Introduction:

The trebuchet, mistaken most commonly as a catapult, is an ancient weapon used primarily by Norsemen in the Middle Ages. Being able to throw very heavy, large objects, normally boulders, caused it to be a highly effective tool in the siege of a castle. Its main purpose was to strike and destroy part of a fortress wall so that soldiers could invade, burn, and pillage. Trebuchets were widely used until the invention of the canon, which was small, maneuverable, and more accurate. Trebuchets were now obsolete, and disappeared from history.

However, the recent rediscovery of these giant devices has caused a massive increase in popularity. A desire to dawn the ability to "fling" something ginormous has sprung up, especially in young people. The Boy Scouts use them to launch water balloons and teach knot tying, enthusiast groups try to throw cars, and others are just in it for the laughs.

The biggest factor that brings interest to trebuchets is the fact that something so simple can chuck something so far. It is this principle that caused us to endeavor to find out more about the workings of the massive machine.
 
 

The Basics:

If you're not familiar with the basic ideas behind how a trebuchet works, it's really quite simple. The potential energy needed to fling an object is created by raising the counterweight. As the counterweight is released, it will cause a torque on the axle. This force will rotate the throwing arm. Thus, the heavier the weight, the farther the toss. Also, as the length of the throwing arm increases, the force on the projectile will increase.

Working Setup:

MATERIALS:

DESIGN:

In the following report, there is quite a bit of subject specific treb (that's what a trebuchet is called for short) vocabulary. We'll try not to recreate a freshman english course for you, but here is a diagram that will help you to understand the parts of a trebuchet.

The Experiment:

•Purpose:

Upon choosing this project, we already knew the basics of the trebuchet. So, we have strived to find something that is not commonly known, or researched. After getting over the shear manly joy of being able chuck something for a school project, we found that none of our sources had tried to theorize about the placement of the throwing arm on the axle vs. the range of the trebuchet. Grunt, grunt, scratch, scratch! We decided to try to answer that question and hypothesized that, in order to make an optimum toss, the axle must be placed on the arm where the maximum torque can be produced.

•Math:

As we said before, the basic workings of a trebuchet are really easy to understand. However, our childhood daydreams about launching fresh fruit were shot out of the sky when we sat down and tried to calculate what our treb could do. Explaining, scientifically, the physics that are involved in this seemingly simple machine is a tedious and frustrating process.

•Formulas:

To be able to accurately input the mass of the counterweight and account for the mass of the beam on the counterweight side of the axle, we used energy to find this formula: (Mtot=total mass, CW=counterweight, B=beam length)
 
 

Mtot(CW)= ((CWmass)(B+Bsin0)+(Beammass)(B+.5Bsin0))/ (B+Bsin0)
 
 

The CW mass total, when plugged into the computer, will allow you to simulate a non-uniform beam more easily.

The next formulas will allow you to try to find the angular acceleration by using torque:

torque on CW side of the axle:

torque=B(CW(9.8))sin(90+0)
 
 

torque on the projectile side of the axle (anti-torque):

torque=(Bon the projectile side)(P)(9.8)sin(90-o)
 
 

By subtracting the anti-torque from the counterweight torque, you can find total torque-- and eventually, the velocity of the projectile at the release point.
 
 

torque=(Moment of inertia)(Rotational acceleration)
 
 

omega2= omegao2+2(rotational acceleration)(0)

You can find omega using these formulas, but we struggled and failed to find a way to determine the angle at which the projectile is released. But, this math aided us in the use of the trebuchet simulator, which is in the next section.
 
 
 
 

•Computer Simulation:

In order to figure out what the heck we were doing, and how we were going to design the mammoth beast, we needed a little help from someone experienced in the art of hucking. After searching the internet for a short amount of time, we discovered The Grey Company homepage: a site dedicated to medieval weaponry. There, we found pictures of real trebs and a handy computer program that simulates a trebuchet.
 
 

This program allows you to plug in all of the independent variables of the treb mechanics. It "performs" the toss similar to that of a real treb, solving for distance and efficiency. MacTreb 3.0 was created by Donald B. Sianno, and is based on math that's in our physics text. So, it's worth the download time.

