Magnus effect and turbulence in football

To the Football, a type of striking of ball known as wrapped striking aims at giving a curved trajectory to the balloon. This type of striking is often used during the shootings of blow-francs to circumvent the wall consisted a line of unfavourable players placed between the balloon and the goal and to make return the balloon towards the goal. This striking, while making whirl the balloon on itself, gives him an effect which modifies its trajectory during its race. Another type of striking, familiarly called " strike banane" , amplifies this phenomenon, the curve of the trajectory being accentuated then strongly at the end of this one accompanied by an acceleration of the balloon.

A famous example

At the time of a match of preparation of the World cup of 1998 in France, the teams of France and Brésil clash with the Stade of Gerland to Lyon. The Brazilian defender Roberto Carlos mark a goal surprising on frank Blow. The diagram opposite illustrates the position of the players and the trajectory of the ball. The fault is whistled with approximately 25 meters of the French goal, slightly on the line. After the striking of Brazilian, the balloon circumvents the wall by the line. It seemed so obvious that the shooting would pass far from the framework, that a pick-up of the balls, instinctively lowered the head. Suddenly, at the end of the trajectory, the deviation towards the left was accentuated and the ball returned with an aim after having run up against the interior of the post. The French guard, Fabien Barthez and his fellow-members were very surprised and incrédules over the moment. The televised idle, camera in the axis of the goal, shows well the curve at the end of the trajectory and the acceleration of the balloon.

Analyzes

This type of striking and the trajectory which is followed from there raises 2 questions:

How to explain the deviation of the ball compared to the beginning of its trajectory?
Comment this deviation can become progressively more marked of its race, without the ball not being touched by another player?

This trajectory can be explained by the simultaneous action of two physical effects:

the Effect Magnus
the air flow on a surface, known as Laminar or turbulent, dependently of the Reynolds number of the situation.

The Magnus effect

The effect given to a soccer ball is with its rotation on him even. If an object is in rotation on an axis perpendicular to its displacement in a fluid, a half of its surface makes rotation in the direction of displacement, other half makes rotation against displacement. The friction between the ball and the air attracts the air in rotation in the same way around the ball. From there, the effect conforms to the Principe of Bernoulli: the air outside the curve is slowed down, increasing its pressure, while the air inside the curve is accelerated, decreasing its pressure. Thus the ball deviates towards the interior of the curve, making it possible the balloon to circumvent the defensive wall and to return then towards the interior (see diagram).

The Reynolds number

The second phenomenon is that of the turbulent Fluide compared with a fluid Laminaire. Turbulence is more easily visible in water than in the air. Thus the wake of a boat becomes less smooth and with more scum when the boat accelerates. A wake foamed is an indication which the fluid which runs out on the body is turbulent, a calm wake that the fluid is laminar.

A fluid is turbulent when the effect of the inertia on various layers of the fluid is greater than the effect of the Viscosité which tends to cancel them. This wants to say that masses of the fluid circulate around the random object of way. If a fluid is laminar, its particles move only the minimum necessary and the viscosity of the fluid retains it on the surface of the object.

To determine if a fluid runs out in a laminar or turbulent way, one uses the Reynolds number (see also Nombre of Richardson and Nombre of Grashof) who gives the relationship between the effects of inertia and viscosity. Generally, a Reynolds number higher than 2300 indicates a turbulent fluid, a lower number indicating a laminar fluid.

Importance in striking banana

Since a soccer ball leaves a wake in the air which can be either turbulent or laminar, and which the ball behaves in a different way in each case, it is the difference between the turbulent flow and laminar which explains the particular trajectory of striking banana. During the turbulent flow, the balloon is surrounded by swirls of air which do not offer great resistance and do not increase its trail relative at its speed. It is thus by creating turbulence that the golf balls fly further because of the small cavities which recover their surface. A soccer ball is smoother, but irregularities, as the points of joining which hold it together, can also create turbulence if the balloon moves quickly.

The low resistance of the air tends to cancel the Magnus effect when the fluid is turbulent. However, the balloon slows down anyway, and early or late, it will cross the threshold of 2300 between the turbulent flow and the laminar flow. There, resistance increases and the Magnus effect takes again its original force. Thus the ball begins its way with a light effect which suddenly (for example, once the crossed defensive wall) is accentuated explaining this trajectory in the banana shape.

To succeed, it is necessary that the balloon is struck very extremely and by giving him much effect so that rotation is not dissipated before the crucial moment between the stage turbulent and the laminar stage. Such a type of striking succeeds better in dry weather. Indeed, the moisture of surfaces of the balloon and the shoe of striking decreases the friction but an important friction is necessary to create an important rotation of the balloon (even if a small rotation is obligatorily generated by the simple deformation of the balloon in contact with the foot of the player at the time of striking). With football, the normal technique is to very extremely strike the balloon with the outside of the foot on the side towards which one wants to curve the ball, that is to say the opposite of a normal wrapped striking. At the time of the above mentioned example, the Brazilian player Roberto Carlos takes the maximum of dash to strongly strike the ball. He strikes it left foot, the left side of the ball and towards the line of the goal. The ball passes on the right from the wall of the French defenders, with a beginning of rather right trajectory before being rather strongly curved in end of the road, horizontally towards the left thus towards the goal to end up running up against the interior amount of the post and returning with an aim.

Turbulence explains also the tendency of the strong shootings and without effect to have unforeseeable slips and jumps in the air (" ball flottante"). Here, in absence of effect, the only influence on the trajectory of the ball is that of the random turbulence and which explains also fears of the goalkeepers when a competition is played with a new balloon. If its weight, volume and its form did not change (parameters standardized in the competitions of football), its surface can be slightly different, then being able to influence the long trajectories.

External bonds and references

Physical Football - Bend It Like Roberto Carlos
The Physics off Football
It of the goal of Roberto Carlos on YouTube

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