SIMPLE NUMERICAL-METHOD FOR SOLVING HORIZONTAL CIRCULAR CURVES

When the radius and deflection angle of a horizontal circular curve ar e given, the other five curve elements can be directly computed. The e lements 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 th is case, however, is not direct. This technical note presents a numeri cal method, called the iteration method, for finding the unknown eleme nts. Unlike the Newton-Raphson (NR) method, the iteration method requi res no derivatives and it generally converges for any initial positive value of the curve radius. Thus, the computations are simpler. The it eration and NR methods are applied to a numerical example, and the res ults show that the iteration method is faster.