Rumaging through my Bin of No Return turned up several vintage parts that struck me as top material. The tops seemed to build themselves, as if by channeled Klingons. They nicely illustrate some of the fundamentals of LEGO top design.
About this creation
Please feel free to look over the images and skip the verbiage.
As the first-born of the 4 high-speed finger tops presented below took shape, almost on its own, the feeling that I might be channeling a Klingon spacecraft designer got harder and harder to shake. The 3 tops that followed in rapid succession only strengthened that suspicion.
But there they were: Four vintage parts I'd never had occasion to use, just crying out to be made into tops.
∧ The 3x6 Technic axle connector block (32307, ca. 2000; 2nd from right) was the first to catch my eye. This dense piece with 6 axle holes looked like a secure way to add mass to the periphery of a top rotor, which is where you want a top's mass to be concentrated when long run times are the goal.
I envisioned a similar role for the 3x7x2 Technic forked liftarm (32308, ca. 2000-2001; 2nd from left) found next, though with less favorable aerodynamics and less useful attachment points.
Then I spotted the 1 x 3 x 7 Bionicle Bohrok shoulders (41672, ca. 2002-2008; far left) and Technic gearbox halves (32166, ca. 1999-2000; far right), both of which had potential as rotor spokes.
These Klingon tops are decidedly more for "show" than "go", but I optimized them for run time and sleeping tendency as best I could while keeping to the Klingon look and feel.
∨ All have 3-spoke rotors of various kinds attached to hubs based on wedge-belt pulley wheels, and all use the same light gray, dark gray, and black color scheme.
All 4 tops spin smoothly and have a pleasing rotational "heft" (tantamount to axial rotational inertia) when twirled -- especially DIngwI'Hom.
Rule 4: Smooth spinning requires (i) a well-balanced rotor and hub, (ii) true axles, (iii) a smooth, rounded tip with a small radius of curvature and no flats, and (iv) smooth, level ground. TLG's precision molding prowess really shines here.
Aerodynamics tend to take a back seat to cosmetics in "show" tops, and so it was with these. All 4 hiss and spin down very quickly after release, even when twirled -- sure signs that their run times are strongly limited by aerodynamic drag (hereafter, just "drag").
∨ Considering the poor aerodynamics, the twirled run times put in by these tops (15-29 sec) are pretty good, but the longer-running "go" tops on my finger top page put them all to shame. The 2 tops below are representative of the 2 ends of the twirled run time spectrum.
∧ The exceptionally dirty rotor of the Honeycomb (above left) causes it to spin down faster and hiss louder than even the Klingons. Its best twirled run time is only 14 sec. A lower CM is the only thing that makes Honeycomb competitive with the dirtiest and shortest-running of the Klingons -- Duj puHlI', 15 sec.
∧ Ultra-clean Stack-of-Dishes, on the other hand, loses speed silently and almost imperceptibly. Its best twirled run time of 82 sec beats those of the longest-running Klingons (gheb wewlI' and HeghmoH yor) by a factor of 2.8.
The maximum speeds reached by the Klingon tops when spun up by motor (~1,300 to 2,700 RPM) are also limited by drag.
Run times by motor are only 7-35% longer than by hand. This surprising result is a direct consequence of...
Rule 5: The drag generated by a rotor component is roughly proportional to the square of the product of the radial distance to its CM and the top's angular speed. The braking torque due to that component is then the product of the radial distance to its CM and the drag it produces. The greater the sum of the braking torques due to all rotor components, the shorter the run time.
The low rotor clearances (10-17 mm) and small grounding angles (10-16°) here reflect an attempt to bolster run times by making their CMs as low to the ground as possible. This strategy follows from Rule 2 above.
∨ Much of the strength needed to withstand the centrifugal forces encountered at high speeds resides in (i) the hubs used (below), and (ii) the many strong attachment points provided by the 4 parts from the Bin of No Return.
Rule 6: The centrifugal force felt by a rotor component is proportional to the product of its mass, the radial distance to its CM, and the square of the top's angular speed. Hence, the heavier and more peripheral the component, and especially the faster the top, the stronger the component's attachments to the rotor must be in both tension and sheer.
