Simple Numerical Method for Solving Horizontal Circular Curves

Abstract

When the radius and deflection angle of a horizontal circular curve are given, the other five curve elements can be directly computed. The elements include tangent distance, external distance, middle ordinate, length of chord, and length of curve. In some practical problems, the radius and deflection angle are unknown and, to layout the curve, two other elements must be known. Seven cases must be solved depending on the known curve elements. The solution for the unknown elements in this case, however, is not direct. This technical note presents a numerical method, called the iteration method, for finding the unknown elements. Unlike the Newton‐Raphson (NR) method, the iteration method requires no derivatives and it generally converges for any initial positive value of the curve radius. Thus, the computations are simpler. The iteration and NR methods are applied to a numerical example, and the results show that the iteration method is faster.