Curvature-Based Geometric Difficulty Analysis of Formula 1 Racing Lines

This paper presents a geometric difficulty analysis framework for Formula 1 racing lines based on telemetry data from the 2024 season. To ensure geometric consistency across multiple laps, a representative racing line is identified using the discrete Fréchet distance, and corner segments are modeled using biarc approximation to estimate stable curvature. Based on the resulting geometric representation, we introduce three curvature-based difficulty metrics—the Curvature Exposure Index (CEI), Maximum Curvature Severity (MCS), and Curvature Variation Index (CVI)—to quantify both local and global track characteristics. This approach establishes a strictly geometric definition of difficulty based on the planar projection of the trajectory, purposely decoupling structural complexity from 3D terrain features, vehicle dynamics, and race context. Experimental results across 24 tracks demonstrate that these metrics effectively capture distinct track characteristics: CEI ranged from 1.97 rad/km (Italian) to 8.44 rad/km (Monaco), MCS from 230.54 km−1 (Spanish) to 1689.54 km−1 (Monaco), and CVI from 7.60 (British) to 9.33 (Monaco and Qatar). Although this framework focuses on planar geometry, it provides a compact, extensible foundation for geometric analysis and future applications incorporating elevation profiles and dynamic variables.