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Dear Ray,

You may know the 550A Porsche Spyder used a modified Watts linkage, having changed from the 550's pure torsion bars to coil springs all the way around, but kept a revised swing axle.

The modifed Watts linkage was to keep the swing out of the swing axle.

I know the Watt's linkage very well. And, like you said, most of todays "control arms" and rods are some variant of the Watts concept.

What I meant by the Watts linkage "wasn't for us" is our true wing axles and diagonal-arm rear suspensions need a lot of work to adapt to control arm linkages, work most people won't do.

FJC

Ah...yes. I agree.
Yeah....it would require having the room opposite the trailing arm inside of teh fender wells to have a range of "arc" for a lever....and then to fabricate body mounts.....after experimenting and calculating. Its a lot of work on a bug.
My 412 is a different story altogether. On this car there are a a pair of loops or bushing mount locations just below the bump stop areas....that are unused. They will be perfect for watts style levers. The sway bar trails from the front.
They may have been mounting points for a factory welding jig...who knows. But they are perfect (especially since these are axial coil spring and shock, two mounting point trailing arms)..... mounting points.
The tough part is drilling through the two layers of teh unibody fender well, putting a spacer between them and welding on a stub and pivot. Ray

FJCamper wrote:Lowering the nose is not greatly changing the roll center itself, but has the effect of leaving the rear center of mass higher (in relation to the front), which affects the forces on the rear suspension.

There is no front center of gravity or rear center of gravity. The CG is at only one point.

What you are experiencing is something else. The motion ratio of the front torsion bars changes when the front is lowered, so the front end becomes softer. The CG of the car is lowered, so the roll stiffness of the suspension should be softened if the same roll angle as earlier is preferred. These are only suggestions, might be something else that I can't think of...

The compliances of the suspension should also be checked, might be that the rubber or urethane bushings at the rear aren't enough for you.. Snap oversteer isn't something that the car should have. Might also want to check if you are hitting your bump stops at the rear.

About the picture on the first page, it should be mentioned that it's from a pre-68 Ghia. On a 1970 Ghia with semi-trailing arm rear suspension both roll centers are on ground level, so the red line is parallel to the ground. The 911 had higher roll center at front than rear, just like the 1302 and 1303 mcpherson beetles with similar suspension geometry.

The geometric roll resistance (from roll centers) doesn't wait for the car to roll or yaw. The springs and anti-roll bars are affected when the suspension is depressed, and have full effect when the car has fully rolled. The dampers affect the roll stiffness whenever there is movement in the suspension, but this usually isn't very adjustable because entry-level shocks have limited adjustability in the low speed range. The roll centers affect the suspension at full effect as soon as there is lateral force, and this effect is directly proportional to the lateral force on the tire. They don't wait for the car to roll like the springs and anti-roll bars or for suspension movement like the dampers.

There is no front center of gravity or rear center of gravity. The CG is at only one point.

That is correct and incorrect. To say that there is only one CG (as the car is built)...is only correct when the vehicle is static.....or sitting still.

The active/dynamic center of gravity changes as the directional momentum of various parts of mass in the car act upon it.

Yes...I agree...its "generally" smarter to soften the suspension stiffness as a car is lowered to offset the now lower CG.....but that is not always the necessary thing to do.

If all that has happened is that the car is lowered.....and the corresponding body attitude is maintained (ie: forward to backward cant)...then nothing has changed that will affect the foward dive that happens due to enertialchange when braking in a straight line. The only thing affected by lowering the center of gravity by lowering the car.....is tangential forces when going through a curve.

By the way...since nothing else changed....you still have a roughly 65/35 rear weight bias......and the car still has a forward enertial shift when braking as that rear mass can't be slowed as fast as the lighter frontal mass......you still have a tendency for the rear in to want to pitch outward through a curve.
The only thing that has corrected some of that characteristic ...is that you have controlled overall body roll.......as was originally induced by the vertical center of gravity....by lowering the car.

There are TWO centers of gravity in all vehicles. When viewed from the end....like standing in front of the car....the height of the vehicle versus the width....pivoting around a central Xaxis .....and affecting body roll in cornering due to enertia and centrifugal force...is one axis.
The other....is viewed from the side of the car....and is referenced by two points of interest. (1) The exact midpoint in wight bias from front to rear...wherein exactly 50% of the weight of the car is exerted on each side. (2) The amount of height of the chassis in reference to the mid axle points of each wheel.....or how low slung between the tires the body is.

