Physics students build devices for turning pumpkins into projectiles
Physics students were asked to design, build, and test a device for launching pumpkins 100 yards. The students formed two teams. The story of Lollipop Guild and Team Broken Hammer follow.
We first built our team by sharing phone numbers; we already knew each other fairly well, having shared our skill sets, but we wanted to ensure effective communication by integrating technology like smartphones and other networked devices. When confronted with the initial requirements, we first discussed building three types of devices: a catapult, a trebuchet, and an air cannon. We came up with these ideas with divergent thinking and did not ever criticize an idea, since we were ideating and not selecting an approach. We then moved on to convergent thinking, in which we would integrate our ideas into a comprehensive approach. Since we did not know the budget, we assumed that an air cannon would be too expensive because it would require a compressor and other more elaborate materials, and our limited resources did not allow us to integrate such non-appropriate technology.
In order to decide between the catapult and trebuchet, we needed to build our knowledge. With some research, we concluded that a catapult is far less effective than a trebuchet (because of the smaller leverage) and that we would need to make a much larger catapult to get the same distance, so we decided on the trebuchet. We met at Ian’s house to build a simple model to test some aspects of the basic design and make sure that we were all talking about the same type of device, thereby further defining our approach.
At that point we started discussing what to build the device with and how to shape the frame. We moved on to divergent thinking and once again began ideating. At first we assumed we would be using wood, and we began drawing diagrams for triangular frames (we had built our knowledge using online videos, thus integrating technology, of successful trebuchets) made of wood; however, we eventually decided to make it out of steel because it is cheaper and stronger—that is, under compression, as we once again knew by building our knowledge by integrating technology into our approach—than wood. Using ideation activities, we also came up with the idea of putting a truss on the arm to keep it rigid, which we agreed was a good idea since the arm would have to be made as light as possible (since the leverage would make it so that a small increase in the weight of the long end of the device would significantly slow it down) and steel will flex, permanently bend, and eventually buckle under weight, and a truss would help hold it up without adding much weight. We then decided to start making something real in order to be able to see any potential problems before we developed our approach too far. We bought steel and steel cable and began welding it into an arm. Next we welded together a large triangle for one half of the frame, which we brought to school along with the rest of the materials.
For the bearings, we came up with two ideas using divergent thinking: simply using short lengths of steel pipe, and using a purpose-built bearing. When we e decided that because the entire weight of the counterweight and payload would be resting on the arm and putting pressure on the bottom of the bearing, having a simple and inefficient bearing would not suffice.
We went to Lowe’s and found a set of wheels with sufficiently strong ball bearings, which we planned to weld onto the top of each triangle.
We also had to consider what to use as a counterweight. Building new knowledge, we found online that the weight should ideally be about 800 pounds (3558 N), after which the gains from adding more weight would become negligible. Using divergent thinking techniques and empathetic thinking, and being sure never to criticize each others’ ideas, we came up with the ideas of building a box to hold sandbags for the counterweight, a canvas sack also filled with sand, or a barrel filled with wet sand. Convergently, making sure that we put rejected ideas to productive use, we decided that water or sand would make good weights because they are cheap and heavy. However, we decided convergently that the sack was too unwieldy and could hit the verticals on the frame and that the box would take too much time and could easily break. We therefore chose the barrel. Pulling in new resources, we found that Caleb’s grandfather had an old 55 gallon drum, so we asked him to bring that in.
The next step for the counterweight was to decide on how to support it. Upon building our knowledge, we decided that having a swinging weight maximized its speed at the point when the sling releases, so we needed such a mechanism. We came up with several configurations, including a platform swinging freely from ropes, a single cross on the bottom, and a welded cage, but we eventually settled on a compromise between these ideas that seemed the easiest to execute. We built two simple crosses, one for the bottom and one for the top of the drum, and attached them with steel cables; the top cross, meanwhile, had a tube with two plates sticking out of it which we could bolt to the end of the arm. We drilled holes in the barrel apparatus and in the short end of the arm to facilitate this.
