Dynamic analysis of a rollercoaster
ME EN 3400 - Professional Communications
Spring 2021
Project Outline
The final project of the ME EN 3400 - Professional Communications course was to work together in teams to design a roller-coaster. My team designed the three sections of the connecting track and it was my job to perform dynamic analysis of the coaster throughout the sections to ensure they fell within ASTM safety standards.
A technical report was written to give an in depth view on every step of the process.
Click below for the full 31-page technical report
The three sections of the track in my analysis were the Exciting Descent, the Thrilling Whoops, and the Thrilling Splash. In order to analyze the track a 2D model is made for each section using parametric equations. The model for The Exciting Descent was built in MATLAB by concatenating parametric spline equations with parametric circle equations manually calculated in order to fit the design plan. The model for the Thrilling Whoops and Thrilling Splash was created by using the website NURBScalculator.in and exporting the non-uniform rational B-spline data to MATLAB for reconstruction using the Curve Fitting package for MATLAB
Analysis
For each section of the track, the tangential acceleration differential equation is built and numerically solved at each point along the track using the Runge-Kutta method with initial conditions specified by the position and velocity determined at the end of previous features. The result is the velocity and tangential acceleration at every point along the track. Now that the velocity and radius of curvature at every point along the track is known, the centripetal acceleration can now be calculated at each point. After converting accelerations to G forces, the areas of high G forces and their durations can be calculated and compared to the ASTM duration limits. Because the height at every position along the track is also known, both the potential and kinetic energy at every point along the track can be calculated.
Results
Using design information from other teams and ANSI standards for analyzing G force events I was able to show that the three sections of the connecting track fell within the safety limits for G force events in both the normal and linear directions.
This was accomplished by modelling the track as parametric equations, finding an appropriate system model for the coaster on the track, and writing code to simulate the coaster throughout the track.Â
Analysis of the velocity, acceleration, and energy of the coaster throughout each track was performed as well to provide other teams with necessary info for their designs.
