Refined method for calculating heading angles of a vehicle at the end of braking

Kholshev, N. V.; Konovalov, D. N.; Lavrenchenko, A. A. · 2021 · DOAJ

DOI: https://doi.org/10.25198/2077-7175-2021-2-86

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Summary

This paper addresses the need for improved vehicle safety systems by refining the calculation of heading angles during braking. Skidding during braking, which causes vehicles to exit their traffic corridor, is a primary cause of road accidents. The authors argue that developing effective safety systems requires accurate methodologies that account for specific vehicle parameters influencing stability. Existing calculation methods rely on simplifying assumptions—specifically, that the front and rear axle track widths are equal and that the vehicle’s center of mass lies on the longitudinal axis. These assumptions reduce computational complexity but compromise accuracy. The study aims to derive refined expressions for both the actual and permissible heading angles at the end of braking, incorporating these neglected geometric and mass distribution parameters. The research is based on theoretical studies and an analysis of existing literature regarding vehicle dynamics and braking stability. The authors examined the mechanism of skidding under conditions where anti-lock braking systems are absent or malfunctioning. They analyzed the forces acting on the wheels, including braking forces and the resulting turning moment, while accounting for the offset of the center of mass from the longitudinal axis and differences in front and rear track widths. The methodology involves deriving new mathematical expressions that integrate these specific vehicle characteristics, such as the actual mass distribution on each wheel and the vehicle’s position relative to the carriageway edge. The study produced a refined technique that includes new expressions for calculating the actual heading angle under various braking modes. These expressions explicitly account for the differences in front and rear axle track dimensions and the lateral displacement of the center of mass. Additionally, the authors derived a new equation for calculating the permissible heading angle, which considers the vehicle’s dimensions, its location relative to the road edge, and the lane width. This allows for a more precise determination of whether a vehicle will remain within its traffic corridor during braking. To facilitate the application of this methodology, the authors developed a computer program designed to increase the efficiency and speed of these calculations. The significance of this work lies in its contribution to the scientific understanding of vehicle stability during braking. By removing the simplifying assumptions present in previous models, the proposed methodology offers higher accuracy in predicting skidding behavior. This precision is critical for the design and improvement of active safety systems, such as electronic stability control and automatic braking systems. The authors conclude that the next step in their research is to assess the adequacy and accuracy of the proposed methodology using the developed computer program, potentially validating the theoretical findings against empirical data. This work provides a more robust foundation for engineering solutions aimed at reducing traffic accidents caused by loss of directional stability.

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• lane positioning