In this paper a vehicle dynamics model is presented, which is an example that contains all the necessary aspects of making a decent vehicle model. Several examples show the use of such a model: basic vehicle dynamics phenomena can be recognized with the simulation of a detailed vehicle model. We are dealing with the connection between downforce and under/oversteer in this paper. In addition, the use of numerical simulations in the field of control systems is pointed out by an example of simulating an ABS control for the vehicle.