Essentials of Vehicle Dynamics

Appendix 7

Empirical Magic Formula Tire Model

In Subsections 2.4.2 and 2.5.2, the empirical Magic Formula is shown to be suited to describe longitudinal and lateral tire characteristics, i.e., longitudinal force F_x versus practical slip κ and lateral force F_y versus slip angle α. The general form of this formula, neglecting horizontal and vertical shifts, reads

$F(s)=D\cdot \sin (C\cdot \arctan (B\cdot s-E\cdot (B\cdot s-\arctan (B\cdot s))))$ (A7.1)

(A7.1)

for slip s, and factors D, C, B, and E. These factors typically depend on wheel load and/or camber within certain additional empirical relationships, as described in Sections 2.4 and 2.5. Expression (A7.1) and the additional relationships ...