Physics: precession of axis of rotation?

[Midlife crisis]

I was returning some of my son's serves today. He has the ability to generate a lot of spin without a lot of ball speed, and I was noticing that some of his serves would curve smoothly all the way until contact with the ground (and sometimes afterwards), while other times, the ball would curve in flight up until the last third or so of its flight, at which time the ball's flight would straighten out.

The serve that smoothly curves all the way until contact has a spin where the axis of rotation is basically perpendicular to the ground (it spins like a saucer). I'm not sure what the other serve's axis of rotation is, but because it straightens out, the axis of rotation must change in flight.

I believe the magnus force acts upon the ball's center of pressure (which is offset from the physical center of the ball), but can't visualize how this can precess the axis of rotation to a laterally ineffective position. Can anyone help satisfy my curiosity?

 

[Solat]

I was returning some of my son's serves today. He has the ability to generate a lot of spin without a lot of ball speed, and I was noticing that some of his serves would curve smoothly all the way until contact with the ground (and sometimes afterwards), while other times, the ball would curve in flight up until the last third or so of its flight, at which time the ball's flight would straighten out.

this is all i understood :grin: :grin: :grin:

 

[Bagumbawalla]

The saucer-like spin is side spin, called slice in a serve. The spin has little effect on the downward curve, except to slow the ball's flight and allow gravity to do it's thing.

The other shot, I can only guess, may be an attempt at a kick serve that will actually force the ball down in a dipping curve. It's possible he does not generate enough spin and the force is depleted part way throught he trajectory????

 

[LuckyR]

There are a couple of reasons why you are noticing that second type of serve. One might be an optical illusion where the axis of the spin (relative to your position) may make the action of the spin difficut for you to see, midflight. A second reason might be that the loss of spin through time might get to the point (midflight) where there is no longer enough spin to produce a change in flightpath. A third would be a change in the axis off rotation through the flight path such that the spin direction changes from, say side spin (whose effect would be quite visible) to underspin, whose effect would be negated by gravity and result in a flatter trajectory.

 

[travlerajm]

A small change in the axis of rotation can produce different effects.

In the air, the effect of gravity will exaggerate the topspin component of the spin, so the more topspin, the more it will appear to curve.

The answer to midlife's question is that both the ball spin and velocity are decreasing during the flight in both cases. In the former case, gravity is acting more in the direction of the spin, so that the ball continues to curve in the same direction even after the spin is no longer causing much effect.

The interesting thing for me is how spin axis affects the bounce direction. The larger the topspin component of the spin, the more the spin of the ball will grab the ground and influence the direction of the bounce.

So if you swing roughly 8 to 2 on the serve, your serve will bounce to your left (a topspin slice serve).

If you swing roughly 7:30 to 1:30, your serve will bounce straight ahead (giving it the illusion that it is pure topspin serve).

If you swing roughly 7 to 1, your serve will bounce to your right (a twist serve).

The only difference between these serves is that the ball grabs the ground better with larger topspin component of the spin.

 

[Koensayr]

The serve that smoothly curves all the way until contact has a spin where the axis of rotation is basically perpendicular to the ground (it spins like a saucer). I'm not sure what the other serve's axis of rotation is, but because it straightens out, the axis of rotation must change in flight.

I believe the magnus force acts upon the ball's center of pressure (which is offset from the physical center of the ball), but can't visualize how this can precess the axis of rotation to a laterally ineffective position. Can anyone help satisfy my curiosity?

What's usually called the Magnus force is a result of different pressures on the 2 sides of the ball (there is no such thing as a "center of pressure"). Because of the symmetry of around the axis of rotation, this force is going to be perpendicular to the spin axis and the direction of travel of the ball.

However, this force is also going to be through the center of the ball, which means that it will not apply any torque along the spin axis. But also means that if there is no torque, you will not get any precession.

While it is true that change in the direction of the axis of spin will change the direction of the curve of the ball, I don't think that's actually what's causing what you are describing here. Only possible way for precession to happen that I can think of is a imperfection in the manufacturing of the ball which creates an uneven distribution which then creates a torque due to gravity. But that's probably not the case cause if it is, you will probably notice that the ball feels funny too.

