Dynamics of the basketball shot with application to the free throw

A completely general three-dimensional dynamic model is presented for the motion of basketball shots that may contact the rim, the backboard, the bridge between the rim and board, and possibly the board and the bridge simultaneously. Non-linear ordinary differential equations with six degrees of freedom describe the ball angular velocity and ball centre position. The model includes radial ball compliance and damping and contains five sub-models: purely gravitational flight, and ball-rim, ball-bridge, ball-board, and ball-bridge-board contact. Each contact sub-model has both slipping and non-slipping motions. Switching between the sub-models depends on the reaction force at, and velocity of, the contact point. Although the model can be used to study shots from any point on the court, we here use it to study the sets of free throw release angle, velocity, angular velocity, and lateral deviation angle that result in success (capture), as well as underhand free throws and those using an under-inflated ball. Free throw shots with larger backspin, lower inflation pressures, and underhand release conditions are shown to result in larger capture percentages.     

Identification with sport teams as a function of the search for certainty

Based on ideas from subjective uncertainty reduction theory, we examined the extent to which individuals hold similar sport team preferences to their family and friends. We also assessed the extent to which perceived sport importance and personal need for structure are influential in the development of team identification. Australian high school students aged 15.5+/-1.0 years (mean+/-s) completed questionnaires containing the Personal Need for Structure Scale, the Relational-Interdependent Self-Construal scale, a Team Identification Scale, and items assessing perceptions of sport importance and team preferences. As expected, correlations indicated that preferences for sport teams were significantly related to the preferences of family and friends. Separate analyses of variance confirmed the remaining hypotheses. More specifically, individuals who perceived that sport was important identified with the team more than individuals who perceived sport to be less important. Also, individuals high in personal need for structure scored higher in cognitive/affective team identification than those low in this need. Individuals with differing needs for structure did not differ in their scores on other dimensions of team identification. The results support the notion that cognitive/emotional attachments to sport teams are influenced by perceptions of the importance of sport and by needs for subjective structure. It is possible that other psychological motives, such as the desire for self-esteem, facilitate the development of evaluative dimensions of team identification.     

The role of effort in moderating the anxiety-performance relationship: Testing the prediction of processing efficiency theory in simulated rally driving

We tested some of the key predictions of processing efficiency theory using a simulated rally driving task. Two groups of participants were classified as either dispositionally high or low anxious based on trait anxiety scores and trained on a simulated driving task. Participants then raced individually on two similar courses under counterbalanced experimental conditions designed to manipulate the level of anxiety experienced. The effort exerted on the driving tasks was assessed though self-report (RSME), psychophysiological measures (pupil dilation) and visual gaze data. Efficiency was measured in terms of efficiency of visual processing (search rate) and driving control (variability of wheel and accelerator pedal) indices. Driving performance was measured as the time taken to complete the course. As predicted, increased anxiety had a negative effect on processing efficiency as indexed by the self-report, pupillary response and variability of gaze data. Predicted differences due to dispositional levels of anxiety were also found in the driving control and effort data. Although both groups of drivers performed worse under the threatening condition, the performance of the high trait anxious individuals was affected to a greater extent by the anxiety manipulation than the performance of the low trait anxious drivers. The findings suggest that processing efficiency theory holds promise as a theoretical framework for examining the relationship between anxiety and performance in sport.     

The distance-time relationship over a century of running Olympic performances: A limit on the critical speed concept

We analyse the evolution of the slope (critical speed) and the y-intercept (anaerobic distance capacity) of the linear distance-time relationship over a century of Olympic running performances. The distance-time relationship of each Olympic Games (1920-2004) was plotted using the performances in the 800-, 1500- and 5000-m track events. Values for critical speed and anaerobic distance capacity were determined by linear modelling. Mean performances for the 800, 1500 and 5000 m were 104.9 +/- 1.5 s (1.4%), 217.2 +/- 2.8 s (1.3%) and 808.9 +/- 18.4 s (2.3%), respectively. Critical speed improved during the first three-quarters of the twentieth century to reach a plateau in 1984. This is in accordance with the literature (Peronnet & Thibault, 1989) and suggests that "human aerobic endurance" has improved within the century (+13.4%) and tends to stabilize. Anaerobic distance capacity was highly variable over the century (coefficient of variation = 9.4%) and did not show a linear improvement over the years as has previously been suggested (Peronnet & Thibault, 1989). This could be due to an artefact in the application of the two-parameter model to only three Olympic performances. A limitation to the use of this linear mathematical model to fit physiological data may have been demonstrated.     

Knee extensor and flexor torque development with concentric and eccentric isokinetic training

This study assessed muscular torque and rate of torque development following concentric (CON) or eccentric (ECC) isokinetic training. Thirty-eight women were randomly assigned to either CON or ECC training groups. Training consisted of knee extension and flexion of the nondominant leg three times per week for 20 weeks (SD = 1). Eccentric training increased ECC knee extension and flexion peak torque more than CON training. The ECC group improved acceleration time and time to peak torque with ECC movements versus the CON group. Slow-velocity ECC isokinetic training yielded greater ECC and similar CON torque development gains versus CON training over the course of 20 weeks in young women.     

