I believe that the term 'spiral spin' is referenced to the ball's trajectory. Since the direction of the trajectory changes because of gravity and the Magnus effects of the air on the spinning ball, it is difficult to know how the 'spiral spin' changes as the ball moves forward. I believe that it is much simpler to not use 'spiral spin' in analysis. Then, a much simpler picture emerges to explain the sideways bounce. I have used 'spiral spin' loosely and incorrectly in the past. I believe that it was Travlerajm that recently pointed this out.
The most instructive publication that I have found on the spin vectors of the kick, slice and flat serves is
PDF | The purpose of this study was to describe three-dimensional ball kinematics including spin axis and spin rate for the flat, slice, and kick serves... | Find, read and cite all the research you need on ResearchGate
www.researchgate.net
The display of ball spin vectors is very informative. They used a coordinate system based on the tennis court lines and the vertical (Z Upward). That coordinate system does not change regardless of what the ball does on its trajectory.
This shows the ball right after impact. The length of each arrow is proportional to the spin rate, in RPM or revolutions/second. The direction of each spin vector is given by the components in the X, Y and Z directions.
Ball Spin Direction Change Along Trajectory. Next, I assume that the direction of the ball's spin vector does not change as the ball travels across the court to the bounce. Justification - I believe that I have read Rod Cross state this. Also, I can often see print on the ball spin up to three revolutions and it appears by eye that the direction of the spin axis is not changing. This issue could easily be proved by simply having a high speed video camera view the ball after impact and another camera view the ball right before bounce. You may consider it a true or false, to be determined, if you like. But it is a very important issue for analyzing the bounce direction.
To consider the bounce direction, imagine the ball spin direction just before the bounce is the same as the ball diagram shown. Imagine extending the arrows through the bottom of the ball. Imagine lowering the spinning balls of the kick, slice and flat serves to the court surface. Imagine the spinning ball first touching the surface - How far away is that first touch from the spin axis passing out of the ball?
1) The flat and slice serves first contact the court very close to where the extended arrows come out the bottom of the ball. The speed of felt there is not very large.
2) When the kick serve, the spin axis is much more tilted and the first felt to touch the court is moving much faster than for the slice and flat serves. This would make the ball bounce to the right for a right handed server as observed.
Ball Distortions During Bounce. But after contact starts, the ball will distort and we can imagine a squished spinning ball interacting more strongly than just the felt speed with friction on the court surface.
It's a simple experiment to point a high speed camera, 100s fps, at the bounce and see spin direction before the bounce. But to see the details associated with a distorted ball bounce on the court requires a camera with 1000s fps and very fast shutter speed - probably a research grade camera.
It is always exciting to see a true or false issue that can resolved by pointing a high speed video camera at it. What a piece of cake project!
Maybe this has been done?