This simple wind-up launcher sends flying rotors based on various 9L and 13L LEGOŽ props to altitudes of 1-6 m. By design, all rotors spin on their tails like tops on landing.
About this creation
Please feel free to look over the images and skip the verbiage.
Several months ago, my ongoing fascination with high-speed rotary motion in the LEGOŽ realm turned to flying LEGOŽ rotors -- "flyers" for short.1 This page presents the first in a series of flyer-related MOCs.
∨ This simple all-LEGOŽ wind-up launcher for ultralight flyers evolved from the top spinner in the lower part of the photo below.
However, the idea of using a pull-back motor (PBM) to launch LEGOŽ flyers came from the only other PBM launcher I've run across: The elegant and much more elaborate LEGO Technic Heli Launcher (2015) by favorite builder Desert752_Kirill (hereafter "DK").
∨ The video below shows my PBM launcher lofting its heaviest flyer. Note what happens after the flyer lands.
Heavy flyers require ripcord-powered launchers2, but TLG's latest and greatest 6x5x3 PBM (12787c01) turns out to have more than enough torque and speed to launch flyers weighing under 10 g (hereafter, "ultralight").
Problem is, this most powerful of all PBMs to date also has more than enough torque to cause rotor blades to slip on any shaft that can't be keyed them. The slip translates directly into loss of altitude and range.
∧ Devout purists will therefore have to forego the highest-flying of all ultralight rotors -- the 9L 3-blade prop on the right. Sorry.
Warning! Always wear eye protection when working or playing with high-speed LEGOŽ rotating machinery and keep valuables and bystanders (including pets) a safe distance away -- especially when testing new designs. Really.
My lovely assistant will now demonstrate the launcher in use.
Step 1: Confirm that the flyer to be launched is right-handed. For example, place the flyer tail-up on a horizontal surface with one blade at 12 o'clock. If the right edge of that blade is closer to the surface, the flyer is right-handed.
∨ Step 2: Grasp the launcher handle with the PBM away from you and insert the flyer's tail into the PBM's orange axle hole.
Step 3: Slide the winder axle in or out as needed to seat the flyer's tail at the optimal depth within the PBM.
∨ Step 4: Wind up the PBM using the ratcheted pull-out winder below it. (Counting your turns will help you avoid over-winding.)
∨ Step 5: To launch the flyer, stiffen your hold on the orange grip (to help you keep your aim) and yank the entire winder out from under the PBM as sharply as possible.
Step 6: Keep ultralight flyers in sight from launch to landing as best you can, as they're very easy to lose.
As explained below, leaving no portion of the winder behind insures that the PBM has nothing to spin up but the flyer itself.
My bare-bones PBM launcher isn't nearly as elegant or as richly featured as DK's, but it offers comparable performance at lower cost. It's also easier to wind up, and the likelihood of unintential discharge is nil.
∨ The preferred flyer for DK's PBM launcher is recreated at far left below. It weighs 3.2 g and consists of a single 9L 2-blade LEGOŽ propeller (2592) mounted on a 12L axle. The long 11L "tail" adds the axial stability the 2-blade rotor lacks in flight. Maximum altitude is reported to be 6 m.
∧ Examples of the preferred flyers for my launcher appear to the right of DK's. They're also based on 9L props (below) but have more blades and much shorter (2-3L) tails.
My 9L flyers reliably reach altitudes of 4-6 m with the PBM launcher featured here. The 4-blade flyer is the best purist solution, but the 3-blade flyers climb a good 20-30% higher when doctored to prevent slippage.
Since all of my 9L flyers have the same diameter, blade design, and tail length, their maximum altitudes depend primarily on (i) ability to withstand the PBM's torque without slipping or coming apart, (ii) axial moment of inertia, and (iii) thrust/weight ratio (TWR) at the end of spin-up.
Item (ii) above limits the angular acceleration the PBM can impart to the flyer and hence the speed of the latter when it finally leaves the launcher. Item (iii) depends in part on the number of blades, but not in any simple way.
∧ My PBM launcher can also loft short-tailed flyers based on the heavier red 13L 4-blade LEGOŽ propeller with studs (4751b) to altitudes of ~1 m.