ALL vehicles experience enertail shifts forward in weight distribution ...based around the central weight bias pivot point. This not only extends rear suspension members while compressing front members...it removes traction weight bias from rear and adds to the front. It also pitches the body forward. Since anti-sway bars and suspension mounting points may be attached to the body...it has affect on teh geometry. This fore/aft moevment and enertia change happens anytime you brake, accelerate or have rapid gear changes. This is just the front to rear roll/privot point we are speaking of....but add to that going through a curve or corner where the central Y axis center of gravity is acted upon by enertia and centrifgual force....and the suspension has to act in several dimensions...and the body will begin to twist.

This is because not only do you have front/rear enertia chanes compressing or extending supension parts...but you have centrifugal force causing wheel lift on the inside of the curve.
Hence....rear engines...high speed curve to the left....with braking ...you get forward pitch and front suspension compression with rear wheel lift and forward body pitch....AND....inside left side body rise...outside right body compression. You will have at this moment...different conditions at all four corners. In this moment...the body attachment points are doing a fair portion of the steering of suspension and anti-roll activity. Ray

Usually the car is considered to be a rigid body, so there is only one CG. Check any book on mechanics.

I have come upon mentioning front and rear CG three times before, one of them was a Carroll Smith book. This has to do with a theory about "mass centroid axis", which doesn't exist.
The principal axis of the moment of inertia do exist, but what you are talking about doesn't seem to be the same thing.

Usually you want the CG as low as possible because there is a big benefit. I see only one way to go if you want to move weight in the front or the rear of the car.

With the beetle rear suspension there isn't much lift in the rear when braking. I'm not sure if the rear end compresses or raises, but it could go any way because the rear suspension geometry has loads of pro-dive under braking. As long as there is enough load to keep the rear wheels on the ground, the rear suspension geometry dictates if the rear suspension compresses or raises when braking. The same applies for the front suspension.

A car doesn't pitch or yaw around the CG, just like a car doesn't roll around the CG.

All of the books I have seen that discuss the mechanics of gravity center (which is front to rear....through the horizontal/longitudinal axis...not through the vertical/longitudinal axis....which is ROLL center).... ALL dance around the important point of fact that (a) automotive bodies are nowhere near rigid (b) It matters not what your STATIC center of gravity is when in motion because it is acted upon and changed by enertia.
(c) You must calculate in (and they can't...too many variables to make universal rules)....what happens when various parts of the suspension MOVE...or flex...allowing parts of the body or suspension to be lifted out of plane with reference to forward movement. This flex can be initiated by braking, gear changes or turning (centrifugal forces).

There is no mystery here. It simple.
You can do this with a model of a car just like a real one. Get a rod...balance the car model on it. Move the rod forward smoothly....while holding the car until they are up to equal speed. Keep moving the rod and let go of the car. The car will fall off.
Enertia will ALWAYS cause the car to fall off of the rod toward the rear...even if you did this in a vacuum.
Now...reposition the rod slighlty rearward of the original calculated ceenter of balance and start over.
You will now find that ENERTIALLY....while in MOTION...the car has an altered center of gravity . It will now balance and stay on the rod at a constant speed. You will have the same effect only opposite when doing this trick while decelerating from forward motion. it will require selecting a new balance point FORWARD of where the static center of gravity was found to be.

Wait....one might point out that the car on the balance beam...is different because there is no ground underneath to keep the car from tipping forward or back and falling off the rod so this does not count.
Wrong.
Because on the real car...that forward enertia from either forward movment or braking....causes compression and changes in alignment to flexible or pivoting suspension components. These change the alignment of the suspension.....and related axes and angle of attack to the body or chassis. It changes the entire attitude of the car, in the process it changes all of your points of balance through enertia.

This is from front to back and has absolutely nothing in this world to do with the cars CG in reference to its height or lowering.

Upon slowing the rod dow...the car tips foward...always. Enertia tipped forward. The center of ENERTIAL balance has changed again.

The thing you cannot see from this simple experiment is that YES...you also have a lateral center of gravity....which is really the ROLL CENTER....AND IS NOT THE CG...for the vehicle.

