ε x is a very small number used to avoid division by zero as F z approaches zero. μ x is the longitudinal load-dependent coefficient of friciton. S Hx and S Vx are offsets to the tire slip and longitudinal force in the force-slip function, or horizontal and vertical offsets if the function is plotted as a curve. The simplest form of Pacejka’s Magic Formula has an equation with constant parameters: \[F_)) Tire Model Magic Formula with Constant Parameters In this article we are going to focus only on the equations for the longitudinal tire force, for braking and acceleration. The parameters are determined as a best fit between experimental data and the tire model. ![]() There are a set of equations and parameters for each: longitudinal tire force, lateral tire force and self-aligning moment. They equations are called “Magic Formula” because there is no particular physical basis for the structure of the equations, but they fit a wide variety of tire constructions and operating conditions. One method of doing it is by using the Magic Formula equations. ![]() The longitudinal, lateral tire forces and the aligning torque depend on four main parameters:įor simulation purposes, we need to have a mathematical expression of the tire forces function of the above parameters. Image: Wheel side force and aligning torqueĬredit: The wheel camber angle is defined as the angle between the vertical axis of the wheel used for steering and the vertical axis of the vehicle when viewed from the front or rear.
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