The influence of moment of inertia on baseball/softball bat swing speed

The speed at which a player can swing a bat is central to the games of baseball and softball, determining, to a large extent, the hit speed of the ball. Experimental and analytical studies of bat swing speed were conducted with particular emphasis on the influence of bat moment of inertia on swing speed. Two distinct sets of experiments measured the swing speed of colege baseball and fast-pitch softball players using weighted rods and modified bats. The swing targets included flexible targets, balls on a tee and machine pitched balls. Internal mass alterations provided a range of inertial properties. The average measured speeds, from 22 to 31 m s⁻¹, are consistent with previous studies. Bat speed approximately correlates with the moment of inertia of the bat about a vertical axis of rotation through the batter's body, the speed generally decreasing as this moment of inertia increases. The analytical model assumes pure rotation of the batter/bat system about a vertical axis through the batter's body. Aerodynamic drag of the batter's arms and the bat is included in the model. The independent variable is bat moment of inertia about the rotation axis. There is reasonable agreement between the model and the measured speeds. Detailed differences between the two suggest the importance of additional degrees of freedom in determining swing speed.     

Field and laboratory measurements of softball player swing speed and bat performance

The swing speed of the bat is one of the most important factors affecting the hit-ball speed. Most field studies tend to focus on measuring ball speed, which is easier to measure and quantify than bat speed. For this reason, relatively little data exist describing bat motion in field conditions. The following describes a relatively large swing speed field study involving bats of the same model with nearly constant weight and varying inertia. The study was conducted using right-handed batters on a regulation outdoor field with a live pitcher. Swing speed was measured by tracking markers on the bat with two high-speed video cameras so that the bat markers could be traced in three-dimensional space. The ball motion was tracked using the same high-speed video cameras and a three-dimensional Doppler radar system. Bat swing speed was observed to be proportional to the batter skill level and the normalised swing speed increased with decreasing bat inertia. The bat centre of rotation during impact was close to the knob of the bat. The bats were tested under controlled laboratory conditions using a standardised performance test. The field and laboratory results showed good agreement including the hit-ball speed and the subtle effect of bat inertia on the maximum performance location. The vibrational response of the bats was considered using modal analysis. The maximum performance location was correlated with the node of the first vibrational mode.     

Gyroscope-based assessment of temporal gait parameters during treadmill walking and running

Wireless sensing solutions that provide accurate long-term monitoring of walking and running gait characteristics in a real-world environment would be an excellent tool for sport scientist researchers and practitioners. The purpose of this study was to compare the performance of a body-worn wireless gyroscope-based gait analysis application to a marker-based motion capture system for the detection of heel-strike and toe-off and subsequent calculation of gait parameters during walking and running. The gait application consists of a set of wireless inertial sensors and an adaptive algorithm for the calculation of temporal gait parameters. Five healthy subjects were asked to walk and run on a treadmill at two different walking speeds (2 and 4?kph) and at a jogging (8?kph) and running (12?kph) speed. Data were simultaneously acquired from both systems. True error, percentage error and ICC scores indicate that the adaptive algorithm successfully calculated strides times across all speeds. However, results showed poor to moderate agreement for stance and swing times. We conclude that this gait analysis platform is valid for determining stride times in both walking and running. This is a useful application, particularly in the sporting arena, where long-term monitoring of running gait characteristics outside of the laboratory is of interest.     

Prediction of shot success for basketball free throws: Visual search strategy

Abstract

In ball games, players have to pay close attention to visual information in order to predict the movements of both the opponents and the ball. Previous studies have indicated that players primarily utilise cues concerning the ball and opponents' body motion. The information acquired must be effective for observing players to select the subsequent action. The present study evaluated the effects of changes in the video replay speed on the spatial visual search strategy and ability to predict free throw success. We compared eye movements made while observing a basketball free throw by novices and experienced basketball players. Correct response rates were close to chance (50%) at all video speeds for the novices. The correct response rate of experienced players was significantly above chance (and significantly above that of the novices) at the normal speed, but was not different from chance at both slow and fast speeds. Experienced players gazed more on the lower part of the player's body when viewing a normal speed video than the novices. The players likely detected critical visual information to predict shot success by properly moving their gaze according to the shooter's movements. This pattern did not change when the video speed was decreased, but changed when it was increased. These findings suggest that temporal information is important for predicting action outcomes and that such outcomes are sensitive to video speed.     

