Development of transitioned vertical curve 1 - Properties

Introducing spiral curves before and after horizontal circular curves has b een widely accepted to enhance traffic safety, highway esthetics, sight dis tance, and driver comfort. Though, vertical curves are still designed as pa rabolic curves that are connected directly to the tangent (without transiti ons). In this paper, a cubic polynomial is used to develop a vertical trans ition curve before and after the parabolic vertical curve. The resulting cu rve, called transitioned vertical curve, consists of transition-parabolic-t ransition segments. Detailed mathematical formulation and derivation of the instantaneous elevation, grade, rate of curvature, and offset from the fir st tangent at any point are presented. The highest (or lowest) point on a t ransitioned crest (or sag) vertical curve, where the instantaneous grade eq uals 0, is determined as it is of particular importance in highway drainage design. The minimum length of a transition curve is derived based on the c riterion of driver comfort. In addition? guidelines are provided to identif y the conditions where the drainage of surface water on transitioned curves can be a concern. Finally, the layout of the transitioned vertical curve i s described and illustrated using two numerical examples. The new transitio ned vertical curve, which exhibits striking similarities to the spiraled ho rizontal curve, should enhance the design of highway vertical alignments. ( C) 2000 Elsevier Science Ltd. All rights reserved.