PLANE COORDINATE PROJECTION TABLES HAWAIIAN ISLANDS

Transcription

1 U. S. Department of Commerce Sinclair Weeks, Secretory Coast and Geodetic Survey Robert F. A. Studd., Director Special Publication No. 32 PLANE COORDINATE PROJECTION TABLES I UNITED STATES GOVERNMENT PRINTING OFFICE WASHINGTON : 1oM For ule by the Superintendent of Documants, U. S. Govmrnmmnt Printins Office Wmahlnnton 25. D. C. - Prlcm 2 cents (papar)

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3 ?.E. t P A c I F I A J - 7 I

4 3 Foreword The plane coordinate system adopted for the Hawaiian Islands consists of five zones, each of vhjc!\ is based on a transverse Ibrcator projection, In the first four zones the scale along the central meridian in each zone is reduced, in order to minimize the scale error throughout the zone, The fifth zone is so narrow that no reduction in scale is made along its central meridian, The tables in this publication are to be used for the conversion of geographic positions to plane coordinates or plane coordinates to geographic positions. The constants for the zones are listed on page 7. The methods of computation have been designed for machine calculation. All of the functions that are required are given in this publication. The formulas and sample computations which follow show the general methods for computing either type of coordinates. Plane coordinates from L geographic positions X = x + ~,OOo D3L * Y -.o+&) - Grid azimuth = geodetic azimuth a& 11 = nklt sin pl + g + C - term where and YO 9 H, V, and 2 are based on the latitude of the geographic position, b, c, and g are based on axt.

5 4 = Central Meridian - and &X tt is the convergence of the meridian at the station with respect to the Central Meridian. The term for the reduction of geodetic to grid azimuths may be neglected for nost work. However, for llms five miles or more in length if the same degree of accuracy is desired as is obtained by geographic computations, this term shoula be evaluated and used. Geographic.- positions from plane coordinates.---- P (~~/1,)~ + d = V ( Ax11/13)2 + c YO = y - P (~~/1,)~ - d Obtain the latitude from the table of yo. Use latitude to obtain H from the table. X' = x = 5, approximate = x' $ H. Determine 5 from latitude and,b from approxinate Ax then The following table8 are based on the Clarke spheroid of 1866,

6 DlRPAIIISNT OF COMMERCE u. 9. -Am? urn CaODmc swum Form Nn. 744b PLANE COORDINATES ON TRANSVERSE MERCATOR PROJECTION (Condensed form for calculating-machine computation).. state Ha Ma I I Zone / Central meridian /55 3' o o * ~ ~ ~ 2=2'+5oo,OOo H and V=Tab. Hand Tab. V. Aa"= AA~I sin6 + g Grid Az. = Geod. Az. - Aa g increasea AX'. sin +numerically.

7 OIECARTMENT OF COMMERCE u. L COALI AWD GcoDflK SURVEY NO.?48a 6 GEODlETIC POSITIONS F'ROM TRANSVERSE MEBCATOR COORDINATES (CALCULATING MACHINE COMPUTA'L1O.V STATE - ZONE d H a b + o.o/ AA=(X8i ab) i H - / 754;?// AA /d 9// I f 3.// 2 Central Meridian / , A=C.M.-AX 155" 59'. + / 9"23:j77 Station X I n Y I,* -1 C X' P d H a b Q - p(&)'l+d - YO I AUYW.AA=X'+ H AA=(XIT ab) i H ox Central Meridian A= C.M.-AX II II I 11 e 81 I II X C - x' Y P(&f+ d - YO a b Q When ab is f; : : ; : p: - : X' numerically I e 88 Central Meridion A= C.M.-AX I1

