An ugly but fully functional and highly effective PF-controlled, F2K-type floating-arm trebuchet capable of hurling LEGO(R) rubber balloon wheels up to 20 m (65 ft) downrange. Motors and pneumatics assist the cock-load-alert-fire workflow, but, as with any true trebuchet, gravity alone accelerates the projectile.
This rather ugly but fully operational and highly effective LEGO® floating-arm trebuchet (FAT) (see primer below) is completely faithful to the advanced F2K design developed by FAT inventor Ron Toms in his quest to re-engineer the Medieval trebuchet from the ground up. His success can be gauged by the fact that an F2K can hurl nearly twice as far as a classical trebuchet of comparable size using the same counterweight mass and projectile.
As with any true trebuchet, my F2K uses gravity alone to accelerate its projectiles. Loading projectiles into the pouch is a delicate operation that must be done by hand, but motors and pneumatics perform the rest of the cock-load-alert-fire workflow under PF remote control.
I've built many a Technic/PF/Mindstorms MOC before and since, but this F2K, completed in early 2013, remains my greatest LEGO® engineering challenge. For starters, the very high operating stresses and shocks push LEGO® materials and parts to their limits WRT both strength and frictional properties. Like all treb builders, both modern and Medieval, I was also determined to wring every last drop of range out of this thing. That turned out to be a lot harder than I ever imagined -- mainly because trebuchets turned out to be a lot more complicated than they look.
Please feel free to scroll right past the endless text. Got way too deep into trebuchets, particularly the F2K, and just couldn't resist sharing what I've learned.
Photos and text
This lateral shot of the "magazine side" of the F2K provides a nice overview. Downrange is to the right. The magazine at bottom center holds 16 rounds of the F2K's projectile of choice -- pumpkin-like hard rubber balloon wheels (4288) weighing 3.7 g each. These can be hurled up to 20 m (65 ft). The sling and empty pouch at left dangle in front of the runway.
The metal counterweight (CW) assembly is perched here in cocked position at the top of the uprights, ready to fall. The uprights enforce a purely vertical fall of the CW during the hurl -- an important efficiency measure central to all FAT designs. A gantry associated with the CW hoist subsystem bridges the tops of the uprights above the CW.
In cocked position, the tip of the black and yellow studded beam (throwing arm) rests on a small beam roller hidden between the uprange ends of a pair of horizontal beam wheel rails (hereafter simply rails) extending downrange to the right between the uprights. The beam is a 1st class lever with the CW serving as effort, the projectile as load, and the beam roller as its initial fulcrum. When the small gray beam wheels (here at 7 o'clock to the CW) touch down on the rails during the CW's fall, however, the beam wheel axle takes over as fulcrum. Since this axle's closer to the CW than the roller, the CW's mechanical advantage over the projectile jumps abruptly at this moment, and projectile acceleration increases violently as the sling amplifies this whipping action.
Directly above the magazine is a self-regulated phased 2-pump air compressor driven by a PF M-motor extending into the magazine. Atop the compressor is a pressure-sensitive switch that maintains enough air pressure to effect an abrupt disengagement of the CW hoist dog clutch (not seen). This action releases the cocked CW to kick off the hurl. The paired red valve paddles at right center operate the pneumatic valve controlling dog clutch engagement. (The 2 small 5.5L dog clutch cylinders actually driving the clutch are hidden.) The valve paddle gearbox behind the paddles is powered by the valve paddle motor -- an old 9V gearmotor (71427) -- to its right.
Below the valve paddles is an even older 9V motor (74569) powering the alert subsystem, which simultaneously sounds a klaxon brick (55206c03) and flashes LEDs above the CW hoist to announce that the F2K is cocked, loaded, and about to be fired. This motor drives the upper 24z gear looped by the chain at bottom right via a 24:1 worm gearbox hidden behind the gear. The chain in turn drives a largely hidden old-style rotary polarity switch serving as the LED flasher. The far end of the gearbox output shaft drives the klaxon actuator on the other side of the largely hidden riser wall supporting the studless superstructure. Both of the F2K's 30 year-old 9V motors still run like new.
