Originally Posted by travlerajm
For someone who is so interested in equations, I'm not sure why you continue to argue against a concept based on Physics 101:
Your arm behaves very much as a physical pendulum. And so does the racquet. And yes, using the assumption that MgR/I = 21.0 to estimate the gravity contribution to the velocity of the hand at the bottom of the swing (from potential energy of the arm), you get about 3m/s. Since a typical high level forehand has forward racquet velocity of about 20m/s, gravity contributes about 15% of the forward racquet velocity of a forehand.
But that is not the point. The point is that, over the first half of the stroke (from top of backswing to the bottom of the swing), if your wrist is relaxed, almost 100% of the racquet's angular acceleration comes from the gravity contribution, which depends on the MgR/I term. So in the absence of any adjustment from the wrist muscles, the angle of the racquetface at the moment you start to apply force to further accelerate the racquet is almost entirely dependent on the MgR/I term.
The point is that tuning the racquet's natural swing frequency to match the natural swing frequency of the arm will significantly improve control. by ensuring that your racquetface naturally stays perpendicular to your target as it passes through the hitting zone.
Also, I point out again that g value can indeed vary by as much as 0.3%, depending on your location on the globe, even for two cities both at sea level. This can make a difference in MgR/I of up to 0.06, enough to throw off your timing if your racquet is perfectly tuned (as I like mine to be). I'm currently building a customized frame identical to my own racquet for a friend I met through TTW who lives in Singapore that tried my frame when he visited in Seattle. The g value in Singapore is only 9.78, so I will need to adjust for that.
I have said several times that my main complain is that MgR/I is the frequency of a single freely swinging pendulum and nothing, I repeat nothing, more. Now you tell me "you see it is a pendulum"!!!!!! Yes, it is the frequency of a pendulum, if you hold the racquet at the but end between your thumb and forefinger MgR/I=21 means that it will swing with 0.73 Hz. But only if the swings are small and you don't move your hand.
I repeatedly ask for some kind proof that you can apply this formula everywhere like you do, and you reply by telling me to take the physics 101! After a number of years of research and teaching at the post doc level, including helping several student to their PhD:s in mechanical engineering, I think I know my physics 101.
You have obviously seen Rod Cross writings about the double pendulum (I recognize some of the statements, even if you write as if they were your own findings). You probaly saw the word "pendulum" and then you found a formula somewhere on the net that also said "pendulum" and used that without understanding what you did.
Rod Cross model includes some radical simplifications, like one that you don't use your wrist, and should be used carefully. But since you re so attached to it lets assume that it is a perfect description. Then behavior of the racquet involves solving eq A10a and A10b in A double pendulum model of tennis strokes
. And I can assure you that the result won't be MgR/I.
As to your hilarious statement that you need to take the variation in gravity into account. The air resistance of the racquet has a much greater influence than the gravity, shouldn't you include the air pressure and temperature as well?
There are a lot of helpful people at this forum and if you had chosen so you could have received help from them (me included) and maybe made this into something useful where you know how and when to apply it. Instead you have the attitude that you know it all and can apply it everywhere, even when it obvious that you don't have a clue what you are talking about. Pity.
Since you not are interested in any feedback except praise of your great finding I won't bother you with comments any more.
Ph.D. (Aerospace Eng.), M.Sc. (Eng. Physics)