Modeling Bicycle-Rider Vibrations: Implications for Materials Selection
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Modeling the Rider In the modern performance-bicycling posture, the arms of the rider are approximately perpendicular to the trunk and support a significant portion of the trunk weight. As such the vibration that enters the body via the handlebar tends to vibrate the rider in a direction perpendicular to the body plane. This mode of vibration is particularly detrimental to the bicycle rider as the human body is approximately 10 times more sensitive to vibrations perpendicular to the body than those in the body plane.1 For this reason, we have focused on the development of a mechanical description of the arms and trunk of the bicycle rider, with the immediate goal of understanding how vibration that enters the body at the handlebar propagates through the arms to the trunk. Once developed the model can be used to guide and assess the effect of different designs and material choices on the vibrational characteristics of the ridden bicycle.
Introduction Over the past several years, the number of materials routinely employed for the fabrication of major bicycle components (e.g., frame, fork, and handlebar) has increased from one (steel) to at least five (steel, aluminum, titanium, fiberreinforced polymers, and magnesium). Historically the primary driving force for implementation of new materials in bicycle manufacture has been the almost fanatical desire to reduce the weight of the bicycle. Although weight reduction of the bicycle will continue to be important, an old design paradigm—driven mostly by the recent popularity of bicycles designed to be ridden off-road (mountain bikes)—has re-emerged: the design of bicycles that minimize the amount of road/trail shock transmitted to the rider. One approach toward this goal is to install suspension elements consisting of spring-dashpot mechanical linkages reminiscent of suspensions found on most motorcycles. A second, complementary approach is to carefully design major structural components of the bicycle (e.g., handlebar, front fork, frame, etc.) to minimize transmitted vibration to the rider. Given the geometric constraints (i.e., generally the part must conform to an industry-standard size/shape) and strength requirements (i.e., the part should not fail under normal riding conditions), the bicycle designer has until recently been somewhat limited in the ability to alter the mechanical properties of a component. With the wide range of candidate materials now available how56
ever, a great range of mechanical properties can be obtained while maintaining the necessary service strength and geometry. For example, handlebars of a given strength constructed out of steel, aluminum, and titanium will possess different values of bending stiffness. Each will therefore change the "feel" of the bicycle by modifying the characteristics of the vibration reaching the rider. Furthermore some of the newer materials such as the fiber-reinforced polymers permit the mechanical properties (e.g., elastic modulus and damping capability) to be tailored for a given strength level, giving the desig
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