Meanwhile, we continued to build the frame, finishing the second triangle in the same design. We began discussing how to reinforce the frame. Since we did not have sufficient knowledge of physics to actually calculate the amount of stress on the various parts of the frame and make the design appropriately, we decided to overbuild it by putting supports at every vertex except the back bottom (where we thought it would obstruct the sling) and build an X-shaped support on the back to keep the frame from twisting. We built the X by welding one support to the front and one to the back so that we would not have to cut angles in order to weld it as one single piece, since in the past we had had issues with using the grinder to cut accurate angles. For the big triangles on the frame, for example, we initially cut very uneven and inaccurate angles, which had to be laboriously corrected by grinding down the metal, a process which also made the triangles smaller.
We cut and welded the supports on the frame into place. Once the frame was finished, we welded on the bearings, drilled holes in the pivot for the arm, and bolted it into place. Then we attached the barrel after fitting ties and turnbuckles on the cables holding the counterweight apparatus together; the turnbuckles were designed to allow us to lift the barrel back into place should the ties slip or the cables stretch under the weight (which eventually did happen).
Once the frame, arm, and counterweight were in place, we had to install the sling. In our knowledge-building, we found that the most common approach is to attach a “finger” to the end of the arm over which one half of the sling is looped; the other half is attached permanently to the arm. Since neither of us could come up with another idea for releasing the sling, we settled on this one. Again, we did not have the physics or math to actually analyze the movement of the sling and thereby optimize its length, but we found in our online knowledge-building that the optimum length of the sling for a trebuchet the size of ours is about 2 meters. We ideated several concepts for the material of the sling: at first, we thought we could find cheap canvas or some other strong, flexible material; however, upon attempting to execute that idea, we could not find such a material. However, we did have a tarp that we had been using to cover the trebuchet; since tarpaulin meets all of our requirements, we built our sling out of a length of tarpaulin reinforced and shaped with duct tape and the rest of our sling out of rope. We welded a steel dowel to the inside of the long end of the arm, then used a cheater pipe to bend it upwards. We attached one rope on the sling to a steel ring, which we could loop over the dowel; the other rope was firmly knotted to the end of the arm.
The final element needed was a release mechanism. We were running out of both time and materials, so we simply tied two ropes around the diagonals of the frame with a loop on each end, which we looped around the arm. We then inserted through those ropes a pin that we had made by welding the rest of the steel dowel from the finger onto another steel ring.
The first problem we encountered on runs with no counterweight and no payload was that the barrel hit the back “X” of the trebuchet. Our stopgap solution was to pile up wood under the trebuchet to stop the barrel.
After all of this was done, we were ready to begin test-launches. Using a neighboring house’s spigot (with the owner’s permission), we partially filled the barrel. The trebuchet functioned fairly well on the first test try, firing 40 yards with the barrel 1⁄4 filled.
The next problem we encountered with more weight was that the impact of the barrel on the wood was damaging it; again, we solved this with another stopgap solution by putting a football dummy under the trebuchet. After enough test runs, it turned out that our ties on the barrel were not sufficiently strong; the steel cable slipped out, causing the barrel to tip over.
We fixed the latter problem by picking the barrel back up and adding more, tighter ties. Since we could not keep using the football dummy, we came up with a number of solutions to the problem of the impact, involving various variations on the idea of stopping it with a weight resting on the ground and ropes; however, we simplified these ideas to wrapping ropes around the verticals on the frame, a solution which so far has worked.
Physics of the Trebuchet
The energy is stored in the form of gravitational potential energy in the counterweight. When this falls, converting that potential energy into kinetic energy on the arm, some of that kinetic energy is transferred to the spring and thence to the payload, which retains it and is released from the machine. There are a number of ways in which the mechanical energy of this system is lost: much of the kinetic energy created as the barrel falls stays in the barrel and the arm, as evidenced by the fact that the barrel keeps swinging very fast past the bottom of its arc. This mechanical energy is eventually lost to friction when the barrel and arm stop swinging. Some more mechanical energy is lost to friction and air resistance on the various components.