The F2K and its color-coded PF controllers from above. The magazine is immediately below the controllers in this image, and downrange is up. The colors distinguish components of the 4 subsystems under remote control: Black for the CW hoist, yellow for the runway, orange for the alert subsystem, and red for the valve paddles. The compressor runs autonomously.
Immediately to the lower controller's left is the valve paddle gearbox driven by the valve paddle motor above it and based on Sariel's "autovalve" design. Below this gearbox is the compressor regulator switch and the yellow elastic bands determining its pressure setpoint.
The CW hoist gantry at left center bridges the tops of the uprights. The white CW hoist cable is off its gantry pulley here.
The 8:1 CW hoist worm drive with a crank handle above for manual operation. The CW hoist dog clutch mates with the 24z gear on the right side of the worm drive but is disengaged and out of sight.
Close-up of the "battery side" of the base. The color-coded dual receivers at right provide the 4 connections needed to control the CW hoist, runway, alert system, and valve paddle motors remotely. The pressure regulator switch connects directly to the battery. There's room here for a 2nd battery if needed. The studded riser behind the electricals is one of two supporting the studless superstructure.
Another lateral view of the magazine side, this time with the CW in resting position at the very bottom of the uprights and the beam tip at top dead center (TDC) between them. The CW axle allows angular momentum to carry the beam tip through TDC at very high speed as the CW bottoms out. Contact between the beam tip and any solid object at this point in the hurl is a good recipe for a shattered beam. Construction of the uprights and the CW hoist gantry must therefore focus on staying out of the beam's way. Sling contact with the gantry as the beam tip passes through TDC is unavoidable, but when the F2K is properly tuned, the projectile is out of the pouch by then, and no harm seems to be done.
Drop is defined as the vertical separation between the CW's cocked and resting positions. Available gravitational potential energy (AGPE) is proportional to the product of CW mass and drop. Energy conversion efficiency (ECE) is the fraction of AGPE actually converted to projectile kinetic energy (PKE) at the time of release, and it is delivered PKE that ultimately limits range. By exploiting both of these avenues to higher PKE, an F2K can outdistance a much larger treb of classial Medieval design with the same CW and projectile mass -- mostly because the F2K geometry accommodates a lot more drop and hence AGPE, but also because the F2K has a much higher ECE, in large part due the purely vertical fall of its CW.
Better look at the CW hoist gantry with CW in resting position.
Oblique view of the magazine side with the CW near its resting position at the bottom of the uprights.
Oblique view of the "uprange end" and magazine side corresponding to a snapshot taken just after the CW has been released from fully cocked position. To understand F2K dynamics, it's helpful to divide the hurl into 2 phases -- one before the beam wheels touch down on the rails, and the other from touch-down onward. During Phase 1, the beam roller is the beam's fulcrum -- one that effectively moves toward the CW as the CW approaches the RUI. Hence, the CW's mechanical advantage over the projectile is relatively small at first but increases steadily during Phase 1. When the beam wheels land on the rails, and the beam wheel axle takes over as fulcrum, however, the fulcrum effectively jumps toward the CW. At this critical moment, the start of Phase 2, the CW's mechanical advantage suddenly jumps to its maximum, and projectile acceleration increases violently as the sling amplifies this whipping action. The CW axle passes through the RUI an instant later.
But wait, there's more! As the CW continues to fall below the RUI, it accelerates the beam wheels down the rails toward the target. This acceleration of the beam fulcrum is amplified by the long arm of the beam and the sling and then added to that of the projectile. Physicists refer to a change in acceleration as a jerk. In an F2K, the entire hurl is a jerk, with the biggest jerk coming at the start of Phase 2. Since the projectile gains most of its launch speed during this phase, an unencumbered CW fall through and below the RUI is essential.
The F2K design coordinates all these actions geometrically: If X is the distance between the CW and beam wheel axles, then RUI height above CW resting position must equal X, and the roller's distance from the RUI must be a little longer than X. That's all it takes!
Oblique view of the uprange end and battery side. As in all photos here, the runway is fully retracted. On the runway at the end of the taut sling is a partially hidden loaded pouch. The F2K could be fired now, but range would suffer, as the CW could be higher.
