Theme Park Ride Design Math Analysis

The Objective

One of my friends at UCSD desperately needed help analyzing the dynamics of a theme park ride that he was designing for a competition. I quickly (in a couple hours) put together some analysis for him to use in his design competition.

The Outcome

In the contest, he ended up getting first place overall and first place in the mathematical analysis section too! I have attached the handwritten analysis work I did below as well as a CAD animation of the ride.