I beleive this is the point you were trying to make. You are speaking of ROLL CENTER....not CG . Forward and backward enertias themselves will have no effect on where the actual roll center is on a vehicle is. Yes RC has to do with height in relation to axle center. That dimension is not changed by front to rear enertia change.
However...RC acts as a multiplier upon enertial changes during combinations of forward motion and lateral motion combined (cornering) or braking and lateral motion. Even in straight line motion and braking you get some effect and multiplication of RC...because of lifting and diving due to enertia. The roll center will be different from front to rear in that case.....and will be different in effect depending upon what volume of MASS is located in those two different locations.

You also have a varying diagonal center of balance that is acted upon by BOTH the ROLL CENTER (what you guys are calling CG...which are not the same thing)....AND the front and back enertial balance point (which shifts during accel and decel and IS the TRUE CG).
That diagonal shift rears its head when you are applying lateral force (turning or skidpad/centrifugal)as well as forward acceleration (shifting enertia to the rear)...and also when you apply braking or deceleration forces (enertia shift to front) as well as lateral (turning/skidpad/centrifugal).

In this last case....you get movement in THREE axis on the body at one time.

The wildcards most suspension "theory" books don't talk about is that they have no idea how a given suspension is tuned...is it stiff...is it soft?, what type it is going to be, what your weight is, where the main points of mass in the car are to be situated (front engine/mid engine/rear engine...wheres the fuel tank?), high soft side walls, low stiff side walls.....or even wether you are running four wheel independent versus a solid axle.... etc, etc, etc, etc.

The move from asolid rear axle to four wheel independent alone....give a radical change to roll center, gravity center/balance and enertial changes to a vehicle. Just look at the changes from swing to IRS!

In this arena...I have seen no real overridingly credible engineering treatise. Its usually just some race driver or car manufacturing engineers personal opinion based on their own experience (and those are good). I deal with too many engineers already . Stick with the physics of motion and you can analyze your own vehcile movement patterns.

Seriously....you do know that there are at LEAST three main axes of force that work within a body or car chassis in motion don't you? ....not even including all of the potenetital variations and permutations from suspension, tires, stiffness, tuning or even whether the ground is even level. Ray

Can anyone give a description of how you find the heigh of the roll center? Am I correct when I say that it is simply the point the car body tries to turn about.

Then in front the car tries to roll around the bottom of the tires, and in the rear it tries to roll about the gearbox?

Hi Redhot,

The roll center of a car is predetermined by the design engineers at the drawing board. Designers plan their roll centers for the intended feel and handling of the car. It is not accidential.

Lines drawn through the suspension arms and their connecting points dictate where a roll center will be.

The line that connects the roll centers determines the roll couple.

...and that is just the beginning.

FJC

redhot wrote:Can anyone give a description of how you find the heigh of the roll center? Am I correct when I say that it is simply the point the car body tries to turn about.

Then in front the car tries to roll around the bottom of the tires, and in the rear it tries to roll about the gearbox?

Defining the roll center is a difficult matter. There are two ways used to define the roll centers. The first one is a kinematic approach, where you only take into account the geometry of the suspension. The second one, which starts to give fairly accurate results, is a force based approach.

The roll center is not the point that the car body turns about. It is just an approximation of how much anti force (=roll resistance) the car suspension generates in roll.


Above is a picture that illustrates the force based roll center in a vw front suspension. The vw front axle is an odd design. It has no roll center movement in bump, but the roll center moves when the body rolls. The blue arrows represent "anti" forces that are dependent on the geometry of the suspension. The anti on the outer wheel is higher than the inner, so the geometry generates some roll resistance through the suspension arms. When there is lateral force and body roll, the roll center moves higher and towards the outer wheel. Also notice that both of the blue arrows point down, generating some jacking in the front. So jacking isn't only something that happens in a Swing axle rear suspension.

But back to the real world. The easiest is just to assume that the front roll center is at ground level and the rear roll center is above the gearbox for swing axle or at ground level for IRS. Then using the values as approximations as you calculate the wanted roll resistance from springs and anti roll bars. After this you go and refine your creation on the race track and test your way to improve the performance of the suspension.

Hi KDF,

It is a pleasure to meet someone who has such common interest in suspension theory and application.

I sit back and read the cam and ignition people's give and take (and we have some really sharp ones here), but you can count on the fingers of one hand those who really want to dig into the details of suspension.

FJC

Thanks. I've always found theory about suspensions interesting. Suspension tuning is not glamorous, and certainly not easy.

