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 under longitudinal, lateral and camber slip conditions. All three conditions 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 about how to estimate the driving part of the longitudinal slip curve are provided, as are methods for representing the characteristic when the tyre is rolling backwards.
Abstract