Characteristic Centerline: A Theoretical Framework for Assessing Erroneous Lateral Position–Induced Risk on Hilly Horizontal Curves

Head-on crashes on two-lane, undivided hilly highways remain among the leading critical road safety concerns, largely due to erroneous lateral positioning of vehicles at horizontal curves. While several lateral position (LP)-based indicators have been developed to evaluate run-off-road risk, little attention has been given to proactively capture the head-on crash risk arising from centerline encroachment. This study introduces the characteristic centerline (CC), a novel theoretical framework that models opposing-direction LP behavior using probability distributions, identifies the critical lateral position ( LP C ) at various sections, and constructs continuous LP C profiles along the curve length. The lateral deviation of the CC from the actual centerline ( Δ L CC ) was computed, and the maximum deviation along each curve ( Δ L max , CC ) was used as a risk measure. The lateral position behaviors on 18 hilly horizontal curves were analyzed using videography surveys, yielding more than 8,700 LP data points. Relative validation of the measure was conducted by first establishing a ground truth and then comparing its crash risk rankings with those derived from curve radius, Δ L max , CC , and time to collision. Results demonstrated strong agreement between the Δ L max , CC ranking and the ground truth ( ρ = 0.89 ), along with consistent correlations ( ρ = 0.63 – 0.82 ) with TTC across thresholds. Further, the empirical validation of Δ L max , CC using field-reported head-on crash data indicates a good positive correlation ( R 2 = 0.61 ). This established the capability of Δ L max , CC to identify head-on crash risk independently and also on par with the established SSM, such as TTC. Across all sites, Δ L max , CC peaked at the midsection of the curve, indicating a heightened head-on crash exposure from frequent encroachments into the inner lane. The findings suggest that