Estimation of aerodynamic coefficients for a ball by using characteristics of trajectory

Abstract

We investigate estimation methods of aerodynamic coefficients for a ball in sports by using characteristic quantities of its trajectory. One method is based on the quantities representing the whole shape of trajectory while the other utilizes local quantities such as curvature and/or torsion. In the former, the flight distance and the maximum height are measured, and the motion equation predicts numerical values of these quantities with measured initial conditions and preset aerodynamic coefficients. Then the optimal combination of the aerodynamic coefficients is determined by minimizing the error between the measured and estimated values of the characteristic quantities. This method is applied to estimate drag and lift coefficients of a soccer ball in back-spinning, and the result shows that the averaged values of CD and CL are 0.205 and 0.237, respectively. In the latter method, the expressions between the aerodynamic coefficients and the geometrical quantities of trajectory are derived, which suggests that the piecewise quadratic interpolation on a trajectory provides the aerodynamic coefficients. This method enables to locally estimate the coefficients, and therefore clarifies the variation of the coefficients along a trajectory. Measured data for a table tennis ball is analyzed with the method and we obtain successfully the drag and lift coefficients in flight condition. The results indicate the qualitative difference of spinning effect in drag and lift coefficients.

Keywords

• sports engineering
• aerodynamic coefficients
• estimation
• trajectory
• soccer ball
• table tennis ball