# A paradox of the table tennis

1. Oct 12, 2007

### pixel01

A paradox of the table-tennis ball?

Some friends my argue about the ball spin and curve. At first I thought it can be explained by bernoulli effect.
But I can see a paradox here. When the ball is top spin, it will dive faster, while the upper part is moving faster than the lower part (see figure), so if following the bernoulli, the top spin ball must float more, not dive as it does.
I hope someone will explain to me.

Thank you.

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Last edited: Oct 12, 2007
2. Oct 12, 2007

### codec9

Why is point 1 moving faster than point 2?

3. Oct 13, 2007

### rcgldr

Forget Bernoulli, here's a link with a more recent explanation of Magnus Effect, except in this case the ball has backspin. The diagram show (although exagerrated) that the air is deflected downwards. This means that the ball imparts a downwards force on the air, accelerating the air downwards, and the air reacts with an upwards force on the ball. The ball also imparts a forwards force on the air (most of this due to the moving void the ball leaves behind it), causing forwards acceleration, of the air and the air reacts with opposing force on the ball (drag).

Magnus Effect .htm

Last edited: Oct 13, 2007
4. Oct 13, 2007

### pixel01

Why not?
In the figure, the ball is moving at velocity V, meaning the ball center is also moving at V. Point 1 is moving faster than the center, at a speed of V+v (v is the linear velocity compare the the center). On the other hand, point 2 is moving at V-v.

5. Oct 13, 2007

### Staff: Mentor

The Bernoulli effect is about air, not points on an object. Friction with the spinning ball slows the air on one side and speeds it up on the other.

6. Oct 13, 2007

### pixel01

According to me the bernoulli effect is about the points on the ball. It is similar to a train moving. No doubt, the bernoulli force increases when the train moves faster . It can be explained exactly the same to the points of the ball's surface.
Or more clearly, the surface of the moving thing has some friction, then it will make some air move along. The bernoulli force appears when there are different layers of air (liquid) moving at different speeds. In the case of the train, the first layer will move at the same speed with the train, and the outer most layer (the bulk) will not move. So the fater the train moves , the bigger the difference of speeds between the layers. The same thing can happen to the ball.
I think the magnus force should be opposite to the benoulli force in the case of the spinning ball and has higher magnitude.

7. Oct 13, 2007

### codec9

With respect to the center of the ball, point 1 is moving at the same speed as point 2. All parts are from the center. I don't see how the velocities you mention have relevance. The directions are the only things that matter to understand why it dives.

Air at the top of the ball pushes against the still air in the top right corner in the picture, but not on the bottom. The still air and the affected air on the bottom are going in the same direction with respect to the ball. So the top has a greater pressure or density of air and the ball tends to move to the less dense bottom area, and so it dives.

Last edited: Oct 13, 2007
8. Oct 14, 2007

### rcgldr

updated post

This is Coanda effect, not Bernoulli effect. It's due to a combination of friction between the air and the surface of an object, and internal friction of the air itself, which is called viscosity.

This isn't true. On some civilian aircraft, such as a Cessna, there is a hole in the side of fuselage, called a static port, which leads to an internal chamber, and the chamber's pressure is basically the same as the static (non-moving) pressure of the external air. Pressure within the chamber is used to determine the altitude of the aircraft. There is a maximum airspeed that this hole in the side method works, but it's well above the maximum speed of a Cessna.

The point here is that it's an open environment. In the classical Bernoulli example, you have a fluid flowing in a pipe that narrows and/or expands, no fluid from outside the pipe can enter or escape, so it's a closed environment, and the amount of mass flowing past any point in the pipe is constant. If there holes all along the pipe, then it's an open environment, and the amount of mass flowing past any point can vary, because the fluid would flow away from higher pressure areas to the surrounding environment, and flow towards lower pressure areas from the surrounding environment.

A link to an article that includes info about the static port:

http://home.comcast.net/~clipper-108/lift.htm [Broken]

This article also mentions the Coanda effect. Friction of the air with the surface of the wing, combined with viscosity of the air, causes the nearby air to follow the upper surface of a cambered airfoil. However, the article leaves out the "void" effect. When a solid object travels through the air, most of the affected air at the front will seperate and flow around the object, but as the back of the object passes by, a low pressure void is created, and air accelerates towards this moving void. A wing is designed so that with an effective angle of attack, this void is introduced with a mostly downwards component (for lift), while minimizing the forwards component (drag). In addition to the surface effects near the wing, there is also significant acceleration of air away from high pressure areas and towards low pressure areas from much further away. The article mentions this and includes diagrams, and explanations of the actual volume of air (per unit time) that is involved.

Last edited by a moderator: May 3, 2017
9. Oct 15, 2007

### pixel01

Hi Jeff, have you ever stood next to the door of a going train?. If yes, you will realize that when there is a train moving in opposite direction (about less than a meter apart), the door is sucked out quite strong (because the door is some what more loosened than other train wall). But if the other train is not moving or moving slowly, that sucking force is very much weaker. I thought that is the bernoulli effect.

So finally, can we explain the curve of a spinning ball by bernoulli? There are a lot of explainations out there (on the internet of even text book) just saying ' bernoulli effect', and I am against that.