Optimum curvature for simple horizontal curves

A model based on an expected total-cost minimization approach is developed for determining the optimal-degree curvature of simple horizontal curves on undivided two-lane highways. Expected total cost is defined as the sum of the construction costs and the expected cost of accidents. Construction cost is treated as a deterministic function of curvature, and the expected cost of accidents is determined in relation to the amount by which required (demand) curvature differs from design (supply) curvature. It is shown that the optimal degree of curvature is highly sensitive to the skewness of the probability distribution of the required curvature. This distribution is derived from the fundamental relationship between speed and degree of curvature, treating speed to be a random variable. The optimal value is shown to change in direct proportion to skewness of the speed distribution. User cost, in terms of travel time, is treated as a special case when examining the sensitivity of optimal design curvature to construction- and accident-cost functions. Model applications in curve design are illustrated by a numerical example.