Table Tennis and Physics

Table tennis is a fascinating sport with a lot of physics elements. This chapter will concentrate on the forces acting on a table tennis ball. Insights from molecular dynamics simulations clarify the basic properties of table tennis balls interacting with surfaces and their high coefficient of restitution. The table tennis ball trajectory is discussed considering the different force balance contributions. The sum of the gravitational force and the forces from aerodynamics, namely drag and lift, determine the flight path. Extensive numerical modeling is used to study the impact of changes in ball size and net height to the game characteristics. Half a billion different initial conditions like hitting location, initial spin and velocities were analyzed to reach sufficient statistical significance for the different cases. An advanced statistical analysis of the database generated by the simulation is presented

Proceedings of Mathsport international 2017 conference

Proceedings of MathSport International 2017 Conference, held in the Botanical Garden of the University of Padua, June 26-28, 2017. MathSport International organizes biennial conferences dedicated to all topics where mathematics and sport meet. Topics include: performance measures, optimization of sports performance, statistics and probability models, mathematical and physical models in sports, competitive strategies, statistics and probability match outcome models, optimal tournament design and scheduling, decision support systems, analysis of rules and adjudication, econometrics in sport, analysis of sporting technologies, financial valuation in sport, e-sports (gaming), betting and sports

Rock-shape and its role in rockfall dynamics

Rockfall threaten infrastructure and people throughout the world. Estimating the runout dynamics of rockfall is commonly performed using models, providing fundamental data for hazard management and mitigation design. Modelling rockfall is made challenging by the complexity of rock-ground impacts. Much research has focused on empirical impact laws that bundle the rock-ground impact into a single parameter, but this approach fails to capture characteristics associated with the impact configuration and, in particular, the effects of rock-shape. While it is apparent that particular geological settings produce characteristic rock-shapes, and that different rock-shapes may produce characteristic runout dynamics, these aspects of rockfall are poorly understood. This study has focused on investigating the mechanics behind the notion that different rock-shapes produce characteristic runout dynamics and trajectories. The study combines field data on rockfall runout, trajectory and dynamics, laboratory analogue testing in controlled conditions, and numerical modelling of the influence of rock-shape. Initially rock-shape, deposition patterns and rockfall dynamics were documented at rockfall sites in Switzerland and New Zealand. This informed a detailed study of individual rock-ground impacts on planar slopes in which laboratory-scale and numerical rockfall experiments were combined to isolate the role of rock-shape on runout. Innovatively, the physical experiments captured the dynamics of impacts and runout paths using high speed video tracking and a sensor bundle with accelerometers and gyroscopes. Numerical experiments were performed using a 3-D rigid-body rockfall model that considers rock-shape, and has allowed the variability of rockfall behaviour to be explored beyond the limitations of physical experimentation. The main findings of the study were on understanding rockfall-ground impacts, the influence of rock-shape on rockfall dynamics, and influence of rock sphericity. By measuring velocity, rotational speed, impact and runout character, it has been possible to quantify the variability of individual rock-ground impacts as a function of rock-shape. Investigation of single rebounds reveals that if classical restitution coefficients are applied, $R_n$ values greater than unity are common and rebounds are highly variable regardless of constant contact parameters. It is shown that this variability is rooted in the inherent differences in the magnitudes of the principal moment of inertia of a rock body brought about by rock-shape. Any departure from a perfect sphere induces increased range and variability in rock-ground rebound characteristics. In addition to the popular description of a rock bouncing down slope, rebounds involve the pinning of an exterior edge point on the rock, creating a moment arm which effectively levers the rock into ballistic trajectory as it rotates. Observations reveal that the angle of the impact configuration plays a key role in the resulting rebound, whereby low angles produce highly arched rebounds, while large impact angles produce low flat rebounds. The type of rebound produced has a strong bearing on the mobility of the rocks and their ability to maintain motion over a long runout. The mobility of rocks is also shown to be related to rotation, which is governed by the differences in the principal inertial axes as a function of rock-shape. Angular velocity measurements about each principal inertial axis indicate that rocks have a tendency to seek rotation about the axis of largest inertia, as the most stable state. Rotations about intermediate and small axes of inertia and transitions between rotational axes are shown to be unstable and responsible for the dispersive nature of runout trajectories, which are inherent characteristics of different rock-shapes. The findings of this research demonstrate the importance of rock-shape in rockfall runout dynamics and illustrate how it is essential that the rock-shape is included in rockfall modelling approaches if the variability of rockfall behaviour is to be simulated

