Modelling Trajectory Deviation to Improve Safety on Four-Lane Rural Highway Curves

Abstract

Drivers adjust their trajectory and speed to safely navigate horizontal curves on multilane highways. Studies on two-lane highways show that curve geometry and operating speed influence vehicle trajectories and may contribute to run-off-road crashes. The present study investigated the combined influence of curve geometry and operating speed on mean trajectory deviation ( TD<inf>_mean</inf> ) for horizontal curves of a four-lane Indian rural highway. A naturalistic driving experiment was conducted on thirty-seven horizontal curves using an instrumented sedan car equipped with a GPS data logger. The selected curve sites were located on plain terrain (gradient ≤ 3%) and featured radius (from 250m to 1200m), uniform carriageway width, lane markings, shoulder and median widths, and smooth pavement. Thirty-four drivers were selected for the study based on age and experience, yielding 1,258 trajectory and speed profiles. After applying the free-flow inclusion criteria, 1,117 valid trajectory and speed profiles were retained for analysis. TD<inf>_mean</inf> was estimated for each trajectory profile by taking the difference between the maximum and minimum lateral placement (in meters) of the vehicle along a curve measured from the median edge. For each curve, the 85th percentile of minimum speed ( V<inf>c_min85</inf> ), mean speed ( V<inf>c_mean85</inf> ), and maximum speed ( V<inf>c_max85</inf> ) were also estimated. Stepwise multiple linear regression analysis, conducted at a 95% confidence level, identified three significant predictors of TD<inf>_mean</inf>: V<inf>c_min85</inf> (coefficient (β) = –0.028, p = 0.014) , radius (β = 0.002, p < 0.001) , and deflection angle (β = 0.023, p < 0.001) . The final model demonstrated an adjusted R² of 0.688. The results show that drivers exhibit greater trajectory deviation at lower operating speeds and on flatter curves with larger radius and deflection angles, consistent with previous studies. The developed model can be applied for evaluating geometric design consistency of horizontal curves on four-lane rural highways. © © 2025. Published by Elsevier B.V.