Just like in all other sports, there are many variables in volleyball that generate a large number of unexpected events. With physics and mathematics, law and order can be given to such events, so that they can be studied and repeated. The advantage of law definition is that it allows for performance improvement and prediction, which renders sterile stats useless. In volleyball, technical gestures are studied in order to correct them as much as possible and to have the greatest strength, power and efficiency. Technical Gestures Technical gestures are an integral part of the skills of an athlete or coach. The effectiveness of the movement is crucial in every action and the greater efficiency of the technical gesture can be crucial to the final outcome of the match. In ancient times, you could only rely on video recordings of matches to analyze the movements. Today, thanks to the use of computers, very fast cameras and, above all, sophisticated software, it is possible to analyze the details and study each gesture, in order to improve the final effects and introduce new features. Physics is always the basis of any manipulation and linear velocity, angular velocity, acceleration and mass are always at the center of any mathematical computation. Through the computerized analysis of the movements, it is possible to improve the performance of the athletes during the match (see Figure 1). We can then replace the passive analysis with an active one. Our focus will be on the best move, this will allow us to try to understand what causes a particular effect, and we will then work with the player to improve their individual gesture. The acquired data is compared and processed through advanced algorithms, optimizing the individual gesture. Figure 1: The study of the best offers is based on complex physical analysis. Volleyball service With a volleyball serve, the body is immersed in a liquid. The distance between the start and end is covered by a trajectory which is affected by various factors such as the starting angle of the ball, direction and speed. With each movement, the ball is returned to play with the serve. Form the team’s first attempt to attack. They can be performed in different ways, with different results in strength and accuracy: from below; floating stop from above; from above while jumping. Hitting the ball can be characterized by power and accuracy. By properly adjusting these two opposite parameters, the team can decide different strategies to be adopted in the match. The position of the hands is very crucial, in fact the serve is completely different if the ball is hit with the palm or the fist. As you can see in Figure 2, the trajectory of the ball varies with different types of transmission. The ball’s trajectory on the low serve is a parabola, so it’s a slow serve with a very predictable trajectory. In a floating transmission, the ball is hit so that it does not rotate around its axis. In this way the ball moves over the net at an unsteady and undulating speed and tends to brake and move out of its trajectory in an unpredictable manner. If the exit angle of the ball is upward, the parabola is lengthened, and if the angle is directed downward, it is shortened. Today, with technology, it is possible to use “ball shooting” machines with which the strongest shots can be simulated in any conditions. The most powerful and powerful shots, on average, can reach a speed of about 100 km / h. However, there were athletes who exceeded the speed limit of 130 km / h (36 m / s). The kinetic energy delivered by the ball at this speed is 181 Joules, according to the following formula: Figure 2: Type of serve conditions, speed and trajectory of the ball. The average characteristics of the ball and the volleyball court are as follows: Circumference: between 65 and 67 cm; Weight: between 260 and 280 grams; Internal pressure: between 0.3 and 0.325 kg/cm; real or artificial leather materials; spherical shape; The color of the ball is white or striped (eg white, red, green); Field length: 18 metres. pitch width: 9 meters; – Height of the net in the center: 2.43 meters (men) and 2.24 meters (women). School teachers suggest to students several mathematical physics problems related to flying shots. For example, these types of questions are interesting: “A volleyball player performs a serve by throwing the ball at the baseline position from a height of 2.30 m and an initial velocity of unit v0, the direction of which forms an angle alpha = 45 degrees with respect to the horizon. Calculate the minimum speed to allow for the ball to cross the net. With physics simulation software, these problems are very easy (see Figure 3). The size of the ball is slightly increased in the drawing, so that it is clearly visible. In the simulation, the ball is thrown at five different initial velocities: 5 m/s; 7 m/s; 9 m/s; 10 m/s; 12 m/s. Figure 3: Using simulation software, it is very easy to solve any kind of problem. The serve in the first two cases is really weak and the ball does not reach the opponent’s court. The third strip touches the net and can barely cross the field. The fourth and fifth columns cross the grid easily. Today there are advanced ball-throwing robots that perform any kind of strike with great accuracy. It’s made of metal and battery-operated, so it can be taken anywhere. The safety is also very accurate, in fact it has sensors that allow the ball to be immediately stopped if there is a person in the immediate vicinity. It makes it possible to set different shooting directions and special effects on the ball. You can also choose the shooting