ࡱ> x  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwyz{|}~Root EntryF=Y^ Book gMBD02966151Fp^p^MBD0295FCB1 Fp^p^MBD029144B9Fp^ǔp^MBD028D80DEFp^Pԗp^Ole CompObj f  !"#$%&'()*+,-./0123456789:;<?CDEFGHIJLNQRSTUVWXYZ[\]^_`abcdefghijlmnopqrsuvwyz{|} FMicrosoft Equation 3.0 DS Equation Equation.39q(KkK  1 =beta1 2 =beta2=phi=lambdaObjInfoOlePres000 (Equation Native DOle   1"2 =alpha1"2 2"1 =alpha2"1 FMicrosoft Equation 3.0 DS Equation Equation.39qCompObj  fObjInfoOlePres000 (Equation Native   VKyK b 0 =a 0 (1"f)n=f/(2"f)L=(L 2 "L 1 )tan 1 =(tanB 1 )(1"f)tan 2 =(tanB 2 )(1"f)a=cb=cos 1 cos 2 cos=a+bcosLsin= (sinL  cos 2 ) 2 +(sin 2 cos 1 "sin 1 cos 2 cosL) 2 c=(bsinL)/sinm=1"c 2 S/b 0 =[(1+f+f 2 )]+a[(f+f 2 )sin"(f 2 /2) 2 cosec]+m["(f+f 2 )/2"(f+f 2 )/2sincos+(f 2 /2) 2 cot]+a 2 ["(f 2 /2)sincos]+m 2 [(f 2 /16)+(f 2 /16)sincos"(f 2 /2) 2 cot"(f 2 /8)sincos 3 ]+am[(f 2 /2) 2 cosec+(f 2 /2)sincos 2 ]'"L c =(f+f 2 )+a["(f 2 /2)sin"(f 2 ) 2 cosec]+m["(5f 2 /4)+(f 2 /4)sincos+(f 2 ) 2 cot]cot 1"2 =(sin 2 cos 1 "cossin 1 cos 2 )/sincos 2 cot 2"1 =(sin 2 cos 1 cos"sin 1 cos 2 )/sincos 1  FMicrosoft Equation 3.0 DS Equation Equation.39qOle =CompObj>fObjInfo@OlePres000A(OK@J e' 2 E"secondeccentsqtan 1 E"tanBeta1sin 1"2 E"sinalpha1"2cos 0 E"cosbeta0 s Equation Native B8Ole KDCompObjMfObjInfoOE"phiS 0 E"phi0E"lambdacos 2 E"cosbeta24F!Direct Case!Object 16 FMicrosoft Equation 3.0 DS Equation Equation.39qOlePres000PEquation Native kSummaryInformation(tDocumentSummaryInformation8xLT \ . .1   &@ & MathType Times New Roman-2 22 12 12 F 22 F 12 F 12 F 02 W12 O 22 w 02 O22 w02 ON22 w02 kA22 02 0Times New Roman!- 2 / cos 2 / cos 2 sin 2 cos 2 4cos2  )2  12  )( 2 v(tan 2 @tan2 `9)2 `22 `(2  /2 L )2 U(2 '2  )2  12 ( Symbol-2 G -2 F  -Symbol-2 / =2 =2  -2 M=2 `-2 `X=2 9-2 ,=2 -2 =Symbol-2 / a2 / b2 a2 b2 b2 mbTimes New Roman-2 / Lg2 - f2 !B2 `sf2 `f2 `:n2  b2 @b2 a2 4e2 Cf2 'a2 .b & "Systemn-0JLI b 0 =a 0 (1"f)e' 2 =(a 0  2 "b 0  2 )/b 0  2 n=f(2"f)tan 1 =(tanB)(1"f)cos 0 =cos 1 sin 1"2 g=cos 1 cos 1"2 oOh+'0HPh Brown NicholasĢƵMicrosoft Excel@/@3@e@p^ 7\pĢƵ BDirect SolutionInverse Solution0 ellipsoidList; $ ;9$ ;<F .solver_adj)+;;! solver_cvgHz> solver_drv solver_est solver_itr, solver_lin solver_neg solver_num solver_nwt* solver_opt:3! solver_pre& .> solver_scl solver_sho solver_timd! solver_tol? solver_typ solver_val=KY.8 @"1Arial1Arial1Arial1Arial1Arial1 Arial1Arial1Arial1 Arial1Symbol1 Arial1Arial1Symbol1 MS Sans Serif1Arial10Arial1Arial1Arial1Arial1Arial1Arial1Symbol1Arial1Symbol1Symbol1Arial1Arial1Arial1Arial1Arial1Symbol1Symbol1Symbol1Arial1QTahoma1BCalibri1 BCalibri1BCalibri1 BCalibri1 BCalibri1BCalibri1BCalibri1,>BCalibri1>BCalibri1>BCalibri1>BCalibri1 BCalibri1BCalibri1?BCalibri1h>BCambria1BCalibri1 BCalibri1BArial1BArial"$"#,##0;\-"$"#,##0"$"#,##0;[Red]\-"$"#,##0"$"#,##0.00;\-"$"#,##0.00!"