BICYCLE SHIMMY: AN ANALYTICAL AND EXPERIMENTAL INQUIRY

Abstract

This project was undertaken to develop both quantitative and qualitative intuition regarding the behavior of bicycle shimmy, a mode characterized by rapid steering oscillations typically on the order of 10Hz. At high speeds, the shimmy mode can be unstable: shimmy is therefore defined by a critical velocity above which the mode is unstable. As many experienced cyclists can testify, shimmy onset is a surprising and potentially-dangerous phenomenon, and a thorough understanding of shimmy behavior is thus quite pertinent to the mechanical design and riding-technique of bicycles, both for racing and for recreation. However, the vast majority of academic and industrial research into the shimmy mode of single-track vehicles has focused on motorcycles: dynamical systems in which the overall mass is dominated by the vehicle. Bicycles differ quite significantly from motorcycles in that the overall system mass is dominated not by the vehicle but by the rider. The first phase of the project presents an analytical model of shimmy: By deriving the full, linearized equations of motion of a bicycle with torsional frame compliance, it is demonstrated that the shimmy mode arises primarily due to the torsional stiffness of the bicycle frame, therefore implying that the bicycle’s shimmy mode is funda- mentally similar to the well-documented shimmy-like behavior exhibited by simple castered wheels (for example, a shopping cart wheel or airplane landing gear). Fur- ther, the addition of damping into the analytical shimmy model reveals a complicated relationship between the shimmy critical velocity and the damping parameters of the bicycle. Because of the relative disparity in mass between the bicycle and rider, much of this energy dissipation occurs at the interfaces between bicycle and rider: the handlebars and the saddle. Armed with theoretical understanding, an experimental inquiry into shimmy was subsequently launched, comprising the second phase of the project. The Author risked his personal bike and safety to repeatably demonstrate unstable shimmy be- havior. A data-acquisition system, capable of recording data from five acclerometers strategically-placed on the Author’s road bicycle at a 1kHz sample rate, was designed and successfully implemented. A GoPro camera was used to record video footage. Experimental data was analyzed to corroborate two predictions of the analytical shimmy model: demonstrating, firstly, that the shimmy frequency stays relatively constant, regardless of forward speed; and, secondly, that the shimmy critical veloc- ity is highly dependent on the damping forces experienced between the rider and the bicycle, meaning that shimmy behavior may be reliably affected by rider adjustments to posture and muscle tenseness.