The effect of surface geometry on soccer ball trajectories

Two different measurement techniques are used to examine the effect of surface geometry on soccer ball trajectories. Five professional players are observed using high-speed video when taking curling free kicks with four different soccer balls. The input conditions are measured and the average launch velocity and spin are found to be approximately 24 m/s and 106 rad/s. It is found that the players can apply more spin (~50%) on average to one ball, which has a slightly rougher surface than the other balls. The trajectories for the same four balls fired at various velocities and spin rates across a sports hall using a bespoke firing device are captured using high-speed video cameras, and their drag and lift coefficients estimated. Balls with more panels are found to experience a higher lift coefficient. The drag coefficient results show a large amount of scatter, and it is difficult to distinguish between the balls. Using the results in a trajectory prediction programme it is found that increasing the number of panels from 14 to 32 can significantly alter the final position of a 20 m-curling free kick by up to 1 m.     

Fundamental aerodynamics of the soccer ball

When the boundary layer of a sports ball undergoes the transition from laminar to turbulent flow, a drag crisis occurs whereby the drag coefficient (C _d) rapidly decreases. However, the aerodynamic properties and boundary-layer dynamics of a soccer ball are not yet well understood. In this study we showed that the critical Reynolds number (Re _crit) of soccer balls ranged from 2.2 × 10⁵ to 3.0 × 10⁵. Wind-tunnel testing, along with visualisation of the dynamics of the boundary layer and the trailing vortex of a ball in flight, demonstrated that both non-spinning and spinning (curved) balls had lowC _d values in the super-critical region. In addition, theRe _crit values of the soccer balls were lower than those of smooth spheres, ranging from ∼ 3.5 × 10⁵ to 4.0 × 10⁵, due to the effects of their panels. This indicated that the aerodynamic properties of a soccer ball were intermediate between those of a smooth ball and a golf ball. In a flow visualisation experiment, the separation point retreated and theC _d decreased in a super-critical regime compared with those in a sub-critical regime, suggesting a phenomenon similar to that observed in other sports balls. With some non-spinning and spinning soccer balls, the wake varied over time. In general, the high-frequency component of an eddy dissipated, while the low-frequency component increased as the downstream vortex increased. The causes of the large-scale fluctuations in the vortex observed in the present study were unclear; however, it is possible that a ‘knuckle-ball effect’ of the non-rotating ball played a role in this phenomenon.     

Determinants of possession of the ball in soccer

Abstract

In research on the importance of the possession of the ball in soccer, little attention has been paid to its determinants. Using data from 170 matches of the 2003 – 2004 Spanish Soccer League, we explain why differences in the possession of the ball among teams are so great. In particular, four variables are examined: evolving match status (i.e. whether the team is winning, losing or drawing), venue (i.e. playing at home or away), and the identities of the team and the opponent in each match. Results of linear regression analysis show that these four variables are statistically significant and together explain most of the variance in possession. In short, home teams have more possession than away teams, teams have more possession when they are losing matches than when winning or drawing, and the identity of the opponent matters – the worse the opponent, the greater the possession of the ball. Combinations of these variables could be used to develop a model that predicts possession in soccer.     

Determinants of possession of the ball in soccer

In research on the importance of the possession of the ball in soccer, little attention has been paid to its determinants. Using data from 170 matches of the 2003 - 2004 Spanish Soccer League, we explain why differences in the possession of the ball among teams are so great. In particular, four variables are examined: evolving match status (i.e. whether the team is winning, losing or drawing), venue (i.e. playing at home or away), and the identities of the team and the opponent in each match. Results of linear regression analysis show that these four variables are statistically significant and together explain most of the variance in possession. In short, home teams have more possession than away teams, teams have more possession when they are losing matches than when winning or drawing, and the identity of the opponent matters - the worse the opponent, the greater the possession of the ball. Combinations of these variables could be used to develop a model that predicts possession in soccer.     

Finite element modelling and experimental study of oblique soccer ball bounce

In this study, we develop a finite element model to examine the oblique soccer ball bounce. A careful simulation of the interaction between the ball membrane and air pressure in the ball makes the model more realistic than analytical models, and helps us to conduct an accurate study on the effect of different parameters on a bouncing ball. This finite element model includes a surface-based fluid cavity to model the mechanical response between the ball carcass and the internal air of the ball. An experimental set-up was devised to study the bounce of the ball in game-relevant impact conditions. Ball speed, angle, and spin were measured before and after the bounce, as well as ball deformation and the forces during the impact. The finite element model has been validated with three different sets of data, and the results demonstrate that the finite element model reported here is a valuable tool for the study of ball bounce. After validation of the model, the effect of the friction coefficient on soccer ball bounce was studied numerically. Simulation results show that increasing the friction coefficient may result in reversal of the horizontal impact force.     

