Curvature-Based Assessment of Left-Turn Trajectories at Urban Intersections Using Video-Extracted Vehicle Paths

Urban intersection design generally assumes that drivers follow idealised turning paths defined by circular arcs and, in some cases, transition curves. In practice, however, observed left-turn trajectories often depart from these theoretical paths. This study proposes a curvature-based framework for quantifying such deviations at the movement level by directly comparing observed vehicle paths with theoretical design arcs derived from intersection geometry. Naturalistic traffic data were collected at five urban intersections in Thessaloniki, Greece, using elevated video cameras. Left-turn passenger-vehicle trajectories were extracted, georeferenced, and compared with corresponding theoretical paths. For each trajectory, a best-fit circular arc was estimated, and the deviation between observed and theoretical path geometry was quantified through radius- and curvature-based percentage indicators. These indicators were then aggregated at the intersection and movement level using medians, deciles and the relative shares of flatter-than-theoretical and tighter-than-theoretical trajectories. The results show that deviations from theoretical geometry are strongly movement-specific and that the strongest flattening and tightening patterns were statistically supported by movement-level Wilcoxon signed-rank tests. In some cases, drivers systematically opened the turn relative to the design path, with median curvature deviations reaching about −14% and flatter-than-theoretical shares as high as 94%. In other cases, the opposite pattern was observed, with median curvature deviations exceeding +37% and tighter-than-theoretical shares reaching 100%. Other movements remained close to the theoretical path or displayed substantial internal heterogeneity. Overall, the proposed framework offers a practical and interpretable way to screen left-turn movements for systematic departure from design intent. This is important because it allows the analysis to move from individual path overlays to a movement-level geometric reading that can support consistency checks, intersection review and future integration with speed- and conflict-based safety analyses. These results should nonetheless be regarded as exploratory and descriptive: neither the circle-fitting residuals nor the coordinate-level geometric accuracy of the extracted trajectories were formally validated in the present study, and the reported RDP/CDP values are, therefore, not intended for use as precision-survey quantities or as a stand-alone design basis.