# Design of a Thrilling Roller Coaster - Module A. Introduction to Roller Coaster Design

Author(s):
Patricia W. Hammer, Jessica A. King, and Steve Hammer

In this module, you will use the interactive coaster window to mark peak and valley points of the indicated straight stretch portions of the real-life roller coasters. Cubic polynomials are automatically drawn to connect successive peak/valley points. Coordinates of the marked points are shown, as well as the slope value at the point of steepest descent/ascent of the cubic polynomial path. You can use this information to calculate the thrill of each drop according to the definition:

The thrill of a drop is the product of the angle of steepest descent in the drop (in radians) and the total vertical distance in the drop. The thrill of the coaster is the sum of the thrills of each drop.

Be sure to record the x and y coordinates of the peak and valley points and the slope at the steepest point. You will need this information to complete parts B - E.

Assignment

For Colossus and Steel Dragon

1. Point and click to mark the peak and valley point of the indicated drop. Choose peak and valley points so that the connecting cubic polynomial provides a close fit to the actual path of the coaster.
2. What is the minimum value of the slope along your path?
3. What is the angle of steepest descent along your path?
4. What is the vertical drop of your path?
5. What is the thrill of your path?

 The Devil Savin Rock, CT
For Greyhound, The Devil, and Shivering Timbers
1. Point and click to mark peak and valley points along the indicated path of the coaster. Choose peak and valley points so that the connecting polynomials provide a close fit to the actual path of the coaster.
2. What is the minimum (maximum) value of the slope along each fall (rise) of your path?
3. What is the angle of steepest descent (ascent) along each fall (rise) of your path?
4. What is the vertical drop of each fall of your path?
5. What is the thrill of your path?

Patricia W. Hammer, Jessica A. King, and Steve Hammer, "Design of a Thrilling Roller Coaster - Module A. Introduction to Roller Coaster Design," Convergence (February 2005)

## JOMA

Journal of Online Mathematics and its Applications