I'm hoping that in time this will wake some questions about roll centers. The above post was just to tell people how much over my head this business about roll centers is. I don't have the tools to do sophisticated analysis of how it works. So I have to use simplified models of it and design the best I can with the resources I have. What I'm trying to say is that I should be aware of the resources I have at hand, and be aware of any weaknesses a car might have. This means the whole package, not just the roll centers...

Some myths about the roll center that I've stumbled upon:
The chassis rolls around the roll center.
The roll center shouldn't be at ground level.
The distance between the roll center and the center of gravity is the length of the moment arm that defines how much the chassis rolls.


Usually when a car is fast it has a good engine or a good driver.

Hi KDF,

Taking these subjects one at a time, let's start with "The chassis rolls around the roll center."

My feeling is the engineers draw lines to show roll, pitch, and yaw, but these lines (such as the roll center line) are really a starting point that have many variables acting on them.

How do you see textbook roll center vs reality?

FJC

as the chassis flexes, and the suspension compresses and extends, those lines are constantly moving. Along with the apparent CG point, due to fore/aft/side forces

I look at it this way.

I have a ghia.
It is IRS.
I now look at what I can do to maximize its potential, with what I have available. (entire 924 for parts, a lot of fab skills, and access to both engineering, and nice machinery).

I will change what I can, and tweak what I need to.

the theoretical side will be saved for my homebuilt (plans on order for 550 spyder)

It's true that not everyone wants to spend time thinking about the theoretical side or engineering of cars.

What originally made me interested in this was a Porsche we built years back. We redid the rear suspension from semi-trailing arm to double a-arm style. I had no responsibility in the project, I just helped out and withnessed my friend struggling with designing and building the car.
We had no idea how big the joints should be, so we used what others had used. We had no idea about geometry, so we just aligned the a-arm horizontal and made the upper one a bit shorter to get camber gain. We did a knife style adjustable front anti roll bar, but had no idea about how stiff it should be or how to design it to meet that stiffness. Last but not least were spring stiffness, we just guessed what they should be. We actually had two stiffnesses of springs to start with, the other set was twice as stiff as the other.

I understand that not many have had the problems we have had, so they haven't had to learn these things. People who aren't interested in roll center don't probably read this thread

FJC, the textbook roll center as defined by SAE isn't very helpful: "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll".
The geometric roll center is not the truth, it's nowhere near the real world. The geometric roll center can give pretty accurate results, but sometimes it is way off. If a formula is only sometimes right, I don't consider it a very good one.
The force based roll center isn't the same as the real world either because it only takes into account the geometry and forces, but because it's force based like the real world, the results are much more accurate than the geometric approach. It has limitations, if you for example put stiff shocks on the car, the roll center changes very much, but according to the calculated model the results don't change.

I believe that the roll center is a concept that came to the automotive engineers from aviation, and it's just an approximation of how much the suspension geometry resists roll. The geometric roll center is the simplest approach. It is the most accurate when the lateral forces are small and there is very little body roll. Most cars on the street rarely exceed 0.2G, so this number works very well when designing something that will just be driven around town.

Nowadays engineers don't use the roll center or pitch center as they used to, but some probably still do. It's all about complicated models that have every parameter included in them. These parameter are for example: suspension/spring mounting point stiffness, bushing stiffness, suspension arm stiffness. Not to forget the very complicated tire models. The values that these programs give to their users tell them how the car performs and how the car feels to the driver. The values are not only starting points, they are simulations that are validated in real world.

Roll, pitch and yaw centers are very important concepts. Especially yaw. If you can manipulate the yaw axis you will see very big improvements in how the car responds to driver input. The yaw axis moves around and is hardly ever at the CG. Everyone probably knows the dumbell effect. The further the mass is from the center if gravity, the harder it is to rotate. What is usually left out of the explanation is that the polar moment of inertia depends also on the how far the masses are from the center of rotation. So two cars with same measured static polar moment of inertia can enter a corner very differently depending on where the yaw axis is.

For your amusement.... years ago I used to scratch build my own RC cars, and it is quite possible to build a "car" with a very high roll center, even above the CG lines of the vehicle.

I had several setups that would literally bank through turns.
(They tended to "skate" at inopportune times, so I lowered it a bit, basically ~even with the CG F&R, banking/chassis contact is bad when you're 1/8" off the dirt/carpet and moving ~40 MPH, 6 cell 1/12th scale carpet car and a bizzaro RC10 based oval tracker)

It was kinda interesting, and worked quite well, as basically one had one spring across the car to support it, and a light sway bar or just damping to keep it level/transients.