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Hans Bastiaan Pacejka (12 September 1934 – 17 September 2017) [1] was an expert in vehicle system dynamics and particularly in tire dynamics, fields in which his works are now standard references. [ 2 ] [ 3 ] He was Professor emeritus at Delft University of Technology in Delft , Netherlands .
Example of the slip angle curve obtained from a Pacejka Magic Formula empirical tire model. In vehicle dynamics, a tire model is a type of multibody simulation used to simulate the behavior of tires. In current vehicle simulator models, the tire model is the weakest and most difficult part to simulate. [1] [2]
Pacejka gives a rule of thumb that "at nominal vertical load the relaxation length is of the order of magnitude of the wheel radius". [1] Relaxations lengths have been found to be between 0.12 and 0.45 meters, with higher values corresponding to higher velocities and heavier loads. [2]
It does assume Coulomb's friction law, which more or less requires (scrupulously) clean surfaces. This theory is for massive bodies such as the railway wheel-rail contact. With respect to road-tire interaction, an important contribution concerns the so-called magic tire formula by Hans Pacejka. [7] In the 1970s, many numerical models were devised.
A coordinate system used for tire analysis by Pacejka and Cossalter. The origin is at the intersection of three planes: the wheel midplane, the ground plane, and a vertical plane aligned with the axle (not pictured).
In current vehicle simulator models, the tire model is the weakest and most difficult part to simulate. [2] The tire model must produce realistic shear forces during braking, acceleration, cornering, and combinations, on a range of surface conditions. Many models are in use. Most are semi-empirical, such as the Pacejka Magic Formula model.
'Deflected' tread path, sideslip velocity and slip angle Graph of cornering force vs slip angle A coordinate system used for tire analysis by Pacejka and Cossalter. The origin is at the intersection of three planes: the wheel midplane, the ground plane, and a vertical plane aligned with the axle (not pictured).
Cornering force or side force is the lateral (i.e., parallel to wheel axis) force produced by a vehicle tire during cornering. [1] Cornering force is generated by tire slip and is proportional to slip angle at low slip angles. The rate at which cornering force builds up is described by relaxation length. [2]