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Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance *
Summary Background Make It Your Own Help Learn More
Difficulty
Time Required Long (2-4 weeks)
Some knowledge of physics will be helpful when doing
Prerequisites
this project.
Material Availability Readily available
Cost Average ($50 - $100)
Adult supervision is required when building and
Safety
operating a trebuchet.
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*Note: This is an abbreviated Project Idea, without notes to start your background research, a specific list of materials, or a procedure for how to do the
experiment. You can identify abbreviated Project Ideas by the asterisk at the end of the title. If you want a Project Idea with full instructions, please pick one
without an asterisk.
Abstract
Before cannons widely replaced them, siege engines were often used by armies to throw large stones and other projectiles to break down castle walls. One of the
most advanced siege engines used in the Middle Ages was the trebuchet, which used a large counterweight to store energy to launch a payload, or projectile.
The horizontal distance the payload would travel is called the trebuchet's range. Figure 1, below, shows a modern reconstruction of a trebuchet.
The range of a trebuchet has always been important. In the Middle Ages, soldiers had to make sure their trebuchets had a long enough range to stay outside the
range of defending archers on castle walls. While they are no longer used in warfare, today people still build trebuchets for fun and use them in contests to see
who can launch things the farthest. There are many different factors that can affect the range of a trebuchet; for example, the mass of the counterweight or the
length of the lever arm. While designers of the Middle Ages had to rely largely on intuition or trial and error to build their trebuchets, modern builders have many
helpful tools available. In addition to building prototypes of a trebuchet, you can also use physics calculations or even a computer simulation to help you design it
to have the best range.
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Figure 1. Reconstructed trebuchet at Château des Baux, France. The payload is loaded into the sling, at the long end of the lever arm (on the left). To launch the
payload, first the long end of the lever arm is pulled down, which raises the counterweight suspended from the short end of the lever arm (on the right). Then, the
long end of the lever is let go, and gravity pulls the counterweight down, whipping the long end of the lever arm up. The sling follows, and the payload is sent flying
through the air (to the right). (Wikimedia Commons user Quistnix, 2005)
This abbreviated engineering project idea will help you get started with three different ways to investigate what factors can increase the range of a trebuchet:
Trebuchet Physics: Use hand calculations to predict the range of a trebuchet based on its dimensions and other variables.
Computer Simulations of a Trebuchet: Use computer simulations to predict the range of a trebuchet and modify its design.
Building a Trebuchet: Build your own trebuchet and test it.
You can decide whether you want to try just one, two, or all three of these approaches. Read the relevant section(s) below for ideas on how to get started on your
project.
Trebuchet Physics
If you want to do hand calculations to design a trebuchet with the best range, you will need to understand the physics involved. Figure 2, below, shows a diagram
of a trebuchet with the main parts labeled. The trebuchet relies on the principle that stored potential energy of the counterweight can be converted into kinetic
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of a trebuchet with the main parts labeled. The trebuchet relies on the principle that stored potential energy of the counterweight can be converted into kinetic
energy of the payload, launching it into the air.
Figure 2. A diagram of the main parts of a trebuchet.
Figure 2 raises several questions about designing a trebuchet. To throw the payload as far as possible, how long should the beam be? Where should the pivot point
be on the beam? How high off the ground should the pivot be? How heavy should the counterweight and the payload be? Figure 3, below, shows a sketch that can
help you start thinking about how to set up the problem, and the variables involved.
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Figure 3. Schematic you can use to start analyzing the physics of a trebuchet. Note that m and m can be treated as point masses (so you do not need to
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account for their diamters), but are drawn larger in the figure.
The variables in Figure 3 are as follows:
m is the mass of the counterweight in kilograms (kg).
1
m is the mass of the payload (kg).
2
h is the initial height of the counterweight off the ground.
L is the distance between the pivot and the counterweight's attachment point in meters (m).
1
L is the distance between the pivot and the sling's attachment point (m).
2
L is the length of the sling (m).
3
L is the length of the rope suspending the counterweight (this distance is zero if the counterweight is fixed directly to the lever arm) (m).
4
How can you use these variables to calculate the range of a trebuchet? There is more than one way to tackle the problem. Depending on your experience levels
with math and physics, you can try the following approaches:
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If you have knowledge of basic physics concepts like projectile motion and conservation of energy, can you predict the maximum possible range of the
trebuchet, assuming all of the counterweight's initial potential energy is converted to kinetic energy of the payload? Hint: Assume the payload leaves the
sling at a launch angle of 45°.
