Exact Mathematical Solution for Maximum Transient Offtracking Calculation of a Single-Unit Vehicle Negotiating Circular Curves

Abstract

The low-speed turning maneuverability of vehicles is closely related to a well-known offtracking phenomenon which occurs when the rear wheels of a turning vehicle deviate towards the inside of a horizontal curve. Although numerous mathematical models and computer programs for vehicle swept path analysis have been developed in the past, only a few of them can calculate the maximum transient offtracking of a turning vehicle, yet with limited accuracy. The authors were motivated by this fact to find a new mathematical solution for maximum transient offtracking calculation of a single-unit vehicle when negotiating circular curves. In the first stage, a transcendental equation defining vehicle maximum transient offtracking position is derived and numerically solved by Python 3.10.12. In the second stage, the polynomial regression model predicting accurate numerical solutions of the transcendental equation with the desired level of accuracy was developed and tested. The new calculation method is simple enough to simply take the vehicle datum length, circular curve radii, and turn angle, while instantly producing the maximum transient offtracking value, without the need to draw any of the vehicle movement trajectories.