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(Utm) Coordinate in Land Measurement of Region in Different Zone

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(Utm) Coordinate in Land Measurement of Region in Different Zone Journal of Theoretical and Applied Information Technology 15th December 2018. Vol.96. No 23 © 2005 – ongoing JATIT & LLS ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195 THE USE OF GOOGLE MAPS AND UNIVERSAL TRANSVERSE MERCATOR (UTM) COORDINATE IN LAND MEASUREMENT OF REGION IN DIFFERENT ZONE 1ADI SETIAWAN , 2EKO SEDIYONO 1Department of Mathematics, Faculty of Science and Mathematics, Universitas Kristen Satya Wacana, Indonesia 2Faculty of Information Technology, Universitas Kristen Satya Wacana, Indonesia E-mail: [email protected] (corresponding) ABSTRACT The methods in determining land area measurement based on UTM coordinate are very few. In this paper, we present the use of Google Maps and Universal Transverse Mercator (UTM) to determine the measurement of land area in two or four different zones of UTM coordinate based on the proposed method. We proposed the rectangular method. The proposed method is then applied in determining of regional area of regencies in Central Kalimantan such as Kapuas Regency and Murung Raya Regency. If the method is applied to determine the measurement of land area in Kalimantan Tengah, the mean of absolute percentage error (MAPE) is 14.45 %. Keywords: Universal Transverse Mercator, Google Maps, Land Measurement, Zone, Coordinate System 1. INTRODUCTION within the regions located in two zones and some in four zones. Measuring the area of land and the establishment of the land boundary is critical. Especially an area of an extensive estate. It needs 2. LITERATURE REVIEW time and money. Universal Transverse Mercator (UTM) In the latitude and longitude coordinate system, coordinate systems are rarely used compared to it is not easy to determine the distance between two latitude-longitude coordinate systems [1]. However, points on the surface of the earth because the in order to determine the distance between two distance Euclid can be used only on the plane while points using Euclid distance method, it will be more the surface of the earth is considered to be an precise to UTM coordinate system (for more ellipsoidal surface. Therefore, the coordinate information of UTM coordinate system see [2]). In system needs to be transformed into Universal the paper [3], it has been explained how the Transverse Mercator (UTM) coordinate system. rectangular method is proposed to determine the The transformation method is described below. area of Gili Air island, Salatiga city, Central Java Many methods can be used to convert province, Daerah Istimewa Yogyakarta province latitude-longitude coordinates into UTM coordinate and Daerah Khusus Ibukota Jakarta province. systems. One of the methods that can be used is However, these areas are within one UTM zone. In described in the article [4], other method have been this paper, it will be proposed how the rectangular described in papers [3] and [5]. Furthermore, by method can also be used to determine the area using UTM coordinates it can be determined the located in different UTM zones. The proposed distance between 2 points using the Euclid distance method is then used in determining the area of provided if the two points are in one zone. The districts in Central Kalimantan. The selection of this method is then used in determining the area of province based on the location of the regencies Gunung Mas Regency by using the rectangular 8071 Journal of Theoretical and Applied Information Technology 15th December 2018. Vol.96. No 23 © 2005 – ongoing JATIT & LLS ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195 v cos3 k method. In this literature review, it is presented the T 7 0 1 tan 2 e'2 cos2 , methods to convert the geographical coordinate 6 vcos5 k based on [4] and the recent paper [5]. T8 0 (518tan 2 tan4 14e'2 cos2 Suppose a point is present on the surface 120 2 2 2 4 4 6 6 of the earth with coordinates (φ, λ) where φ 58tan e cos 13e cos 4e cos v cos 7 k T 9 0 61 479 tan 2 179 tan 4 tan 6 , representing latitude coordinate and λ representing 5040 longitudinal coordinate. To facilitate the calculation such that the Easting coordinate is of the distance between two points on the surface of N FN(T1()2T2()4T3()6T4()8T5), the earth then the coordinate system needs to be and the Northing coordinate is transformed into a UTM coordinate system by E FE (T 6 ()3T 7 ()5T8 ()7T9). using the following calculation (in meter) [4] : Suppose that the coordinates A1 and B1 are (-0.289287, 113.41617) and (-1.653229, a = 6378137 ( semi-major axis ), 113.504159), respectively, where