New transition curves maintaining constant normal accelerations for vehicles

Abstract

New transition curves from straight paths to circular paths are proposed for the first time in this study. The paths enable the vehicles to maintain constant normal acceleration components when the vehicle has a given tangential deceleration component. The differential equation describing the path for an arbitrary tangential deceleration component is given first. Several special cases corresponding to different deceleration functions in terms of velocity and position are derived. The path equations are third order ordinary differential equations with high nonlinearities. The equations are cast into a non-dimensional form which enables to define the dimensionless parameters affecting the curves. Two of the special cases are numerically treated: (1) Deceleration proportional to the velocity, (2) Deceleration exponentially decaying with path length. The effects of dimensionless parameters on the solutions are exploited in the figures. The transition curves may be employed in determining the paths of land, aerial and marine vehicles.