Originally Posted by SystemicAnomaly
Close, but not quite.
A serve whose spin is primarily side-spin (vertical-axis), will not normally kick. As psv255 and I have indicated, a kick serve normally requires a significant topspin component. Vertical-axis sidespin will only affect the left/right deviation of the ball traveling thru the air (Magnus Effect). This type of spin has no direct effect on the bounce (direction or height). Physicist, Rod Cross, had indicated this in some of his writings on tennis physics.
However, it you lob the serve with an open racket face with sidespin, it will bounce quite high even tho' it may not have very much topspin. This high bounce might be considered a kick by many.
A topspin serve or a topspin kick serve will usually also have a small amount of a sidespin component (just as most slice serves will have some degree of a topspin component). If your serve has sufficient components of both topspin and sidespin, we refer to it as a topspin-slice serve.
The "reverse bounce" seen in the twist version of the kick serve is due to spiral spin and not due to our garden-variety (vertical axis) sidespin. Think of the spin on the spiral pass of an American football or the natural spin on a badminton shuttle. This is spiral spin -- also known as spiralspin, gyrospin, corkscrew spin (or cork spin in table tennis). Its axis of rotation is more-or-less horizontal and in the direction of the flight path of the ball (or shuttle).
There is no Magnus effect associated with spiralspin so it has no effect on the trajectory of the ball as it flies thru the air. This is why spiral spin is often applied to bullets (with rifling of the barrel) and sometimes to arrows. However, when a ball with spiralspin hits the ground, it will bounce to the left or the right.
If the ball has mild spiraspin, then the left/right bounce deviation will be only slight. We might see this with a topspin-slice serve. If the spiralspin is negligible, then after the bounce, the ball will continue in the same direction is was traveling immediately prior to the bounce. If this serve has a moderate amount of spiralspin then we will see the ball direction straighten out with the bounce.
We might refer to a kick serve that does this as a twist serve -- cuz the ball is moving in a direction after the bounce that is somewhat different than the pre-bounce direction. It the amount of spiralspin is relatively generous on a topspin-slice kick serve, then the effect is very dramatic. The ball path curves in one direction (left or right) prior to the bounce due to (vertical-axis) sidespin. However, the ball bounces in the opposite direction due to the spiralspin component. This action is what we normally think of when we refer to a twist serve.
This corkscrew spin business is not easy to understand because you cannot picture it easily. Here is the best way to do so, IMO. Either imagine or put a tennis ball in front of you. There are 3 directions: x (left and right), y (forward and backwards) and z (upwards and down, aka into the air or through the table). Top spin is a pure positive y direction forwards spin, as in the ball will roll away from you. Backspin is the negative y direction, as in towards you. Side spin is a pure x direction spin, so either rolling to the left or the right. The corkscrew spins ABOUT the z-axis. It does not move in space, it simply sits where you puts it and spins. To picture that, imagine spinning the ball like a top. There's your z-axis or corkscrew spin.
Indeed, your analysis is correct. It's generating that extra component that causes the twist portion. It's how you generate it that causes all of the difficulty with this serve.