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Author Topic: Oiled Mirror vs Dry Mirror - Use Your Head!  (Read 11810 times)

Aerobie

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #45 on: August 14, 2016, 06:00:05 PM »

ForeverSpin DLC Mirror Disappointing:
I tested my 47g tungsten and 43g bronze tops on this mirror.  Decay times, at low speed where tip drag dominates, were about equal for the 47g and slightly worse for the 43g, compared to my 3x glass mirror with a very thin haze of forehead oil.
The DLC mirror is deeply concave, perhaps about 10x.  As I've mentioned above, high magnification mirrors are inferior to lower magnification mirrors.
Alan
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Aerobie

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #46 on: August 17, 2016, 12:27:12 AM »

Predicting minimum RPM (topple speed):

I think the topple speed is affected by balance, but I haven't attempted to measure balance.  Ignoring balance, this formula works pretty well for me most of the time.

minimum RPM = (500/top diameter)*(Hcg/Ball diam)^0.5

(Ball is the tip ball)

All dimensions are in inches.  Give it a try and let us know how it does for you.

Alan
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Iacopo

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #47 on: August 17, 2016, 04:07:06 PM »

minimum RPM = (500/top diameter)*(Hcg/Ball diam)^0.5

Sorry for the Foreverspin mirror, I really thought it would have performed better than so.  Maybe with skin oil ?

Usually I use spiked tips for my tops, but I have data for two tops for which I used a diameter mm 4 sapphire tip:

Top Nr. 8
minimum RPM: 320
diameter: 1.73
Hcg: 0.55
Ball diam:  0.16

Top Nr. 6
minimum rpm:  190
diameter:  2.95
Hcg:  0.63
Ball diam:  0.16
 
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Jeremy McCreary

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #48 on: August 17, 2016, 04:34:10 PM »

ForeverSpin DLC Mirror Disappointing:
I tested my 47g tungsten and 43g bronze tops on this mirror.  Decay times, at low speed where tip drag dominates, were about equal for the 47g and slightly worse for the 43g, compared to my 3x glass mirror with a very thin haze of forehead oil.
The DLC mirror is deeply concave, perhaps about 10x.  As I've mentioned above, high magnification mirrors are inferior to lower magnification mirrors.
Alan
I don't have any hard data, but my sense is that LEGO tops behave the same way on concave surfaces of all kinds: The greater the surface curvature at the contact patch (magnification in the mirror's case), the shorter the spin time. The tips involved have all been of ABS plastic with hemispherical ends and radii of curvature of 1.5, 3.0, and 5.0 mm. The only dynamically significant variable in such tests would seem to be tip friction.

I should test flat-ended tips as well, as the contact patch area would be a different function of mirror and tip curvature.
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Jeremy McCreary

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #49 on: August 17, 2016, 05:38:09 PM »

Iacopo and Alan: What constitutes a "toppling" event WRT your data?

I ask because the formulas generally given for the minimum angular speed wmin (rad/sec) for stable sleeping or steady precession refer to the speed at which wobbling becomes possible, not the speed at which the top ultimately falls to the ground. (See the last 1/3 of my post at http://www.ta0.com/forum/index.php/topic,1496.msg46533.html#msg46533 for details.)

These formulas assume no perturbations due to imbalance, air currents, or tip or surface irregularities. To first order, however, they're independent of the dissipation involved, including tip friction. A top spinning without wobble can continue to do so below wmin in a metastable state. However, it doesn't take much of a perturbation to trigger wobbling below wmin.

These formulas can't predict the speed at which the top ultimately falls to the ground, and I have yet to see an analytical (as opposed to numerical) treatment that even tries to do so. Below wmin, the math becomes intractable, and too many unknowables enter the problem.

The upshot: To compare observed minimum speeds to each other and to well-established formulas in a meaningful way, I suggest that we report only the speeds at which major wobbling begins. Of course, identification of the onset of "major wobbling" will be somewhat subjective, and we'll be assuming that metastable states don't last long. But that's probably the best we can do in the real world.
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Aerobie

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #50 on: August 17, 2016, 07:27:03 PM »

minimum RPM = (500/top diameter)*(Hcg/Ball diam)^0.5

I have data for two tops for which I used a diameter mm 4 sapphire tip:

Top Nr. 8
minimum RPM: 320
diameter: 1.73
Hcg: 0.55
Ball diam:  0.16

Top Nr. 6
minimum rpm:  190
diameter:  2.95
Hcg:  0.63
Ball diam:  0.16

My formula gives 535 and 336 RPM for these tops, which is way too high.  Ditto for two tops which I made with 0.156" diameter tips.  I could change the constant (now 500) for small diameter tips, but what I really want is a formula which works for a wide range of tops.  Well, it's a start.

Alan
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Aerobie

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #51 on: August 17, 2016, 07:42:01 PM »

Iacopo and Alan: What constitutes a "toppling" event WRT your data?

I ask because the formulas generally given for the minimum angular speed wmin (rad/sec) for stable sleeping or steady precession refer to the speed at which wobbling becomes possible, not the speed at which the top ultimately falls to the ground. (See the last 1/3 of my post at http://www.ta0.com/forum/index.php/topic,1496.msg46533.html#msg46533 for details.)

