Force-Based Roll Centers and an Improved Kinematic Roll Center

Roll Centers are an important tuning tool but their importance is often misunderstood. The roll center has too often become a mysterious concept rather than a simple descriptive parameter. Roll Centers may be determined from forces (the Force-Based Roll Center) or the more familiar kinematic method. This paper will explain and reconcile the difference between these roll centers. That explanation will show how the roll center should be used in understanding the behavior of a vehicle.

The most familiar roll centers are for independent front suspensions with two a-arms or wishbones, also known as SLA or Short Long Arm suspensions. For these suspensions this paper will derive a method to construct a more accurate kinematic roll center which explains the differences between the Force-Based Roll Center (FBRC) and the Kinematic Roll Center (KRC).

The common kinematic roll center is based on four links between the upright/spindle/wheel/tire and the sprung mass of the chassis. But there are five links between those parts: the missing link is the steering tie-rod. The steering link accounts for the differences between FBRC and KRC. Proper accounting for the forces on the steering link explains the differences.

The difference between FBRC and KRC would be more significant but the following analysis will show that minimizing bump steer reduces the difference. The practical desire to eliminate bump steer minimizes the theoretical difference between FBRC and KRC.