Effect of Trebuchet Arm Length or Counterweight Mass on Projectile Distance

Objective

The goal of this project is to determine how changing the length of throwing arm or the mass of the counterweight will affect the distance that a projectile can be thrown by a trebuchet.

Introduction

A trebuchet is kind of catapult that uses a counterweight to supply the energy for throwing the projectile. They were used as siege engines in the Middle Ages in Europe to hurl heavy stones at castle walls. The power of the trebuchet is based on a simple machine: the lever.

Figure 1, below, is a picture of a reconstructed trebuchet, at Château des Baux, France. The counterweight hangs from the short end of the lever arm, and the projectile is held in a sling attached to the long end of the lever arm. To prepare the trebuchet for firing, the long end of the lever arm is pulled down, which raises the short end of the lever arm, along with the counterweight that hangs from it. The counterweight is much heavier than the projectile, so when the lever arm is let go, the counterweight falls, whipping the long end of the lever arm up into the air. The sling increases the whipping action and hurls the projectile into the air.

Figure 1. Reconstructed trebuchet at Château des Baux, France. The projectile is held in the sling, at the long end of the lever arm (at left). The long end of the lever arm is pulled down, raising the counterweight suspended from the short end of the lever arm (right of center). When the long end of the lever is let go, the counterweight pulls the short end of the lever down, whipping the long end of the lever arm up. The sling follows, and the projectile is sent flying through the air. (Wikipedia, 2006)

As you can see from Figure 1, most of the material that goes into building a trebuchet is used to make a solid supporting structure for the lever, but it is the lever that does the work. Figures 2 and 3, below, strip away the support structure to focus on the trebuchet lever.

Figure 2. Diagram of a trebuchet lever arm. The pivot point is off-center, so a 10 kg counterweight on the short arm just balances a 2 kg projectile on the long arm, at 5× the distance. (Diagram modeled on Gurstelle, 2004, page 144.)

The key to the trebuchet lever arm is the location of the pivot (or fulcrum). The pivot is off-center, with the counterweight suspended from the short arm. Figure 2 shows the trebuchet lever in a balanced condition. A 10 kg counterweight just balances a 2 kg projectile because the projectile is five times further from the pivot point. In actual use, the counterweight would be much heavier than the projectile.

Figure 3 shows what happens when the loaded trebuchet lever is released. The counterweight falls, raising the long end of the lever arm. In this case, the long end of the lever would fly up five times faster than the counterweight falls. The lever provides a mechanical advantage, trading the weight of the falling counterweight for speed of the long lever arm.

Figure 3. Diagram of a trebuchet lever arm in action. The trebuchet uses the mechanical advantage of the lever to trade weight for speed. (Diagram modeled on Gurstelle, 2004, page 144.)

For the army attacking a castle with a trebuchet throwing distance was very important, in order to stay out of range of the defending archers. What lever arm length produces the greatest hurling distance? What is the best weight to use for a particular lever arm and projectile? In this project, you can build a model trebuchet and find out for yourself.

Terms, Concepts and Questions to Start Background Research

To do this project, you should do research that enables you to understand the following terms and concepts:

• catapult,
• trebuchet,
• fulcrum (or pivot),
• lever,
• mechanical advantage.

More advanced students should also study:

• momentum,
• kinetic energy,
• potential energy, and
• Newton's laws of motion.

Questions

• How does placement of the pivot point on the lever arm affect the mechanical advantage of the trebuchet?
• What should the mechanical advantage be for optimal throwing distance?
• What should the mass of the counterweight be for optimal throwing distance?
• What should the length of the sling be for optimal throwing distance?
• How is throwing accuracy affected by the above-mentioned factors?