These formulas assume no perturbations due to imbalance, air currents, or tip or surface irregularities. To first order, however, they're independent of the dissipation involved, including tip friction. A top spinning without wobble can continue to do so below wmin in a metastable state. However, it doesn't take much of a perturbation to trigger wobbling below wmin.

These formulas can't predict the speed at which the top ultimately falls to the ground, and I have yet to see an analytical (as opposed to numerical) treatment that even tries to do so. Below wmin, the math becomes intractable, and too many unknowables enter the problem.

The upshot: To compare observed minimum speeds to each other and to well-established formulas in a meaningful way, I suggest that we report only the speeds at which major wobbling begins. Of course, identification of the onset of "major wobbling" will be somewhat subjective, and we'll be assuming that metastable states don't last long. But that's probably the best we can do in the real world.

My formula is an attempt to fit math to experimental observations.

All but one of my tops go from major wobble to falling within a second.  Only one top precesses at about 30 degrees lean for about 5 seconds.   

I'm calling minimum RPM the last reading, within a second of falling.  Sometimes I extrapolate this point by extending the last RPM reading by using the last decay reading.  But I'm only doing this to intervals of about ten seconds.

A nice low minimum RPM might contribute to total spin time.  Because at the end of spin, my better tops are loosing less than one RPM per second.  My new 3" best is loosing about 1/4 RPM per second near the end.  So reducing min RPM by 50 (by lowering Hcg) might add 200 seconds at the end-of-spin. 

But moving the body of the top closer to the tip increases the aero drag shear on the bottom surface, which would cause end-of-spin to occur sooner.  So, as I've written before, "There's no free lunch".

Alan
« Last Edit: August 17, 2016, 07:48:59 PM by Aerobie »
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Iacopo

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #52 on: August 18, 2016, 03:04:10 AM »

Iacopo and Alan: What constitutes a "toppling" event WRT your data?

In my case I mean RPMs when the top topples down.
Wobbling appears and builds up very gradually, during the last 2 - 5 minutes of the spin.

About spinning surfaces curvatures: I have conflicting data so I am not sure how much the curvature of the spinning surface influences spin time.  My best spin (57 minutes) has been obtained on a spinning surface with a very little radius of curvature (about mm 4.5).  The tip is spiked, but the contact point of the tip is a flattened area with diameter about 0.1 mm.  More precisely, not perfectly flat, but slightly rounded, like the section of the surface of a sphere, with a diameter of maybe mm 2, or something so.
« Last Edit: August 18, 2016, 03:24:17 AM by Iacopo »
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Aerobie

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #53 on: August 18, 2016, 11:57:24 AM »

Hello Iocopo,

It appears to me that your tip shapes work better with curved mirrors than balls do.  I would guess that there is little increase in contact area due to base curvature.

Alan
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Aerobie

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #54 on: August 18, 2016, 12:02:17 PM »

How Much Oil is Best With my Heavy Top?

I've previously written that a very thin "haze" of oil has been best.  I re-visited this with my newest 440 gram top, thinking perhaps this heavyweight liked more oil.

But the thin haze was still best.

My method is to measure decay at low speed, where tip drag dominates.

Regards,

Alan
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Dick Stohr

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #55 on: August 18, 2016, 01:59:32 PM »

The ball bearing example supports what you are saying. Serious yo-yo and spin top players all clean their bearings and play them DRY. Ball bearings at high speed need oil to reduce the heat from friction. We play at speeds not high enough for friction to be a problem.
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Jeremy McCreary

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #56 on: August 18, 2016, 08:00:30 PM »

Iacopo and Alan: Thought I'd share some of the things I just learned about the surfaces of concave mirrors. The goal is to be able to compare the radius of curvature of the mirror to that of the tip. The formulas apply to both spherical and parabolic mirrors, but only near their centers, where tops usually end up.

Consider a concave mirror with the parameters below and assume that the glass thickness is a small fraction of the mirror's radius of curvature (reasonable for a typical cosmetic mirror).
d == rim diameter, taken through optical axis
h == rim height at center
f == focal length
R == radius of curvature at center
s == distance from center to subject (e.g., eyebrows in a cosmetic mirror)
m == magnification of subject seen at distance s from mirror

Parameters d and h are easily measured, and the rest are easily calculated from them. Parameters h, f, R, and s are all distances from the mirror surface along the optical axis perpendicular to its center. Near the axis, we have

f = d2 / 16 h

m = s / (f - s)

R = 2 f = d2 / 8 h = 2 s (1 + 1 / m)

Most of the practical points one can draw from these equations are already familiar, at least qualitatively:

(i) The radius of curvature R is just twice the focal length f.

(ii) The more deeply dished the mirror (i.e., the greater the central depth h at fixed mirror diameter d), the shorter the focal length f, and the smaller the radius of curvature R.

(iii) The magnification m depends on both focal length f and subject distance s in nonlinear ways. Calling a mirror "5x" means that m = 5 at some unspecified subject distance s.

