Accuracy in the badminton short serve: A methodological and kinematic study

In sports, accuracy is an essential component of actions such passing, shooting, and aiming. Executing a movement or action that requires a high degree of accuracy is a critical determinant of success in many individual and team sports. Each sport has different methods for evaluating accuracy, however an overarching goal is to determine whether an object hits its target, or assess the distance by which it misses. However, in some sports accuracy is not readily measureable because an object might not reach a target, i.e. the object is intercepted, or it collides with another object or a person, or an endpoint might not be visible. One example of this is the badminton serve, where the shuttlecock is normally hit by a receiving player before it reaches the ground, its intended endpoint. The goal of one common serve type, the short serve, is to force the opponent into hitting the shuttlecock upward at a steep angle in order to clear the net, allowing a serving player to hit the shuttlecock from a point high above the net from which it is easier to score. The optimal trajectory of the short serve, therefore, is one in which the apex occurs before the shuttlecock crosses the net and results in a steep downward trajectory. To accomplish this, the swing trajectory of the racquet must be accurate itself, which is usually accomplished by use of a short period of swing (i.e. swing length). In practice the analysis of both swing technique and shuttlecock trajectory is usually done subjectively (by the coach), however objective quantification is necessary in order to determine the shuttlecock trajectories and racquet swing techniques that provide the best serve result to allow correct representation of serve accuracy. The main issue is that an objective measurement is needed, and since the shuttlecock doesn’t land on the ground, it makes it difficult to determine serve accuracy with the existing protocols. The broad aims of this Master’s thesis were to (i) develop a new method of measuring accuracy of the short serve;(ii) compare and contrast the technique/s of elite badminton players using principal component analysis; and, (iii) determine the magnitude of variability in the movement patterns of elite players performing the short serve. In the first study (Study I), a specific definition of accuracy was presented that allowed assessment when the endpoint is not reached (i.e. when the shuttlecock does not land on the court). The accuracy of an object’s trajectory is typically evaluated by determining whether it hits a target, or measuring the distance by which it misses. For the badminton short serve, the rules dictate that the shuttlecock must land on or beyond the service line (1.98 m from the net) after traversing the net. However these constraints are insufficient to distinguish poor from good serves; a serve where the shuttlecock clears the net by a small margin but continues and does not reach its apex until after it passes the net might be considered poorer in accuracy (easier for receiver to return) than one in which the shuttlecock reaches its apex before the net even if its height over the net is greater. In this study, short serve trajectories were recorded with and without a receiver present. Two separate data collection sessions and 13 players were tested across both sessions (Session A and B) (age: 23.4 ± 5.1 years, body mass: 73.2 ± 11.1 kg, height: 175 ± 8.6 cm). Data from trials with full trajectory (without an opponent) were used to create a model enabling the prediction of shuttlecock landing. This model was then used to predict the shuttlecock landing point in trials with a receiver, with an important finding being that 69% of serves would have landed on or short of the service line. Thus, receivers might benefit from leaving a majority of serves in competition in order to win the point; servers make the assumption that receivers will return most serves and therefore choose to serve short. Using the new accuracy method, serve accuracy was categorised as accurate, inaccurate, apex good, and clearance good. This provided individual and group accuracy ratings. In Study II a three-dimensional model was developed to examine the upper body kinematics during the badminton short serve. Textbook definitions hold that push-like movement patterns produce trajectories of the highest accuracy, however reducing complexity (i.e. degrees of freedom) is also stated as essential. Nonetheless, these patterns may be mutually exclusive, since push-like patterns may exhibit considerable complexity. The purpose of Study II was to describe the short serve movement patterns used by elite badminton players to determine whether push-like or low-complexity (or both) patterns predominate. Eight participants were recruited from the Senior Australian National Doubles Badminton squad (mean age: 23.4 ±5.1 years, body mass: 73.2 ±11.1 kg, height: 175 ±8.6 cm). Three-dimensional kinematics were measured with an opponent present and analysed using principal component analysis to determine what movement patterns were used in this accuracy-based skill. Results showed that all players adopted a push-like movement pattern, but the most accurate servers also constrained the number of degrees of freedom by allowing movements of the elbow and wrist joints only in a single plane. The main objective of Study III was to understand the role that movement variability plays in a precision-based movement. Little research has been published examining movement variability in sports, specifically in skills that require accuracy. The badminton short serve provided a unique opportunity to examine how elite athletes vary their movement patterns, since it requires precise multi-joint coordination to achieve an accurate serve. Recent research has shown that a rigid or inflexible system may not be good for performance and that it is more appropriate to understand the adaptability of a movement in an ever-changing environment. A three-dimensional motion analysis of eight elite badminton players performing30 short serves with an opponent present to replicate match condition s was conducted. The results identified that players incorporate variability in specific phases of their movements reduce variability at racquet-shuttlecock contact. Higher medio-lateral (transverse plane) variability was displayed in most joint angles across all players. This strategy incorporated variability in the task-redundant dimension (transverse) to reduce variability in the task-relevant dimension (sagittal), which directly impact accuracy of the serve. Variability was also present in the timing of the swing itself, varying the timing of the backswing to reduce the variability at the contact point was a common feature displayed across all subjects, irrespective of whether the serve was accurate or not. Findings suggest elite badminton players use joint and timing variability in a functional capacity. In conclusion, the methods developed to analyse the accuracy and kinematics of an accuracy-based task such as the badminton short serve revealed a greater insight into what defines an accurate serve, and how elite players coordinate and vary their movement to achieve accuracy. The results from Study I suggest that training either with an opponent present or serving on or slightly short of the service line may lead to better serve performance. The results from Study II provide the coach or player with information on the ideal movement patterns for short serve accuracy i.e. reducing the number of degrees of freedom involved (i.e. reduce movement complexity), using a push-like movement, and paying close attention to the movement from the elbow and wrist joints. The final study (Study III) revealed that elite badminton players vary their movement in a plane (transverse) that has less impact on the outcome of the task, thus reducing the variability in the plane (sagittal) that has the larger impact on the serve movement