Can you derive equations that describe the position of the payload as a function of time, before and after it leaves the sling? Assume the trebuchet starts
from rest with the counterweight at height h above the ground. What variables do you need to use to fully define the position of the trebuchet and the
payload? Hint: They are not labeled in Figure 3. One of them is the angle of the lever arm, but do you need more than that?
In either case, can you make your analysis more realistic by accounting for things like friction and air resistance? What about moments of inertia, which are
not labeled in Figure 3?
This is a complex physics problem, so there are some references in the Bibliography to help get you started. If you get stuck, you may need to consult a physics
textbook, ask your physics teacher for help, or do your own internet search for "trebuchet physics." Once you have derived an equation for the range of a trebuchet
based on the physical parameters above, can you come up with any design guidelines or rules of thumb for designing a trebuchet with the best possible range?
Computer Simulations of a Trebuchet
Sometimes, the calculations required to analyze a mechanical system get too complicated for even a professional engineer to do by hand. When this happens,
modern engineers can use computer simulations to predict how a physical system will behave. A computer simulation of a trebuchet allows you to rapidly check
how different parameters (like the mass of the counterweight) affect the range of the trebuchet, and makes it easier to include things that are difficult to model in
hand calculations, like friction.
The video below shows how you can use a computer-aided design (CAD) program called Autodesk Inventor to simulate a trebuchet. To follow the video tutorial,
you will need to:
Download and install a copy of Autodesk Inventor (free for students) from http://www.autodesk.com/education/free-software/inventor-professional (requires
creating an Autodesk.com account).
Download the Inventor files for the trebuchet. You can use this file to get started following the tutorial, and create your own design later when you are more
familiar with the software if you'd like.
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A video tutorial for using Autodesk Inventor to simulate a trebuchet. Note: this video is part two of a five-part series entitled "Dynamic Simulation & Finite Element
Analysis (FEA) — Autodesk Inventor 2011" available on YouTube. The part about dynamic simulation that you need for this project starts at the 6 minute mark of
this video, so you can skip to that point in the video to get started. If you want to learn more about using Inventor, you can watch all five videos, starting with the
first one. You can find the other videos in the YouTube sidebar or on the author's YouTube channel.
Can you use Autodesk Inventor to see how changing different parameters affects the performance of a trebuchet? Can you find a design that gives the farthest
range? You could also try comparing the simulations in Autodesk Inventor to hand calculations (see previous section).
Building a Trebuchet
This is probably the most exciting part of investigating how trebuchets work: actually building one! There are many different approaches to building a trebuchet, and
you can find many different guides and designs online and in books (see the Bibliography for one example). Before you start building a trebuchet, ask yourself the
following questions to help you pick a design:
How much space do you have to test your trebuchet? Do you have a large outdoor area to test a big one? Do you need to build a miniature trebuchet that
fits on a tabletop? Or something in between?
What is your budget, and what materials do you have access to? Do you need to use household materials like cardboard, duct tape, and string? Can you
make a trip to the hardware store and build your trebuchet with wood, nuts, and bolts?
What tools and safety equipment do you have access to? Will you need help from an adult to use tools like a power drill or saw?
How much time do you have to build your trebuchet? Do you have time to do a fancy design, or do you need to build one quickly?
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What should the various dimensions and parameters (lever arm length, counterweight mass, etc.) of your trebuchet be? Can you pick these parameters
based on hand calculations or computer simulations (above), or based on design information you found through your own research?
Do you want any of the parameters to be adjustable; for example, a bucket that you can fill with different weights for the counterweight, or a lever arm with
notches or holes so you can change the pivot location and adjust the relative lengths of each side (L and L in Figure 3, above)?
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What factors can increase the range of a real trebuchet, based on the one you build and test? For a very impressive science project, you could also compare the
range of the trebuchet you build to predictions based on hand calculations and/or computer simulations you make (above). How closely do they match? What real-
world things (like air resistance, or how exactly the payload is released from the sling) were difficult to account for in your calculations or simulations?
Objective
The goal of this project is to determine how different physical parameters can affect the range of a trebuchet, using hand calculations, computer simulations, and/or
physical experiments.
Credits
Ben Finio, PhD, Science Buddies
Cite This Page
MLA Style
Science Buddies Staff. "Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance" Science Buddies. Science Buddies, 9 Apr. 2015. Web. 25
July 2015 <http://www.sciencebuddies.org/science-fair-projects/project_ideas/ApMech_p013.shtml>
APA Style
Science Buddies Staff. (2015, April 9). Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance. Retrieved July 25, 2015 from
http://www.sciencebuddies.org/science-fair-projects/project_ideas/ApMech_p013.shtml
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Last edit date: 2015-04-09
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