Response to Comments on "A Novel Approach to Determine the Astronomical Vessel Position"

Abstract

Paper Submitted 05/17/04, Accepted 06/07/04. Author for Correspondence: Jiang-Ren Chang. E-mail: cjr@sena.ntou.edu.tw. *Associate Professor, Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, 2, Pei-Ning Road, Keelung, Taiwan 202, R.O.C. **Assistant Professor, Department of Merchant Marine, National Taiwan Ocean University, 2, Pei-Ning Road, Keelung, Taiwan 202, R.O.C. ***Associate Professor, Institute of Civil Engineering, National Taiwan University, 1, Sec. 4, Roosevelt Road, Taipei, Taiwan 10617, R.O.C. In response to the comments regarding our recently published paper in the Journal of Marine Science and Technology [3], we would like to begin by expressing our appreciation to Professor Yves Robin-Jouan for his positive remarks. After careful consideration, we offer several points, as follows. Originally, due to the necessities of teaching, we found that some formulae, which appear in spherical trigonometry, could be reinterpreted using vector algebra, and could further be applied to resolve two classical navigational problems: the great circle sailing (GCS) and the astronomical vessel position (AVP). We made a chance discovery that the geometrical properties of spherical triangles could be formulated in a vector form. Thus, by using the trigonometric equation solving technique to yield these theoretical formulae, they can be applied to construct direct calculation methods, namely the Simultaneously Equal-altitude Equations Method (SEEM) and the Great Circle Equation Method (GCEM), respectively [3, 4]. Aimed at the methodology for solving AVP problems, the available alternatives can generally be categorized into the spherical triangle method and the matrix method. Since the matrix is a vector formulation, the SEEM can be considered a matrix method. In fact, the SEEM is formulated using a fixed coordinate system and relative meridian concept, in conjunction with vector algebra, to deal with the AVP problem. Therefore, simultaneous equal-altitude equations can be constructed as: cosd1 • cost1 • cos1 + sind1 • sinL = sinH1, (1)