Scaling the pitch for junior cricketers

Although cricket is played around the world by all ages, very little attention has been focused on junior cricket. The research presented here evaluated the effects on junior cricket of reducing the pitch length, developed a method for scaling the pitch to suit the players and applied this method to the under-11 age group. In the first of four studies it was established that shortening the cricket pitch had positive effects for bowlers, batters and fielders at both club and county standards, consequently resulting in matches that were more engaging. The second study found that top under-10 and under-11 seam bowlers released the ball on average 3.4° further below horizontal on a 16 yard pitch compared with a 19 yard pitch. This was closer to elite adult pace bowlers release angles and should enable junior players to achieve greater success and develop more variety in their bowling. The third study calculated where a good length delivery should be pitched to under-10 and under-11 batters in order to provoke uncertainty, and also examined the influence of pitch length on batters decisions to play front or back foot shots according to the length of the delivery. A shorter pitch should strengthen the coupling between the perception of delivery length and appropriate shot selection, and the increased task demand should lead to improved anticipation; both are key features of skilled batting. In the final study a method of calculating the optimal pitch length for an age group was developed which used age-specific bowling and batting inputs. This was applied to scale the pitch for under-11s giving a pitch length of 16.22 yards (14.83 m), 19% shorter than previously recommended for the age group by the England and Wales Cricket Board. Scaled in this way across the junior age groups, pitch lengths would fit the players better as they develop, enabling more consistent ball release by bowlers and temporal demands for batters, as well as greater involvement for fielders

Advanced modelling and design of a tennis ball

Modern tennis has been played for over a hundred years, but despite significant improvements in the design and manufacture of tennis balls to produce a long-lasting and consistent product, the design of a tennis ball has barely changed in the last century. While some work has been done to better understand the dynamic behaviour of a tennis ball, no structured analysis has been reported assessing how the typical constructions of the inner rubber core and cloth panels affect its behaviour and performance. This research describes the development of an advanced and validated finite element (FE) tennis ball model which illustrates the effects of the viscoelastic and anisotropic materials of a tennis ball on ball deformation and bounce during impacts with the ground and the racket,representative of real play conditions. The non-linear strain rate properties exhibited by the materials of a tennis ball during high velocity impacts were characterised using a series of experiments including tensile and compressive tests as well as low and high velocity impact tests. The impacts were recorded using a high speed video (HSV) camera to determine deformation, impact time, coefficient of restitution (COR) and spin rate. The ball material properties were tuned to match the HSV results, and the ball s model parameters were in good agreement with experimental data for both normal and oblique impacts at velocities up to 50 m/s and 35 m/s, respectively. A time sequenced comparison of HSV ball motion and FE model confirmed the accuracy of the model, and showed significant improvement on previous models. Although the existing construction of tennis ball cores was found to provide a sufficiently uniform internal structure to base competition standard tennis balls, the anisotropic nature of the cloth panels resulted in deviation angles as high as 1.5 degrees in ball bounce. Therefore, new cloth panel configurations were modelled which allowed the cloth fibre orientations around the ball to be adjusted resulting in better bounce consistency. The effect of cloth seam length on ball flight was explored through wind tunnel tests performed on solid balls made by additive manufacturing (AM) and on actual pressurised tennis ball prototypes. A reverse Magnus effect was observed on the AM balls, however, this phenomenon was overcome by the rough nature of the cloth cover on the real tennis ball prototypes. A ball trajectory simulation showed that there was no obvious dependence between seam length and shot length or ball velocity. Finally, a basic panel flattening method was used to determine the 2Dsize of the cloth panel patterns corresponding to the new configurations, and tiling methods were designed to estimate cloth wastage. The traditional dumbbell design appeared to result in the minimum amount of waste. The work reported in this thesis represents a significant improvement in the modelling of tennis ball core, cloth and seams, as well as the ball s interaction with the ground and racket strings. While this research focused on woven cloth, needle cloth is also widely used in the manufacture of balls in the US. The modelling of needle cloth could therefore be part of a future study. Additionally, details such as the depth and roughness of the cloth seam could be included in the model to study their effect on spin generation. Also, including cloth anisotropy in the flattening method would allow a better prediction of cloth wastage which could then have an influence on the configuration of the cloth panels

