Ronaldo's Impulsive Backheel Goal!

If you missed Cristiano Ronaldo's backheel goal to beat Rayo Vallecano today, find it on YouTube. Real Madrid's superstar's goal in the 54th minute provided the only scoring in the match.  Almost 11 m (12 yards) from the goal, and nearly aligned with the right goal post, Ronaldo backheeled the ball, which sent it rolling toward the left portion of the goal.  The ball traveled about 12.3 m (13.5 yards) from Ronaldo's heel to the goal line.  It was an amazing demonstration of athletic ability and awareness on the pitch.


After picking up my jaw upon seeing Ronaldo's great goal, the first bit of physics that entered my mind was that of impulse.  In physics we define impulse in one of two ways.  It's the change in linear momentum (mass times velocity), which is the same as the net force times the collision time.  This all comes from Newton's second law, but the details are not so important right now.  We make use of this idea a lot in everyday life.  Usually, the change in linear momentum is something we cannot control.  Imagine driving in a car and having the misfortune to slam into a tree.  Multiply your mass by the change in your velocity and that's your change in linear momentum.  You can't change that because your car's speed goes from what it was before the collision to zero after the collision.  Fortunately, there is another way to write impulse, as I noted earlier, and that is force times collision time (there is an integral here, but just think average force when I write force).  If you can do something to extend the collision time, you can reduce the force needed to stop you while you are in contact with the tree.  You already know I'm referring to an air bag.  If it can increase the collision time by, say, a factor of ten, then the force on you goes down by a factor of ten.  It's better to hit the air bag than to hit the windshield, steering wheel, or dashboard.


You can think of many other examples.  If you jump from some elevation, you bend your knees upon hitting the ground so as to extend the collision time with the ground.  Pole vaulters prefer landing pads to the ground.  Long jumpers like the sand pit instead of hard ground.  You wear a padded glove while playing baseball, again so as to extend the collision time when you catch a baseball.  Padding in American football and boxing gloves are yet more examples of ways to extend collision times.


The concept of impulse also helps us get some idea of the size of the average force when a collision takes place.  The collision time between Ronaldo's boot and the football is nearly 0.010 s.  I estimate that the ball left his boot at a speed around 13 m/s (30 mph).  It was rolling at about 1 m/s (2.2 mph) in the opposite direction just before Ronaldo kicked it.  The magnitude of the balls' velocity change was therefore about 14 m/s (31 mph).  With a 440-gram (0.97 pounds) football and a collision time of 0.010 s, the average force on the ball from Ronaldo's boot was about 616 N (138 pounds).  That might seem like a large force, but that average force lasts only ten milliseconds.


Think about Newton's laws and note that the Second Law tells us that the ball was slowing down the entire time after it left Ronaldo's boot. The Third Law tells us that Ronaldo's boot felt the same force that the ball felt during the collision.  A little padding in the back of the boot helps extend the collision time between Ronaldo's heel and his boot.  Football players are more than comfortable kicking the ball a lot harder than Ronaldo did.  Of course, Ronaldo most certainly had no complaining from his heel after such a remarkable goal!