Pneumatic tires always roll with slip unless traveling straight ahead with their loaded rolling radius coinciding with their effective radius – an infrequent circumstance. Slippage in the contact patch is further exacerbated by vehicle braking, driving and/or cornering. Even tires rolling and turning at low speed on a dry surface will undergo overall longitudinal slip and lateral scrubbing coupled with individual tread element squirm. Such relative motion between tires and roads promotes tread wear. To help minimize unnecessary tire sliding during vehicle cornering, a four-bar linkage with an isosceles trapezoid planform, or Ackermann geometry, is generally used as the foundation for front-wheel steering control. Most road car steering is based on this layout; this also provides a symmetric response for both left- and right-hand turns.
The story of Ackermann steering begins with a rough sketch in an obscure note written by Erasmus Darwin (1731-1802) to James Watt (1736-1819) in 1767, depicting carriage wheels and axles. Darwin was an English physician with an interest in mechanical inventions (and best known today as the grandfather of Charles Darwin) and Watt was a well-known Scottish inventor. Recall that the Ackermann principle is based only on geometry: if the inside wheel on a front axle turns through a greater angle than the outside wheel, both wheels can be made to track around a common center determined solely by wheelbase and radius. On vehicles equipped with pneumatic tires, a common turn center minimizes tire scrub and steering effort. This concept, the kinematics of steering, was captured in Darwin’s sketch 253 years ago for a horse-drawn carriage featuring axletrees paired with wooden wheels – though Darwin did not secure a patent.
The idea was independently reinvented by Georg Lankensperger (1779-1847) in Munich almost a half-century later in 1816. Lankensperger was a wagon maker, wheelwright and inventor who built coaches and sleighs for the Bavarian court. Rudolph Ackermann (1764-1834), his German-born agent living in London, filed for a British patent (GB 4212) in 1818. Although Lankensperger was named as the inventor in the text, his contribution has been mostly forgotten.
The main drawback of pure Ackermann steering for today’s automobiles is that its premise is based on low-speed turning – quasistatic motion. Traversing a curve during moderate- or high-speed driving produces a centrifugal force that is balanced by a cornering force acting on each tire. These equilibrating forces cause the laterally flexible tires to generate increased slip angles. These angles, averaged at the front and rear, can be accommodated, with simplifying but reasonable assumptions, within an expanded ‘dynamic Ackermann’ equation. Importantly, the cornering-force-induced slip angles reduce turn radii and assist vehicle handling. Although not immediately self-evident, rear tires also steer via these angles – but passively.
Automobile steering mechanisms are generally designed to operate in the sector between low-speed Ackermann and parallel steer. Sports cars tend to be configured toward parallel steer while sedans tend toward pure Ackermann. Both vehicle platforms would normally have tire toe-in for stability. Race cars, on the other hand, might utilize parallel steer, or even reverse or anti-Ackermann, with toe-out for maximizing tire scrub and steering. The supposition follows: if steered wheels remain parallel during cornering, or operate with reverse Ackermann, the outside tire-wheel assembly, already more heavily loaded due to centrifugal force, would suffer additional lateral scrubbing, which would further improve handling. Rapid tread wear is the penalty. Conversely, vehicles featuring either rear-wheel steering systems (such as forklifts) or four-wheel steer are apt to remain relegated
to niche applications. Both steering modes tend toward oversteer at moderate to higher speeds, but operate well at low speeds when maneuverability is required.
Steering systems such as rack-and-pinion mechanisms conforming to variations in early four-bar trapezoidal linkages began in earnest with the development of motorized road transport, and improvements continue today. Rightfully or wrongfully, Ackermann’s name survives with these newer systems, not Darwin’s or Lankensperger’s – two centuries after publication of his eponymous British patent.
