Design Process
Our group, consisting of Nick, Michael, Jack and Eric, spent a considerable time generating ideas to find the best design meeting the requirements. Our only limitation was that the catapult must be able to fit inside of a 60x60x60 cm box. While other groups modeled their designs based on what had been historically successful, our group, being intellectually adventurous, thought about a novel approach. While at a Dallas Mavs game, we marveled at the enormous power that the T-shirt elastic catapults appeared to produce. With this in mind, our group thought about applying a design model similar to a cross-bow.
Our group created a series of drawings to apply our slingshot approach into a functional catapult. Once we had a basic design created we divided up the tasks among our group members. Nick was in charge of designing a carriage to carry the apple as it accelerated out of the device. Nick started by taking a piece of large PVC pipe and cutting it in half with the Rikon band saw. Then he took a small piece of plastic sheet and used the band saw and the bell sander to give it a circular shape to match diameter of the PVC. He then used the epoxy to attach the two plastic pieces. The two plastic pieces were later braced together by a metal clasp that Jack diligently tightened because the epoxy could not hold the the pieces together as they soon separated. This problem only temporarily was solved because during our test lauch it broke. Our group had to tighten the clasp and add plastic braces to hold the two plastic pieces together. Another problem our group faced with the carriage was that the carriage sepparated from the wooden piece that the metal rod ran through. This piece of wooden 2x4 was used to attach the carriage to the elastics. To solve this, our group entered 3 screws through the plastic sheet backing into the 2x4. During our final assembly of our many pieces, we realized that the carriage was being suspended from a single rod, which spun freely. Since the carriage wanted to face down, our group had to add another plane of support by bending a coat hanger aroung the front end of the carriage. Originally, this coat hanger was attached only by some electrical tape. After our first test launch, we soon realized that the coat hanger is mangled as it crashes at high speed to the end of the rail. In order to allow our catapult work for more than one time, our group tightened the coat hanger to the carriage permanently with a few tight screws, preventing the coat hanger from sliding and not working for the next launch.
While Nick was creating and perfecting the carriage, Michael, Jack and Eric created the railings for the pin to slide through. Michael took the initiative of finding the correct dimensions and lengths of the 1X4's. Jack and Eric cut the pieces to size using the compound miter saw and marking the correct angles and measurements with some basic geometry and a T-square. Eric then took the two rails and cut a slot about an inch wide and spanning the majority of the length of the rail, before realizing that there was an inefficiency. Eric saw that the friction between the metal rod and the rough wood would slow down the carriage, and then he decided to line the rails with cut PVC. Jack, Nick and Michael cut the PVC using the Band Saw and then Eric glued it to the rails with epoxy and further securing it with some electrical tape.
While Nick and Eric were absent, Michael and Jack were busy asssembling the rails to the 60x60 cm base that they cut from plywood. By using plastic braces, the rails and vertical supports were attached. Then Michael and Jack screwed the rails to the plywood and braced them with 2x4's using screws which went through the bottom on the ply-wood. During this time, our group realized that the glue holding the carriage together was not sufficient. Because of its inability we placed screws into the plastic to make sure our carriage was secure. Our carriage also did not want to face in the correct direction when placed into position, therefore we bent a coat hanger to provide support. The time came to power our catpult with the sergical tubes and bungee cords. Because the elastics only pull the carriage for a partial distance of the rail, we tried to maximize this distance by tieing the elastics closer to the base. We attached a cross piece between the rails and tied both ends to this wooden piece which we attached with screws. The elastic was then wrapped over the metal rod we intserted in the top of the rail and finally attached to the metal rod behind the carriage. We had to be careful to not tie the surgical tubes too tight as they would crush the coat hanger while it is in resting position. To solve this problem, we inserted wooden restraints for transportation and time between launches.
Calculations and Factors We Considered
Proof of a "45-45-90" right triangle side length correlation- this was used to find the maximum length of the rails. In this case, x=60cm and c=84.85cm (60 times root 2)
"45-45-90" right triangle applied to create optimal dimensions
The Design of Our 2 Pin Channel Pieces
This is how we envisioned that our launcher would operate
Units and More Calculations
As labeled in our sketches above, we converted all measurement into SI units to better understand and put our design into perspective.
Conversions/Dimensions/Calculations:
1. The catapult was required to fit inside of a 60cm x 60cm x 60cm box
2. As accepted in projectile motion physics, the ideal launching angle to maximize distance (assuming perfect external elements are omitted) is 45 degrees. Therefore, we angled our catapult to fire at 45 degrees.
3. Our rails which guided the apple inside of the carriage were made from 1x4's. This can be translated into 2.5 cm x 10.2 cm. On their longer base (directed upward) the trapezoidal prisms were 84.85 cm. On their shorter base, these rails were 64.6 cm (84.85 cm - 8 in (8 in is 20.3 cm) = 64.6 cm) (see drawing for basic 45, 45, 90 degree triangle calculations and proof)
Projectile Motion In Basic Form
Assembly Process
We diligently assembled our catapult, conquering challenges as they arose. Our design went through a metamorphosis as we kept trying to make the catapult more efficient and conserve energy by eliminating friction and impediments. This may have been a reason for our catapult's short launch distance- our catapult was very complicated and had many moving parts which had to operate in order to get a good launch.
WORK IN PROGRESS
FINAL PRODUCT
One modification, or addition, to our original design that we made was inserting PVC pipe lining into the pin channel, as friction between the metal pin and plastic was far less than the rough wood cuts. Our original idea of mounting the elastics was also modified. We thought that if we increased the length of the bungees, there would be less drag. At certain point, the bungees were no longer accelerating the apple in the carriage, but were actually colliding with the apple's path and slowing it down. To accommodate this original design flaw, we tied the bungees down toward the base and had them wrap on top of the pins that acted as a pivotal point or hinge for the elastics. After developing our model, our group carefully considered how to make an effective carriage to carry the apple. We cut a PVC pipe in half and glued/screwed a circular backing to it. The plastic carriage was then backed by a cut from a 2X4 in which we drilled a hole in order to insert a metal rod. Once we had the catapult assembled, we soon realized that there was not a brace to prevent the carriage from falling face-down and dropping the load. As a result of Michael and Eric's creativity, we were able to save the carriage that had received great attention by manipulating a pliable coat hanger under the front of the carriage to keep it aimed in the correct, forward, upright direction. The solution of the coat hanger was not perfect and was only temporary because launching the device resulted in its destruction.
Performance
Our catapult was a disappointment. Our group saw a great potential in this design but the tensional force of the bungees was enormous and proved to be uncontrollable. The device was so powerful that when it was launched, it self-destructed and was easily damaged as a result of its complexity and fragile nature. This was evident in the fact that the first launch was significantly better than the next two. The catapult had several parts that were glued together and fell apart in the high stress joints. Back-up bracing would have been beneficial and made this design more successful.
In Conclusion...
As awesome and original as our catapult design was, it did not win the contest. In many ways it was a disappointment. Our group worked hard to create a quality machine, but too many complex factors and moving parts allowed room for error. Our apple soared 11 yards. In future catapults, our group would try develop a simpler more elegant machine that takes advantage or torque and more efficiently directs the elastic power.
Borrowed Pictures
http://tedlington.files.wordpress.com/2009/12/crossbow.jpg
http://www.ajdesigner.com/phpprojectilemotion/range_equation.php
