Dynamic Characterization of Arrows through Stochastic Perturbation

Abstract: Current arrow spine measurements rely on statically hanging a known weight at the shaft center and measuring the maximum deflection. This archaic method of measuring arrow stiffness ignores dynamic nature of the arrow when released from the bow. For this project, we built an apparatus to measure the dynamic characteristics of the arrow to better indicate arrow performance. Using stochastic perturbations from a voice coil actuator and displacement measurements, we successfully estimated the natural frequency, damping parameter, and mechanical stiffness of carbon, wood, and aluminum arrows of varying spines. Parameter estimates using a second order parameterized model showed agreement with the manufacturer rated spine values. In addition, high cycle fatigue testing was completed on each arrow material but showed no significant changes in arrow parameters.