Radial Stiffness and Damping of Mountain Bike Tires Subject to Impact Determined Using the Coefficient of Restitution

Mountain bikes are essentially ruggedized versions of a standard bicycle with geometry and features suited to off-road cycling. Their intended use case has them encountering jumps, bumps, drops, and impact. As such, their designs have evolved to include front and often rear suspension systems composed of springs and dampers in sometimes elaborate kinematic arrangements. Despite extensive design resources spent optimizing and tuning mountain bike suspension systems, very little has been published regarding the in-plane behavior of their tires or bicycle tires in general. In this work, a drop test bench is utilized to measure the dynamic radial stiffness and damping of numerous mountain bike tires including four common sizes spanning 29er, plus-sized, and fat tire variants, as well as various constructions ranging from trail, through enduro, and downhill. The tire is treated as a classical, lumped Kelvin-Voigt model with a parallel arrangement of a spring and damper. Identification of the system parameters is accomplished by treating the tire as a bouncing ball and using the coefficient of restitution from pre and post impact velocities to determine the dynamic stiffness and damping. The advantages of this approach in comparison to a classical logarithmic-decrement approach are discussed. Results suggest that due to its viscoelastic nature mountain bike tire dynamic radial stiffness is appreciably higher than its quasi-static value. Furthermore, although its damping is relatively low (spanning 2 to 5% of critical), it can affect subjective “trail feel” and can be perceptibly influenced by tire selection, size, construction, and inflation pressure.