The physics behind Danilo Gallinari’s amazing behind the back pass

It was declared on Sunday afternoon by Yahoo! Sports to be "the fastest behind-the-back pass we've seen in a while" but for Denver Nuggets forward Danilo Gallinari, the play was more than just a highlight reel. It was a feat of physics. The moment came with 2:46 left in the Nuggets 98-91 win over the Boston Celtics on Saturday night as Gallinari controlled a cross court outlet pass, somehow he kept his body inbounds and then, moments later, fired the back pass to teammate Kenneth Faried for a layup. Dr. Jon Eric Goff, Associate Professor of Physics at Lynchburg College sees the play as more than two points in a Nuggets win. He sees the angles that made the two points very special and unique. "My best estimate is that Gallinari is halfway between the line joining the two baskets and the 94 feet-long out-of-bounds line. Given that the width of the court is 47 feet that would put Gallinari 12.5 feet from Faried's catch location," Dr. Goff said. "Gallinari moved about two feet during the roughly .45 seconds the ball was in flight. That means the ball was thrown at a speed of roughly 27.8 feet per second, which is about 19 miles per hour. The forward part of the velocity is about 4.4 feet per second, which is around three miles per hour. The ball's net velocity is thus about 28.1 feet per second or 19.2 miles per hour." Dr. Goff, who also authored the book Gold Medal Physics: The Science of Sports, said that the most astonishing part of the play wasn't just how the ball was delivered but how it ended up in Faried's hand. The quality of the pass is not to be outdone by the fact that Gallinari served it up behind his back. "Freeze the video at the 10 second mark. The ball appears in the still frame between Gallinari and Faried. There are two velocities at play when analyzing the pass. At the time Gallinari let go of the ball, he is moving away from the baseline — he is perpendicular to the base line. His hand imparted a velocity to the ball that is parallel to the base line; that velocity is much larger than the other velocity," Dr. Goff said. "The ball's velocity as seen by someone in the stands is the vector sum of the two aforementioned velocities. In other words, the ball's velocity has a component that is along the base line and another component that is perpendicular and away from the baseline. What makes the pass perfect is that little bit of velocity that is perpendicular to the base line. Not only is Faried getting the ball fed to him from the side, there is a small component of the ball's velocity that is actually toward Faried, away from the baseline. A perfect pass!" Perhaps as impressive as the no-look assist was Gallinari's body control when he caught the long pass at the start of the fast break. He expertly controlled the ball as he kept his right leg in bounds, which allowed his body to stay upright and maintain composure to resume his dribble. "The ball is in his right hand while his left arm is extended in the direction of the base line. His right leg is off the court so as to not step out of bounds," Dr. Goff said. Gallinari's body is in what Dr. Goff calls a "V shape" with the opening of the V in the direction of the base line. This is necessary because the friction from the ground on his shoe halted his motion and kept him from going out of bounds "He needs his center of gravity to the right of his foot. There is thus a gravitational torque that tries to rotate Gallinari clockwise. The two torques essentially cancel, which keeps Gallo stable as his moves along the baseline." Published on Yahoo! Sports NBA Ball don't lie on 22th March 2012.