The free-kick from Roberto Carlos, in a match against France in 1997, is regarded as one of the wonders of football. The ball took effect in such a way that left the French goalkeeper, Fabien Barthez, completely motionless. What many may consider it a stroke of luck, in fact due to mathematical questions.
This was explained by Professor of Mathematics at the University of Coimbra, Eduardo Marques de Sá, in a lecture days ago in Science Faculdade Universidade de Lisboa (FCUL)
, entitled, "Euler, Roberto Carlos and the wonder goal." According Marques de Sá, the wonder goal by Roberto Carlos has three players: Roberto, Carlos, the ball and the air. " Although it seems a truism claim, this goal has the property to include "a ball that curves and at the end of the path the increase of curvature increases." "This phenomenon of a ball that is fired in a straight line and then begins to curve and get the doorman surround is very interesting. "
How
" Bernoulli's theorem and the effect Magnu s what they say is about how the relationship between flow rate and pressure within this fluid " . The Magnus effect is a manifestation of Bernoulli's theorem in a more sophisticated than was explained by Leonhard Euler and his followers. "
Thus, if imaginásemos to launch the soccer ball toward the goal, air passes through it and move, it drags a little air to rotate. When the ball and the air is moving in the same direction, the speed is higher and therefore the pressure is lower. When air moves contrary to the ball, the speed is lower and therefore the pressure is higher. This makes that the ball is diverted from its original path, thereby producing the Magnus Effect, managed by Roberto Carlos in his goal. "This is a mathematical justification of this kind of phenomenon."
Magnus Effect via
Wikipedia
- Author Bartosz Kosiorek
Fluid theory, the Newton first explained. However, "Euler was considered as the pioneer of Fluid Mechanics," although it was Magnus who detected, measured and established equations the effect. "
The spiral obtained in the Roberto Carlos goal is achieved" in the equations for the change in any of the parameters "and if" change the parameters of these coils, we reached a collection of spiral-type EURL "although these curves "are not yet studied. The Euler spiral, has a" very interesting geometric property "and that" the curvature of the initial part is zero and then increases as you go ".
In 2010 , was published in the New Journal of Physics
The spinning ball spiral
(Guillaume et al
(Guillaume et al
Dupeux, 2010).
This article used a small pistol to shoot bullets into water at 100 kilometers per hour, as the speed at which it is believed that the ball had Roberto Carlos. In doing so, discovering that the trajectory of a sphere that rotates a spiral.
Figure 1.
Chronophotography of the Impact of an iso-density sphere (R = 3.5 mm) penetrating a bath of water at 0
U = 35 ms -1
and spinning at ω ≈ 0 1200 rad s -1 . The time step entre images not is constant. t = 0 is the Impact time, t = -0.5
1 ms, t 2
= 2.8 ms, t
3 = 2.8 ms, t
= 13 ms, t
4
= 42 ms, t
5
= 76 ms, t
6
= 101 ms, t 7 = 169 ms and t 8 = 216 ms. The arrows indicate the sphere velocity.
Figure 2. Multi-pose image showing the trajectory of the ball of figure
1 . The time step between successive ball locations is Δt = 10 ms. This image reveals a spiral trajectory. Figure 3. Effect of spin on the trajectory of a sphere (density ρ s) after impact in water: (a) U0 = 33 ms-1, R = 3.5 mm, ρ s = 1410 kg m-3, ω0 = 0 rad s-1, time step Between images Δt = 2 ms. (B) U0 = 20 ms-1, R = 2.4 mm, ρ s = 920 kg m-3, ω0 = 1740 rad s-1, Δt = 3.75 ms. (C) U0 = 24 ms-1, R = 2.4 mm, ρ s = 920 kg m-3, ω0 = -1740 rad s-1, Δt = 3.2 ms. The Bends trajectory only if the spin is Present and the sign of the ITS Curvature changes "with the sign of the spin. The spinning ball spiral (Guillaume Dupeux et al). El Efecto Magnus que hablaba del Marques de Sá, is responsible for the ball to acquire this "rope" when turning, but also is responsible for what they called the "spiral of rotating ball." The spiral appears after about 40 meters, because when the ball loses speed, the Magnus effect becomes more pronounced, creating a spiral. "The important thing is that while the ball loses speed, the rotation is the same, so that path is just becoming more curved and that creates a spiral."
Unlike other free kick taker, Roberto Carlos gives effect to the ball and more importantly, it comes from a greater distance so well is it possible to achieve this effect.
Note
important for the readerDupeux
I do not know physics or mathematics that are used and they cause this effect. Any feedback on the effect will be grateful. The news was met by "Mathematics says Roberto Carlos golo maravilha" page Portuguese Science and Hoje explanation figures are taken from the article that explains this effect: Guillaume et al
2010 New J. Phys
12 093004 doi: 10.1088/1367-2630/12/9/093004
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