Transition Curve Modeling with Kinematical Properties: Research on Log-Aesthetic Curves

Log-aesthetic curves (LACs), which are generally used in industrial design for aesthetic shape modeling, are examined for implementation as transition curves despite their non-trivial representation in terms of incomplete gamma functions, or Fresnel integrals which appear in the parametric equations of a certain spirals. The family of log-aesthetic curves includes well-known spirals as Euler, Nielsen, logarithmic spiral, and involutes of a circle. The horizontal geometry of the route can contain classical transition curves, which are formed by transition curve-circular arc-transition curves. In order to compare the examined family of log-aesthetic transition curves with the classical transition curve in terms of vehicle-road kinematics, the curvature and superelevation functions are derived, and functions of lateral change of acceleration (LCA) curves are obtained and illustrated graphically using a constant motion model. The discontinuities in the form of jumps in the graphs of the lateral change of acceleration are taken into consideration in order to compare log-aesthetic curves and clothoids.