Coefficients of Restitution of Balls Used in Team Sports for the Visually Impaired

Size: px

Start display at page:

Download "Coefficients of Restitution of Balls Used in Team Sports for the Visually Impaired"

Florence Mosley
5 years ago
Views:

1 INTERNATIONAL JOURNAL OF SPORT BIOMECHANICS, 1987, 3, Coefficients of Restitution of Balls Used in Team Sports for the Visually Impaired Peter McGrain, James Van Dyke, and James Mastro This study examined the coefficients of restitution (e) of selected balls used in team sports for the visually impaired: beep baseball and goal ball. Specifically, a basketball was compared to two men's standard goal balls, and a softball was compared to three different types of beep baseballs. The e for all balls was calculated by dropping each ball five times from heights of 6 ft (1.83 m) and ft (5.88 m). A Sony reel-to-reel videotape recorder was used to record rebound heights on a background scale for each ball dropped. Reliability tests of the procedures yielded correlation coefficients (r) of and for the 6 ft (1.83 m) and ft (5.88 m) drops, respectively. Two two-factor analysis of variance (ANOVA) tests yielded significant differences across ball type and height of drop for the basketball and goal balls and for the softball and beep baseballs, < 0.001). The es for the more recently developed beep baseballs are close to that of the standard softball, indicating a possible danger to visually impaired participants in beep baseball. Over the past several decades there has been an increasing awareness of disabled individuals and their rights to as normal a life as possible. The numerous pieces of legislation passed by state and federal lawmakers has provided opportunities for disabled individuals such as access to public buildings and employment. A commensurate change in life-style of disabled individuals has brought about recreational and sports opportunities for various disabled groups. Several games have been invented and adapted for the visually impaired, among them goal ball and beep baseball; both games feature a ball that emits a sound during play. Peter McGrain is with the Division of Physical Therapy, University of North Carolina at Chapel Hill; James Mastro is director of the Braille Sports Foundation, Minneapolis; and James Van Dyke is a director for Rem-Indiana, Inc., Lafayette, IN. Direct all correspondence to Peter McGrain, Division of Physical Therapy, Medical School Wing E 222H, University of North Carolina at Chapel Hi, Chapel Hill, NC

2 64 McCRAIN, VAN DYKE, AND MASTRO Beep baseball is played with a maximum of six visually impaired players and two sighted players, who play the pitcher and catcher. The object of the game is similar to regular baseball: to score more runs than the other team in six innings of play. Runs are scored by a batter hitting a fair ball and reaching a base 90 ft (27.4 m) away before a defensive player can raise the ball in the air, otherwise the batter is out. The ball and the base emit sounds of different frequency to help distinguish the two, and to enable the batter to find the base and the defensive players to locate the ball. The pitcher is sighted and throws an underhand pitch from a position of 20 ft (6.1 m) in front of the batter, a location that may be dangerous if the batter hits the ball hard. A beep baseball is constructed from a regulation 16-in. (40.6 cm) circumference softball1 with a cylinder cut from the middle of the ball approxirnately 2 in. (5.1 cm) in diameter. A 9v battery, speaker, electrical wiring, solder, and rubber cap are inserted into the cylinder and then a new exterior surface is placed on the ball.2 Goal ball is played by three visually impaired players on each team. The game is usually played on a gymnasium floor with a court 18 m long and 9 m wide. The object of the game is to score the most points in two 7-min periods. A point is scored by throwing the ball so that it remains between the two side lines, does not bounce, and passes beyond the opposing defenders. The coefficient of restitution of the goalball affects the mechanics of the ball release; a high e will cause the ball to bounce and could make a throw illegal. The goal ball is made of molded rubber with a hollow core in which 8 to 10 bells are placed. The goal ball resembles a cross between a basketball and a medicine ball.3 In 1980 the design of the beep baseball was changed to make the ball more durable.' This was accomplished by adding a rubberized plastic coating to the outside of the ball and then recovering it. Players reported that the new ball moved off the bat faster, bounced higher, and flew farther.2 Only changes in the audible device construction have been reported since the 1980 change in design. Recently a new prototype ball with a rechargeable battery has been used.2 At approximately the same time that the beep baseball underwent changes in design, the manufacturer of goal balls changed. The new manufacturer produced a ball that reportedly collapsed partially on the side that comes in contact with the hand during a throw. Players reported having to adjust their throwing styles to accommodate the new characteristic of the ball.3 The placement of the audible device(s) within a beep baseball or goal ball may lead to alterations in rebound characteristics. This may have implications for rebound potential that may adversely affect player safety and game strategy. The purpose of this study was to investigate the coefficient of restitution of balls used in beep baseball and goal ball, and to compare these to balls used in similar sports for the general population. Selected comparisons were also made between different models of balls used in these two sports for the visually impaired. The coefficient of restitution (e) is a number that describes the rebounding potential of two objects colliding with each other when approaching along a straight line. The loss in velocity after impact reflects the tendency of the bodies to lose their shape after impact. The algebraic calculation of the coefficient of restitution of a ball dropped to the earth can be proven equal to the square root of the height of the bounce after initial impact, divided by the height of the drop before impact (Hay, 1985). Several investigations have been conducted on the coefficient

