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2014 | Vol. 60, nr 3 | 295--305
Tytuł artykułu

Determining the geometrical parameters of exploited rail track using approximating spline functions

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The process of railway track adjustment is a task which includes bringing, in geometrical terms, the actual track axis to the position ensuring safe and efficient traffic of rail vehicles. The initial calculation stage of this process is to determine approximately the limits of sections of different geometry, i.e. straight lines, arcs and transition curves. This allows to draw up a draft alignment design, which is subject to control the position relative to the current state. In practice, this type of a project rarely meets the requirements associated with the values of corrective alignments. Therefore, it becomes necessary to apply iterated correction of a solution in order to determine the final project, allowing to introduce minor corrections while maintaining the assumed parameters of the route. The degree of complexity of this process is defined by the quality of determining a preliminary draft alignment design. Delimitation of the sections for creation of creating such a design, is usually done by using the curvature diagram (InRail v8.7 Reference Guide [1], Jamka et al [2], Strach [3]), which is, however, sensitive to the misalignment of the track and measurement errors. In their paper Lenda and Strach [4] proposed a new method for creating curvature diagram, based on approximating spline function, theoretically allowing, inter alia, to reduce vulnerability to interference factors. In this study, the method to determine a preliminary draft alignment design for the track with severe overexploitation was used, and thus in the conditions adversely affecting the accuracy of the conducted readings. The results were compared to the ones obtained using classical curvature diagram. The obtained results indicate that the method allows to increase the readability of a curvature graph, which at considerable deregulation of a track takes an irregular shape, difficult to interpret. The method also favourably affects the accuracy of determining the initial parameters of the project, reducing the entire process of calculation.

Opis fizyczny
Bibliogr. 11 poz., il.
  • Faculty of Mining Surveying and Environmental Engineering, AGH University of Science and Technology, Kraków,
  • 1. Bentley InRail v8.7 Reference Guide, Bentley Systems 2005
  • 2. JAMKA M., LISOWSKI S., STRACH M.: Application of modern geodetic technologies in determining the track in the aspect of allowable train velocities. Zeszyty Naukowo – Techniczne Stowarzyszenia Inżynierów i Techników Komunikacji Rzeczpospolitej Polskiej. Oddział w Krakowie, 149, 567–581, Kraków 2009 [in Polish]
  • 3. STRACH M.: Assessement of ability of using the satelite technology RTK GPS in train track axis regulation. Ph.D. Thesis, Kraków 2003 [in Polish]
  • 4. LENDA G., STRACH M.: Determining the railways geometry using the approximating spline functions. Pomiary Automatyka Kontrola, 12, Gliwice 2012, in print [in Polish]
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  • 7. STRACH M.: Using the Bentley company’s application for railway transport design. Geodezja, 12, 2, 181–189, Kraków 2006 [in Polish]
  • 8. DIERCX P.: Curve and surface fi tting with splines. Oxford University Press, New York 1995
  • 9. KICIAK P.: Basics of modeling of curvatures and surfaces. WNT, Warszawa 2000 [in Polish]
  • 10. FLOATER M. S., Surazhsky T.: Parameterization for Curve Interpolation. Studies in Computational Mathematics, 12, 39-54, 2006
  • 11. HARON H., REHMAN A., ADI D. I. S., SABA T., LIM S. P.: Parameterization Method On B-Spline Curve. Mathematical Problems in Engineering, 2012
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