Evaluation of a Differentiation Scheme for Estimating Angular Acceleration from Angular Velocity

Abstract

Headform impact testing is commonly used in the evaluation of helmets and head gear, head impact sensors and in sports related accident reconstruction. While linear acceleration of the headform center of mass can be measured using three linear accelerometers, the preferred method for measuring rotational acceleration of the headform requires six or more additional accelerometers. Some measurement systems use gyroscopes to directly measure headform angular velocity and obtain angular acceleration through differentiation. This approach simplifies instrumentation of the headform and reduces costs, but at the expense of accuracy. Error introduced through differentiation of angular velocity data can be prohibitively large for some sports applications, particularly in the consideration of un-helmeted headform impacts. This work considers the application of a new, optimization-based differentiation technique to improve the fidelity of headform angular acceleration estimates based on gyroscope measures of headform angular velocity. A Hybrid III headform instrumented with three gyroscopes and nine linear accelerometers was subject to drop impacts, as well as being impacted with soccer balls and softballs projected over a range of velocities. Measures of resulting headform angular acceleration were obtained from the gyroscope data using five-point stencil differentiation and the new optimization based algorithm. These results were compared to the nine accelerometer array measurements of angular acceleration across impact scenarios.

Keywords

• acceleration
• headform
• impact