The Physics Behind a Football's Wobble

[PhilG]

I've noticed that a football (American) wobbles a little bit even when you throw it with a near perfect spiral. Why is this?

 

[Andrew Mason]

I've noticed that a football (American) wobbles a little bit even when you throw it with a near perfect spiral. Why is this?

Aerodynamic drag forces are not perfectly symetrical so they create torque on the ball. This means that dL/dt is non-zero so the angular momentum is not constant. So it has to precess. Even bullets precess slightly (bullet yaw). It can be minimized but not eliminated.

AM

 

[PhilG]

Okay. I thought it might have something to do with aerodynamics, but I didn't know if the forces would be enough to produce visible motion. The football is pretty symmetrical except for the threads. What causes the imbalance in drag forces?

 

[whozum]

Pockets of varied air pressure, the thread themselves too. Also, you can't throw a perfect spiral, and that has something to do with it. Also, the wind direction not being completely parallel/antiparallel will make a difference.

 

[PhilG]

Right. But does the football cause those air pockets or are they already there? Also, I've seen this even when there's practically no wind.

 

[HackaB]

The uneven drag happens because u throw it at a slight angle to its initial velocity. "Air pockets" don't cause a regular precession.

 

[PhilG]

Okay, just to make sure I understand: if the football were thrown in vacuum, you wouldn't see the wobble, since there are no aerodynamic forces, right?

 

[DaveC426913]

Well, no. The air also stabilizes the ball on its longitudital axis. In a vacuum, it would keep whatever spin you put on it, even if that were quite small.

 

[PhilG]

So you don't need aerodynamic forces to make it wobble?

 

[FredGarvin]

Don't also rule out imperfections in how the ball is made. The uneveness of the material and construction will move the center of mass from the longitudinal axis of the ball. There is no such thing as a perfect anything.

 

[DaveC426913]

Eeeehhhhh...

Aerodynamic forces will/may impart some wobble on the ball, yes. They also will tend to keep it from going wild, yes.

If there were no aerodynamic forces, AND you could throw the ball with a spin one only the longitudinal axis, AND you had a perfect ball with no imperfections, then you would get no wobble.

A ball with imperfections would still likely wobble a bit merely because the axis of rotation about its centre of mass would not run exactly through the long axis of the ball (say, the threads add a little weight on one side, your centre of mass is off by a mm, etc.)

But if you threw the ball with any imprefection in the spin, and there were no airflow to dampen it, the ball would tumble in all three axes. It would spin quickly around the long axis, as you intended, but additionally would tumble end over end slowly - something that it would not do in the presence of air.

 

[PhilG]

Thanks for clearing that up, Dave. If the ball is tumbling and spinning at the same time, isn't its angular momentum changing?

 

[HackaB]

If the ball is tumbling and spinning at the same time, isn't its angular momentum changing?

Seems like it would be...

 

[DaveC426913]

Why? It's, merely rotating on two axes.

 

[HackaB]

It takes a torque to rotate something about a non-principal axis.

 

[PeteSF]

Toss a pen in the air so it rotates end over end.
Now repeat, but put a spin on the pen as you toss it.

There you have it. Rotation on two axes. No torque applied after the initial impetus.

 

[Cyrus]

I know bullets have spiral in them in order to keep them stable in flight. I would assume that the football needs the same thing in order to move in a predictable arc. Perhaps the amount of spin required to obtain a very stable flight is hard/usually not obtained when a person throws a football, which explains why you see (some) wobble no matter how hard you try?

 

[HackaB]

Toss a pen in the air so it rotates end over end.
Now repeat, but put a spin on the pen as you toss it.

It doesn't rotate end over end if you put spin on it. It does wobble though.

There you have it. Rotation on two axes. No torque applied after the initial impetus.

What do you actually mean by "rotation on two axes"? The result has to be equivalent to rotation about one axis (not necesarily a principal one). Would you say that axis of rotatoin is moving or fixed?

