Proposing an Elliptic Equation for the Symmetrical Sag Vertical Curvesbased on Sight Distance in Highway

Abstract

The sight distance at night is one of the most important driving safety factors. Sag vertical curves are one of the important elements of roads, which require a sufficient sight distance at night. The headlight sight distance is used for determining the length of the sag vertical curves. Presently, the parabolic curve is mainly used in symmetrical sag vertical curves. The present study aimed to propose the elliptic curve as a new alternative for the parabolic curve. An elliptic equation is developed for use in vertical curve and sight distance of the sag elliptic vertical curve in nighttime is calculated based on the characteristics of the road geometry. Results indicate that contrary to the parabolic curve, the sight distance of the elliptic curve varies depending on the vehicle location and increases as the vehicle moves forward on the curve; therefore, driver sees the end of curve in elliptic curves much earlier than parabolic curves. The results also indicate that the sight distance of the parabolic curve is more than that of the elliptic curve in the shortest length after the curve beginning (up to 8% of the curve length) while the sight distance of the elliptic curve is more than that of the parabolic curve at the rest of the curve (at least 92% of the curve length). Based on the obtained results, for S > L, the stopping sight distances of the elliptic and parabolic vertical curves are equal.