Roll Center - Theory

Theory

There are two definitions of roll center. The most commonly used is the geometric (or kinematic) roll center; the Society of Automotive Engineers uses a force-based definition.

The location of the geometric roll center is solely dictated by the suspension geometry, and can be found using principles of the instant center of rotation. The SAE's definition of the force based roll center is, "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 lateral location of the roll center is typically at the center-line of the vehicle when the suspension on the left and right sides of the car are mirror images of each other.

The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass and the roll center a moment arm is created. When the vehicle experiences angular acceleration due to cornering, the size of the moment arm, combined with the stiffness of the springs and anti-roll bars (anti-sway bars in some parts of the world), dictates how much the vehicle will roll. This has other effects too, such as dynamic load transfer.