Bibliography

• A good place to start your research is this Wikipedia article on trebuchets:
  Wikipedia contributoros, 2006. "Trebuchet," Wikipedia, The Free Encyclopedia [accessed November 9, 2006] http://en.wikipedia.org/w/index.php?title=Trebuchet&oldid=87386114.
• The PBS NOVA Online website has an episode on Medieval Sieges that has information on trebuchets. You can play an interactive game to destroy a castle (requires Shockwave) and learn about the mechanics of trebuchets:
  WGBH, 2000. "Secrets of Lost Empires: Medieval Siege," WGBH Educational Foundation [accessed November 9, 2006] http://www.pbs.org/wgbh/nova/lostempires/trebuchet/.
• More advanced students should also study Newton's three laws of motion, which are introduced in these four lessons from The Physics Classroom:
  Henderson, T., 2004. "Newton's Laws," The Physics Classroom and Mathsoft Engineering & Education, Inc. [accessed November 8, 2006] http://www.physicsclassroom.com/Class/newtlaws/newtltoc.html.
• This book has detailed plans for building seven different historic catapult types, as well as information on the history and mechanics of catapults:
  Gurstelle, W., 2004. The Art of the Catapult: Build Greek Ballistae, Roman Onagers, English Trebuchets, and More Ancient Artillery. Chicago, IL: Chicago Review Press, Inc.
• Filip Radlinski did a school physics project based on a trebuchet and put together this excellent website that summarizes his work (includes building tips and photographs):
  Radlinski, F., 1997a. "The Physics of the Trebuchet," Filip Radlinski personal website [accessed November 9, 2006] http://www.geocities.com/SiliconValley/Park/6461/trebuch.html.

Materials and Equipment

There are many trebuchet plans to choose from. The book The Art of the Catapult, by William Gurstelle (Gurstelle, 2004), has several plans. You can also find plans online by doing a web search on 'trebuchet plans.' Here are some things to look for in a good plan:

• appropriate size for your test area ("tabletop" models are probably your best bet unless you have lots of space for testing),
• readily available materials,
• clear illustrations and instructions.

For building the trebuchet, you will need:

• wood,
• fasteners,
• glue,
• sandpaper, and
• tools for cutting the wood to size.

You'll also need:

• a projectile (e.g., practice golf balls or other small, light balls), and
• a tape measure.

Experimental Procedure

Safety note: adult supervision is required for this project. Trebuchets have moving parts and are designed to throw projectiles. Exercise proper caution when building and using your trebuchet.

1. Choose a trebuchet design (see the Materials and Equipment section above, for suggestions).
2. Build your model.
3. Try different lengths for the long end of the lever arm. Remember that you'll need to plan for extra materials in order to build the different lever arms for testing.
4. Try different masses for the counterweight.
5. For each condition, conduct at least 10 trials to test the throwing distance. Measure and record the distance from the trebuchet to where the projectile first lands.
6. Calculate the average distance for each condition. More advanced students should also calculate the standard deviation.
7. Graph your results. Which condition produced the longest throw? Do the data show a consistent trend? Do your data suggest that you could make further increases in throwing distance?

Variations

• Determine the accuracy of your trebuchet. Fire a large number of shots with identical conditions (i.e., same payload, counterweight, lever arm, launch angle). Record where each shot lands (distance and angle from trebuchet). Graph the results. What is the average distance for a shot? What is the scatter? How do distance and scatter change as you systematically vary one shooting parameter (e.g., payload weight, lever arm length, counterweight mass)?
• For another project featuring catapults, see the Science Buddies project Bomb's Away! A Ping Pong Catapult.
• What is the optimal length for the sling that holds the projectile? Design an experiment to find out.
• Compare different trebuchet designs and see if you can determine which feature(s) are important for increasing the distance a projectile can be thrown. Then build two or more trebuchets to compare the feature (or features) you've identified and how it affects performance.

Credits

Andrew Olson, Ph.D., Science Buddies

Sources

This project is based on:

• McGiffen, K.C., 2003. "Investigations into the Art of Hurling: Effects of Trebuchet Arm Length and Counterweight Mass on Projectile Distance," California State Science Fair Project [accessed November 9, 2006] http://www.usc.edu/CSSF/History/2004/Projects/J0220.pdf.

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