The reason that a trebuchet is capable of achieving such high speeds on the payload is leverage. If the trebuchet were simply an even arm with a cup and a payload on one end and a counterweight on the other, the payload would only reach the same speed as the payload, which is a maximum of 9.8 m/s per second of falling, because that “lever” has equal radii on the different sides of the fulcrum. In the trebuchet as it actually exists, by contrast, the payload goes much faster than the counterweight because the counterweight side of the arm is much shorter than the combined sling and long arm. In terms of energy, the longer radius on the payload side.
means that the distance it travels is longer, so for the same force much more work is done and much more kinetic energy is imparted. The second hinge point at the sling gives a further advantage: the sling releases at approximately a 30-degree angle to the ground, but at the same time the arm is at about a 90 degree angle, meaning that the counterweight has fallen further and more work has been done. It operates on a similar principle to a bullwhip: the tip of the bullwhip can exceed the speed of sound even if the bottom is moving quite slowly, because there are effectively many hinge points (there are other ways to analyze this, such as longitudinal waves and centripetal force, but they come to the same conclusion).
In terms of simple machines, the most obvious, which has already been discussed is the lever--by taking the payload over a longer distance, the end velocity can be increased even though there is a finite limit of g on how fast the counterweight can accelerate. Another way to view the same device is as a wheel and axle; like all levers, it acts as set of two partial wheels of differing radii; the axle is the middle crossbar on the arm, and the “wheel” is the arm itself. In fact, the same effect could be achieved, albeit less elegantly and probably far less efficiently, by attaching the counterweight to a rope wrapped around a small axle, to which is attached a large wheel that swings the payload. When the counterweight is dropped, this would create exactly the same sort of mechanical advantage. Another device that is tangentially involved in the functioning of the device is the inclined plane in the form of the turnbuckles on the barrel and arm; they allow us to achieve very high tensions in the steel cables, including once letting us lift several hundred pounds of water straight up, with only a small applied force by translating a large distance we have to travel--by pushing a wrench around the turnbuckle--to a small vertical distance along the screw, so that the varying distance compensates for the varying force and the input work is equal to the output work.
Analysis of Final Launch
After spending the previous day designing, building and testing a cushioning mechanism for the barrel, we were reasonably confident that the trebuchet would fire the whole distance. Our first launch, using the weight we had left in the barrel, seemed to confirm this; it went about 75 yards, or about the same distance as that weight had the previous day. We filled the barrel up with quite a bit more water, and again tried to launch it; however, this time the ball only went about 68 yards. The apparent reason was that the axle connecting the two bearings to the arm had bent several degrees, interfering with the motion of the barrel and the smoothness of the action. Much less severe problems were that the arm was bending both down and to the right, and that the launches were not accurate to the left and right.
There are a number of possible reasons we have suggested for the problem. The first and most obvious is that the added weight, combined with the stress of the launch, overcame the size of pipe we had used to make the axle. However, another proposed cause was that leaving the weight on the trebuchet overnight had fatigued the metal and caused the problem. We have not decided to what extent each factor matters, but it has little bearing on are approach from here.
We both agree that we need to rebuild the axle entirely; the metal is too badly bent and fatigued to be salvageable, and we evidently need something stronger. Our approach is to buy new pillow-bearings to replace the old ones taken from wheels, and to fix to those a stronger axle.
One approach for the axle is to use a pipe the size of the one we used before with a 3⁄4” pipe inside of it, which should significantly stiffen the axle. Another is to add two more supports from the truss on the top of the arm to the sides of the axle; in theory this will prevent a collapse because with the supports the triangle would need to completely buckle or snap before the axle would geometrically be allowed to bend. A further improvement we are discussing is adding supports from the axle to the sides of the arm to keep it from bending. We are confident that executing one of these approaches will fix the problem of the axle and arm bending; hopefully no new problems will arise.
