Roll Centers
Put as simply as possible, the roll center is the point around which the chassis rolls. We all know what body roll is, right? Well, it's actually a pretty complicated subject. The dynamics of roll centers- where they are, and how they migrate around the chassis while driving- is one of the fundamental concepts of chassis design. This article isn't written just for chassis designers, though. No, anybody who plays with the ride height of their vehicle is also changing their roll center- sometimes drastically- and should take precautions to know how.
This animation shows how to find the basic roll center of your vehicle while at rest. An Ariel Atom was used as an example because its exposed suspension arms make the illustration very easy. This car uses a double wishbone suspension up front, which can clearly be seen by a pair (upper and lower) A-shaped arms.
To find the roll center a vehicle with double wishbones, simply draw the suspension to scale on paper. Draw lines extending from each wishbone past the center of the car and off into space. At some point, those lines will intersect. This is the instantaneous center, and there will be one instantaneous center on each side of the car (on the left side for the right suspension, and on the right side for the left suspension). Next, draw a line from each instantaneous center to the center of the tire's contact patch. Where these lines intersect is your roll center, and for a car with similar suspension geometry on both sides of the car, this will always be directly between the left and right wheels. The variable you measure here is height, which is important.
Now let's look at the roll center of the front of a Subaru WRX STI as calculated by a computer modeling program. Notice that this is a model of a strut-based suspension, which is very different from a double-wishbone suspension. To model a strut suspension, where the struts themselves act as the upper suspension linkage, draw your imaginary lines directly perpendicular to where the top of the strut mounts, as shown:
The grayed-out values shown are of the suspension at the factory ride height, where the roll center height is 3.2 inches above ground. Once the car is lowered one inch by installing new springs and struts, the roll center drops to 0.6 inches above ground. So, the roll center dropped 2.6 inches with a mere 1 inch change in ride height. This is quite a significant change.
However, just the roll center at the front of the car should not be looked at in isolation. Plotting the front and rear roll centers gives us what is known as the roll axis, which is said to be the axis around which body roll occurs. There's nothing fancy here, just a line drawn between the front and rear roll centers. Shown here is the roll axis of a Mazda6 sedan:
With the roll axis plotted, we can find one very important spot on the roll axis. That spot is the point directly below the car's center of gravity. For a car with a 50/50 weight distribution, that spot will be directly between the front and rear axles. For a car with a 60% / 40% weight distribution, that point will be only 40% of the wheelbase away from the front axle.
You may recall from reading elsewhere on this site that weight transfer is caused by having a center of gravity above ground. The sum of all cornering forces in the car can be lumped together and said to originate, as a whole, at the center of gravity. The forces pushing on your tires can be said to originate from the center of gravity. The tires resist that force, but do not push back at the center of gravity. Instead, the forces from your tires can be said to react on the chassis along the roll axis, centered directly below the center of gravity.
Here is a simplified diagram showing where forces originate and act between the chassis and tires:
The important thing to realize here is that the center of gravity is above the center of roll. Because of this, when cornering forces push on the center of gravity, the chassis wants to react with roll. The larger the distance between the center of gravity and the center of roll, the larger the torque arm which will cause body roll. This torque arm is called the vehicle's roll couple.
If the roll center was instead the exact same height as the center of gravity (roll couple = 0), the vehicle would not have any body roll. The chassis would still have weight transfer, but the chassis would not react to it by rolling. Instead, it would just try to slide left or right. Pretty wild to think about, eh? But there are numerous drawbacks to this design, one of which is that manufacturers have discovered that drivers subjectively prefer feedback through body roll.
Now, let's go back to the example earlier where we found that lowering a Subaru WRX STI drops the front roll center by 2.6 times as much as the chassis height (which also means 2.6 times as fast as the chassis's center of gravity). As it turns out, a one-inch lower ride height actually increases the vehicle's roll couple by about 18%, which means body roll will also increase by 18% unless firmer springs are used to resist this force. The springs would need to be 18% firmer just to maintain stock-like chassis roll numbers. Again, that's 18% just to break even!
Additionally, because changes in roll center height change how the chassis reacts to cornering forces, they also can change the car's handling bias. A high roll center discourages body roll whereas a low roll center encourages body roll. If the roll center is lowered in the front of the car but not the rear, the front will now encourage more body roll for a given cornering force. Thus, the tendency of the body to roll will increase, but the front of the car will be less willing to resist that roll. This means the rear of the car will pick up the additional work of resisting that roll, meaning more weight transfer in the rear relative to the front. This causes oversteer.
Tuning chassis dynamics with roll centers is quite complex, and this article has barely scratched the surface. However, an analysis of roll centers will often show why some vehicles will feel very responsive despite soft springs and why others will not, or why some cars feel more stable at their limits than others. Continue reading the other articles on roll centers to find out more.