According to current highway design standards, horizontal and vertical alignments are treated separately in two-dimensional (2D) projections. In this paper, a model developed by the writers is used to study the effects of considering three-dimensional (3D) alignment on design requirements for sight distance. First, the paper examines the required minimum radius of a horizontal curve combined with a crest or sag vertical curve in a cut section. Also, the required minimum length of a crest vertical curve combined with a horizontal curve in a fill section is studied. The results show that the 3D design requirements may differ significantly from those in separate 2D projections. Depending on the vertical alignment and on the cut side-slope, 2D design may underestimate or overestimate the required radius. In fill sections, the 2D alignment overestimates the required length of the crest vertical curve when combined with long horizontal curves. In summary, the 2D alignment can compromise both safety and economics of highways. As a result, it is concluded that 3D-based design standards should be developed and used in highway geometric design.

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Journal Journal of Transportation Engineering
Hassan, Y, Easa, S.M. (S. M.), & Halim, A.O. (1997). Design considerations for combined highway alignments. Journal of Transportation Engineering, 123(1), 60–68.