Fire Away

Proof of Efficacy

Our task was to create a trebuchet or catapult to launch a projectile. The assignment was just to launch it in general, but of course everyone wanted there’s to go the farthest. Said trebuchet had to be less than a meter in all dimensions and able to project the ball of clay just by releasing an arm. We originally created a very basic machine that was sufficient in catapulting balls of clay, but wasn’t successful enough for our liking, so we modified it.

Our machine consisted of:

Two legs at a diagonal slant
An axle
A base
An arm with a screw on bottom to attach rubber bands
A stopper at the bottom (so the arm wouldn’t hit the ground)
A hook in base to attach the rubber bands

This original design worked well and would cast the ball ab 25 meters each time. However, our peers were reaching 40 and 50 meters, so my group and I knew we had to make adjustments.

Higher Arms: The higher arms raised the axle which gave the ball a higher release point. This higher release point allowed for the ball to go farther due to a more advantaged start.
Two Screws on Bottom: The two screws allowed for more rubber bands to be placed with a more even distribution which would encourage a more straight release rather than crooked, which means it will go farther.
More Rubber Bands: By adding more rubber bands we added more Potential Energy, Kinetic Energy, Velocity, and distance. It would also release the arm with much more force making the ball be flung harder, faster, and farther.
Two Hooks in Base: With two hooks we could of course add more rubber bands, but we also had to points of attachment in different placements. With one hook further back the rubber bands on that hook had more tension put on them and therefore more Potential Energy and so on. This made the release of the arm even more powerful. And occasionally with our original design the hook would be ripped out of the base because the arm was swung with such force.
Different Rubber Bands: We used two different types of rubber bands, originally because we ran out of the first type, but when then realized that some rubber bands had more elasticity than others and because we had two hooks, one further back than the other, we needed rubber bands that were stretchy enough to reach the back hook, but could still recoil enough to give a strong discharge.
Placement of Hooks: We chose to place the main hook directly underneath the axle because based on findings in another experiment, that is the most beneficial placement for the rubber bands. It provides enough potential energy to project the ball without having too much force and releasing it completely upwards.

Our modifications greatly enhanced the efficiency of our machine. Our average distance went from about 25m to over 40m. The added strength and even distribution of said strength allowed for our trebuchet to improve.

CLEAR Paragraph

The closer the rubber bands are to being underneath the axle the further the ball is projected. We experimented on our trebuchet, which consists of a base with a hook in it to attach rubber bands, two legs, an axle, an arm with a screw on top for releasing the ball and a screw on bottom to attach rubber bands, and a stopper so the arm doesn’t hit the ground. In order to come to this conclusion we conducted an experiment placing the rubberbands at 12cm intervals with one directly under the axle and then one on either side 12cm away. The balls shot from the hook 12cm behind the axle covered an average distance of 20.5m. They didn’t go that far because they were shot with so much force, velocity, and speed, because the rubber bands were pulled back so far, that the ball was released downward. The balls released from 12cm in front of the axle didn’t have enough PE so they were shot even shorter than with an average of 14.3m. However balls shot from the hook underneath the axle had a sufficient amount of PE without having to much velocity which gave it a maximum average distance of 24.3m. The balls shot from the center hook went the furthest therefore, underneath the axle is the ideal positioning for rubber bands when making a trebuchet.

Calculations

Horizontal velocity: The ball travelled at a horizontal speed of 22.2m/s and a total distance of 44m.
Vertical velocity: The ball travelled at a vertical speed of 11.09m/s and a vertical distance of 5.49m.
Total velocity: In total, the ball travelled at a speed of 24.82m/s and was in the air for a total of 1.98s
Spring constant: The force at which the 28 rubber bands contracted was 1,574N/m
Spring PE: The energy the rubber bands had due to being stretched was 7.1J
Spring KE: The energy the ball had while being projected was 66.53J
Energy Conversion: About 9.37% of the PE was converted into KE meaning only about 9% of the initial energy the arm had was transferred to the ball.
Angle of Release: Our projectile was released at a 26.54 degree angle from the arm.

KEY FACTORS

I would credit most of our machines success to:

Long arm
High axle
Many rubber bands
Hook under axle

Building Process

On the first day of building we built our entire trebuchet and of course we were a little too confident. We were the first ones done and it shot projectiles at about 30m, which at the time, we thought was very far. However, once other people started finishing and launching, their balls were going 40m and we felt defeated. We wanted to make our trebuchet more efficient, but we had too many solution, but no identified problem. We moved the axle higher, made the legs straighter, added more rubber bands, move the rubber band hook back, and many more things. However, we tried all these things at once because we had limited building time, so I don't know what exactly to credit for the enhancement of our trebuchet.