DISCLAIMER;
I do not mean to belittle or insult anyone in anything I ever say. Should you find this proceeding example unnesessary, that is fine. I post this in hopes that SOMEONE reading this thread will benefit! Thank you.
Get a soda can, a paper, a pencil, and some string. Wrap the paper around the can (Any cylinder will do, really) and draw a line with the pencil straight up and down the can (Line A). Now, draw a line starting from the same point going up again, but as you go up TURN the can (Line B) and be sure that your pencil is going straight up as the can turns. Get a string and measure the two lines. Line B will be longer.
Assume that both lines are drawn at the same speed in terms of going "up" the can. The only difference between the two, then, would be that one line is drawn straight up while the other is drawn as the can turns. Line A would reference a straight up swing, while Line B would represent pronation. Now, lets work with the formula Acceleration = Distance traveled/Time taken. As said before, the time taken for both lines to be drawn was the same, however Line B was longer than Line A; therefore Line B has more acceleration. We will now refer to the "lines" as "swingpaths".
Now, let us apply this to the formula Force = Mass x Acceleration to the tennis serve. Mass will be the same for both serves A and B (since your arm and racket do not magically adjust) , however as stated before the acceleration is higher on swingpath B and therefore Serve B will inheirently have more force.
Things to consider
As you have already stated, pronation itself is a result of a good swing. In otherwords, simply swinging up with your racket (Line A) is NOT a good swing! I oftentimes find that people who consciously attempt to pronate through their serves also tend to "arm" their balls. I feel this is a result of people not understanding how large a role their bodies really do play. While the swing is obviously important, I feel that proper rotation of the shoulders/hips, drive of the legs, and a number of other things to be equally important. For example, if one were unable to rotate his shoulders, he would not be able to swing properly! Understanding what the arm itself does is fine, but it is also important to understand the rest of the body.
About your thoughts on the wrist snap:
This is a tough one, in my opinion. I personally am in the camp that you do not need to purposely think about snapping the wrist. I feel that if the toss is in the correct position, and the correct swing is used, the "wrist snap" should happen naturally.
I understand your point where should your forearm continue at a constant speed, your wrist would be "dragged" behind the forearm itself slows down, allowing the wrist which is moving at a higher speed to "snap out", much like a pendulum motion. However, given the fact that our arms are not perfectly straight , I prefer to think of it more of a whip. The same principle applies to a whip (The tip will not "snap" out until the handle goes in another direction), however this only applies if we are talking in one direction. For example, whips are often "waved" (I don't know the proper term) in two opposite directions (but on the same plane). A simple way to show this would be to take a string and go up and down, and watch the tip.
The serve, however, has several different directions going on. In a previous thread, you discussed the racket drop and how it effects the serve. As the racket begins to drop, however, our bodies are begining to rotate and push up with our legs. This gets our swing going, however our arm does not need to slow down right before contact because the "handle" of our serve is not our shoulder, but our torso. As the body is being propelled up, and our shoulders rotating, that would be the "initial" action (Much akin to say, lifting up a string). The reason why we do not have to decelerate our arm is because our body stops moving once our shoulders have opened up and our feet off the ground, we hit a point where our bodies are no longer accelerating and we are coming down into the court. That action would be the "second" action (quickly bringing the string down). The whip involved here is the up-down motion of bodies. The core muscles act more like bending a plastic ruler, and then letting it go. The result is the majority of the energy used to pull the ruler back propels it forward as well. The shoulder rotation adds another dimension.
Conclusions
I feel that pronation is, as you said, a result of a good swing, but that you do not need to consciously think about snapping your wrist. My basis for this is that pronation is the most efficient way of increasing acceleration, and that same efficient swing also lends hand to a natural wrist snap, like the end of a whip.
I would love to discuss this further with you and the other members of the board. Again, I do not mean to insult anyone or try and "prove them wrong". I am not here to "be the bigger man", but to discuss and learn more about tennis.
