A Trebuchet

 

Building a Trebuchet

Design

We’ve had this technology for centuries. How hard can it be?... Well, as it turns out, pretty difficult. My goal was to launch a baseball the length of a football field. To reach this, I needed to know how far a baseball would travel with air resistance, how fast the trebuchet would launch it, the structure’s dimensions to withstand the forces, etc… It was an ordeal.

Manufacture

When I began this project, I had very little wood working skills, almost no tools, and I was living on the third story of an apartment building. Not ideal conditions for building a trebuchet. Trying to discreetly cut lumber using your engineering books as a chopping block makes for a tough time. It was a slow process building this trebuchet, but I learned many new, hands-on skills.

Performance

Seeing a project you’ve spent months on finally working is a unique feeling. Inevitably, the first launch never works perfectly. After designing and manufacturing, there is still plenty of work to be done. I had to add minor tweaks after each test launch: redesigned projectile pouch, adjusted sling length, extended launch pad, etc. The joy after the first successful launch though is priceless.

Design

Step 1: figure out how far a baseball will go when not in a vacuum. Sorry physics 101, not good enough. I first started with the standard trajectory equations, then included the effect of drag using numerical approximations. Click the picture to acce

Step 1: figure out how far a baseball will go when not in a vacuum. Sorry physics 101, not good enough. I first started with the standard trajectory equations, then included the effect of drag using numerical approximations. Click the picture to access a Google drive link with an Excel file of my work. It includes a macro that solves the numerical equations and graphs the results.

Solving the trebuchet motion was a lengthy process. I first found the equations of motion of the 3 degrees of freedom system using Lagrangian mechanics. I then found the solution equations to the system of 2nd order differential equations using linea

Solving the trebuchet motion was a lengthy process. I first found the equations of motion of the 3 degrees of freedom system using Lagrangian mechanics. I then found the solution equations to the system of 2nd order differential equations using linear algebra. Finally, I used 4th order Runge-Kutta to solve the solution equations. Click the picture to access a PDF of my full work.

I used an Excel macro to graph the motion of the trebuchet, as seen above, and output the velocity of the projectile. Click on the picture to access a Google drive link with an Excel file of my work. The Excel file includes a macro that solves the 4t

I used an Excel macro to graph the motion of the trebuchet, as seen above, and output the velocity of the projectile. Click on the picture to access a Google drive link with an Excel file of my work. The Excel file includes a macro that solves the 4th order Runge-Kutta equations and creates a graph.

I used the peak accelerations during the launch motion that I found with the Excel macro in the last step to determine the maximum forces each member would undergo. I designed the structures to handle the largest normal and shear stresses by manipula

I used the peak accelerations during the launch motion that I found with the Excel macro in the last step to determine the maximum forces each member would undergo. I designed the structures to handle the largest normal and shear stresses by manipulating material selection and cross-sectional geometry. The picture links a PDF of my work.

I followed the same process for the pivot beam as I did for the launch arm as these two would sustain the largest bending moments and shear forces. For more thorough details, click the picture to find a PowerPoint of my full design.

I followed the same process for the pivot beam as I did for the launch arm as these two would sustain the largest bending moments and shear forces. For more thorough details, click the picture to find a PowerPoint of my full design.

Manufacture

Don't have a chopping block? Just use your largest engineering book.

Don't have a chopping block? Just use your largest engineering book.

Launch arm. The neighbors didn't seem overjoyed during this process..

Launch arm. The neighbors didn't seem overjoyed during this process..

Counterweight

Counterweight

Launch finger

Launch finger

Frame

Frame

Assembled

Assembled

Performance

 

Theoretical v Reality

The results from my model for the trebuchet motion gave an expected release velocity of 90 mph. By counting frames and using known distances, the measured release velocity was 88 mph. Pretty close. My model for a baseball flying at 88 mph launched at 34° predicted a flight distance of 311 ft. The measured result was 235 ft. Not as close… but aerodynamics is a very complex subject. Overall, I was excited with my creation and impressed by my models. A 2% error for the projectile release velocity is nothing to sneeze at.

Skills Used During This Project

Engineering

  • Lagrangian Mechanics

  • Euler’s Method

  • Runge-Kutta, 4th order

  • Shear Force and Bending Moment Diagrams

  • Excel / Excel VBA

Manufacturing

  • Woodworking: circular saw, drill, clamps

  • Knots: adjustable grip hitch, bowline

  • Sewing

  • Installing grommets