8 TRANSVERSE MERCATOR PROJECTION HAWAl IAN ISLANDS 7 Constants Zone Constant 1 Hawaii 2!laui Lanai Molokai Ka hoolawe C Central Xeridian Scale reduction along central meridian 5,. ft, 1553~2 1: 3, x1 ~,. ft. 156O : 3, Zone constant 3 Oahu 4 Kauai 5 Niihau I C central?kwidian 5,. ft. 158 I :'oo 5,. ft '! 5,. ft, 16 1' Scale reduction along central meridian 1: 1, ~1 1: 1, None ~1

9 8 -- Lat ~ Yo feet. oo R TRANSVERSE MERCATOR PROJECTION ZONE 1 Table I AYo per H AH per AV per A Al a / R , R s , a R

10 Lat Yo feet TRANSVERSE MERCATOR PROJECTION ZONE 1 Table I AYo Per H AH per _ V A :?e; 437 1, A _-. AV pei ~ ioo.ee R.18 16@ e , A eon eo BO $ i; yo M ft M a e ,7U a85 a W.81 Table I1 - - A XI4 C b Ab C. om O*% O*Ooi; z? ,36 M W = Wt % a O ,

11 1 Y 1, 2, 3, 4, 5, 6, Table IV X' 5, 1 XI 25;ooo 3,O~ 5, 1, 15, 2, 25, 3, 35, bo, 45, 5, 55, 6, 65, 7 75, 8, 85, 9 95, 1, TRANSVERSE M ERCATOR PROJ ECTlON d ZONE 1 Table I11 P AP I M * Table V e 1" 2" M MOO , , , M.1 M.1 MOO1. I I I, , " I e.7 I 1 I I 1 1 Table VI Scab fact or s XI loo, ,, , ~~, , , 13, ooo 135, 14, 145, 15, 155, 16, 165, 17, 175, 18, 185, 19, 195, 2, &, , i ,OOOO 59 i oOOo 126 XI 2, 25, 21, 215, 22, 225, 23, 235, 24, 245, 25, 255, 26, 265, , 28, 285, 29, 1, , i i. 328 i. 356 i,ooo~ 384 i i. 632

12 TRANSVERSE MERCATOR PROJECTION Lat. Yo AYo per feet ;di H n AH per V.BO1 656.eo2 199.en2 742.en3 284.e eo AV per n3 9. n5 9.n * , BO7 76.EO e8 697.E on AM b b U b n en R R nil ' u R R , A El A A A , R A.e e ' Y l--- Q R , on a.753 a R R e R A18 94.A e e2 56.e R23 74.e e A , U i76.3n e e27 422, , R A 2 9 i76.7n 1'16.R A i e29 nil A A OU Y A e e32 71.R e A

13 12 TRANSVERSE M ERCATOR PROJ ECTl ON ZONE 2 - A2-1 2 G am 9 lo b Ab. o b, -,1 -.m1 -, , ,5 -,6 - a Table I1 - ah" b Ab +O.O9+ +Om a a41 -, C -, , 13 - a aOll m , 6 -,3 15 -,1 3, Y 1, 2, tg:% Table I11 P. AP M AM, , , ,3 7% ,3 8116,93758,3 868 Table IV I X' I d I 5,d 1, 15, 2, 25, 3, OOo i I,oo. +O 1 +o 1 +O,o Table V

14 TRANSVERSE MERCATOR PROJECTION ZONE 2 13 Table VI Scale factors X' X' 5, 1, 15, 2, ~, 155, 15, 9 165, 17, , 3, QOO 35, 49, 45, 5, 55, 6, 65, 7, , , , 18, la 5, 19, 195, 2, 25, 21, 215, 22, , 81 i.oooo 13 1, 126 1, 149 3, , , 8, 85, 9, 95, 1, 15, 11, 115, 12, 125, 13, 135, lb, 145, , , , , ,3 23, 235, 24, 245, 25, 255, 26, 265, 27, 275, 28, 285, 29, 1, 248 1, , , oooo 567 1, ,

