GEOMETRICAL ANALYSIS OF NON-LINEAR CURVATURE TRANSITION CURVES OF HIGH SPEED RAILWAYS

The transition curves in the modern railway construction are route elements equally crucial as alignment and tracking. For high speed routes, in order to prevent a sudden change of the centrifugal force , the nonlinear curvature transition curve must be applied due to the impact of the motion in a sharp curve. This article proposes a new curve representing transition curve as a polynomial non - linear curvature transition curve which is considered as a remodeling of the third degree parabolic non – linear transition curve.Formulation of the curve relies on a pre – valuation of the lateral shock such that it increases gradually to the maximum value at the midpoint, then decreases gradually and tangent to x – axis at both the start and end points.Various transition curves adjusted for the high speed railways tracks, including the proposed one, are geometrically examined for the purpose of studying the possibility of considering such transition curves in high speed railways network. The concerned curves are the new and these needed to be optimized, which are designed for high speed up to 350 km/h.Based on the enhancement of the effect of the dynamical elements, i. e. lateral shock, curvature and lateral displacement, the comparative study cited from the geometrical analysis assured that he second degree parabolic non – linear and the proposed transition curve are the most relevant curves to be connected to the railways routes.