where K is the restoring force of the strings (Force/displacement) and X is the displacement of the string. However, this does not consider the real life situation of elastic limits.

Looser strings return more energy to the ball. This finding goes against what I might have naively guessed without considering ball deformation, but that is what experimental science is all about. Looser means small K and for a given impact force will result in more displacement and more time in contact with the strings.

The reason for looser strings is because the tennis ball deforms tremendously under extreme force. The ball returns a lot of the energy involved in its deformation upto a point. If the ball is deformed too much the energy return begins to lessen to the extreme of the ball breaking under the stress. Of course, there is a limit as Brody says, "...clearly a butterfly net is unacceptable."

Brody's conclusion was that the "sweet spot" defined as the region of greatest power returned to the ball lies between the throat of the rakcet and the center of the strings. A good ground stroke player will hit the ball somewhere between the throat and the center much of the time after having learned this by experimentation. Less effort is required to hit a true strike at the "sweet spot" which will result in less fatigue and more success on the court. The advantage of modern rackets is that the "sweet spot" has been enlarged to make the chance of hitting a ball in the "sweet spot" more likely.

Typically the ball is in contact with the strings for about 5 milliseconds. A fair amount of spin can be imparted to the ball because of the contact time with the strings and the compression of a tennis ball when struck with significant force. This can result in the really cool "top spin lob" in which the ball falls sort of the simple projectile model predicted distance. It can also result in a wicked slice or hook on a serve.

The extreme example of racket and ball interaction is in ping pong where the grab of the racket combined with a sideways motion of the paddle at time of contact can create all sorts of curve on the ball's path.

A ball hit closer to the frame of the racket (where the strings attach) will have less energy return and will tend to fly in a less predictable direction. This is because the racket will twist in the player's handand the restoring forc e of the strings will have a component toward the middle of the racket.

I have played tennis many times and I have always preferred a racket with more tension because it requires a little less effort on my part to hit a return in a predictable fashion. This real life observation was found to be true. Basically, the resistance by the strings to distortion does not provide as much power to the ball, but it limits the effect of hitting off center.

A faster serve is generated by strike between the center of the strings and the tip of the racket.

This just makes good physical sense. When serving in a typical windmill fashion, the point farthest from the server's shoulder is moving the fastest and typically a good serve has the element of speed. During ground stroke play the key to success is reaction and location and speed is usually of secondary importance.

I hope this answers can guide you in further thinking about the interaction of the tennis ball and racket. Sincerely,

Tom "Barred from Wimbeldon" Cull