The smooth runway allows the projectile to pick up more speed prior to lift-off. This is an opportunity too good to pass up, because the CW isn't working against the projectile's weight at this stage in the hurl. Fully extending the runway makes it easier to load the projectile into the pouch. To maximize range, however, the runway must then be retracted to a position that (i) pulls the sling taut, and (ii) insures that the projectile won't reach the end before lift-off.
View looking straight downrange with the CW in resting position and the beam tip between the uprights at TDC. The studded base supporting the studless superstructure consists of 2 sturdy 2x8x24 risers resting on a raft of 12x12 modified bricks (52040) paved over with 2 layers of large overlapping plates for stiffness. The sideways rubber tires supporting the raft damp vibrations and keep the F2K from sliding in recoil, as these unwanted motions sap energy from the hurl. The risers are just tall enough to provide adequate clearance for the runway in between. The long vertical gizmo with yellow forks at both ends in the far left foreground is a tool used to trim up the projectile within the loaded pouch prior to firing.
Looking downrange again, this time zoomed in on the RUI with the beam removed. The beam roller is clearly visible between the rails.
Maximum efficiency demands an abrupt CW release and an unencumbered CW fall. The CW hoist dog clutch is engaged with the CW hoist worm drive. At right is the dog clutch actuator. The 2 black 3x3 are on the dog clutch axle, which is also the axle for the hidden CW hoist cable reel. Retracting the hidden dog clutch pneumatic cylinders forces the dog clutch lever (vertical thin black liftarm) against the inboard disk, as shown here. This forces the dog clutch axle to the left, engaging the clutch. The hoist worm drive can then lift the CW into cocked position and hold it there, even with the hoist motor off. Extending the cylinders fires the F2K by kicking the outboard disk and hence the dog clutch axle to the right. This jerks the clutch out of engagement, leaving the CW free to fall. When the dog clutch lever and disks are properly positioned, the clutch lever will then bounce inboard, out of contact with both disks as the CW falls. The CW's only encumbrances at this point are friction against the uprights and the hoist cable, which readily spools out from the reel on the now freely spinning dog clutch axle.
When this photo was taken, an L-motor powered the CW hoist gearbox, but an M-motor proved adequate.
Dog clutch lever pressing dog clutch into engagement.
Dog clutch at opposite end of the dog clutch engaged.
Dog clutch lever in firing postion between dog clutch plates. Lack of lever-disk contact allows CW hoist cable to spool out readily as CW falls.
Dog clutch disengaged.
Another look at the beam roller.
Close-ups of the beam tip, launch pin (LP), and sling. Note that the sling has a fixed end tied to the beam and a free end looped over the LP. The projectile is released from the pouch when the free end of the sling slips off the LP. Exactly when that occurs during the hurl is determined by several factors, particularly the launch pin angle (LPA) and the static and sliding friction between sling and LP. The best LP material turned out to be 3 mm rigid tubing, because (i) it holds a bend well, even after several bends in search of the optimum LPA, and (ii) its matte surface favors later releases.
The timing of the release sets the projectile launch angle (PLA) -- i.e., the angle between the projectile's trajectory and the horizontal at the moment of release. Together, PLA and PKA determine the projectile's ballistic (unpowered) trajectory. Finding the LP angle that maximizes range for a given CW mass and beam ratio is just one part of the tedious trial-and-error process known as tuning. Tuning would be a lot simpler if you could observe PLA directly, but for that, you'd need ultrahigh-speed imaging equipment.
Detached beam with CW assembly and beam wheels in position. The black plates jacketing the beam above and below delay failure, but beam reinforcement must be kept to minimum, as increasing beam mass generally reduces range. For a host of reasons, a studless beam would be unworkable at this scale.
When the beam wheel axle takes over as beam fulcrum, the beam's long lever arm becomes the distance between there and midpoint between the 2 sling attachments, and the short lever arm becomes the distance between the beam wheel and CW axles. The effective beam length is the sum of these arm lengths. The beam ratio (long divided by short arm length) reaches its maximum and stays there for the rest of the hurl, but thanks to the sling, the CW's advantage over the projectile continues to grow for 2 reasons: (i) The sling has become so taut that it might as well be a rigid rod hinged to the tip of the beam, and (ii) centrifugal force on the projectile is increasing the total beam wheel axle-projectile lever arm by progressively straightening the beam-sling angle.
