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Roberto Carlos’s famous free-throw puzzle (physics of football)

Roberto Carlos’s famous free-throw puzzle (physics of football)

Bill Shankly, former Liverpool manager, once said: “Football is not a matter of life or death, but more important than that.” After every sporting event, all that remains is a number of television replays and an endless number of guesses about What was to happen.

This is the side of football that fans love and others hate, what if the penalty has entered the goal? What if the player is not fired? What if you did not bend that free kick around the wall and hit the goal.

Many football fans remember the free kick by Brazilian Roberto Carlos at the World Cup in France. The location of the kick was far from the opponent’s goal about 30 meters and to the right slightly. Carlos kicked the ball very far to the right, where it initially moved away from the wall of the block for about a meter. What made the boy collect the balls, who appeared a few meters from the goal, head in despair, then, as if by magic the ball bent to the left and entered the far right corner For the goal, amidst the surprise of players and guard and the media as well.

Carlos seems to have been training this kick all the time during the training sessions. According to his intuition, he knew how to curl the ball with a specific velocity and a specific rotation. He probably did not know the physical background about the subject.

Aerodynamics of Sport Balls:

The first explanation of the lateral deviation of the rotary elements is attributed to Lord Rayleigh by a work done by the German physicist Gustav Magnus in 1852. Magnus was actually trying to determine why the missiles and the rotating bullets diverged to one side, but its interpretation also applies to the balls.

In fact, the basic mechanics of bowing in football is the same in other sports as baseball, golf, tennis, and cricket.

Consider a ball around a vertical axis on the air current around it (see attached figure). The air moves faster for the center of the ball as the surface of the outer ball moves with the direction of the airflow, reducing the pressure according to the Bernoulli principle. The opposite effect occurs on the other side of the ball, where the air moves slower for the ball center. There is an imbalance of power and a twist of the ball, or as JJ Thomson put it in 1910: “The ball follows her nose.” This deflection of the ball during flight is generally known as the Magnus effect.

The moving forces divide the moving ball in the air usually into two types:

 lifting force and drag force. Lifting is the force that drives up or to the aspects responsible for the Magnus effect. Traction affects the opposite direction of the path of the ball.The traction coefficient is suddenly reduced when the airflow at the surface of the ball changes from smooth and linear to turbulent (see attached figure).

When the flow is linear and the traction is high, the marginal layer of air on the surface of the ball breaks up relatively early when it occurs above the surface of the ball, producing swirls in its effect. However, when airflow is disturbed, the marginal layer sticks to the ball for longer, causing a late separation and a little drag (see attached figure).

Therefore, the value of the Reynolds number, where the traction value is reduced, depends on the surface roughness of the ball. For example, a golf ball has a lot of cavities

When calculating the forces affecting the ball in a free kick the information of the data. Assuming that the speed of the ball ranges between 25 and 30 meters per second (about 100 kilometers per hour) and the number of cycles between 8 and 10 cycles per second, we find that the lifting force of about 3.5 Newton. The rules require professional football to be between 410 and 450 grams. This means that it accelerates by 8 m / s².

Assuming that the ball takes one second to cut a 30 meter track, the lift will make the ball drift off a distance of up to 4 meters from its original straight path, enough to confuse any goalkeeper.
Surface and surface roughness to a large extent, thus reducing the traction coefficient at relatively low values of Reynolds number (2.104)

Football is much easier than a golf ball and the critical shift occurs at much higher values for the Reynolds figure (about 4.105).

The conclusion of the above is that slowly moving football balls are subject to relatively high disability. But if it is possible to kick the ball fast enough to make the air pass around turbulent, the ball will have a smaller disability force (see attached figure). So moving balls are quickly a double problem for goalkeepers, not because they move very fast, but because they are

Do not slow down as much as expected. Perhaps the best goalkeepers understand physics more on intuition than they realize.

Where: D is the ball diameter, μ is the motor viscosity of the air.

In 1976, Peter Bearman and his colleagues from the Royal College of London conducted a series of experiments on golf balls. The researchers found that the increased rotation of the ball produced a higher lifting factor and therefore a greater amount of Magnus power, but increased speed at a specific rotation caused the reduction of the lifting factor. What this means for football is that the slowly moving ball with a lot of gyro has greater side forces than the moving ball with the same amount of rotation. So when the ball starts to slow at the end of its path, the curvature is hurt
H more pronounced.