tempo, from a few shots per minute up to 100 and more shots per minute. All professional volleyball teams train with these machines. Ball deformation in volleyball The phenomenon of deformation of the ball occurs every time it hits the hands of athletes. In fact, the ball undergoes deformation due to the impulse generated on the surface. The deformation is visible on impact with the ground and in the opponent at the moment of the blow. It can only be distinguished in a “still image” of a high-speed capture video, since it only lasts a few milliseconds. The ball returns to its original state during the parabola and this happens, on average, before passing over the net. Restoration of the state of equilibrium occurs because the internal pressure, due to the air inside, is pushed in the same way in all directions, returning the ball to its original shape, taking into account the elasticity of the components. When the ball comes into contact with another athlete again, it returns to its original shape and will undergo new deformation after the new contact. As can be seen from Figure 4, it is calculated that, on average, during a strong blow, the ball is deformed with a diameter of about 6 cm (3 cm on one side and 3 cm on the other side). It is temporarily reduced, from 21 cm to 15 cm. Figure 4: While serving, the ball experiences impressive temporary structural deformations. Equivalent movement in volleyball A volleyball serve can be accommodated with the equivalent movement of a slash shot. The ball is thrown at a speed of “v0” at an angle of release “alpha” relative to the horizontal. With a reference system with an “O” origin at the ball’s starting point, the ball falls back to the ground after describing an equivalent trajectory. The motion of the ball, at any moment, is the result of two different independent motions that occur in the x and y axes. It undergoes a decreasing acceleration of an intensity proportional to the gravitational acceleration and is equivalent to: on the x axis the motion is uniformly straight with a constant horizontal velocity equal to v (0x). The law of the clock is equal: on the y axis the motion is uniformly straight during ascent (from O to V) and straight acceleration during descent (from V to A). The law is: where v (0y) is the component of the initial velocity along the y axis. The components of velocity are calculated by the following relations: We get the equation of time: and the equation of the parabola (see Figure 5): also with the following two constants: The equation of the parabola is as follows: the parabola has a vertex at point V and the concavity is downward. Figure 5: Parabola path The “rise time of the ball”, the time it takes to go from O to V, is characterized by uniformly decelerating rectilinear motion (acceleration equal −g) with initial velocity equal to v (0y) and final velocity on the y axis equal to zero . It is equivalent to: the flight time, i.e. the time taken to travel the distance from O to A, is equal to twice the time of the climb. Determining the maximum height of the ball is also very interesting and is equal to: as evidenced by all the formulas and equations, the force of gravity plays a fundamental role in any direct and indirect motion. A volleyball match played on another planet is surely going to be a different story and the athletes will act as if they have never played any sport before. The lower extremities are in a waiting position, the legs are slightly bent and the feet are spread one in front of the other. This position is used to get better balance while working. As can be seen from Figure 6, there are three types of positions, depending on the bending angle of the different limbs: Feet in the high position: spaced apart and parallel. The heel touches the ground. The split never exceeds the shoulder width of the calf and thigh: slightly bent. The angle formed by the two parts is about 140 ° Bust: the upper limbs are slightly bent forward: flexed on the girdle with the forearms in the sagittal plane, the average position of the feet: wide apart. The heel touches the ground. The split does not exceed the width of the shoulders Leg and thigh: the angle formed by the two parts is about 100 ° Bust: the upper limbs bent forward: bent. The angle of the ‘arm and forearm’ is approximately 140° low, positions characterized by greater angle closure than previous models Figure 6: Lower extremities in waiting position Conclusions The most important technical gestures in volleyball, such as mass, protrusion, dunking and serving can be interpreted, analyzed and improved thanks to mathematics and its physical algorithms. The volleyball of the future (but in general the sports of the future) will increasingly make use of mathematics and information technology and the computer will work hand in hand with the coach to try to raise the athlete’s performance to the highest level. Current projects are related to improving energy, improving results in volleyball, and analyzing and studying technical and physical properties using “data intelligence”. Automatic trajectory tracking enables objective classification, maximizing an athlete’s movement and relating it to his or her performance. The new sophisticated algorithms do not “look” at training as a human does, but rather focus on some key points in the body that are not considered in the study. Each bodily gesture generates a set of curves in space that represent the movement of different limbs and the new software attempts to optimize this vector data for each individual athlete. .

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