Further Validation of Equations for Motorcycle Lean on a Curve

Previous studies have reported and validated equations for calculating the lean angle required for a motorcycle and rider to traverse a curved path at a particular speed. In 2015, Carter, Rose, and Pentecost reported physical testing with motorcycles traversing curved paths on an oval track on a pre-marked range in a relatively level parking lot. Several trends emerged in this study. First, while theoretical lean angle equations prescribe a single lean angle for a given lateral acceleration, there was considerable scatter in the real-world lean angles employed by motorcyclists for any lateral acceleration level. Second, the actual lean angle was nearly always greater than the theoretical lean angle. This prior study was limited in that it only examined the motorcycle lean angle at the apex of the curves. The research reported here extends the previous study by examining the accuracy of the lean angle formulas throughout the curves. The degree to which these equations can be used to model the development of lean as the rider enters a curve is evaluated. The prior study was also limited in that it only examined maneuvers on an oval track in a flat parking lot. The current study examines the accuracy of the theoretical lean angle formulas on a mountainous highway with curves of varying radius and changing banking and slope. The real-world data presented in this study is also utilized in conjunction with the lean angle formula to examine the interplay between the geometry of a curve, the motorcycle speed, and the rider’s skill level. Introduction Three basic factors limit the speed at which a motorcyclist can traverse a curve. The first of these is the limit of the available friction between the motorcycle tires and the roadway. The second is a geometric limit that is defined by the lean angle at which components of the motorcycle (a foot peg, for instance) come into contact with the roadway or at which the geometry of the tire prevents additional leaning. The third is the limit imposed by the rider’s psychological limits their willingness to approach either the geometric or friction limits of their motorcycle [Hugemann, 2013]. Previous studies by Rose [2014] and Carter [2015] have described methods for analyzing each of these limits. Of relevance to the present study is the fact that many riders will reach a psychological limit on their willingness to increase the lean angle of their motorcycle before they reach either the friction limit of their tires or the geometric limit of their motorcycle [Bartlett, 2011; Hugemann, 2013]. Watanabe and Yoshida found that the maximum lean angles utilized by novice riders were typically in the range of 15 to 25 degrees and those used by experienced riders were in the range of 34 to 40 degrees [Watanabe and Yoshida, 1973]. These results imply that the experienced riders used maximum lean angles that would approach the lean angle limits of many motorcycles, whereas novice riders stopped well short of the motorcycle limits. The middle values of these lean angle ranges imply that on a flat curve with a 250-foot radius, an experienced rider would be willing to lean far enough to traverse the curve at a speed of 53 mph whereas a novice rider would only be willing to lean far enough to traverse the curve at a speed of 37 mph. This further implies that the speed at which a motorcyclist can successfully follow a particular curved path depends on their own skill level and their willingness limits. Motorcycle Lean on a Curve The lean angle required for a motorcyclist to traverse a particular curved path will be the angle that brings the overturning moment generated by the tire frictional forces into balance with the opposing moment generated by the tire forces perpendicular to the road surface. The required lean angle increases with increasing speed and decreasing path radius. Fricke [2010] and Cossalter [2006] report that the lean angle of a motorcycle for a particular path and speed can be calculated with the following equation: q = æ è ç ö ø ÷ tan v gr mc 1 2 (1) Downloaded from SAE International by Neal Carter, Monday, April 02, 2018