About Roll Centers of Double A-Arms

[MikeMargarido]

Hello, all.

I'm looking for some orientation regarding how to calculate Roll Centers (first, IC's and finally the Roll Center, for each axle) of a double wishbone assembly as can be found here:
http://www.steerbythrottle.com/hccyong/ ... SIGN~1.HTM

or more specifically:
http://www.steerbythrottle.com/hccyong/ ... Image3.jpg
and
http://www.steerbythrottle.com/hccyong/ ... mage58.jpg

From a front-view perspective, RC's seem apparently straightforward to find:
- extend lines from upper control arm and lower control arm, check their intersection point
- do the above for both sides, in order to find the IC's
- from the IC's, extend lines to the center of the contact patch of each tire
- where these lines intersect, we should find the RC's

Problem is:
- on a double a-arm assembly as depicted in the site dedicated to a SAE car, each arm (upper or lower) has 2 different mounting points to the chassis

So, how are the lines from upper and lower arms drawn in order to check their intersection points (IC's), taking into account the mounting points to the chassis?

Thanks in advance for any help on this.

[Tim.Wright]

Problem is:
- on a double a-arm assembly as depicted in the site dedicated to a SAE car, each arm (upper or lower) has 2 different mounting points to the chassis

You simplify the 3D geometry into a 2D problem like this:

• Each control arm is made of 3 points which define a plane
• Add another vertical plane which runs transverse across the car and goes through the wheel centre point of the left and right wheels
• The line of intersection between each control arm plane and the transverse plane is the then the control arm line

From there I think you know what to do.

One thing though, don't break your balls trying to control your lateral and vertical roll centre movements in roll. They are not as critical as people will lead you to believe.

[MikeMargarido]

Thank you both for your answers.

Shooty81,

my focus is not on the front view and solely on width&height location; I am interested in locating the IC's and RC's in 3-dimensional space (therefore, width/height/length - just to avoid xyz as different orgs use different axis).

You simplify the 3D geometry into a 2D problem like this:

• Each control arm is made of 3 points which define a plane
• Add another vertical plane which runs transverse across the car and goes through the wheel centre point of the left and right wheels
• The line of intersection between each control arm plane and the transverse plane is the then the control arm line

From there I think you know what to do.

I had assumed that much, Tim, indeed, and it makes sense.

I had (initially) assumed that attachment points of the wishbones would not establish lines (from the ball joint to each attachment point in the chassis), as these lines would normally diverge and thus establish 2 different IC's per side (and one behind the other).

Instead, I thought (as you suggest) of a plane defined by the ball joint and the 2 attachment points to the chassis (in effect, a wishbone defining a plane). A vertical plane passing through the ball joints (and wheel hubs) of opposite sides would help establish a line - actually, a normal line passing through the ball joint and bisecting the line between attachment points.

Perhaps my initial idea was not incorrect, that the front attachment points would not define the lines whose intersection point formed the IC.

One thing though, don't break your balls trying to control your lateral and vertical roll centre movements in roll. They are not as critical as people will lead you to believe.

Perhaps not "controlling" but at least be aware of both the CoG and RC's migrations in order to realistically predict the dynamic behaviour in non-transient conditions.

Again, my thanks to both.

Any more suggestions are welcome, though.

[Tim.Wright]

One thing though, don't break your balls trying to control your lateral and vertical roll centre movements in roll. They are not as critical as people will lead you to believe.

Perhaps not "controlling" but at least be aware of both the CoG and RC's migrations in order to realistically predict the dynamic behaviour in non-transient conditions.

A kinematic roll center is a famously unstable parameter and the meaning of its location becomes more useless the closer to the ground that it moves because near to the ground its always on the verge of being mathematically undefined. Small changes in imposed roll angle give huge changes in the roll centre location which are completely meaningless.

Then there is a question mark over the roll movement that you impose when you are analysing the roll centre migration. Do you put symmetrical opposing wheel travel? Do you incrementally roll about the roll centre you solve for at each step? Is your reference system moving with the body or the ground?