Close-up of the rail-upright intersection (RUI) from the magazine side with the CW in cocked position and the beam resting on the beam roller. The RUI is the structural and kinematic heart of the F2K design. Only studless construction could provide the smooth, flat, parallel bearing surfaces needed within the RUI to allow both vertical passage of the CW axle and horizontal passage of the beam wheels with no snagging and the least possible friction. The heavy reinforcement around the RUI was needed to maintain critical clearances throughout the hurl and to withstand the shocks generated when the CW bottoms out and the beam wheels bump through (see below).
Another close-up of the RUI, this time occupied by the CW axle. The beam wheels at far left are on their rails, and the beam wheel axle is now the beam fulcrum. As the CW continues to fall below the RUI, it levers the beam tip downrange on the fulcrum and pulls the fulcrum downrange at the same time. This compound motion results in a violent downrange jerk of the beam tip. The sling turns this jerk into the crack of a whip with the projectile poised to fling off its end.
Yet another RUI close-up, this time with the beam wheel axle occupying the RUI. This configuration occurs at least twice during the firing cycle -- first when the beam tip passes through TDC late in the hurl, and finally when it settles down into resting position. In the first instance, the beam wheels must bump their way through the gap left in the rails for the falling CW as angular momentum carries the beam tip through TDC. This bump, inherent to the F2K design, becomes an inefficiency affecting range only when the projectile is still in the pouch. That's often not the case, but even so, the inefficiency would be greatly offset by F2K's much larger inherent efficiency gains.
The real problem with the bump is the punishment it adds to the beam's most common point of failure -- the hole hosting the beam wheel axle. The shear stress focused there when the beam wheels slam down on their rails is probably worse, but the bump certainly doesn't help.
Typical beam failure at the beam wheel axle. Most failures appear to start as tension cracks in one or both bottom edges with no evidence of shear. Unnoticed cracks will eventually propagate upward through the entire beam, as seen here. This failure mode suggests that the dominant failure mechanism may be the abrupt change in the balance of moments along the beam occuring when the projectile leaves the pouch. At that point, the only thing keeping the beam tip from flying downrange is the beam itself, and the weak link there is the brutalized plastic around the beam wheel axle hole.
Surprisingly, these beams can withstand ~20 hurls at the maximum attempted CW weight (~0.5 kg) before failing, sometimes spectacularly. Eye protection is therefore strongly advised. In contrast, the highly reinforced studless superstructure and studded base have sustained hundreds of hurls without complaint -- a true testament to the great strength of proprietary LEGO® ABS plastic and the use of 3L friction pins at every opportunity.
MOC on display at a trebuchet competition at the Colorado School of Mines in 2013. Trebs of all kinds competed, but an FAT won by a wide margin. A well-built but poorly tuned F2K came in 2nd.
Since the hard rubber projectiles of choice have been known to knock paint off interior walls 8 meters away when shot from my F2K, I also recommend either outdoor operation or a talent for paint repair.
WARNING: A device this powerful should never be fired or even cocked when people, animals, or valuables have any chance of being hit.