Each top has its own character, both visually and dynamically. Specifics and close-ups follow.
gheb wewlI' (horns that glow)
∨ I call the first top to emerge from the bin "gheb wewlI'", meaning "horns that glow".
This top has a rotor diameter of 170 mm and a mass of 46 g. Rotor clearance and grounding angle are 17 mm and 10.5°, respectively. Best run times and maximum speeds are 29 sec/690 RPM twirled and 31 sec/1,515 RPM by motor.
Note the huge disparity here: Motorized spin-up improves maximum speed by 120% but run time by only 7%! Welcome to Rule 5.
∧ The Bohrok shoulders make for long, stiff, high-drag rotor spokes with visually interesting offsets and lots of strong attachment points.
∧ All 4 tops use the low-friction tip design above, my best to date. As seen in the video, it promotes sleeping, reduces precession, and all but eliminates walking.
∧ Free axle holes in the 3x6 connector blocks at the ends of the spokes allowed me to add a little extra mass to their undersides at little cost in drag. (See Rule 3 and Rule 5.)
When I mentioned earlier that the Klingons qualify as high-speed finger tops, I left out one small detail: The loosely attached horns on this one tend to fly off at ~1,400 RPM (see Rule 6). (Frankly, it's a miracle they hang on that long.)
∨ However, when the horns are replaced by parts of the same mass but with stronger attachments (below), gheb wewlI' stays in one piece to its maximum speed by motor (1,515 RPM). Since the horns were just gratuitous ornaments, that qualifies it as a high-speed top in my mind.
Having more axial rotational inertia and a smaller grounding angle than DIngwI'Hom (the smallest top here) makes gheb wewlI' the harder of the two to twirl WRT both finger strength and skill. The same reasons make HeghmoH yor a harder twirl as well.
HeghmoH yor (top of death)
I call this top "HeghmoH yor" ("top of death") just because Klingons really go for that stuff.
It has a rotor diameter of 168 mm and a mass of 58 g. Rotor clearance and grounding angle are 17 mm and 11.5°, respectively. Best run times and maximum speeds are 29 sec/580 RPM twirled and 32 sec/1,304 RPM by motor.
As with gheb wewlI' above, motorized spin-up produces a paltry gain in run time despite a large gain in maximum speed thanks to Rule 5.
∧ Note the extra mass added to the forked liftarms at the ends of the rotor spokes -- surely with a drag penalty in this case. Testing to see if run time is ultimately helped or hurt is on the to-do list. (See Rule 3 and Rule 5.)
Duj puHlI' (landing craft)
Words for weapons, gore, and spacecraft dominate the Klingon vocabulary, but coming up with the Klingon equivalent of "landing craft" turned out to be surprisingly difficult. "Duj puHlI'" was the best I could do.
This top has the worst aerodynamics and run times by far, but it's still a lot of fun.
This top has a rotor diameter of 136 mm and a mass of 33 g. Rotor clearance and grounding angle are 10 mm and 10°, respectively. Best run times and maximum speeds are 15 sec/846 RPM twirled and 19 sec/2,110 RPM by motor.
∨ The wheels mounted beneath the gearbox halves making up its rotor allow Duj puHlI' to roll to a stop when it finally topples.
∧ The tires damp out some of the bouncing excited when the wheels first touch down.
The ever-present conflict between CM height and grounding angle was particularly acute in this top. Adding rotor clearance to increase its grounding angle would make twirling it less a test of skill but would also raise its CM, thereby reducing a run time already severely impacted by drag per Rule 5.
Unfortunately, this top's twirled run time turned out to be particularly sensitve to CM height. The 10 mm rotor (wheel) clearance and 10° grounding angle, both the smallest here, were the best I could do without disqualifying Duj puHlI' as a finger top.
DIngwI'Hom (little spinning one)
The Klingon name "DIngwI'Hom" ("little spinning one") acknowledges this top as the smallest here. It's also the cleanest aerodynamcially, the longest-running by motor, and not far behind gheb wewlI' and HeghmoH yor in twirled run time.
This top is the only one to show a significant gain (34%) in run time via motorized spin-up -- a direct consequence of its superior aerodynamics.
