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, generally provide high prediction accuracy. However, their predefined functional structure and large number of coupled parameters are designed for broad applicability across many tire types rather than for specific racing tires. This often results in limited interpretability, nontrivial parameter identification, and unnecessary model complexity for specialized applications such as Formula Student.
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.
The methodology is applied to experimental tire test bench data, focusing on the lateral force – slip angle relationship at constant vertical load. In a first step, the symbolic regression algorithm is utilized to derive a set of candidate mathematical expressions. These models are subsequently benchmarked against 200 independent data sets comprising various tire types and vertical loads. The evaluation reveals that the identified models approximate the measured tire behavior with accuracy comparable to, and in many cases exceeding, the Magic Formula, while exhibiting lower model complexity.
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.