Roberto Carlos' free kick: The physics behind 'impossible' strike, 20 years on
Twenty years ago, Roberto Carlos impressed the world with one of the most spectacular free kicks in football history.
On June 3, 1997, the former left-back scored the most famous goal of his career: a beautiful free kick for Brazil in a 1-1 tie against France in the opening game of the 1997 Tournoi de France.
The kick left goalkeeper Fabien Barthez perplexed, as the ball apparently was headed to the corner flag. However, it curved back, glanced the edge of the post, and stopped only when it hit the net.
Two decades later, Roberto Carlos says he is still impressed when he sees footage of his kick.
"To be honest, until this day I don't know how I did that," he jokes, in an exclusive interview with ESPN Brasil.
"It was a beautiful goal. It required a lot of training and hard work throughout my career. But that hard work paid off, as I was able to score such a wonderful goal, which was a special moment for me."
When he scored that famous goal, the left-back was just starting his career. He was in his second season for Real Madrid, and came to Spain after a short term at Inter Milan, who bought the young player from Brazilian champions Palmeiras for $8 million -- a fortune in 1995.
In Madrid, he would win title after title, becoming an idol and a legend; his is still an international ambassador for los Merengues. While his star rose in the Spanish capital, he became Brazil's starting left-back in the 1998, 2002 and 2006 World Cups. He won in South Korea/Japan in 2002 having been a runner-up in France four years earlier.
Roberto Carlos continued playing until 2015, when he retired after a short stint with Delhi Dynamos of the Indian Super League.
Throughout the 18 years that passed between his famous free kick against France and his retirement, Roberto Carlos never tried to strike the ball in the same way, as he knew it was practically impossible to repeat such perfection.
"I never tried to kick like that again, because I know I would never have scored," he says with a laugh.
"There are lots of good kickers nowadays. It might take some time, but someday someone will score a similar goal. But I was the first."
Science, however, is not so sure that such a goal will be repeated...
The impossible kick?
Roberto Carlos' goal in 1997 defied physics and still impresses scientists today.
When the famous free kick happened, physicists from all around the world were baffled by the images. That goal was the catalyst for lots of studies and analysis about aerodynamics and the ball's curve that day at the Stade de Gerland in Lyon.
One of the most famous 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.
In this study, the physicists conduct a series of experiments and analyses, which result in an equation that explains the ball's trajectory and all the forces that were in action at that precise moment.
"The case of soccer, where ℒ is twice as small as L, is worth commenting on. The ball trajectory can deviate significantly from a circle, provided that the shot is long enough. Then the trajectory becomes surprising and somehow unpredictable for a goalkeeper," they wrote.
"This is the way we interpret a famous goal by the Brazilian player Roberto Carlos against France in 1997. This free kick was shot from a distance of approximately 35 metres, that is, comparable to the distance for which we expect this kind of unexpected trajectory. Provided that the shot is powerful enough, another characteristic of Roberto Carlos' abilities, the ball trajectory brutally bends towards the net, at a velocity still large enough to surprise the keeper."
Dupeux, Le Goff, Quere and Clanet conclude that if the correct calculations were made, and the distances and forces were repeated, the famous goal could be replicated by another player.
This, however, is impossible, in the opinion of one of Brazil's most important physicists. He describes Roberto Carlos' masterpiece as a "football miracle".
"Although physics explain perfectly the ball's trajectory, the conditions in that moment, such as the power 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 call that a miracle," says professor Luis Fernando Fontanari of Sao Roberto Carlos Physics Institute, a branch of the University of Sao Paulo -- the most respected university in the country.
Fontanari is one of the editors of "Physics of Life Reviews" and "Theory in Biosciences," two of the most important scientific journals in the world. He adds that, if the ball hadn't stopped in the net, it would have continued in the air, drawing an incredible spiral trajectory, as the image above shows.
"I don't believe that we will see something like that happening again," Fontanari says.
Israeli scientist Erez Garty also theorised about Roberto Carlos' kick. In a YouTube video, he gave a lesson for "physics dummies," which explains the magic.
What was the Tournoi de France?
The FIFA Confederations Cup didn't become a "test event" for the World Cup until 2001, when it was played in South Korea and Japan. So in 1997 France decided to organise a friendly tournament to test the country's preparation for the 1998 World Cup.
The French Football Federation invited Brazil, England and Italy for the short tournament, which consisted of six matches. The venues were Stade de la Beaujoire in Nantes, Stade de la Mosson in Montpellier, Stade de Gerland in Lyon and Parc des Princes in Paris.
Brazil, then managed by the legendary Mario Zagallo, had one of the best attacks in the world: "Ro-Ro" (Ronaldo and Romario). The starting XI was made up of Claudio Taffarel; Cafu, Celio Silva, Aldair, Roberto Carlos; Mauro Silva, Dunga, Giovanni, Leonardo; Ronaldo and Romario. On the bench was Djalminha, Denilson, Paulo Nunes and Ze Roberto.
The Selecao started the Tournoi by drawing 1-1 with France -- the match in which Roberto Carlos scored the screamer.
After that, another draw, 3-3 with Italy, in a great match. Romario, Ronaldo and an Attilio Lombardo own goal accounted for Brazil's tally, and an Alessandro Del Piero brace and an Aldair own goal for the Azzurri.
Brazil's last match was a 1-0 victory against England, with another Romario goal. In the end, however, the Selecao scored only five points and ended up as runners-up, as England, with the likes of Alan Shearer, Paul Scholes and the young David Beckham, defeated France and Italy, earning six points and winning the Tournoi de France.
The competition would end up building Zagallo's squad for the 1998 World Cup, when the manager lined up Taffarel, Cafu, Aldair, Junior Baiano, Roberto Carlos, Cesar Sampaio, Dunga, Rivaldo, Leonardo, Bebeto and Ronaldo.
Romario was left out shortly before the World Cup, with an unfortunate injury.
This article was translated for ESPN FC by Francisco De Laurentiis of ESPN Brasil.