A MULTISCALE CORRECTION METHOD FOR LOCAL SINGULAR PERTURBATIONS OF THE BOUNDARY

International audienceIn this work, we consider singular perturbations of the boundary of a smooth domain. We describe the asymptotic behavior of the solution uε of a second order elliptic equation posed in the perturbed domain with respect to the size parameter ε of the deformation. We are also interested in the variations of the energy functional. We propose a numerical method for the approximation of uε based on a multiscale superposition of the unperturbed solution u0 and a profile defined in a model domain. We conclude with numerical results

Artificial boundary conditions to compute correctors in linear elasticity

International audienceIn this paper, we derive artificial boundary conditions for the computation of correcting terms in a perturbed problem of linear elasticity. Theses conditions appear to be of Ventcel form, and lead to a non-coercive boundary value problem

On generalized Ventcel's type boundary conditions for Laplace operator in a bounded domain

acceptée dans la revue SIAM J. Math. Anal.International audienceVentcel boundary conditions are second order differential conditions that appear in asymptotic models. Like Robin boundary conditions, they lead to wellposed variational problems under a sign condition of a coefficient. Nevertheless situations where this condition is violated appeared in several works. The wellposedness of such problems was still open. This manuscript establishes, in the generic case, the existence and uniqueness of the solution for the Ventcel boundary value problem without the sign condition. Then, we consider perforated geometries and give conditions to remove the genericity restriction

Artificial conditions for the linear elasticity equations

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Load allocation problem for optimal design of aircraft electrical power system

More and more electric systems are embedded in today aircraft. As a result, the complexity of electrical power system design is increasing and the need of generic and efficient design methods is today required. Among numerous design tasks, the allocation of electric systems on the busbars of the electrical power system is considered as an important one since it has a direct impact on the aircraft mass. But due to the high number of possible allocations and regarding the large diversity of potential sizing cases for the equipments, finding the optimal allocation of electric loads is a hard task. In this paper, the problem is formalized mathematically. Then, four stochastic optimization methods are assessed on complex load allocation problems. Based on this assessment, a genetic algorithm using niching method is considered as the most appropriate algorithm for solving this aircraft design proble

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E