Analysis of Ackermann Steering Geometry

Ackermann steering geometry relates the steer angle of an inside tire to that of the outside tire. When turning the inside tire travels a shorter radius than the outside tire and thus must have a greater steer angle to avoid tire scrub. Classic Ackermann minimizes scrub by positioning both tires perpendicular to the turn center. It can have a significant impact on tire wear [1]. Ackermann analysis can also be used as a tuning tool in cases where classic Ackermann may not be the objective.

Ackermann has been around longer than the motor vehicle - over a century - but there is little rigorous analysis in the literature. There are two common measurements of Ackermann which give very different results. Both are used in texts and computer programs[8] Yet a literature search revealed only a couple sentences discussing the relationship between the two.

This paper presents a mathematical analysis of Ackermann which explains the two measurements and develops a formula relating the two metrics. It also derives additional analytical tools which provide better understanding of Ackermann steering geometry.