As can be seen from watching table tennis games of elite players, they are capable of extremely fast rallies. The translational velocity of a ball right after it is hit by a racket can reach speeds up to 100 km/h (Xie et al., 2002). In addition, players often apply various types of spin to the ball, which greatly influences the behavior of the ball after it is hit by a racket or bounces off a table (Tiefenbacher and Durey, 1994). Since the time to react to the ball is limited because of the fast rallies, it is assumed that players anticipate the approximate amount and direction of the spin applied to the ball, velocity of the ball and the resulting trajectory of the ball that is returned by the opponent player. If the players do not accurately predict the ball spins and simply swing the racket without adding any counter-spin movements, then the balls do not fly in the desired direction. The fact that players can maintain such fast rallies during the game, despite the various spin on the ball, is obvious evidence that they anticipate or predict the spin applied to the ball, in addition to reacting to it. Therefore, it is believed that players accumulate information regarding how the behavior of the ball in various circumstances would be through long time practice and experience.
Previously accumulated information regarding the behavior of table tennis balls primarily pertained to celluloid balls, which have been used appreciably since their introduction in 1900 (
Meyer and Tiefenbacher (2012) reported that seamless plastic balls showed greater deceleration in the horizontal direction and higher rebound in the vertical direction than celluloid balls. Moreover, they reported that players recognized certain changes between the behavior of the celluloid and plastic balls. Thus, it is expected that some differences exist between old and new balls. However, since the behavior of the balls differs greatly depending on the conditions how they are hit by a racket or how they collide with the table, a detailed analysis under a controlled initial condition is needed to understand the differences and similarities between them. Therefore, the main purpose of this study was to compare the characteristics of the plastic balls with those of the celluloid balls and determine potential differences under various initial ball impact conditions. In addition, since the criteria for approved plastic balls were modified to be more stringent in January, 2016, it was expected that plastic balls comprised of the renewed material would be sold, and companies producing plastic balls would continue to improve the quality of the balls. Since the official game ball varies depending on the event, players must adjust to different balls for each event. Thus, the secondary purpose of this study was to identify effective ways of evaluating the characteristics of the balls.
The characteristics of celluloid and plastic balls were analyzed by quantifying the behavior of the balls before and after collision with the table. Both the celluloid and plastic balls used in this study contained seams, had same quality ranking and were produced by the same company (3-star Premium, Nittaku). Five balls were randomly selected from each type of balls for the study and were tested under the various conditions detailed below. The mean diameter of the celluloid balls was 3.96 ± 0.00 cm, and that of the plastic balls was 4.00 ± 0.02 cm. The mean mass of the celluloid balls was 2.742 ± 0.007 g, and that of the plastic balls was 2.726 ± 0.008 g. .
The balls were launched from a table tennis ball machine that controls the spin and velocity of the ball using three rotors (Ozaki et al., 2013). By modulating the spin rate of the rotors, five different sets of velocity conditions were designed, ranging from 15 to 115 km/h. For all velocity conditions, back-spin was applied to the balls. The behavior of the balls before and after collision with the table was recorded using two synchronized high-speed cameras at 1000 Hz (Phantom V310, Vision Research).
Based on the brightness and configuration of the ball, the position of the ball in each of the two camera’s images was detected (Tamaki and Saito, 2015). The three-dimensional positional data of the center of the ball was reconstructed using a three-dimensional direct linear transformation (DLT) method. The reconstructed positional data were divided into before-collision and after-collision trajectory groups, then the center of the ball of each group was smoothed individually using a Savitzky Golay filter (Savitzky and Golay, 1964). Then the velocities of the ball immediately before (vertical component:
The coefficient of restitution (
Although the third law of friction states the coefficient of friction is constant regardless of the sliding velocity, this is generally not valid in the real world (Braun and Peyrard, 2011). This implies that the coefficient of friction can be influenced by initial velocities of the contact point of the ball with the table. Therefore, the velocity of the contact point of the ball with the table (
The coefficients of restitution for a given
Simple regression analysis was conducted to compute the regression coefficient and the regression equation between the
The coefficient of restitution was similar between the two types of the ball when the
The coefficient of friction was also higher for plastic than celluloid balls when
The post-collision trajectories of balls of a different type having the same initial conditions were compared. To simulate a service, the initial conditions were set as follows:
To simulate a smash, the initial conditions were set as follows:
To simulate a drive (a fast ball with greater topspin is called “drive” in table tennis) trajectory, two sets of initial conditions with the same speed but different spin rates were set as follows:
The purpose of this study was to compare the behavior of celluloid balls, which had been long used in table tennis, with that of the newly introduced plastic balls, and understand their differences and similarities. The results of this study show clear differences between the two types of the ball when the initial conditions correspond to the region where differences in the coefficients of restitution and friction are large between the two types of balls. In other words, if the characteristics and behavior of balls are to be investigated, testing at multiple initial conditions should be conducted since the behavior of the balls is greatly influenced by their initial conditions.
