THE MAGIC FORMULA TYRE MODEL

TLDR

The Magic Formula tyre model version 3 is presented as the latest iteration of the model. The model is intended to provide an accurate description of measured steady‑state tyre behaviour. It employs mathematically derived equations that compute longitudinal, lateral, and camber slip forces and moments, with coefficients representing key tyre characteristics, physically based formulations that eliminate correction factors, and double‑sided pure slip curves as the basis for combined slip calculations. When coefficients are properly selected, the model reproduces side‑force, aligning‑torque, and fore‑aft‑force characteristics, and the authors offer guidance for estimating the driving portion of the longitudinal slip curve and for representing rolling‑back behaviour.

Abstract

Abstract An account is given of the latest version 3 of the Magic Formula tyre model. The model provides a set of mathematical formulae from which the forces and moment acting from road to tyre can be calculated at longitudinal, lateral and camber slip conditions, which may occur simultaneously. The model aims at an accurate description of measured steady-state tyre behaviour. The coefficients of the basic formula represent typifying quantities of the tyre characteristic. By selecting proper values, the characteristics for either side force, aligning torque or fore and aft force can be obtained. The new version of the model contains physically based formulations to avoid the introduction of correction factors. Double-sided, possibly non-symmetric pure slip curves are employed as the basis for combined slip calculations. Suggestions are given to estimate the driving part of the longitudinal slip curve and to represent the characteristic at rolling backwards.