even with rigid tyres.

Sure but that is irrelevent to the issue I am trying to explore and laterally-rigid tyres mak it easier to understand that issue. Its a bit like determining roll centres based on suspension geometry alone - without consideration of flex in the chassis, suspension links, bushings, wheels and tyres. Its obviously a fantasy but we do it anyway to simplify analysis.

[meb58]

TC3000,

So as I understand this, the closer RC gets to CofG the faster the tires load up...and if the RC runs through the CofG tire loads are instantaneous...or nearly so? So then we might expect a tire to lift off the ground if the RC is above the CofG?

I ask this question because one of my repsonses to gruntguru was that literal RC location affects how much tire deflection we might expect to see...20" below CofG and we get X defelction, 10" below CofG and we get 2(X) deflection - this is just a comparison, not literal. And how will either if these RC/CofG examples afftect elastic or non-elastic suspension components? In the same fashion as tire delfection...higher RC loads up pneumatic linkages faster.

For the purpose of my learning, what is the diference between geomentric RC and force based RC?

maybe it helps if we devide the load transfere into a elastic part (via the springs,dampers, ARB etc.) and an unelastic part via suspension arms etc.
this analogy is more comonly used for pitch and squat motions of the car, to explain the "anti-" kinematics, but works in lateral direction as well.

You can design a "anti-roll" kinematic/suspension, but you will still have load transfere and therefore tire deflection.
If you design an "anti-roll" suspension i.e. putting your roll axis through your CoG, your damper/spring and ARB setups will have no/very little effect
to the timing of your load transfer, and your tires will load very instantly.

The absolute amount of load transfer and therefore tire deflection is independent of your roll centre height.
with different roll centre heigths you can alter the portion of the elastic vs. unelastic part but the sum of both will allways be total load transfer.
What you can do is change the timing of the loadtransfer/tire loading but not overall amount ( for a given CoG height, track wide and lat accel.)

Edited by meb58, 20 September 2010 - 12:37.

[meb58]

TC 3000,

Thank you! You've illustrated many points that I understood, these are therefore galvanized. And completely off topic, when I increased the track width on my car by 30mm the results were fairly noticable! ...30mm front and 10mm rear to be clear. Great illustrations!

Pneumatic should have been kinematic, sorry - rubber bushings.

If we look at gruntguru's orginal question and assume that everything about the car is rigid except the tires and we apply a side force to the car, the tires deflect, yes? My addition to this question is, if we take two rigid cars with rubber tires, one with a high RC one with a low RC - CofG is at the same height in both cars - a given side force will cause more tire deflection on the car with the lower RC?

Hope you don't mind my interjecting here gruntguru?

[Johan Lekas]

For the purpose of my learning, what is the diference between geomentric RC and force based RC?

I think I have come across three roll center methods.
First is the classic geometrical metod (see for example the first picture in TC3000 post above)
This method has the problem that is does not take into account that during cornering the outside wheel produces more cornering force than the inner wheel. In reality, when the inner wheel lifts, the RC is actually above the inner wheel contact patch, but the classic geometrical method fails to describe this.

This is what Mark Ortiz resolution line method takes care of. It is best described in his own newsletter (May/June 2009, "The anti controversy"), but essentially you draw a vertical line dividing the distance between the contact patches in proportion to the cornering force they make. This vertical line intersects the IC-lines from each contact patch, and the RC is halfway between these two intersections.


The force based roll center method is described (developed?) by Wm C Mitchell (Linked to in previous posts). It essentially takes all the forces acting on the car and calculates (with the Center of gravity as reference point) where the RC is (the RC being the height at which a force can be applied without causing roll)

An obvious problem is that you have to know how much cornering force the inner and the outer wheel develops, but there is no way around that.

Comparing the Resolution line RC method and the force based RC method the former is a lot easier to use. Of course if you want to take bushing flex, contact patch position, tire compliance etc into account it's not easy with any method.

Edited by Johan Lekas, 21 September 2010 - 06:22.

[Greg Locock]

Here's another way. it may produce the same result as one of the other methods.

Apply a force Fy to the contact patch. Measure the change in vertical force at the contact patch. Then RCH=semitrack*dFz/dFy

This is essentially the height of the FVIC< I think, and for a typical IRS is similar to the RCH (note that it sort of assumes that the FVIC is on the centreline).

More usefully it directly tells you about the load transfer, which is often what you want to know.

I don't get too hung up on these things, the rig results and calcs tend to trend the same way, and the results in the vehicle seem to track them, but we still come back to the original conundrum I have with them.

A vehicle is fitted with a competent live axle and watts link. Its GRCH is something like 305 mm.

We design an IRS with a GRCH of 150mm. On the track the difference between the two is generally negligible.

On the front suspension we adjust the RCH by 20mm by raising the UCA inboard end. The difference is significant. We fit 10mm larger tires, increasing the RCH by 10mm, the difference is tiny.

[gruntguru]

On the front suspension we adjust the RCH by 20mm by raising the UCA inboard end. The difference is significant. We fit 10mm larger tires, increasing the RCH by 10mm, the difference is tiny.

Did the larger tyres raise the CG by 10mm also?

[Greg Locock]

Did the larger tyres raise the CG by 10mm also?

yes, good point, we should be referenced to cg not cp, sort of

[meb58]

TC3000,

Again, thank you...I understand in concept...I have to envision the movements in my head for a bit. Essentially the spring is absorbing a portion of the weight transfer as it compresses the spring and eventually, based upon the spring weight, car weight, CofG location (height and % front to rear) the weight transfer eventually moves to the contact patch. If we use a soft spring, the tires will load up more slowly...and vise versa...?

Greg,

I envision a rig holding a car. This rig has the ability to move sidways abruptly. We use sensors under each wheel in addition to high speed cameras to evaluate what happens to the car as a whole. I thought about this before reading your reply...

Johan Kekas,

I think I understand TC3000's image is a concept that illustrates the relationship between CofG and RC, but excludes literal geometry...which defines instant center and RC migration. The significance of your sentence below is lost on me, however. I think you were making a point and I wanted to write that I get it...but I'm not sure I do. Don't most designers use literal suspension geometry when evaluating RC locations?

"In reality, when the inner wheel lifts, the RC is actually above the inner wheel contact patch, but the classic geometrical method fails to describe this."

Edited by meb58, 21 September 2010 - 20:26.

[Johan Lekas]

I think I understand TC3000's image is a concept that illustrates the relationship between CofG and RC, but excludes literal geometry...which defines instant center and RC migration. The significance of your sentence below is lost on me, however. I think you were making a point and I wanted to write that I get it...but I'm not sure I do. Don't most designers use literal suspension geometry when evaluating RC locations?

"In reality, when the inner wheel lifts, the RC is actually above the inner wheel contact patch, but the classic geometrical method fails to describe this."

Maybe not the best example, but I was trying to describe a situation were the classic geometric RC model differs from reality. A bit misleading also because, as you say, the the lateral position of the RC is not relevant, only the RC height.

[meb58]

TC3000,

No shooting anyone down! I appreciate the guidance, the links...all of it! Thank you.

Johan Lekas,

Thank you, I understand...a year or so ago I would not have. It is always conforting to have one's thinking either confirmed or burned.