Improved Sight Distance Model for Sag Vertical Curves with Overpasses

On sag vertical curves underpassing a structure, the fascia of the structure may cut the line of sight and limit the available sight distance. The current AASHTO model for symmetric sag curves with overpasses is intended for those that lie close to the point of vertical intersection on long sag curves. This paper presents an improved model that provides the exact minimum sight distance (S-m) for any conditions including non-centered overpasses and short sag curves, which are typical in urban areas. The model explicitly includes as variables the overpass location, the overpass width, and the configuration of the first and second grades of the sag vertical curve. The model is formulated by using mathematical optimization that involves an objective function and constraints. The objective function minimizes the available sight distance subject to constraints involving the geometry of the curve and the overpass. The model is spreadsheet based and is solved with powerful optimization software. Application of the model is illustrated with some examples and the results show that the AASHTO model may underestimate S-m by 10% to 30%. A closed-form model for S-m on single-arc asymmetric sag curves is also presented for S-m > L. The proposed model provides a friendly, flexible, and accurate tool for sight distance analysis and should be of interest to highway designers and practitioners.