UPC Workshop

Yigao Fang

Oct. 15, 2021

Basic Tools

• Latex/Overleaf

• C/C++, Python, Matlab

• Solidworks, Python, Origin

   

Arrangement

• Work distribution:

  • Modeling (together)
  • Coding
  • Graphing
  • Writing

• Time Arrangement:

  • Half day: Search and discuss, choose a problem you prefer
  • One day: Build your model and do some codings
  • Half day: Finish your report

Paper Structures

Problem B: Design a Roller Coaster

You must design a roller coaster ride to be as exciting as possible, yet safe. The roller coaster will begin with a 20 meter horizontal segment, where passengers board, then climb up a hill to its highest point, taking it to an altitude 30 meters above the starting location. This gravitational potential energy will be the only source of energy for the roller coaster’s motion. Precisely describe the path that the roller coaster track would follow, through three-dimensional space, and indicate the orientation of the car as it follows this track. The track must form a closed loop, with the ride ending at the starting location. At no point may the track descend below its starting altitude. Analyze the dynamics of a roller coaster car and determine the total duration of the ride. Use your analysis to make a persuasive case that your design would be safe, but riders would find it to be especially exciting.

Abstract

• Around 150 words
• Very important, should be written when all of your other parts settled done.
• Paraphrase your structure of your report.

In this problem, we are required to design a safe and exciting roller coaster.(Goal) To solve the problem, we set up a design model of the trajectory with Solid-works and Planet Coaster. Then we derive the equations of motion based on basic dynamic laws. Next with Euler’s method, we estimate the solutions and simulate of the roller coaster’s motion using MATLAB. For safety and excitement judgement, we define several parameters related to position, velocity, and acceleration to represent the degree of safety and excitement. The value of these parameters and their simulation with time are also obtained with MATLAB. Finally we come to the conclusion that the designed roller coaster is safe and exciting.(Achievement)

Introduction

• Describe the problem in your own words, and make some specifications on the questions.

  • How can we define safe & exciting?
  • How to analyze the dynamics and duration?

• Give the outline of your paper.

Model

• Give your assumptions here.

  Assumption is important, it can help you solve the complex problem in a simple way!

• Define your variables.

  The original problem is usually qualitative, so you must define some quantities so that you can solve and measure them in a quantitive method.

• Briefly introduce the method you apply to solve the problem.

• Remember to have one beautiful and attracting picture of your model! (Important)

• If the question is complicated, you can divide it into several parts and solve them separately.

Results

• Answer the question in the problem.

  Analyze the dynamics of a roller coaster car and determine the total duration of the ride

• Beautiful graphics that can give a straightforward view on your results.

• Tables include some important data(If you have plenty of data, you can include them in Appendices).

Discussion

• Conclusion

  • Whether and how well you achieve your original goals.

• Advantages

  • Why you choose the model?
  • What is the advantages of your assumptions?

• Limitations and Possible Improvement

  • If you have some great ideas but is hard to fulfil within the two days, you can state them here and explain how will you possibly apply these ideas to improve your model.
  • You can search for how others do similar problems and list some of their ideas for future improvement.

Reference & Appendices

• Give a list of paper that you find useful
• Code/data/plots

My paper can be found here: http://uphysicsc.com/2019-GM-B-190.pdf

Hope you have good grades!