The role of biomechanics in achieving different shot trajectories in golf

In golf, a range of shot types are necessary for successful performance, with driving and iron-play constituting the long-game. It is possible to vary long-game shots through altered trajectory, for example, by utilising right-to-left or left-to-right ball flight curvature, providing course management advantages. However, how golfers vary their biomechanics to achieve different trajectories is not scientifically understood. Therefore, the purpose of this thesis was to biomechanically investigate different trajectories hit with the same club. To investigate shot trajectories, accurate measures of performance were necessary. Launch monitors (TrackMan Pro IIIe and Foresight GC2+HMT) are bespoke technologies capable of tracking the clubhead and ball through impact. However, their accuracy for scientific research has not been independently validated. Therefore, a novel purpose-designed tracking method was developed using a three-dimensional optical tracking system (GOM). The accuracy of this method was validated and the system used as the benchmark to which the two launch monitors were compared through limits of agreement. The results showed, in general, the launch monitors were in closer agreement to the benchmark for ball parameters than clubhead. High levels of agreement were found for ball velocity, ball path, total spin rate and backspin. However, poorer agreement was shown for ball sidespin and spin axis as well as clubhead velocity, clubhead path and clubhead orientation. Consequently, the launch monitors were deemed unsuitable for inclusion in scientific research across a range of impact parameters. Draw and fade trajectories with a driver and draw, fade and low trajectories with a 5-iron were investigated biomechanically. The clubhead and ball were tracked using the optical method developed in this thesis. Key biomechanical variables (address position and whole-swing) were defined based on coaching theory. Statistically, analysis of variance (address) and principal components analysis (whole-swing), were used to compare draw against fade and low against natural trajectories. Multivariate correlation was used to identify swing pattern similarities between golfers. The group-level comparison showed draw-fade address differences whereby for draw trajectories, the ball was positioned further away from the target, the lead hand further towards the target and the pelvis, thorax and stance openness closed relative to the target line. Over the whole-swing, the draw when compared to the fade demonstrated a pelvis rotation, more rotated away from the target with later rotation; lumbar forward flexion, with slower extending in the downswing; lumbar lateral flexion, with more flexion towards the trail throughout and prolonged trail flexing through ball contact; thorax lateral flexion, with greater, slower lead flexing in the backswing and greater, more prolonged trail flexing in the downswing; pelvis translation further towards the target throughout, with earlier forward translation and centre of pressure, with an earlier, quicker, greater forward shift. Cluster differences were evident, with both Clusters I (57% of golfers with the driver) and II (71% of golfers with the 5-iron) showing greater, earlier thorax rotation towards the target and a tendency for greater lumbar forward flexion over the whole-swing (Cluster II) and backswing (Cluster I). For the group-level low-natural comparison, golfers positioned the ball further away from the target and their lead hand further towards the target for low trajectories. Further, Cluster IV (45% of golfers), narrowed their stance width and laterally flexed their thorax towards the lead, for the same trajectories. Over the whole-swing, the low when compared to the natural showed the pelvis translated towards the target throughout, with later, lesser forward shift for the low trajectories. Furthermore, centre of pressure displayed a greater forward shift for the same shots. Finally, both clusters (Cluster III 36% of golfers and Cluster IV) differed in lumbar forward flexion when playing low trajectories; over the backswing, Cluster III extended, whereas Cluster IV flexed. Cluster IV also showed greater extending in the downswing. Finally, Cluster IV showed more lumbar lateral flexion towards the lead throughout. The results of this study have implications for scientific researchers as well as golf coaches, club-fitters and professionals. Commercially available launch monitors appear accurate enough for coaching applications, however caution is needed for scientific research when tracking a range of clubhead and ball parameters. Furthermore, changes in biomechanics when playing different trajectories has implications for future research and interpretation of published work, as well as for coaching theory. Future work following this thesis could utilise the optical tracking method to validate further commercial systems and for more detailed experimental investigation of clubhead-ball impacts. Furthermore, additional biomechanical investigation into a wider range of shot trajectories across more variables could be conducted, with a more in-depth understanding gained from principal components analysis and golfer clustering

