PARIS — Thirteen years after Roberto Carlos stunned onlookers with his amazing "banana" free kick that seemed to defy the law of physics, scientists have finally worked out just how he did it.

In what many people regard as the best free kick ever, the Brazil defender struck the ball with the outside of his left foot 35 yards out, bending it around the outside of France's three-man wall during a friendly tournament in Lyon in 1997.

The ball looked way off target to the right -- a ball boy standing 10 yards from the goal even ducked his head -- but at the last moment, it swerved dramatically inside the post and into the net. The bewildered France goalkeeper, Fabien Barthez, had not even moved.

Many people thought the shot was a fluke, but researchers say it can all be explained by science.

"What happened that day was so special," researcher David Quere told The Associated Press. "We are confronted with an unexpected law of physics, but it's possible to see this again."

Quere, a physicist at the ESPCI and Ecole Polytechnique in Paris, and his colleagues have developed an equation to explain the bizarre trajectory of the shot. Using a small pistol to fire bullets into water at the speed of 100 km/h -- approximately the speed of Roberto Carlos' shot -- they discovered that the path of a sphere when it spins is actually a spiral.

Quere said the study, which has been published in the New Journal of Physics, confirmed the "Magnus effect" -- which is responsible for the curved motion of a spinning ball -- but it also revealed what the scientists call the "spinning ball spiral."

The spiral effect appears after about 40 yards with a soccer ball. As the ball slows down, the "Magnus effect" becomes more and more pronounced, which eventually creates a spiral.

"The crucial thing is that while the ball is slowing down, the rotation is the same," Quere said. "Hence the trajectory of the ball is going to be more and more bent, that is what creates the spiral.

"When Michel Platini or David Beckham were kicking free kicks from 20 metres, they were bending the ball in an arc. It's not the same thing with Roberto Carlos' goal. He can have this kind of effect because he kicks from long range.

"Another player could repeat it -- on the condition that the ball is kicked hard enough, that the kick is taken from about 40 metres and that the player gives some effect to the ball."

Roberto Carlos claimed at the time he had done it before -- against Roma while playing for Inter Milan -- although he never quite managed to repeat his 1997 trick.

"It's difficult to say whether it was a lucky goal," Quere said. "There is something close to perfection in this trajectory that let me think that Roberto Carlos has probably always taken these kinds of free kicks from long range, and he should have realized that he could take advantage of it."

Barthez said after conceding the goal that he didn't set his wall correctly, but Quere said the goalkeeper probably just thought Roberto Carlos had fluffed his shot.

"Barthez was a very good keeper, at the peak of his art," Quere said. "But the trajectory was eccentric and he didn't move."