Error Analysis of Aerodynamic Force Estimation for Balls by Flight Experiment

Abstract

We investigate the accuracy of an estimating method for aerodynamic coefficients of balls in flight by using its trajectory data. The error in estimating the aerodynamic coefficients includes measurement and truncation errors: The latter arises in approximating the velocity and acceleration from the trajectory. The motion equation of two-dimensional projectile motion with drag and lift is written in simple expression by introducing complex number form. The relative error of the aerodynamic coefficients is obtained as a function of time interval for interpolation, and it is shown that the error has the minimal value. This fact means that the estimation error remains in principle and never vanishes even in the infinitesimal limit of time interval, and there exists the optimal value of the interpolation interval given according to the terminal velocity and measurement error. Moreover, we apply the result of the present analysis to measured trajectory data of table tennis balls without spinning. In particular, the estimation error in the drag coefficient is clarified from the two-dimensional data of the flight trajectories. As the results, the error is less than about 2% with the optimal interpolation interval at each measured position, and the range of the error in the drag coefficient becomes narrower and also its value tends to decrease gradually as coming closer to the optimal value of the interpolation interval.