Long derided for their fabricated/manipulated history and lack of scientific information, Pakistanis seem to be turning a new leaf or a new page, at least as far as STEM education is concerned, amid reports of India’s decline in textbook writing. Today I read about a 9th grade physics textbook in Pakistan that asks a question about Babar Azam’s cover drive: “Babar Azam achieved a cover drive by applying 150j kinetic energy to the ball with his bat. (a) At what speed will the ball travel to the boundary if the mass of the ball is 120 g? (b) How much kinetic energy must a football player give to a football with a mass of 450 g to make it move at this speed?”
I’m sure Virat Kohli fans and science teachers will find plenty of holes to sort through the whole thing, but Pakistanis at least think for mythology — or for a change, fiction — and don’t attribute the cover drive, mashallah, to divine forces. Meanwhile, some Indian school boards are busy embracing and mistaking mythology and fiction for history. Apparently Sachin Tendulkar’s pristine straight drives and the purity of Saurav Ganguly’s cover drive didn’t appeal to them.
On a more serious note – and as the World Cup is almost upon us – the sporting moment that gave rise to some of the most passionate and insightful scientific studies and commentary is Roberto Carlos’ famous 1997 free kick – a 35 meters to produce what is arguably the greatest free kick goal in football history, and a goal that eventually became a case study in aerodynamics. (you can see the kick online; look for Roberto Carlos’ incredible free kick).
Here’s how one study described the physics behind the target: According to Newton’s first law of motion, an object will move in the same direction and speed until a force is applied to it, regardless of the strength of the force. When Carlos kicked the ball, he gave it direction and speed, but what force made the ball swerve and score one of the greatest goals in the history of the sport?
The trick was in the spider…
Carlos placed his kick in the bottom right corner of the ball, sending the ball high and to the right, but also spinning on its axis. The ball started its flight in a direct route, with air flowing on both sides and slowing it down. On the one hand, the air moved in the opposite direction of the ball’s spin — creating more pressure, while on the other, the air moved in the same direction as the spin, creating an area of lower pressure. The difference between the pressures caused the ball to curve to the lower pressure zone.
The sweeter you hit it, the more swerve you get, and Roberto Carlos caught it just right. The way it worked, it was perfection. The free kick, the study says, left the Fabien Barthez – France goalkeeper in hopeless despair and bewilderment as the ball bounced back from yards outside his left post.
One of the most famous free kick studies was conducted by four French scientists — Guillaume Dupeux, Anne Le Goff, David Quere and Christophe Clanet — and published in the New Journal of Physics in September 2010. This from ESPN: In this study, the physicists conduct a series of experiments and analyzes that Result in an equation that explains the trajectory of the ball and all the forces in action at the time.
“The case of football, where ℒ is twice as small as L, is worth mentioning. The trajectory of the ball can deviate significantly from a circle, provided the shot is long enough. Then the trajectory becomes surprising and somehow unpredictable for a keeper,” they wrote.
“This is how we interpret the target. This free kick was shot from a distance of about 35 meters, ie comparable to the distance for which we expect such an unexpected trajectory. Provided the shot is powerful enough, another hallmark of Roberto Carlos’ abilities, the trajectory of the ball boldly bends towards the net, with a speed still great enough to surprise the keeper.”
Dupeux, Le Goff, Quere and Clanet concluded that if the correct calculations were made and the distances and forces repeated, the famous goal could be replicated by another player. But Brazilian physicist Luis Fernando Fontanari of the Sao Roberto Carlos Physics Institute disputed this, calling Roberto Carlos’ masterpiece a “football marvel.”
“Although physics explains the trajectory of the ball perfectly, the conditions at the time, such as the force of the kick, the point of impact of Roberto Carlos’ foot on the ball and the distance to the goal, were so rare that we can mention that’s a miracle,” he claimed.
Many fine free kicks have been scored since that unparalleled moment in 1997, but none, including Beckham’s, have come close to Carlos’ masterpiece.
The above views are those of the author.
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