Interpretable Tire Force Modeling for Formula Student Vehicle Dynamics and Lap Time Applications

Accurate tire models are a key enabler for vehicle dynamics simulation, control design, and lap time optimization, particularly in the context of Formula Student race cars, where vehicle setups and tire characteristics differ significantly from production vehicles. State-of-the-art tire models, such as Pacejka’s Magic Formula, provide high accuracy but rely on predefined functional structures and a large number of parameters, which limits interpretability and adaptability to new tire compounds. This paper presents a data-driven approach for deriving compact and physically interpretable tire force models using symbolic regression. The proposed method employs an intelligent tree search to systematically explore the space of mathematical expressions and identify models that optimally balance prediction accuracy and structural simplicity. In contrast to black-box machine learning approaches, the resulting models consist of explicit mathematical expressions that enable physical interpretation and efficient evaluation. Dimensional analysis is integrated directly into the model generation process, ensuring dimensional consistency and reducing the effective search space by operating on dimensionless groups. The methodology is applied to experimental tire test bench data, focusing on the lateral force – slip angle relationship at constant vertical load. The symbolic regression approach identifies multiple candidate models that approximate the measured tire behavior with accuracy comparable to, and in some cases exceeding, the Magic Formula, while exhibiting significantly lower model complexity. Portfolio-based evaluation highlights favorable trade-offs between accuracy and interpretability. The results demonstrate that symbolic regression can uncover alternative tire models that better represent the characteristics of Formula Student racing tires than conventional approaches. Owing to their compact structure and physical consistency, the derived models are particularly well suited for real-time vehicle simulations, parameter studies, and control-oriented applications in Formula Student vehicle development.