A new technology for resolving the dynamics of a swinging bat

Hitting a major league fastball, with approximately half a second to react, poses one of the greatest challenges in sports. The ability to hit the ball derives from the dynamics of the bat swing which can be measured using video motion capture. However, doing so necessitates swinging the bat within the confines of a motion capture laboratory, often with considerable time and expense. This paper introduces an inexpensive and highly portable measurement method for use right on the field of play to support player training, coaching, rehabilitation, and player-bat fitting. The method employs a highly miniaturized, wireless MEMS inertial measurement unit (IMU) affixed to the knob of the bat. The IMU incorporates three-axis sensing of bat acceleration and angular velocity with a low-power RF transceiver to transmit this data to a host computer. Analysis of this data yields a near-instantaneous and highly resolved summary of three-dimensional bat dynamics. This paper describes this novel technology for use in baseball and softball, presents example results, and reveals new features of bat motion overlooked in previous studies.     

Warm-up with baseball bats of varying moments of inertia: effect on bat velocity and swing pattern

The purpose of this study was to determine if warm-up with baseball bats of different moments of inertia has an effect on swing pattern and bat velocity. Ten experienced baseball players (ages 20-25 years) voluntarily participated in this study. Each participant was required to complete 10 dry swings (5 warm-up and 5 postwarm-up) at maximum effort within 3 different conditions. Post warm-up was always with a standard bat (I = .27 kgm2; 83.8 cm, 9.1 N). Warm-up for Condition 1 was with the standard bat. Condition 2 required participants to warm up with a standard bat plus a 6.1 N lead donut (I = .49 kgm2, 83.8 cm, 15.6 N). Condition 3 required participants to warm up with a hollow plastic bat (I = .08 kgm2; 83.8 cm, 3.34 N). Quantitative and qualitative analyses indicated that following warm-up with the weighted bat (largest moment of inertia), swing pattern was significantly altered, and post warm-up velocity was the lowest of the three conditions.     

乒乓球运动员训练数据实时采集系统研制与应用

通过在乒乓球球拍的拍把上加装加速度传感器,并开发相应的击球力量训练数据实时采集系统,实时采集乒乓球运动员训练时挥拍的加速度数据,通过运动学和动力学分析,得出乒乓球运动员挥拍的速度、位移和力量等实时动态参数,并以曲线的形式实时、直观地显示给教练员和运动员,为教练员了解乒乓球运动员挥拍的力量等数据提供科学手段,为制订有针对性的技战术和体能训练计划提供科学依据。此外,采集的训练数据实时存储在后台数据库中,便于对运动员的击球力量等数据进行长期、科学的跟踪,以提高运动训练监控的针对性和科学化水平,提高乒乓球运动员的运动水平和比赛成绩     

A comparative study of baseball bat performance

The results of a comparative study of five aluminum and one wood baseball bats are presented. The study includes an analysis of field data, high-speed laboratory testing, and modal analysis. It is found that field performance is strongly correlated with the ball–bat coefficient of restitution (BBCOR) and only weakly correlated with other parameters of the bat, suggesting that the BBCOR is the primary feature of a bat that determines its field performance. It is further found that the instantaneous rotation axis of the bat at the moment of impact is very close to the knob of the bat and that the rotational velocity varies inversely with the moment of inertia of the bat about the knob. A swing speed formula is derived from the field data and the limits of its validity are discussed. The field and laboratory measurements of the collision efficiency are generally in good agreement, as expected on theoretical grounds. Finally, the BBCOR is strongly correlated with the frequency of the lowest hoop mode of the hollow bats, as predicted by models of the trampoline effect.     