The difference in the coefficient of restitution between the two balls was higher when
This indicates that the horizontal velocity after collision was determined not only by the coefficient of friction, but also by the coefficient of restitution, as well as horizontal and vertical initial velocities of the center of the ball. The horizontal deceleration rates were still different between the two types of the ball for very fast
In addition to considering the area associated with greater differences in the coefficients between the two types of the ball, it is necessary to consider the direction of the contact point velocity if differences are expressed in terms such as acceleration and deceleration. With regard to horizontal acceleration and deceleration, since the frictional force depends on the direction of the contact point velocity, the behavior largely depends on the combination of the horizontal velocity of the ball center and the spin rate. In the case of back spin services, the contact point velocity generated by the back spin is oriented towards the same direction that the ball travels. Therefore, the ball experiences a decelerating force from the table during collision. Table tennis players often use the expression that “a ball stops at the collision in services”, which describes the deceleration of the horizontal velocity. In services having back-spin, players are expected to encounter more “stops” with plastic balls than celluloid ones.
However, services with plastic balls do not always give the impression of more stops than with celluloid balls. If top-spin is applied to the service, then the contact point velocity may be opposite to the direction that the ball travels if
To bring all the results together and consider game situations, some adjustments for predicting ball trajectories of plastic balls are suggested. First, as mentioned above, since services with back-spin will experience greater deceleration upon collision with the table, players can serve the ball that does not approach too close the opponent. When the ball decelerates upon collision with the table on the opponent’s side and does not go beyond the end of the table, but instead stays within the table boundary, it is more difficult for the receiver to return the ball with great top-spin since the table obstructs the swing of the racket. Therefore, a server can make use of this phenomenon with plastic balls and the receiver should expect a higher possibility of its occurrence with plastic balls than with celluloid ones. In addition, since plastic balls have a higher coefficient of friction with the table, they are expected to present greater changes in trajectories to their post-collision trajectory, not only regarding back-spin, but also side-spin or combinations of back-spin and side-spin. Therefore, players should expect greater changes in trajectories with plastic balls and consider new tactics to make use of these characteristics of plastic balls.
In addition to adjustments in the prediction of ball trajectories of slower balls such as a service, some adjustments are suggested for plays with faster balls such as a smash or a drive. Players should expect drives to accelerate more with a plastic ball having greater top-spin upon collision with the table than a celluloid ball, so the plastic ball approaches the player faster than expected. A smash with a plastic ball having greater initial vertical velocity will bounce off higher than expected in a smash with a celluloid ball. These behavioral changes between the two types of the ball may possibly influence defensive players who play far away from the table (often referred to as a “chopper”). If their opponent smashes a plastic ball, the ball will bounce off higher than expected in a smash with a celluloid ball, giving the player more time to react and hit the ball as precisely as they desire. On the other hand, if the opponent responds to a back-spin ball hit by a chopper with the back-spin “stop” technique, which also decelerates the ball with counter back-spin, causing the plastic ball to experience more stops upon collision with the table, choppers will have to travel back and forth for greater distances. However, since the behavior of the balls upon collision with the racket was not investigated, future research should be conducted if specific tactics are to be recommended with regard to the change in ball materials. Moreover, since only balls having back-spin were tested in this study, further research is required to identify how side-spin or other types of spin with different velocities affects the behavior of the two types of the ball.
Changes between the trajectory of celluloid balls, which had been long used in table tennis, and newly introduced plastic balls were investigated in this study. Plastic balls demonstrated a higher coefficient of restitution than celluloid balls when the initial vertical velocities were higher. Moreover, the coefficient of friction was higher for plastic balls when the initial horizontal contact point velocities were lower. As a result, for slower balls with back-spin, as in the case of a service, plastic balls are expected to experience more deceleration upon collision with the table than celluloid balls. On the other hand, for faster balls with greater amounts of top-spin, plastic balls are expected to experience greater acceleration upon collision with the table than celluloid balls. Since the behavior of the ball is largely influenced by the initial conditions, testing at various initial conditions is necessary to understand the characteristics of each type of the ball.
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