Lap Time Performance Sensitivity to Tire Model Parameters: An Optimal Control Framework for Model Selection and Calibration

The push for vehicle development through virtual prototyping and testing in motorsports highlights the critical challenge of tire model selection and calibration, especially when vehicle dynamics must be accurately captured. The calibration process for tire models such as the Pacejka Magic Formula (MF) relies on parameter identification and experimental data fitting. While optimization algorithms have been implemented to calibrate tire models, few studies explore the effects of parameter selection on overall vehicle performance, complicating prioritization for the vehicle’s modeling and simulation strategy. To bridge this gap, this paper leverages optimal control methods to quantify how the variability of MF tire model parameters propagates to the overall vehicle model and impacts lap time prediction accuracy. To achieve this, a subset of parameters critical to combined slip of the MF tire model are varied through a Design of Experiments (DOE). These variations are executed on a flat oval track to simplify the dynamics yet exhibit combined slip characteristics using a fixed vehicle configuration. The minimum lap time problem is solved using collocation methods via Dymos, an optimal control library for multidisciplinary systems. A neural network surrogate model enables an interactive profiler to visualize lap time sensitivity to tire model parameters. The primary contribution of this work is a framework that parametrically connects high-level, vehicle-wide metrics such as lap time to the calibration process and selection of tire models. The parametric and interactive nature of the framework allows high-level insights across the whole design space of tire model parameters. Insights derived from this framework provide a basis to develop a strategy for prioritizing testing and calibration efforts driven by vehicle level impacts of model parameter uncertainties.