Table of features and stats
266 x 306 x 456 mm (10.5 x 12.0 x 18.0 in) in LxWxH including magazine
1.9 kg (4.2 lb)
Studded base, beam, runway, portions of the valve paddle and alert subsystems; studless otherwise
Steel and lead weights on 4.8 mm steel axle, ~0.5 kg max so far
Projectile of choice:
LEGO® rubber balloon wheel (4288), 3.7 g, 20 mm max diameter
19.8 m (65 ft) max with 0.446 kg CW
Not observable but probably <45°
Projectile kinetic energy:
Energy conversion efficiency:
Good (27% of theoretical)
Effective beam length and mass:
260 mm, 27 g
2.61 (long/short arm length)
Cocked beam angle:
Beam service life:
~20 hurls at maximum CW weight
Onboard air compressor:
Self-regulated with 2 phased 5.5L pumps
Powered, with pneumatic dog clutch serving as CW quick-release (trigger)
CW hoist cable:
Heavy-duty kite string
000 surgical silk
Cut from 10x10 net (71155)
Powered extension and retraction for easier loading of projectiles into pouch
2 small (5.5L) cylinders acting in parallel to disengage CW hoist dog clutch
Flashing PF LEDs over CW hoist; klaxon alarm brick (55206c03)
5 -- 1 PF medium each on air compressor, CW hoist, and runway; 1 old 9V (71427) working the valve paddles; 1 old 9V (74569) driving both alert system actuators
IR receiver connections:
4 -- 1 for each motor other than the compressor's
1 PF rechargable battery or AAA battery box (2 for prolonged compressor use)
Modified LEGO® parts:
Bent 3 mm rigid tubing (launch pin), pouch
CW assembly, CW cable, sling
Several mechanisms adapted from The Unofficial LEGO® Technic Builder's Guide by Pawel "Sariel" Kmiec, No Starch Press, 2013 (highly recommended)
The classical Medieval trebuchet (CMT) By definition, a trebuchet (treb for short) is a lever-like hurling device powered solely by the gravitational potential energy (GPE) stored in a suspended counterweight. By far the most fearsome weapon and most advanced mechanical engineering achievement of its time, the Medieval trebuchet reigned supreme as the offensive siege weapon of choice in Europe and adjoining parts of Asia for at least 300 years (roughly the 12th-15th centuries CE). The trebuchet quickly supplanted torsion-powered devices by virtue of greater range at much lower risk of catastrophic failure. A typical large Medieval treb in fully developed "classical" form (say, ca. 1300 CE) could hurl 50-100 kg projectiles (usually boulders) up to 0.3 km downrange at 2-3 shots per hour with only a few meters of spread on target -- typically, a defensive wall to be breached. (There are, however, accounts of the use of much heavier projectiles.) It took 200 years of metallurgical advancement after the introduction of firearms to the West for the cannon to supplant the CMT.
The classical Medieval trebuchet (CMT) had 5 defining features:
A long, rigid throwing arm or beam pivoting like a lop-sided seesaw on a massive frame
A hinged counterweight (CW) -- often a wooden box of dirt and rock weighing several tonnes -- attached to the short end of the beam by a hinge
that allowed the CW to swing freely parallel to the beam
A projectile pouch on a flexible sling attached to the long end of the beam
Some means of releasing the projectile from the pouch at the right time
A projectile runway paralleling the beam beneath the frame
Full-size working reconstruction of a quintessential CMT at Chateau des Baux de Provence, France. CW hinge is the dark triangular structure between the end of the light colored beam and CW box below. Since a CW-runway impact would be catastrophic, the distance the CW can be allowed to fall is quite limited considering the CMT's overall size. Rounded boulders like those at bottom center were the most commonly used CMT projectile when breaching a wall was the goal.
The CMT substantially outperformed earlier designs with projectile holders, CWs, or both rigidly attached to the beam. Respectively, the CW hinge and sling of the CMT improved range (i) by reducing CW deviations from a purely vertical descent, and (ii) by amplifying the whipping action of the beam. The runway, added later to ease the initial (horizontal) phase of projectile acceleration, was typically greased with animal fat. Note that the CMT has a single fulcrum (the pivot) fixed to both beam and frame. In contrast, the F2K variant of the modern floating-arm trebuchet uses 2 fulcrums in succession -- the 1st moving relative to the beam, and the 2nd moving relative to the frame.
Medieval trebuchet design and tuning (see below) quickly came to focus on maximizing range, as even modest CMTs were massive timber constructions that could only be assembled on site -- generally under heavy defensive fire. Accordingly, CMTs grew steadily in size over time to take advantage of the linear scaling between range and beam length, with some reaching over 10 m in pivot height. Then, near the end of routine CMT use, came a puzzling development -- somewhat smaller CMTs and fixed-CW trebuchets mounted on small wheels. These new-fangled CMTs were clearly no more transportable than their predecessors had been, so why the wheels?