Development of Immersive and Interactive Virtual Reality Environment for Two-Player Table Tennis

Although the history of Virtual Reality (VR) is only about half a century old, all kinds of technologies in the VR field are developing rapidly. VR is a computer generated simulation that replaces or augments the real world by various media. In a VR environment, participants have a perception of “presence”, which can be described by the sense of immersion and intuitive interaction. One of the major VR applications is in the field of sports, in which a life-like sports environment is simulated, and the body actions of players can be tracked and represented by using VR tracking and visualisation technology. In the entertainment field, exergaming that merges video game with physical exercise activities by employing tracking or even 3D display technology can be considered as a small scale VR. For the research presented in this thesis, a novel realistic real-time table tennis game combining immersive, interactive and competitive features is developed. The implemented system integrates the InterSense tracking system, SwissRanger 3D camera and a three-wall rear projection stereoscopic screen. The Intersense tracking system is based on ultrasonic and inertia sensing techniques which provide fast and accurate 6-DOF (i.e. six degrees of freedom) tracking information of four trackers. Two trackers are placed on the two players’ heads to provide the players’ viewing positions. The other two trackers are held by players as the racquets. The SwissRanger 3D camera is mounted on top of the screen to capture the player’

Continuously updating one’s predictions underlies successful interception

This paper reviews our understanding of the interception of moving objects. Interception is a demanding task that requires both spatial and temporal precision. The required precision must be achieved on the basis of imprecise and sometimes biased sensory information. We argue that people make precise interceptive movements by continuously adjusting their movements. Initial estimates of how the movement should progress can be quite inaccurate. As the movement evolves, the estimate of how the rest of the movement should progress gradually becomes more reliable as prediction is replaced by sensory information about the progress of the movement. The improvement is particularly important when things do not progress as anticipated. Constantly adjusting one’s estimate of how the movement should progress combines the opportunity to move in a way that one anticipates will best meet the task demands with correcting for any errors in such anticipation. The fact that the ongoing movement might have to be adjusted can be considered when determining how to move, and any systematic anticipation errors can be corrected on the basis of the outcome of earlier actions

Sports Performance and Health

Sports performance is primarily associated with elite sport, however, recreational athletes are increasingly attempting to emulate elite athletes. Performance optimization is distinctly multidisciplinary. Optimized training concepts and the use of state-of-the-art technologies are crucial for improving performance. However, sports performance enhancement is in constant conflict with the protection of athletes’ health. Notwithstanding the known positive effects of physical activity on health, the prevention and management of sports injuries remain major challenges to be addressed. Accordingly, this Special Issue on "Sports Performance and Health" consists of 17 original research papers, one review paper, and one commentary, and covers a wide range of topics related to fatigue, movement asymmetries, optimization of sports performance by training, technique, and/or tactics enhancements, prevention and management of sports injuries, optimization of sports equipment to increase performance and/or decrease the risk of injury, and innovations for sports performance, health, and load monitoring. As this Special Issue offers several new insights and multidisciplinary perspectives on sports performance and health, readers from around the world who work in these areas are expected to benefit from this Special Issue collection