This work tackles the problem of misconception when using sophisticated mathematical tools, nonlinear optimization in this particular case, to solve a navigational problem. Namely, to reach the Great Circle vertex with two rhumb line legs ensuing the optimized distance, an initial rhumb line course equal to the orthodromic course at middle latitude may be used. The initial course is thereupon optimized by the incremental value steps. The optimized distance is achieved if the rhumb line course is altered towards the vertex at the orthodrome-loxodrome intersection point. As determination of this point cannot be formulated in a closed form, an iterative solution is to be applied. The derived transcendental equation forms a basis for an iterative solution of intersection using the Newton-Raphson method. To the contrary, finding solutions to a system of nonlinear equations can mislead a researcher unable to comprehend and grasp the mathematical meanings of the algorithm. The gist of this essay is a novel concept showing an intrinsic property i.e. orthodrome-loxodrome correlation using a well-known formula.


    Access

    Download


    Export, share and cite



    Title :

    Middle Rules and Rhumb-Line Sailing


    Contributors:


    Publication date :

    2017




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    Unknown




    Middle Rules and Rhumb-Line Sailing

    Petrović, Miljenko | Online Contents | 2017



    Practical Sailing Formulas for Rhumb-Line Tracks on an Oblate Earth

    Kaplan, G. H. | British Library Online Contents | 1995



    Rhumb Line On A Spheroidal Surface

    Hsu, D. Y. / Institute of Navigation | British Library Conference Proceedings | 1997