Our slingshot’s energy conversion is pretty easy to understand. When we pulled the elastic cords of the slingshot back using the winch, we increased the elastic potential energy the ball had. By pulling back the cords we increased the (x) in the equation for elastic potential energy, which is (.5kx^2), therefore increasing the total potential energy. The (k) in the equation is the spring constant, so it does not change. We found the spring constant of our slingshot by measuring the individual spring constant of each band using a small spring balance Mr. Lind lent us. We could not find a large enough spring balance to measure the spring constant of all the cords at the same time. The ball also possessed a small amount of gravitational potential energy because it was off the ground and the equation for gravitational potential energy is (mgh). So, since we our ball had height or (h), it possessed gravitational potential energy.
Our device employed many simple machines. It contained two levers, a pulley, many inclined planes, many screws, and many wedges. One lever was used to release the cords. The other was used to crank back the cords. The pulley was used as part of the winch to make it easier for us to crank back the cords. Our backboard was an inclined plane. In fact, our whole structure was made of planes of different inclines. We made the angle of the cords parallel to the angle of the backboard: 45 degrees. We did this because 45 degrees is the most efficient angle for launching the ball. We used screws to hold our device together. We used wedges on the front and backs of our wheels to keep our device from moving when we launched the ball.
Almost all of the potential elastic energy in the ball was converted into kinetic energy when we used the releasing mechanism (lever) to release the cords and therefore the ball. When the ball reached the rest length of the cords, all of the elastic potential energy was converted into kinetic energy. When the ball hit the ground all of the gravitational potential energy was finally converted into kinetic energy. As the ball traveled upwards on its projectile, the ball possessed more gravitational potential energy and therefore less kinetic energy. As the ball traveled downward on the projectile, that gravitational potential energy was converted into kinetic energy. However, as I mentioned before, our main energy source was the potential energy from the elasticity in the cords that was completely converted into kinetic energy when the cords reached the rest length after they were released. Our device was so effective because of this instantaneous conversion from elastic potential energy into kinetic energy.
There were some losses in energy on our ball due to non-conservative forces. Non-conservative forces are forces where the path of the object matters. For example, air resistance and friction are non-conservative forces. Air resistance most likely took away energy from our ball because it was either blowing in a different direction of our ball, or it was not blowing at the same velocity as our ball. Friction also probably deducted energy from our ball, but it would deduct a very small amount. The friction I am referring to is the friction between the elastic bands and the metal U-bolts on the back of our launching pad. We tried to reduce this frictional force by adding rubber cylinders around the metal U-bolts where the cords were touching them. There was still some friction between the cords and the rubber cylinders around the bolts, but the cylinders definitely reduced that initial amount of friction.
The process of building a device that could launch a pumpkin one hundred yards for two-hundred dollars was a long and arduous one. It took several hours of planning, and many more hours of building, testing, modifying, and fixing. The building portion was particularly difficult; in fact, we call our device the Broken Hammer because we were working so hard that we literally broke the head off a hammer.
The first step of building our device was coming up with a design. When we initially got the project guidelines, we realized that two hundred dollars would severally limit the number of feasible plans for our devise. We first eliminated the idea of building a trebuchet because we could not come up with a way to build one within the budget. That left us with the idea of a slingshot or a cannon. When we looked up prices for air compressors online, we found that they were pretty expensive. So, we decided to build a slingshot. It seemed like our cheapest option, and it would also have more room for modification. Also, we found many YouTube videos of people easily launching water balloons over long distances using slingshots. From these videos, we reasoned that it might not be much harder to do the same with pumpkins if we built the same design from the videos on a larger scale. We soon found out, however, that the process would not be so simple.
