Improving Steep Bends as Hairpin Curves on Mountainous Roads

Steep bends on mountainous roads (i.e., horizontal curves that are as sharp as well as steep) are recognized traffic hazards, but quite often they are left as such, since simultaneous easing of curvatures and gradients might require expensive realignments. In such a situation, an easier alternative is to refashion the steep bend as a hairpin curve that, by lengthening the alignment, helps correct both the curvature and the gradient. Effective use of this form of alignment requires an analytical design procedure that treats the hairpin curve in its entirety, as is attempted in this paper. The proposed design methodology allows for the possibility that the center of the middle arc of the hairpin curve might have to differ from the intersection point of the approach tangents for optimizing the alignment location in relation to the actual ground conditions. The parameters characterizing the individual components of the hairpin alignment are identified and their interrelationships are established, providing the basis for analytical design. The suggested design procedure is illustrated with worked‐out examples.