A mathematical analysis of the motion of an in-flight soccer ball

In this paper, an analytical and numerical study of the three-dimensional equations describing the motion through the air of a spinning ball is presented. The initial analysis involves constant drag coefficients, but is later extended to involve drag varying with the spin ratio. Excellent agreement is demonstrated between numerical, analytical and experimental results. The analytical solution shows explicitly how the ball’s motion depends on parameters such as ball roughness, velocity and atmospheric conditions. The importance of applying three-dimensional models, rather than two-dimensional approximations, is demonstrated.     

Hardness measurement of natural and hybrid turf soccer fields

Understanding the surface hardness of soccer fields is essential to evaluate the risk of injury and also its influence on the playing behavior of soccer players. In this context, newly developed hybrid turf systems have to be tested for their surface hardness with regard to the increased risk of injury on hard sports surfaces. The hardness of a soccer field can be quantitatively measured using an apparatus with a cylindrical weight that is dropped from a defined height. Since this procedure was first used for road construction, there are few studies investigating its use on sports grounds. This has led to inconsistencies in methodology and the absence of evaluation guidelines for classifying the hardness of soccer fields. This paper considers how turf systems (natural turf and hybrid turf) differ in their hardness and how this method can be used for different soccer turf systems. Natural turf systems, stitched turf systems, hybrid turf-bearing layer systems and woven mat systems were investigated. The assessment results from a comparative representation of hardness values of different soccer fields. By comparison, natural turf systems were found to be the softest, while woven mat systems were the hardest. Furthermore, the parameters that might affect the hardness were investigated. The influence of the measured soil parameters decreases with an increasing number of measurements per measuring point. Turf system-specific correlations make it possible to reduce the amount of measurement effort.     

Determinants of the half-turn with the ball in sub-elite youth soccer players

We explored the biomechanics of the 180° change-of-direction with the ball (half-turn) in soccer. We aimed at identifying movement strategies which enhance the players’ half-turning performance, by characterising technique kinematics and understanding the structure of biomechanical and anthropometrics variables. Ten Under-13 sub-elite male players were recorded with an optoelectronic motion analyser while performing a 5-m straight dribbling followed by a half-turn with the sole. Joints kinematics differences between faster and slower trials were found in support-side hip rotation, driving-side hip adduction, trunk flexion and rotation, and arms abduction. To unveil the data-set structure, a principal component (PC) analysis and a stepwise linear discriminant analysis were performed using 30 biomechanical parameters and four anthropometric variables for each trial. Seven retained PCs explained 79% of the overall variability, featuring combinations of original variables that help in understanding the factors facilitating fast half-turns: keeping short steps, minimising lateral and forward body movements, and centre-of-mass lowering, even with ample lower limbs ranges of motion (RoM); abducting the upper limbs while limiting trunk flexion and pelvic inclination RoM. Balance and task-constrained exercises may be proposed to improve this technique. Moreover, a quantitative knowledge of the movement structure could give coaches objective insights to better instruct young players.     

Modelling the flight of a soccer ball in a direct free kick

This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m·s^?1, the ball's initial elevation must be constrained between 16.5° and 17.5° and the ball kicked with almost perfect sidespin.     

Modelling the flight of a soccer ball in a direct free kick

This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m x s(-1), the ball's initial elevation must be constrained between 16.5 degrees and 17.5 degrees and the ball kicked with almost perfect sidespin.     

Three-dimensional kinematic correlates of ball velocity during maximal instep soccer kicking in males

Abstract

Achieving a high ball velocity is important during soccer shooting, as it gives the goalkeeper less time to react, thus improving a player's chance of scoring. This study aimed to identify important technical aspects of kicking linked to the generation of ball velocity using regression analyses. Maximal instep kicks were obtained from 22 academy-level soccer players using a 10-camera motion capture system sampling at 500 Hz. Three-dimensional kinematics of the lower extremity segments were obtained. Regression analysis was used to identify the kinematic parameters associated with the development of ball velocity. A single biomechanical parameter; knee extension velocity of the kicking limb at ball contact Adjusted R² = 0.39, p ≤ 0.01 was obtained as a significant predictor of ball-velocity. This study suggests that sagittal plane knee extension velocity is the strongest contributor to ball velocity and potentially overall kicking performance. It is conceivable therefore that players may benefit from exposure to coaching and strength techniques geared towards the improvement of knee extension angular velocity as highlighted in this study.     

