Originally Posted by kaiser
So you are saying that because of the many possible differences in body proportions between different players, the optimal configuration of a racket can vary considerably? That would make sense to me.
This leaves one crucial component in your theory I never understood. In your formula there is only one acceleration term, g, which in your posts you have related to a high take-back. Does this mean that the primary force acting on the racket in your model is gravity? In other words, that in your model the tennis stroke is treated as a dual pendulum consisting of racket and arm swung through an arc from the highest takeback position by the force of gravity alone?
Does your model account for the acceleration of the racket and arm due to the hip and shoulder turn? Why is there no term in your formula which expresses this acceleration?
When I first started trying to relate a tennis swing to physical parameters, I made some of the same misassumptions that most people make. I wrongly assumed that the swingweight is what determines how much effort goes into getting the racquet to "come around."
I eventually found that a much more accurate way to model a swing is to divide it into two distinct parts. The first part is the mostly gravity-powered part of the swing where the racquet goes from the top of the backswing to the bottom of the swing. The second part is the portion of the swing where the player adds force behind the racquet handle to accelerate the racquet forward and upward against gravity and through the hitting zone.
During the first part of the swing, the face of a the racquet naturally rotates toward the ball. If the racquet has a "tuned" MgR/I value, then no added torque from the wrist muscles is needed to ensure that the racquet is facing the target at the end of the this part of the swing. Since gravity is providing nearly all of the acceleration, the final angle of the racquetface at the end of this gravity-powered first portion of the swing is nearly entirely determined by the MgR/I value (assuming a relaxed wrist is used).
I believe that our brains sense the bottom of the swing as the cue to "switch on" the applied force that starts the acceleration through the hitting zone. However, without a tuned MgR/I value, you cannot use a relaxed wrist, and your arm will tend to wear out over the course of a match from exerting the wrist muscles on every shot.
Once the second part of the swing begins, most of the acceleration is applied by the player. As long as the racquet starts the hitting zone with the right racquetface angle, the player can easily vary the applied force to achieve different results on the ball. But if MgR/I is not tuned, then the second part of the swing will begin with the racquetface not quite at the right orientation, leading other adjustment forces from the wrist to be needed during the second part of the swing as well.