What Do You Do With Your Top(s)?

[Jeremy McCreary]

....The "Quark" top was sold with a laser pointer and instructions for balancing.  They claimed that the more perfect the balance, the longer the spin.  So balance (or perhaps unbalance) deserves a spot in the Sc formula.

Does anyone know where I can get instructions for balancing a Quark top?

Best,

Alan

Sorry, Alan, not familiar with that top.

The approximate critical speed formula I posted gives the lowest speed at which sleeping is a stable dynamic for a perfectly symmetrical sleeping top with its CM on the axis of symmetry. (That last condition guarantees perfect balance.) Below critical speed, the top begins to wobble and precess as a prelude to toppling.

I can think of at least 3 ways that imbalance shortens spin time -- all related to the induced wobbling: (i) By shunting spin kinetic energy into precession and wobble when the energy could have gone to keeping the spin rate supercritical for a longer time. (ii) On slicker surfaces, by shunting extra spin kinetic energy into frictional losses as the induced wobbling jerks the tip back and forth across the surface. (ii) By shunting spin kinetic energy into elastic energy as the induced wobbling flexes the top's structure.

Flexure probably isn't much of a problem for throwing tops, but it's definitely something I have to deal with in larger LEGO tops like the one below.

[Jeremy McCreary]

.... I know absolutely nothing about the critical spin rate and that formula, which is interesting: in very poor words it says that a low and large top is more stable than a tall and narrow one.
I don't have data for transverse moment of inertia, and I don't know if I can measure it with the pendulum, because I know that the pendulum will tend to rotate around the CM of the top and not around the tip.

Sorry, should have been clearer. This particular critical spin rate is measured not when a top finally falls over, but at the moment a sleeping top stops sleeping and starts wobbling.

Yes, more stable in the sense of being able to stay asleep at lower speeds. Moving a top's mass "down and out" (i.e., axially downward toward the tip and radially outward away from the spin axis) lowers the critical spin rate S_c by increasing I₃ (AMI) and reducing both h and I₁, the transverse moment.

At constant release speed, aerodynamic drag, and tip friction, the lower S_c, the longer the sleeping time, and usually the longer the total spin time as well.

[ta0]

Alan:  I do have the instructions for the Quark top but I am traveling (I missed my plane back today). Balancing does increase its spin time (but I never got close to the time claimed for the tungsten version).

Iacopo: I am glad somebody else tried the torsion balance. I look forward to your video. To calculate the transversal moment of inertia at the tip you can measure it around the center of mass and use a simple formula to translate it.

[Aerobie]

Alan:  I do have the instructions for the Quark top but I am traveling (I missed my plane back today). Balancing does increase its spin time (but I never got close to the time claimed for the tungsten version).

Iacopo: I am glad somebody else tried the torsion balance. I look forward to your video. To calculate the transversal moment of inertia at the tip you can measure it around the center of mass and use a simple formula to translate it.

Jorge,
When you can, post the Quark balance instructions here.  I have a Quark, but what I really want to do is apply laser balancing to my homemade tops.

I have a couple that have the Cg about 1cm above the tip.  They topple at about 300 RPM.  With a string I've launched these two at over 6,000 RPM and timed them each for just over 30 minutes spinning on a mirror.

Alan

Best,
Alan

[Kirk]

I can think of at least 3 ways that imbalance shortens spin time -- all related to the induced wobbling: (i) By shunting spin kinetic energy into precession and wobble when the energy could have gone to keeping the spin rate supercritical for a longer time. (ii) On slicker surfaces, by shunting extra spin kinetic energy into frictional losses as the induced wobbling jerks the tip back and forth across the surface. (ii) By shunting spin kinetic energy into elastic energy as the induced wobbling flexes the top's structure.

4) Moving the boundary layer of air in waves.  Put your ear near a wobbling top and you can hear it.

[Aerobie]

As spin rate slows, eventually the moment due to imbalance exceeds the available gyroscopic force, which is keeping the top from falling.

But with perfect balance, it should take less gyroscopic force to prevent falling.  So the minimum spin rate Sc, should be lower.

Alan

[Jeremy McCreary]

4) Moving the boundary layer of air in waves.  Put your ear near a wobbling top and you can hear it.

Ah, yes, Kirk, forgot about that one. Many of my dirtier LEGO tops hiss audibly, and you can often hear the modulation due to wobbling.

[Jeremy McCreary]

As spin rate slows, eventually the moment due to imbalance exceeds the available gyroscopic force, which is keeping the top from falling.

But with perfect balance, it should take less gyroscopic force to prevent falling.  So the minimum spin rate Sc, should be lower.