Return to Roberto Carlos:

How does all this explain the free kick by Roberto Carlos? 
Although we can not be quite sure, it is likely that the following can be considered a logical explanation of what happened:

Carlos kicked the ball on the outside of his left foot to make it turn counterclockwise. The weather was so dry that the amount of rotation he gave to the ball was high, probably more than 10 cycles per second. His kick to the ball on the outside of his foot allowed him to strike the ball with a force of more than 30 meters per second (108 kilometers per hour).

The air flow around the surface of the ball was disturbed, giving the ball a relatively low traction. Somewhere on the path of the ball, perhaps within 10 meters (or at the place of the wall), the speed of the ball dropped to the point where it was allowed to enter the linear airflow system. This caused a significant increase in the impact traction on the ball, making it slow down more speed, and enabled the power of Magnus side, which was bending the ball towards the goal, to become more effective. Assuming that the amount of rotation did not decrease significantly, then the traction coefficient increased, resulting in the emergence of a much larger lateral force that caused the ball to bend more.

Finally, the slower the ball becomes, the more obvious the bending (perhaps because of the increased lift coefficient) until the ball hits the net, so that the physicists are happy with the crowd.

Current research on football:

There is more research on football than just studying the movement of the ball when flying. Researchers are also interested in how the soccer player kicked the ball. For example, Stanley Plagenhof of the University of Massachusetts studied kinetics, kicking the ball, in other words, ignoring the forces of influence.

Other researchers, such as Elizabeth Roberts and her colleagues at the University of Wisconsin, conducted a dynamic analysis of kicking the ball, taking into account influential forces.

These experimental methods have produced some good results, although some challenges still exist. One of the critical problems is the difficulty of measuring the physical movement of humans, partly because their movements are very unpredictable.

However, recent developments in the analysis of computer movement have received more attention in the science of sport, and with the help of modern scientific methods, accurate measurements can be done in an acceptable way to human movement.

For example, two authors of TA and TA and a team of researchers at Yamagata University in Japan used a computer-based scientific method and integrated it with more traditional dynamic approaches to simulate the way players kick the ball. This simulation allowed the creation of virtual football players of all specifications – from beginners and young children to professionals – playing in virtual places and time on the computer. Sports equipment manufacturers such as the ASICS group, which is funding the Yamagata University project, are also interested in this work.

They hope to use these results to design higher-performance and safer sports equipment that can be manufactured faster and more economically than existing ones.

The movement of the players was followed by a high-speed video of 4500 frames per second, and then the effect of the foot on the ball was studied by finite element analysis.

Initial experience has shown what most footballers know: If you kick the ball with your foot in the right position so that the foot hits the ball with a line from the center of the weight of the ball, then the ball goes straight. If you kick the ball at the instep and at a 90o angle with the foot and foot (see attached figure).
H more pronounced.

Return to Roberto Carlos:

How does all this explain the free kick by Roberto Carlos? 
Although we can not be quite sure, it is likely that the following can be considered a logical explanation of what happened:

Carlos kicked the ball on the outside of his left foot to make it turn counterclockwise. The weather was so dry that the amount of rotation he gave to the ball was high, probably more than 10 cycles per second. His kick to the ball on the outside of his foot allowed him to strike the ball with a force of more than 30 meters per second (108 kilometers per hour).

The air flow around the surface of the ball was disturbed, giving the ball a relatively low traction. Somewhere on the path of the ball, perhaps within 10 meters (or at the place of the wall), the speed of the ball dropped to the point where it was allowed to enter the linear airflow system. This caused a significant increase in the impact traction on the ball, making it slow down more speed, and enabled the power of Magnus side, which was bending the ball towards the goal, to become more effective. Assuming that the amount of rotation did not decrease significantly, then the traction coefficient increased, resulting in the emergence of a much larger lateral force that caused the ball to bend more.

