Middle rules and rhumb-line sailing

• Autorzy: Petrović M.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

marine navigation; middle latitude; middle longitude; orthodrome; loxodrome

• Wydawca: Gdańsk University of Technology, Faculty of Ocean Engineering & Ship Technology
• Czasopismo: Polish Maritime Research
• Rocznik: 2017
• Tom: nr 2
• Strony: 13--16
• Opis fizyczny: Bibliogr. 10 poz., rys., tab

Twórcy

autor

Petrović M.

• Stonska 1A, 10020 Zagreb Croatia

Bibliografia

• 1. Bowditch N.: The American Practical Navigator. Bicentennial Edition, National Imagery and Mapping Agency (NIMA), Bethesda, Maryland 2002.
• 2. Clough-Smith J. H.: An Introduction to Spherical Trigonometry. Brown, Son & Ferguson, Ltd., Glasgow 1978.
• 3. Greenberg M.: Advanced Engineering Mathematics. Prentice-Hall Int., New Jersey 1998.
• 4. Han-Fei Lu, Hsin-Hsiung Fang and Chung-Hsiung Chiang: Trans-oceanic Passages by Rhumbline Sailing. The Journal of Navigation, London-Cambridge, U.K. 1991, Vol. 44, pp.423-428.
• 5. Kurtz M.: Handbook of Applied Mathematics for Engineers and Scientists. McGraw-Hill Inc., New York 1991.
• 6. Petrović M.: A note on mid rules optimization of distance on the sphere. Scientific Journal of Maritime Research, Rijeka, Croatia 2015, Vol. 29, pp. 122-124.
• 7. Petrović M.: Orthodrome-Loxodrome Correlation by the Middle Latitude Rule. The Journal of Navigation, London-Cambridge, U.K. 2014, Vol. 67, pp. 539-543.
• 8. Petrović M.: Orthodrome. Graduation thesis at the College of Maritime Studies, Dubrovnik, Croatia 1990.
• 9. Smart W.M.: Textbook on Spherical Astronomy. Cambridge University Press, London 1986.
• 10. Tseng W.K.: The Shortest Overall Distance of Two Piecewise Rhumb-lines. 10th International Conference on Natural Computation (ICNC), Xiamen-China 2014, pp. 1153-1157.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)