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Studless tops
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All of these tops have rotors built up almost entirely from studless Technic parts. They include some of my all-time favorites.
About this creation
Please feel free to look over the images and skip the verbiage.

This page showcases a large collection of "studless tops" -- i.e., spinning tops with rotors built up almost entirely from studless Technic parts. The 2 group videos below show all of them in action.





Some of the more interesting specimens are highlighted below. The need to stiffen rotors and tip assemblies to reduce wobbling (aka nutation) in larger tops is a recurring theme.

Additional studless tops can be found in my Topped out folder.

On this page...


Overview

The studless tops presented here have rotors built up from mostly studless parts. (Though technically studless, rotors consisting only of wheels don't qualify.) Any studded parts used (e.g., as decorations) make minor contributions to the tops' total axial moment of inertia (AMI). (See the AMI primer below for details.)

Most of the tops of interest fall into 3 broad structural categories based on rotor construction and mass distribution: (i) Spoke tops, (ii) ring tops, and (iii) hybrids.

Studless spoke tops

"Spoke tops" have 3 or more evenly spaced identical spokes accounting for most of their rotor mass and total AMI. Spooner and Tree Frog below are perfect examples.



Earlier posts qualifying as studless spoke tops include my Klingon tops and the Round Up top in the next 2 photos.





The spokes can be of any size or shape as long as they're well separated over most of their lengths, especially peripherally. In a studless spoke top, the spokes should also be built up primarily from liftarms, axles, axle joiners, angle connectors, or other studless Technic parts.

If interconnections between spokes exist beyond the hub (e.g., to stiffen up the rotor, as in the Maltese Twins below), their contributions to the top's total AMI should be minor.



Studded rotor components should also be minor in the same sense, but that's a stretch in the Maltese Twins' case. No question that they're spoke tops, but at best, they're mostly studless by mass and semi-studless by AMI.

The spokes attach directly to a more or less cylindrical "hub" assembly of relatively small radius. The hub provides a central axle hole for the top's through-going "main axle", which coincides with the top's spin axis.

Some of my favorite hub elements appear below. Note the peripheral pin or axle holes serving as spoke attachment points. The dark orange Hero Factory rapid shooter barrel (98585) at bottom right comes in especially handy in 4-spoke tops.



The tip assembly usually mounts directly on the main axle. In lighter tops like Tree frog, the "stem" -- the part grasped by the fingers during a twirl -- is often just the other end of the main axle.

In heavier tops like Spooner, however, the stem is usually a separate coaxial assembly designed to reduce the muscle needed to get the top spinning from rest.1 My Round Up top appears with its red tip and stem assemblies removed 3 photos back.

The main axle and the stem, hub, and tip assemblies make up the top's through-going central "spindle".



The spindle above is pretty typical. It includes (i) a 7L LBG main axle, (ii) a lime hub with a yellow spoke root attached, (iii) a yellow 2x2 dome serving as tip holder, and (iv) a yellow axle joiner serving as stem holder.

A rotor consisting only of N identical evenly spaced spokes has N-fold rotational symmetry, with N being the "order" or "degree" of symmetry.

Wings below has a rotor with 3-fold symmetry.



Studless rotors with 3, 4, and 6 spokes are fairly easy to arrange. Eight- and 12-fold rotors take more doing. Spoke tops with only 2 spokes are inherently unstable and fall right over.

Studless ring tops

A ring top is basically a spoke top with a substantial, well-defined ring-like structure joining the spokes near their outer ends. Together, the ring and spokes form the rotor. To be a studless ring top, nearly all of the rotor's AMI should come from studless parts -- especially in the ring.

Tank Top Too below is the quintessential ring top.



Studless rings are usually polygonal in planform with 3-, 4-, 6-, 8-, 12-, or 16-fold symmetry, but higher symmetries are also possible. Importantly, the ring and spoke symmetries need not match. For example, Tank Top Too's ring and spokes are 54- and 3-fold, respectively.

The ring is the star of show in a ring top for one simple reason: For a given maximum radius, no shape packs more AMI per unit mass than a thin ring. The ring may or may not account for most of the top's rotor mass, but it will supply most of the top's total AMI in a true ring top. (See AMI primer.)

The spokes and spindle serve as the ring's "suspension system". The wider and heavier the rotor, the more rigid the suspension system needs to be to keep the top from wobbling (nutating) as it spins and precesses. Wobbling detracts from both smoothness and spin time.

The studded ring tops in the next 2 photos differ from studless ring tops only in having, well, studded rings.



I make frequent use of the studless 3-spoke suspension system seen in the colorful Reuleaux top above.



The black and white ring top illustrates a useful rule of thumb equally applicable to its studless counterparts: A 2-spoke ring top won't have any trouble staying up if the AMI of the ring greatly exceeds that of its suspension system.

It's no coincidence that the 7 longest spin times on this page all go to ring tops. Nor is it a coincidence that the smoothest-spinning tops are mostly ring tops.

Compared to a spoke top of the same total mass and center of mass (CM) height, a ring top will have the greater AMI and therefore the lower "topple speed" -- i.e., the speed at which the top loses stability and falls over.

Given identical release speeds and aerodynamic and frictional losses, the ring top will therefore stay up longer because it will need more time to spin down its lower topple speed. But the "ring top advantage" doesn't end there, for the aerodynamic and frictional losses often tilt in the ring top's favor as well.

