Evaluation of Flight Trajectory and Unsteady Fluid Forces on Kicked Non-Spinning Soccer Ball by Digital Image Analysis

This paper describes the experimental method for evaluating the flight trajectory and the aerodynamic performance of a kicked non-spinning soccer ball. The flight trajectory measurement is carried out using the digital image analysis. A centroid method and a template matching method are tested for the flight trajectory analysis using the artificial images generated by the data of a free-fall experiment. The drag coefficient obtained by the centroid method is better suited for the sports ball experiment than that by the template matching method, which is due to the robustness of the centroid method to the non-uniform illumination. Then, the flight trajectory analysis is introduced to a kicked experiment for a non-spinning soccer ball. The experimental result obtained from the stereo observation indicates that the S-shaped vari ation is found in the three-dimensional flight trajectory and in the side force coefficient during the flight of the non- spinning soccer ball.

• Non-Spinning Soccer Ball; Fluid Force; Flight Trajectory; Measurement; Stereo Image Analysis

4. Conclusion

In this study, three-dimensional flight trajectory analysis and unsteady fluid-force measurement are carried out to understand the aerodynamic performance of a kicked non-spinning soccer ball. In the flight trajectory analysis, a centroid method and a template matching method were tested and the accuracy of the flight trajectory analysis was evaluated from the artificial images combined with free-fall experiment. The results indicate that the centroid

method is better suited for the flight trajectory analysis of the sports ball under the influence of non-uniform illumination. Then, the flight trajectory analysis and the unsteady fluid-force measurement are demonstrated for the kicked non-spinning soccer ball using stereo cameras. The result indicates that the S-shaped variation of flight trajectory is observed in the flight trajectory measurement of non-spinning soccer ball, and the flow around the soccer ball can be in the super-critical regime at the final stage of observation. The S-shaped variation of the soccer ball might be due to the appearance of the large scale structure of vortex shedding in the wake.

5. Acknowledgements

This research was supported by the Grant-in-aid for Scientific Research (B), No. 20300207 in the fiscal year 2009-2010. The authors would like to express thanks to Prof. Y. Mori from Faculty of Education, Niigata University and Mr. Y. Yamaguchi who is an undergraduate student of Faculty of Engineering, Niigata University for their help in the experiment.

Nomenclature

A: projected area;

a: acceleration;

C_d: drag coefficient;

C_l: lift coefficient;

C_s: side force coefficient;

d: balldiameter;

F: Force vector;

F_d: drag;

F_l: lift;

F_s: side force;

g: gravitational acceleration;

m: mass;

Re: Reynolds number (= |U|d/ν);

t: time;

U: velocity vector;

|U|: magnitude of local ball velocity;

u, v, w: velocity components in x, y, z directions, respectively;

X: position vector;

x, y, z: coordinates;

x’, y’: relative coordinates from ball center;

Δt: time interval between sequential images;

ν: kinematic viscosity of air;

ρ: density of air.

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