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[Jeremy McCreary]

Nice precession demo...



The change in angular momentum triggering precession can come from within.

[Iacopo]

I had to think for some time because I was not understanding what it is happening in the video:
the wheel apparently seems centered so that when it is in tilted position there should be not torques on it due to gravity.
There could be precession during the brief tilting movements of the wheel, but not after.

I believe that this is not real precession, (torque induced).
I see that the wheel has blades so it pushes air, and for reaction there is a push, (air drag), on the wheel, in opposite direction.
When the wheel is tilted, a component of the torque due to the air drag is responsible for the apparent precession.

A nice demo, yes, not of precession, but of a torque working at an angle.  The torque applied at 90° has no effect, but even a little difference from 90° produces a component of the torque sufficiently strong to make the whole object to "precess".

[ta0]

There could be precession during the brief tilting movements of the wheel, but not after.

I would say that there can only be acceleration during the tilting. But once it stops tilting it can continue rotating with an inertial movement.
If you think in terms of conservation of rotational moment, the frame has to rotate opposite to the direction the tilted wheel is spinning (as seen from above = proportional to the sine of the angle). This is because the tilting motors do not have any torque around the vertical plane.

When the wheel is tilted, a component of the torque due to the air drag is responsible for the apparent precession.

Yes, you are right. The motor is working against the air friction and ads a vertical torque.
But even if the wheel did not have a motor to keep it going, or it was in vacuum, iI think it would continue rotating by just inertia.

[Iacopo]

But even if the wheel did not have a motor to keep it going, or it was in vacuum, iI think it would continue rotating by just inertia.

I don't know.  My gyroscope refuses to rotate by inertia along the vertical axis if the rotor is spinning.
A temporary push in the direction to cause rotation doesn't cause rotation but nutation of the rotor, and nothing else.

[ta0]

I don't know.  My gyroscope refuses to rotate by inertia along the vertical axis if the rotor is spinning.
A temporary push in the direction to cause rotation doesn't cause rotation but nutation of the rotor, and nothing else.

The push should not be in the horizontal direction. It has to be in a direction and strength just right to achieve this inertial "precession" around the vertical. It's achieved automatic in the video because of the initial conditions. And there will still be nutation unless you do it very slowly.

[Iacopo]

The push should not be in the horizontal direction. It has to be in a direction and strength just right to achieve this inertial "precession" around the vertical. It's achieved automatic in the video because of the initial conditions. And there will still be nutation unless you do it very slowly.

You might be right...  if the weight of the rotor is little compared to that of the stator, the inertia of the stator could make it rotate along the vertical axis, in spite of the spinning rotor.  Because a spinning rotor by itself would refuse to tilt simply by inertia, whatever the direction of the push. 

[ta0]

Because a spinning rotor by itself would refuse to tilt simply by inertia, whatever the direction of the push. 

It will refuse to tilt in the direction you push it. That happens in the video. That does not mean that it cannot have a precession-like rotation.
The frame complicates things in the video as the complete device is not a solid but has several independent parts. But even a spinning wheel by itself, in the absence of gravity, can have inertial precession, as we have seen before.  It happens when the total rotational moment is in a different direction than one of the principal axes.

[Iacopo]

But even a spinning wheel by itself, in the absence of gravity, can have inertial precession, as we have seen before.

The inertial precession you are referring to is nutation, (torque free precession), isn't it ?

This is how my gyroscope behaves if I try to induce an inertial rotation along its vertical axis:



It refuses to rotate, it nutates instead.
There is no way to make it rotate simply by inertia.  I can make it rotate if I introduce a torque on the rotor, putting a weight on a side of a gimbal, in which case I have torque induced precession, and a motion similar to that in the video posted by Jeremy.

But it doesn't seem to me that the motion in the video posted by Jeremy is torque induced precession. 
Not even it does seem to me an inertial torque free precession, (nutation), because the kinematics is different.

Then there are the blades.  Why a rotor with blades was used ? I don't think it was a random choice. I believe that without the blades there would be no precession.
If Jeremy has the necessary Lego pieces, maybe he could make a similar machine, but using a wheel without blades;
I think that without blades there would be a temporary precession only during the tilting movement of the wheel.
As the wheel stops the tilting motion, the precession too should stop.
The inertia wanting the precession to continue would cause some nutation and not a continuation of the precession.
A bit of temporary nutation is recognizable in the video posted by Jeremy, everytime a precession is stopped.

[ta0]

I imagine Jeremy is working hard assembling one like this 

Iacopo: while you push down on the wheel you need to let it rotate in the direction it wants to go (but I imagine this is easier said than done).

[Jeremy McCreary]

I have the parts to make a version with a more aerodynamic flywheel, but it's not a trivial build, and it wouldn't prove anything.

