Hyperbolic transition curve

Kisgyörgy, Lajos; Barna, Zsolt

doi:10.3311/ppci.7433

Cited by 8 publications

(9 citation statements)

References 3 publications

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“…Based on this law, the coordinates of the points of the simulated curve are calculated. This is the difference between the proposed approach and those approaches reported in [1][2][3][4][5][6][7][8][9][10][11][12][13][14] that consider the construction of a railroad track's curvilinear sections. In those papers, a curve is constructed, and then the distribution of the curvature and its derivative are determined.…”

Section: Discussion Of Results Of Studying the Geometric Modeling Of ...mentioning

confidence: 99%

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Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

Borisenko

Ustenko

2022

EEJET

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This paper proposes an approach to arranging curvilinear sections of the railroad track, which involves the replacement of two transitional ones and a circular curve with one curvilinear section. Modeling this section implies the construction of a curve in the plan and profile, the joint consideration of which forms the spatial appearance of the curve, which ensures a smooth transition between the rectilinear rails. The need for such transitions is due to the terrain, the need to bypass settlements, and the presence of geological, geographical, and other obstacles that occur when laying railroads. A curvilinear section is modeled in the plan using a curve that is represented in natural parameterization under the law of curvature distribution in the form of a fifth-power polynomial. At the same time, at the start and end points of the section, the curvature and its derivative accept zero values. The outer rail elevation retraction (modeling in the profile) is performed using the curve built, whose sections are also represented in natural parameterization with the dependences of the curvature distribution on the arc length in the form of fourth-power polynomials. At the docking point of the sections, the third order of smoothness is ensured, which implies the equality of values of the functions, their derivatives, the curvature, and a derivative of the curvature from the length of its natural arc. Measures have been proposed to ensure the predefined track gauge retraction. The application of the proposed approach to model a railroad track along the curvilinear section with a variable-radius curve could make it possible to achieve a favorable curvature distribution, a smooth elevation retraction of the outer rail and the track gauge. That would consequently improve the safety of rolling stock running along the curvilinear section of the track, reduce the lateral and vertical efforts that predetermine the wear of rails and wheelsets.

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Section: Discussion Of Results Of Studying the Geometric Modeling Of ...mentioning

confidence: 99%

“…An example of the use of sinusoidal hyperbolic functions in the construction of transition curves is given in [14]. It is noted that the sinusoidal hyperbolic functions lead to shortened transition curves, which, in some cases, is undesirable, especially at high speeds of trains.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Devising an approach to the geometric modeling of railroad tracks along curvilinear sections

Borisenko

Ustenko

2022

EEJET

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“…Based on the sine hyperbolic function [6] introduced the concept of the parametric hyperbolic transition curve and described the basic relationships. The curvature function of the hyperbolic geometry is: Fig.…”

Section: Basic Geometry Of Hyperbolic Transition Curvementioning

confidence: 99%

“…Using parameterization by arc length this point is located at l = L / 2, where L is the length of the transition curve. The curvature of hyperbolic geometry at location l = L / 2 is [6]:…”

Section: Basic Geometry Of Hyperbolic Transition Curvementioning

confidence: 99%

Analysis of Hyperbolic Transition Curve Geometry

Barna

Kisgyörgy

2015

Period. Polytech. Civil Eng.

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IntroductionThe transition curve geometries (clothoide, cosine, parabolic etc.) were developed several decades ago and no new transition geometry appeared since. Therefore there is no current research analyzing of the basic transition geometries. Instead researches focus along the well-known basic transition geometries on the examination of the vehicle-track complex system [8], evaluated the dynamic effects and suggested complex solutions for the curvature change [4].Our research dealt with something new, a new transition geometry, the hyperbolic transition. Therefore we had to go back to the beginning, to the analysis of the basic characteristics of the new geometry. This way we were behind the current research activities in complexity, because we had to demonstrate the characteristics of the hyperbolic geometry -just like it had been done several decades ago for the other geometries. The detailed modeling of the track and vehicle relationship would be a further step after getting to know the basic characteristics of the geometry.In our paper we compare the hyperbolic transition curve to two frequently applied transition geometries, to the clothoide and the cosine transition curves. Our research question was if the application of the S-shaped hyperbolic transition curve offered definite practical advantages over the application of the traditional geometries.

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“…For this purpose a unified motion geometry theory can be applied, which enables the determination of correct track geometry on differential geometric basis [1,[7][8][9][10].…”

Section: Kinematic Characteristics Of Railway Tracksmentioning

confidence: 99%