Journals - MOST Wiedzy

Logo

MIDDLE RULES AND RHUMB-LINE SAILING

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.

Keywords:

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

Details

Issue
Vol. 24 No. 2(94) (2017)
Section
Latest Articles
Published
22-07-2017
DOI:
https://doi.org/10.1515/pomr-2017-0045
Licencja:
Creative Commons License

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

Open Access License

This journal provides immediate open access to its content under the Creative Commons BY 4.0 license. Authors who publish with this journal retain all copyrights and agree to the terms of the CC BY 4.0 license.

 

Authors

Miljenko Petrović

Download paper