Path of a spinning ball as given by NASA?

[Shooting Star]

Check out this page:

http://www.grc.nasa.gov/WWW/K-12/TRC/Aeronautics/Ping_Pong_Curve.html

Here's the picture.

 

[cesiumfrog]

Hmm.. I'd like to see a bit more explanation than just a mention of Bernoulli.

 

[rcgldr]

Well for one thing, the path of the ball as shown is confusing. The picture's frame of reference is the balls initial velocity, and the the ball is slowing down (drag) and curving to the right (lift).

Also, the Bernoulli reference about faster moving air is mis-leading. It's not the speed of the air, but what causes the change in speed.

It's easier to understand what's going on if a no-wind air is used as the frame of reference, since this is what a person will observe, a ball moving through still air. Using the same picture, but with the air as the frame of reference, the ball would be moving upwards through still air. The left side of the ball accelerates the air upwards more than the right side of the ball, and combined with the air's momentum, the resistance to this acceleration results in higher pressure on the left side of the ball than on the right, which accelerates the air to the left (outwards), with a reaction force that curves the ball to the right (inwards), corresponding to "lift". Air is also being accelerated upwards (relative to picture), with a downwards reaction force corresponding to "drag".

Link to updated gif:

http://jeffareid.net/misc/pingpong.gif

 

[Shooting Star]

I had posted the picture for what seemed to me like gross inaccuracy. But upon closer inspection, if the arrow in "path of the ball" is reversed, the situation may be restored. The explanation given is the usual one given for the Magnus effect. A lot has been written recently about it, and I don't want to bore people further.

 

[rcgldr]

I had posted the picture for what seemed to me like gross inaccuracy. But upon closer inspection, if the arrow in "path of the ball" is reversed, the situation may be restored.

The arrow is correct, if the picture is relative to the ball's initial velocity. Relative to the ball's initial velocity, the air will blow it downwards and to the right, which matches the path shown.

 

[Shooting Star]

Hi Jeff,

Yes, I had made the same silly mistake as you had done, which you had mentioned in the pre-edited version of your post. Intuitively, we assume that it’s the ball that is moving and the air is still.

But if the situation is as given in the picture, the path of the ball shown is correct. Here, the wind is blowing downward wrt the picture frame and the ball has been spun and put as shown in the initial position. Then it will take the path shown.

But why did you say that the Bernoulli reference was misleading? This phenomenon is mainly caused by a combination of the formation of a boundary layer and Bernoulli effect.

 

[rcgldr]

But why did you say that the Bernoulli reference was misleading?

As I posted in the other thread regarding spinning ping pong ball and it's curved path, I've never like using "Bernoulli" effect to explain lift. I prefer the Newton explanation that air is accelerated and responds with a reactive force, and it's clear that work is being done on the air. The Bernoulli effect methods sometimes ignore the fact that work is being done on the air. It's not the horizontal airflow that causes lift, it's the downwards acceleration of air.