$"#,##0.00;[Red]\-"$"#,##0.003*0_-"$"* #,##0_-;\-"$"* #,##0_-;_-"$"* "-"_-;_-@_-*)'_-* #,##0_-;\-* #,##0_-;_-* "-"_-;_-@_-;,8_-"$"* #,##0.00_-;\-"$"* #,##0.00_-;_-"$"* "-"??_-;_-@_-2+/_-* #,##0.00_-;\-* #,##0.00_-;_-* "-"??_-;_-@_-"$"#,##0_);\("$"#,##0\)"$"#,##0_);[Red]\("$"#,##0\) "$"#,##0.00_);\("$"#,##0.00\)%""$"#,##0.00_);[Red]\("$"#,##0.00\)52_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_),)_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)=:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)41_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)0.0000000000000.000 0.000000000 0,000,000.0000.000\ 000\ 000\ 000 0.00000 000,000.000 0.0000 000,000.0000 00,000.000 0,000.000000.00 00.000000.00\00\' 0.00000\" 0.000\" 00.000\" 00.00000\"0.000\ 000\ 000\00\0.000\ 000\ 00000.000\ 000\ 000\ 00.000\ 00\"0.000\ 000\ 0000 0.00000000000 0.0000000000 0.00000000.000000000000000 0.000000 0.00000000 00.0000\" 00.000000\" 000,000.00 000,000.0 000,00000.00\ 000\ \"0.00000000000000.00000000000000 0,000,000.00.000\ 000\ 000\ 00,000,000.0000000\ 00.000\ \" 00.0000\ \" 00.000\ 000\"00.000\ 000000\" 00.00000\ \" 0.00\" 00.00\" 00.000\ 0\" 00.0000000\"                $ $ $ $ $ $ $ $ $ $ $ $ % % % % % % % % % % % % & ' A.I. (     ) * + @q, @7- 6- . A.I. / 0  A,I, 1 A~I~ 2 3 qp4   #     @  $ #0  @  h  (  @" #|  l  l  l  $  $    l  $  $  $  $  $ #| @  l H@  h AH@  ( (        l  h          h  l !|       l  l &      !4 "8   h  ` A  l A l A `    " "0  ! & &8 !| @  l A  &    #8 # #8 @# @#x @#x A@ #x @#| @#| A@#8 #x A  !| !| @  "| "| I@  l H@  h H@  l AH@ " @I@  @I@ " @I@ # @I@ # @I@ ! @I@ # @I@  $ "8 #| !|  ( @ (  $  A  ( @ (  $  @ $ @ @@  ( @@#| A l A!| A1 !   !        & & !| A@ ! !  $  $  !|    !| @ #| !| A@ "8 @@ @ # AI@  20% - Accent1M 20% - Accent1 ef % 20% - Accent2M" 20% - Accent2 ef % 20% - Accent3M& 20% - Accent3 ef % 20% - Accent4A* 20% - Accent4 % 20% - Accent5M. 20% - Accent5 ef % 20% - Accent6M2 20% - Accent6  ef % 40% - Accent1M 40% - Accent1 L % 40% - Accent2M# 40% - Accent2 L渷 % 40% - Accent3M' 40% - Accent3 L % 40% - Accent4M+ 40% - Accent4 L % 40% - Accent5M/ 40% - Accent5 L % 40% - Accent6M3 40% - Accent6  Lմ % 60% - Accent1M 60% - Accent1 23 % 60% - Accent2M$ 60% - Accent2 23ږ % 60% - Accent3M( 60% - Accent3 23כ % 60% - Accent4M, 60% - Accent4 23 % 60% - Accent5M0 60% - Accent5 23 %! 60% - Accent6M4 60% - Accent6  23 % "Accent1AAccent1 O % #Accent2A!Accent2 PM % $Accent3A%Accent3 Y % %Accent4A)Accent4 d % &Accent5A-Accent5 K % 'Accent6A1Accent6  F %(Bad9Bad  %) Calculation Calculation  }%  * Check Cell Check Cell  %????????? ???+ Comma,( Comma [0]-&Currency.. Currency [0]/Explanatory TextG5Explanatory Text %0Good;Good  a% 1 Heading 1G Heading 1 I}%O 2 Heading 2G Heading 2 I}%? 3 Heading 3G Heading 3 I}%23 4 Heading 49 Heading 4 I}%5InputuInput ̙ ??v% 6 Linked CellK Linked Cell }% 7NeutralANeutral  e%"Normal8Noteb Note   9OutputwOutput  ???