UDC: 
DOI: 
10.22389/0016-7126-2020-956-2-2-6
1 Medvedev P.A.
Year: 
№: 
956
Pages: 
2-6

Omsk State Agrarian University named after P.A. Stolypin

1, 
Abstract:
Comments on the algorithms, published in this journal (№ 8, 2013; № 2, 2014) are given for calculation of the meridian arc length, plane rectangular coordinates, connecting meridians and Gauss – Kruger’s scale of projection in hexagonal meridian zone. The algorithms’ disadvantages in Gauss – Kruger’s projections, suggested by GOST (RF State Standard) P 51794–2008 are mentioned above in these publications and simpler ones are offered instead of them. The main disadvantage of the suggested algorithms is the lack of reliability evaluations of the results determined by them. It is shown on a numerical example that the formula for calculation of meridian arc length is given in a wrong view that leads to incorrect results during the calculation of the x abscissa. The formulas for error estimation of the given algorithms enable carrying out the investigation with methods of differentials calculus. For comparison, the solution of this problem by A. Schodlbauer according to Euler’s method is given. The aim of this article is not to improve the suggested algorithms but to mention their disadvantages, derive the error estimates and specify some other ways to output the algorithms.
References: 
1.   Balandin V.N., Bryn M.J., Menchikov I.V., Firsov Yu.G. (2014) Calculation of the plane rectangular coordinates, meridian rapprochement and Gauss projection scale in the 6th grid zone using geodetic coordinates. Geodezia i Kartografia, 884(2), pp. 11-13. (In Russian). DOI: 10.22389/0016-7126-2014-884-2-11-13.
2.   Balandin V.N., Efanov A.I., Menchikov I.V., Firsov Yu.G. (2013) National Standard of the Russian Federation GOST R 51794-2008. Geodezia i Kartografia, 878(8), pp. 55-56.
3.   Balandin V. N., Men’shikov I. V., Firsov Yu. G. Preobrazovanie koordinat iz odnoy sistemy v druguyu. Sankt-Peterburg: Sborka, 2016, 90 p.
4.   Medvedev P.A., Novgorodskaya M.V. (2017) Development of mathematical model Gauss – Kruger coordinate system for calculating planimetric rectangular coordinates using geodesic coordinates. Geodezia i Kartografia, 926(8), pp. 10-19. (In Russian). DOI: 10.22389/0016-7126-2017-926-8-10-19.
5.   Hristov V.K. Koordinaty Gaussa – Kryugera na ehllipsoide vrashcheniya. M.: Geodezizdat, 1957, 264 p.
6.   Euler L. (1753) Elemens de la Trigonometrie spheroidicue tires de la metode des plus grands et plus petits. Histoire del,Academie Royale des sciences. Anne-1749, Paris, pp. 258–293.
7.   Kruger L. (1912) Konforme Abbildung des Erdellipsoids in der Ebene. Veroff des Preus. Geod. Jnst., N. F., 52, Potsdam. 172 p.
8.   Schodlbauer A (1981) Gaußsche konforme Abbildung von Bezugsellipsoiden in die Ebene auf der Grundlage des transversalen Mercatorentwurfs. Allg. Vermess, Volume 88, no. 5, Nachr, pp. 165–173.
Citation:
Medvedev P.A., 
(2020) Comments on Gauss – Kruger’s projection algorithms for hexagonal meridian zones. Geodesy and cartography = Geodezia i Kartografia, 956(2), pp. 2-6. (In Russian). DOI: 10.22389/0016-7126-2020-956-2-2-6
Publication History
Received: 19.06.2019
Accepted: 12.09.2019
Published: 20.03.2020

Content

2020 February DOI:
10.22389/0016-7126-2020-956-2

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