All of the ultralight LEGOŽ flyers discussed here have (i) a thrust-generating "rotor" consisting of a LEGOŽ propeller with 2 or more blades, and (ii) a cross-axle "shaft" connecting the rotor to the launcher during spin-up.
Some ultralights also need (iii) a "hub" connecting rotor and shaft -- ideally, without slip. The portions of the hub and shaft below the rotor make up the flyer's "tail".
Three- and 4-blade rotors have their pros and cons. DK's 2-blade rotor produces thrust more efficiently, but the stabilizing effect of adding even one more blade obviates the need for a long, heavy tail.
The mass saved by using tails just long enough to seat properly in the launcher is substantial, and the savings go straight to maximum altitude and range. As a result, my short-tailed 3- and 4-blade 9L flyers are 22-42% lighter than DK's. And though less efficient, the ones that don't slip attain comparable maximum altitudes.
∨ The real reason I like short-tailed 3- and 4-blade flyers, however, is that they spin on their tails like tops after landing. (See video above.)
∨ Flyer1: The rotor of this 9L 4-blade flyer consists of a pair of right-handed 9L 2-blade props with central axle holes -- hence no need for a separate hub to prevent slip. The stopped 3L shaft leaves a 2L tail.
∧ A maximum altitude of ~4 m with this PBM launcher makes Flyer1 (2.9 g) the best purist performer. Its 4-blade rotor also serves well as a top rotor (center).
∨ Flyer2: This big red purist flyer is the one launched in the video. The rotor is a rare right-handed 13L 4-blade LEGOŽ prop with studs (4751b); the shaft, a 3L stopped axle.
∧ The 13L prop has a central pin hole, but the studs allow it to be keyed to the tail using either a Technic bush or a 2x2 round plate as a hub. The bush hub saves a little mass (7.2 vs. 7.5 g) but shortens the tail even more than the round plate does (2/3 vs. 4/3 LU).
This heavy flyer has a maximum altitude of ~1 m with the launcher featured here but comes into its own with a ripcord launcer powerful enough to spin it up properly. (Stay tuned!)
∨ Flyer3: The rotor here is the right-handed 9L 3-blade LEGOŽ prop (30332 or 15790); the shaft, a 3L axle. A 3L bush pin hub mates rotor to shaft, as the prop lacks a central axle hole.
∧ Flyer3 comes in pure (Flyer3P) and impure (Flyer3I) variants. The pure version (far left, 2.6 g) suffers from hub-rotor slip severe enough to keep it from leaving the launcher most of the time. The best altitude I've seen is ~0.5 m.
In stark contrast, Flyer3I (far right, 2.7 g) outclimbs Flyer1 by 20-30% and almost matches Flyer4. The difference: Just 1.5 turns of cellophane tape on the pin part of the hub to eliminate slip.
∨ If only these high-flying 9L 3-blade props had central axle holes! I have yet to find a purist hub that doesn't slip badly under the torque of this PBM -- let alone that of a ripcord launcher. The white-hubbed attempt at center comes apart instantly.
∧ The 9L 3-blade prop also works well as a top rotor (top center).
∨ Flyer4: This impure flyer (all black at far left) is the lightest and highest-flying of the bunch. The rotor is a 9L 3-blade prop; the shaft, a very light 3L axle pin (bottom center). As with Flyer3I, the hub is 1-2 turns of cellophane tape.
Flyer4 weighs a mere 2.1 g and reaches altitudes approaching 6 m with the PBM launcher featured here. The bad news: It won't stand up to the torque of a ripcord launcher and needs to be retaped a lot more often than Flyer3I to keep the slip away.
∨ Flyer5: This impure flyer flies almost as high as Flyer4 with this PBM launcher and many times higher than Flyer4 with a ripcord launcher. The rotor is once again the 9L 3-blade prop, but this time, the shaft is a stopped 3L axle. The hub is (gasp) superglue.
∧ The longer variant (Flyer5L, far left) has a 3L tail; the shorter (Flyer5S, far right), a 2L tail. Both variants weigh 2.3 g and reach altitudes of ~5 m with the launcher featured here.
With a ripcord launcher, however, they can climb 15-20 m! (Stay tuned!)
