Super ellipse as tyre-ground contact area

Abstract

In tyre-ground interaction studies there is a need to describe the contact area between a tyre and the ground. Tyre load and contact area give the ground pressure, which is important in evaluating environmental impact. The super ellipse provides an excellent means for describing, in a simple mathematical way, the shape and size of widely varying contact areas ranging from circles over ellipses to squares or rectangles. In the most complicated case, eight parameters are used, but usually only five are needed. The suggested mathematical expression gives greater flexibility in designing contact areas. It provides explicit border values for integration of ground pressure over the contact area. Thus a more accurate location of ground pressure centre is expected.