Indeed, from a performance perspective, it's fair to say that ring tops put their mass to better use than just about any other design, including the spoke top. The only way to improve on that is to spend a little mass on cleaning up the aerodynamics, as I did with the clear fairings applied to the rotor on my Technic free gyro:



Hybrids

Spoke tops and ring tops represent two ends of a spectrum in rotor design. In between are tops with substantial peripheral linkages between spokes but no distinct ring. I think of them as spoke-ring hybrids, or "hybrids" for short. As usual, most of the rotor's AMI will come from studless parts in a studless hybrid.

The next photo shows some typical studless hybrids. Tops with rotors built up from thin liftarms generally fall into this category.



The next hybrid is anything but studless.



Hybrid rotors tend to be web-like, without clear boundaries between the spokes and their linkages.

The bad news: That makes for a lot of aerodynamic drag, and spin times suffer accordingly -- often severely.

The good news: Hybrid rotors, with all their intricacies, often produce striking optical effects when spinning under pulsing light sources like overhead LEDs on dimmers.

<< Back to top




Featured tops

Below are photos and additional videos of some of the more interesting specimens from the group videos at the top of the page.

The spin times reported below represent the best out of at least three twirls by hand on a best-case surface (polished fine-grained granite). Times on the glass table top in the group videos and photos can run shorter by as much as 50%. The glass also exacerbates wobbling and squeaking.


Spooner
Type = 6-fold spoke; diameter = 186 mm; mass = 70 g; spin time = 8 sec
Tree Frog
Type = 3-fold spoke; diameter = 137 mm; mass = 32 g; spin time = 23 sec

I was drinking down the last of a midnight bowl of soup when I saw it: All 6 kitchen ceiling cans visible at once in the spoon I'd placed upside down on the counter. A BrickLink order later, I had "Spooner", with 6 convex reflectors made from shiny black Bohrok windscreens (41671).





The spoke colors of the smaller top -- another clear-cut studless spoke top -- are those of certain tree frogs and the flag of the Federal Republic of Germany (FRG).

Spooner doesn't stay up long, but it's excellent at what it was designed to do -- namely, to generate swirling orbits of light from overhead fixtures. You can see it in action at the end of the video below.



My tops seem to be popular at shows. None gets more "oohs" and "aahs" than a Spooner spinning under convention hall lights.


Dark Green
Type = 4-fold spoke; diameter = 112 mm; mass = 37 g; spin time = 13 sec
Black and White
Type = 6-fold spoke; diameter = 99 mm; mass = 37 g; spin time = 25 sec

Here we have 2 more simple studless spoke tops with different hubs but similar spokes built up from thick Technic liftarms. You can't see it in the videos, but "Dark Green" smears out to form a handsome glistening surface of revolution when spinning.





Four-fold rotors are easily arranged in studded tops but much harder than 3- and 6-fold rotors in studless ones. The easiest foundation for a 4-fold studless hub is the 40-tooth spur gear seen here on the left.


Wings
Type = 3-fold spoke; diameter = 243 mm; mass = 22 g; spin time = 12 sec

Here's an even simpler spoke top. Exceptional smoothness and a very low topple speed endow "Wings" with a certain stately elegance in motion.


48


The spokes really are wings, BTW. They generate lift when spinning counterclockwise (as seen from above) and downforce when spinning the other way. By counteracting gravity to some extent, lift ought to keep the top up longer, but spin times are about the same in both directions.





Each spoke consists of a pair of black axle joiners, a white #6 long smooth Technic fairing, and various axles and fasteners. Spinning Wings up with a motorized tool can easily send the spokes flying, but it holds together well enough when twirled by hand.


Tank Top (DBG)
Type = 51-fold ring with 3 spokes; diameter = 200 mm; mass = 112 g; spin time = 38 sec
Tank Top Too (black)
Type = 54-fold ring with 3 spokes; diameter = 214 mm; mass = 135 g; spin time = 36 sec

The original DBG "Tank Top" below (the one in the group videos) is a classic ring top with a huge AMI that limits release speed (my fingers are only so strong) but reduces topple speed even more. The net result is the 2nd longest spin time on this page.









It never fails: The best way to find out how you should have made an MOC is to start a MOCpage for it. All the flaws and missed opportunities come leaping off the screen. The good news: Overlooked solutions are often not far behind.

Hence, "Tank Top Too" below. This dashing black and red version isn't just better-looking. It's also much smoother and much more inclined to sleep than precess.









The small hit in spin time (36 vs. 38 sec, still the 5th best on this page) could reflect differences in aerodynamics or tip friction, but Tank Top Too's greater AMI pushes my fingers to the limit. Hence, the added AMI may well have reduced release speed more than topple speed in this case.


Tube Top
Type = 16-fold ring with 4 spokes; diameter = 128 mm; mass = 151 g; spin time = 46 sec
Circle and Square
Type = 16- and 4-fold rings with 4 spokes; diameter = 128 mm; mass = 53 g; spin time = 37 sec

These 2 ring tops sport compound rings. Both produce long, smooth spins and interesting optical effects.

Yellow and black "Tube Top" is the longest-spinning top here by a wide margin. Its tall ring -- a stack of 7 rings of #3 angle connectors -- accounts for nearly 80% of its total mass and nearly all of its AMI.





"Circle and Square", the smaller white, red, and black top, has 2 rings, one 16-fold and the other 4-fold. In motion, the spokes and other black parts vanish, leaving the colored portions of the rings to smear out concentric white and red circles with an interesting 3D relationship.

Coming up with a sufficiently rigid but unobtrusive suspension system was the big challenge in both cases.







Thanks to friend and fellow DENLUG member Shawn Kelly for suggesting the spiral pattern on Tube Top's ring.


