The Marshmallow Trebuchet

Introduction

For my Physics 123 class, each team was to come up with a group project somehow related to physics in which we would research a topic, build something to perform experiments with (optional), write a paper, and present our project to the class at the end of the quarter. We decided on building a trebuchet small enough that we could fire it in a fairly large lecture hall. But what to use for projectiles? We needed something that wouldn't hurt any one or damage school property if errant shots when flying where they weren't supposed to. We quickly settled on marshmallows over a lunch meeting. They are light and soft, two properties not typically found in projectiles so it would be a good challenge to see how far we could hurl them. We set out a goal to launch them 20-30 feet, assigned roles to team members, and turned in our project proposal which was quickly approved. 

My part of the project was the design, fabricate, and build portion. Other team members were tasked with researching the history and present day uses of the trebuchet and to make an attempt at working out the physics and math of the trebuchet. The math proved to be one of the most difficult aspects of the project since there is a whipping action where the fixed end of the whip is moving through an arc path while the sling accelerates through it's own path. 

This instructable will focus on our design selection and the actual design we built. 

Step 1: A Little History & Design Selection

History

After some initial research to see what different styles of trebuchet there were, we set about deciding on what to build. The original trebuchet were based on the sling staff, basically a human powered trebuchet. The Chinese developed the traction trebuchet in approximately 400 BC which was a large lever arm and a sling for projectiles. The force to hurl the projectile was generated by many people simultaneously pulling down on ropes connected to the lever arm. 

A long time later in approximately 1100AD, trebuchet with swinging counterweights arrived on battlefields. The hanging mass provided gravitational potential energy which would be relatively the same for every fire providing much greater accuracy. The swinging pendulum action reportedly brought the trebuchet to a stop faster and caused less wear and tear on the machine. 

The trebuchet was the seige machine of choice for centuries but faded out of use around 1400AD with the advent of black powder and cannons. Fast forward to present day and they have become one of the tools of choice for launching pumpkins at the Punkin' Chunkin' festival, as well as projects for DIYers, backyard engineers, and physics & engineering students. 

Design Selection

I had seen a trebuchet used for Punkin' Chunkin' called Merlin and was partial to that design. We initially looked at building that design in a scaled down version but due to the complexity, difficulty of the math involved, and limited time frame, it was eventually ruled out. The floating arm trebuchet was also considered but ruled out for the same reasons. We found an interesting design that was invented by some high school students and refined by their professor L.D. Vance known as the Murlin (creative naming huh?) which stands for multiple radius-linear node. The design features a hanging mass connected to a rope wrapped around multiple decreasing length arms. As the weight falls, the rope pulls faster due to acceleration and due to a changing arm length ratio. This design seemed very effective with Vance's golfball flinging version hitting a range of 636 feet. It was also simple enough for us to tackle in our time frame so we moved forward with the design phase.

Videos of Inspirations for Our Potential Designs

Step 2: Design & Build Process

Design & Build

We decided rather than going with the discrete length linear arms, we would use a continuously changing radius curve similar to the Fibonacci spiral. Before I could design anything to be made, I first needed to understand the motion and what affects the operation of a trebuchet. I used Interactive Physics to model several variations of trebuchet allowing my to show and discuss ideas with my team. The software allows modeling of projectile motion with gravity and air drag for 2D physics problems. It was clear that the limitations of the software wouldn't allow a reasonable test of the design we planned to build so I moved on to developing the 3D components in SolidWorks.

The trebuchet arm was a laminated construction made from 4 layers of 1/4" plywood which allowed a recessed track for the ropes to ride in and an internal spline pattern accepted the finger. The splines were 30° apart and allowed to rotation of the finger into different launch angles. From four different fingers, we were able to achieve most angles from -50° to +50° relative to the arm. The frame was designed from 1/2" plywood and folds up fairly small for transport. Spanning the frame from side to side is a number of sections of aluminum tubing scrounged from scrap bins at my work inside of which is all-thread with nuts on each end. These spacers and threaded rods hold the whole thing together. 

