Measurements of the horizontal and vertical speeds of tennis courts     

Rod?CrossEmail author 《Sports Engineering》2003,6(2):95-111

Tennis courts are normally classified as fast or slow depending on whether the coefficient of sliding friction (COF) between the ball and the surface is respectively small or large. This classification is based on the fact that the change in horizontal ball speed is directly proportional to the COF if the ball is incident at a small angle to the horizontal. At angles of incidence greater than about 16° it is commonly assumed that the ball will roll during the bounce, in which case one can show that the ratio of the horizontal speed after the bounce to that before the bounce will be 0.645 regardless of the angle of incidence or the speed of the court. Measurements are presented showing that (a) at high angles of incidence, tennis balls grip or ‘bite’ the court but they do not roll during the bounce, (b) the bounce:speed ratio can be as low as 0.4 on some courts and (c) the normal reaction force acts through a point ahead of the centre of mass. An interesting consequence is that, if court A is faster than court B at low angles of incidence, then A is not necessarily faster than B at high angles of incidence. An exception is a clay court which remains slow at all angles of incidence. The measurements also show that the coefficient of restitution for a tennis ball can be as high as 0.9 for an oblique bounce on a slow court, meaning that the ball bounces like a superball in the vertical direction and that slow courts are fast in the vertical direction.  相似文献   

Oblique impact of a tennis ball on the strings of a tennis racket   总被引：1，自引：1，他引：0  

Rod?CrossEmail author 《Sports Engineering》2003,6(4):235-254

Measurements are presented of the friction force acting on a tennis ball incident obliquely on the strings of a tennis racket. This information, when combined with measurements of ball speed and spin, reveals details of the bounce process that have not previously been observed and also provides the first measurements of the coefficient of sliding friction between a tennis ball and the strings of a tennis racket. At angles of incidence less than about 40° to the string plane, the ball slides across the strings during the whole bounce period. More commonly, the ball is incident at larger angles in which case the ball slides across the string plane for a short distance before gripping the strings. While the bottom of the ball remains at rest on the strings, the remainder of the ball continues to rotate for a short period, after which the ball suddenly releases its grip and the bottom of the ball slides backwards on the string plane. The bounce angle depends mainly on the angle of incidence and the rotation speed of the incident ball. Differences in bounce angle and spin off head-clamped and hand-held rackets are also described.  相似文献   

Drawing together teaching methods and strategies into a model for science education     

Rod Francis 《Research in Science Education》1987,17(1):175-181

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Perceived submaximal force production in young adults     

Jackson AW  Ludtke AW  Martin SB  Koziris LP  Dishman RK 《Research quarterly for exercise and sport》2006,77(1):50-57

The purpose of this investigation was to examine the force production patterns using perceived stimulus cues from 10% to 90% of maximal force. In Experiment 1, 54 men (age: 19-34 years) and 53 women (age: 18-37years) performed leg extensions on a dynamometer at a speed of 60 degrees/s. Participants produced actual forces perceived to be 10-90% of maximal force in 10% increments followed by a maximal force. A 2-min rest interval was maintained between each increment. Participants rested 5 min and repeated the protocol. Desired forces were calculated as the required percentage of the produced maximalforce. In Experiment 2, 40 men (age: 18-30years)followed the protocol ofExperiment 1, but the submaximal stimuli were randomly presented. In Experiment 1, test-retest results indicated consistency between the trials for actual and maximal force (r = .90). The correlations between actual and desired forces were moderately high (r > .76). Actual forces trended above desired forces at 10% of maximal, with median errors ranging 33-40% for men and 60-73% for women. From 30% to 90% of maximal forces, actual trended below desired forces, with median errors ranging from a low of 1.5% to a high of 37%. A power function analysis relating the change in actual force with desired force stimuli produced exponents of 0.68 (.95 CI = 0.62-0.74) for men and 0.5 7 (.95 CI = 0.52-0.62)for women. Findings were similar in Experiment 2, indicating that individuals tended to overshoot and then undershoot desired force production through perceptual force ranges of 10-90% of maximal forces and that force production grew more slowly than perceptual stimulus cues. The results of the present study, along with findings from past research, indicate that production of submaximal force using perceptual cues or stimuli display a great deal of specificity. This specificity is related to type of contraction, amount of muscle mass involved, and number and types of stimuli.  相似文献