A Compound Catapult

by Malcolm Durkin

Below is pictured a unique catapult I built as a member of the Worthington Kilbourne High School Science Olympiad Team. This device placed third in the Storm the Castle competition at the Ohio State tournament held on Apr. 24, 2004 (see Worthington Suburban Newspaper article). I like to believe it would have come in first or second if I had aimed it better.

The other devices in the competition were either conventional trebuchets or catapults. My device worked differently. When the arm is released the weight begins to fall providing a constant acceleration of the projectile at the end of the arm. While the shaft rotates through 2.5 revolutions a tether slowly tightens. When the tether goes taught the arm stops and the projectile continues on its way at high velocity. It will outperform either a conventional trebuchet or catapult as is shown in the calculations below. With a 3 kilogram counter weight I was able to consistently fire a golf ball 18-19 meters. The shots land typically within a ½ meter radius at this distance.

An avi movie file of the launch can be found here.catapult_files/slaunch.avi.

The same avi movie file in slow motion can be found here.catapult_files/slaunch2.avi

Physics

Conservation of Energy: Gravitational Potential Energy = Kinetic Energy

Range (45 degree angle):

Solving for Range:

This is the same equation one would derive for either a conventional catapult or trebuchet. The advantage of the compound catapult is clear. One wants to minimize while maximizing h. Of course there is a point at which there is not enough torque to move the arm. The limit is . For conventional throwers one cannot exceed h=2r for falling distance. In my Compound Catapult one can drop the mass M the full 75 cm allowed by the rules. One is then able to set the ratio as one chooses. Making the wheel and arm fairly small serves to decrease the moment of inertial (ignored in the calculation above) of the PCV pipe, which will further increase distance.

Construction

My compound catapult was constructed using standard ½ inch PVC pipe. The wheels were 3 ¾ inch laundry line wheels purchased at the hardware store drilled to fit over the ½ inch PVC pipe. Since the laundry wheels were not PVC I had to use PL premium construction adhesive (available at any hardware store) to attach the wheels to the pipe. The throwing arm is approximately 18 inches in length. Roller blade bearings were positioned at each end of the axel pipe. By coincidence they fit nicely inside a PVC ½ inch to ½ inch joint piece with a little sanding. I used a ¼ inch threaded inside the roller blade bearings securing the ends with ¼ inch nuts.

Note in the picture there are two laundry wheels. Once is for the dropping weight while the other acts to precisely stop the arm at 45 degree (adjustable) after multiple turns. My device rotates 2 1/2 turns before releasing.

I designed multiple throwing heads using plastic cups with vertical sides. This is a trial and error procedure but is much easier than constructing a trebuchet sling.

Competition Hints

- Make throwing heads easily interchangeable

- Be sure not to violate the rule against adding energy with the device. Start arm closer to the ground than it finishes.

- With the stopping mechanism keep it simple. Here are some pictures describing a reliable stopping mechanism.

For the stopping mechanism I used fishing line (the expensive 65 lb non-stretch “fireline” works very well), which slowly tightens pulling the line taught at the projectile’s release. Unfortunately, this design alone has a nasty habit of the line leaving the spool and getting tangled in the throwing arm, thus one loses all control over the device. This is especially bad on a windy day. The solution is to thread a nut or a washer through the line. Use it to weigh the line down and when the device fires, it will slide down to one end of the fishing wire. The control spool has to take a lot of force, though. If not attached properly, it will break. Make this spool connection as strong as possible.

- If you experience troubles with the projectile falling off of the device at random, angle the heads slightly.

- Trajectory is very important. The control of the firing anlge is a major advantage.

- Do target practice. My team came in third because we had only about 6 hours of true target practice (We built this specifically for the state tournament. New technology is hard to test).

- Check out your opponent’s launchers. You might see something very interesting.

- When tying the counterweight use a figure eight knot.

- Many teams use complicated firing mechanisms, which look pretty but don’t work very well. Wedging a PVC pipe underneath or above the arm works surprisingly well.

- Warning- if something goes wrong, a compound catapult has the ability to launch the projectile backwards as well as forwards. This is especially dangerous when using golf balls projectiles. Don’t stand behind the device or put anything valuable behind it.

Summary

Advantages

1) The distance h the mass is dropped is independent of the ratio r/R.

2) The throwing arm can be made short thus decreasing its moment of inertia.

3) The design is simple and easy to build.

4) With no slings the device is easier to operate than conventional trebuches.

Disadvantages

1) Multiple rotations impose large stresses on device frame.

2) The release point of the projectile must be finely tuned.