A Mathematical Model of the Braking Dynamics of a Car

The braking efficiency of a vehicle is its most important operational property. However, in practice, researchers utilize simplistic physical-mathematical models for the process of vehicle braking that leads to accuracy reduction of these models predictions. The literature data show that the error in assessing braking efficiency can reach 30%. One of the main indicators of the efficiency of a braking system is deceleration. Most accurately, this value can be determined by experimental measurements. However, this is not always possible due to various technical reasons. The existing models typically ignore the impact of the car design and its speed on deceleration. They also either neglect air resistance completely or account only for its horizontal component. This paper presents an improved mathematical model written in the differential form that takes into account the impact of the lifting or downforce components of the aerodynamic forces. The proposed model accounts for the dependence of car wheels adhesion with a road surface on the vehicle’s speed. Model analysis and computation showed that all these factors improve braking performance of the car. Thus far, vehicle deceleration was represented by a discrete set of points obtained experimentally. The model proposed in the paper represents vehicle deceleration as a non-linear function of time, which is a solution to some differential equation. Numerical experimental studies conducted to validate this model demonstrate its efficiency. Results of this study can be used in enhancing the braking system of a vehicle, investigating traffic accidents, and also designing or improving racecars.