Exact Minimum Sight Distance on Sag Curve with Centered Overpass

The solution presented in highway literature for the minimum sight distance, $S_m$, on a sag vertical curve with a centered overpass is approximate for the case in which $S_m$ is greater than the curve length. The solution relies on the assumption that the driver and object are equidistant from the point of vertical intersection. In this technical note, an exact solution for $S_m$ is derived. The available sight distance, S, is related to the curve parameters, the driver and object heights, their positions on the curve, and the overpass vertical clearance. The exact solution is then obtained by considering the optimum condition. The exact and approximate solutions were compared for the case of a truck driver's eye height, the standard object height, and the minimum vertical clearance for a range of curve length and grade differences. While the difference in the minimum sight distance is not large, the positions of the driver and object at minimum sight distance are quite different from those of the approximate solution. The exact solution also yields a shorter minimum sight distance. The exact solution, which is as simple as the approximate solution, can be directly used by highway professionals.