Underhand
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The underhand serve is the most basic
serve in volleyball. Typically used only by new, young, or recreational
players, the underhand serve has less speed, and creates a steep parabolic
path. However, it is the easiest of all the serves.
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Image located at http://www.sook.org/images/Volleyball%202%20low%20res.jpg
The Laws of Physics give us some equations that model projectile motion. Projectile motion is always parabolic (in the presence of gravity). Also we know that the initial velocity (Vi) will exactly equal the final velocity (Vf) from two points of the same height H. Simply stated that means as fast as you hit it up, that's how fast it's coming down.
One of our goals in serving is to have it come down hard and fast; we achieve this by serving the ball really hard. However if we hit it too hard it will go out of bounds. And if we have too high of an angle theta, then the other team will have too much time to prepare for the serve (or the ball will hit the ceiling).
As far as real numbers go, for an underhand serve a launch angle of about 40-50 degrees is optimum. Experimenting with different velocities can give different results, but the ball should always just be barely clearing the net to gain the most speed from the serve.
Serves