Fire Away!
Our Trebuchet
The Assignment
The assignment was to create a catapult/trebuchet from which we could launch our projectile and maximize distance with the given requirements (below) to see who's machine went the farthest. Then we would all collect data upon a variable, such as number of rubber bands, projectile type, etc. Lastly, we would improve our machines based on others' data to again see who's improved machine could launch the farthest.
The Process
The first part to making our catapult, like all building projects, was to plan and design it. Our original idea was to make a counterweight on the opposite side of our trebuchet to make its arm swing, while most other people used rubber bands. Next, we had to build our machine. In our school's maker space, we chose a table and got to work. The requirements for our trebuchet were that it had to have a base, any number of legs, a wheel and axle, an arm, and it couldn't be longer than a meter by any dimension. Our trebuchet was built all out of wooden pieces, except for our arm, which we used a PVC pipe for. The first part of our build was the base and legs. We used a thick wooden block as our base and then for the legs, we decided to do an A frame instead of the traditional two straight legs. This ended up working out really well later and improved our machine's stability overall. Next, we built the arm and the wheel and axle. For the wheel and axle, we drilled holes in the top of our A frame on either side and stuck it through those and we also made holes in our PVC pipe for it to go through. We figured out that the effort-load ratio for our arm had to be 5:1, so after measuring the length on our arm and drilling the holes, we added it to our trebuchet. Finally all that was left to do was to add the counterweights. Eventually, however, we had started testing and realized with the counterweights, there wasn't enough change per counterweight mass to make a difference, so we changed our machine and added rubber bands. This was a huge improvement and our machine went way farther than ever before and both before and after the improvements, went the farthest out of the whole class.
After we finished building our machine, the next step was to test our variable to find which was the best way to get it to go far. Our original variable was going to be counterweight mass, but like I mentioned earlier, we ended up switching to projectile shape/type because there wasn't enough difference in the data table to make a useful chart. We tested 3 different projectiles with our trebuchet. We figured out that a spherical projectile would be the best because it would have less air resistance due to lower surface area and smoother surface. We chose then to test a golf ball, a clay ball, and a rubber bouncy ball. Our tests concluded that the clay ball was by far going the farthest out of all of them with it flying 47.2m from the starting point. After we finished testing, we took data from everyone else's tests and then input it by changing our own machine. We were required to change at least 8 things on our machine and so we changed: 1) the number of rubber bands-10 to 20 2) length of string attached to clay ball- added about 10cm 3) lubricant-none to using saliva 4) pull back angle-35 degrees to 65ish degrees 5) effort-load ratio-5:1-1:1 1/2 6) stopper-small stopper to no stopper 7) projectile mass 8) projectile type. For the last two change factors, we included those by changing what projectile we were using. After we made some modifications, our machine was launching the ball really high in the air, but the distance had gone down to about 38m. The clay was also getting launched so fast and so high that it would split in half and we would have to search for both parts. We finally resolved the problem by switching to the rubber bouncy ball, and that worked way better. By the end we got it to go 55m.
It took a lot of effort, but we finally were able to get our machine running well, and we were able to get it to go really far without running into too many problems.
Our Proof of Efficacy Document
Calculations and Concepts
Calculations
Projectile Mass-The mass of our projectile was 0.015kg.
Horizontal Distance-The horizontal distance our ball was shot was 55m.
Average Time-The average time of our ball in the air was 3.02s.
Vertical Distance/Height-Our ball traveled upwards 11.0225m.
Horizontal Velocity-Our ball's horizontal velocity was 18.21m/s, or around 40 mph.
Vertical Velocity-Our ball's vertical velocity was 14.7m/s, or 33 mph.
Total Velocity-Our ball's total velocity was 23.4m/s, or 52.5 mph.
Release Angle-Our ball's average release angle was 39 degrees.
Spring Constant-Our machine's spring constant was 1633.3N/m.
Spring Potential Energy-Our machine's spring potential energy was 18.37J.
Kinetic Energy-The ball had 4.216J of kinetic energy when it landed.
% Efficient-Our machine was 23% efficient.
Concepts
Here are a few of the new concepts we learned during this project. All of the ones that we learned before this are explained in depth on either the Rube Goldberg Machine page or the Physics of Sports Video page.
Spring Potential Energy
Spring Potential Energy, also called Elastic Potential Energy, is the energy stored in an object due to expansion or compression. The equation for spring potential energy is PEspring (Spring Potential Energy) = 1/2 k (Spring Constant) x (distance spring stretched) ^2. You generally use spring potential energy when calculating the potential energy of springs or other stretchy items, such as rubber bands.
Spring Constant
A spring constant is how rigid (or resistant to expanding/contacting) an object is. The variable sued to show the spring constant is k. The equation for spring constant is k (spring constant) = F (force) / d (distance). The more rigid/stronger an object is, the higher the spring constant will be and the weaker an object is, the lower the spring constant. The distance in the equation stands for moved distance of the spring due to the force.
Thermal Energy
Thermal Energy is the energy transferred or lost to heat. The abbreviation used for thermal energy is TE and the unit is J (joules). The equation is TE (thermal energy) = Total E (total energy) - PE (potential energy) - KE (kinetic energy). Over time, all energy will transfer to thermal energy, as long as the object stays in motion