Topspin, Slice, and Flat









Air is not a friction less substance so when a ball flows through this fluid forces of friction act upon it.

https://media.licdn.com/mpr/mpr/p/2/005/089/036/344d07d.jpg
Looking at the image above (and ignoring the dotted line) we can see the relative trajectories given to a tennis ball when hit with the three spins of tennis. The reason that a tennis ball changes its trajectory when it is spinning and moving through the air is because of the Magnus effect.

http://twu.tennis-warehouse.com/images/aerodynamics/spinflow.jpg
As we see from this image topspin shots are pushed down by the Lift Force. What we don't see is that air resistance is creating this force from a high pressure zone above the ball and a low pressure zone below the ball. Slice or Backspin is the opposite direction of rotation so the lift force is underneath the ball. This means on a slice shot the high pressure zone is below the ball and the low pressure zone is above the ball.

http://twu.tennis-warehouse.com/images/aerodynamics/laminarviscousflow.jpg
This figure shows a flat shot because it is showing no spin. We then can assume that the drag force is being equally distributed on both sides of the ball and the force that is pulling the ball to the ground is gravity.















  Angle of Return









Because we now know the trajectories of tennis balls and the relative angle they approach the ground to each other, we can discuss how the tennis balls will behave when they bounce off the ground. Topspin shots approach the court at a higher angle so it makes sense that they bounce at a higher angle. But we have to account for the forward spin.

http://ffden-2.phys.uaf.edu/webproj/211_fall_2014/Max_Hesser-Knoll/max_hesserknoll/Images/TopspinBounce.png
In this diagram we can see that since the ball was rotating forward and so it spent less time in contact with the court the angle of return was lower.

http://ffden-2.phys.uaf.edu/webproj/211_fall_2014/Max_Hesser-Knoll/max_hesserknoll/Images/UnderspinBounce.png
Since the ball is rotating with backspin when it contacts the surface it must change its direction of rotation and that causes the angle of return to be higher. Now an intermediate tennis player might look at this picture and say but wait, topspin shots bounce higher than slices. Topspin shots do bounce higher because their incoming angle is much higher than slice shots due to the Magnus Effect pushing them downwards into the ground.