Superglue may not be the best adhesive here, as both variants have been known to lose their tails on impact -- especially Flyer5L.
∨ I prefer to hold PBM launchers in my left hand and do everything else with the right. This launcher and winder were designed with the ergonomics of that usage in mind.
∨ Jerking the winder out from under the launcher releases the PBM spring, which then spins up the flyer. The orange grip helps steady the launcher during winder detachment.
∨ A flyer intended for a PBM launcher has to produce upward thrust when spun in the PBM's free-wheeling (as opposed to winding) direction. This launcher was configured for the right-handed 9L and 13L rotors featured above.
∨ Left-handed rotors like the yellow 5.5L 2-blade propeller and the blue 13L 3-blade "Ninjago Airjitzu Flyer Vortex Rotor" (18592) below will go nowhere in this launcher configuration, as they'll be generating downward rather than upward thrust on spin-up.3
∨ The job of holding the flyer's tail during spin-up falls to the PBM itself.
∨ The PBM's loosely fitting 24 mm-deep power take-off (PTO, orange axle hole at right center) transmits torque to the tail while keeping it upright.
Ratcheted pull-out winder
∨ Flyers with their rotors solidly keyed to their tails like Flyer1 and Flyer2 below can be used to wind the PBM directly.
∨ However, winding with a flyer takes more effort than with a dedicated winder, and a way to keep the PBM from unwinding prematurely is still needed. The anti-unwinding tool below works only for flyers with tails longer than 5L -- hence, with none of the flyers featured here.
Moreover, winding the PBM with an impure flyer like Flyer3, Flyer4, or Flyer5 might well shorten the life of the tape or glue needed to keep its rotor from slipping on its shaft or hub.
∨ The ergonomic ratcheted pull-out winder below addresses all of these issues.
∧ For important reasons explained below, nothing remains attached to the lower end of the PTO when the winder comes out.
∨ The heart of the winder is the simple but robust ratchet mechanism below. It prevents both premature unwinding and unintentional discharge.
∨ Additional goals for the winder included the following:
Reversibility without modification
Adjustability of tail seating depth over the entire useful range
Ease of winding
Ease of detachment to minimize the impact of the launching process on the user's aim
Sufficient internal strength to withstand the torque of the fully wound PBM.
Flyer tails definitely encounter friction against the motor's PTO as they slide out during take-off. How much friction is a complicated function of flyer mass and "tail seating depth" (the length of tail inside the PTO at the start of spin-up) that I have yet to sort out.4
Tail seating depth is adjusted by changing the length of winder axle inside the lower end of the PTO. As discussed below, maximum altitudes turn out to be quite sensitive to seating depth in all my flyers.
∨ Though the photos above show the winder with a stopped 8L axle, my optimal tail seating depths of 4-6 mm can only be enforced with a 9L or longer winder axle.
Ground effect platform and launch box
DK's launcher lofts a long-tailed 9L 2-blade 3.2 g flyer to a maximum altitude of ~6 m. My much lighter short-tailed Flyer4 (9L, 3 blades, 2.1 g) has the same maximum altitude.
Q1: But how could that be, given that (i) both launchers spin their flyers with the same PBM without gearing, and (ii) DK's flyer surely suffers much more tail-PTO friction due to its greater seating depth?
Experiments with DK's flyer indicate that most of the answer lies in the greater efficiency that comes with fewer blades in propellers of all kinds. (That also explains why my 3-blade rotors outperform their 4-blade counterparts.) But there's another possibility.
Q2: Could the ground effect well known to helicopter designers and pilots also play a significant role?
∧ To test Q2, I used the detachable 12x12 tiled "GE platform" above to provide my flyers with a GE comparable to that experienced by DK's flyer.
The short answer to Q2: GE boosts altitude for some of my flyers with the GE platform attached, but only slightly. It must do the same for DK's flyer.
The rest of this section is devoted to the long answer to Q2 and a related question.
∨ The GE platform increases altitude by 5-10% at best, but only for the 3 flyers shown below: From bottom to top, (i) a variant of Flyer1 with a 4L stopped axle for a shaft, (ii) Flyer5L, and (iii) Flyer3I.
