Shakehand Beats Penhold in Table Tennis!

My pre-Olympics pick for the gold in the men's singles table tennis event was Wang Hao of China.  My pick fell short today as fellow countryman Zhang Jike defeated Wang in the final match, four games to one.  The final point came as Zhang smashed Wang's serve back into Wang, who was to the left side of the table, and Wang miss-hit the ball up into the air.  That the gold-medal point went to Wang's left is significant, as I'll return to in a moment.  Zhang becomes the fourth table-tennis player to win the Olympic gold, World Championships, and World Cup, something Wang would've done had he defeated Zhang today.


Okay, so what's so special about Wang's left side?  Wang uses a penhold grip (we in the US might call this an "upside down" grip) whereas Zhang employs a shakehand grip.  As someone who uses a penhold grip himself, though infinitely less skilled than Wang Hao, I picked Wang for gold.  Some have criticized those who use penhold grips because of weakness on the backhand side.  What intrigued me about Wang's approach is that he uses both sides of his racquet (my racquet has only one playing surface).  Penhold-grip users are capable of imparting enormous amounts of spin with their forehand shots.  Lots of friction between the ball and the racquet's spongy surface generates large torque on the ball, which creates significant angular acceleration to cause the ball to leave the racquet with enormous spin.  The blue forehand side of Wang's racquet is more spongy and tackier than the red-colored backhand side.  Because he is more comfortable hitting with his forehand, Wang uses a backhand surface that gives him more control due to the inability of the surface to create as much spin as the forehand side.  But, alas, today was a day for the shakehand users as Zhang earned his well-deserved gold with a dominating performance.


Table tennis balls have a mass of only 2.7 grams (about 0.095 ounces in weight).  Because they are so light, air forces greatly influence the ball's trajectory.  Consider a forehand smash that imparts topspin to the ball.  Typical values for initial speed and spin are 20 m/s (45 mph) and 120 rev/s (7200 rpm), respectively.  I plot below the aerodynamic forces on just such a smashed ball as it travels a horizontal length of the table, which is 2.74 m (9 feet) long.  Click on the graph below for a larger image (so that everyone's happy with game labels, I label my graph with the term "ping pong" for table tennis).

By the time the ball has moved 2.74 m in horizontal distance, its speed has been reduced to 14 m/s (32 mph), a reduction of 30%.  The terminal speed for a table tennis ball is approximately 8.8 m/s (20 mph), meaning the ball speeds players witness are often well past terminal speed.  Note in the above graph that the initial drag force is just over five times the ball's weight.  Imagine having wind hit you with a force five times your own weight!  The Magnus force on the ball, due to its spin, is initially more than twice the ball's weight.  The Magnus force has a downward component for a ball with topspin, like a curveball in baseball, which means that the air pushes the ball down.  By the way, the buoyant force on the ball due to the ball displacing air is only about 1.5% of the ball's weight.  When the ball reaches the opposite side of the table, the topspin causes the ball to accelerate off the table due to the friction force between ball and table.  Good luck if you ever face a topspin from the likes of Zhang or Wang!  Oh, and don't forget that the ball takes only one-sixth of a second to traverse a horizontal distance equal to the table's length.  How are your reflexes?  It is easy to see why players often stand a good bit back from the table when smashes are going back and forth.

The next time you play table tennis and put lots of spin on the ball, note carefully how the ball moves.  Lots of wonderful physics in that motion!