Modelling of Tyre Force and Moment Generation

  • H. B. Pacejka
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 411)


The paper gives an overview of different types of mathematical models describing tyre force and moment generating properties that may be used in vehicle dynamics simulation studies. First a physical model based on the brush concept is treated in detail. Then. an empirical model is discussed. This model that is known by the name ‘Magic Formula’ gives a relatively good approximation of measured data. Finally, the non-steady-state behaviour is briefly discussed. The low frequency transient tyre performance is modelled by a first-order differential equation in which the relaxation length serves as parameter. The higher frequency behaviour is modelled by introducing the dynamics ofthe tyre belt.


Slip Angle Side Force Tyre Model Contact Patch Relaxation Length 
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Copyright information

© Springer-Verlag Wien 2000

Authors and Affiliations

  • H. B. Pacejka
    • 1
  1. 1.Delft University of TechnologyDelftThe Netherlands

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