Design of sag vertical curves in three-dimensional alignments

Headlight sight distance has been an important element in designing sag vertical curves because nighttime drivers need sufficient sight distance for stopping, and also because they depend on the road marking to maintain uniform speed and proper lane positioning. Considering an isolated sag vertical curve in a two-dimensional projection based on the sight distance needs for stopping, the current design standards recommend a minimum length of the sag curve. However, little research work has been directed toward determining the available headlight sight distance in three-dimensional highway alignments. A new analytical model developed by the writers for 3D analysis of headlight sight distance has shown that the 2D analysis may overestimate the available headlight sight distance on sag vertical curves combined with horizontal curves. In this paper, a computer program based on the 3D analytical model is used to evaluate the current 2D standards for sag vertical curves on fill sections, The results show that the current 2D design standards overestimate the available headlight sight distance and therefore underestimate the required length of sag vertical curves combined with horizontal curves. In this paper more accurate values for the required length of sag vertical curves combined with horizontal circular curves are developed. A more economical design is also suggested through the use of asymmetrical (compound) sag vertical curves.