Dynamics

Now that the geometry of a roller coaster track has been established, the dynamics a passenger experiences while riding this track will be determined. The quantities that will be calculated are:

Speed $(v)$

The forward velocity of the car's center of gravity along the track. This should always be positive.

Acceleration $(a)$

The forward acceleration of the car's center of gravity along the track.

Seat Force $(F_{s})$

The force exerted on the passenger by the seat. This force may be positive or negative, but should stay within the range of values specified in section 1.1.

Up Vector $(\ensuremath \mathbf{\widehat{u}})$

The orientation of the car must be determined such that there is no lateral acceleration. The direction of the up vector is specified to accomplish this.

Rail position

The position of the rails needs to be known. The position defined in chapter 2 was that of the center of gravity of the car. That information can be used along with the up vector to determine the rail positions.