A dynamic model of the head acceleration associated with heading a soccer ball

This study develops a dynamic model of head acceleration, which incorporates physiologically related neck muscle contributions, to further the understanding of the mechanical behaviour of the head-neck system during soccer heading. An inverted pendulum is combined with a linear visco-elastic element to model the head-neck system following a half-sine input force. Model parameter values were varied to obtain agreement with previously published experimental data (Naunheimet al., 2003), and were subsequently compared to literature values. The model predicted the same mechanical angular kinematics as observed experimentally both during and post impact. The greatest acceleration was in the anterior direction at the instant the ball left the head, attributed to the elastic stiffness of the neck musculature. The head-neck stiffness and damping coefficients determined from the model (350 N m rad^-1 and 4 N m s rad^-1, respectively) were similar to those reported elsewhere when subjects were asked to resist maximally. The model may be subsequently used to investigate differences in technique and ability with respect to the salient model parameters to further our biomechanical understanding of soccer heading.     

球类集体项目运动员对球队组织信任量表的建构

研究目的:确定我国球类集体项目运动员对球队组织信任的结构维度,编制相应的测量量表。研究方法:理论探讨、深度访谈、问卷调查、数理统计。研究结果:对214名篮球运动员的有效问卷进行探索性因子分析和验证性因子分析表明,运动员对球队组织信任量表包括能力信任和公正一致性信任2个维度,再用407名运动员的有效问卷进行了跨样本效度检验,进一步证明了2维结构模型具有合理性。研究结论:本研究编制的信任量表具有较好的信度和效度,可在今后以信任为基础的相关实证研究中使用。     

Mechanical factors associated with the development of high ball velocity during an instep soccer kick

The purpose of this study was to determine whether joint velocities and segmental angular velocities are significantly correlated with ball velocity during an instep soccer kick. We developed a deterministic model that related ball velocity to kicking leg and pelvis motion from the initiation of downswing until impact. Three-dimensional videography was used to collect data from 16 experienced male soccer players (age = 24.8 ± 5.5 years; height = 1.80 ± 0.07 m; mass = 76.73 ± 8.31 kg) while kicking a stationary soccer ball into a goal 12 m away with their right foot with maximal effort. We found that impact velocities of the foot center of mass (CM), the impact velocity of the foot CM relative to the knee, peak velocity of the knee relative to the hip, and the peak angular thigh velocity were significantly correlated with ball velocity. These data suggest that linear and angular velocities at and prior to impact are critical to developing high ball velocity. Since events prior to impact are critical for kick success, coordination and summation of speeds throughout the kicking motion are important factors. Segmental coordination that occurs during a maximal effort kick is critical for completing a successful kick.     

足球运动踢球腿摆动阶段的不同时相运动特征

运用生物力学手段对5名高水平足球运动员摆动腿进行研究发现:根据摆动腿环节摆动顺序与环节摆动速度相结合的方法可将其划分为用力蹬伸、主动后摆、大腿前摆、小腿前摆,脚触球5个阶段.其中,用力蹬伸阶段是不可忽视的重要阶段之一,主动后摆阶段摆动腿应在不影响前摆速度的前提下尽力后摆;大腿前摆阶段摆动腿应在大腿摆到一定幅度时进行积极制动,摆动幅度不宜过大;小腿前摆阶段摆动腿除了膝关节的积极制动外还应主动施力.     

The relative age effect and success in German elite U-17 soccer teams

The aim of the study was to determine whether there is empirical evidence for advantages in performance of soccer teams because of their relative age. The practice of selecting youth players according to their momentary performance leads to relative age effects, which in turn lead to inefficient talent selection. We used the median of the birth dates as a measure of the effect size of the relative age effect and the Kolmogorov-Smirnov test to assess its significance. For the 2008-2009 season, birth dates in the three German U-17 first leagues for soccer were examined (911 players). More than half of the 41 teams differed significantly from the distribution of the corresponding German cohort. There was a significant correlation between the relative age effect and success defined by teams' final rankings (Spearman's ρ = 0.328, P = 0.036). Regression analyses revealed that with a median of birth dates one month earlier the team is expected to finish 1.035 ranks better. Accordingly, selecting early born athletes is an important aspect of success in youth soccer. However, teams with no relative age effect are able to compete in the league, having the benefit to promote players with a better perspective for long and successful careers at an adult age.     

