The catapult project was a joint math/art project. In math, we were doing a unit on quadratic functions, and projectile motion was an excellent physical application of quadratics. This was my class' first project for Mr. Sevilla's art class, and we were mainly learning about design thinking - empathizing with the problem, defining the problem, ideating, prototyping, testing, and revising - although some perspective drawing was mixed into the project. The final product of the project was a working catapult that would launch a baseball as far as possible; in math, we then used projectile motion equations to make calculations based off of the launches, and in art, the goal had already been accomplished, design thinking having been used to create the catapults.
The three images above are of my revised concept sketches for my catapult idea (the original three sketches can be viewed in my previous post). My revision was the addition of shadows to the drawings. I chose relatively simple light directions for the center and right sketches, but the left sketch was a challenge, because I had to create the shadows for the triangular structures as opposed to two vertical posts; these shadows had to be warped in some places as they passed over objects, and they had to overlap in other places. I added the dimensions in Photoshop after scanning the images to create a sense of scale. My group's scale drawing (below) was done on isometric graph paper to create a 3D graph plane. We decided to graph it both because it looked professional and because it gave the drawing a definite scale.
We built our catapult based off of our concept sketches. It looks practically identical to our final 3D-graphed drawing because we made the drawing after building the catapult. The process of building our catapult's body went smoothly; we cut the wood, fit it together, trimmed it where necessary, and screwed it together. We ran into a large potential problem when we accidentally made 45º miter cuts at the ends of the wrong pieces of wood: we had intended to miter the 48-inch pieces for the catapult's base but instead mitered two of the 33-inch pieces for the triangular structures. We got extremely lucky, though: upon further measurement and inspection, it turned out that 45º was the correct miter cut for those pieces as well, and so our mistake didn't actually impact us negatively. We ran into another problem when it came time to attach the 24-inch vertical posts to the base, and we realized that just putting wood screws in through the bottom of the base and into the vertical posts would not be as strong as we needed. Chase Ragan came up with a solution: we could cut notches out of the base on either side and fit the upright pieces into those notches. Then, the wood screws could be attached on the side, which would be much more secure. This solution worked beautifully, and we didn't run into any more problems while building the catapult. Below are three photographs of our catapult under construction. At this point, the building phase is almost complete, and we are just drilling holes in the frame into which we could insert the wooden dowel rod that would serve as the pivot point for our throwing arm.
Our final and largest problem did not fully rear its ugly head until we began testing our catapult, although we had some idea of it before we started construction. We had a 90º PVC angle connector at the end of our PVC throwing arm to hold the projectile, but it was far too small to hold a baseball securely - the most it could hold was a ping-pong ball. While we were testing, we used temporary solutions such as trimmed paper cups while I worked on a 3D digital model of a baseball holder at home in a CAD program called SolidWorks (which I have access to because of my membership on HTHNC's robotics team). This baseball holder could be 3D printed with Mr. Sevilla's printer. However, our final baseball holder came from one of our temporary solutions. While we were waiting for the digital model to be 3D printed, we decided to run some more tests of our catapult; I found a plastic funnel lying next to the trash can in Mr. Sevilla's classroom that I thought might make a good temporary solution. It turned out to be even more effective than the 3D printed holder! Below are pictures of the digital model for our 3D-printed holder and the final 3D-printed version, as well as the SolidWorks and .STL files.
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After building, testing, revising, testing, and testing some more, the final step was launching our catapult in a class event to demonstrate its capability for a grade. Our catapult's maximum distance was 105 feet, which wasn't bad, considering its relatively small size. Below are some photographs of our catapult from that event.
MATH REFLECTION QUESTIONS
1. What was the project about? Why did we do this project? What mathematics (Ms. Vee’s class) and design (Mr. Sevilla’s class) concepts were applied?
This project was probably originally created as a math project, since projectile motion may be one of the best real-world applications for quadratics that one could base a project off of. I would guess that art class was brought in after the project was already created, since it would be appropriate to art class, particularly the first project in art class, if we were to create something tangible. Of course, there were excellent art concepts involved in this project as well, including design thinking, perspective drawing, and a general introduction to power tools for those who hadn't used them before.
2. Describe the prototyping process. Does your final catapult resemble the prototype? Why or why not?
The firing mechanism from our final catapult resembles the firing mechanism from our mangonel prototype exactly. Actually, we took the launch arm from our prototype, made a few minimal changes, and put it directly onto our final catapult, since our prototypes were full-scale. In terms of construction, our final catapult is completely different from our prototype; whereas our prototype was merely two posts held upright and parallel by a piece of plywood, our final catapult was a sturdy, stand-alone structure. Our prototypes were intended to be constructible within a couple of days so that we could experiment with them and find out which design was more effective. They were full-scale, as we thought that a full-scale proof-of-concept would do its job better than a miniature model, but haphazardly constructed and not intended to be extremely effective. Once we knew which mechanism was more effective, though, we were finished designing the mechanism, and our concept sketches were all focused on designing the body of the catapult.
