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Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance

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Areas of Science
Time Required
Long (2-4 weeks)
Some knowledge of physics will be helpful when doing this project.
Material Availability
Readily available
Average ($50 - $100)
Adult supervision is required when building and operating a trebuchet.

Ben Finio, PhD, Science Buddies

*Note: For this science project you will need to develop your own experimental procedure. Use the information in the summary tab as a starting place. If you would like to discuss your ideas or need help troubleshooting, use the Ask An Expert forum. Our Experts won't do the work for you, but they will make suggestions and offer guidance if you come to them with specific questions.

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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.

A reconstructed trebuchet
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:

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 energy of the payload, launching it into the air.

Diagram of a trebuchet
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.

Schematic of a trebuchet

m1 is the mass of the counterweight in kilograms (kg). m2 is the mass of the payload (kg). h is the initial height of the counterweight off the ground. L1 is the distance between the pivot and the counterweight's attachment point in meters (m). L2 is the distance between the pivot and the sling's attachment point (m). L3 is the length of the sling (m). L4 is the length of the rope suspending the counterweight (this distance is zero if the counterweight is fixed directly to the lever arm) (m).

Figure 3. Schematic you can use to start analyzing the physics of a trebuchet. Note that m1 and m2 can be treated as point masses (so you do not need to account for their diamters), but are drawn larger in the figure.

The variables in Figure 3 are as follows:

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:

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?

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:

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?


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.


These references will be useful for learning about the physics of trebuchets. Some of these references contain advanced math, including calculus and differential equations, but you can still use them to help you get started.

If you search online, there are many different plans and designs for building a trebuchet. This book also contains some useful designs and building tips:

Autodesk Inventor software is available as a free download for students from:

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MLA Style

Science Buddies Staff. "Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance." Science Buddies, 23 June 2020, https://www.sciencebuddies.org/science-fair-projects/project-ideas/ApMech_p013/mechanical-engineering/effect-of-trebuchet-arm-length-or-counterweight-mass-on-projectile-distance. Accessed 30 Nov. 2023.

APA Style

Science Buddies Staff. (2020, June 23). Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance. Retrieved from https://www.sciencebuddies.org/science-fair-projects/project-ideas/ApMech_p013/mechanical-engineering/effect-of-trebuchet-arm-length-or-counterweight-mass-on-projectile-distance

Last edit date: 2020-06-23
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