The height of the high-speed section of the sorting slide. Design of high-speed section of the marshalling hump. To prove mathematically the absence of theoretical basis of the formula by which the height of the first profile section of the marshalling hump is calculated in current method of calculation of marshalling humps. The paper uses the theorem on the change of kinetic energy for a non-free material point in the final form, known from theoretical mechanics. The results of the research revealed that the formulas by which the height of the first profile section of the marshalling hump is calculated contradict the theorem on the change of kinetic energy for a non-free material point in the final form. The results of the research can be used in the processing of the normative-technical document on the design of hump devices on railways and making adjustments to the dynamics of rolling the car in textbooks for universities of railway transport. The results of the calculations proved the incorrectness of the derivation of the formula for calculating the height of the first profile section of the marshalling hump in the normative-technical document “Rules and standards for the design of sorting devices on the railways with gauge 1 520 mm”.

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The content of the article is based on the classical provisions of mechanics (the Dalembert principle) for non-ideal communication. The analytical proof is given that the linear acceleration of the car with its equally accelerated movement along the descent part of the sorting slide depends on the force under the influence of which the car rolls down the slope of the slide, the strength of resistances of all kinds, on the reduced mass of the car with the load, taking into account the moment of inertia of the rotating parts. At the same time, the results of calculations proved that taking into account the mass of rotating parts practically does not affect the acceleration of the carriage along the slope of the slide. The acceleration formulas and the resulting forces acting on the car are presented in the generally accepted notation and in the usual sense, followed by the calculated data.