Fourth-grade students' motivational changes in an elementary physical education running program

Achievement goal theory and the expectancy-value model of achievement choice were used to examine fourth-grade students' motivational changes in an elementary physical education running program. In fall and spring of the school year, participants (N = 113; 66 boys, 47 girls) completed questionnaires assessing achievement goals, expectancy beliefs, subjective task values, and intention for future running participation. They also completed a timed 1-mile (1.6 km) run. The number of laps they ran/walked during the school year was used to assess students' persistence/effort. Results indicated the students improved their run but became less motivated about running while participating in a year-long running program. Children's beliefs about how good they were in the running program (i.e., expectancy beliefs) and their perceptions of how interesting and fun it was (i.e., interest) emerged as the strongest positive predictors of their motivation for running over time. These findings provide strong empirical evidence that expectancy beliefs and interest are essential to children's motivation in elementary physical education.     

Food attitudes in female athletes: association with menstrual cycle length

The aim of this study was to examine the relationship between indicators of risk of disordered eating, body image and varied menstrual cycle lengths. Altogether, 151 female athletes were invited from 16 sports and 70 female non-athletic controls were recruited from a university lecture class. The participants completed several surveys, including demographics, menstrual cycle history, physical activity, Eating Disorder Inventory (EDI) and the Three Factor Eating Questionnaire (TFEQ). Selected EDI subscales were summed to reflect eating disorder risk and body image. Menstrual cyclicity was based on self-reported cycle length for the last 6 months (normal cycles = 26-32 days, irregular cycles < or =26 or >32 days). Athletes overall had more irregular cycles (29.1%) than the non-athletes (15.7%) (P < 0.05). There were significant differences in scores for eating disorder risk, body dissatisfaction, drive for thinness, cognitive restraint (TFEQ) and disinhibition (TFEQ), only when athletes were divided based on menstrual cyclicity (i.e. irregularly cycling athletes had higher scores than athletes with normal menstrual cycle lengths). No differences in these scores were found between non-athletes with normal or irregular menstrual cycle lengths. In conclusion, irregularly short or long menstrual cycle length is associated with subtle indications of higher risk of disordered eating in female athletes.     

A comparison of physiological and anthropometric characteristics among playing positions in sub-elite rugby league players

This study compared the physiological and anthropometric characteristics of specific playing positions and positional playing groups in sub-elite rugby league players. Altogether, 415 sub-elite rugby league players underwent measurements of standard anthropometry (body mass, height, sum of four skinfolds), muscular power (vertical jump), speed (10-m, 20-m, and 40-m sprint), agility ("L" run), and estimated maximal aerobic power (multi-stage fitness test). Props were significantly heavier and had a greater skinfold thickness than all other playing positions. Centres, fullbacks, and hookers were faster than props over 40 m. When the data were analysed according to positional commonality, props were taller, heavier, had a greater skinfold thickness, were less agile, and were slower over 10 m than all other positional groups. The hookers/halves and outside backs positional groups were significantly faster over 40 m than the backrowers and props positional groups. In addition, the hookers/halves and outside backs positional groups had significantly greater estimated maximal aerobic power than the props positional group. The results of this study demonstrate that few physiological and anthropometric differences exist among individual playing positions in sub-elite rugby league players, although props are taller, heavier, have greater skinfold thickness, slower 10-m and 40-m speed, less agility, and lower estimated maximal aerobic power than other positional groups. These findings provide normative data for sub-elite rugby league players competing in specific individual positions and positional playing groups.     

Extending validity evidence for multidimensional measures of coaching competency

This study extended validity evidence for multidimensional measures of coaching competency derived from the Coaching Competency Scale (CCS; Myers, Feltz, Maier, Wolfe, & Reckase, 2006) by examining use of the original rating scale structure and testing how measures related to satisfaction with the head coach within teams and between teams. Motivation, game strategy, technique, and character building comprised the dimensions of coaching competency. Data were collected from athletes (N = 585) nested within intercollegiate men's (g = 8) and women's (g = 13) soccer and women's ice hockey (g = 11) teams (G = 32). Validity concerns were observed for the original rating scale structure and the predicted positive relationship between motivation competency and satisfaction with the coach between teams. Validity evidence was offered for a condensed post hoc rating scale and the predicted relationship between motivation competency and satisfaction with the coach within teams.     

The graph-theoretic field model— II. application of multi-terminal representations to field problems

This paper is a sequel to a paper entitled “The Graph-Theoretic Field Model—I: Modelling and Formulations” (1). Herein, the Theory of Multi-Terminal Representations is applied to the Graph-Theoretic Field Model to provide mathematical models of finite elements. The element models are obtained solely from the algebraic building blocks of the Graph-Theoretic Field Model, without recourse to any functional mathematics. The theory of Multi-Terminal Representations is developed for both linear and non-linear problems. Examples of the application of the theory to one- and two-dimensional field problems are presented from heat conduction and electrostatics.