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Transport Problems

Silesian University of Technology

Subject: Economics , Transportation , Transportation Science & Technology


ISSN: 1896-0596
eISSN: 2300-861X





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VOLUME 14 , ISSUE 4 (December 2019) > List of articles


Oleksandr PSHINKO / Liudmyla URSULYAK * / Serhii KOSTRYTSIA / Yevhen FEDOROV / Anzhela SHVETS

Keywords : mathematical modelling, the parameters of the longitudinal profile, regulating braking, longitudinal forces of impact and quasistatic character, braking distances

Citation Information : Transport Problems. Volume 14, Issue 4, Pages 161-172, DOI:

License : (CC BY 4.0)

Received Date : 05-March-2018 / Accepted: 11-October-2019 / Published Online: 08-December-2019



The main objective of the simulation is to study the effect caused by the parameters of the longitudinal profile on the maxima of longitudinal forces in freight trains of increased length during adjustment braking and running-out. To decrease the number of numerical experiments, some empirical formulae for estimating the maximum longitudinal forces during the motion of freight trains along the track with various configurations of its longitudinal profile's gradient changes have been obtained for the first time. Comparison of those forces with the permitted values, from the point of view of the railway stock strength and eventual vehicle derailment, has been performed. As a result of numerical integration of the system of non-linear differential equations of train motion for the considered driving modes, the values of the greatest longitudinal shock and quasi-static forces, as well as the dependence of the latter on the train length, initial braking velocity, on the algebraic difference of gradients and the length of the horizontal area that separates two gradients with opposite signs are estimated. The proposed mathematical model and methodology can be applied during standardization of the longitudinal profile's parameters from the point of view of the freight traffic safety for the trains of various length.

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