Repulsion of the Futsal Ball Depending on the Pressure in it

The aim of this research is to determine the elastic (repulsive) properties of the futsal ball depending on the air pressure in it. Futsal ball of standard dimensions was released on the fl at solid surface from the height of nine meters for four times. At the fi rst release the air in the ball was under prescribed pressure. At the second release the pressure in the pumped ball is reduced by 5%, at the third reduced by an additional 5%, at the fourth reduced by another 5%. The setting of the experiment was carried by cinema shooting of free fall of the prescribed futsal ball and a series of rebounds after the rejection of solid surfaces. One can conclude that the distance crossed and the total duration of four successive bouncing mostly dependent on inner pressure. In this study, the initial speed of a futsal ball was unchanged and only inner pressures were changed. It was determined how much the height of the rebound is reduced and the duration of the rebound, respectively, depending on the reduction of inner pressure. Overall, it can be concluded that the initial speed of the ball can be increased by increasing the inner pressure in the ball.


Introduction
Within physical development program the games have a dominant role, and among all games the most important are the ball games. In our environment the futsal occupies one of leading roles when the ball games are in focus. Th e most important equipment of these games is ball (Karimi et al., 2015). Today, all kind of balls are produced whose construction has been getting closer to full symmetry, but the ideal symmetry of the ball has not been reached yet! Basically, the futsal match is, strategically speaking, the battle for space and time. Th ose are the most important components in the ball games (Bjelica, Popović, Gardašević, & Krivokapić, 2016). Ball sports such as futsal place large metabolic demands on players (Hatamoto et al., 2014). In a good match, each player makes a lot of elementary muscular contractions at the fi eld, providing a series of complex movements, in a struggle to come into possession of the ball before the opponent player, to enter the zone from where the score can be reached before being distracted by the opponent player (Bjelica, Popovic, Tanase, & Gardasevic, 2017;Bjelica, Popović, & Gardašević, 2016a;2016b). Since such maneuver takes place continuously and it is time-consuming, furthermore the modern maneuver, where there are already well-coordinated combinations, is being performed in the highest speed and in a state of maximum fatigue, each good futsal game maximally exhaust all players at the fi eld.
Th e result of a futsal game is not been assessed by the level of motor performance nor who ran longer, or who is running faster, or who has jumped more, but by the number of goals scored. Th erefore, all maneuvering movements during a game are subordinated to the ball movement. Ball is a machine, whose properties each player must be fully aware of (Bjelica, 2008). Th is is the primary reason why every player must be fully aware of the nature of the elastic properties of a futsal. Th e aim of this research is to determine the elastic (repulsive) properties of the futsal ball depending on the air pressure in it, which basically fall under the kinematic researches.

Method
Research conducted in this study primarily refers to the standard futsal ball for seniors with the following performances (Table 1.): Recently, sophisticated fi nite element models of sports ball impacts have been developed for various sports (Nevinsa & Smitha, 2013). A standard futsal ball with full symmetry was acquired from the licensee manufacturer. Both layers, one of which is required to construct a ball, have inevitable fl aws, affecting the appearance of asymmetry, not huge but enough to cause changes, which do not exist in the ideal spherical body. Since in the cavity of the inner layer has to be pumped the air, there must be a valve, which, no matter how small is represents the asymmetry of the ball.
Futsal ball of standard dimensions was released on the fl at solid surface from the height of nine meters for four times.
Th e fl ight of a ball through the air is a key part of many popular sports (Barber, 2009). At the fi rst release the air in the ball was under prescribed pressure -p (Table 2.). At the second release the pressure in the pumped ball is reduced by 5% -p1 (pressure prescribed minus 5%, Table 2.). At the third release the pressure in the pumped ball is reduced by an additional 5% -p2 (pressure prescribed minus 5%, minus 5%, Table 2.) At the fourth release the pressure in the pumped ball is reduced by another 5% -p3 (pressure prescribed minus 5%, minus 5%, minus 5%, Table 2.) By calibrated gauge pressure the internal pressures were respectively measured. A rather demanding calculation of repulsions coeffi cient value was made with one of the basic programs. Th e setting of the experiment was carried by cinema shooting of free fall of the prescribed futsal ball and a series of rebounds aft er the rejection of solid surfaces. Th e recording was performed with the rapid-professional digital movie camera JVC GY-HM750E with fi ft y shots per second and the exposure sec/100. During the shooting, the camera was completely immobilized. In the projection of the futsal ball movement the markers were measured (in meters), in order to determine the extent (R) between the size of the screen and the real size (R-size screen natural). During the research the area of the collision was determined by transmission contrasting colors of the ball and surface before the collision with the ground and measuring the surface impressions on the ball and the ground aft er the rebound. Th e duration of the movements is measured in seconds, i.e. every fi ft y positions lasted one second and the duration between two neighboring positions lasted sec/50. Th e processing took positions of falls of each ball and its four rebounds.

