The shortest overall distance of two piecewise rhumb-lines

This paper presents the simple and logical algorithms of piecewise rhumb-lines. Using the formulae of rhumb-line sailing and mathematical optimization may calculate the minimum overall distance for piecewise rhumb-lines. By constructing the piecewise rhumb-lines sailing, readers can quickly comprehend and grasp the meanings of equations. In the numerical test section, one specific example of one turning point is selected here which its results points out that the turning point with shortest overall distance is not the intersection of the great circle and the rhumb-line with initial course equal to the course of middle latitude along the great circle. The conclusion provided by this work is against the statement provided by Petrović (2014).