Ripsaw
Type = 16-fold (outer) ring with 4 spokes; diameter = 160 mm; mass = 65 g; spin time = 37 sec
Pulsar
Type = 6-fold (outer) ring with 6 spokes; diameter = 143 mm; mass = 48 g; spin time = 21 sec

As required, these ring tops get most of their AMI from their distinct outer rings. Their lesser inner rings (hidden beneath the domes in smaller Pulsar's case) promote smoothness by damping out rotor vibrations that could otherwise lead to wobbling. The studded ornaments have little effect on their behavior.



Like Spooner's Bohrok windscreens, the shiny convex dark orange dishes adorning Ripsaw's spokes generate whirling orbits of light from the reflections of overhead light fixtures.



The fins and small holes in Ripsaw's otherwise circular ring reduce its rotational symmetry to 16-fold. Without them, its ring symmetry would be almost "continuous" -- i.e., of infinite degree.

Pulsar's mass distribution is perfectly symmetric, but its color distribution is not. This asymmetry and the stark black-white contrasts combine to produce a flashing appearance in motion.







Moving the white parts around the rotor alters the frequency and relative phasing of the inner and outer flashes.

To test the theory that Ripsaw's stiffening inner ring has much to do with its exceptional smoothness, I built a test top with the same outer ring but left the spokes unlinked.





It wobbles a good bit more than Ripsaw, but I like the way it looks.


Black and Blue
Type = 4-fold hybrid; diameter = 133 mm; mass = 50 g; spin time = 14 sec
Blue and Yellow
Type = 4-fold hybrid; diameter = 110 mm; mass = 43 g; spin time = 15 sec
Green and Orange
Type = 4-fold hybrid; diameter = 80 mm; mass = 35 g; spin time = 18 sec

These colorful hybrids fall somewhere between spoke and ring tops. Their extremely rigid rotors make for smooth spins, but lousy aerodynamics cut deeply into their spin times.





As mentioned earlier, the intricate rotor geometries and high-contrast colors generate interesting dynamic patterns under pulsed light sources like LED overheads on dimmers.


Ellipse
Type = 2-fold elliptical ring with 4 spokes; diameter = 112 mm; mass = 43 g; spin time = 23 sec
Squircle
Type = 4-fold ~circular ring with 4 spokes; diameter = 52 mm; mass = 17 g; spin time = 33 sec

Little yellow "Squircle" (from "squared-off circle") is one my favorite tops. It has a very pleasant feel when twirled and cranks out long, smooth spins every time. It has the 6th longest spin time on this page.



Squircle's clearly a ring top with 4-fold rotor symmetry.



"Ellipse", the larger top, is harder to classify, being somewhere between a ring top and a hybrid. For reasons I won't go into here, its 2-fold ring and spoke symmetries don't render it unstable, but they do increase its topple speed considerably.


Big Bird
Type = 3-fold hybrid; diameter = 116 mm; mass = 115 g; spin time = 7 sec

Big yellow things always remind me of Big Bird, the Sesame Street character. Twirling this Big Bird takes a lot of muscle and practice, but it's remarkably smooth for its size, and it loves to sleep.







Big Bird is clearly a hybrid. This is what passes for a spoke.



Polygonal rotors make for bumpy landings, and triagonal rotors are the worst by far. These little landing gears turned Big Bird's touch-downs from violent to smooth.



It took me a long time to tumble to rhythmic flexing of rotors and tip assemblies as a major cause of the wobbling that had plagued so many of my large tops. Big Bird came on the heels of that discovery. Cross-bracing the heck out of its rotor and heavily reinforcing its tip assembly worked well.


Maltese Twins
Type = 4-fold spoke; diameter = 204 mm; mass = 110 g; spin time = 8 sec

My experiments with studless tops were just getting underway when I came into a large number of largely unwanted gold 2x2 round tiles. They clashed with nearly everything I owned but went pretty well with some dark green and dark blue 12x3 wedge plates I happened to have on hand. The "Maltese Twins" were born.





The Twins qualify as spoke tops because the stiffening struts between spokes don't contribute much in the way of mass or AMI. Truth be told, their studded ornaments disqualify them as "studless", but they're mostly studless by mass if not by AMI.

The dark blue version has always wobbled less than its dark green twin, identical except for color. Since succumbing to my ongoing top obsession a year ago, eliminating mysterious wobbles in large tops has become a way of life.


Diffractor
Type = 3-fold hybrid (originally 6-fold); diameter = 176 mm; mass = 75 g; spin time = 13 sec

Why settle for a fixed color scheme when your top can change its own colors just by doing what comes naturally (precessing and wobbling)? That's the premise behind "Diffractor".



The video above shows the original Diffractor at work in late afternoon sun. Pretty trippy, huh?

Diffractor's basically just a vehicle for a disk of "holographic paper" (read "cheap diffraction grating") salvaged from some blank DVD packaging. A more recent version appears in the group videos and the next 3 photos.







Prior versions of Diffractor were all classic spoke tops with completely separate spokes. Problem was, those long, slender spokes were inclined to bend back during spin-up and then oscillate like horizontal pendulums during spin-down. The result was a chronic wobble that detracted from both spin time and the desired optical effect.

However, nearly all of the wobbling went away when I fitted a sturdier tip assembly and the lime spoke cross-braces seen in the current Diffractor below.





For all you symmetry buffs out there, the new braces effectively reduce spoke symmetry from 6-fold to 3-fold.


