Dynamics

The dynamics of the coaster were calculated from the geometry data, as well as from the forces exerted on the coaster. The forces considered consisted of gravitational force, the seat force, and the frictional force. The resulting accelerations were the forward and centripetal accelerations. The friction model used was undoubtedly a simplification of reality, due in part to obvious experimental limitations. Using Newton's Second Law, a Runge-Kutta-Fehlburg integration routine, and the values of the geometric parameters specified previously, the position, speed, and accelerations of the car were calculated everywhere along the track. The orientation of the car was then determined from the seat force, speed, and curvature such that no lateral force was exerted on the car. This was accomplished by rotating the car about the forward vector such that the resultant of all forces not acting in the forward direction pointed in the local up direction.