New Transition Curve Joining Two Straight Lines

Baykal, Orhan; Tarı, Ergin; Çoşkun, Zeki; Şahin, Muhammed

doi:10.1061/(asce)0733-947x(1997)123:5(337)

Cited by 31 publications

(11 citation statements)

References 1 publication

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“…The differences between the B ezier and B-spline solutions are more marked because, at the internal knots, z(t) is discontinuous in the cubic splines (Cases b and c). In addition, in Case b, the peak value of z(t) slightly exceeds the recommended maximum for travel comfort (Baykal et al 1997). In contrast, the B ezier solution [z(t)] shows no internal discontinuities in all examples, albeit in Case e a septic polynomial is needed instead of a quartic spline.…”

Section: Examplesmentioning

confidence: 86%

“…However, the clothoid is not the option of choice in terms of comfort, in particular regarding the change of lateral acceleration. Thus, Baykal et al (1997) and Bosurgi and D'Andrea (2012) advocate a curvature given by quintic polynomial functions. The resulting transition curve is more flexible, displays advantages regarding ride quality, and can be optimized from a dynamic perspective (Bosurgi et al 2016).…”

Section: Transition Curvesmentioning

confidence: 99%

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Nonparametric Bézier Representation of Polynomial Transition Curves

Sánchez-Reyes

Chacón

2018

J. Surv. Eng.

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In a series of papers in this journal, polynomial solutions of transition curves are introduced for road design, constructed as graphs of polynomial functions. These curves admit a simple expression in nonparametric B ezier form, which facilitates their implementation into commercial software and data exchange. Furthermore, in this B ezier representation, few compact formulas describe all possible cases, and the boundary conditions defining the curves translate into intuitive geometric arrangements of the control points. This is illustrated with several examples, including cases where, at the endpoints, zero curvature and smoothness of the curvature diagram are required. The authors also consider an alternative using a nonparametric B-spline curve of lower degree, but at the cost of a more complex model. Quartic splines, at a minimum, are required to ensure a continuous change of lateral acceleration along the transition.

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Section: Examplesmentioning

confidence: 86%

Section: Transition Curvesmentioning

confidence: 99%

Nonparametric Bézier Representation of Polynomial Transition Curves

Sánchez-Reyes

Chacón

2018

J. Surv. Eng.

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“…In addition, there are single spline curves that connect two straight lines without a circular arc [3].…”

Section: Horizontal Geometry Of Route Alignmentmentioning

confidence: 99%

“…(3): k = k(l) the function of the variation of the curvature functions; u = u(l) the function of the variation of the superelevation functions; and v = v(l) where the function of variation of the velocity functions should be known to calculate the lateral change of acceleration [3].…”

mentioning

confidence: 99%

Transition Curve Modeling with Kinematical Properties: Research on Log-Aesthetic Curves

Arslan

Tarı

Ziatdinov

et al. 2014

Computer-Aided Design and Applications

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Log-aesthetic curves (LACs), which are generally used in industrial design for aesthetic shape modeling, are examined for implementation as transition curves despite their non-trivial representation in terms of incomplete gamma functions, or Fresnel integrals which appear in the parametric equations of a certain spirals. The family of log-aesthetic curves includes well-known spirals as Euler, Nielsen, logarithmic spiral, and involutes of a circle. The horizontal geometry of the route can contain classical transition curves, which are formed by transition curve-circular arc-transition curves. In order to compare the examined family of log-aesthetic transition curves with the classical transition curve in terms of vehicle-road kinematics, the curvature and superelevation functions are derived, and functions of lateral change of acceleration (LCA) curves are obtained and illustrated graphically using a constant motion model. The discontinuities in the form of jumps in the graphs of the lateral change of acceleration are taken into consideration in order to compare log-aesthetic curves and clothoids.

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“…Satellite measurements play essential role in this process [5]. Within the scope of creating a theoretical basis for the new designing method works such as [2][3][4][5][6][7][8][9][10][11][12] may be mentioned.…”

Section: Introductionmentioning

confidence: 99%

The analytical design method of railway route’s main directions intersection area

Koc

2016

Open Engineering

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Abstract:The paper presents a design method related to railway track sections situated in a bend. In the method advantage is taken of an analytical form of description by using appropriate mathematical formulae. This may become particularly useful when the investigations are based on the data obtained from mobile satellite measurements. In the paper attention is concentrated on an universal approach creating an opportunity to diversify the type and length of the transition curves in use. The design procedure of the geometric lay-out is allocated to a particular local system of coordinates to be followed by a special transfer of the obtained solution to the national frame of space references 2000. The adopted course of procedure together with adequate theoretical relations has been provided. All the study has been illustrated with calculation examples based on data obtained from the railway line in operation.

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New Transition Curve Joining Two Straight Lines

Cited by 31 publications

References 1 publication

Nonparametric Bézier Representation of Polynomial Transition Curves

Nonparametric Bézier Representation of Polynomial Transition Curves

Transition Curve Modeling with Kinematical Properties: Research on Log-Aesthetic Curves

The analytical design method of railway route’s main directions intersection area

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