I am currently interning as a mathematician helping engineers who need to know the measurements to construct amusement parks, more specifically roller coasters. Roller coasters are extremely popular attractions at amusement parks because of the “ups and downs” and the exhilarating experience it provides for the riders. I will analyze one type of roller coaster that involves loops, a drop and determine how trigonometric functions play a role in making the ride happen smoothly. Rationale Last summer, I was in the USA and I went to Six Flags which is an amusement park with many different rides. I had never realized until math classes this year that trigonometric functions are used everywhere at amusement parks. Trigonometric functions help shape …show more content…
Assumptions Roller coasters have a start and end point but if roller coasters never stopped and kept going on forever, the trigonometric function would be continuous. Roller coasters use different kinds of trigonometric functions to create the curves, inclines and declines of different sizes and heights. I assume that roller coasters are modifiable and the height and length can be altered. Roller coasters also sometimes contain loops, however, for this exploration, I focused on the standard wave shape of the roller coaster assuming it never touches the ground and has a maximum height of 120 meters. Body Most roller coasters are designed in a way that models a sine curve equation. When creating a roller coaster, it’s important to know the size of the first hill which represents the sine curve. The sine curve represents the amount of potential energy the coaster will have. The higher the height of the sine curve, the more potential energy will be stored. If the sine curve is lower, then less potential energy will be stored in the coaster. If any hills are higher after the first one, the coaster will not be able to climb them because it won’t have …show more content…
All roller coasters have a midline where the incline starts and decline ends but they differ in how far away from the ground they are located. The coaster travels up from the midline to the top of the hill and then descends down back to the midline. This looks like a sine graph where there is an x-axis, and both ends of the graph cross it. The equation for the roller coaster can be modeled using the sine function as: I am designing a roller coaster with these measurements: The amplitude is 60 meters, making the drop of the roller coaster 120 meters from the highest to the lowest point. The period would be The minimum point of the roller coaster is at 45 meters. The midline ensures that the roller coaster is not dropping below ground level, nor does the coaster come into contact with the ground. Additionally, a roller coaster has an amplitude, which is the magnitude of the oscillation of a sine function. It can be referred to as the “maximum point” of the graph or the peak from the center of the graph. The amplitude of a roller coaster varies and has direct impacts on how high the inclination