# Mathematical Modelling of Vehicle Drifting

• Reza N. Jazar RMIT University, Australia
• Firoz Alam RMIT University, Australia
• Sina Milani RMIT University, Australia
• Hormoz Marzbani RMIT University, Australia
• Harun Chowdhury RMIT University, Australia
Keywords: Vehicle Dynamics, Vehicle Drifting, Vehicle Stability

### Abstract

A mathematical model and condition for drifting of vehicles are presented in this paper. Employing the condition for possible steady-state drifting, the mathematical model of a vehicle with lateral weight lift during turning and drifting as well as adopting a combined tyre force model enables to reduce the number of equations of motion to a set of nonlinear coupled algebraic equations. The solution of the equations are the longitudinal and lateral components of the velocity vector of the vehicle at its mass centre and the vehicle’s yaw rate. The numerical values of the variables are associated with an equilibrium at which the vehicle drifts steadily. The equilibrium point should be analysed for stability by examining for any small disturbance should disappear. The procedure applied to a nominal vehicle indicates that an equilibrium point exists for every given value of the steering angle as the input. Also, it is shown that the equilibrium point is unstable. Hence, to keep the vehicle at the associated steady-state drifting, the value of the yaw rate must be kept constant.

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### References

Abdulrahim, M. (2006). On the dynamics of automobile drifting. Technical Paper 2006-01-1019, SAE 2006 World Congress & Exhibition, https://doi.org/10.4271/2006-01-1019

Bobier-Tiu, C. G., Beal, C. E., Kegelman, J. C., Hindiyeh, R. Y., & Gerdes, J. C. (2019). Vehicle control synthesis using phase portraits of planar dynamics, Vehicle System Dynamics, 57(9), 1318-1337

Edelmann, J., & Plöchl, M. (2009). Handling characteristics and stability of the steady-state powerslide motion of an automobile. Regular and Chaotic Dynamics, 14(6), 682, https://doi.org/10.1134/S1560354709060069

Hindiyeh, R. Y., & Gerdes, J. C. (2009). Equilibrium analysis of drifting vehicles for control design. ASME 2009 Dynamic Systems and Control Conference. DSCC2009-2626: 181-188, https://doi.org/10.1115/DSCC2009-2626

Hindiyeh, R. Y., & Gerdes, J. C. (2014). A controller framework for autonomous drifting: Design, stability, and experimental validation. Journal of Dynamic Systems, Measurement, and Control, 136(5), DS-12-1023: 051015. https://doi.org/10.1115/1.4027471

Jazar, R. N. (2019). Advanced vehicle dynamics, Springer, New York

Milani, S., Marzbani, H., & Jazar, R. N. (2019). Vehicle Drifting: Mathematical Theory and Dynamic Analysis, 5th Recent Advances in Automotive Engineering (ReCAR 2019), Mechanical Engineering Multi-Conference 2019, Universiti Kebangsaan Malaysia, Selangor, 20-22 August 2019

Shi, S., Li, L., Wang, X., Liu, H., Wang, Y. (2017). Analysis of the vehicle driving stability region based on the bifurcation of the driving torque and the steering angle. Proc. Inst. Mech. Eng. Part D J. Automob. Eng. 231, 984–998

Tavernini, D., Massaro, M., Velenis, E., Katzourakis, D. I., & Lot, R. (2013). Minimum time cornering: the effect of road surface and car transmission layout. Vehicle System Dynamics, 51(10), 1533-1547

Velenis, E., Frazzoli, E., & Tsiotras, P. (2010). Steady-state cornering equilibria and stabilisation for a vehicle during extreme operating conditions. International Journal of Vehicle Autonomous Systems, 8 (2-4), 217-241

Velenis, E., Katzourakis, D., Frazzoli, E., Tsiotras, P., & Happee, R. (2011). Steady-state drifting stabilization of RWD vehicles. Control Engineering Practice, 19(11), 1363-1376

Voser, C., Hindiyeh, R. Y., & Gerdes, J. C. (2010). Analysis and control of high sideslip manoeuvres. Vehicle System Dynamics, 48(S1), 317-336

Published
2020-12-16
How to Cite
Jazar, R. N., Alam, F., Milani, S., Marzbani, H., & Chowdhury, H. (2020). Mathematical Modelling of Vehicle Drifting. MIST INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY, 8(2), 25-29. https://doi.org/10.47981/j.mijst.08(02)2020.187(25-29)
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