It has a rotor diameter of 120 mm and a mass of 35 g. Rotor clearance and grounding angle are 14 mm and 16°, respectively. Best run times and maximum speeds are 26 sec/906 RPM twirled and 35 sec/2,670 RPM by motor.
I was able to pack a lot of low-drag peripheral mass under the 3x6 connector blocks at the ends of the rotor spokes. Hence, axial rotational inertia per unit mass is quite high in spite of the smallish rotor diameter. (See Rule 3.)
Mass vs. mass distribution
Total mass and mass distribution -- i.e., where the mass is located WRT the tip and spin axis -- are recurring themes on this page. Top behavior depends critically on both, and I had to pay extra attention to both to get decent run times out of these tops in spite of their lousy aerodynamics.
The good news: Fine-tuning mass and mass distribution is a heck of a lot easier in tops made with LEGOŽ. And LEGOŽ precision molding really shines when it comes to one aspect of mass distribution -- balance.
The center of mass (CM) of a perfectly balanced top lies on its spin axis. Imbalance shortens run time by diverting rotational energy into unwanted motions like hopping and vibration.
In a well-balanced top, mass and mass distribution affect run time mainly through "topple speed" -- i.e., the speed at which a spinning top becomes unstable and falls over. For a given starting speed and aerodynamic drag coefficient, the lower the topple speed, the longer the run time.
Rule 1: Reducing total mass lowers topple speed by weakening gravity's downward pull on the top's CM. It also reduces friction at the tip.
Rule 2: Moving mass toward the tip in a balanced way parallel to the spin axis lowers topple speed by lowering the height of the top's CM. A lower CM gives gravity less leverage on the top.
Rule 3: Moving mass outward (i.e., directly away from the spin axis) in a balanced way lowers topple speed by increasing the top's ratio of axial rotational inertia (aka moment of inertia) to total mass.
The term "axial" means "with respect to the spin axis".
The tops on this page were designed to be high-speed finger tops.
∧ By "finger top", I mean a top that routinely stays up at least 10 seconds without flying apart when "twirled" (spun up with a twirl of the fingers) with a reasonable amount of muscle and skill (practice).
All of the tops in the photo above from my first finger top page qualify as high-speed tops (defined in a moment), but the blue/orange, black/orange, and DGB tops in the upper right corner fail the (totally arbitrary) 10-second criterion. The rest make the grade as finger tops.
"Ground" here refers to the surface supporting the top's weight via its tip, and "grounding angle" to the spin axis tilt at which the spinning rotor first touches ground.
In this context, "skill" refers to the user's ability to twirl and release a top without tilting it enough to ground its rotor. Skill comes with practice, and some tops demand more than others.
∧ Tops that perform satisfactorily only when spun up with a mechanical aid like the wind-up spinner above and the motorized spinners below don't qualify as finger tops.
These include (i) tops with too much axial rotational inertia for finger strength to overcome, and (ii) tops with wide, low-slung rotors and very small grounding angles.
I think of a "high-speed top" as one that stays together reliably when spun up with a high-speed motorized spinner like those below. The original 9V Technic motors (2838) in these spinners are >30 years old but still going strong.
∨ The smaller motorized spinner is more ergonomic for top spinning purposes but lacks the handy old-style power switch/polarity reverser built into the larger one.
∧ Some tops plateau farther below the no-load speed of ~4,400 RPM than others. Aerodynamic braking is the main culprit here. The braking added by friction between tip and ground is very sensitive to tip design.
Quoting Nerds forprez
Jeremy, I see that you have added video. I have done so in the past with success, but now it won't work. When I embed a vid, it says it will not accept iframes. Any advice?
After much gnashing of teeth, I finally found the secret: In the embedding code, find the string 'src="https://www.youtube.com/embed/*"'. (Using '*' as placeholder for the rest of the URL in this example) Just delete the 'https:' part to make the string read 'src="//www.youtube.com/embed/*"'. No idea why this works.
Thanks for the "well done", Giorgio. Since you're already multilingual (at least Italian and English), you may well know a lot more Klingon than I do (next to none). Did I come anywhere close on the top names?