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УДК 528.913:528.235
ВЫЧИСЛЕНИЕ РАВНОВЕЛИКОЙ ЦИЛИНДРИЧЕСКОЙ ПРОЕКЦИИ ДЛЯ ТОПОГРАФИЧЕСКОЙ КАРТЫ МОНГОЛИИ В МАСШТАБЕ 1 : 200 000
Даш Оюунцэцэг
Монгольский государственный университет науки и технологии, Горно-геологический институт, 14191, Монголия, г. Улаанбаатар, Сухэбаатарский район 8, Бага тойруу 34, главный корпус МонГУНиТ, кандитат технических наук, профессор, зав. кафедрой геодезии, тел. +976-11-452485, тел. +976-11-99172910, e-mail: daoyunaa@yahoo.com,daoyunaa@must.edu.mn
Пурэвжав Эрдэнэчимэг
Монгольский государственный университет науки и технологии, Горно-геологический институт, 14191, Монголия, г. Улаанбаатар, Сухэбаатарский район 8, Бага тойруу 34, главный корпус МонГУНиТ, магистр технических наук, преподаватель кафедры геодезии, тел. +976-11-452485, моб. +976-11-88056133,e-mail:erde_amara@yahoo.com
Ранее топографические карты Монголии составлялись в проекции Гаусса - Крюгера в эллипсоиде Красовского, а тематические карты - в нормальной равновеликой конической проекции с двумя стандартными параллелями. В законе «О геодезии и картографии» Монголии от 1997 г. было установлено использование всемирной системы WGS-84. В данной статье рассматривается вопрос о выборе и вычислении нормальной равновеликой цилиндрической проекции Монголии в масштабе 1 : 200 000 в системеWGS-84, вычисление масштабов m и n, построение графика масштаба длин и площадей.
Ключевые слова: равновеликая коническая проекция, масштаб длин, масштаб площадей.
CALCULATION OF CONFORMAL CYLINDRICAL PROJECTION FOR 1 : 200 000 SCALE TOPOGRAPHIC MAP OF MONGOLIA
Dash Oyuntsetseg
Mongolian University of Science and Technology, School of Geology and Mining, 14191, Mongolia, Ulaanbaatar, Sukhbaatar district 8thkhoroo, Bagatoiruu 34, Doctor of Science (Ph. D.), Professor, Head of the Department of Geodesy, tel. (976)-11-452485, tel. +976-11-99172910, e-mail: daoyunaa@yahoo.com, daoyunaa@must.edu.mn
Purevjav Erdenechimeg
Mongolian University of Science and Technology, School of Geology and Mining, 14191, Mongolia, Ulaanbaatar, Sukhbaatar district 8thkhoroo, Bagatoiruu 34, Master of technical Sciences, lecturer, Department of Geodesy, tel. +976-11-452485, e-mail: erde_amara@yahoo.com
Transformation parameters for the coordinate systems in Mongolia are discussed. Up to now there is no clarity of parameter transformation for medium-scale topographic mapping. How to choose and calculate a normal conformal cylindrical projection for the topographic map of Mongolia at scale 1 : 200 000 in WGS-84 as well as to calculate scales m and n, and scales of length and square measure are considered.
Key words: coordinate system, projection, conformal cylinder, coordinate grid.
Implementation of the Land Law of Mongolia has been intensively carried out with respect to the transition of Mongolia into the market economy relations and adoption of the new Constitution of Mongolia. Within the scope of policy approved by the Government of Mongolia, measures such as enhancing of land relations, improvement of land registration, development of legal environment, creation of conditions for extension and implementation of land possession, land use and ownership rights of citizens, legal entities and organizations, proper land use, bringing land into the economic turnover and flow and upgrading of security and liabilities have been prioritized.
According to the Resolution 25 of the Government of Mongolia dated as of January 28, 2009 on "Transition to consolidated coordinates system", the international geodetic coordinates of WGS-84 shall be used for geodetic observations and processing, the Baltic sea structure shall be used for heights networking and the UTM projection of the universal transversal Mercator shall be used for large and medium scale topographic mapping respectively based on Article 5.2.1 of the Mongolian Law on Geodesy and Cartography. The Resolution has been in use since May 01, 2009. Mapping and data conversion previously made by digital mapping have been finished [3].
