Analysis of the Reconstruction of Rail Geometry from Curvature Data

The reconstruction of rail geometry from measured curvature data is analyzed. The mathematical concept of curvature is developed and utilized in numerical integration of differential equations describing the rail path. Formulas are derived for various chord-displacement methods of measuring curvature and for their measurement response functions. The reconstruction of rail shapes is demonstrated by means of computer simulation, and the effects of measurement response and measurement error are analyzed. Accuracies are compared with those that might be obtained with accelerometer devices used to measure curvature. The techniques and results can be applied to the design of practical rail measurement systems.