‘A Vector Solution for Navigation on a Great Ellipse’

Earle, Michael A.

doi:10.1017/s0373463301009705

Cited by 9 publications

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“…One deficiency of Bowring's normal sections paper is that the arrival azimuth (true bearing) is not addressed. More recent papers have used vector analysis on the great elliptic arc for azimuth calculation, but left the issue of arc length to numerical integration techniques. This paper is intended to serve two purposes.…”

Section: Introductionmentioning

confidence: 99%

Earth Section Paths

Gilbertson

2012

Navigation

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The shortest path between two points on a surface are called geodesics. Geodesics on oblate spheroids are rather complex curves described by differential geometry. While these Geodesics have non‐zero torsion, there are plane curves that are good approximations for guidance purposes in aviation and sailing. This paper offers a unified approach to Earth section paths, offering good approximate solutions to both the direct and indirect problems of geodesy. Common examples of Earth section paths include normal sections and great ellipses. Copyright © 2012 Institute of Navigation.

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Section: Introductionmentioning

confidence: 99%

Earth Section Paths

Gilbertson

2012

Navigation

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“…The calculation of the length of the arc of the meridian is a basic prerequisite for many accurate sailing calculation methods on the ellipsoid concerning both Rhumb-Line Sailing (RLS) and shortest sailings on the ellipsoid such as Great Elliptic Sailing (GES). A lot of specific papers present in detail the advantages and benefits of these methods [2,6,9].…”

Section: The Length Of the Meridian Arc In Sailing Calculationsmentioning

confidence: 99%

On Computational Algorithms Implemented in Marine Navigational Software Used in Marine Navigation Electronic Devices and Systems

Weintrit¹,

Kopacz²

2012

Annual of Navigation

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In the paper the authors attempt to present the computational problem related to the navigational algorithm (meridian arc formula) implemented in the software applied in marine navigation electronic devices and systems, such as GNSS (GPS, GLONASS, Galileo), AIS, ECDIS/ECS, and other marine GIS. From the early days of the development of the basic navigational software built into satellite navigational receivers, it has been noted that for the sake of simplicity and a number of other reasons, this navigational software is often based on the simple methods of limited accuracy. It is surprising that even nowadays the use of navigational software is still used in a loose manner, sometimes ignoring basic computational principles and adopting oversimplified assumptions and errors such as the wrong combination of spherical and ellipsoidal calculations in different steps of the solution of a particular sailing problem. The lack of official standardization on both the ‘accuracy required’ and the equivalent ‘methods employed’, in conjunction to the ‘black box solutions’ provided by GNSS navigational receivers and navigational systems (ECDIS and ECS) suggest the necessity of a thorough examination of the issue of sailing calculations for navigational systems and GNSS receivers

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“…William's method for the computation of the distance along the great elliptic arc. This work of Earle (2000) has been recently updated for the calculation of azimuth (Earle 2008). These formulas have the general form of the integral of Formula (2).…”

Section: E X I S T I N G M E T H O D S F O R T H E S O L U T I O N O mentioning

confidence: 99%

“…Williams (1996) provides formulas for the computation of the sailing distance along the arc of the great ellipse. The first paper of Earle (2000) also presents the results of comparative calculations for the great elliptic arc distance using the same eight test lines used by Williams (1996) and Haiwara (1987). For the computation of the eccentricity e ge and the geodetic great elliptic angle Q ge of Formula (2), Williams provides simple and compact formulas.…”

Section: E X I S T I N G M E T H O D S F O R T H E S O L U T I O N O mentioning

confidence: 99%

“…These eight lines lie on the successive parallels 10x, 20x … 80x and all of them have the same difference of longitude equal to 100x. The numerical tests and comparisons of Williams (1996) and Earle (2000) are restricted to the calculations of the sailing distance only and do not include other computed elements of the great elliptic sailing, such as the coordinates of intermediate points. The numerical tests and comparisons of Williams (1996) and Earle (2000) are restricted to the calculations of the sailing distance only and do not include other computed elements of the great elliptic sailing, such as the coordinates of intermediate points.…”

Section: N U M E R I C a L T E S T S A N D C O M P A R I S O N S Formentioning

confidence: 99%

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New Algorithm for Great Elliptic Sailing (GES)

Pallikaris

Latsas

2009

J. Navigation

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An analytical method and algorithm for great elliptic sailing (GES) calculations is presented. The method solves the complete GES problem calculating not only the great elliptic arc distance, but also other elements of the sailing such as the geodetic coordinates of intermediate points along the great elliptic arc. The proposed formulas provide extremely high accuracies and are straightforward to be exploited immediately in the development of navigational software, without the requirement to use advanced numerical methods. Their validity and effectiveness have been verified with numerical tests and comparisons to extremely accurate geodetic methods for the direct and inverse geodetic problem.

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‘A Vector Solution for Navigation on a Great Ellipse’

Abstract: The following misprint should be corrected in the paper published in Vol. 53, No. 3, P. 477, line 13 -Equation 18 : for Similarly with υ φ l cυ\cθ we can show that Q v φ Q= l r= cos=(θ) read Similarly with υ θ l cυ\cθ we can show that Q v θ Q= l r= cos=(θ)

Cited by 9 publications

References 0 publications

Earth Section Paths

Earth Section Paths

On Computational Algorithms Implemented in Marine Navigational Software Used in Marine Navigation Electronic Devices and Systems

New Algorithm for Great Elliptic Sailing (GES)

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