# How does top-spin effect a tennis ball's flight?

## Main Question or Discussion Point

As a tennis player, I'm interested in the effects of top spin in tennis.

I've done some research, but find myself somewhat confused about the concepts.

(my questions assume the ball has top-spin)

Magnus force & separation wake: in what direction do they act? do they act straight downwards or in a downwards direction? I can't seem to find anywhere in which it explains the direction they act in.

When the balls approach high speeds, why does the boundary layer become turbulent and what affect does it have on the ball? And how can the boundary layer possibly 'reverse' or have no velocity?

When the symmetry of the pressure forces are no longer equal behind and in front of the ball (due to turbulence/ unequal separation wake - delaying/hastening of airflow), how does this cause it to move downwards?

I have many other questions, but i won't flood you guys.

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When the symmetry of the pressure forces are no longer equal behind and in front of the ball (due to turbulence/ unequal separation wake - delaying/hastening of airflow), how does this cause it to move downwards?
If memory serves, this is according to Bernoulli's principle. When velocity of a fluid increases, pressure decreases. Air, being a fluid, flows faster on one side of the ball and slower on the other (due to the spin given to the ball) which creates a pressure difference on the two sides. A net force acts on the ball towards the area of low pressure causing the ball to swing.

rcgldr
Homework Helper
Magnus force & separation wake: in what direction do they act? do they act straight downwards or in a downwards direction?
Magnus effect is by definition a lift force, so it's perpendicular to the direction of movement, in this case "straight downwards". The separation wake only has a small upwards component, most of its velocity is "forwards", in the direction of travel.

wayback_machine_magnus_effect.html

When the balls approach high speeds, why does the boundary layer become turbulent and what effect does it have on the ball?
The boundary layer is a shear layer where the air at the surface has zero speed relative to the surface, and the outer boundary is usually defined as where the speed relative to the surface is 99% of the relative speed of the air to the object. Unless the speeds are very slow, or unless there's a pressure gradient where pressure decreases in the direction of relative flow, turbulence will occur within the boundary layer. Once the pressure starts increasing in in the direction of flow, then turbulence will eventually occur. Turbulence also occurs outside the boundary layer for the same reasons, and most of the wake at all but the slowest of speeds is turbulent.

And how can the boundary layer possibly 'reverse' or have no velocity?
I'm not aware of this effect. There are some theories that if a ball was smooth enough, and viscosity was low enough and/or speeds were fast enough you'd get a reverse Magnus effect.

When the symmetry of the pressure forces are no longer equal behind and in front of the ball (due to turbulence/ unequal separation wake - delaying/hastening of airflow), how does this cause it to move downwards?
In the article mentioned above, the flow remains attached a bit longer on the "backwards" spinning surface, resulting in a diversion of the wake perpendicular to the direction of travel, in this case the diversion is upwards, so you end up with the ball exerting an upwards (and mostly forwards) force on the air, coexistant with the air exerting an equal and opposing downwards (and mostly backwards) force on the ball, the Newton third law pair of forces at work.

The other source of Magnus effect is that the forwards spinning surface acclerates the air forwards a bit more than the backwards moving surface, and the greater rate of acceleration corresponds to a greater amount of pressure. Apparently, this effect is less significant than the diversion of the wake aft of the ball.

Does the "fuzziness" of a tennis ball affect spin?

Here is some description of different spins:
http://www.unc.edu/~sheng1/spin.htm [Broken]

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