Explained: Roll center

[hybrid 1039]

Hey guys,

Thought I might start a series of posts on suspension characteristics and the reasons why or why not things are done on a vehicle (specifically BMW 3series) I'm no expert on the topic .. I'm marely researching it myself for my own projects and thought I would post findings here.

Feel free to add to the topic with credable howtos, car setup data, FYIs.

Most automotive enthusiasts have heard of the term "roll center". It is a property of both front and rear automobile suspensions and determines, among other things, how far a car rolls during cornering. A roll center which moves around a lot as the suspension compresses and extends is considered undesirable, and can make a car "feel weird" to drive. A small amount of motion of the roll center in the vertical direction is tolerable, but movement of the roll center in the lateral direction is not good.

It is the location of the roll center in relation to the center of mass that governs how far one end of a car will tend to want to roll during lateral acceleration (cornering). This is called the "roll-couple". The ratio of the front roll-couple to the rear roll-couple is one of several factors that determines the tendency of a car to either oversteer or understeer.

An explanation of how the roll center and center of mass combine to form the roll-couple can be found here: "How lowering a car affects roll-couple"

http://e30m3performance.com/myths/Weight_T...t_transfer2.htm

To visualize the rear roll center you really need a picture. The digital drawings that follow are large - they need to be in order to show the detail properly. I suggest the reader have a look at the first drawing and then come back to the text:

Semi-trailing arm ROLL CENTER for a standard configuration.

Note the references to "IC" which stands for "instant-center". The instant center is the virtual location about which a wheel "rotates" at any particular time (as seen from the front of the car or from the side). Here we are not referring to the wheel rotating about its axle as the car rolls down the road. Rather we mean the "imaginary" location about which a wheel rotates as it moves through its suspension range of travel. Although one would like the roll center to stay in one place, it is quite normal for the instant centers to constantly change location as the wheels move up and down. What you want is that as a car rolls, and one side of the suspension compresses while the other side extends, that the two instant centers move in such a way that the relationship of the roll center to the chassis remains relatively unchanged. That being said, since a semi-trailing arm has a fixed instant axis (it's axis of rotation) then the instant centers on a semi-trailing arm suspension remain fixed relative to the chassis. This results in a camber curve which is a straight line.

Observe that the instant center for the right rear wheel is on the left side of the car and visa versa. Once you find the instant centers, locating the roll center is easy. You simply draw a line between each tire contact patch and its instant center. The intersection of these two lines (one for each wheel) is the roll center.

[hybrid 1039]

What we will now concentrate on is how the static roll center moves as the geometry of the rear trailing arms is changed. If you have read the section on camber and toe change of a rear semi-trailing arm suspension then you

know about the so called "sweep angle" of the trailing arms.

http://e30m3performance.com/tech_articles/...urves/index.htm

During the BMW Motorsport days of racing E30 M3's in Gr A there were two different rear suspensions available, each with a different sweep angle (11° or 15°). The change in the sweep angle altered the camber and toe curves for the rear suspension. But it also changed the rear static roll center as shown in the following diagram:

Semi-trailing arm ROLL CENTER for reduced sweep angle.

The net effect of reducing the sweep angle of the rear semi-trailing arm suspension is to move the rear static roll center down. If the center of gravity at the rear end of the car remains unchanged then the net effect is that the rear roll couple is increased, and thus the rear of the car will want to "roll more" during cornering. This is not necessarily a bad thing, and depending on overall chassis setup it might actually be a desirable outcome. A roll center which is too high will introduce "jacking" forces such that the car is raised during lateral acceleration.

Another way that the rear semi-trailing arm geometry can be changed is by moving the trailing arm pivot points up or down. This configuration is sometimes seen in pictures of the last generation Gr A cars. The outer trailing arm pickup points can be adjusted for camber, as in earlier versions. But the camber adjustment does not move the pickup point (as it's on the trailing arm, not the chassis). However, there is a second adjustment which allows the outer trailing arm pickup point to be moved up and down. This type of adjustment mechanism is shown in this photograph of what is most likely a late model Gr A e30 m3 car.

The red arrow highlights the roll center adjustment while the purple arrow shows the camber adjustment. Adjusting the location of the outer trailing arm pickup point will obviously affect the camber and toe curves to some extent, but the main reason to make this adjustment was probably to effect a change in the location of the rear roll center (thanks to Paul Franz for pointing this out to me). How the roll center responds to a change in the vertical location of the outer trailing arm pickup point is shown in the next diagram:

Semi-trailing arm ROLL CENTER for raised outer pickup point.

The result of this change is that the static roll center moves downwards. Note that the same effect could be achieved by moving the inner trailing arm pickup points down (instead of moving the outer pickup points up). And conversely, moving the outer pickup points down (or the inner ones up) will raise the static roll center, instead of lowering it.

With a set of careful measurements of the E30 chassis one could calculate the actual location of the rear roll center. But that will not be done in this article. Furthermore, determination of the rear roll couple would require knowledge of the distribution of the center of gravity along the chassis. That is not trivial information to obtain, therefore such an exersise is left for the reader 8^)

[kiwi535 538]

errr thanks....I will have to read this two or three times first...

[tire 10]

errr thanks....I will have to read this two or three times first...

Same here, + another few hundred!

[Guest Simon*]

Thanks Josh - i think it's a good idea to post up your findings like this

I'm currently trying to educate myself somewhat so as to better understand the handling characteristics of my own car. It has a nice tight and low suspension setup and handles very well in the twisties in my opinion but I still freak out a bit when I look at all the negative camber on the back wheels.

The previous owner went through five completely different combos of springs, shocks and setup and finally arrived at this - and I don't want to just nod dumbly when someone goes over it for me. Hence the self education.

Keep up the good work

[Greg111 13]

Camber=Gangster though

Edited February 29, 2008 by Greg111

[E30BMA 0]

Camber=Ganster though

Im pretty sure you mean Gangster, Greg???

Dont 4get Camber also = empty pockets for greg when his tyres wear extra fast...

[PBOY23 0]

Dont 4get Camber also = empty pockets for greg when his tyres wear extra fast...

a HIGH 5 to that 1 it sucks!

[westy 614]

This only applies to E30 rear tho dosnt it?

E36 Z arm rear a lot more effective.

Ps. camber rocks