Symbolical Expressions of Rhumb Line's Forward and Inverse Solution

Abstract:

In order to solve problems that deal with rhumb lines solution based on different reference ellipsoids in maritime navigation, the rhumb lines basic equations were established. After the symbolical formula of meridian arcs inverse solution being introduced, rhumb lines forward and inverse expressions which are non-iterative were derived. Finally, numerical examples were given to testify the accuracy of the forward and inverse expansions derived in this paper. Theory analysis and numerical results show that these new formulas have compact and symbolical form, and the precision of the inverse formulas is up to , which can satisfy practical utilization.

• Periodical: Applied Mechanics and Materials (Volumes 448-453)
• Pages: 3586-3590
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.448-453.3586
• Online since: October 2013
• Authors: Fang Neng Li*, Hou Pu Li, Hong Biao Qi, Jiang Ning Xu
• Keywords: Forward and Inverse Solution, Navigation, Rhumb Line, Symbolical Form

References

[1] DING Jia-bo. Practicable formula of the conformal course solution on the earth ellipsoid[J]. Navigation of China, 2005(1): 74-76. (in Chinese).

[2] LI Hong-li. On the solution and inverse of rhumb line[J]. Navigation of China, 1989(1): 47- 52. (in Chinese).

[3] ZHAO Jun-sheng, LIU Yan-chun, ZHAI Guo-jun, et al. Study on the difference between the loxodromes and geodetics in length [J]. Hydrographic Surveying and Charting, 2007, 27(4): 1- 5. (in Chinese).

[4] HU Jiang-qiang, YANG Yan-sheng, LI Tie-shan. Accurate calculation of the course and distance in rhumb line[J]. Journal of Dalian Maritime University, 2005, 31(2): 11-14. (in Chinese).

[5] ZHANG J P, YANG S R. Study to improve middle latitude sailing[J]. Journal of Dalian Maritime University, 2002, 28(Suppl. ): 51-55.

[6] BIAN S F , CHEN Y B. Solving an inverse problem of a meridian arc in terms of computer algebra system[J]. Journal of Surveying Engineering, 2006, 132(1): 7-10.

DOI: 10.1061/(asce)0733-9453(2006)132:1(7)

[7] LI Hou-pu, BIAN Shao-feng. A new solution to expansions of conformal latitude[J]. Hydrographic Surveying and Charting, 2007, 27(4): 6-10. (in Chinese).

[8] Bian Shao-feng, Xu Jiang-ning. Computer Algebra System and Mathematical Analysis in Geodesy [M]. Beijing: National Defense Industry Press, 2004. (in Chinese).