The extended steady state lap time simulation combines a quasi steady state approach with a transient vehicle model. The transient states are treated as distance dependent parameters during the calculation of the optimal lap by the quasi steady state method. The quasi steady state result is used afterwards to calculate a new dynamic behavior, which induces in turn a different quasi steady state solution. This iteration between the two parts is repeated until the dynamic states have settled. An implementation of the extended quasi steady state simulation is built up to determine the capabilities of the approach. In addition to pure steady state simulation abilities, the method is able to judge the influence of the transient or time variant vehicle states on lap time. Sensitivity studies are generated to analyze the influence of basic parameters like mass, but also the influence of parameters with transient interaction like vertical damping or tire temperature. The extended quasi steady state lap time simulation approach provides an accurate possibility to integrate dynamics into the quasi steady state approach.

The potential of a race tire strongly depends on its thermal condition, the load distribution in its contact patch, and the variation of wheel load. The approach described in this paper uses a modular structure consisting of elementary blocks for thermodynamics, transient excitation, and load distribution in the contact patch. The model provides conclusive tire characteristics by adopting the fundamental parameters of a simple mathematical force description. This then allows an isolated parameterization and examination of each block in order to subsequently analyze particular influences on the full model. For the characterization of the load distribution in the contact patch depending on inflation pressure, camber, and the present force state, a mathematical description of measured pressure distribution is used. This affects the tire's grip as well as the heat input to its surface and its casing. In order to determine the thermal condition, one-dimensional partial differential equations at discrete rings over the tire width solve the balance of energy. The resulting surface and rubber temperatures are used to determine the friction coefficient and stiffness of the rubber. The tire's transient behavior is modeled by a state selective filtering, which distinguishes between the dynamics of wheel load and slip. Simulation results for the range of occurring states at dry conditions show a sufficient correlation between the tire model's output and measured tire forces while requiring only a simplified and descriptive set of parameters.