網球單打比賽之單球攻防模擬

The Simulation of One Serving and Returning in Tennis Singles

10.5297/ser.200509_7(3).0017

邱靖華(Ching-Hua Chiu)

三度空間 ； 防守位置 ； 數學模式 ； three dimensions ； defense positions ； mathematic model

大專體育學刊

7卷3期（2005 / 09 / 30）

215 - 227

繁體中文;英文

本研究的目的在於應用數學方法，建立網球單打比賽的單球攻防系統，模擬選手如何在比賽中取得有利的打點位置、防守位置，及將攻防系統開發成電腦軟體。研究方法：第一步驟，首先以攝影方法，分析一位受測選手在防守時擊球的反應時間，及測試均勻分佈在三度空間中的100個擊球位置的擊球時間，再運用Spline曲線函數，建構受測選手從預備動作至擊球的防守空間範圍。第二步驟，根據流體力學及數值方法，建立網球擊球後的飛行數學方程式，模擬網球從擊球復至第二次落地的飛行軌跡。第三步驟，將步驟一、二所建立之數學模式，以 C(上標 ++)程式語言編寫成電腦軟體，進行選手攻與防的模擬分析。結論：一、根據電腦模擬打點分佈位置得知，攻者得分球的落點位置，偏離防者愈遠愈能得分。愈偏離防者預備位置的打點愈靠近球場邊線，相對的也愈會打出界外，造成失誤。二、模擬的結果顯示選手的防守位置，以復半場的中央位置，做為隨時準備接下一球預備位置，可以取得較大的防守優勢。三、本研究所建構的數學模式，有助於受測選手在比賽中取得有利的打點位置，以及防守位置，並且可以發展成為實際的應用程式軟體，提供給選手在賽前進行模擬分析。

The purpose of the study was to apply the mathematic methods to establish an offense and defense system of one service in tennis singles to find out the optimal positions for serving and returning respectively. Next, the offense and defense system was developed into the computer software. Photography was used to analyze the reaction time of the subject in returning the service. The subject was required to return the balls served from different positions. The returns added up to one hundred. The time of each return was calculated and collected. The math equation of the ball in play was established to simulate the flying track of the ball from the time the service was delivered to the time it hit the ground the second time. C++ language was adopted to design a software program which is capable of simulating offense and defense conditions based on the math models established in the first two steps. This study reached at the following conclusions. First, as shown in the distribution of simulated positions, it is easier for the server to score a point if the position where the service hit the ground was away from the receiver at rest. However, it is also more likely to be outside of the lines which bound the opponent's court. Second, the result of simulation showed that the optimal defense position for the receiver is in the center of his court. Third, the math models established in this study can be developed into a software. With the analysis and simulation provided by the software, the tennis players are able to adjust to the optimal offense and defense positions simulated by this study, thus resulting in good performance in competition.

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