足球曲線自由球射門飛行軌跡之模擬分析

The Simulation and Analysis of Flight Trajectory of Curving Free Kicks in Soccer

邱永興(Yung-Hsing Chiu) ； 涂瑞洪(Jui-Hung Tu)

《大專體育學刊》 8卷4期 (2006/12) Pp. 91-100

https://doi.org/10.5297/ser.200612_8(4).0007

摘要

本研究主要目的是藉由實際測量足球曲線自由球射門時初始狀況與飛行軌跡之運動學參數，建立飛行軌跡之數學模式，以模擬真實比賽情境，並提出成功曲線自由球射門所需具備之條件。受試者為三名男子國家足球隊成員，平均年齡為19.7±1.5years，身高174.7±1.5cm，體重68.0±5.2kg。本研究利用2台Redlake高速攝影機以及4台JVC數位攝影機，分別以250Hz與120Hz進行足球射門飛行初始狀況與軌跡之拍攝，並以APAS動作分析系統將影片3D數位化，求出相關飛行參數以進行探討，有效樣本共計19次射門。研究結果發現球體在飛行時的旋轉會產生麥格納斯效應，使其受到側向力的作用，並垂直於轉軸方向，所造成的側向偏移量將對飛行軌跡造成明顯的變化。飛行軌跡的擬合方程式與預測方程式之相關可達.93以上，能夠有效的預測飛行路徑。經由電腦模擬預測發現，球員在面臨真實比賽情境時，能夠利用不同的拋射角與方向角等飛行初始參數，視當時情況擬定出各種射門策略，以避開對方人牆與守門員的層層防守，直攻對方大門，成功以曲線自由球射門得分。

關鍵字

旋转 ； 转速 ； 初始状况 ； 空氣動力學

並列摘要

This study developed a mathematical model of the ball flight to simulate free kicks under virtual matches, trying to point out the required final conditions that are connected with the successful curving free kicks. It could be observed through the realistic measurement of the kinematical parameters under the initial conditions and the flight trajectory in curving free kicks of soccer. Three male soccer players in the national team volunteered to join the study. In addition, the average age was 19.7±1.5 years, the average height was 174.7±1.5 cm, and the average weight was 68.0±5.2 kg. This study employed 2 Redlake high-speed cameras and 4 JVC digital cameras to take the flight initial conditions and the flight trajectory with 250 Hz and 120 Hz separately in the course of shooting. Furthermore, the films were digitized with the Ariel Performance Analysis System to determine the flight parameters in order to carry on the discussion. The valid sampling size was 19 totally. The results showed that the rotation of the ball would generate Magnus effect during the flight to make it subject to the lateral force perpendicular to the direction of the spinning axis. The lateral deflecting displacement that resulted from lateral force would cause a distinct change for flight trajectory. In addition, the correlation reached more than .93 between fitting and predicting equations of the flight trajectory that could predict flight path efficiently. With the prediction through the computer simulation, the results indicated that while the kicker was facing the true match situation, he could employ different flight parameters, including projection angles and direction angles, and so on, to draw up the different tactics of shooting for avoiding the layers of defense of the opponent's wall and goalkeeper. The most important was that the kicker could attack the goal post directly to score with the curving free kick successfully.

並列關鍵字

spin ； rational speed ； initial condition ； aerodynamics

參考文獻

Asai, T.,Carre, M. J.,Akatsuka, T.,Haake, S. J.(2002).The curve kick of a football I: impact with the foot.Sports Engineering.5,183-192.

Bray, K.,Kerwin, D. G.(2003).Modeling the flight of a soccer ball in a direct free kick.Journal of Sports Science.21,75-85.

Dapena, J.,Harman, E.,Miller, A.(1982).Three-dimensional cinematography with control object of unknown shape.Journal of Biomechanics.15(1),11-19.

Frohlich, C.(1984)。Aerodynamic drag crisis and its possible effect on the flight of baseballs。American Journal of Physics。52(4)，325-334。

Grant, A. G.,Williams, A. M.,Reilly, T.(1999).Analysis of goals scored in the 1998 World Cup.Journal of Sports Sciences.17,826-827.