Natural Sciences >> Physics

Analysis- Roller Coaster Loops

by Sundus Al Shibani


Submitted : Fall 2015

Using simplified unreal values in two approaches; physics and calculus to compare bottom and top parts velocities of circular and clothoid shape loops in a roller coaster, while assuming that the surface of the loop is frictionless. With the aid of physics and calculus, the analysis aims to clearly state the reason why engineers changed from constructing a circular shape loop to a clothoid shape loop in constructing roller coasters. After the comparison, it appears that circular loops exert higher launching velocity and its value in the top part of the loop is very high and, therefore, it is more dangerous for the riders as the forces acting on them are very strong and could lead to serious injuries. Conversely, clothoid loop launching velocity is relatively lower and the velocity on the top part of the loop is much lower than the circular loop, which allows the train to go through the loop without any potential injuries for the riders. Maximum velocity was calculated which shows that clothoid loop would reach to a lower maximum velocity than a circular loop, hence emphasizing that the safety achieved on a clothoid loop is much better than the circular one.

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Advisors :
Arcadii Grinshpan, Mathematics and Statistics
Zhimin Shi, Physics
Suggested By :
Zhimin Shi