These modules involve a mathematical definition of thrill and calculation of thrill for several real coasters (Module A), design and thrill analysis of single-drop coaster hills (Modules B and C) and design and thrill analysis of several-drop coasters (Modules D and E). The ultimate goal of this interactive project is successful completion of an optimization problem (Module F) in which you must design a straight stretch roller coaster that satisfies coaster restrictions (see the box below) regarding height, length, slope, and differentiability of coaster path and that has the maximum thrill, according to the following 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