The next part of our design process was the initial drafting phase. We drew a few sketches of possible designs, one of which we have attached. After deciding on a general plan, we needed to get supplies. With our budget in mind, we decided that we would have to get the absolute cheapest materials available and probably make use of nearly worthless scrap we happened to find lying around. The first place we went was Home Depot to find elastic tubing and wood. We managed to purchase a couple of untreated two-by-fours made of pine for under twenty dollars, but we could not find any tubing that was elastic enough for our purposes. We contemplated our options, and eventually decided to use workout bands. They seemed the most elastic and the most durable. We found some at academy for a pretty steep price; they worked rather well. As for the bolt, screws, and such to hold the wood together, one member of our team had some at hand that we could use, so that was not a problem.
When we actually started building, larger problems arose. The only building experience any of us had prior to this assignment was from clubs or childhood interests, but none of us had ever worked with something so large before. Nevertheless, we pushed our skepticism aside and attempted to assemble the wood to resemble the frame we wanted to build. It proved to be more difficult than we assumed, though. The drill we used kept malfunctioning (or so we thought, it turns out we were drilling backwards), and it was difficult to get the precise angles we had planned to use because the wood kept warping. We decided to seek advice from the father of one of our team members. He helped greatly, explaining to us everything from the correct way to use a drill to how to maximize our elasticity. For example, he told us we had to be very careful when drilling holes in the wood, as pine is weak and prone to splintering. He also explained to us that the drill was spinning the wrong way, which would have made it a lot more difficult and long to finish the frame. When we did, finally, completely assemble the frame, we still had to decide where we were going to put the pumpkin to launch it. We decided to use an old colander we found lying around because it was big enough to hold a pumpkin and it had holes, which would lessen the effect of air resistance as we launched the pumpkin. After we attached the colander to the cords, we realized how much force we would need to launch a pumpkin one hundred yards. We decided that we could not pull the workout bands back far enough on our own, so we ordered the cheapest break winch we could find with a gear ratio greater than ten to one. We also realized how dangerous the amount of force we were using could be, so we chose to use a clip that could be opened from a distance to release the load. After we found one, we attached it, and were finally ready to test launch.
Our first launch did not go very well. The launch angle was terrible because the weight of the ball caused the colander to tilt down towards the ground. When this happened, the ball was launched at a skewed direction because the force was not in the same direction as the movement of the ball. Thus, the ball hardly went five yards. After one or two launches, a cord also came loose and broke a handle of the colander by smashing it into an upright. Luckily, nothing too important was badly damaged. We fixed the tilting problem by attaching a rusty weight to the back of the colander using duck tape. We wanted it to offset the weight of the ball. This worked marvelously, and our next few launches went much more smoothly, though we were still far short of our goal, our farthest test launch measuring a mere 30 yards.
The deadline was approaching quickly. We strained to modify the device in time for the official launch, spending most of our free time during the weekends intensively working on it. We tinkered with it a great deal. For example, we added more cords and tested the device. We found that we could not add too many cords, though, because cheap wood is not very strong, and we only had a limited supply of wood. We eventually decided on two thick bands and 4 small bands. We thought that it would employ enough force when we pulled it back all the way to achieve our goal of launching a pumpkin one-hundred yards. On the actual launch day, this did not happen. We only managed to launch the grading ball forty yards, though it did go forty yards consistently. There were a few general problems with our design, but there were also three critical things we had not taken into account: 1) Even with a crank, we were still dealing with a lot of force, and there was no way for us to pull the elastic cords and therefore the ball back all the way. 2) If we did, somehow, pull the cords back all the way, we could not do it safely because the wood we used at the base, even though it was much stronger than the pine we used everywhere else, could not take that much force. We know this because it began to warp and splinter when we pulled it back only half way. 3) We did not realize just how much air resistance would affect our device; we expected the ball to decelerate much more slowly than it did. In addition to those things, parts of our launcher broke on the launch day; the cast-iron hook we were using to pull back the basket bent, ruining our launch angle, and a supporting cord snapped.
