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Wyznaczenie lokalizacji obiektu logistycznego z zastosowaniem metody wielkiego koła

Zaręba Marek

Zeszyty Naukowe / Lotnicza Akademia Wojskowa

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2018

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nr 1-2

391--418

PL

Poruszony problem wyznaczenia lokalizacji obiektu logistycznego z zastosowaniem metody wielkiego koła rozpatrywany jest podczas konfigurowania sieci logistycznej w celu minimalizacji kosztów logistycznych oraz optymalizacji poziomu obsługi klienta. W artykule przedstawiono trzy metody obliczania odległości między dwoma punktami, czyli metodę wyznaczania odległości na krótkich dystansach bez uwzględniania krzywizny Ziemi, metodę związaną z loksodromą i wyznaczaniem odległości na średnich dystansach z uwzględnieniem krzywizny Ziemi, a także metodę wielkiego koła i ortodromy służącą do wyznaczania odległości na długich dystansach z uwzględnieniem krzywizny Ziemi. Na podstawie uzyskanych wyników, w których analizowano także poziom skomplikowania obliczeń, stwierdzono, że metoda wielkiego koła, czyli związana z ortodromą charakteryzuje się możliwością zastosowania we wszystkich przypadkach zarówno krótkich, średnich i długich odległości, a jej dokładność jest porównywalna z metodami preferowanymi dla danych dystansów.

EN

The goal of the article is to present three methods for determining the location of a logistic facility with minimum logistic costs and optimum level of customer service. In the first method, path over short distances is calculated, without taking into account the curvature of the Earth. The second method, in which a loxodrome and the curvature of the Earth are taken into account, is used to determine the route on medium distances. The third method, used to determine route over long distances combines the formula of the great circle path with an orthodrome, with the curvature of the Earth taken into account. On the basis of the results obtained with each method, it was found that the great circle method associated with orthodrome may be applied for any distance, offering accuracy comparable with the methods preferred for given distances. The complexity of calculations when either the great circle method or the loxodrome are applied is definitely higher than when the method for short distances is used.

2

A systematic approach for solving the great circle track problems based on vector algebra

Chen C. L.

Polish Maritime Research

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2016

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nr 2

3--13

EN

A systematic approach, based on multiple products of the vector algebra (S-VA), is proposed to derive the spherical triangle formulae for solving the great circle track (GCT) problems. Because the mathematical properties of the geometry and algebra are both embedded in the S-VA approach, derivations of the spherical triangle formulae become more understandable and more straightforward as compared with those approaches which use the complex linear combination of a vector basis. In addition, the S-VA approach can handle all given initial conditions for solving the GCT problems simpler, clearer and avoid redundant formulae existing in the conventional approaches. With the technique of transforming the Earth coordinates system of latitudes and longitudes into the Cartesian one and adopting the relative longitude concept, the concise governing equations of the S-VA approach can be easily and directly derived. Owing to the advantage of the S-VA approach, it makes the practical navigator quickly adjust to solve the GCT problems. Based on the S-VA approach, a program namely GCTPro_VA is developed for friendly use of the navigator. Several validation examples are provided to show the S-VA approach is simple and versatile to solve the GCT problems.

3

On computational algorithms implemented in marine navigational software used in marine navigation electronic devices and systems

Weintrit A., Kopacz P.

Annual of Navigation

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2012

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No. 19, part 2

171--184

EN

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.