Various vehicle and tire dynamics models with different levels of complexity have been developed and used for predicting and studying vehicle traction and handling. This paper offers an overview of research work that was done on the tire relaxation length and time constant in the longitudinal and lateral directions with regard to tire/vehicle traction and handling characteristics. Several analytical and empirical models of the tire relaxation length and time constant from technical literature are compared by applying these models to a tire and, thus, analyzing and comparing computational results that come out from the models.

Based on the overview and analysis of the longitudinal/lateral relaxation length and time constant data, the paper also provides an analysis of the impact of the tire normal reaction, tire inflation pressure, tire slippage and wheel actual velocity on the relaxation constants.

The paper concludes with recommendations on the analytical methods and experimental data of the tire relaxation length and time constant computing that are more suitable for real-time modeling of agile traction and handling characteristics and, thus, can be profound for agile control synthesis. Therefore, the core contribution of the paper is to provide a fundamental analysis of the relaxation length effect for its further incorporation in agile tire slippage control.

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