The objective of this study is to examine the geometric description of the spiral sections of railway track systems, in order to correctly define the relationship between the geometry of the right and left rails. The geometry of the space curves that define the rails are expressed in terms of the geometry of the space curve that defines the track center curve. Industry inputs such as the horizontal curvature, grade, and superelevation are used to define the track centerline space curve in terms of Euler angles. The analysis presented in this study shows that, in the general case of a spiral, the profile frames of the right and left rails that have zero yaw angles with respect to the track frame have different orientations. As a consequence, the longitudinal tangential creep forces acting on the right and left wheels, in the case of zero yaw angle, are not in the same direction. Nonetheless, the orientation difference between the profile frames of the right and left rails can be defined in terms of a single pitch angle. In the case of small bank angle that defines the superelevation of the track, one can show that this angle directly contributes to the track elevation. The results obtained in this study also show that the right and left rail longitudinal tangents can be parallel only in the case of a constant horizontal curvature. Since the spiral is used to connect track segments with different curvatures, the horizontal curvature cannot be assumed constant, and as a consequence, the right and left rail longitudinal tangents cannot be considered parallel in the spiral region. Numerical examples that demonstrate the effect of the errors that result from the assumption that the right and left rails in the spiral sections have the same geometry are presented. The numerical results obtained show that these errors can have a significant effect on the quality of the predicted creep contact forces.
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