Tractrix Trajectory with Slip Steering

Abstract

The tractrix curve, sometimes called the pursuit curve has long been the standard used to describe the path of a pig trailer behind a prime mover. This ideal path still has validity today provided the speed is very low and the trailer is unloaded. During a common phenomenon of snaking or fishtailing, the trailer sways back and forth in relation to the prime mover centreline axis. Often regarded as the nightmare of caravanning, the action does not follow the tractrix curve but follows a shorter path to the common centreline of prime mover and trailer. This paper explores the shorter path in response to a tyre reaction to centripetal force causing slip steer. An example derived by drafting progression steps to how quantitatively that speed causes early cross-over carrying more energy into the next fishtailing phase is presented. It is believed the inclusion of slip steering to modify a tractrix curve is a novel development.