Radius Requirements for Trucks on Three-Dimensional Reverse Horizontal Curves with Intermediate Tangents

Abstract

Minimum radius requirements for reverse horizontal curves are currently based on the design of each arc as a separate simple horizontal curve on flat terrain, with the effects of reverse horizontal curvature and vertical alignment being ignored. This paper establishes minimum radius requirements for trucks on three-dimensional (3-D) reverse horizontal curves with intermediate tangents on the basis of vehicle stability. With vehicle simulation software, vehicle dynamics were recorded for the base case of two-dimensional simple curves and for reverse curves superimposed with different vertical alignments (upgrade, downgrade, crest curve, and sag curve). The simulation was run for two maximum superelevation rates, three design vehicles, and different vertical grades. Two mathematical models were developed for flat and 3-D reverse curves. The models provided the minimum radius of the sharper arc of the reverse curve as a function of design speed, maximum superelevation, ratio of flatter to sharper curve radius, design vehicle, and intermediate tangent length. The results showed that an increase in the minimum radius of existing design guides (ranging from 5% to 27%) was required to compensate for the effects of reverse curvature and vertical alignment. The required increase can be reduced by using longer intermediate tangents. Design requirements for the spiral length of reverse curves are also presented.