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

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.

Minimum Clearance Offsets for Providing Desired Stopping Sight Distances at Simple Curves with Variable Operating Speeds

Lateral clearance on the inside of horizontal curves is required by all geometric design guidelines in order to provide at least stopping sight distance. There already exist graphical models, analytical models, and design charts for determining minimum clearance offsets to meet the requirement. Some of these models determine the offsets based on constant design sight distance values on the assumption that drivers negotiate horizontal curves at constant speed. Therefore, those models are suitable for sites where there is no difference in speeds between tangent and curved sections. Past studies have reported that there are sites where drivers decelerate on entering horizontal curves and accelerate on departing from the curves. At those sites stopping sight distance for a given driver varies with driver location due to variable speed. This paper presents an analytical model and a chart for determining minimum offsets needed to provide desired sight distances at horizontal curves with variable operating speeds. At those sites the offsets yield roadside clearance boundaries that have transition arcs with performances that are similar to those of elliptical arcs. Therefore, practitioners may choose to use elliptical equations or equations and the chart developed herein. Results of this study will be of value to practitioners in the area of roadside design.

Suitability of the Euler’s Spiral for Roadside Clearance in Order to Provide Stopping Sight Distances

The AASHTO’s guideline for geometric design, also known as the green book, requires that the inside of horizontal curves be cleared of obstructions to sight lines in order to provide sufficient sight distances. Recently, innovative use of Euler’s spiral for determination of clearance offsets has been proposed. However, suitability of the offsets as minimum criteria has not been evaluated. This paper presents comparison between the proposed offsets and minimum offsets determined with the computational method suggested in the green book. Results of comparison show that offsets determined with innovative use of the Euler’s spiral are always longer than minimum values determined with the computational method. The differences in lengths of the two sets of offsets increase with decrease in curve radii. Therefore, on sites with large radii offsets determined through innovative use of the Euler’s spiral may be implemented in the field since the offsets are only slightly longer than minimum offsets. On sites with short radii some offsets on tangent sections are very long such that they result in extra cleared areas that will not accommodate sightlines. The areas that do not accommodate sightlines may result in unnecessary extra earthwork costs where highways are located in cut zones. Additionally, it has been suggested in this paper that designers also consider other curves, including elliptical arcs, for roadside clearance envelopes. One advantage of elliptical arcs is that they are flexible to align with boundaries of clear zones on tangent sections regardless of sizes of radii of horizontal curves. Besides, most offsets to elliptical arcs are comparable to those determined with the green book’s computation method. An example of design chart has been presented for practitioners to use. The chart is for minimum offsets needed to provide a given sight distance while gradually transitioning clearance from boundaries of clear zones on tangent sections.