Modellazione di circuiti motoristici per applicazioni di tempo minimo.

This work deals with the modelling of tracks used in motor racing competitions with the aim of assessing their performance and enhancing their safety. The purpose is to develop a methodology to support the industry professionals in the objective identification of critical sections of a circuit and their possible solution by means of automatic procedures. First, a detailed explanation is given regarding the mathematical modelling of a circuit, focusing the attention on minimum lap time applications. A procedure for collecting and reconstructing data from real circuits using GPS technologies is described. Second, a multibody model of a human body is developed and validated against experiments. The model implements four different anthropometric models, selected from those available after a thorough review of the literature. Through the validation process, a single anthropometric model is selected as the one that best fit a motorcycle rider characteristics. Third, different approaches to vehicle modelling are described: quasi-steadystate, symbolic and numerical multibody models. The equations of motion of a steady state motorcycle are described, together with the analitical derivation of it’s g-g diagram limits. After that, a symbolic dynamic multibody model is briefly described in its main characteristics, including tyre relaxation equations and model states and inputs. Finally a numerical multibody model is developed, to include the MagicFormula tyre model, non-linear suspensions and chassis structural stiffness. The sliding dynamics of a human body on a three-dimensional surface is studied afterwards and the equations of motion are derived analytically. Typical values for friction and aerodynamic coefficients are identified through a video analysis process of MotoGP riders crashes. Subsequently, the numerical motorcycle multibody model together with the validated rider model are used for stability analysis, carried out through a screw axis approach instead of the classic frequency domain approach. The equations for the Mozzi’s axis animation from the eigenvectors components are derived and the method is applied to the weave and wobble modes. Finally, a tool for the racing tracks safety assessment is described, including features such as the automatic generation of gravel run-off areas and the identification of the ideal barriers profile. An example of application is reported using a 3D model of the well-known Mugello-Circuit.