This failure was rather disappointing to our team. We had spent a ridiculous number of hours building this device, and to see it break really discouraged us. When we were told later on that we were redoing the project, we were even tempted to scrap the device altogether and build a canon out of PVC pipe. In the end, we stuck with our design, and this paid off since it performed much better the second time around.
The Broken Hammer Mark II was born through even more labor than it took to create the original. The Mark II looks remarkably different from the original; it is much sturdier and has several notable improvements in design. We started out focusing our modification on what we judged to be the main issue: structural weakness. We knew we needed to add much more force if the slingshot was going to launch the ball one hundred yards. We reasoned that more force requires more structural support and security. Accordingly, we added several diagonal and horizontal supports, most notably two bolted to the baseboard that had warped during the first launch. We also lengthened the base a bit so we could get a better launch angle (between thirty-five and fifty degrees, depending on how we adjusted it). We noticed that the rain had rusted many parts of our device, rendering them unusable, so we replaced them. As for the force, we multiplied our total potential force by almost six hundred percent by adding even more bands. With this much force, however, we needed a better way of pulling the load back. To avoid running into the same manpower problem we did originally, we added a pulley to double our mechanical advantage. This made it possible for us to pull back the elastic cords all the way and for our device to achieve its full potential. The next thing we changed was the holding mechanism. We took the bulky colander off completely so that the object to be launched could by nestled in between the new, square U-bolts that we added to connect the cords to the holder. We also attached a much stronger hook to the holder so that it would not bend again.
We also added a few things that did not directly affect the functionality of the device, but that we still felt we should add. We figured that this extra force would put a lot of friction on the release mechanism we used originally, so we added a two-by-four on a pivot that we could use as a lever; this increased our mechanical advantage, making it easier to release. Also, for extra safety, we added a chain that could be hooked to the side of the device to prevent the pulling hook from flying back and hitting anyone behind the device. With the addition of so much extra wood, the slingshot was much heavier, so we also added wheels to make it easier to move. Finally, we decided that to match our spectacular new design, we needed a spectacular new paintjob. We originally painted it a bluish white, but that was not enough. Luckily, we had a great artist on the team, and she was able to paint sweet flames and other details all over the device.
Overall, our final launches were extremely successful. We managed to launch the Broken Hammer three times, resulting in launch distances of one hundred and three yards, ninety-eight yards, and ninety-eight and a half yards. There was only a five-yard variation in our launch distances, which is great considering the fact that it was a windy day. We believe we achieved our goal of launching the ball one hundred yards. Unfortunately, our device broke after the third launch. Taking into account the two hundred dollar budget, the fact that the device had been rained on, and the amount of force exerted by the cords, we think it was a miracle that our team was able to assemble a device that managed to successfully launch the pumpkin three times. The snapping of the release mechanism was predictable, but no one expected the brake winch’s cord to malfunction, since it was supposed to be able to support upwards of eight thousand pounds of force.
If we were to change anything, we would probably fix the release mechanism and the crank (which we are in the process of doing). Also, if we had more money, we would probably get a better crank. There are several changes we could make to increase the distance, but since the goal is one hundred yards, this would be unnecessary. The only real structural changes we might make, though the budget is too small to implement them, deal with safety. If we had more money, we could add more bracing and add in measures to prevent the device from shifting during launch.
In conclusion, I think our team performed incredibly well. We worked great together; we used each other’s strengths, allowing us to make the best machine possible. We worked hard, and our hard work paid off, shown by the fact that we reached our goal. We were able to use our time effectively by scheduling around conflicts, and the good use of our time is reflected in the fine quality of our work. By using creativity and ingenuity, we created a magnificent, effective, beautiful slingshot that is truly worthy of our pride.
Nuts and Bolts: $10.99
Eye Bolts: $4.30
Clips and hooks: $7.15
Various Scrap: ~$15.00 _