 

[PeteSF]

It doesn't rotate end over end if you put spin on it. It does wobble though.

It surely does. I'm doing it right now. Try it again.

What do you actually mean by "rotation on two axes"?

I mean two components of rotation, with two different periods.

The result has to be equivalent to rotation about one axis (not necesarily a principal one).

Why?

Would you say that axis of rotation is moving or fixed?

One axis (the end-over-end rotation) is moving in a parbolic arc, but always points in the same direction.
The rotation period about this axis is in the order of 1 second.

The other axis (The spin of the pen) is changing direction - it is rotating with the end-over-end motion.
The rotation period about this axis is in the order of 0.1 seconds.

 

[PeteSF]

Consider Asteroid Toutatis. It seems that it has a complex tumbling motion that does not correspond to rotation on a single axis.

Mpg animation of Toutatis's spin

 

[HackaB]

It surely does. I'm doing it right now. Try it again.

U are right, I was putting too much spin and not enough end-over-end impulse on it. However, the faster you spin it, the more it deviates from a pure end over end rotation. It wobbles in a sideways direction too. I don't think you can avoid it, but I could be wrong.

It is a theorem in kinematics that the most general motion of a rigid body is a translation of the center of mass plus a rotation about a single axis through the center of mass. Actually, the reference point doesn't have to be the CM, but it's the most sensible. And the axis doesn't have to have a constant direction. So what I'm asking is if u think this axis has a fixed direction in space for the pen or football. If so, there has to be a torque acting on the body (assuming it isn't a principal axis).

That asteroid clip is cool. It does not seem to be rotating about a fixed axis. Is that what you mean by not rotating about a "single axis"?

 

[DaveC426913]

What do you actually mean by "rotation on two axes"? The result has to be equivalent to rotation about one axis (not necesarily a principal one).

No. Rotation about two axes is not equivalent to rotation about one axis - even if you choose it carefully. The football is an excellent example:
I float around in the shuttle bay.
I take the ball and put a strong spin on it like a spiral throw (but I don't throw it).
Now I give it a slight (slow) nudge about an axis perpendicular to its fast spin.
It is now roatating about tow axes. No single-axis rotation can match this.


However!

You may be thinking of three axes. Rotation about three axes can be simplified to rotation about only two axes, if you choose your axes carefully.

Would you say that axis of rotatoin is moving or fixed?

Well, if an axis is "moving" and the ball is not, then that axis (of rotation) must be, itself, rotating. i.e. two axes of rotation.

 

[PhilG]

Hmm...There doesn't seem to be a consensus on what's going on here. Thank you for all the replies, though

 

[HackaB]

No. Rotation about two axes is not equivalent to rotation about one axis - even if you choose it carefully. The football is an excellent example:
I float around in the shuttle bay.
I take the ball and put a strong spin on it like a spiral throw (but I don't throw it).
Now I give it a slight (slow) nudge about an axis perpendicular to its fast spin.
It is now roatating about tow axes. No single-axis rotation can match this.

I see what you mean now. Can you explain how the angular momentum stays constant while the angular velocity vector moves around in a complicated way?

 

[DaveC426913]

I see what you mean now. Can you explain how the angular momentum stays constant while the angular velocity vector moves around in a complicated way?

No.

I mean, no I can't. I'm don't have the math.

 

[PBRMEASAP]

Can you explain how the angular momentum stays constant while the angular velocity vector moves around in a complicated way?

You might do a google search on "regular precession". Actually, it would be better to look it up in a book on mechanics (Classical Mechanics by Goldstein is good). Here's the idea: for a rigid body, such as a football, with two equal principal moments of inertia, the most general force-free motion is for the ball to spin on its axis, which itself rotates about the constant angular momentum vector with a constant frequency. The axis of the ball makes an acute angle with the angular momentum vector (for a football). The total angular velocity vector also rotates around the angular momentum vector with the same frequency--it lies in the plane formed by the axis and the angular momentum.

Also, I think this is what you were getting at in an earlier post.