Importance Of Roller Coasters

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Geometry plays a vital role in the creation of a roller coaster. The shape of the loop and the tracks must be able to safely support the motion and the riders. Typically roller coasters are comprised of a variety of shapes. It will begin with an uphill motion followed by a downhill motion. To optimize excitement and feelings of weightlessness that so many find thrilling, the track is designed to duplicate projectile motion and make the riders feel as if they are in free fall. This is demonstrated in Figure 1. In order to do this the track cannot be completely linear. It must curve to a certain extent (typically 35-55 degrees to the tangent line as shown in Figure 2). This curve prevents the riders from a sharp collision with the track or even…show more content…
Additionally, the shape of the loop is a critical aspect of the coaster. If you really notice the shape of the loop, you will notice it is not a circle. It looks like an inverted raindrop known as the clothoid. This shape assists in the creation of a safe ride. Another way to perceive the clothoid is the resultant shape of two intersecting circles as depicted in Figure 3. There are various reasons that the loop is a clothoid and not a circle. One of the main reasons being that to complete a circle shaped loop, the coaster would have to go at an incredible speed. This speed would result in a greater acceleration and according to Newton's Second Law which implies that acceleration and net force are proportional when there is a constant mass (here the constant mass is that of the coaster which stays constant throughout the ride), the net force would also increase. This would mean that in order to have an increased net force, the normal force would have to be much larger at certain points in the loop, because with a constant mass, the force of gravity will also remain…show more content…
Out of this context, a clothoid is a curve where its curvature changes linearly with its curve length. The curve length is the reciprocal of the radius. In context, the clothoids linear change allows for an adjustment in acceleration that is much safer. This smooth transition is known as easement, which is quite literally what we want in the situation of designing a roller coaster. The shape of the clothoid requires a smaller speed at the top of the loop than that of a circular loop. What makes the clothoid a lot better is also our ability to adjust the clothoid’s radius in order to keep a constant centripetal acceleration all the way around the loop. You can see how the radius and velocity change throughout the loop by comparing figures 4 and 5. This is important because at the bottom of the loop, the kinetic energy is greater than at the top of the loop, where it is at it’s lowest due to the height factor. This would mean that at the top of the loop, the speed would be it’s slowest. If the radius was constant throughout then at the top, it would run the risk of not having enough speed and thus getting stuck or even worse falling