25 June 2014

Messi's Incredible Free Kick

No matter how many times I've seen Lionel Messi play the beautiful game, I always see something special each time.  To end the first half against Nigeria today, Messi delivered a perfect free kick.  It was his second goal of the game and fourth of this World Cup.  The image below shows one view of the initial setup (click on the image for a larger view).
Messi is just about to connect.  He is about 27 yards (24.7 meters) perpendicular distance from the goal line.  The image below shows a good look at the defensive wall (click on the image for a larger view).
Messi launched the ball off his left boot with a speed of 55.4 mph (89.1 kph) and launch angle of 18.5 degrees.  Note that the Nigerian goal keeper is left of center in the goal (as seen by Messi).  The goal keeper's initial position was critical because Messi imparted a great deal of clockwise spin (as seen from above) on the ball.  His target was well away from the goal keeper!  The image below shows Messi introducing his left boot to Brazuca (click on the image for a larger view).
Note how his foot is left of center on the ball so that he can drive his boot through, thereby torquing the ball.  Note, too, the lean in his legs.  He has moved his rotation radius so as to increase his boot's distance from that axis.  The pitch provides the counter-torque to keep Messi stable because his right boot pushes to his left, which means the pitch pushes on his boot to his right.  The torque from the pitch nearly balances the torque from his weight; balance is further aided by his arm movements.

It took the ball just 1.2 seconds to reach its target.  The image below shows a three-dimensional trajectory (click on the image for a larger view).
The red curve is the real trajectory; the red dashed curve is the shadow on the pitch.  The thin black curve is what the kick would have looked like with no spin and no knuckling (black dashed curve is the shadow of that kick).  Now you see why the kick was perfect!  Messi used the Magnus effect to curl the ball into the upper-right portion of the goal.

The ball crossed the goal plane at 42.0 mph (67.6 kph).  Had the ball not been spinning, it would have crossed the goal plane about 10.8 feet (3.28 meters) left of where it actually crossed the goal plane.  The goal keeper would have surely blocked the kick.

Once again, Messi has dazzled the soccer world!

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