The resumption of the European Rugby Cup is a reminder that the English and Irish teams excel in the art of up-and-under in English, or “chandelle”, in French. It is a kicking shot forward and very high in order to allow the same player, on his pitch, to recover the ball when it falls, before the opponent. But how can you put all the chances on your side to succeed?
A team from the Ecole Polytechnique, associated with the Racing 92 club, presented the first answers during the third Physics of Sport congress, at ENS Lyon, on December 6.
The recipe depends mainly on the angle of fire. Below 70 degrees, there is little hope that the shooter will be able to retrieve his ball within the approximately four seconds of flight of the ball. Beyond this angle, the chances increase, provided that one is more skillful than the opponent, who also waits for the ball – a circumstance not taken into account by the researchers. Obviously, the higher the speed, the longer the distance to be covered, but the fewer defenders there are, which is a rather favorable situation. For example, for 70 degrees, the reception is around 15 meters after the point of a shot at 20 meters per second, but beyond 30 meters for a shot two and a half times faster.
No parabolic trajectory
The result, which is being compared with field data, was obtained by looking for the crossing conditions of two curves: that of the ball in the air and that of the player. In a first article, in 2014, the team had already shown that the flight of the ball is not parabolic, unlike that of a pétanque ball, but that its descent is more abrupt because of the friction of the air. . An equation, taking this drag into account, thus describes the trajectory to the ground.
For speed, the researchers used the commonly accepted hypothesis that it follows a law of growth over time, until it reaches a maximum. This makes it possible to calculate the distance traveled over time and to know in which zone the player will not have time to go according to the initial conditions of the throw (speed and angle of fire). The method also works for other shots, such as the one sent to a laterally shifted player.
But in rugby nothing is easy. As the ball is not round and players generally hit its point for a candle, it spins on itself, which changes its trajectory and generally causes it to go less far. Such a flight would drop the ball 5 meters before the point planned for a non-rotating trajectory 20 meters long for example.
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