Existing sight distance models are applicable only to two-dimensional (2-D) separate horizontal and vertical alignments or simple elements of these separate alignments (vertical curve, horizontal curve). A new model is presented for determining the available sight distance on 3-D combined horizontal and vertical alignments. The model is based on the curved parametric elements that have been used in the finite element method. The elements presented are rectangular (4-node, 6-node, and 8-node elements) and triangular. These elements are used to represent various features of the highway surface and sight obstructions, including tangents (grades), horizontal curves, vertical curves, traveled lanes, shoulders, side slopes, cross slopes, superelevation, lateral obstructions, and overpasses. The available sight distance is found analytically by examining the intersection between the sight line and the elements representing the highway surface and the sight obstructions. Application of the new model is illustrated using numerical examples, and the results show that existing 2-D models may underestimate or overestimate the available sight distance. The proposed model should be valuable in establishing design standards and guidelines for 3-D highway alignments and determining the effect of various highway features on sight distance.

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Series Transportation Research Record
Hassan, Y, Easa, S.M. (Said M.), & Halim, A.O. (1996). Analytical model for sight distance analysis on three-dimensional highway alignments. Transportation Research Record.