There’s no particular reason why a sports story should be included in the New Journal of Physics. Just browse the titles of papers presented in September’s issue:
-Electronic and geometric corrugation of periodically rippled, self-nanostructured grapheme epitaxially grown on Rui(0001);
– Total and positronium formation cross sections for positron scattering from H2O and HCOOH;
-Interplay between excitation kinetics and reaction-center dynamics in purple bacteria;
and our favourite:
-Broadband nano-focusing of light using kissing nanowires
Nothing here even remotely related to sports. Some sexy science, perhaps, but not sports.
Yet within this high-brow jargon is something we might understand. The ‘Spinning ball spiral’ is a research paper conducted on Roberto Carlos, the Brazilian left back footballer whose 1997 free-kick against France was described by pundits to have defied physics, so sharp a curve it took. The research in this month’s New Journal of Physics may have proved once and for all that the long-held assumption that one of football’s most spectacular goals was a fantastic fluke is wrong.
A French team of scientists discovered the trajectory of the goal and developed an equation to describe it. The journal’s abstract says:
"We discuss the trajectory of a fast revolving solid ball moving in a fluid of comparable density. As the ball slows down owing to drag, its trajectory follows an exponential spiral as long as the rotation speed remains constant: at the characteristic distance where the ball speed is significantly affected by the drag, the bending of the trajectory increases, surprisingly. Later, the rotation speed decreases, which makes the ball follow a second kind of spiral."
We said we "might" understand. We believe that when translated into English, the physicists were trying to say that Carlos’ shot could be repeated if a ball was kicked hard enough, with the appropriate spin and, crucially, the kick was taken sufficiently far from goal.
For those who never saw the goal, on June 3 1997 during the inaugural match of the Tournoi de France, a friendly international football tournament that was held in France ahead of the 1998 World Cup, Carlos took a left-foot free kick that was 35 metres from goal. The ball, in the center of the field, had to swerve around a wall of three defenders, curve a bit more to evade another Frenchman, before hitting the left post and dropping in, leaving goalkeeper Fabian Barthez stranded.
A camera angle taken behind Carlos shows that when he shot, the ball was initially way off target and looked going out by a country mile but suddenly, half-way though its trip, the ball veered back on course as if a strong gust of wind had pushed it back on target. It was a stunner which 13 years on has yet to be replicated.
But actually a similar if not better dead ball wonder strike was scored before, 24 years earlier. It zoomed off the boots of another Brazilian, Edu, who, too, was a left back. The site, though, was Cairo Stadium, the teams were Santos of Brazil and Egypt’s Ahly and the encounter was a friendly played in early 1973.
Though Santos won 5-0 and two of the goals were scored by the incomparable Pele, it was the first goal, the one scored by Edu, which lives in memory. The ball was sitting sharply to the left of goal, seven metres outside the penalty box. When Edu connected, like that of Carlos, the ball at first appeared it would sail into the stands. But it defied gravity as well as logic, dropping when it should have continued onwards, taking the wickedest of curves before – would you believe it? – it sort of slowed down, even braked, then resumed velocity before landing squarely in the uppermost left of goal. Goalkeeper Essam Abdel-Moneim, now a renowned sports columnist and TV football analyst, could only watch askance.
What made the goal all the more stunning was how it was shot – with the left foot, when the right would have been the more conventional.
If you think we’re making this up, just ask anyone of the 120,000 spectators who was in the stadium that day, including the writer, and the millions who saw it on TV. A long search on the web could not dig the goal up but it is in the archives of Egyptian TV.
For many years thereon, the match was replayed loads of times but with the plethora of games at home and abroad that now need to be covered, reruns have all but disappeared.
Pity because Edu’s goal was truly spectacular, on a par with that of Carlos and perhaps even more difficult. But Edu’s piece of art and science is not nearly as well known as the Carlos marvel, even though it is worthy enough to bestow upon it some nanophysics.