Reply from Certified Ball Control Coaches on acceleration:

We appreciate your analysis of this very subtle, and important, phenomenon, which was not addressed even by Isaac Newton, who was criticized by Robert Hooke of Hooke's Law, which describes the force produced by a spring, such as the tennis string.

When the string is indented, there is a spring force pushing the ball out. This spring force can be balanced by an applied acceleration or force. If a constant acceleration is applied before the contact, it will increase the speed of the racket (before contact) and indent the spring even more. The additional indentation of the spring will produce an additional force to push out the ball. The advantage here is there will be a slightly longer distance of contact. A constant acceleration produces just the minimum advantage in ball control.

A better stroke is to increase acceleration during the impact. Nothing personal, the rate of increase of acceleration is call jerk. When a jerk is applied through the impact, the force applied when the ball is indenting the string is less than the inward force due to acceleration when the ball is being pushed out of the string. This type of ball control is done by almost all the professional players, in not just tennis.

Occasionally, the world produces players who can apply jumpulse, a sudden increase of force, near the precise moment when the ball is leaving the string or even have already left the string slightly, but can still be caught up by the racket, AND can produce an extraordinary high acceleration. We are fortunate to witness the still developing Roger Federer in tennis ball control. Federer's muscles have been trained to apply jumpulse. His entire body participates in the stroke not as much to generate speed as to jointly add acceleration to the racket at the precise moment of impact. WEadmit, ball control stroke is very difficult involve a combination of many factors. To me, physical education is definitely more complex than physics. In theory and in a laboratory, a ball can be kept on a racket forever with a jumpulse.

Federer does not always hits the ball on the sweet spot, but his ball control will more than compensate for the miss hit or miss timing. The worst can happen is that the stroke degenerates into one of the above cased. In fact, he may purposely make off-center hits so that he can lift the ball from a low to a high position during the prolonged contact. The design of a good ball control stroke, or the application of prolonged contact, is another intriguing and complex problem. Federer does not only linearly, but also rotationally, follow through. The pronation probably can make the racket play an active, rather than passive, role during the impact. Anyway, it all seems to serve him well. We believe that with better understanding of the physics of ball control, he can improve even more. We really hate to see that someday he lose if because of a lack of understanding. He can make an important contribution to knowledge by empirically verify prolonged contact, which no robot can do, but all our Pee Wee students can do for soft shots or stationary balls.

Many professional player can hit a soft volley with long contact time or distance because only a low jerk or acceleration is needed for ball control when the impact velocity is low. Mainly for this reason, the regulation on double hitting was modified in the 1980s to allow double hitting when it is not done intentionally. We really hope that some camera technicians will slow down their slow motion even more near the moment of contact to observe the double hitting, which is a frequent consequence of ball control (the racket must decelerate at some point). With the understanding of ball control, USPTA coaches now can explain the correct reason for following through, as an indication that one has applied the maximum jumpulse, jerk, or acceleration which one possibly can. Many thanks for making us work. ###

Reply from Certified Ball Control Coaches on Timing of Acceleration:

Thank you for your very detailed description of your view on ball control and follow through. I am under the obligation to fulfill the will of my teacher the late Dr. Ta-You Wu (Father of Chinese Physics) to promote the solution to touch and ball control. Dr. Wu coined the word "jumpulse" to denote a sudden change of force, as impulse is a sudden change of momentum. I hope that you and the other readers will put up with the formal style of my explanations. Identifying the main reason for follow through separates Ball Control Tennis from the current tennis. Jumpulse also put all the physicists, including Newton, in a position to choose between accept or deny the solution of touch and ball control (be careful when you mention jumpulse to any physics professor). It appears, for example, from what you say that tennis players are way ahead of physicists and researcher in robotics. Your and other readers' contributions will be very important for knowledge. For that I thank you all.

Between feeling and expecting, ball control is done by expecting. The fast incoming ball becomes a blur within 5 feet from the hitter. Within 5 feet, the process goes into auto-pilot with expected adjustments. The reaction time is about 50 millisecond, while the interaction time (natural period) is less than 5 millisecond; there will not be enough time to react to the feeling. This conclusion is verified empirically by my Pee Wee students who have never see a ball coming to them. The initial formation of a mental picture of how a ball bounce and moving toward them is from being completely blind to the coming ball to very gradually, but still within the one hour class time, storing the image in their mind, and finally hitting the ball. The process of learning the mental image is quite an experience the first few time I observed it. Therefore, ball control requires, in addition to training acceleration muscle, the training in the precise mental images for ball control. Yes, this is difficult, needing a great deal of training in seeing an enormous large number of balls coming at you and in hitting them at the precise predetermined time. At all times, one should keep one's eyes on the ball, even more now that one can no longer see that ball during impact because one must know the exact initial condition before the ball becomes a blur at close range and then would let the trained mental image take over the movement of the body.

Practicing acceleration is described in the web site http://www.ballcontrol.net, for beginning students. For advanced players, one can hit against a wall and try to purposely double hit every stroke. Double hitting is a sign of accelerating and close enough timing. After one can double hit against a wall, which trains the acceleration muscle and precise timing, one can double hit against a ball machine or another steady player. The visible double hitting is just for the drill in ball control, not for the real games, where, nevertheless, double hitting is still present microscopically. After our initial publication of the discovery of ball control and the prediction of double hitting in ball control, the tennis regulation on double hitting was modified to allow it. But, today all the other sports still deny the presence of double hitting and physics.

Thank you for your collaboration in explaining ball control in real playing situations. ###