Blue Rose
Type = ~12-fold hybrid; diameter = 110 mm; mass = 78 g; spin time = 22 sec

The 12-fold hub for this almost 12-fold rotor came from friend and fellow DENLUG member Ian Davis, who devised it for a project having nothing to with tops but knew exactly what I'd do with it.







The rotor also had perfect 12-fold symmetry until I added the inner set of 6 cross-linking 1x3 liftarms to suppress wobbling. The resulting uneven spacing of the spokes reduced the symmetry to 6-fold, but the top does spin a lot more smoothly now.


Quadcopter
Type = 4-fold spoke; diameter = 158 mm; mass = 72 g; spin time = 9 sec
Three Aces
Type = 3-fold spoke; diameter = 116 mm; mass = 31 g; spin time = 6 sec

Neither of these spoke tops stay up long, but they're fun anyway.





Black and white "Quadcopter" rose out of a determination to find a use for the "Round 7x7x4 Dome Top" (57587) forming its superstructure. Quadcopter also reminds me of a spacecraft.


qlj Duj
Type = 3-fold hybrid; diameter = 121 mm; mass = 48 g; spin time = 15 sec
Doq Duj
Type = 3-fold spoke; diameter = 147 mm; mass = 35 g; spin time = 13 sec

Behold the latest additions to my fleet of Klingon tops: "qlj Duj" (black ship) and "Doq Duj" (orange ship).2





Like all Klingon tops, they're studless, belligerent, funky, and into old grays. Their short spin times, representative of the genre, reflect the characteristically lousy aerodynamics. The great rigidity of qlj Duj's rotor makes it the smoother of the two by far.


Six-wheeler
Type = 3-fold hybrid; diameter = 100 mm; mass = 61 g; spin time = 15 sec

I just couldn't resist turning the cool wheels favorite builder David Roberts put on his Wheelie Big Bike into a top. (Warning: Stealing ideas from David Roberts may be habit-forming.)





Black cross-braces bind the 6 rays emanating from the hub into 3 spokes of 2 wheels each. The rubber tread binding the spokes together would have 36-fold symmetry if the black wheels didn't make it so lumpy. The top is a lot smoother than I ever expected.


Iris
Type = 16-fold expanding ring with 4 spokes; diameter = 162 mm at rest; mass = 110 g; spin time = 10 sec
Governor
Type = 3-fold spoke; diameter = 119 mm at rest; mass = 41 g; spin time = 17 sec

Centrifugal force is a fact of life in spinning top rotors. These "centrifuge tops" put it to good use.

"Iris" is a true studless ring top whose ring happens to expand under centrifugal force during spin-up and retract under rubber band tension during spin-down. The ring design incorporates a planar version of the bent scissors linkage used in Hoberman spheres.





"Governor" (named for its mechanical resemblance to a centrifugal governer) is clearly a spoke top but doesn't really qualify as a studless one, as most of its AMI resides in the studded black and orange "flyballs" at the ends of its folding spokes.

The bronze return spring wrapped around Governor's main axle is one of only 2 non-LEGO® parts on this page, the other being Diffractor's diffraction disk.




Turntable, Yellow
Type = 4-fold ring; diameter = 113 mm; mass = 57 g; spin time = 27 sec
Turntable, Black
Type = 4-fold hybrid; diameter = 86 mm; mass = 43 g; spin time = 9 sec

Can a Technic turntable be subverted into a top hub? I kinda doubted it when the question first entered my mind, but these two hybrids answer in the affirmative.





The yellow one, which I consider a ring top, claims the 7th longest spin time here and spins quite smoothly. The black one, which approaches a ring top, needs some stiffening, but I like the way it looks.


Diamonds and Rubies
Type = 6-fold hybrid; diameter = 181 mm; mass = 70 g; spin time = 5 sec

This crystalline hybrid has a lot of visual appeal in the right light, both at rest and in motion. I'm also rather proud of the way its rotor came together.







However, it's no gem when it comes to performance. It has the shortest spin time on this page and a nasty wobble that just won't go away.

<< Back to top




Primer: Axial moment of inertia (AMI) in tops

After spending most of this obscenely long page blathering on about axial moment of inertia (AMI), I should probably blather on a while longer about the nuts and bolts of AMI and its implications for the design and use of LEGO® spinning tops.

Be forewarned: The picture/text ratio is about to go way down.

AMI as a rotational analog of mass

As the embodiment of inertia, mass measures a body's resistance to (linear) acceleration by an external force. This is the gist of Newton's Second Law,

F = m a,

where F is the net force acting on the body in Newtons (kg m s-2), m is the body's mass in kg, and a is the resulting (linear) acceleration of the body's center of mass (CM) in m s-2.

The boldface symbols above denote quantities that are properly vectors with both magnitude and direction. In the special cases of interest here, however, we'll be able to treat all quantities as scalars with magnitude only.

An important lesson from the Second Law is that if the mass doubles, so does the net force required to achieve the same acceleration.

In the realm of purely rotational rigid body motion inhabited by tops that spin in place, the analog of mass is moment of inertia (MI).

The rotational equivalent of Newton's Second Law in a top context is

T = I3 α,

where I3 is the magnitude of the top's MI about its spin axis in kg m 2. We've assumed that the spin axis (here identified by its conventional subscript "3") coincides with the top's axis of rotational symmetry and passes through its CM, as it would in any well-balanced top. Hence, I3 goes by the name "axial moment of inertia", or AMI for short.

The analog of force here is T -- the magnitude of the net torque applied about the spin axis in N m (say, by the fingers to the stem during a twirl). And the analog of linear acceleration is α -- the magnitude of the resulting angular acceleration about the spin axis in radians per second per second (rad s-2 or just s-2).