Any real flywheel with the necessary spin angular momentum will generate drag -- even if perfectly streamlined and polished, as in Iacopo's beautiful free gyro. How much drag is enough to fundamentally change the dynamic in the way Iacopo suggests?

IMO, flywheel drag controls only the rates of the 3 observed rotations, not the basic dynamic. And then only by limiting the max flywheel speed attainable with a given pair of spin-up motors, gearings, and applied voltages. Which in turn limits max flywheel angular momentum for a given flywheel. Which then limits the conspicuity of the desired responses.

Quite sure that the green flywheel was chosen in spite of the fins, as it has the largest AMI and AMI per unit mass of any one-piece LEGO wheel. Which maximizes flywheel angular momentum for a given operating speed. This wheel probably also has a smaller central TMI/AMI ratio than most. That would reduce the torque needed to to tilt the flywheel and inner gimbal at max flywheel speed.

To make a LEGO flywheel of comparable max radius and AMI, you'd have to put heavy wheels with rubber tires on long spokes. In the process, you'd lose a lot of rigidity, gain a lot of mass, and probably make the drag even worse. Heck, even if you shaved off all the fins and polished the green wheel's rim to a mirror finish, it'd still produce a good bit of drag -- especially from the spokes.

To achieve the same flywheel angular momentum, you could also go with a smaller, more streamlined flywheel of lesser AMI operating at higher speed. But would the total aerodynamic braking torque in operation be any less? Hard to say.

Bottom line: I'd choose the green wheel for this demo, too.

Sorry, I think we're once again talking apples and oranges by mixing kinematic and dynamic viewpoints without due precautions.

[Iacopo]

Iacopo: while you push down on the wheel you need to let it rotate in the direction it wants to go (but I imagine this is easier said than done).

I am not sure what do you mean here. In my gyroscope the spinning wheel tends to maintain its orientation.  In whatever direction I push it, there is no way to start a precession about the vertical axis simply by inertia, the only thing I can cause is a temporary pure nutation, (the motion I showed in the video above).  The only way to start a precession is by introducing a torque on the spinning wheel, like putting some weight on the gimbal.  Playing with a gyroscope similar to the mine would give the feeling of what I say.

[Iacopo]

IMO, flywheel drag controls only the rates of the 3 observed rotations, not the basic dynamic.

I believe that the flywheel drag produces the precession. No air drag, no precession, in that setting.
I think that without those fins the air moved from the flywheel would be quite less, so the difference of behaviour would come up, (if you could find a smooth flywheel).

I realized that I can replicate the experiment with my gyroscope; there are some differences but they are not important; my flywheel spins by inertia and without motor. For to tilt the spinning flywheel I pull the gimbal with a string instead to use motors.
When I pull the string for to tilt the spinning wheel, I cause a temporary precession.  The same happens in the "nice precession demo".
When I stop pulling the string, I trigger a bit of temporary pure nutation, (the motion shown in my video above).  The same happens in the "nice precession demo".
When I stop pulling the string, the precession stops instantly.
In the "nice precession demo" instead the precession continues, which to me seems possible only because of the air drag of the fins.

Quite sure that the green flywheel was chosen in spite of the fins, as it has the largest AMI and AMI per unit mass of any one-piece LEGO wheel.

I didn't know this, and I trust you. This doesn't change the things anyway, the fins are there, and certainly produce some air drag.

Sorry, I think we're once again talking apples and oranges by mixing kinematic and dynamic viewpoints without due precautions.

I thought to this.  Maybe who made the video used the term "precession" as a kinematic term, knowing that the motion is produced by the air drag.
But I suspect that, more probably, he simply used the term precession thinking to the motion of gyroscopes, for similarity of motions, maybe without realizing that the nature of the motions is different.

[ta0]

I was thinking only in terms of conservation of momentum along the vertical axis, but that was wrong as you have to consider the conservation in the horizontal direction. The conclusion is that it has to do a "nutation" movement (really an inertial precession around a horizontal axis). Without friction it should not stop when the torque finishes, but in reality it will. So, I believe you are right, the apparent precession around the vertical axis is due to the reaction of the motor.

[Jeremy McCreary]

At 1:15 in the video below, Iacopo sets up his brass gyroscope with the flywheel's spin axis roughly horizontal. He then places a small test weight on the inner gimbal at a point directly above one end of the flywheel axle.



That point drops ever so slightly at first, but the inner gimbal's tilt  then stabilizes -- even though the test mass and its gravitational torque on the inner gimbal are still present.

Meanwhile, the flywheel axis starts rotating at a constant rate about the vertical, as allowed by the outer gimbal.

Yes or no: Is it valid to call the rotation about the vertical here "precession"?

[ta0]

Yes or no: Is it valid to call the rotation about the vertical here "precession"?

Of course! Isn't that the classic example of (torque induced) precession?