Pacejkaféle

Pacejkaféle refers to a family of tire models based on the Pacejka Magic Formula, a semi-empirical model used to describe tire forces as functions of slip and normal load. Developed by Hans Pacejka and collaborators in the 1980s, these models are widely employed in vehicle dynamics to predict longitudinal and lateral tire forces under varying conditions, including different loads, speeds, road textures, and temperatures. The term is used in Hungarian technical literature to denote Pacejka-type formulations.

The core idea is a flexible algebraic form that fits measured tire force data with a small set of parameters. The classic Magic Formula expresses a friction force F as a function of slip x through a structure such as F = D sin( C arctan( B x − E ( π/2 − arctan(B x) ) ) ), where x is slip (slip ratio for longitudinal forces or slip angle for lateral forces). The four main parameters B, C, D, and E control stiffness, shape, peak value, and curvature of the friction envelope, and they generally depend on normal load, tire construction, temperature, and surface. In practice, separate parameter sets are used for longitudinal and lateral directions, and additional terms may be included to account for offset or load- and camber-dependent shifts.

Usage and limitations: Pacejka-type models are valued for their balance between accuracy and computational efficiency, making them standard in real-time vehicle dynamics simulations and tire design tools. They require calibration with experimental data for each tire and condition, and while they capture essential features of tire behavior, they may not reproduce all dynamic hysteresis or highly nonlinear transitions without extensions or additional terms.