Clearly, doubling the AMI doubles the torque needed to achieve the same angular acceleration about the same spin axis. (Note that we're able to stick with scalars here only because all the players -- the AMI, net torque, and angular acceleration -- refer to the same axis.)

Example: AMI, torque, and angular acceleration on a carousel

You're on a small carousel at rest when the operator starts the "spin motor" -- the one that causes the carousel to spin. A separate motor moves the horses up and down. Since we're focused exclusively on motions about the carousel's vertical spin axis here, the horses' vertical motions parallel to the spin axis will have no bearing on our conclusions.

A patient friend waits on a bench beside the carousel. As the carousel speeds up, the angle between you and your stationary friend, taken at the spin axis, starts to increase at an increasing rate -- i.e., to accelerate. At any given instant, the angle's observed rate of change per unit time is your "angular speed" ω, and the observed rate of change of ω per unit time is your "angular acceleration" α. (If f is the carousel's "rotational frequency" in RPM, then ω = π f / 30.)

The "angular" quantities ω and α are clearly analogous to speed and acceleration in a car, respectively, but they differ fundamentally in perspective. Angular measures of motion focus specifically on the accumulation of angular separation from a particular starting angle in the course of a rotation about a particular axis.

"Linear" measures of motion focus instead on the accumulation of distance along a particular path through space from a particular starting point, whether or not that path happens to be a straight line. Each perspective can always be transformed into the other, but the math involved is simple only in the very special case we're interested in here -- namely, motion along a circular path, with the axis of interest perpendicular to the plane of the circle and through its center.

Now back to the carousel: If you and your horse move as one, and the carousel is the rigid body you hope it is, then every other horse, pole, plank, nut, and bolt on the carousel will see the same α and ω about the spin axis that you do. (Likewise, every part in a perfectly rigid LEGO® spinning top sees the same α and ω.) Less well-behaved fellow riders might be a different story, but assume for now that everyone onboard moves as one with their horses.

If the total AMI of the carousel and all its occupants about the spin axis is I3, then the net torque about the spin axis due to the spin motor, friction, and air resistance combined must be T = I3 α.

A heavy passenger texting while riding an outermost horse now drops his brand new cell phone and leaps clear off the carousel after it. The sudden loss of peripheral mass causes a significant instantaneous decrease in the small carousel's total I3. If the net torque T stays the same, at least transiently, you'll observe at least a transient surge in α (and therefore in ω), because the carousel just lost some its resistance to angular acceleration by a net torque.

The carousel's speed has finally leveled off, meaning that the angular speed ω is now constant, and the angular acceleration α has gone to zero. The latter can only mean that the net torque T about the spin axis has gone to zero as well.

The spin motor's straining less now, because all it needs to do to maintain a constant ω is to offset the opposing torques about the spin axis due to friction and air resistance at that speed. The operator's spin motor torque gauge now reads Tsm = 1,000 N m. Hence, the combined torque due to friction and air resistance at that moment must be -1,000 N m. Simple as that.

AMI, muscle, and spin-up time

Now let's apply the last equation to the act of twirling a top with the fingers. If we accelerate the top from rest to a given release speed (ω0, in rad s-1) in a given spin-up time (Δt, in s),

α = ω0 / Δt,

where α is now the magnitude of the average angular acceleration during the twirl.

The magnitude T of the average torque needed to reach release speed ω0 in a spin-up time Δt would then have to be

T = I3 α = I3 ω0 / Δt

Hence, doubling the AMI doubles the average torque needed to reach the same release speed in the same spin-up time.

The simple relationships among AMI, torque, release speed, and spin-up time developed here are approximate, to be sure. However, they're still quite useful in thinking about and manipulating real top behavior.

For example, we now understand why Tank Top Too, the big black ring top below, is much harder to spin-up quickly than Squircle, the little yellow one.





The masses and maximum radii of Tank Top Too and Squircle differ by factors of ~8 and ~4, respectively. However, their AMIs differ by a factor of well over 100. Hence, my fingers have to work much, much harder to get the bigger top up to, say, 42 rad s-1 (400 RPM) in a 1-second twirl.

Truth be told, I'd be lucky to get Tank Top Too to 400 RPM by hand, and holding Squircle down to 400 RPM would take a very delicate touch.

AMI and spin-down

As we saw at the end of the carousel example, the relationship between torque and angular acceleration cuts both ways, in that the absence of angular acceleration implies the absence of net torque. The converse is also true: The presence of an angular acceleration or deceleration is a sure sign of a causative net torque at work.

The braking torques that cause real tops to lose angular speed during the spin-down phase following release are twofold -- frictional and aerodynamic. The frictional torque acting on the tip is complex, but a portion of it is roughly proportional to the top's weight and therefore to its total mass.

With a low-friction tip design like the one used here, however, the dominant braking torque will generally come from aerodynamic drag acting on the rotor. That's certainly the case with really dirty tops like the 3 hybrids below. (Also note the low-friction tips.)



Better aerodynamics -- e.g., through avoidance of exposed studs and axle and pin holes, or the addition of smooth fairings -- can substantially reduce the deceleration during spin-down by attacking the drag itself, with potentially big gains in spin time. Sleek Stack of Dishes below stays up 82 sec due a combination of low drag and high AMI.



And that brings us to a crucial role of AMI during spin-down: Doubling the AMI halves the deceleration resulting from the same braking torque.

