New and improved single-arc unsymmetrical vertical curve for highways

Abstract

Existing unsymmetrical vertical curves consist of two parabolic arcs smoothly connected at the point of common curvature. As such, each arc has a constant rate of change in grade. This paper presents a new and improved single-arc unsymmetrical vertical curve for highways that takes the form of a cubic function. The curve has a rate of change in grade that varies gradually between the beginning and end of the curve. The new curve lies below the sharper arc and above the flatter arc of the existing equal-arc unsymmetrical (EAU) vertical curve, thus smoothing out the EAU curve. In addition, the new curve slightly improves highway sight distance in most of the cases studied. The single-arc curve exhibits several interesting properties. The forward and backward offsets are not equal, nor are the basic and reverse offsets. The offsets of the new and EAU curves are equal at the mid-point of the curve. Also, the rate of change in grade of the new curve at the mid-point equals the average of the rates of change in grade of the two arcs of the EAU curve. The new curve exhibits several important properties and, as such should be of interest to highway designers.Key words: unsymmetrical vertical curves, single arc, highways, offset, sight distance, driver comfort.