The 3L tails common to all these flyers give their rotors ~7 millimeters of clearance above the GE platform at optimal tail seating depths (~4 mm for all 3). This kind of clearance appears to be necessary for a significant GE in my setup, and I see a similar clearance in DK's.
Thus it would appear that GE makes a minor contribution to DK's maximum altitude.
Among other things, ground effect refers to the efficiency boost a helicopter rotor sees when in close proximity to the ground. The result: Increases in both thrust/power and thrust/speed ratio that can be quite substantial -- especially when the rotor's less than a rotor radius off the ground.
A rotor at an altitude low enough for a significant GE is said to be "in ground effect" (IGE). At higher altitudes, it's said to be "out of ground effect" (OGE) or "in free flight".
For manned helicopter rotors, the maximum IGE altitude is roughly 1 rotor diameter, but that figure may be as high as 5 diameters for the rotors on small quadcopters. The latter are comparable in diameter to the rotors used here, though with wider blades.
GE is most pronounced over smooth, flat, hard surfaces at all scales, and DK's launcher provides just that for his flyer. His loaded rotor sits in a shallow cylindrical "launch bowl" with a tiled floor sitting several millimeters below the blades. Since that gap's a small fraction of rotor radius (36 mm), his rotor should be strongly IGE on take-off.
∧ Without the GE platform, my rotors are only partially IGE on take-off, as the PBM underlies only ~60% of the rotor disk, and the surrounding terrain is anything but flat, much less smooth.
With the platform, my flyers become fully IGE at launch and gain the same advantage DK's flyer has. I don't use the platform regularly, but I keep it handy in case DK shows up looking for a showdown.
∨ Before closing out Q1, I had one more possibility akin to GE to test. My experience with 9L props on boats indicates that their outflow in water is mostly radial, and the same surely obtains in air. If the sidewalls of DK's launch bowl were to deflect some of the radial outflow from his 9L prop back under his rotor, there might be a brief gain in thrust just before lift-off.
Q3: Could the sidewalls of DK's "launch bowl" give his flyer an additional boost in thrust over and above that due to GE?
To test Q3, I turned my GE platform into the "lauch box" above and ran more altitude tests.
The short answer to Q3: Probably not. Adding sidewalls to my GE platform made no discernable difference in flyer altitude.
And my final conclusion WRT Q1: The known influence of blade number on rotor efficiency explains most of the similarity in our maximum altitudes. The small GE provided by DK's launcher explains most of the rest.
Flyers as tops
Big red Flyer2 may be a poor climber, but it spins longer and more smoothly than any other flyer here in post-landing "top mode".
∧ Not coincidentally, its 13L rotor also makes an excellent top rotor (top center).
The worst performers in top mode are the pure and impure variants of Flyer3. The remaining 9L flyers occupy the middle ground, with Flyer1 leading the pack, and Flyer5L trailing.
These oberved rankings are easily understood in terms of the main factors controlling spin times in tops.
For any flyer to perform well in top mode, the following conditions must be met:
The short-tailed 3- and 4-blade flyers presented here meet all these criteria. As with throwing tops, the last 2 requisites give my flyers enough angular momentum to keep the tail-down orientations they maintain in flight after impact.
DK's long-tailed 2-blade flyer was never intended to spin like a top after landing. Nor could it, as it lacks the necessary rotor symmetry, has an impossibly high center of mass, and is at a distinct disadvantage WRT radius of gyration due to its smaller number of blades.
Flyer2 has the largest axial radius of gyration and the lowest center of mass of the any of the tops here. These attributes make it shine in top mode, but the large radius of gyration works against it in flyer mode by limiting its angular speed at the end of spin-up. The low speed takes a big bite out of climbing ability, as thrust varies roughly as the square of angular rotor speed.
The PBM delivers only so much torque. The angular speed the flyer can attain during spin-up is limited by (i) the PBM's torque-speed curve; (ii) the combined axial moment of inertia of the flyer and everything else attached to the PTO; and (iii) losses to tail-PTO friction and rotor and shaft distortion. Most of these factors are under the designer's control to some extent.
Hence, to maximize altitude or range, the PBM should be asked to spin up nothing but the flyer itself.
In practice, that means that anything used to wind up the PBM or keep it wound should be detached from the PBM completely on or before launch.