15 14 Lat TRANSVERSE M ERCATO R PRO J ECTlO N ZONE 3 Table I AYo per t H AH per v A A AV per R R a F 99F 99A a e E R Rn A ? n e A A e A A nR. R R.75 e ? 8.73 e.?? n 9R9 9R R7 9R oa A R R.82 'lr e e45 25R Y.A n e.7n P R R 2 9R , I347 33R , A A4R 'f R4R e Table I b Ab C Ab I c W O Om57 12 W.52.ooo O.62 e.122 We179 +O 231 w.276 we313 w.34 W.356 W. 358 w.45 *e37 +Om27 W ooo.ooo. 15.OOo.ooo.ooo.ooo.ooo

16 TRANSVERSE MERCATOR PROJECTION ZONE 3 15 Table I11 X' Table IV d. 5,. 1,. 15,. Table V y # 1OOo" 2" Table VI Scale factors X' 5, 1, 15, 2, 25, 45, 5 55, 6, 65, 7, 75, X' 75, 8, 85, 9, 95, 1, 15, 11, 115, 12, 125, 13, 135, 14, 145, 15, g39 3, , , , , ,oooo 158

17 16 La t Y YO A Y ~ feet ;35 TRANSVERSE MERCATOR PROJECTION ZONE 4 Table I per H AH per , I ~ V A e A A52 51R.A A A54 67 AV per hn R. 5A a , e3 1.9A s R A8.a R55 97.A A A F 8.58 e.5e e a s a j A2 1R A LA5.* R5.85.e ~ 5 a 183.A A59 2Y.e59 7a2.A6 234.A6 746.A61 25R.A61 77.e R62 792, e. 55 e R R R , n , Table I1 2 I am 9 lo O. 62 a O O.231 +o. 276 Me313 W.34 w.354 +O. 358 w.345 +om 316 +O o. 21 W.113 +O. 62 +O. 6 2:z; +o. Woo37 WOO O dt o..om.13 O.Oo.om 1oc)o

18 TRANSVERSE MERCATOR PROJECTION ZONE 4 Table I11 17 Table IV Table V g xr " Z I 23 1" 2".. woo2 4.2 w.2 1 Table VI Scale factors X' 5, 1, 15, 2, 25, 3, 35, 4, 45, 5, 55, 6, 65, 7, 75, X' 75, 8, 85, 3, 95, 1, 1~, 11, 115, 12, 12 5, 13, 135, 14, 145, 15, i O Q 1,oooc) 65 1, 73 1, 94 1, 19 1,

19 18 Lat YO feet. OO TRANSVERSE MERCATOR PROJECTION ZONE 5 Table I AYo per AH per H R lr a a A7.E A R A SO '; ' R R S ~ 445.A5 962.a : nnn -1.noo -1.nno R2.AO R PO A a53 3.e R i.nno OU H R,.47 1~13.6 lr R A55 93.A ~ 5 6 la3.r nno -1.ono -1.nn a Table I1 I * f l b Ab C O.O M.22 w W OOo

20 TRANSVERSE MERCATOR PROJECTION ZONE 5 19 Table I11 I x' 5, CXJo 1, Table IV..,OO Table V I ;io I. O.O 1 1 I I Table VI Scale factors X' 5, 1, 15, 2, 25, 3, 35, 4, 45, 5, 55, 6, 1, 1. 1, oOoo 5 1, 7 1, 1 1, 14 1, 18 1, , 41

21 2 TRANSVERSE MERCATOR PROJECTION CCRRECTIONS TO NATmAL SCALE FACTORS* (In units of the 7th decimal place) AX (feet) Correction (plus 1 Ax Correction (feet) (plus 1 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14,3 15', 16, 17, 13, 19, 2, 21, ;t , 22, 23, 24, 25, 26, 27, 28, 29, 3, 31, , 34, 35', plane coordinate distance = geodetic distance Xscale factor * The scale factor interpolated for the mean ~ 'of the ends of a line and corrected by the above table is a true mean value accurate to within one unit' in the seventh decimal place. U 5. GOVERNMENT PRINTING OFFICE. le81 O--llS-!J44