基于动态时间规整算法的青少年乒乓球运动员击球动作合理性评价——以反手拉上旋弧圈球为例

运用高速动作捕捉技术,在采集国家队优秀乒乓球运动员(以下简称"国家队运动员")和青少年乒乓球运动员(以下简称"青少年运动员")基本技术动作的空间特征数据基础上,以反手拉上旋弧圈球为例,构建国家队运动员基本击球动作模型。运用动态时间规整(Dynamic Time Warping,DTW)算法,将青少年运动员的击球动作曲线与国家队运动员基本击球动作模型进行相似度比较,并结合击球质量数据对青少年运动员击球动作的合理性进行评价,分析其击球过程存在的问题。结果显示:①基于高速动作捕捉技术构建的国家队运动员击球动作模型能有效地对青少年运动员击球动作的合理性进行评价,具有一定的科学性。②将青少年运动员击球过程中各主要关节点运动轨迹和身体重心变换与国家队运动员的动作模型进行比较,可揭示青少年运动员击球过程中引拍、挥拍击球、还原三阶段各主要关节点运动轨迹和身体重心变换的合理性及不足,评价结果具有一定的可靠性。③通过对青少年运动员反手拉上旋弧圈球动作的合理性分析发现,该运动员引拍阶段右肩关节带动手臂向前移动的幅度较小,导致引拍不到位;还原阶段右肩关节还原幅度较小,重心稳定性较差。     

Describing the plastic deformation of aluminium softball bats

Hollow aluminium bats were introduced over 30 years ago to provide improved durability over wooden bats. Since their introduction, however, interest in hollow bats has focused almost exclusively around their hitting performance. The aim of this study was to take advantage of the progress that has been made in predicting bat performance using finite elements and apply it to describe bat durability. Accordingly, the plastic deformation from a ball impact of a single-wall aluminum bat was numerically modelled. The bat deformation from the finite-element analysis was then compared with experiment using a high-speed bat test machine. The ball was modelled as an isotropic, homogeneous, viscoelastic sphere. The viscoelastic parameters of the ball model were found from instrumented, high-speed, rigid-wall ball impacts. The rigid-wall ball impacts were modelled numerically and showed good agreement with the experimentally obtained response. The strain response of the combined bat-ball model was verified with a strain-gauged bat at intermediate ball impact speeds in the elastic range. The strain response of the bat-ball model exhibited positive correlation with the experimental measurements. High-speed bat-ball impacts were performed experimentally and simulated numerically at increasing impact speeds which induced correspondingly increased dent sizes in the bat. The plastic deformation from the numerical model found good agreement with experiment provided the aluminium work hardening and strain rate effects were appropriately described. The inclusion of strain rate effects was shown to have a significant effect on the bat deformations produced in the finite-element simulations. They also helped explain the existence of high bat stresses found in many performance models.     

Physical Activity Correlates for Children With Autism Spectrum Disorders in Middle School Physical Education

Bat/ball contact produces visual (the ball leaving the bat), auditory ( the “crack” of the bat), and tactile (bat vibration) feedback about the success of the swing. We used a batting simulation to investigate how college baseball players use visual, tactile, and auditory feedback. In Experiment 1, swing accuracy (i.e., the lateral separation between the point of contact and “sweet spot”) was compared for no feedback (N), visual alone, auditory alone, and tactile alone. Swings were more accurate for all single-modality combinations as compared to no feedback, and visual produced the greatest accuracy. In Experiment 2, the congruency between visual, tactile, and auditory was varied so that in some trials, the different modalities indicated that the simulated ball contacted the bat at different points. Results indicated that batters combined information but gave more weight to visual. Batting training manuals, which typically only discuss visual cues, should emphasize the importance of auditory and tactile feedback in baseball batting.     

Softballs

There is currently much debate about the safety of the sport of softball. Batted‐ball speed and average pitcher reaction time are factors often used to determine safe performance. Batted‐ball speed is shown to be the most important factor to consider when determining safe play. Average pitcher reaction time is explained and directly correlated to batted‐ball speed. Eleven aluminum multi‐wall, three aluminum single‐wall and two composite softball bats were tested with mid‐compression polyurethane softballs averaging 1721 ±62 N/6.4 mm to represent the relative bat‐ball performance for the sport of slow‐pitch softball. Nine men and six women were chosen for this study out of a test group of over three hundred slowpitch softball players. On average, aluminum bat performance results were within the recommended safety limits established by the national softball associations. However, when composite bats were used, their performance results exceeded the recommended safety limits which can pose a significant safety risk. Using aluminum softball bats, batted‐ball speeds ranged from 80 to 145 km.h^‐1. Using composite softball bats, batted‐ball speeds ranged from 146 to 161 km.h^‐1. The scientific relevance of this study is to provide performance information that can lead to injury prevention in the sport of softball.     

