Optimum vertical curves for highway profiles

Information on the vertical alignment of existing old highways is often not available. To evaluate the highway alignment, it is necessary to fit verti cal curves (parabolic curves and associated tangents) to the observed profi le data. This paper presents a linear optimization model that determines th e best parabolic curve/ tangents that fit a given profile. The decision var iables of the model are the grades of the first and second tangents and the location of the start and end of the parabolic curve. The objective functi on of the model minimizes the sum of the absolute deviations between the ob served profile and the vertical curve. The model includes a constraint to m ake the point of vertical intersection lie in the middle of the curve, thus ensuring that the estimated grades are indeed tangents to the parabolic cu rve. Extensions of the model to accommodate another objective and multiple vertical curves are presented. The application of the model was illustrated using a numerical example involving a crest vertical curve. The proposed m odel can be easily solved using optimization software that are readily avai lable in practice.