The 1:200 000 scale topographic map of the territory of Mongolia based on astronomic points was created during 1932-1937 with the assistance of the former Soviet Union.
For the years of 1938-1950 the first national geodetic network was created and topographic maps at scales 1:100 000, 1:200 000, 1:500 000 and 1:1 000 000 covering the entire territory of Mongolia were re-produced and published in the Mongolian language.
The projection has to be calculated before the map compilation according to the following requirements:
1. Projection should be conformal
2. Deformations shall be as small as possible.
For this purpose a mapping scale, design, grids and average meridian line should be known well in order to calculate the projection. Projection compression (a) must be considered for 1:5 000 000, or larger scale map [1].
Cylinder projection has been calculated in accordance with the formula of "two parallel lines of conformal standard" [1].
Rectangular coordinates of conformal cylindrical projection are determined by the following formula:
X = 1lg U * j*100cm mod 2
" (1)
Y = p*A = P* A P
It: X, Y - rectangular coordinates p - Projection constant
U - function for each latitudes u - scale A - longitude p = 57.3°
mod = 0.4342945
Calculations have been made by Microsoft Office Excel 2010 and data processing was carried out by AutoCad 2010 and AutoCad Land 2002 software.
In order to calculate coordinate grids of Mongolia we used the following values:
North latitude: = 52°10' South latitude: = 41°30' Left longitude: A = 119.75°
Right longitude: Aw = 87.75°
Calculation data:
- Scale: u = 1:200000
- Ellipsoid: Krasovski
- Semi-major axis: a = 6378245 m
- Semi-minor axis: b = 6356863m
- Eccentricity: e = 0.006693427m 2
- Average latitude: po = 46°50'
- Latitude's frequency: Ap = 10'
- Average longitude: A° = 103.75°
- Longitude's frequency: a A = 15'
- Mathematical constants that should be calculated: mod = 0.4342945 ; p = 57.3°
Rectangular coordinates were calculated as follows:
• y angle at each latitude
• U function for each latitude
• Surface radius of primary vertical at average latitude
• Projection constant P
• Projection rectangular coordinates.
The territory of Mongolia is covered by 323 sheets of 1:200 000 scale. Rectangular coordinates of 4,225 points have been determined and the coordinate grid has been created.
As length scales along the meridian line (m) and parallel line (n) of the conformal cylindrical projection are equal (m=n), the following formula is used when determining the projection deflection [1]:
ß.
m = n = —. r
2
p = m ; co = 0 ;
(2)
Where:
m - length scale along the meridian line n - length scale along the parallel line p - area wise deformation
Calculations:
• Surface radius of primary vertical at each latitude:
N = 6387638.060 m
• Parallel radius at each latitude:
r = 4784058.072m
Projection deformations according to the above radius calculations are as follows:
m = n = 1.332 p = m = 1.774
1.774 1.625
41.30 42 43 44 45 46 47
1.774 1.625
49 50 51 52 52.10 41.30 42 43 44 45 46 47
49 50 51 52 52.10
Deformation chart
The deformation charts has been created by m, n (m=n) and p, where: p - Area-wise deformation line m - Length scale along the meridian line (p - Latitude
m
P
P
m
0
0
CONCLUSION
1. There are less errors or deformations when creating cartographical grid by means of conformal cylindrical projection calculation. 0.004 cm of error has been estimated while creating the meridian and parallel lines. Theoretically, such errors should be less than 0.01 cm.
2. 1:200 000 scale topographic map of Mongolia should be calculated by the normal conformal cylindrical projection.
REFERENCES:
1. Vachrameeva, L.A., Bugayevsky, L.M., Kazakova Z. L. Mathematical cartography. Moscow, Nedra, (1986), 98-113 pp.,
2. A. Damdinsuren, J. Altantsetseg, B. Ragchaa. Geodesy (First volume), Ulaanbaatar, 2007.
3. Law of 2003, Geodesy and Mapping Law of Mongolia [electronic version]. Web-site: http://www.nottingham.ac.uk/iessg/
© Dash Oyuntsetseg, Purevjav Erdenechimeg, 2016
