Let’s continue our journey to examine other aspects related to the physics of the game of football. The famous Captain Tsubasa will help us with this. We will see that many of the phenomena in those stories cannot be real and sometimes can be completely physically impossible. The soccer player’s speed in the soccer game is speed. If you run faster, you will get the ball first and beat the opponent. Football today respects this rule very much. Whatever the role of the player (defender, midfielder or striker / striker), running at a centimeter speed is one of the most important characteristics. One of the many rankings found online shows that the following players are the fastest in the world: Kylian Mbappe (Paris Saint-Germain): 36 km/h Inaki Williams (Athletic Bilbao): 35.7 km/h Pierre-Emerick Aubameyang (Arsenal): 35.5 km/h Cream Blaraby (Bayer Leverkusen): 35.27 km / h Kyle Walker (Manchester City): 35.31 km / h Leroy Sane (Manchester City): 35.04 km / h Mohamed Salah (Liverpool) 35 km / h Kingsley Coman (Bayern Munich): 35 km Alvaro Odriozola (Bayern Munich): 34.99 km/h Nacho Fernandez (Real Madrid): 34.62 km/h A speed of 36 km/h (10 m/s) allows you to go the distance. 100 meters in 10 seconds or 1 kilometer in 1 minute 40 seconds. These numbers refer to the maximum speed reached (peak speed), not the average speed. As we can see from the graph in Figure 1, super sprinter Usain Bolt is much faster than all football players, and this is also due to the fact that he does not carry the ball. His world record top speed was 44.72 km/h with an average of 37.58 km/h. Figure 1: The world’s fastest soccer players compared to Usain Bolt The kinetic energy of the fastest players (and Bolt) takes into account their speed and body weight and is calculated with the following formula: Results are impressive. Usain Bolt develops double kinetic energy for Kylian Mbappe. If these two players collided head-on, at their full speed, the effect would almost certainly be fatal. The mileage of a football field The football fields where Captain Tsubasa’s players seemed to be playing were huge and the footballers seemed to be able to perform amazing feats with the ball, bypassing any physical principle. From these stories we can understand that: the football field was much longer than the organizational procedures. In some stories, the players’ running speed seemed too high. However, these are two different absurdities. It should be considered that a normal football field has an average length of 100 meters and a player can cover it in about 12 seconds at full speed. Also, no human can exceed a speed of 45 km / h for a long time, but in the imagination anything is possible. Distorted ball The strikers’ shots in Captain Tsubasa’s stories were so strong that they distorted the ball (see Figure 2). In theory, this could be possible by applying a force equal to a few “tons/force” for short moments. With this force applied, it can really hurt the ball and may even demolish the concrete masonry. When a soccer player kicks a ball, various events occur. The leg transmits kinetic energy on it. Moreover, the ball undergoes a slight deformation of a few milliseconds. Before the ball touches the player’s foot, the internal air pressure is uniform. But after contact, it deforms and the air pressure around the deformed area increases due to the reduced volume of the ball. The energy in the collision is equal to the sum of the kinetic energy of the foot and the energy stored in the deformed ball and it also generates some heat. The more the ball is deformed, the greater the energy loss in heat. Thanks to the conservation of energy, the ball is faster than the foot. The formula for calculating the speed of the ball is as follows: the coefficient “e” in the formula is the “return coefficient” and it can be between 0 and 1: • A value of 0 indicates that the ball does not bounce at all; • A value of 1 indicates that the ball bounces and reaches the same pitch with each bounce. The return coefficient can be easily calculated by the following formula: where: h0 is the initial height of the launch; h1 is the height reached after the first bounce. For example, a ball thrown from a height of 10 meters and bouncing up to a height of 7 meters has a coefficient of return of 0.836. The Football Regulations state that the ball must: be spherical in shape; be made of compatible materials; Its circumference ranges from 68 cm to 70 cm; Weighing between 410g and 450g at the start of the bout; It is inflated at 0.6-1 atmospheric pressure (600-1100 g/cm2) at sea level. Also, if you drop the ball from a height of 2 metres, it must not exceed 70 cm on the first bounce, with a regression coefficient of about 0.69. If the soccer ball falls on a hard surface, it will bounce less from the starting position. Different types of balls have different bounce abilities. For example, a baseball is less bouncy than a soccer ball and will bounce to a much lower position than a soccer ball if it is dropped from the same height. Rebound is determined by the elasticity of the ball. Figure 2: Intense forces are required (temporarily) to deform the soccer ball In bouncing the ball, the kinetic energy before impact is always greater than that after impact. In fact, no ball is completely elastic. The coefficient of recovery is higher in a more elastic ball. Figure 3: Energy is not destroyed but converted As can be seen from Figure 4, a value of 1 indicates a perfectly elastic ball bouncing infinitely on a solid surface while being zero for a ball of putty “sticking” to the ground. The soccer ball’s reaction coefficient is about 0.7, so its speed decreases by 20% after each collision.Another formula for calculating this coefficient is: Figure 4: Bounces of some balls with different recovery coefficients To study the phenomenon, it is necessary to observe the force of the ball’s reaction during the collision with an accurate video no Less than 5000 frames per second During contact with the foot, peak forces and pulsations are recorded that replace the ball’s geometric center and center of gravity. Several studies note a maximum impact force on the metatarsal of about 2400 N and a toe force of about 2200 N (see Figure 5).Studies show that the reaction force of the ball repeatedly acts on the foot during impact, precisely because of its elastic structure.Theoretically, the ball will be able to damage the anatomical structures of a football player, who strives for a higher ball speed By submitting to the force Greater reaction to the foot. Figure 5: The force generated by the foot pulling like the ball Many soccer players can shoot the ball following the direction of a parabola (see Figure 7), but there are clearly many rules of physics behind this. To create a curved path, the ball must be kicked slightly off center by rotating it horizontally. As the ball travels through space, air (which is a dense liquid) moves over the ball. Air will move faster on one side and slower on the other, with differences in pressure. Thus, the ball moves from the direction of high pressure to the direction of low pressure, making the path curve. However, at the beginning of the flight, the ball will follow a short, linear path. It will start to skew when decelerating. Rotational speed indicates a different final trajectory. The phenomenon is stronger when the ball is irregular or has some small “pits”. With a perfectly smooth sphere, the parabola will be much smaller. Air resistance affects the movement of the soccer ball. It is not the only force exerted but it is possible that it exerts a lift force acting perpendicular to the ball. Unlike drag force, lift force pushes the ball sideways up or down causing it to bend in flight. Parabolic Shots (horizontal or vertical) are great tricks to deceive your opponent footballers. To follow a curved path, the ball must be spinning very fast. This is the “Magnus” force created by the dual effect of the rotating ball and the viscosity of the air. For a rotating ball, air passing in the same direction as the contact surface on one side of the ball moves in the opposite direction on the other side. In practice, the airflow around the rotating ball is not uniform. Once again, Holly and Benji managed to give the ball impossible paths that would have been inaccessible to any goalkeeper. The ball even seemed to be remote controlled. Figure 6: Creating the magic parabola path for the ball requires a great deal of skill from the player. Studies on this topic are becoming more and more detailed and soon we will see bots playing a perfect game with the help of artificial intelligence. To properly handle the physical aspects, the concept of a reference system as 3D coordinates, parabola paths and angular velocities of shots must be considered. But we must also monitor the acceleration and forces systems. You see any artistic gesture as the embodiment of a material principle, ideally represented by mathematical laws.

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