Procedural Method for Finding Roller Coaster Rails Centerlines Based on Heart-Line Acceleration Criteria

Acceleration and jerk on a roller coaster circuit are measured at an imaginary curve passing through the heart of passengers. In this paper, Non Uniform Rational B-Splines are used to represent the heart-line path of roller coasters. Frenet Trihedron is used as the main curve framing, and an additional vector called gravity projection is deducted for generating a framework even at heart-line straights segments and inflection points, when curvature vanishes. A methodology for obtaining track and rails centerlines derived from the heart-line curve is proposed. Using this procedural method, track roll angle is fully determined by local curvature and speed of train. Four cases of study are presented: (1) generating track centerline with Frenet frame, (2) generating track centerline with gravity projection, (3) computing track centerline by the composition of Frenet frame and gravity projection and solving continuity-related problems and (4), generating rails centerlines. It is shown that using composite method all accelerations projected laterally on passengers become null and a continuous, smooth non-jerky track layout is obtained.