New Spiral Curves for Appropriate Transition of Minimum Roadside Clearance on Simple Curves

Abstract

Guidelines for geometric design of highways require that the inside of horizontal curves be cleared of obstructions to sight in order to provide necessary sight distance. Many of these guidelines use one analytical model for determining minimum clearance offsets. These offsets are suitable for middle sections of long curves because the analytical model was derived with consideration that drivers on the curves are able to see downstream curved sections whose lengths are equal to stopping sight distance. Applying these offsets to straight sections near beginnings and ends of the curves results in unnecessary clearance costs since sightlines are accommodated within lanes and wide shoulders. This paper presents a new analytical model for gradual transition of clearance from zero on straight sections to the minimum value required at the middle of horizontal curves. The model is based on new spiral curves whose mathematical equations incorporate driver location, object location, radius of horizontal curve, length of horizontal curve, and design sight distance. Moreover, the already known Euler’s spiral curve is examined whether or not it is also suitable for transitioning clearance. It is found that the Euler’s spiral consistently underestimates clearance offsets. Underestimation of the offsets is due to high degree of sharpness of the Euler’s spiral which renders the spiral unsuitable for transitioning clearance. Finally, the analytical model is presented in the form of a design chart. Without compromising safety and mobility of highways, use of either the design chart or the analytical equations will help agencies save money that would otherwise be spent for unnecessary extra clearance of roadside areas near beginnings and ends of horizontal curves.