3. What were some last minute adjustments you had to make to your catapults prior to LAUNCH DAY?
The most important last-minute adjustment was determining whether the 3D-printed cup or the funnel - which had shown itself to be surprisingly effective - would work better. From a few last-minute tests, it appeared that the funnel was the more effective baseball holder. The 3D-printed cup did a much better job of firing the baseball along the intended path, but for an unknown reason, the deviation from the intended path caused by the funnel actually propelled the baseball farther.
4. This question is pertaining to your group research: when making calculations, what were some of your limitations? What were some things you “ignored” for the sake of simplicity?
We completely ignored air resistance; since it is a fairly negligible force at relatively low speeds such as the ones involved with the launch, we did not include it in our graphs or calculations. In addition to this, while we had the tools to actually graph a flight path for our baseball before the launch, we could not do so, as that would have required calculating the force of the elastic tubing, and we did not know how to do so. Fortunately, graphing a flight path was not required.
5. What were some of successes you experienced while working on this project?
I was pleased that our building went about as smoothly as one could hope for. Save for the two minor problems outlined in the third paragraph, we built the catapult quickly and efficiently, with minimal wasted material or effort. In addition, the feeling we all felt when we tried the funnel, not expecting any particular result, and saw it go at least twice as far as it had ever launched before, was somewhere close to ecstatic; this is the most prominent success that I can think of.
6. What were some challenges you experienced while working on this project?
The largest challenge that I can think of was finding/making an effective baseball holder. Prototyping was tricky, but I had two years' worth of Robotics experience to draw from in that regard, and it didn't prove too much of a challenge.
1. What was the project about? Why did we do this project? What mathematics (Ms. Vee’s class) and design (Mr. Sevilla’s class) concepts were applied?
This project was probably originally created as a math project, since projectile motion may be one of the best real-world applications for quadratics that one could base a project off of. I would guess that art class was brought in after the project was already created, since it would be appropriate to art class, particularly the first project in art class, if we were to create something tangible. Of course, there were excellent art concepts involved in this project as well, including design thinking, perspective drawing, and a general introduction to power tools for those who hadn't used them before.
2. Describe the prototyping process. Does your final catapult resemble the prototype? Why or why not?
The firing mechanism from our final catapult resembles the firing mechanism from our mangonel prototype exactly. Actually, we took the launch arm from our prototype, made a few minimal changes, and put it directly onto our final catapult, since our prototypes were full-scale. In terms of construction, our final catapult is completely different from our prototype; whereas our prototype was merely two posts held upright and parallel by a piece of plywood, our final catapult was a sturdy, stand-alone structure. Our prototypes were intended to be constructible within a couple of days so that we could experiment with them and find out which design was more effective. They were full-scale, as we thought that a full-scale proof-of-concept would do its job better than a miniature model, but haphazardly constructed and not intended to be extremely effective. Once we knew which mechanism was more effective, though, we were finished designing the mechanism, and our concept sketches were all focused on designing the body of the catapult.
3. What were some last minute adjustments you had to make to your catapults prior to LAUNCH DAY?
The most important last-minute adjustment was determining whether the 3D-printed cup or the funnel - which had shown itself to be surprisingly effective - would work better. From a few last-minute tests, it appeared that the funnel was the more effective baseball holder. The 3D-printed cup did a much better job of firing the baseball along the intended path, but for an unknown reason, the deviation from the intended path caused by the funnel actually propelled the baseball farther.
4. This question is pertaining to your group research: when making calculations, what were some of your limitations? What were some things you “ignored” for the sake of simplicity?
We completely ignored air resistance; since it is a fairly negligible force at relatively low speeds such as the ones involved with the launch, we did not include it in our graphs or calculations. In addition to this, while we had the tools to actually graph a flight path for our baseball before the launch, we could not do so, as that would have required calculating the force of the elastic tubing, and we did not know how to do so. Fortunately, graphing a flight path was not required.
5. What were some of successes you experienced while working on this project?
I was pleased that our building went about as smoothly as one could hope for. Save for the two minor problems outlined in the third paragraph, we built the catapult quickly and efficiently, with minimal wasted material or effort. In addition, the feeling we all felt when we tried the funnel, not expecting any particular result, and saw it go at least twice as far as it had ever launched before, was somewhere close to ecstatic; this is the most prominent success that I can think of.
6. What were some challenges you experienced while working on this project?
The largest challenge that I can think of was finding/making an effective baseball holder. Prototyping was tricky, but I had two years' worth of Robotics experience to draw from in that regard, and it didn't prove too much of a challenge.