Design of Reverse Curves Adapted to the Satellite Measurements

The paper presents a new method for designing railway route in the direction change area adapted to the Mobile Satellite Measurements technique. The method may be particularly useful in the situations when both tangents cannot be connected in an elementary way using a circular arc with transition curves. Thus, the only solution would be the application of two circular arcs of opposite curvature signs, that is, the use of an inverse curve. It has been assumed that the design of the geometrical layout will take place within an adequate local coordinate system. The solution of the design problem takes advantage of a mathematical notation and concentrates on the determination of universal equations describing the entire geometrical layout. This is a sequential operation involving successive parts of the mentioned layout. This universal algorithm can be easily applied to the computer software which will allow generating, in an automatic way, other geometrical layouts. Then, the choice of the most beneficial variant from the point of obtained trains velocities while minimizing the track axis offsets will be held using the optimization techniques. The current designing methods do not provide such opportunities. The presented method has been illustrated by appropriate calculation examples.

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