论足球的魅力及体验

足球运动中的胜负美、整体精神美、球星的个性魁力使人憧憬着未来，为未来创造美好；球迷的悲喜体验、归属感与潮流体验、足球背后的极端体验以及无球日子的体验等，都包含着人生最丰富以及最刻骨的体验。足球体验中这种磅礴的、恢弘的精神气势，推动着人类的进取精神，推动着世界体育文化的发展。     

Relative age effect: Characteristics of youth soccer players by birth quarter and subsequent playing status

Purpose: To compare characteristics of club level male soccer players 11 and 13 years of age, and to evaluate playing status in soccer two and 10 years after baseline by birth quarter (BQ).

Methods: Youth players 11 (n = 62, born 1992, observed December 2003) and 13 (n = 50, born 1990, observed April 2004) years were grouped by BQ. Baseline data included stature, weight, maturity status, functional capacities, soccer skills, goal orientation, and coach evaluation of potential. Playing status in soccer in 2006 and 2014 was also available. Baseline characteristics and subsequent playing status were compared by BQ.

Results: Baseline characteristics did not differ by BQ except for age and percentage of predicted adult height. Though not significant, coaches tended to rate players in BQ1as higher in potential. For those competing in soccer as adults, BQ2 (4), BQ3 (5) and BQ4 (2) were represented among players11 years, and BQ1 (3), BQ2 (2), BQ3 (1) and BQ4 (4) among players 13 years.

Conclusion: Although limited to small numbers, differences among players by BQ were inconsistent. The results indicate a need to extend potential explanations of the RAE to include behavioral variables, coaches, training environment, and perhaps the culture of the sport.     

流、球瑜伽对大学生心血管功能影响的比较

为了探究不同类型瑜伽对防治大学生心血管疾病的积极作用,更有针对性地推广瑜伽。从华中师范大学瑜伽俱乐部中随机抽取大学生120名进行比较研究:对照组40名进行常规的学习与生活,实验1组40名进行18周的流瑜伽练习,实验2组40名进行18周的球瑜伽练习。实验组每周练习3~5次,每次90 min,运动强度为中等(心率控制在120~150次/min)。结果显示:两个实验组实验前后,HR、SV、HOI值降幅明显,且差异有非常显著性意义(P<0.01),CO、SI、CI值升幅明显,且差异有显著性意义(P<0.05);PP、MAP值降幅较小,差异无显著性意义(P>0.05),MSP、MDP、MAP值降幅明显,且差异有显著性意义(P<0.05),TR值降幅明显,且差异有非常显著性意义(P<0.01),AC值升幅明显,且差异有显著性意义(P<0.05);BV、OV值无明显变化,差异无显著性意义(P>0.05),V值降幅明显,且差异有显著性意义(P<0.05),ALK值升幅明显,且差异有显著性意义(P<0.05),ALT、TM值降幅较大,且有非常显著性意义(P<0.01)。结果说明:18周的流瑜伽练习和球瑜伽练习均能够有效改善大学生心血管功能,且球瑜伽对改善大学生心血管功能的作用较之流瑜伽的效果更好。     

Tennis ball diameter: the effect on performance and the concurrent physiological responses

The aim of this study was to examine the influence of a pressurized tennis ball 6% greater in diameter (Type 3) than a standard sized (Type 2) ball on performance and the physiological responses to the Loughborough Intermittent Tennis Test (LITT) (Davey et al., 2002). Eight competitive tennis players (males, n = 4, age 24.8+/-3.5 years, body mass 81.3+/-3.1 kg, height 1.74+/-0.02 m, estimated VO2max 54.4+/-2.6 ml x kg(-1) min(-1); females, n = 4, age 26.3+/-3.1 years, body mass 67.0+/-6.7 kg, height 1.68 + 0.02 m, estimated VO2max 49.9+/-3.3 ml kg(-1) min(-1); mean+/-s(x)) completed two main trials of the LITT with either the Type 2 or Type 3 tennis balls to the point of volitional fatigue. The mean time to volitional fatigue was 29.5% greater during the Type 3 trials than during the Type 2 trials (56.9+/-6.4 min vs 40.1+/-3.7 min; P < 0.05). The mean percentage accuracy and mean percentage consistency recorded for the entire LITT were greater for the Type 3 than the Type 2 trials (9.2+/-1.5 vs 4.0+/-0.3% and 61.1+/-0.6 vs 51.3+/-0.6%, respectively; P < 0.01). A significantly lower mean heart rate and blood lactate concentration were observed during the Type 3 than during the Type 2 trials. There was a clear effect of ball diameter on tennis performance and certain physiological responses.