∧ The prototype in the lower part of the photo below violated that principle by leaving a 6L axle and a 24-tooth ratchet gear coupled to the PBM during spin-up.
It definitely paid the price. Getting rid of those encumbrances upped Flyer4's maximum altitude by 25%. Other flyers saw similar gains.
Important events during spin-up
The spin-up phase of the launch begins when the winder is yanked out of the launcer and ends when the flyer finally clears the launcher. The details in between have much to do with the maximum altitude or range attainable with a given flyer at a given launch angle.
This final section assumes a vertical launch with tail seating depth d0 at the start of spin-up (t = 0).
The upward thrust developed by the flyer during spin-up varies roughly as the square of angular speed (Ω). The thrust first exceeds the flyer's weight at critical speed (Ωcrit). However, the flyer will have to continue accelerating to lift-off speed (Ωlo) in order to overcome tail-PTO friction and start rising out of the PTO at time t = tlo.
Once the tail has risen a distance d0, it will clear the launcher at time t = tclear at speed Ωclear. The higher Ωclear, the greater the thrust at take-off, and the higher the flyer will go.
If the PBM's speed peaks before reaching Ωlo, the flyer will never budge. If it peaks at time t = tpeak such that tlo < tpeak < tclear, the flyer may well rise part way out of the PTO and then fall back in.
If, on the other hand, the flyer clears while the motor is still accelerating (i.e., tclear < tpeak), then some of the motor's power will have been wasted. In short, the flyer will fail to reach its highest altitude attainable with that motor.
The goal, then, is to have tclear ≈ tpeak. Once a particular flyer and motor have been selected, the only control one has in that regard is the choice of seating depth (d0).
Of course, d0 must at least be deep enough to keep the flyer from toppling during early spin-up. How much deeper it needs be to maximize altitude is a matter of tuning by trial and error.
The optimal seating depth for Flyer4 is ~4 mm from the top of the PTO. For Flyer1, it's more like 5-6 mm.
Flyer spec symbols and units: R ≡ radius (mm); L ≡ axial length (mm); Z ≡ blade count (--); M ≡ mass (g); A ≡ maximum altitude (m).
Superglue or tape to prevent slippage between the rotors and tails of Flyer3I, Flyer4, and Flyer5
Modified LEGOŽ parts:
1 Motorized LEGOŽ devices will remain too heavy to fly under their own power for the foreseeable future -- at least with LEGOŽ motors and props. (See, for example, Sariel's "Why LEGO can't fly" video.)
However, lightweight LEGOŽ flyers of various kinds can be made to fly with all-LEGOŽ external launchers powered by ripcords and wind-up and electric motors.
2 My more powerful ripcord-based launchers and flyers will be posted in the coming weeks. In the meantime, here are some excellent examples by 2 favorite builders.
3 The blue Airjitzu rotor won't go anywhere anyway, as LEGOŽ PBMs lack the oomph needed to get its 11.1 g mass airborne -- even with a much lighter hub than shown. The 1.2 g 5.5L 2-blade prop, however, is a very different story, though a rather impure one. Stay tuned!
4 I sense that tail color also plays a role in tail-PTO friction -- hence, the preponderance of dark tan among the 3L stopped axles used in most my ultralight flyers. By the same token, Flyer3's black 3L axles should probably have been LBG instead.
Formally, Rg is the square root of the object's moment of inertia to mass ratio. Hence, it corresponds to the distance at which a particle of the same mass would have to rotate around the chosen axis to have the same moment of inertia.
Bouadbdallah, S., 2007, Design and control of quadrotors with application to autonomous flying, published doctoral thesis.
Bouadbdallah, S. and Siegwart, R., 2007, Full control of a quadrotor, IEEE/RSJ International Conference on Intelligent Robots and Systems, p.153-158.
Powers, C., Mellinger, D., Kushleyev, A., et al., 2013, Influence of aerodynamics and proximity effects in quadrotor flight, Experimental Robotics, STAR88, p.289-302.
Wald, Q.R., 2006, The aerodynamics of propellers, Progress in Aerospace Sciences 42:85-128 (an excellent treatment if you have access and don't mind the heavy math)