Improved Horizontal Curve Design Consistency Approach Using Steady-State Bicycle Model Combined with Realistic Speeds and Path Radii

Three safety concerns have been identified in the conventional design consistency assessment procedure for horizontal curves: approximation of the vehicle by the point-mass model, use of unrealistic speeds, and the assumption that the path radius is equal to the design curve radius. This study presents a novel approach to the consistency assessment of horizontal curves in terms of vehicle stability (represented as the safety margin). The novel approach involves calculating the safety margins using the steady-state bicycle model to account for the nonuniform distribution of friction among individual axles due to grade and speed changes and using more-realistic driver behavior parameters. In this study, the realistic driver behavior parameters refer to the modeled operating speeds and calculated vehicle path radii, which were defined based on naturalistic driving data collected through a real-world experiment on a section of a two-lane state road using a GPS device. The analysis showed that the traditional safety margins for sharp curves are unrealistically large compared with the margins defined by the proposed approach; this indicates that the conventional approach uses a larger friction margin than the optimum friction margin. Consequently, the conventional approach results in the application of curves with radii smaller than those required for safe driving. Moreover, the results show that braking on a sharp curve on a steep downgrade is the most critical situation for the loss of lateral vehicle stability. Overall, this study highlights the significance of incorporating additional factors in the design procedure for horizontal curves that affect the safety of the curve, which are not considered in the point-mass model. The most significant factors considered in this study were the grade, driving maneuver in terms of speed change, operating speed, and vehicle path radius.

The primary objective of this research was to establish a reliable road design methodology for reducing single-vehicle accidents on horizontal curves. The proposed approach enables the identification of horizontal curves with insufficient side friction, by calculating the difference between the available side friction factor and side friction demand. In a conventional road design practice, the vehicle is approximated as a point mass, and the effects of grade, speed change, vehicle dimensions, and uneven force distribution on individual axles are ignored. Instead, in the novel approach, the steady-state bicycle model was used, considering the aforementioned factors combined with more-realistic speeds and path radii. The improved approach provides a more comprehensive understanding of the design of safe curves, with an emphasis on previously neglected important influential factors (longitudinal grade and driver behavior in terms of operating speed and path radius). The improved design consistency approach could be used for quantifying the risk of skidding, both in the design stage of new roads and for improvement of existing roads.