What's most likely happening is that the other shot which you describe has just enough spin so that, part way through the flight of the ball, the spin slowly down enough such that the pressure difference becomes negligible and you no longer see the curving effect and the ball straightens out.

Edit: Travler, is this stuff you are saying also from that book? If so, you seriously need to stop taking your physics from that book.

 

[travlerajm]

What's usually called the Magnus force is a result of different pressures on the 2 sides of the ball (there is no such thing as a "center of pressure"). Because of the symmetry of around the axis of rotation, this force is going to be perpendicular to the spin axis and the direction of travel of the ball.

However, this force is also going to be through the center of the ball, which means that it will not apply any torque along the spin axis. But also means that if there is no torque, you will not get any precession.

While it is true that change in the direction of the axis of spin will change the direction of the curve of the ball, I don't think that's actually what's causing what you are describing here. Only possible way for precession to happen that I can think of is a imperfection in the manufacturing of the ball which creates an uneven distribution which then creates a torque due to gravity. But that's probably not the case cause if it is, you will probably notice that the ball feels funny too.

What's most likely happening is that the other shot which you describe has just enough spin so that, part way through the flight of the ball, the spin slowly down enough such that the pressure difference becomes negligible and you no longer see the curving effect and the ball straightens out.

Edit: Travler, is this stuff you are saying also from that book? If so, you seriously need to stop taking your physics from that book.

What book? I'm a physicist. I write books about this stuff for a living.

 

[ubel]

What book? I'm a physicist. I write books about this stuff for a living.

LOL, owned. Sorry, I couldn't help myself

As for the differences between 8/2, 7:30/1:30, 7/1, are you serious about that? I was actually thinking about the ball bounce last night before I fell asleep and believed it to bounce kind of like a tilted sine graph depending on the direction in which you make contact with the ball at. Obviously 6/12 would be a straight up/down bounce, while 7/1 would be tilted so the top is to the right more; thinking about it now, the varying amounts of slice plays a huge role in the direction that the ball travels.

I'm guessing the 8/2 has so much slice that air-resistance will force the ball to go the left pre-bounce, 7:30/1:30 will have just a little leftward slice along with topspin but evens out on the bounce due to rightward directional spin, and 7/1 is almost all topspin with just enough rightward directional spin that it forces the ball right. Is that all correct?

 

[travlerajm]

LOL, owned. Sorry, I couldn't help myself

As for the differences between 8/2, 7:30/1:30, 7/1, are you serious about that? I was actually thinking about the ball bounce last night before I fell asleep and believed it to bounce kind of like a tilted sine graph depending on the direction in which you make contact with the ball at. Obviously 6/12 would be a straight up/down bounce, while 7/1 would be tilted so the top is to the right more; thinking about it now, the varying amounts of slice plays a huge role in the direction that the ball travels.

I'm guessing the 8/2 has so much slice that air-resistance will force the ball to go the left pre-bounce, 7:30/1:30 will have just a little leftward slice along with topspin but evens out on the bounce due to rightward directional spin, and 7/1 is almost all topspin with just enough rightward directional spin that it forces the ball right. Is that all correct?

That's basically the idea. The numbers I gave are not exact - they would need to be determined experimentally.

One of Sampras's strengths that people didn't realize is that he could vary the spin axis of his 2nd serve, and he could do it with the same toss. The beauty of this type of disguise is that the ball looks about the same in the air, but you don't know which direction it will bounce! Edberg and Rafter were also able to do that, but Sampras was able to do it with much more pace. This is something that Roddick doesn't seem to have in his repertoir.

 

[Koensayr]

What book? I'm a physicist. I write books about this stuff for a living.

Out of curiosity, what books have you written? I would like to buy some.

 

[travlerajm]

Out of curiosity, what books have you written? I would like to buy some.

Well, I haven't published any books. But I do work physics problems for a living.

However, I am planning to publish a book on designing tennis racquets for maximum performance, but a few of the subjects are still awaiting patent protection, so if I publish it it probably won't be for another year or two.

I'm also planning to publish an article in a scientific journal on the subject of weight customization - I hope to have it ready for publication within the next six months.

 

[Midlife crisis]

Thanks for all the replies. I caught a bit of a bowling tournament I had accidentally earlier recorded (just after an ESPN tennis match) and noticed there also that as the ball curves due to rotation, the axis of rotation noticeably changes, and if there is insufficient rotation or insufficient tilt of the axis of rotation in reference to the lane, the ball will curve only so much and then roll straight.