Knowing that our throwing arm was 12 feet long, we used a highly scientific method (trial and error) to speculate the placement of the axle. Keeping the weight of the projectile and the counterweight constant, we were able to adjust the axle back and forth easily on the arm. After the trials, we decided that the axle on our throwing arm should have been placed 3 feet from the counterweight. We increased the masses of the projectile and the counterweight, maintaining a constant ratio of 11/250 lbs. At several different mass settings, the ranges of the tosses were not the same; all of these trials were done with a 12 foot throwing arm. When we increased the throwing arm by the same amount as the masses, the range remained constant.
 
 

The simulator provided us with the following prophesies for our trebuchet:

With a 250 lbs counterweight an 11 lbs projectile should be thrown 42.7 feet

With a 460 lbs counterweight an 11 lbs projectile should be thrown 85 feet

With a 250 lbs counterweight a 5 lbs projectile should be thrown 62.5 feet

•Construction

Once we got over the adrenaline rush of getting to finally build something gigantic, we began construction of the mighty chucker (actually, we waited (procrastinated (slacked)) three months before we built). We gathered our materials and shouldered the burden of the bitter cold. First, we lashed (that's the Boy Scout word for: tied together) 6, 8 foot, wooden poles together for the two A-frames. After 3 or 4 trips to the hardware store, we bolted (that's the Boy Scout word for "lazy") 3, 8 foot poles for our throwing arm. We used a 55 gallon drum as our counterweight. Like the computer simulation suggested, we fastened our axle to the throwing arm approximately 3 feet from the counterweight.

•Error and Trial

Now, it was time for the first real toss. After spending immense amounts of energy to cock the treb and load "Billie" (the bowling ball), we let go of the trigger. Billie went 20 feet-- backward. Not satisfied with this result, we loaded the treb for another throw. It went 25 feet this time-- still backward. It was at this time that both of us realized the problem with our design; the sling was not functioning according to plan. The computer program suggested that we use a foot long sling, however, we had neglected the need for a specific design for it. On the next several launches, we attempted to find the bug in our release mechanism. We found that if we decreased the angle of the finger, it would throw the projectile forward.

So, we decreased the angle of the finger-- which caused it to throw straight into the ground. When we finally did get the projectile to go into the air, it went straight up. After some thought, we figured that the treb would throw farther if we moved the counterweight to the underside of the throwing arm. This would cause the arm to come to rest naturally at a more vertical angle then before and, hopefully, the ball would now release and throw forward. After making this adjustment, we were able to accomplish a throw of 30 feet. Although, the treb didn't have the range that the computer said it would, which was 42.7 feet, it had 70% efficiency compared to the program.

•Why our trebuchet was only 70% efficient

We started this project with the impression that trebuchets were simple machines. We now know that they are far from simple. The mathematics behind the dynamics of a treb were too hard for us to do and understand entirely. Also, we learned that a single flaw in the design of the machine can cause a major decrease in efficiency.

Our design, on the other hand, was not flawed in one way-- it was flawed in many ways. First, we had no idea how to properly angle the finger in order to ensure an efficient toss. Our treb, consequently, threw the projectile backward or straight into the ground. Second, our throwing arm was not uniform like the computer simulated arm. This probably caused our calculations to be slightly uncertain. Third, the counterweight on the simulator was concentrated in one point at the end of the arm; our counterweight was acting on about 3 feet of the arm. Therefore, the force on the arm was not focused at the end. The 55 gallon drum we used as our counterweight was only filled half way. As the arm rotated, the water in the drum sloshed around. The force on the rotation was not constant.

CONCLUSION:

Even though our trebuchet was not as effective as we would have liked, it's near failure aided us in forming a more thorough conceptual understanding of how one works. If we could do more trials, we would be able to make educated choices about our design and rectify some of the setbacks that we encountered in first attempt. We would start by hanging the counterweight from the end of the throwing arm, which would concentrate the force there. Using something other than water as the counterweight, something solid, would cause a constant force on the rotation and a smoother toss. That would probably cause a treb to show results similar to our calculations. In conclusion, we are definitely more skilled at rolling bowling balls at pins than trying to throw them at castles.

Links to related sites:

The Grey Company Trebuchet Page is a page totally devoted to trebs and how they work. A must see page.

The Algorithmic Beauty of The Trebuchet is created by Donald B. Sianno (the guy who wrote MacTreb). This site explains, in detail, the mechanics of trebuchets. Simulators are available for free on this site.

Timber Framers Guild Home Page contains pictures and designs for working trebuchets.

NOVA has more historical info, pictures, and a downloadable Treb videogame.

A Dead Cow? need I say more?

http://trebuchet.com/ explores the fundamentals of trebuchet-aided flight.