3 BALLS USED IN TEAM SPORTS 65 of restitution of balls used in sporting events such as volleyball, tennis, and basketball (Baila, 1966; Hay, 1985; Plagenhoef, 1971). We found no research on the coefficient of restitution of balls used in sports for the visually impaired. Baila (1966) investigated the effects of heating and cooling on coefficients of restitution for several different balls. The balls were dropped under three conditions: (a) cooled for 1 hour in a freezer, (b) normal conditions, and (c) heated for 15 min at 225" F. Baila reported that the coefficients of restitution increased following heating and decreased following cooling. Hay (1985) reported coefficients of restitution for several different balls dropped from a height of 72 in. (1.83 m) onto a hardwood floor. Coefficients of restitution for the balls included 0.76 for a basketball and 0.32 for a softball. Plagenhoef (1971) examined the coefficient of restitution of several balls dropped from a height of 100 in. (2.54 m), and the same balls kicked or thrown at a velocity of 50 to 60 miles per hour ( mls) onto a hardwood floor. The coefficient of restitution for all balls was higher for the 100-in. (2.54 m) drop than it was for the balls propelled at the higher velocity. Representative coefficients of restitution for the 100-in. (2.54 m) drop included 0.75 for a basketball and 0.55 for a softball. Methods Two experiments were conducted to determine the coefficients of restitution of balls used in team games for the visually impaired. In the first experiment, differences among three types of beep baseballs and a standard 16-in. (40.6 cm) softball were analyzed. The differences among two types of goal balls and a regulation basketball were analyzed in the second experiment. The calculation of each e was performed by finding the square root of the height of the rebound divided by the height of the drop, as described by Hay (1985). For each experiment, a two-way analysis of variance was used to test for differences across ball types and the two drop heights. A Pearson product moment correlation coefficient (r) was computed to test the reliability of rebound height measurement. For both experiments, each ball was dropped five times from heights of 6 ft (1.83 m) and ft (5.88 m). A Sony reel-to-reel videotape recorded the drop and rebound of each ball for all trials. No spin on the ball was present during ball drops, since this may affect the variability of the calculated e. The video camera was positioned to allow for a large image size and minimum perspective error for ease of analysis of rebound height. A background scale was constructed to enable the investigators to measure the rebound height of each ball from the videotape data. Drop height and rebound height were measured from the floor to the bottom of each ball. A steel scaffolding was used to drop the balls from the ft (5.88 m) height and a volleyball referee's stand was used to drop the balls from the 6 ft (1.83 m) height. All testing was performed in the Texas Woman's University gymnasium, which was maintained at a constant temperature of 72" F (23" C). Results Reliability tests on the procedures for determining e at each drop height were calculated by repeating 20 of the drops randomly. The r for the 6 ft (1.83 m) drops was calculated to be At the ft (5.88 m) drop, the r was

4 McCRAIN, VAN DYKE, AND MASTRO Table 1 Descriptive Statistics for the Basketball and Goal Ballsa Ball type 6 ft drop (1.83 m) ft drop (5.88 m) M e SD M e SD Basketball Old goal ball New goal ball ameans and standard deviations were determined over five trials; all pairwise differences across ball type were significant at both heights, p <.05. Table 2 Descriptive Statistics for the Softball and Three Types of Beep Baseballsa Ball type 6 ft drop (1.83 m) ft drop (5.88 m) M e SD M e SD Soft ball Old beep baseball New beep baseball New prototype beep baseball ameans and standard deviations were determined over five trials; significant post hoe analysis appear in Table 3. Means and standard deviations calculated for all coefficients of elasticity are reported in Tables 1 and 2. The results of the ANOVA for the basketball and two types of goal balls were significant across ball types, F(2,24) = 905.6, p <.001, and across drop heights, F(l, 24) = 99.3, p <.001. No significant interaction was present. The results of the ANOVA for the beep baseballs and the standard softball were also significant across ball types, F(3,32) = 12.6, p <.001, and across drop heights, F(l, 32) = 23.3, p <.001. Again, no significant interaction was present. A Tukey post hoc analysis was performed on the results of each experiment to determine where there were significant differences among the types of balls investigated for each drop height. The results of the post hoc analysis for the beep baseballs and softball are presented in Table 3. Post hoc differences among the goal balls and the basketball revealed significant differences, p <.05, between all pairs of ball types for each drop height (see note under Table 1).