Granted, total drag is roughly proportional to exposed surface area, and greater AMI generally means more spinning surface area in contact with the surrounding air. (Ultimately, that harks back to the fact that LEGO® parts don't vary much in average density). However, upping the AMI as a defense against drag can still pay royally.

In ring tops, for example, AMI tends to grow much faster with rotor radius than exposed surface area does. If the spokes don't get too dirty in the process, going for more AMI by enlarging the ring radially can significantly reduce the deceleration due to drag braking, even if tip friction and rotor drag end up growing some along the way.

AMI and mass distribution

Mass and AMI both depend on the amount of matter the top contains. Indeed, AMI is proportional to total mass. But unlike mass, AMI also depends -- and quite strongly so -- on the top's shape, internal mass distribution, and orientation relative to the axis of interest (here, the top's spin axis).

Here's the difference in a nutshell: Simply reshaping a lump of clay won't change its mass, but it can easily change the lump's AMI about a given axis if the reshaping shifts mass toward or away from the axis.

It follows that a LEGO® top's AMI is sensitive to both the masses of its parts and the distances between their individual CMs and the spin axis -- especially the latter. Given 2 tops with the same mass, the one with more of its mass farther from the spin axis will have the larger AMI -- perhaps much larger.

AMI's strong dependence on mass distribution explains why ring tops have greater AMIs than spoke tops of the same mass, and why hybrids tend to fall between these extremes.

The original Tank Top (all gray, 112 g) and the blue and green Maltese Twins (110 g) below are cases in point. Their masses are nearly identical, but the peripheral concentration of mass in the ring top makes for a much greater AMI, and that by itself makes the ring top a good bit harder to twirl.





AMI, angular momentum, and spin time

AMI and CM height (measured with the top vertical) are the 2 most important direct controls on spin time in the absence of aerodynamic drag and friction. Next in line is the transverse moment of inertia (TMI) taken through the tip about an axis perpendicular to the spin axis. AMI correlates strongly and positively with spin time, while CM height correlates negatively and even more strongly. TMI's effect is also adverse.

Moment of inertia is also the rotational analog of mass when it comes to momentum:

p = m v          ⇔          L = I3 ω

where p is the (linear) momentum in kg m s-1, v is the (linear) velocity in m s-1, L is the angular momentum about the spin axis in kg m 2 s-1, and ω is the associated angular velocity about the spin axis in rad s-1 or simply s-1.

Since angular momentum about the spin axis is ultimately what keeps a spinning top up against gravity, we'll prolong the top's spin by endowing it with a large I3, a high release speed (ω0), or both.

In practice, however, I3 and ω0 eventually come into conflict via the maximum torque the fingers can apply to the stem. Once I3 becomes too large to handle, release speed ω0 inevitably suffers. If the "topple speed" (at which the top loses stability and falls over) remains constant, the only result can be a shorter spin time.

The sweet spot in this highly nonlinear trade-off between AMI and release speed depends critically on the twirler and the recent practice he or she has had with high-AMI tops. Finding the sweet spot involves careful (read "tedious") measurements of the release speeds and spin times the twirler can reliably generate.

Relative ring and spoke contributions to AMI in ring tops -- a simple model

You can get a good feel for the relative contributions of the ring and spokes to a ring top's AMI with a simple model that describes Tank Top, Tank Top Too, and Tube Top (on the right below) fairly well. Not coincidentally, these 3 ring tops are among the 4 longest-spinning tops on this page.



Now for the model: Assume a rotor consisting solely of (i) a thin circular ring of mass Mr and radius R, and (ii) a set of identical thin rod-like spokes of length R and combined mass Ms. "Thin" here means that the thicknesses of the ring and the spokes (in planes perpendicular to the spin axis) are small compared to R.

For a given maximum radius (here R), no shape packs more AMI per unit mass than a thin circular ring. The AMI due our ring alone is

I3r = Mr R 2,

while the combined AMI due to all the spokes is

I3s = Ms R 2 / 3

Note the strong dependence on R in both cases. Note also that Is doesn't depend on the number of spokes making up Ms.

If we write the ring/spoke mass ratio as

qM = Mr / Ms

and let I3 be the total AMI of the rotor, then

I3 = I3r + I3s

I3r / I3s = 3 qM

I3r / I3 = 3 qM / (3 qM + 1)

To get a feel for what these equations really mean, consider the reference case of a rotor with half of its mass in the ring:

qM = 1, I3r / I3s = 3.0, and I3r / I3 = 0.75.

In other words, a ring accounting for 50% of the rotor mass contributes 75% of the rotor's total AMI. The reason: The ring's half of the mass is on average farther from the spin axis.

Now look at the numbers for the 3 ring tops that best fit our simple model:

Tube Top: qM = 4, I3r / I3s = 12, and I3r / I3 = 0.92.

Tank Top: qM = 1.7, I3r / I3s = 5.2, and I3r / I3 = 0.84.

Tank Top Too: qM = 1.6, I3r / I3s = 4.8, and I3r / I3 = 0.83.

Some final words about transverse moment of inertia (TMI)

In top parlance, any axis perpendicular to the spin axis is a "transverse axis". The only transverse axis of interest in top dynamics is one through the top's tip, not its CM, and that's the one to which the top's "transverse moment of inertia" (TMI) is referred.

What's so magic about this particular transverse axis? Simple: It's the axis about which the torque exerted on the top by gravity acts. That "gravitational torque" appears the moment the spin axis leaves the vertical and only grows as the top leans toward the horizontal. Though aerodynamic drag and friction may slow a top before its time, gravitational torque is ultimately what brings it down.

