本文为美国华盛顿州立大学（作者：JASON JOHN MARTIN）的硕士论文，共210页。

多普勒雷达正在世界各地的棒球场和垒球场投入实用，以跟踪投球和击球的轨迹。雷达单元位于本垒板后面，可以跟踪投球和击球速度、旋转速度、角度和球的位置。这些数据被用来衡量玩家的表现，以及保持对比赛过程的统计。这些雷达装置也被体育用品制造商用来测量设备的性能。这项研究的目的是确定雷达报告数据的准确性。

与高速视频相比，雷达测得的本垒板附近的命中和投送速度精度分别在2.8%和2.3%以内。相关角度在1.2°以内。雷达的命中测量距离在激光测距仪的5%以内。与红外视频跟踪相比，主板附近的击中、投送速度和角度分别在0.2%和0.6°以内。在水平角增加的情况下击球时，雷达噪声增大，最佳垂直角为15°时，噪声最小。初始球位误差为4米（13.1英尺），导致投送速度和角误差分别为4米/秒（8.9英里/小时）和8°。对比赛和现场研究数据的分析提供了一种测量球场垂直和水平释放点的方法。当投送起点保持恒定时，在水平和垂直位置观察到0.03 m（0.09 ft）和0.04 m（0.13 ft）的标准偏差。利用比赛数据计算了低缝垒球和高缝垒球的气动特性。平缝垒球的提升和拖曳系数分别为0.25<Cd<0.4、0.05<CL<0.4和0.3<Cd<0.5、0.05<CL<0.24。Cd值对自旋速率的依赖性最小，而CL值对自旋速率的依赖性更强。

Doppler radar is being implemented inbaseball and softball venues around the world to track the trajectory ofpitched and hit balls. The units are positioned behind home plate and can trackthe pitch and hit speeds, spin rates, angles, and ball positions. The data isused to measure the performance of players, as well as keep statistics on thegame. The radar units are also used by sporting goods manufacturers to measurethe performance of equipment. The goal of this study was to determine theaccuracy of data reported by the radar. When compared to high speed video, theradar measured the speeds of the hit and pitch near home plate to within 2.8%,and 2.3% respectively. The associated angles were within 1.2°. Hit distances ofthe radar were within 5% of a laser range finder. The hit and pitch speeds andangles near home plate were within 0.2% and 0.6°, respectively when compared toinfrared video tracking. Balls hit at increasing horizontal angles experiencedincreasing radar noise and an optimal vertical angle of 15° minimized noise. Anerror of 4 m (13.1 ft) in the initial ball position resulted in an error of thevelocity and angles of a pitch of 4 m/s (8.9 mph) and 8°. An analysis of gameand field study data provided a measure of the vertical and horizontal releasepoint of the pitch. When the starting point of the pitch was held constant, astandard deviation of 0.03 m (0.09 ft) and 0.04 m (0.13 ft) in the horizontaland vertical position was observed. Game data was used to calculate theaerodynamic properties of a low seam softball and raised seam baseball. Thelift and drag coefficients were, 0.25 < Cd < 0.4 and 0.05 < CL <0.4 for flat seamed softballs and 0.3 < Cd < 0.5 and 0.05 < CL <0.24 for raised seam baseballs. The Cd values were shown to have a minimaldependence on spin rate, while the CL values were shown to have a strongerdependence on spin rate. 

1. 引言

2. 文献回顾

3. TrackMan雷达系统

4. 雷达测量精度

5. 提升与拖曳

6. 比赛数据

7. 结论

附录A 用于跟踪比赛场景的不同设置

附录B 田径运动员棒球术语表

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