the first axis is b = 6356752.314245 (semi-major axis), latitude coordinate and the second axis is longitude f = (a-b)/a, coordinate. Coordinate A1 can be converted to UTM a2 b2 e2 , coordinates by using a2 f = 0.00335281, a b f e2 = 0.00669438, n , ’2 a b 2 f e = 0.0067397, a(1 e 2 ) n = 0.00167922, , (1 e 2 sin 2 ) = 6335440.94905524, = 6378137.54423084, a 2 2 1 / 2 , A = 6367449.14582333, (1 e sin ) B = 16038.50866311, S A Bsin 2 C sin 4 Dsin6 Esin8, C = 16.83261326, 5 2 3 81 4 5 D = 0.02198440, A a 1 n n n n n , 4 64 E = 0.00003115, 3 7 55 B a n n 2 n 3 n 4 n 5 , S = 768997.22156522, 2 8 64 T1 = -31974.90817774, 15 3 C a n 2 n 3 n 4 n 5 , T2 = -16094.92794697, 16 4 T3= -6787.608130672, 35 3 4 11 5 T4 = -2809.243975975, D an n n , 48 16 T5 = -1105.580064766, 315 4 5 T6 = 6375505.02454235, E an n , 512 T7 = 1069690.91279259, 0 = longitude of the meridian, T8= 270651.53490600, 0 T9 = 77148.40380713, k0 = central scale factor = 0.9996, such that the Easting = 768936.077649187 FN = False Northing, 768936.08, the Northing = 9967996.448422255 FE = False Easting (= 500000), 9967996.45 and located in zone 49 M. Similarly, E = grid easting, the coordinates of Easting and Northing are N = grid northing, 778624.15 and 9817092.27, respectively and T1 Sk 0 , located in zone 49 M. Since both points are in one v sin cos k T 2 0 , UTM zone and by using the Euclid distance, it can 2 3 be obtained that the distance between point A1 and v sin cos k0 2 '2 2 '4 4 T 3 5 tan 9e cos 4e cos , point B2 is 24 vsin cos5 k 0 2 4 '2 2 T 4 (6158tan tan 270e cos 2 2 720 d (768936.08 778624.15) (9967996.45 9817092.27) 2 2 2 4 4 6 6 330tan e cos 445e cos 324e cos d (9688 .07) 2 (150904 .17) 2 680tan2 e'4 cos4 88e'8 cos8 600tan2 e5 cos6 192tan2 e8 cos8 ), i.e. 151.2149 km. The distance is relatively close to the Vincenty distance between the two points i.e. v sin cos 7 k T 5 0 (1385 3111 tan 2 543 tan 4 tan 6 ), 40320 151,1311 km (for more information of the Vincenty T 6 v cos k , distance see [6] and [7]). 0 8072 Journal of Theoretical and Applied Information Technology 15th December 2018. Vol.96. No 23 © 2005 – ongoing JATIT & LLS ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195 Conversely, if the UTM coordinates (E, N) and ET14 (E)3 T15 (E)5 T16 (E)7 T17. 0 the zone of the location are known then to obtain The coordinate UTM (E, N) = ( 768936.08, the geographical coordinates can be used the 9967996.45) in zone 49 M will be converted into following procedures. Suppose geographical coordinate with the following steps. , M 0 0 Because the location in zone 49 M, i.e. in the N Southern Hemisphere then it is obtained M M , 0 k M = -32016.3565426178, 0 e2 = 0.00669438, 1 ’2 2 e = 0.0067397, 1 1 e 2 , e = -0.0050281291, 1 1 2 e1 = 0.0016792204, 1 1 e 2 T11 = -6.423472123 10-31, -45 M , T12 = -6.450735067 10 , T13 = -6.4019633487 10-59, e2 e4 e6 1 3 5 T14 = 1.5685032305 10-7, 4 64 256 T15 = 6.4748986901 10-22, 3 27 -36 ' 3 T16 = 3.9878759867 10 , sin 2 e1 e1 2 32 T17 = 2.8273808024 10-50, 21 2 55 4 151 3 so that the result of latitude coordinate is sin 4 e e sin 6 e 1 1 1 16 32 96 = -0.289287 and the longitude coordinate 1097 4 = 113.416170. Thus the result is the same as the sin 6 e1 512 previous geographical coordinate. E E FE , Based on the recent paper, this following tan ' procedure can be used to convert the geographical T10 , 2 vk 2 coordinate into the UTM coordinate more briefly 0 that the previous procedure. Let the geographical tan ' T11 (5 3 tan 2 'e '2 cos 2 '4e '4 cos 4 ' 3 4 coordinate ( , ) where representing latitude 24 v k 0 2 '2 2 coordinate and representing longitudinal 9 tan 'e cos ') , coordinate [5] : tan ' T 12 (61 90 tan 2 '46 e '2 cos 2 '45 tan 4 ' a = 6378137 ( semi-major axis ), 720 v 5 k 5 0 f = 1/298.257223563, 2 '2 2 '4 4 '6 6 252tan 'e cos '3e cos '100e cos ' k0 = 0.9996 2 '4 4 4 '2 2 f 66 tan 'e cos '90 tan 'e cos ' n , 88 e '8 cos 8 '225 tan 4 'e '4 cos 4 ' 2 f 2 4 84 tan 2 'e'6 cos6 '192tan 2 'e'8 cos8 ') , a n n A 1 ...., tan ' 1 n 4 64 T13 (1385 3633 tan 2 '4095 tan 4 ' 40320 v 7 k 8 2 3 0 n 2n 5n 1575 tan 6 ' ) , 1 , 2 3 16 1 , T 14 13n 2 3n3 v cos ' k 0 , 2 48 5 1 2 '2 2 , T 15 (1 2 tan ' e cos ' ) 3 6 v 3 cos ' k 3 61n 0 , 1 3 T 16 (5 6e '2 cos 2 '28 tan 2 ' 240 120 v 5 cos ' k 5 0 2 n 2 n 3e '4 cos 4 '8an 2 'e '2 cos 2 '24 tan 4 '4e '6 cos 6 ' 1 1 t sinh tanh sin tanh sin , 2 '4 4 2 '6 6 1 n 1 n 4 tan 'e cos '24 tan 'e cos ' ) , 1 T 17 (61 662 tan 2 '1320 tan 4 ' 7 7 5040 v cos ' k 0 6 720 tan ' ) , then the latitude and longitude can be found by formulas 2 4 6 8 '(E) T10 (E) T11 (E) T12 (E) T13, 8073 Journal of Theoretical and Applied Information Technology 15th December 2018.
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