2017 HiMCM A题特等奖学生论文下载8393

2017 HiMCM A题特等奖学生论文下载8393

 

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论文摘要如下：

20th Annual High School Mathematical Contest in Modeling (HiMCM) Summary Sheet

Team Control Number: 8393

Problem Chosen: A

Summary
For problem A, our team was tasked with the creation of an aerial light show in a large city’s annual outdoor festival. The show would be divided into three separate displays, two of which were provided in the task and one that was up to our team’s creativity. The requested displays included a ferris wheel and dragon, and we chose to model a solar system in the final display. To create the displays, we debated between creating a grid of drones or setting exact positions for them in each display. For accuracy, we chose to set specific courses and positions for each drone in the model. We began determining the mathematical parameters of each display with a simple sketch. We sketched first the ferris wheel, then the dragon and solar system and plotted points where each of the drones would be placed. From this, we determined 400 drones would be sufficient in modeling all of the displays. We considered safety requirements including the necessary distance between each drone and the orientation of the launch area. With a 5-foot safety distance between each drone, there is room for any sort of interference of the wind or slight inconsistencies in the technology. Our display is designed to be safe for an audience. In terms of launching our drones, we decided to lay each drone on the ground to avoid any problems associated with stacking. We represented each drone a 1-foot-radius circle to ensure that no two drones would be too close together. For the most efficient use of ground space, we use a hexagonal packing method. We then decided to use nine distinct drone launches to ensure that no two drones are closer than five feet when in the air. Then, we modeled the points and molded our displays to fit within our safety guidelines. There are two different options regarding costs, which vary whether the city decides to rent or buy the drones. With the recommended method of buying the drones, the one-time cost would total roughly 100,000 dollars. For renting the drones, a cost of 36,000 would be spent each year or for each event with drones. As for the necessary air space, we found the area used in each display, added a buffer zone and followed FAA’s requirements.

 

 

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