Compound Catapult #2 (Multiple Rotation Trebuchet) 2005

Malcolm Durkin

 

 

 

Despite the success of my Compound Catapult (3rd place finish in the Ohio State Finals of the Science Olympiad), it was clear that upgrades were necessary. One step was making the arm lighter, and the other was adding a sling to make the release smoother. The result was a major increase in range (25+ meters with 2.5 kg and golf ball (46g). My friends think the other one is cooler to watch because it is more violent). Movies of the device firing are given in the following links (movie1.avi ,movie2.avi or movie1.mov ,movie2.mov ). The counterweight is a 1.5 kg brick and the projectile is a 46 gram golf ball.

 

We separated the digital files into separate frames, and using Adobe Photoshop measured the position of the golf ball in each frame (every 1/30 of a second). A picture of the digitized positions superimposed on the initial frame is shown below.

 

 

 

 

From the last two digitized points we measure that the release velocity of the golf ball is 16 m/s at an angle of 58 degrees. Show below is a plot of the velocity measured from the frames as a function of time and angle respectively.

 

Speed (m/s)

 

Time (seconds)

 

 

 

Figure 1: Speed of the golf ball as a function of time

 

 

Speed (m/s)

 

Angle (degrees)

 

Speed (m/s)

 

Angle (degrees)

 

 

 

Figure 2:Speed of the golf ball as a function of angle

 

These plots are odd to say the very least. The initial acceleration is tremendous, and the speed seems to rise in steps.This is not the behavior expected from what at first glance is a simple Atwood’s machine.

 

To understand this behavior we attempted to mathematically model this device. The derivation of the equations of motion are complex (see derivation) but doable (with help from my father). There probably is no closed form solution to these differential equations so they were solved numerically on a computer (C-code is here). The following movies show the result of the calculations (fast.avi, slow.avi, slow.mpg, fast.mpg ).

 

 

 

The motion is clearly a succession of the golf ball lagging behind being dragged forward by the arm. The tension in the string at several points gets so large that is stops the arm, and thus the large mass from moving.This is why people build trebuches. At this magical point only the golf ball is moving. There is nothing else moving, so all of the potential energy of the falling mass has gone into kinetic energy of the golf ball. If you look at slow motion movies of the actual trebuchet launch you can see the mass stops moving at about 20 degrees past vertical on the first rotation (slowmovie1.avi , slowmovie2.avi, slowmovie1.mpg , slowmovie2.mpg ).

 

 

Even with the relative sparse number of frames we have to analyze it is seen the mathematical model does not fit the real trebuchet very well. The model seems to describe the first rotation quite well. Damping in the device (bending rods, arms, and wood) probably account for the slightly smoother behavior of the real trebuchet.

 

For the Compound trebuchet (or multiple Rotation Trebuchet), since it rotates around two and a half times, this magic point happens nearly periodically in the simulation. The graphs below show the rotation speed of the arm (red), the golf ball relative to the end of the arm (blue), and the golf ball with respect to the lab. One can tune these magic points by varying the arm to sling length ratio.

 

Time (seconds)

 

Speed (m/s)

 

 

 

 

Figure 3: Speed versus time for golf ball (black), end of arm(red), golf ball

relative to end of arm (blue)

 

 

Speed (m/s)

 

Angle (degrees)

 
 

 

 


Figure 4: Speed versus angle for golf ball (black), end of arm(red), golf ball

relative to end of arm (blue)

 

 

 

 

 

 

 

 

 

 

 

 

Practical Stuff

 

How do you implement a sling into the setup?

 

Fig 12

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


The system is very similar to last years’ string pull system only it does so by pulling a pin out of a ring that is holding the sling in place. (sandwiched between the two teal plates).

 

 

 

stationary objects

 

Moving objects

 
 

 

 

 

 

 

 

 


Fig 13

 

 

 

 

 

 

 

 

The real challenge is how to retract the string in the proper fashion over multiple rotations. This is done by wrapping the string around a stationary cylinder shown in fig 12 in white and in fig 13 in red. As the arm rotates, string is wrapped around the stationary cylinder by the ring in fig 13. In this fashion, the sling can be released accurately. (Make a strong sling. I’ve messed up by making the sling too weak before. The result is a horrible misfire. Once you get in a few fires, the pin release system is as reliable as anything. Pull excess string straight down before fire (experience teaches best))

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


Quick Adjustments of Fire Angle.

 

Over much of the winter, I would increase the circumference of the cylinder by sliding nails between the string and the cylinder. This was a fast, but inaccurate way to change the angle of fire. A better way is to make the cylinder’s position adjustable. There are many ways of doing this, including adding pins, but my favorite is just having a tight fitting cylinder holder and a handle like projection that serves as an angle guide, a handle for moving the tight cylinder, and an additional position holder. Adding angle marks for the release point of the arm also helps. I have it set to 5 degree increments per notch. ( I have a little help from dry pl adhesive on my cylinder holder to have a tighter fit and keep the cylinder in place)This setup can save lots of time (hours) and makes this thing accurate.

 

 

Materials

Some key materials are shown bellow. The chassis can be made in almost any way.

 

Threaded wire to rotate around

 

Nuts to keep the arm in position (double nut or it will move around over time)

 

Roller skate bearings,

 

Pvc pipes and connectors

 

Fishing line (Get spider line… If you don’t it might not work as well. Compound catapult #1 is why I love the stuff)

 

Optional materials

 

3cm carbon fiber, (advantage of FATs, if you want to upgrade to carbon fiber, you easily can do it for about $10 from Midwest and still have excess left over.)

 

more details can be found on the original site

 

http://www.physics.ohio-state.edu/~durkin/durkin.html

 

 

What I have Now