A Mathematical Model of the Braking Dynamics of a Car
Published October 5, 2018 by SAE International in United States
Annotation of this paper is available
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.
CitationSaraiev, O. and Gorb, Y., "A Mathematical Model of the Braking Dynamics of a Car," SAE Technical Paper 2018-01-1893, 2018, https://doi.org/10.4271/2018-01-1893.
- Robert Bosch Gmbh, BOSCH Automotive Handbook, Second Edition Rev. and extra, M.: ZAO “Kzhi “Driving,” (2004), 992.
- Saraiev, O.V., “Information and Metrological Assurance of the Analogue-Digital Measuring System for the Study of Operational Properties of the Vehicle,” Radodendron I Computern System: Naukovotenny Magazine 2(66):155-163, 2014.
- Mironov, Y.A., Investigation of the Processes of Braking of Cars of Foreign and Domestic Production: Methodical Recommendations, Mironov, A.Y. and Kitaygorodsky, E.A., (M.: Forensic Science Center of the MIA of Russia, 2005), 176.
- Grishkevich, A.I., Cars: Theory: Proc. for Universities, Minsk: High School., 1986, 208.
- Jazar, R.N., Vehicle Dynamics: Theory and Application (New York: Springer, 2008), 1015.
- Pacejka, H.B., Tyre and Vehicle Dynamics (Oxford: Butterworth-Heinemann, 2005), 621.
- Pontryagin, L.S., Ordinary Differential Equations (Moscow: Nauka, 1982), 332.
- Saraiev, O.V.V., “Estimated Evaluation of the Braking Performance of a Car, Taking into Account the High-Speed Operation Mode,” Nukov Notatki. Mgwsi Zbirnyk (Palusami Knowledge “Techno Science”) 55:350-354, 2016.
- Klimenko, V.I., Davudenko, I.A., and Saraiev, O.V., “Dozen Vpliva Antiblockage System on Efektivnosti Galimovna Passenger Automoble,” Auto Transport: Collection of Scientific 29:245-249, 2011.
- Turenko, A.N. and Saraiev, O.V., Once Efektivnost Galimovna Transport Zasobu in Structur Dozen, Dorozhno-Transportno Be Useful: Monograph (Kharkov: KHADI, 2015), 360.