Yes, reasonable way to look at toppling speed. But S_c as I defined it refers to the minimum spin rate for stable sleeping. The toppling speed will be lower -- in practice, sometimes much lower.

[Kirk]

you can often hear the modulation due to wobbling.

Now that is interesting.

But with perfect balance, it should take less gyroscopic force to prevent falling.  So the minimum spin rate Sc, should be lower.

Yes, reasonable way to look at toppling speed. But S_c as I defined it refers to the minimum spin rate for stable sleeping. The toppling speed will be lower -- in practice, sometimes much lower.

I think that the difference between sleeping speed and toppling speed depends on several things. I have a lathe turned HDPE koma that sleeps so well it is in a coma.  When is falls over there is almost no spin left.  On the other hand, we all have tops that skitter across the floor when they fall because they wobble and thus have a fair amount of energy left over when they hit the ground.
The dynamics of falling over are a bit more complex. 
Not only is balance important as Alan mentions but I think tip shape also plays a role. Consider a dull pointed top. When thrown at an angle it will travel in a circle and correct itself to vertical (sleeping) more quickly than a sharp pointed top. A leaning top will travel in proportion to the lean, the tip geometry (distance from the axis to the contact point) and the speed.  (and of course the surface conditions) The travel is perpendicular to the lean and thus exerts a moment to correct the top. 
However the energy of travel is taking away rotational energy.  I'm not sure which will win.

[Iacopo]

Iacopo: I am glad somebody else tried the torsion balance. I look forward to your video. To calculate the transversal moment of inertia at the tip you can measure it around the center of mass and use a simple formula to translate it.

Thank you Ta0.  I want to make a step at a time, and, if/when I will need that data, I will remember that it is possible to have it.

[Jeremy McCreary]

I think that the difference between sleeping speed and toppling speed depends on several things....
Not only is balance important as Alan mentions but I think tip shape also plays a role....
However the energy of travel is taking away rotational energy.  I'm not sure which will win.

I see what you see WRT the sleeping/toppling speed gap, Kirk.

The minimum sleeping speed formula I gave assumes a point-like tip contact patch but doesn't care about tip friction. In practice, tip size and shape are huge here. For example, the tip I use to encourage travel has a radius of curvature of 5.0 mm; the tip used to encourage sleeping, 1.5 mm. Both have smooth spherical contact patches.

Let's use "broad tip" to refer to a tip with a relatively large radius of curvature over its contact patch. In my experience, broad tips consistently promote certain behaviors that may or may not be desirable in a particular top: (ii) Initial precession, (i) self-righting (above a critical starting inclination), (iii) travel, and perhaps (iv) some wobbling -- i.e., anything but sleeping initially, but with a strong self-righting tendency.

Most of my tops have a "critical starting inclination" (beyond which self-righting never appears). I sense that a broader tip increase this critical angle but can't prove it.

[ta0]

I believe the formula Jeremy posted and a different one I once posted give an estimate on the transition speed between precession at a more or less uniform angle and the start of large oscillations (nutation). If I recall correctly, it starts when the energy of spin is of the magnitude of the gravitational energy.

I have seen a few tops rise from nearly touching the floor to standing up and sleeping.

[Aerobie]

I've been graphing my homemade machined metal tops -- speed vs elapsed time. 

I was surprised to observe that most of these tops lose approximately 10% of RPM per minute over their spinning lifetime.  (They range from -9% to -13% per minute)  This is when spinning on a concave mirror that I've wiped with a verrry thin film of forehead oil.  The range of decay rate is surprisingly narrow.

Iacopo, what's the decay rate of some of your beauties?

Alan

[ta0]

Alan:

Iacopo's decay measurements are here: Test: which are the best contact points for a finger top ?

For small tops with good bearing tips I get about 40% decrease per minute (decay constant -0.008 1/s). You can see the graphs and calculations here: Spin decay comparison of Throwback and Gates tops

[Jeremy McCreary]

I believe the formula Jeremy posted and a different one I once posted give an estimate on the transition speed between precession at a more or less uniform angle and the start of large oscillations (nutation). If I recall correctly, it starts when the energy of spin is of the magnitude of the gravitational energy.

I have seen a few tops rise from nearly touching the floor to standing up and sleeping.

My formula for s_c really does estimate the minimum spin rate for stable sleeping, as opposed to stable steady precession at constant inclination, but it has some issues. The kinetic and potential energies typically equalize at a lower speed, but there are complications here as well.

See the new "Minimum critical spin" topic ta0 created at http://www.ta0.com/forum/index.php/topic,4455.0.html for details.