From a practical standpoint, high AMI/TMI ratios generally promote long, smooth spins, with the smoothness coming by way of reduced "wobbling" -- the pesky nodding motion also known as nutation. And this correlation also plays in the ring top's favor, as a high AMI/TMI ratio generally follows from a high AMI per unit mass.

TMI has no direct effect on the muscle required for spin-up, and therefore no direct effect on release speed. However, it does have a predictable adverse effect on topple speed in that it increases topple speed, which in turn decreases spin time at constant release speed. TMI's effect on topple speed isn't as dramatic as those due to AMI and CM height, but it's still quite significant.

TMI and CM height (h, taken with the spin axis vertical) are deeply interwined. Increasing h affects a top in 2 critical ways: (i) By amplifying the gravitational torque in direct proportion to h, and (ii) by effectively moving the rotor's mass away from the tip, where the TMI is taken. By the parallel axis theorem, the latter effect bumps up the TMI by an amount equal to m h 2, where m is the top's total mass. Both effects hasten the top's fall.

As alluded to earlier, TMI also influences the frequency and amplitude of wobbling. Since wobbling frequency is proportional to the top's AMI/TMI ratio, the higher the TMI, the slower the wobble. The relationship between TMI and amplitude is much more complicated. However, if they wobble at all, fast-spinning tops with high AMI/TMI ratios tend have high-frequency, low-amplitude wobbles that are often little more than inconspicuous shivers.

Since TMI's harder to deal with mathematically than AMI in tops, I'll leave it at that for now.

<< Back to top




Specifications
(Tops with photos on this page only)
Types:Studless spoke, ring, hybrid, and miscellaneous
Maximum rotor diameters:52-243 mm
Total masses:17-135 g
Best spin times by hand:5-46 sec
Modified LEGO® parts:All tips (cut from 4L round-tipped antennas)
Non-LEGO® parts:Diffraction disk on Diffractor; return spring on Governor
Credits:All tops are original MOCs, but the idea for Six-wheeler came from favorite builder David Roberts





Footnotes

1 Tops that take a lot of muscle to twirl benefit from stems of 2 different diameters -- a larger one lower down to get the top going and a smaller one above to finish at the highest possible speed. Such stems are essentially 2-speed transmissions.

