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The slipping velocity (difference between the velocity of the car and the velocity of the tire in the contact point) will change very quickly and the model becomes a stiff system (a system whose eigenvalues differ a lot), which may require a special solver. The general form of the Magic Formula, given by Pacejka, is: [8]
Tire model. Example of the slip angle curve obtained from a Pacejka Magic Formula empirical tire model. In vehicle dynamics, a tire model is a type of multibody simulation used to simulate the behavior of tires. In current vehicle simulator models, the tire model is the weakest and most difficult part to simulate. [1][2]
Figure 1 Hard wheel rolling on and deforming a soft surface, resulting in the reaction force R from the surface having a component that opposes the motion. (W is some vertical load on the axle, F is some towing force applied to the axle, r is the wheel radius, and both friction with the ground and friction at the axle are assumed to be negligible and so are not shown.
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In current vehicle simulator models, the tire model is the weakest and most difficult part to simulate. [2] The tire model must produce realistic shear forces during braking, acceleration, cornering, and combinations, on a range of surface conditions. Many models are in use. Most are semi-empirical, such as the Pacejka Magic Formula model.
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1710 Stringtown Rd, Grove City, OH · Directions · (614) 871-6016