Abstract: This invention includes a method for estimating the shape of a section of railroad track from so-called chord offsets measured along it without prior assumptions about the locations and orientations of arcs and tangents that together could define a shape to which the track might be made to conform. This invention also includes a method for finding a configuration of tangents, arcs, and spirals that are as close as practical to a set of existing points along a section of track and that can define a desired shape for calculating instructions to a track lining machine.

Abstract: A prior method for designing transition curves for railroad tracks and other vehicle guideways begin with a choice of a roll function representing a functional form for variation of the track or guideway roll or cant angle as a function of distance and requires the curvature of the transition shape to keep the components of centripetal and gravitational acceleration in the plane of the track or guideway equal at each point along the shape and integrates the equation expressing that equality as part of a procedure for determining the resulting transition curve shape. That method is supplemented by a method of defining basic roll functions in terms of Gegenbauer orthogonal polynomials, including roll functions which generate simple spirals as well as more complex shapes (referred to as bends, jogs, and wiggles).

Abstract: Transition spirals for successive sections of railroad track with different degrees of curvature are designed by first specifying the manner in which the bank angle of the track should change with distance along a transition spiral. Functional forms for bank angle are provided as a function of distance along the spiral, which can also be used in traditional conceptual frameworks, and interpreted in that context to define track curvature as a function of distance. Also included are functional forms obtained by raising the longitudinal axis about which bank angle change takes place so that the axis is above the plane of the track. The resulting transition spirals reduce the transient lateral accelerations to which passengers are subjected when passenger vehicles traverse the spirals and reduce the damaging transient lateral forces that heavy freight locomotives and freight cars apply to the track structure near the ends of the spirals.

Abstract: Transition spirals for successive sections of railroad track with different degrees of curvature are designed by first specifying the manner in which the bank angle of the track should change with distance along a transition spiral. Functional forms for bank angle are provided as a function of distance along the spiral, which can also be used in traditional conceptual frameworks, and interpreted in that context to define track curvature as a function of distance. Also included are functional forms obtained by raising the longitudinal axis about which bank angle change takes place so that the axis is above the plane of the track. The resulting transition spirals reduce the transient lateral accelerations to which passengers are subjected when passenger vehicles traverse the spirals and reduce the damaging transient lateral forces that heavy freight locomotives and freight cars apply to the track structure near the ends of the spirals.