Eric Collins Ted Dorris Drew Ellis Will Glass The Polar Express 12/06/08 Reviewed by Eric Collins, Ted Dorris, Drew Ellis, and Will Glass
Abstract The objective of our team s project was to construct a rollercoaster in which a vehicle travels from a specified starting point to a specified ending point in about fifteen seconds. Our rollercoaster consisted of a poster-board track attached to the outside of a Christmas-tree-shaped spiral structure. A marble was the vehicle of the rollercoaster. Through testing and operation, we found that the duration of the ride was around ten seconds. Also, we calculated the theoretical speed of the marble at the end of the rollercoaster as 5.99 meters per second. In conclusion, our rollercoaster was successful in that it carried a vehicle from a specified starting point to a specified end, but with the additional friction caused by the tape brakes, it did not fulfill the time requirement. ii
Introduction The objectives of this project were listed as the following: Solve an open-ended problem while working as a team Demonstrate ways that engineers communicate Apply principles taught in EF 151 and EF 105 Have fun The purpose of our team was to design and build a roller coaster that transports an object from a start point to an end point in a specified time. The resulting product is an expanding downward spiral track on which a marble travels from the top point of the roller coaster to the end of the track at the bottom, at which point the marble is halted by the breaking system. In order to reach the time requirement of 15 seconds, the design features braking spots throughout the track. These serve to delay the marble from finishing by preventing it from obtaining too much speed as it travels down the track. The skeleton of the design is comprised of a Christmas ornament. The track is made of construction paper taped to the ornament, and the breaking system consists of masking tape. The materials used fit well within the limitations of the budget, and our team of four hard-working young men was sufficient man power to complete the task. The roller coaster meets the dimension requirements in its folded up position; however, it sometimes falls short of the time objective. Design Process In deciding what our rollercoaster project would consist of, and how we were going to construct it, our team had very vague ideas. It was not until we went out in search of supplies that we came up with a definite plan. First, our team decided that we wanted a simple design that would work consistently. Early on, we decided that a marble or a ball would be the best vehicle for a rollercoaster, because it can travel in any direction. With a marble, we decided, our track could consist of tubes, ramps, parallel lines of track, and many other possibilities. When we were searching for supplies and ideas, we happened upon some Christmas decorations. We decided we wanted to have a Christmas theme, and then we saw a spiral Christmas tree with lights. We checked its dimensions, and it became the skeleton of our rollercoaster. Next, we had to decide on the type of track. One option was to attach two parallel lines of clothesline wire along the outside of the structure of the tree as a track. We decided not to go with this option, because it would be difficult to shape the wire. Also, the assembling of the tree involved pulling the middle of the spiral the top of the tree over a tall pole. In this case, wire may have been too stiff to compress or unfold when assembling or disassembling. We finally decided to use folded poster board for the track. Poster board is fairly flexible, so it did not deform much when the tree was assembled and disassembled. The poster board track was attached to the outside of the spiraling tree structure. It was bent in the shape of an L, so that the bottom of the L provided the surface the marble could roll on, and the side of the L provided a wall to keep the marble on the track. Because the marble is traveling down 1
the spiral, its tangential acceleration pushes it to the outside of the spiral. So, there did not have to be a wall on the inside of the track. Our rollercoaster had a simple process and worked consistently. Resulting Product After the design process, we made the greatness that is the Polar Express, which is the coolest rollercoaster ever according to my teammates and me. The coaster consisted of an exhilarating spiral in which a vehicle travels at such break-neck speeds that the insurance company made us install brakes, simple strips of doubled over masking tape which were primitive but worked just fine! The track wound through an amazing array of Christmas lights and ended with an abrupt stop right before you would normally fall into oblivion. The rollercoaster is 6.0 feet tall, and is shaped as a Christmas tree (Figure 1). Along the outside of the existing tree structure are L-shaped pieces of poster board. They are attached to the track of lights as seen in Figure 3. The marble travels along the inside of these L-shaped pieces. Figure 1: Side view Figure 2: Top view Figure 3: The L-shaped track Motion Analysis/Results Initial Potential energy was calculated using the age old principle of MGH. The height is 1.8288 meters and, when used in the formula, results in an initial Potential Energy of.00897 Joules. Surprisingly, all the energy of the 0.5g marble is used up throughout the course of the entire roller coaster. If there were no brakes (tape) on the coaster, the final velocity of the marble would be 5.99 m/s. That was calculated using the conservation of energy equation. Since the coaster is a cone with an ever increasing radius, the various accelerations such as tangential and normal can be calculated, but only for specific parts of the coaster. At the theoretical velocity mentioned above, 5.99m/s, the radius of the curvature is.25 meters, so the normal acceleration is equal to the v^2/r, which gives the value of 143 m/s^2, which is quite a large acceleration. That is actually equivalent to 14.63 g s, which would surely rip any human 2
passenger to shreds, so out of a concern for safety, the brakes were installed, which successfully slows the coaster to a stop at the bottom and prevents the g s from ever reaching such a shockingly high value, and would keep the passengers alive. The theoretical velocity was calculated assuming no energy loss, but in actuality, there were many ways energy was lost. The coaster would shake from side to side, there was tape to slow the ball down, and the track itself was quite bumpy. All these factors added up all the energy present in the initial state being expended throughout the coaster. What a wild ride that would have been. Finances/Budgeting The project cost $35. Prices were as follows, $15 for Christmas tree, $5 for tape, $7 for fishing line, and $3 for posters, and $5 for marbles. Conclusions Overall, our team was successful. We worked together to ideate, design, and construct the roller coaster. We had to work though time conflicts and other small problems to finish the product. Perhaps the only aspect that we failed was the time requirement. Our device fell five seconds short in the classroom demonstration, although it worked perfectly when nobody was looking. Also, the team was successful in creating a useful power point to communicate to the class our ideas. We used principles from module 5 in calculating the theoretical energy and speeds of the marble, and also experimentally finding the energy lost in the system. We even succeeded, more or less, in having fun while working together on the construction. Although the group agrees, this written paper is not fun. References Overall, our team did not have many references. Our team came up with the idea for the project by searching to find what materials were available and what could be constructed. We did not get the idea from any source. As far as calculations, we used formulas and concepts taught to us in the Engineering Fundamentals 151 class. These concepts include: potential energy, kinetic energy, and conservation of energy. There were few sources for our project, so our references are limited. 3