So, with a pure slice serve, where the off-center center of pressure created by the magnus force doesn't precess the axis of rotation (Koensayr, this is using the direction of travel of the ball as a frame of reference), the ball continues to spin in the same way but at a slower rate as the ball curves. This allows the ball to continue to curve throughout its flight path.

For the other serves, the center of pressure created by the magnus force precesses the axis of rotation into a less effective position, which combined with the loss of spin and decreased ball speed through the air makes the ball straighten out.

In thinking about it, I guess these same principals can also be observed in Frisbees.

Thanks for helping me with this thought exercise. We got a heap of snow in the area today but the indoor courts are open, and I'm going to grab some two-panel tennis balls to play around more with this.

 

[El Diablo]

"I write books for a living"...."I haven't published any books"....you sound a little confused about yourself. Your anticipated publication sounds more like something an engineer might be publishing. What area of physics do you work in? (I know some physicists and have a sibling in theoretical astrophysics, so I'm curious about a physicist who concerns himself with something so mundane as the dynamics of tennis racquets.)

 

[sureshs]

Isn't all of this someway related to aerodynamics? On one side of the ball, the velocity is higher due to rotation and the way the ball drags a layer of air with it. On the other side, the rotation is opposite to the direction of motion and velocity is less. This creates a difference in pressure by Bernoulli's theorem - higher velocity, less pressure, and the ball moves from higher to lower pressure region.

 

[Midlife crisis]

Isn't all of this someway related to aerodynamics? On one side of the ball, the velocity is higher due to rotation and the way the ball drags a layer of air with it. On the other side, the rotation is opposite to the direction of motion and velocity is less. This creates a difference in pressure by Bernoulli's theorem - higher velocity, less pressure, and the ball moves from higher to lower pressure region.

Yeah, it does, but my original question had to do with how these forces act to precess the axis of rotation of the spin on the ball. I hadn't thought it through well enough, and some of the other posts, along with seeing the bowling clip, got me to where I think I understand it at a satisfactory level.

 

[Koensayr]

midlife, the bowling ball is very different case because it's always in contact with the ground, anytime if the axis of rotation is not perfectly perpendicular to the ground, it's going to directly affect the direction of travel of the ball.

As for the tennis ball, it is due to the pressure differences created on the sides of the ball due to the spin. Once again, this is NOT going to cause precession of the ball because the force due to that pressure difference is going to be applied through the center of mass of the ball. Precession only happens when you apply a torque which is a force applied a non-zero distance from the center.

In your case where the ball straightens out, it is most likely due to the fact that the ball's spin has slowed down enough mid-flight to no longer create a noticeable pressure difference.

Yeah, it does, but my original question had to do with how these forces act to precess the axis of rotation of the spin on the ball. I hadn't thought it through well enough, and some of the other posts, along with seeing the bowling clip, got me to where I think I understand it at a satisfactory level.

 

[Midlife crisis]

midlife, the bowling ball is very different case because it's always in contact with the ground, anytime if the axis of rotation is not perfectly perpendicular to the ground, it's going to directly affect the direction of travel of the ball.

As for the tennis ball, it is due to the pressure differences created on the sides of the ball due to the spin. Once again, this is NOT going to cause precession of the ball because the force due to that pressure difference is going to be applied through the center of mass of the ball. Precession only happens when you apply a torque which is a force applied a non-zero distance from the center.

In your case where the ball straightens out, it is most likely due to the fact that the ball's spin has slowed down enough mid-flight to no longer create a noticeable pressure difference.

Two thoughts.

One is that a tennis ball may not always be symmetrically balanced due to manufacturing artifacts and defects. The axis of rotation would then be displaced from the physical center of the ball. Is this too small to have an effect?

Second is that if you look at a bowling ball from a vantage point directly above the ball as it rolls down the lane, the frictional forces are acting at a point directly below the physical center of the ball (which again is not likely to be the center of mass of the ball), yet there is precession of the axis of rotation. Isn't this a similar situation to observing a tennis ball from the vantage point of the person striking the ball? Can't a similar precession of axis of rotation happen?

Thanks.