Finally, 
the slower the ball becomes, the more obvious the bending (perhaps because of the increased lift coefficient) until the ball hits the net, so that the physicists are happy with the crowd.

Current research on football:
There is more research on football than just studying the movement of the ball when flying. Researchers are also interested in how the soccer player kicked the ball. For example, Stanley Plagenhof of the University of Massachusetts studied kinetics, kicking the ball, in other words, ignoring the forces of influence.

Other researchers, such as Elizabeth Roberts and her colleagues at the University of Wisconsin, conducted a dynamic analysis of kicking the ball, taking into account influential forces.

These experimental methods have produced some good results, although some challenges still exist. One of the critical problems is the difficulty of measuring the physical movement of humans, partly because their movements are very unpredictable.

However, 
recent developments in the analysis of computer movement have received more attention in the science of sport, and with the help of modern scientific methods, accurate measurements can be done in an acceptable way to human movement.

For example, two authors of TA and TA and a team of researchers at Yamagata University in Japan used a computer-based scientific method and integrated it with more traditional dynamic approaches to simulate the way players kick the ball. This simulation allowed the creation of virtual football players of all specifications – from beginners and young children to professionals – playing in virtual places and time on the computer. Sports equipment manufacturers such as the ASICS group, which is funding the Yamagata University project, are also interested in this work.

They hope to use these results to design higher-performance and safer sports equipment that can be manufactured faster and more economically than existing ones.

The movement of the players was followed by a high-speed video of 4500 frames per second, and then the effect of the foot on the ball was studied by finite element analysis.

Initial experience has shown what most footballers know:
 If you kick the ball with your foot in the right position so that the foot hits the ball with a line from the center of the weight of the ball, then the ball goes straight. If you kick the ball at the instep and at a 90o angle with the foot and foot (see attached figure)
The experimental results also showed that the rotation of the ball is strongly related to the friction coefficient between the foot and the ball and the distance of the foot shifted from the center of the weight of the ball. The Finite-element model – written with DYTRAN and PATRAN from the MacNeal Schwendler group – was used for the digital analysis of these events. The study showed that the increase in the coefficient of friction between the ball and the foot made it acquire a greater amount of rotation. The rotation also increases when the displacement distance is increased from the center of the ball’s weight. Two other interesting factors were noted.

First, if the distance of the deviation and the foot of the foot increases for less time and covers less space, then both speed and rotation decrease. So there’s a perfect place to kick the ball if we want to get the big turn: if you kick the ball too close or too far from the center of gravity, the ball does not gain any rotation.

The other important factor is that even if friction is absent, the ball will still gain some rotation if we kick it with a distance of deviation from the center of gravity.

Although in this case there is no peripheral force parallel to the circumference of the ball (as long as the friction coefficient is zero), the ball is still distorted towards its center, producing a small force that affects the center of gravity. So it is possible to rotate the ball on a rainy day, although the rotation is much lower under dry conditions.

Of course, this analysis has many limitations and limitations. 
The air was ignored outside the ball, and the air inside the ball was considered to have a behavior similar to that of a viscous liquid viscous fluid. Ideally, air inside and outside the ball and viscosity should be considered using the Navier-Stokes equations.

The foot was also assumed to be homogeneous and homogeneous while it is clear that the real foot is more complex than that. Although it may be impossible to create an ideal model that can take all factors into account, this model includes the most important characteristics.

Two authors (TA and TA) are planning in the future to study the effect of different types of shoes on kicking the balle. At the same time ASICS is combining the simulation of the Yamagata elements with biomechanics, physiology and material science to design a new type of football shoe. But basically, the player is the one who makes the difference and without that capability, the technology is useless.



End whistle:

So what can we learn from Roberto Carlos ?. I have kicked the ball hard enough to make the airflow around the surface of the ball turbulent, then the traction force remains low and the ball actually flies. If you want the ball to bow, give it a large amount of rotation by kicking it away from its center. This is easier on dry days than wet days, but it can be done regardless of weather conditions. The ball will bend as much as possible when it slows down to enter the linear flow zone, so training is needed to make sure that this shift takes place in the right place (right after the ball crosses the wall). If the weather is wet, it is possible to get the circulation, but it is still better to dry the ball and shoes

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