Patent ID: 7027966

Claim:
A computer-implemented method for designing a railroad track curve transition spiral comprising the steps of: a) choosing a mathematical expression that is a function of distance along the spiral, that specifies a value of the bank or roll angle of the track as a function of the distance along the spiral, and that includes a length of the spiral as a variable parameter; b) establishing balance at each point along the spiral between transverse components of centripetal and gravitational acceleration in a plane defined by the track for a vehicle traversing the track at a designated speed; c) integrating a differential equation expressing the established balance with respect to the distance along the spiral, obtaining, as a function of the distance along the spiral, a compass-bearing angle of the track relative to a bearing angle of the track at the beginning of the spiral; d) integrating sine and cosine expressions that are the sine and the cosine of the track compass bearing angle obtained in the preceding integration with respect to the distance along the spiral to obtain Cartesian coordinates of points along the spiral relative to coordinates of the beginning of the spiral, thereby completing definition of the spiral corresponding to the chosen mathematical expression; and e) repeating steps a) through d) with different choices for the chosen mathematical expression until a spiral shape is provided that substantially connects to neighboring track at each end of the spiral.