<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

Middle Rules and Rhumb-Line Sailing

Polish Maritime Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Middle Rules and Rhumb-Line Sailing"}

This work tackles the problem of misconception when using sophisticated mathematical tools, nonlinear optimization in this particular case, to solve a...

Middle Rules and Rhumb-Line Sailing

Online veröffentlicht: 22. Juli 2017

Seitenbereich: 13 - 16

DOI: https://doi.org/10.1515/pomr-2017-0045

Schlüsselwörter
marine navigation, middle latitude, middle longitude, orthodrome, loxodrome

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Middle Rules and Rhumb-Line Sailing

Online veröffentlicht: 22. Juli 2017

Seitenbereich: 13 - 16

DOI: https://doi.org/10.1515/pomr-2017-0045

Schlüsselwörtermarine navigation, middle latitude, middle longitude, orthodrome, loxodrome

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
marine navigation, middle latitude, middle longitude, orthodrome, loxodrome