This paper mainly focuses on the design of transition curves of the cubic parabola type in track alignment design. Equations for the transition curves are first derived from the theory of cubic parabolas using calculus techniques. They are then analyzed using numerical analysis methods. The proposed formulation is evaluated by comparison of its calculated results with data in 684 actual cases of transition curves. The accuracy of the proposed method is verified in this study by comparing the estimated results with collected data from actual engineering projects, and the applicability of the new method to the engineering practice of track alignment design is justified. The chainage and coordinates of the control points as well as other curve points and the tangential angle can be easily calculated using the transition curve equations.

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