Kits are available for purchase over the internet. However we didn't have time to wait for shipping. Instead I
Design criteria required throw weights from 5g to 20g.
A simple catapult is an easy design, lever powered by a spring mechanism (probably a rubber band in this case). I recall constructing one in Boy Scouts in the previous millennium. The downside A catapult needs a stop mechanism equal to the power of the torsion mechanism. This is a waste. I'd rather put the effort into power than brakes, cuz brakes only slow you down! I also recall the Boy Scout catapult didn't last very long.
The Trebuche is a more elegant design, but still simple enough. It uses a lever arm powered by a counter weight hanging off the short end of the lever. The long end of the lever pulls a sling to take advantage of the whipping action to accelerate the projectile. The sling is held captive on one side at the end of the lever arm and the other held loosely on a "finger". Release point is adjusted by adjusting the finger angle.
We hit Home Depot for supplies. First we checked the 55 cent rem bucket for a something to use as a base. The rem bucket was no where in sight, but there was an 18" section of 2x6 in the garbage can. That went into the cart. (side note: The HD Cashier accepted the explanation and gave us the board. Hence the plug as a quid-pro-quo). We also picked up a 1/2" and 3/8" dowel, a bolt and a stack of fender washers (at $0.18 each!). That and four 87cent 4-packs of incandescent bulbs (banned by congress after 2012) still came in under $10.
Measurements and design were from the TLAR* school of engineering. The axle is ~9" off the platform and the beam is ~13" long. The main uprights are 1/2" dowel while the lever arm and struts are 3/8" dowel. A cut off 16 penny nail forms the axle while a 3/8" bolt suspended the counterweights. The SCQueen had the sewing machine setup for Christmas gifts and sewing the sling was a two minute job.
Historical accounts from the 12-15th century talk about throwing 2-300lb stones 300 yards with 12,000lb counter weight. The stones would hit with enough force to knock down the castle walls of the day and forced a complete defensive rethink. I needed the data to estimate a ballast/projectile ratio. 50:1 is in the ballpark. That means ~500g (one pound-ish) to throw the 10g weight. That would provide an over/under for the other weights. Clearly the fender washers purchased were well under weight. We scrounged around the house looking for appropriate ballast. The Hornady box of 100 150 grain 30-06 bullets was heavy enough and plenty dense. But even if sealed in an opaque container (probably a cloth sac), there is a chance the beans might spill and cause exploding PSH that could splash back on the SCClan. That idea was rejected.
The SCQueen found a couple large sockets in the tool box. Experimenting around we found a couple sockets that would nest conveniently and a longer bolt to suspend the stack. It was still short enough to allow the beam to swing freely. Total weight of the three socket stack was about 1.5 lb (750gram).
Kitchen table experiments showed this was a little overpowered for the 5gram weights. (The SCQueen was seriously concerned for the safety of the pictures on the far wall of the SandCastle.) One socket was removed to de-power the weapon. I could also see the points on the end of the lever arm could harm an unwary user and added a couple warning labels "Sharp points" and "Safety Glasses required". Probably not enough to satisfy OSHA or a PI lawyer but I tried. My son was a probable operator so I'm well motivated to ensure he's not hurt in the process. Still I insisted on eye protection for all team members.
The team's first attempts to throw were unsuccessful. I suspected operator error and suggested some training. We bumped into the teacher at a school function. It just so happened I had some time off the next day and I offered to work with the team. She gladly accepted and offered "any time". That night we again scrounged the garage for accurate masses. The bolt bucket held masses that were close but high. This is good as the grinder can fix that! Within 30 minutes we had 5, 10, 15 and 20g masses accurate to a couple .01g.
The team's problem likely was related to the plastic "Easter eggs" their masses were contained in. They were simply over sized for the sling. Sorry, that wasn't in the Design objective document ;-) The Frankford Arsenal scale I'd borrowed from the reloading bench showed their weights were 5g over.
The trebuchet was well tuned for the 5gram weights. They were consistently thrown in the 18 foot range. We didn't retune for different weights and as a result while some 20g weights flew 36 inches, some released prematurely and only flew a high arc landing only ~11 inches from the datum.
A co-worker asked "was on wheels?" and pointed out that they later found it would throw about 30% further with less stress on the structure if it had wheels. The idea is that the ballast wants to fall straight down but the lever arm forces it to translate aft. If the device is on wheels, the falling weight pulls the rest of the structure forward instead of the mass aft, imparting even more speed to the tip of the lever. It works even better if just the axle is allowed to float as only the mass of the axle, lever arm and projectile are accelerated rather than the entire structure. (I smell a v2.0 in the works).
I fear my zeal for technology (in a medieval way) may have overshadowed the point of the exercise. The real goal was probably to show the F = MA effects. For a given force, higher mass means less acceleration, less "muzzle" velocity, less distance. The straight catapult would probably have provided a more consistent F with fewer variables to control. But the Trebuchet scores an order of magnitude higher on the coolness scale! And besides, I always wanted to build one! I'm an engineering geek, guilty as charged. (I'll skip the proper analysis of how the catapult's F varies with position/spring tension that is a staple of a decent DiffyQ class. Too many years of dis-use. The Trebuchet is that times 5 and I'm not going there either ;-) For this age "lighter = further" is probably all the results they need.
Meanwhile, these pikers*** had so much to work with and yet stopped short of their capability. If they had placed the projectile near the base with the tip of the throwing arm near the ground, they could have thrown considerably further.
* She knew we would be spending all day Saturday coaching another school function.
** TLAR = "That Looks About Right"
*** While I "disparage" them for the near miss, I envy what they did and always wanted an excuse to link their geekery!