Solving Circular Curve Using Newton‐Raphson's Method

In highway, railway, canal, and pipeline locations, the horizontal curves employed at points of change in direction are arcs of circles. A circular curve can be described by seven principal elements: (1) Radius of the curve; (2) deflection angle between tangents; (3) tangent distance; (4) external distance; (5) middle ordinate; (6) long chord; and (7) length of curve. In conventional surveying, the radius of the curve is given, and the deflection angle between the tangents is measured; all other elements can be calculated. However, these two elements sometimes are unknown in the fieldwork. In this case, a new method must be considered. In this paper, a numerical solution called the Newton‐Raphson's method is presented. Using this method, the radius of a curve and the deflection angle between the tangents can be calculated so long as two of the other principal elements are given. To be convenient for actual use, a computer program is included.