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 navigational problem. Namely, to reach the Great Circle vertex with two rhumb line legs ensuing the optimized distance, an initial rhumb line course...
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2017-06-01
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| Series: | Polish Maritime Research |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/pomr-2017-0045 |
| _version_ | 1818580771866148864 |
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| author | Petrović Miljenko |
| author_facet | Petrović Miljenko |
| author_sort | Petrović Miljenko |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-16T07:22:54Z |
| format | Article |
| id | doaj.art-c4cbf09f1fea479a9652936f1996a500 |
| institution | Directory Open Access Journal |
| issn | 2083-7429 |
| language | English |
| last_indexed | 2024-12-16T07:22:54Z |
| publishDate | 2017-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Polish Maritime Research |
| spelling | doaj.art-c4cbf09f1fea479a9652936f1996a5002022-12-21T22:39:36ZengSciendoPolish Maritime Research2083-74292017-06-01242131610.1515/pomr-2017-0045pomr-2017-0045Middle Rules and Rhumb-Line SailingPetrović Miljenko0Stonska 1A, 10020 Zagreb, CroatiaThis 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.https://doi.org/10.1515/pomr-2017-0045marine navigationmiddle latitudemiddle longitudeorthodromeloxodrome |
| spellingShingle | Petrović Miljenko Middle Rules and Rhumb-Line Sailing Polish Maritime Research marine navigation middle latitude middle longitude orthodrome loxodrome |
| title | Middle Rules and Rhumb-Line Sailing |
| title_full | Middle Rules and Rhumb-Line Sailing |
| title_fullStr | Middle Rules and Rhumb-Line Sailing |
| title_full_unstemmed | Middle Rules and Rhumb-Line Sailing |
| title_short | Middle Rules and Rhumb-Line Sailing |
| title_sort | middle rules and rhumb line sailing |
| topic | marine navigation middle latitude middle longitude orthodrome loxodrome |
| url | https://doi.org/10.1515/pomr-2017-0045 |
| work_keys_str_mv | AT petrovicmiljenko middlerulesandrhumblinesailing |