The answer came only at the end of 20th century, when field testing of historical reconstructions revealed -- somewhat counterintuitively -- that the first motion of a recoiling CMT-on-wheels is a downrange lurch toward the target. Since this motion precedes projectile release, a portion of the downrange momentum acquired by the CMT frame is then transferred to the projectile via the beam, just as some of the momentum a baseball pitcher gains by stepping down off the mound toward the batter transfers to the ball via his or her arm. Energetically, by allowing the entire trebuchet to float in recoil, the wheels effectively deposit in the projectile some of the beam kinetic energy (KE) that would otherwise be lost to acceleration, deformation, and vibration of the trebuchet structure. (If you're beginning to suspect that trebuchets might be more complicated than they look, you're catching on.)
The modern floating-arm trebuchet (FAT)
Fast forward now to 1998, when enthusiast Ron Toms undertook a complete re-thinking of the trebuchet with the express purpose of designing a machine that could reliably out-hurl a CMT of much greater overall size and weight at reasonable cost. Out of this successful effort came the modern floating-arm trebuchet (FAT) and the more advanced "F2K" variant on which this MOC is based. (Toms went on to found (RLT Industries, now a leading manufacturer of working treb kits for enthusiasts and educators. The RLT site is an excellent resource on FATs, F2Ks, and hurling devices in general.)
A well-built, highly efficient FAT based on inventor Ron Toms' original design with the CW in resting position. The FAT bears little resemblance to a CMT. The red steel uprights confine the barbell-like CW to a purely vertical fall. The available drop -- i.e., the vertical separation between the CW's cocked and resting positions -- is roughly double that of a CMT of comparable height, but since the black beam wheels remain on their wooden rails throughout the hurl, the drop can't be more than twice the distance between the beam wheel and CW axles.
F2K kit manufactured by RLT Industries, here with its black CW boxes in fully cocked position and its beam wheels high above their rails. This ability to start a hurl with the beam wheels above the rails gives the F2K nearly twice the available drop of an original FAT and far more drop than any CMT of comparable size could muster. The F2K owes its unsurpassed range to its great drop and the high efficiency with which it turns that drop into range.
To understand why the FAT and F2K look and work the way they do, consider the factors that limit trebuchet range:
In the end, the range of any treb is limited by projectile kinetic energy (PKE) and projectile launch angle (PLA) -- i.e., the angle between trajectory and the horizontal -- at the time of release. PKE is of course proportional to both the projectile's mass and the square of its release speed. In real trebs, the optimal PLA will always be a few degrees less than the ideal 45° taught in high school physics. Range is also limited to a lesser extent by loss of initial PKE to air resistance in flight; how much depends in part on projectile shape and texture, with smooth spherical projectiles generally flying farthest.
PKE is limited in turn by (i) the available GPE (AGPE) stored in the raised CW, and (ii) the treb's energy conversion efficiency (ECE) -- i.e., the fraction of AGPE actually converted to PKE. An ECE of 50% is excellent.
Since GPE is proportional to both mass and drop, AGPE is limited (i) by the maximum CW mass the treb's structure -- especially the beam -- can safely handle, and (ii) by the maximum drop that the treb's geometry and structure can safely accommodate.
Finally, ECE is limited by a very complex interplay of factors, most notably (i) projectile/beam and beam/CW mass ratios; (ii) no less than 4 length ratios relating total beam length to pivot location along the beam, pivot height, sling length, and CW hinge length; (iii) the degree to which the CW deviates from a purely vertical path during its fall; (iv) PLA, which depends on details of the sling release mechanism and the characteristic mass and length ratios as well; (v) bearing friction, especially the pivot's; (vi) structural rigidity, especially the beam's; and (vii) details of recoil behavior.
Now that brings a purely wicked smile to my face! It reminds me of being on an aircraft carrier in San Diego and having the guide tell us that the shuttles on the deck could launch a VW Bug all the way to Tijuana. So, of course the first thing we think of is where we can get our hands on a Bug to wage war with TJ. Nothing in my house would be safe from my siege with that around! Just way too cool!