Mathematical Modelling of Road Gradient Effects on Vehicle Braking Efficiency
DOI:
https://doi.org/10.63561/jmns.v2i4.1118Keywords:
Road gradient, Vehicle braking performance, Deceleration, Braking force, Gravitational force, Aerodynamic dragAbstract
The impact of road gradient on vehicle braking performance is critical for the safety, stability, and control of vehicles operating in diverse topographic conditions. This paper presents a mathematical modeling approach to analyze the effect of road gradient on vehicle braking performance, with a focus on braking force (bf), aerodynamic drag (Fd), net braking force (Fnet), and resulting deceleration (a). Using Newton’s Second Law, the study develops gradient dependent formulations incorporating the gravitational component along the slope and aerodynamic resistance, which increases with the square of vehicle speed. The braking force is modeled as a function of tyre-road friction and normal load, while aerodynamic drag is expressed in terms of frontal area, drag coefficient, and air density. The combined model expresses net braking force as the sum of resistive forces acting along the slope, enabling accurate calculation of deceleration profiles under various slope angles and speeds. Simulation results using MATLAB/Simulink illustrate that road gradients significantly affect braking distance, with downhill slopes (θ < 0) increasing the braking demand while uphill slopes (θ > 0) aid deceleration. The analysis further confirms that while vehicle mass linearly influences the magnitude of braking forces, the braking distance increases significantly on negative gradients, necessitating higher braking force to maintain desired deceleration rates, whereas positive gradients assist in reducing braking distance. Validation using prototype test data confirms the model’s reliability within 5% accuracy across varying slopes and initial vehicle speeds. The developed model provides a foundation for predictive braking distance estimation and control system calibration in advanced driver-assistance (ADA) and safety systems, ensuring reliable vehicle operation across varying terrain conditions.
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