Results
Table 3. shows a global view of spatiotemporal parameters of repulsion of the futsal ball with full symmetry depending on the air pressure in it. At the fi rst phase, the diagrams 1, 2, 3 and 4 shows the futsal ball paths with spatiotemporal parameters in the fi rst four rejections of solid surface, depending on the air pressure in it. In the vertical, there are culmination points of each rejection of the surface, measured in meters, and in the horizontal the length of each rejection of the surface is shown in seconds. At the second phase it was carried out the interpolation of diagrams of duration of individual rebounds in a function of distance covered on diagrams 5, 6, 7 and 8, as well as interpola-tion of diagrams of culmination points of individual rebounds over the time in diagrams 9, 10, 11 and 12 with the entered data. At the fourth phase were shown indexes of total duration and distance taken for futsal ball for four rebounds and four val-ues of inner pressure (Table 4.  At the fi ft h phase calculated are the repulsion coeffi cients for futsal ball, for each pressure, for each duration and each height reached (Table 5.). In the event of an impact of the falling ball with a solid surface, the force of the collision depends on the mass of the body in motion and acceleration that has a falling body at the moment of collision (Bjelica, 2014). Collision of elastic bodies takes place in two stages. In the fi rst stage the substance of the collisional bodies is compressed, and this phase is called the period of compaction or compression. Due to elastic properties of substances in an impact, aft er the compression the second stage of a collision takes place, which is called the period of return to the previous state or restitution (Bjelica et al., 2016). Futsal ball, no matter how many times aft er its release moved vertically in free fall, it had no vertical rebound out of four successive bouncing. To be able to determine the rules of repulsions with futsal ball, it is necessary to determine two sizes. Spatial, i.e. the height of culmination center of gravity of each ball rebound on one hand, and the temporal, i.e. the moment of a rebound, on the other hand.

Discussion
Looking at the sum of ball paths from the time of release to the culmination point of the fourth rebound as well as the duration of the bouncing ball from the start of the free fall until culmination point of fourth rebound, one can conclude that the distance crossed and the total duration of four successive bouncing mostly dependent on inner pressure. Infl ated futsal ball, with the compressed air pressure greater than atmospheric, when the pressure decreases, it less bounces from the ground even though nothing in its structure has changed. Th e rebound of the ball is a consequence of the aspirations of compressed air, that in the period of restitution "correct" the deformed part of the ball, which was created by compression. When the air pressure in a ball is higher, the bigger is the compression, and the bigger compression, the greater will be the restitution i.e. the harder rebound from the ground.
Th e heights of culmination points of a futsal ball with all four rebounds, of which almost all were taken into account when concluding, are the metric values, which in this experiment at least unreliable. Th e degree of deviation from the ideal value is almost negligible and based on the obtained height values of culmination points can be reliably concluded. Aft er calculating the futsal ball repulsions coeffi cient, for every air pressure and every rebound it was found that the repulsions coeffi cient is from 0.38 to 0.57.
In this study, the initial speed of a futsal ball was unchanged and only inner pressures were changed. It was determined how much the height of the rebound is reduced and the duration of the rebound, respectively, depending on the reduction of inner pressure. Overall, it can be concluded that the initial speed of the ball can be increased by increasing the inner pressure in the ball.