My advice is to setup the roll centre height looking only at parallel vertical wheel travel and choose a vertical migration limit which is meaningful (i.e. you don't want to change your LLTD by 5% when you change the ride height for aero reasons). Forget what the roll centre is doing with arbitrarily imposed roll movements. If you are really interested in the wheel loads (which is why you are interested in the roll centre right?) then you are better off looking into some of the force based methods for defining LLTD.

[MikeMargarido]

A kinematic roll center is a famously unstable parameter and the meaning of its location becomes more useless the closer to the ground that it moves because near to the ground its always on the verge of being mathematically undefined. Small changes in imposed roll angle give huge changes in the roll centre location which are completely meaningless.

I understand. From that perspective, I fully agree.

Perhaps focusing more on the distance between RC's and the CoG is more appropriate and with visible consequences in terms of behaviour.

Then there is a question mark over the roll movement that you impose when you are analysing the roll centre migration. Do you put symmetrical opposing wheel travel? Do you incrementally roll about the roll centre you solve for at each step? Is your reference system moving with the body or the ground?

In terms of suspension movement, yes, my tool uses the body (centerline and wheel hubs) as the frame of reference. As such, yes, wheel travel is "symmetrically opposed". The car rolls (a little, given the constraints imposed by the suspension designs) and RC's are recalculated.

My advice is to setup the roll centre height looking only at parallel vertical wheel travel and choose a vertical migration limit which is meaningful (i.e. you don't want to change your LLTD by 5% when you change the ride height for aero reasons). Forget what the roll centre is doing with arbitrarily imposed roll movements. If you are really interested in the wheel loads (which is why you are interested in the roll centre right?) then you are better off looking into some of the force based methods for defining LLTD.

Indeed. The objective is to accurately predict TLLTD in transient and non-transient conditions, with or without aerodynamic load. The target is for TLLTD to remain within 2 to 5% in front of the static WD.

Curiously, while experts point to the "magic number" of 5% (no pun intended towards OG), race car engineers I work(ed) with believe there is too much understeer upon corner entry and mid corner if TLLTD is "projected" at 5% or immediately above.

But I reckon those are somewhat muddy waters.

Thanks for the clarification, Tim.

[Jersey Tom]

...while experts point to the "magic number" of 5%...

I'd say that's generally sold as a conservative starting point, just to get you in the ballpark (which it most likely will).

[MikeMargarido]

I'd say that's generally sold as a conservative starting point, just to get you in the ballpark (which it most likely will).

Exactly what engineers say.

As far as I have seen, projected TLLTD (and more or less confirmed by telemetry) for several GT1 and GT3 cars is anywhere from 1.5% to 3.5%. Bordering 5% or going further than that and we had pilots complaining of understeer (in different degrees, true).

[silente]

Well,

actually for a rear wheel drive car, TLLTD depends very much also in tires behavior (front to rear), engine torque, differential settings, TC or not, etc.

I wouldn't say that a weight transfer on the front axle 5% higher than the front axle static weight distribution is always too much...

But we were talking about suspension geometry...

[Greg Locock]

"Just find the virtual centerpoint of your 3d-curve of your virtual contact point (for example by using the 3-point method)."

Yup, bingo.

The reason that you don't need to worry too much about RC migration is that your very simple analysis ignores the fact that the car will pitch as it rolls, which has a far greater effect than roll on RCH.

Geometrical based RCH is a bit of a drawing board game, Force Based Roll Centre Height is much more useful, and the fact that the two often move in different directions in a corner tell you that GRCH is not telling you what you think it is.

that being said GRCH is useful, mostly in low g steering feel.

[Greg Locock]

The classical way to do it is to look at the instantaneous velocity of the contact patches, in front view, as you hold the body grounded. However that makes an awful lot of assumptions.

[sakooon]

The objective is to accurately predict TLLTD in transient and non-transient conditions, with or without aerodynamic load. The target is for TLLTD to remain within 2 to 5% in front of the static WD. ???