5 BALLS USED IN TEAM SPORTS Table 3 Significantly Different Cell Means for es in Post Hoc Analysis of Softball and Beep Baseball Dataa Comparison of coefficients of restitution Drop height in feet (& meters) Old beep baseball (0.472) vs new beep baseball (0.556) Old beep baseball (0.399) vs new beep baseball (0.492) Old beep baseball (0.472) vs softball (0.558) Old beep baseball (0.399) vs softball (0.538) New beep baseball (0.556) vs prototype beep baseball (0.529) New beep baseball (0.492) vs prototype beep baseball (0.409) Softball (0.558) vs prototype beep baseball (0.529) Softball (0.538) vs prototype beep baseball (0.409) 'All are significant at p <.05 Discussion From the results of this study, several points warrant further discussion. These include the calculated standard deviations of the coefficients, the difference in the coefficients of restitution between drop heights, the relationship of these results to past research, and the implications of the observed differences among the various balls tested. With one exception, balls used in sports for the visually impaired have higher deviations from the mean value of e as compared to balls used in sports for the sighted (see Tables 1 & 2). For example, the standard basketball had the highest e among all balls tested, yet exhibited a very low standard deviation from the mean when dropped from both heights (SD at 6 ft = 0.006; SD at ft = 0.007). In comparison, the old goal ball exhibited one of the lowest values for e, yet had standard deviations of -041 and.013 at drop heights of 6 ft (1.83 m) and ft (5.88 m), respectively. Circumstances were similar between the softball and the various types of beep baseballs. It is apparent that the addition of the audible devices affected the rebounding characteristics of balls used in sports for the visually impaired. The effect was to increase the range of velocity after impact with a gymnasium floor, probably due to the unsymmetrical and variable distribution of mass in the balls. This supports past research concerning the decrease in e as impact velocity increases. Plagenhoef (1971) determined that the coefficients of restitution of balls dropped from 100 in. (2.54 m) were higher than the calculated coefficients when balls were propelled at 50 to 60 mph ( mls). Hay (1985) and Plagenhoef (1971) calculated the coefficients of restitution for a standard basketball and determined an e of 0.76 (72-in. drop) and an e of 0.75 (100-in. drop), respectively. Additionally, Plagenhoef calculated the e for a softball dropped from 100 in. (2.54 m) to be This study revealed similar

6 68 McGRAIN, VAN DYKE, AND MASTRO values for the basketball (0.786 dropped from 72 in.), and softball (0.558 dropped from 72 in.). The observed differences among the coefficients for the various types of goal balls and beep baseballs have important implications for coaches, players, and manufacturers of these balls. The significant increase in e from the old goal ball (0.432 & 0.351) compared to the new goal ball (0.468 & 0.388), and from the old beep baseball (0.472 & 0.399) compared to the new beep baseball (0.556 & 0.492), or new prototype beep baseball (0.529 & 0.409), may affect the play of these games. These increases in e cause the ball to move faster after it hits the bat or the ground. The increased velocity of the ball in either sport will result in less time for the fielders to react. The result of this change will probably be beep baseball games with many runs scored and goal ball games with a high number of goals scored. These increases in e, however, particularly in the case of beep baseball, may sacrifice player safety. The manufacturing process for the new beep baseball has produced a ball that is extremely similar to a softball in terms of velocity after impact. Considering that the pitcher in beep baseball is only 20 ft (6.1 m) from the batter, and the visually impaired defensive players are usually less than 50 ft (15.2 m) from the batter, this increased elasticity of the ball may be dangerous to the defensive team. The increased velocity of the ball may lead to a commensurate increase in injuries to the visually impaired players unable to react fast enough to avoid being struck by a high-speed ball. In conclusion, it is suggested that balls used in sports for the visually impaired should be standardized. If standardization produces a beep baseball with elastic characteristics similar to those of a softball, then the pitcher and the defensive visually impaired players should be required to wear protective equipment to prevent bodily injury. References Baila, D.L. (1966, September 16). Fast ball-hot or cold? Science World, pp Hay, J. (1985). The biomechanics of sports techniques (3rd ed.). Englewood Cliffs, NJ: Prentice-Hall. Plagenhoef, S. (197 1). Pattern of human motion: A cinematographic analysis. Englewood Cliffs, NJ: Prentice-Hall. Notes 'Wilson Sporting Goods, 2233 West St., River Grove, IL lmerrimack Valley Works Chapter #78 Telephone Pioneers, 1600 Osgood St., 00601, North Andover, NH American Foundation for the Blind, 15 West 16th St., New York, NY

APPROACH RUN VELOCITIES OF FEMALE POLE VAULTERS

APPROACH RUN VELOCITIES OF FEMALE POLE VAULTERS Peter M. McGinnis, Physical Education Department, SUNY College at Cortland, Cortland, New York INTRODUCTION Running speed is an important determinant of