All of the wood components were cut out on my Carvewright CNC router and then sanded to remove sharp edges and splinters. Making all of the parts took about 6 hours and about 15 hours had been spent on the design process. The whole team got together for the final assembly and initial test fires. The arm would be set into motion by ropes wrapped around the curved section, threaded through a double pulley, and connected to a hanging mass. One last thing we overlooked was the sling. A sling was quickly fashioned out of rope, a metal ring to slide over the finger, and duct tape. Our total assembly time was around 30 minutes. 

Tools Used

CNC Router
Metal Band Saw
Metal Lathe
Hand Drill
Various Hand Tools
Sanding Blocks & Paper
Scissors
Lots of Duct Tape

Materials Used

1/4" plywood (leftovers from a project)
1/2" plywood (salvaged from dump trailer at my work)
3/4" OD aluminum tubing (salvaged from scrap bins at my work)
1/2" OD steel tubing (purchased @ Lowes ~ $6.00)
3/8-16 steel all thread & nuts (salvaged from scrap bins at my work)
3/16" 40lb nylon rope (purchased @ Lowes ~ $5.00)
1" diameter metal rings (purchased @ Lowes ~ $1.70)
Double pulley (purchased @ local hardware store ~ $4.00)
5lb rusty old dumbbell weight (not sure where it came from but its been floating around my garage for years)
Old bike spokes (free, used to make mass hanger and reinforce pouches)
Bag of Jumbo Campfire Marshmallows of avg weight 21g/marshmallow (purchased @ local grocery store ~ $3.50)
misc hardware...

Total cost: Less than $30.00 out of pocket

The video below highlights three of the simulations and some of the manufacturing steps. Also shown is an exploded view of the 3D assembly. 

Step 3: Test Firing & Troubleshooting

Test Firing & Troubleshooting

Once the build process was completed, it was time to try firing our contraption. It took a bit of trial and error with the different finger angles but eventually, we got it to shoot forward about 15 feet. This was with an impromptu hanging mass made from a 1-2-3 block and a 2lb sand bag ankle weight. It was dark by the time we got it to fire so everyone went home for the evening and we reconvened the following day at a grade schools play field. In the morning, I spent some time tweaking the design and lobbed three marshmallows up into my neighbors trees at a high velocity. 

The weight was replaced by a 5lb dumbbell weight which allowed for a greater vertical drop and in turn, more energy introduced into the system. We ran out a 100ft tape and proceeded to test our creation with numbered marshmallows and carefull data logs of each fire. We were disappointed when our first several test fires were a failure after the three perfect shots at my house. Adjusting angles and fussing with loading methods eventually got us up and running. Video was shot from several angles for analysis in LoggerPro software which we later used to determine our launch velocities. Although we did get some nice tight clusters of consistent shots, there were some that shot straight back, almost straight up, and one that landed on the roof of the school behind us. I'm sure someone will be wondering why there is a numbered marshmallow on the roof. 

Analysis of the video footage frame by frame revealed that the marshmallows were sometimes rolling out of the sling partway through the whipping motion. Several other sling designs were tested and one that was based on L.D. Vance's golf ball sling yielded our max distance of 52.5 feet although degraded the more we used it eventually to the point of no longer firing the projectile. This was due to all of the force on the sling stretching and distorting the duct tape used for construction. The sticky nature of abraded marshmallows certainly didn't help matters either. 

The video below was created by two of my team mates highlighting some of our test fires. 

Step 4: Conclusion

Conclusion

We exceeded our original goal of 20-30 feet with a longest recorded launch of 52.5 feet and launch velocities upwards of 45 MPH. Comparison between the kinetic energy of the projectile and the gravitational potential energy of our hanging mass showed an efficiency of a little over 16%. We feel this can be greatly improved upon with the following tweaks:

1. Replace stretchy rope with Spectra or similar low to no stretch line.
2. Improve sling/pouch design.
3. Replace or modify firing fingers with design that allows ring to slide off smoothly and consistently.
4. Leave marshmallows in a paper bag for several days (they get much harder).
5. Eliminate slop in frame design.
6. Stake frame down to the ground.
7. Replace plastic bushings from arm with better bushing/bearing arrangement.
8. Increase pulley diameter.
9. Increase height of hanging mass to ensure potential energy remains for full travel of arm.
10. Improve launch angle to approach or hit 45°.

After seeing what this design can do, I think it is feasible to hit the 100 foot mark if sufficient efficiency improvements were to be made.