Two-Dimensional Mathematical Model of Sports Surfaces with Angled Multi-Intensity Impact Tests ^†

The purpose of this study is to propose a two-dimensional (2-D) mathematical model of sports surfaces for evaluating the shock attenuation and deformation properties in both the vertical and horizontal direction, especially in competitive track and field materials. We develop a 2-D impact test device that can control the initial impact angle and intensity with parallelogram linkage. Using this device, various intensity impacts with angles ranging from 5–25 degrees were performed on test specimen. A 2-D mathematical model for sports surfaces and parameter identification method is also proposed for evaluating such surfaces, especially for polyurethane competitive track and field materials. The model is constructed from vertical and horizontal elements, and the parameters for each element are identified separately. Finally, vertical and horizontal forces with various angles and intensities can be estimated with an identified parameter set.