A Polynomial Parametric Curve (PPC‐CURVE) for the Design of Horizontal Geometry of Highways

Abstract: The use of transition curves in the road design is a solution to make the gradual evolution of curvature and, at the same time, to improve the comfort level of drivers and provide a good visual perception of the curve. Clothoid is the most widely used transition curve in road design so far, because it ensures the continuity of the curvature with the other geometric elements of the alignment. However, several researches allow the use of polynomial functions as an alternative to the clothoid. Such use is permitted in accordance with the verification of allowable vehicle–road dynamics. Polynomial solutions of transition curves can be a valuable alternative for the traditional solutions (first transition curve, circular arc, second transition curve). A fifth-degree polynomial parametric curve (PPC-curve) for the design of highway alignment is proposed in this article. An analysis of the theoretical aspects to solve more complex geometrical problems recurring in practical highway geometric design is carried out. With regard to this problem, a shape parameter giving flexibility to the polynomial solution in relation to project needs has also been introduced. To implement the procedure, an original computer program has been developed. Numerical applications have been performed for comparison with the traditional solutions.