(iv) The greater the magnification m at fixed subject distance s, the shorter the focal length f, and the smaller the radius of curvature R.

(v) The image is upright when the magnification m is positive (s < f) and inverted when m is negative (s > f). Hence, the image flips at s ~ f. This fact can be used to estimate f and therefore R without having to do the math.

Now consider a top spinning at the center of the mirror. Assume a tip that approximates a spherical cap with radius of curvature r < R. Increasing magnification closes the gap between R and r. When R = r, we would expect full tip-mirror contact and maximum friction.

All of the cosmetic concave mirrors at my house have conspicuous dimples and rigdes when viewed from a distance. These irregularities represent significant departures from ideal geometry, but the mirrors are probably closer to spherical than parabolic, as the former are cheaper to make.
« Last Edit: August 20, 2016, 12:51:21 PM by Jeremy McCreary »
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Jeremy McCreary

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #57 on: August 20, 2016, 03:46:50 PM »

A nice low minimum RPM might contribute to total spin time.

Couldn't agree more! Each of my tops seems to have a maximum attainable release speed for each spin-up method (hand, string, etc.). Hence, best spin times are strongly limited by the minimum speed wmin for stable sleeping or steady precession. And the strongest single influence on wmin is CM height, followed closely by axial moment of inertia.

This isn't just theoretical. Many of my tops have readily adjustable CM heights. The correlation between CM height and spin time is obvious.



But moving the body of the top closer to the tip increases the aero drag shear on the bottom surface, which would cause end-of-spin to occur sooner.  So, as I've written before, "There's no free lunch".

I may have some good news here: As long as the ground clearance c beneath the rotor exceeds d, the boundary layer thickness over the lower rotor face, the supporting surface won't affect the drag on the rotor.

This effect is well known to engineers who worry about windage on rotors in tightly fitting shrouds. Taking advantage of it in top design calls for an estimate of d. For a top with laminar swirling (von Karman) flow over a flat lower face of radius R,

d = 5.4 sqrt(v / w) = 5.4 R / sqrt(Re),

where d and R are in meters, v ~ 1.5e-5 is the kinematic viscosity of room temperature air in m^2/s, w is the angular speed in rad/sec, and Re is the dimensionless rotational Reynolds number given by

Re == w R2 / v

This formula for d is valid for Re < 300,000. Counter-intuitively, the boundary layer thickens as spin-down proceeds.

For your 47-gram tungsten top spinning upright at 2,000 rpm,
R = 0.50 in = 0.0127 m
w = 209 rad/s
Re = 2,252 (well within the laminar regime)
d = 0.0014 m = 1.4 mm

Upshot: You can reduce CM height until c ~ d without incurring a drag penalty, but twirlability will suffer if c gets too small.

One measure of twirlability is the "grounding angle" a between the stem and the vertical when the top is leaning on its rotor:

a = tan-1(c / R)

The smaller the grounding angle, the less wiggle room the twirler has to avoid a rotor strike. For your 47 g tungsten, a is only 6° when c = d = 1.4 mm. That's pretty tight for a twirl by hand but easily doable with your string-launch system.

A simple spin-up aid like the one below really helps with tops with small grounding angles, as it lets one hand control the stem angle  while the other applies the spin-up torque. This division of labor tends to benefit both spin time and the likelihood of getting a sleeper from the get-go.

https://www.youtube.com/watch?v=SL9KBh2z6uQ
« Last Edit: August 20, 2016, 03:57:01 PM by Jeremy McCreary »
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Iacopo

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #58 on: August 20, 2016, 04:33:05 PM »

I tell you about a little experiment with oil, which I made months ago.
I made the top spin in a base with a lot of motor oil, (level of the oil about mm 3).
So the tip was fully submerged in the oil.  Not only the tip, but also the support of the tip was in contact with the oil.
The diameter of the support, cylindrical, was about mm 10, (I modified the support and I don't remember the exact diameter).

How much drag from all this oil had the top ?
The weight of the top is 329 grams, radius of gyration mm 30.2.
In normal conditions, with only a very thin layer of oil, this top could spin for up to about 27 minutes.

With mm 3 of oil, the spin time has been only 9 minutes.  Which is a dramatic reduction of the spin time !
So the level of the oil is important as for the spin time, because oil adds viscous friction at the sides of the tip, the larger the quantity of oil, the worse.

On the other hand, the oil between the contact points lowers their friction.

As Alan, I too had my best spin times with a very thin layer of oil. 
Without any oil at all, my spin times generally result slightly shortened.

 
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Jeremy McCreary

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Re: Oiled Mirror vs Dry Mirror - Use Your Head!
« Reply #59 on: August 20, 2016, 08:20:47 PM »

In normal conditions, with only a very thin layer of oil, this top could spin for up to about 27 minutes.

With mm 3 of oil, the spin time has been only 9 minutes.  Which is a dramatic reduction of the spin time !
So the level of the oil is important as for the spin time, because oil adds viscous friction at the sides of the tip, the larger the quantity of oil, the worse.

That's a quite an effect, Iacopo! Clearly, dissipative forces don't need large contact areas or long lever arms to generate significant braking torques on spinning tops.
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