Bat speed,trajectory, and timing for collegiate baseball batters hitting a stationary ball

The aims of this study were to examine whether batters hit stationary balls at the time of peak speed of the bat head and whether the impact occurs at the lowest point of the bat trajectory. Eight university baseball players hit three balls, each hung with a string; each ball was made of a different material and was different in weight. Bat movement was captured by four 240-Hz infrared cameras and analysed three-dimensionally. Time for peak speed of the bat head varied according to the conditions. When stationary balls of standard weight were used, the bat head was at maximum speed at impact with the ball; then, it decelerated drastically owing to the impact. In contrast, maximum speed was obtained after impact when lightweight stationary balls were used. The time–speed profile of the bat head before impact in the lightweight ball condition was identical with that in the standard weight ball condition. Regardless of conditions, the timing of the lowest point of the bat head was nearly identical for each batter and most participants hit the stationary balls at about the lowest point of the bat trajectory     

Measurement error associated with the SAGIT/Squash computer tracking software

Abstract

The velocities and distances covered by players during competition serve as a basis for planning fitness regimes according to the specific demand of the sport. The techniques used to calculate these movement parameters have ranged from human judgements to technological solutions such as GPS and computer vision. This paper evaluates the accuracy of a computerized motion tracking system (SAGIT/Squash) that uses computer vision methods on video captured via a fixed single camera located centrally above the court. Digital images were processed automatically with operator supervision so that any tracking errors could be rectified and manual tagging of all shots added. Four separate experiments were used to assess the error associated with tracking adult players' velocities and positions with respect to the court floor. Experiment 1 involved players standing still in different areas of the court. The tracking software was found to be more accurate when a player was stood in the centre of the court (1.33 m · min^?1 error) than in the corners (2.61 m · min^?1 error), predominately due to systematic errors (e.g. calibration). Experiment 2 was conducted in the same manner as Experiment 1 except that the players vigorously swung a racket around their body continuously. This resulted in 15 times the error found in Experiment 1 for the distance covered during 1 min. However, this is an unrealistic estimate of the true error when assessing matches, as during matches the racket is only swung approximately 35% of the time. Experiment 3 involved a player running at different speeds around a rectangular path on the court. The resultant trajectory, as captured by the software, was compared using different Gaussian smoothing equations of kernel widths 0.25 s, 0.5 s, and 1 s. The best solution (0.5 s) resulted in the most accurate trajectory, although the difference in distance calculated between the different equations was negligible. Experiment 4 used the 0.5-s smoothing equation to assess the tracking accuracy for a player running at a relatively steady speed in a more realistic circular trajectory. The trajectory of the pixel image was shown to have a smaller radius than the reference trajectory at increased speeds, due to the tendency of the player to lean over when negotiating a circular path. The error associated with the distance covered over 1 min was shown to range between 1.33 and 21 m depending on the nature and position of the player's movements. Values, typically somewhere in this range, are likely to be evident during typical use of this software.     

Bat speed, trajectory, and timing for collegiate baseball batters hitting a stationary ball

The aims of this study were to examine whether batters hit stationary balls at the time of peak speed of the bat head and whether the impact occurs at the lowest point of the bat trajectory. Eight university baseball players hit three balls, each hung with a string; each ball was made of a different material and was different in weight. Bat movement was captured by four 240-Hz infrared cameras and analysed three-dimensionally. Time for peak speed of the bat head varied according to the conditions. When stationary balls of standard weight were used, the bat head was at maximum speed at impact with the ball; then, it decelerated drastically owing to the impact. In contrast, maximum speed was obtained after impact when lightweight stationary balls were used. The time-speed profile of the bat head before impact in the lightweight ball condition was identical with that in the standard weight ball condition. Regardless of conditions, the timing of the lowest point of the bat head was nearly identical for each batter and most participants hit the stationary balls at about the lowest point of the bat trajectory.     

