How I do Laser Balancing:
This method is my adaptation of the Quark instructions:
Make a shiny flat disc, 360 degrees of the upper surface of the top. It needn't be a mirror, any shiny surface works. I've used the shiny surface of clear polycarbonate. I've also just polished the upper surface of my top. There are many shiny tapes available, which could be attached to the upper surface of your top. You could also attach a thin disc of shiny plastic. Attachments should be lightweight, to have minimal influence on balance.
Block the reflectivity of a radial stripe running from the center outward on your shiny disc. I've used a narrow strip of matte finish "Magic Mending Tape". It's clear, but not shiny. I chose it because it's thin and lightweight. I've also used my radial stripe of Scotchlite, which is always there for the optical tachometer. You can see that on the tops in all of my photos. You could also sand a radial stripe on your shiny disc with sandpaper to kill the shine.
Shine a laser downward at the spinning top, striking it at 3:00 o'clock.
View the reflected laser on the ceiling. The top must be spinning slow enough to wobble. The pattern on the ceiling will be a circle with a break caused by the non-shiny strip. Imagine that you are looking at an ordinary clock on the ceiling. The part of the circle nearest you is 12 o'clock. Note the o'clock position of the gap.
Hold the top viewing its bottom, with the non-shiny strip at your left, which is 9 o'clock. The azimuth of the gap you saw on the ceiling needs more weight. If you are moving the pivot, it should be moved away from the azimuth where you noted the reflected gap.
Thanks for posting your "laser method" for locating unbalances, Alan. Now that I have a laser pointer bright enough to test it on LEGO tops with known unbalances, I have 2 main findings to report:
(A) Your non-reflective strip trick works like a charm. The reflection gap projected onto the ceiling is clearly seen, and its azimuth is easy to determine to at least the nearest "hour" (i.e., to the nearest 30°).
(B) With the LEGO tops tested so far, the reflection gaps always point to the
heavy side, regardless of speed, CM height, or degree of unbalance. This contrasts with your finding of reflection gaps pointing to the light side at relatively low speeds.
The discrepancy in (B) doesn't invalidate the laser method by any means, but it does underscore the need to pin down the phase angle (180°, 0°, 90°) in effect under the test parameters involved before correcting the top in a permanent way. We've already seen this problem with the paintbrush method. Reports to date indicate that paint piles up 180° from the heavy side in most cases. However, we've also seen phase angles of 0° and 90° now and then, and phase angles that change with CM height or speed have also been reported.
Hence, both methods leave us with a practical dilemma: In a top with unknown unbalance, which phase angle applies? Unfortunately, there's no way to predict given our limited understanding of how tops respond to unbalance. Safest, then, to test hypothetical phase angles in 180° -> 0° -> 90° order to see which one applies before committing to an irreversible balance correction.
I'm guessing that Finding (B) above reflects a difference in phase angle -- 180° in my case and 0° in yours.
MethodologyThe photo below shows a typical LEGO test top with a dozen black 0.24 g "test masses" and my new green laser sight. The perfectly balanced "bare top" without test masses weighs 28.1 g. The 2 white wheels making up the "rotor" can host up to 12 test masses in the holes just inboard of their rims.
Release speeds range up to ~6,400 RPM by motorized spinner (below) and ~1,500 RPM by hand. With the rotor at its lowest position -- i.e., with the top at minimum center of mass (CM) height -- spin times are ~55 and ~35 sec, respectively. Aerodynamic drag around the spokes accounts for the modest spin times and the meager bump in spin time (57%) from a 427% bump in release speed. (Covering the spokes with smooth fairings more than doubles spin times but blocks access to the test mass holes.) Topple speed at minimum CM height averages ~480 RPM without test masses and higher with.
Sliding the rotor along the top's central black axle varies overall CM height from ~24 to ~72 mm. This adjustment has no effect on the test top's AMI (axial moment of inertia), but increasing CM height increases its TMI (transverse moment of inertia about the tip) and decreases its AMI/TMI ratio. The net result is a strong adverse effect on spin time via the minimum speed for stable sleeping or steady precession. Nonetheless, the bare test top sleeps well at all CM heights.
To unbalance the test top, I just add test masses in pairs (0.48 g increments) above and below the rotor so as maintain static unbalance and avoid couple and dynamic unbalance. All test masses sit 32 mm from the spin axis. The 6-fold symmetry allows total static unbalances of 7.7, 13.3, and 21.0 g mm. The photo below shows the test top in a state of maximum unbalance with 3 pairs of test masses onboard. Note the wedge of dull black friction tape on the otherwise shiny black disk serving as laser reflector.
Test tops deliberately unbalanced in this manner "wobble" at all tested speeds, CM heights, and total unbalances -- usually with minor precession. The wobbling is clearly modulated by gyroscopic effects, but I still think that it represents a form of rigid body whirl rather than gyroscopic nutation.
Prior to testing the laser method, I checked the unbalanced test top for phase angle relative to the known unbalance vector using an adaptation of the paintbrush method (post coming soon). The result was a constant 180° phase angle at all speeds, CM heights, and total unbalances. No surprise then that results with the laser method were also identical under these conditions.
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Topic: Balancing a finger top (twirler) (Read 21123 times)