Sight distance relationships for symmetrical sag curves with noncentered overpasses

Recent development and research in the United States have indicated the need for increased stopping sight distance and the consideration of decision sight distance. For sag vertical curves with overpasses, the current mathematical methodology considers only the case where the overpass is centered at the point of vertical intersection. The other case of a sag curve with a noncentered overpass, which provides greater sight distances, can only be checked graphically. There is no exact analytical solution available for determining the available minimum sight distance for sag curves with noncentered overpasses. This paper first derives geometric relationships that relate the available sight distance to the vertical curve parameters, vertical clearance, location of the overpass on the curve or tangent, and locations of the observer and object. These relationships are useful for establishing the sight distance profile. Closed-form solutions of the available minimum sight distance are then derived. Values of the minimum sight distance are established for a wide range of the curve parameters and overpass locations, for highways with trucks and for parkways restricted to passenger cars. The presented methodology should prove useful in evaluating the sight distance adequacy and related cost-effectiveness analysis at critical highway locations.