Validation of a videogrammetry technique for analysing American football helmet kinematics

ABSTRACT

Professional American football games are recorded in digital video with multiple cameras, often at high resolution and high frame rates. The purpose of this study was to evaluate the accuracy of a videogrammetry technique to calculate translational and rotational helmet velocity before, during and after a helmet impact. In total, 10 football impacts were staged in a National Football League (NFL) stadium by propelling helmeted 50th percentile male crash test dummies into each other or the ground at speeds and orientations representative of concussive impacts for NFL players. The tests were recorded by experienced sports film crews to obtain video coverage and quality typically available for NFL games. A videogrammetry procedure was used to track the position and rotation of the helmet throughout the relevant time interval of the head impact. Compared with rigidly mounted retroreflective marker three dimensional (3-D) motion tracking that was concurrently collected in the experiments, videogrammetry accurately calculated changes in translational and rotational velocity of the helmet using high frame rate (two cameras at 240 Hz) video (7% and 15% error, respectively). Low frame rate (2 cameras at 60 Hz) video was adequate for calculating pre-impact translational velocity but not for calculating the translational or rotational velocity change of the helmet during impact.     

The sweet spot of a cricket bat for low speed impacts

The impact location of a cricket ball on a cricket bat has a large influence on the resulting rebound velocity of the ball. To measure this, a cricket bat was swung in a pendulum motion towards a cricket ball suspended in space. The position of the ball was modified so that it impacted the bat at 24 different positions on the face of the bat. This included six positions longitudinally and four positions laterally. The speed of the bat and each rebound were measured by a radar gun so that the apparent coefficient of restitution (ACOR) could be calculated. Impacts occurring centrally and 1?cm either side of the midline produced significantly higher rebound speeds and ACOR??s than impacts occurring 2 and 3cm off centre (p?<?0.01). Impacts occurring 15?C20?cm from the base of the bat produced the highest rebound speeds (p?<?0.01) and impacts occurring 20?C30?cm from the base of the bat produced the highest ACOR values. Implications for higher speed impacts and game scenarios are discussed.     

Assessment of softball bat safety performance using mid-compression polyurethane softballs

There is currently much debate about the safety of the sport of softball. Batted-ball speed and average pitcher reaction time are factors often used to determine safe performance. Batted-ball speed is shown to be the most important factor to consider when determining safe play. Average pitcher reaction time is explained and directly correlated to batted-ball speed. Eleven aluminum multi-wall, three aluminum single-wall and two composite softball bats were tested with mid-compression polyurethane softballs averaging 1721+/-62 N/6.4 mm to represent the relative bat-ball performance for the sport of slowpitch softball. Nine men and six women were chosen for this study out of a test group of over three hundred slowpitch softball players. On average, aluminum bat performance results were within the recommended safety limits established by the national softball associations. However, when composite bats were used, their performance results exceeded the recommended safety limits which can pose a significant safety risk. Using aluminum softball bats, batted-ball speeds ranged from 80 to 145km x h(-1) Using composite softball bats, batted-ball speeds ranged from 146 to 161 km x h(-1). The scientific relevance of this study is to provide performance information that can lead to injury prevention in the sport of softball.     

The dynamic impact characteristics of tennis balls with tennis rackets

The dynamic properties of six types of tennis balls were measured using a force platform and high-speed digital video images of ball impacts on rigidly clamped tennis rackets. It was found that the coefficient of restitution reduced with velocity for impacts on a rigid surface or with a rigidly clamped tennis racket. Pressurized balls had the highest coefficient of restitution, which decreased by 20% when punctured. Pressureless balls had a coefficient of restitution approaching that of a punctured ball at high speeds. The dynamic stiffness of the ball or the ball-racket system increased with velocity and pressurized balls had the highest stiffness, which decreased by 35% when punctured. The characteristics of pressureless balls were shown to be similar to those of punctured balls at high velocity and it was found that lowering the string tension produced a smaller range of stiffness or coefficient of restitution. It was hypothesized that players might consider high ball stiffness to imply a high coefficient of restitution. Plots of coefficient of restitution versus stiffness confirmed the relationship and it was found that, generally, pressurized balls had a higher coefficient of restitution and stiffness than pressureless balls. The players might perceive these parameters through a combination of sound, vibration and perception of ball speed off the racket.