2 If Klingons really can pronounce "qlj", and I have my doubts, the question becomes, why would they want to??



Comments

 I made it 
  November 15, 2015
Quoting Oliver Becker Another great wheel going round, Jeremy! I like your video- clips, also nice music! But here I thought "Spinning wheel" by Blood, Sweat and Tears could match also... ;)
Many thanks for those kind words, Oliver. I'll have to try that tune with my next top video.
 I like it 
  November 15, 2015
Another great wheel going round, Jeremy! I like your video- clips, also nice music! But here I thought "Spinning wheel" by Blood, Sweat and Tears could match also... ;)
 I made it 
  November 7, 2015
Quoting Nerds forprez All those colors!! I love it. Have to say, dangerous for kids to watch though..... Our 5 year old neighbor was over while I was watching the youtube vids.... he then thought it would be fun to emulate the tops for the next 20 minutes..... lol....
Thanks! To make up for that unintended consequence, I worked out a fix for you: Sit the kid down on the sofa and apply 2-inch wide Velcro straps as needed across torso and all extremities. They stick to most upholstery really well.
 I made it 
  November 7, 2015
Quoting Nick Barrett The simple elegance and high performance of the three bladed Technic panel one steals the show for me; fascinating post Jeremy, thanks for sharing.
Too kind, Nick. I like that one a lot, too. Some tops just turn out to be nice objects -- in some cases, when at rest, and in others, when spinning. Not art, perhaps, but they provide that kind of outlet.
 I like it 
  November 7, 2015
The simple elegance and high performance of the three bladed Technic panel one steals the show for me; fascinating post Jeremy, thanks for sharing.
 I made it 
  November 6, 2015
Quoting Clayton Marchetti Outstanding collection of Tops!
Thanks, Clayton!
 I like it 
  November 6, 2015
All those colors!! I love it. Have to say, dangerous for kids to watch though..... Our 5 year old neighbor was over while I was watching the youtube vids.... he then thought it would be fun to emulate the tops for the next 20 minutes..... lol....
 I like it 
  November 6, 2015
Outstanding collection of Tops!
  November 5, 2015
I know what you mean about how terrible the older wind-up motors were. When I built a whole bunch of wind-up cars (which is how I was introduced to Technic) all Lego had was the older-style ones. I got around the performance handicap about 2 years ago when I created a hybrid 4WD wind-up car that used a rubber band and gearing platform to drive the front wheels. But then I got the new motor when it came out and was shocked at how fast and powerful it was! I believe a new 4WD hybrid is in order soon...
 I made it 
  November 5, 2015
Quoting Didier B Wow ! Impressive work. I published one spinning top yesterday maybe few minutes after yours. But, I see your page now because of server down. As you seem to be specialist I would appreciate to get your opinion on mine too. Thanks Didier
Thanks, Didier! My wife would favor the term "obsessionist" over "specialist", but I like your spin better. Loved your top! Designing for visual effects in motion is one of my favorite parts of top-building.
 I like it 
  November 5, 2015
Wow ! Impressive work. I published one spinning top yesterday maybe few minutes after yours. But, I see your page now because of server down. As you seem to be specialist I would appreciate to get your opinion on mine too. Thanks Didier
 I made it 
  November 5, 2015
Quoting Topsy Creatori Hey, hey... the pages are working! Now that I know their names I can say... #1 Iris is my favorite for looks. #2 Pulsar is my favorite for looks and rotation time. #3 Blue Rose is a win for its use of those, what I consider, useless Technic capital L pieces! #4 Big Bird reminds me of Pascal's triangle... wellll.... sort of! :)
Thanks for the ranking, Topsy! Your picks aren't far from my own, though I'm particularly partial to Spooner for its optical effects. Hadn't thought of Pascal's triangle, but I can see it now that you mention it. As for those L-pieces, consider them the main enforcers of perpendicularity and rigidity in the studless realm, though they do neither in Blue Rose.
 I like it 
  November 5, 2015
Hey, hey... the pages are working! Now that I know their names I can say... #1 Iris is my favorite for looks. #2 Pulsar is my favorite for looks and rotation time. #3 Blue Rose is a win for its use of those, what I consider, useless Technic capital L pieces! #4 Big Bird reminds me of Pascal's triangle... wellll.... sort of! :)
 I made it 
  November 5, 2015
Quoting jds 7777 Another massive article to cement you as one of the most detail-oriented people on Mocpages. (At least in terms of performance. Which is great!) An excellent post! If you use a new-style lego wind-up motor you could really see these things go! The Tank Top II could really get going then!
Many thanks, JDS! You're spot-on about the latest wind-up motor. The reversible flying rotor launcher I posted a while back at http://www.mocpages.com/moc.php/418125 started out as a top spinner. None of the older wind-ups I've tried can hold a candle to the current one for either purpose.
 I made it 
  November 5, 2015
Quoting Gabor Pauler MOAT = Mother Of All Tops
Thanks, Gabor! MOATC = Mother of all Top Compliments
 I made it 
  November 5, 2015
Quoting David Roberts Sorry, yes thank you for crediting my builds! As others have said, you've definitely succeeded in your intention of providing a reference book. In my opinion this is a great reference for some interesting building techniques and not just spinning tops. I hope more people discover it, comment on it and like it.
Too kind, David. As they say, finding solutions is usually a matter of asking the right questions. Studless tops just have a way of bringing up questions I'd never thought to ask before.
 I made it 
  November 5, 2015
Quoting Matt Bace Wow! It looks like you have been pretty busy. These are all pretty impressive, but I think my personal favorite is the Round Up Top. Many of these have interesting and somewhat complicated geometries (like the Big Bird Top). I am definitely going to have to come back here at some point in the future, because I am certain that there are quite a few good building tricks involved in some of these creations. Great job!
Many thanks, Matt! Agree, the geometries make this top genre especially fun. The fact that there's almost always a decent-looking solution, no matter how improbable the geometry, never ceases to amaze me.
 I like it 
  November 5, 2015
Another massive article to cement you as one of the most detail-oriented people on Mocpages. (At least in terms of performance. Which is great!) An excellent post! If you use a new-style lego wind-up motor you could really see these things go! The Tank Top II could really get going then!
 I like it 
  November 5, 2015
Sorry, yes thank you for crediting my builds! As others have said, you've definitely succeeded in your intention of providing a reference book. In my opinion this is a great reference for some interesting building techniques and not just spinning tops. I hope more people discover it, comment on it and like it.
 I like it 
  November 5, 2015
MOAT = Mother Of All Tops
Jeremy McCreary
 I like it 
Matt Bace
  November 4, 2015
Wow! It looks like you have been pretty busy. These are all pretty impressive, but I think my personal favorite is the Round Up Top. Many of these have interesting and somewhat complicated geometries (like the Big Bird Top). I am definitely going to have to come back here at some point in the future, because I am certain that there are quite a few good building tricks involved in some of these creations. Great job!
 I made it 
  November 4, 2015
Quoting Nils O. Very cool, I love the idea of building toys with Lego parts. I've also built some tops for my son, but haven't found the time to make some decent photos, yet. You tops are a great inspiration for future projects. Great job! :-))
Thanks for the kind words, Nils. Really looking forward to seeing your tops. I share your affection for the idea of being a LEGO toymaker.
 I like it 
  November 4, 2015
Very cool, I love the idea of building toys with Lego parts. I've also built some tops for my son, but haven't found the time to make some decent photos, yet. You tops are a great inspiration for future projects. Great job! :-))
 I made it 
  November 4, 2015
Quoting David Roberts Disappointingly, pressing the "excellent" smiley button several times still only gives you one smiley face. This is a tour de force. Are you going to publish a Ph.D. eventually? There's such a variety of shapes and colours and construction techniques to be found here. I like the simple ones, such as the black Technic tracks; the improbable ones, such as the brick bent triangle which looks like it'll wobble; and especially the moving "governer" mechanism ones. There's a wealth of ideas for other builders to take on and explore. I like the top with minifigures and it makes me think of potential spaceships or lunar rovers...
Many thanks, David! That means a lot coming from you. Did you notice the top I made from your Big Wheelie Bike wheels? (I gave you credit.) I'd love nothing more than to see the page used as an "idea book" for studless tops. I like the centrifuge tops, too, and will be posting quite a few more of them soon.
 I like it 
  November 4, 2015
Disappointingly, pressing the "excellent" smiley button several times still only gives you one smiley face. This is a tour de force. Are you going to publish a Ph.D. eventually? There's such a variety of shapes and colours and construction techniques to be found here. I like the simple ones, such as the black Technic tracks; the improbable ones, such as the brick bent triangle which looks like it'll wobble; and especially the moving "governer" mechanism ones. There's a wealth of ideas for other builders to take on and explore. I like the top with minifigures and it makes me think of potential spaceships or lunar rovers...
 
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