Alternative Solutions for Horizontal Circular Curves by Noniterative Methods

Abstract

The most common type of horizontal curves used to connect intersecting straight sections of highways and other infrastructures are circular curves. Given the radius and the deflection angle of a horizontal circular curve, the other curve elements can be explicitly determined. However, there are 10 practical situations in which these parameters are unknown, and they have to be determined from two other given elements. In the present paper, these cases are classified into three groups according to their solution type. In the first group, direct analytical solutions can be easily obtained using simple algebraic operations. In the second group, full analytical solutions with physical meaning are not available, and in the third group, existing methods rely on a tedious trial procedure for most cases. The paper develops noniterative exact solutions for the two cases of the second group and noniterative near-exact solutions for the four cases of the third group. The proposed near-exact solutions for the third group, which have a maximum percentage error less than