%????????? ???:$Percent;Title1Title I}%<TotalMTotal %OO= Warning Text? Warning Text %8 ``i̜̙3f3333f3ffff333ff333f33f33BBB2 EllipsoidsADirect SolutionxInverse Solution Test Data 7 4l41;;  dMbP?_*+%=&C&F&REllipsoids&L&D&CGDA Technical Manual&?'?(?)?MHP LaserJet 4M PlusanualpS A4` 4 5''''" d??Direct SolutionInverse SolutionU} ISo} $So} So} $So} So} So} $So} So 4@!   ,,,o~ ?(D% BeGRS80(ir@D% Be(+-6Zwk?D% Be(@TXAD% Be uuuuuvv0 ?@@@@@@  GRS80 WGS84 ANS WGS72  Clarke 1858 Sphere User ir@mtr@r@ @@mB~ r@ 1/f+-6Zwk?D(Zwk?Dܜwk?Dv8gIwk?D k?D-q=Dܜwk?D ffJfJTXA^JGiTXAڄTXA aphNOTE: ĢƵ became aware that the GRS80 flattening parameter was incorrect in June 2014. {sThe parameter was reported as 298.2572221088 instead of 298.25722210088. It has been corrected in this spreadsheet.%Changes made on 24 June 2014.\&1@ 7,,,>oWA/0123/^0^ 1^^2^3^P  ]. un /@XText 12INSTRUCTIONS (1) Enter in Cell A5, the number of the ellipsoid required, selected from A13:G13. The name and parameters for the required ellipsoid will automatically be shown in A5:A9. You may enter your own parameters in User cellsHI4 andH5. NOTE: Only a and 1/f need be entered, f and b are automatically calculated. (2) Proceed to the Inverse Case or Direct Case worksheet. 5 6 6666E6F666? 9GRS80 is the ellipsoid used with GDA94 and with the ITRF.k eWGS84 is the ellipsoid used with the GPS sysyem. It is for all practical purposes, the same as GRS80.9 3ANS is the ellipsoid used with both AGD66 and AGD84 WGS72 is the ellipsoid used with GPS prior to 27 January 1987, and with the Transit Doppler Broadcast ephemeris, prior to 27 January 1989.j dThe Clarke 1858 ellipsoid was widely used in Australia prior to the introduction of the AGD in 1966. To use a sphere, enter the required radius in the semi-major axis field, and leave the inverse flattening as a very large number. Enter the value of the semi-major axis (a) and the inverse flattening (1/f) to define your own ellipsoid. The values of f and b will be calculated automatically.=KY.8 > 4"""" 7 ^I](nds  dMbP?_*+%=&C&F&RDirect Solution&L&D&CGDA Technical Manual&?'?(?)?M\\AUSLIGPRINT1\ALG3Geod01 semi-  3FXA4 210 x 297 mmine your own ell&@'''',,<-XX<-XX<-j-(None)(None)H(None)(None)z <&" F?? EllipsoidsInverse SolutionU} So} So} ISo} So}  So} $So} ISo} So} I So} m So} So} So} So} m So} ISo} $So} m So} So} So ^@h;;!;; ! ;! ;! ;! !!!!w!!!!!!!!!!w!!w!!!H Ellipsoid(H ZGRS80 Station 1y Flinders Peak yy Station 2y Buninyong }z Latitude (j1)    bBLL@lxz, @ Azimuth (a12)  p s@LJ@ˡE}@Longitude (l1)    bb@L9@?=@Ellipsoidal Dist (s)q'1@ cXBD,B(C5D,D<B.S O$D,DD<qcX Latitude (j2)   RB4D9NC@#D $DAB9S O$@!#D $DAB%Reverse Azimuth (a21)_@ D9B(|$@D9D<B-cy)9@D9DD<Longitude (l2)   a@+D6B(|K@D6D<B-l#A@D6DD< COLOUR KEYY User input [ CCFijjkEEZResult [CCCC ]a( f@TXA Z j_ Dec Deg Radians ]] [ CCCC ^b$ f?XA D D  _ j1_ `EvB ID DAD<DDD<DB" `ʗ#2  D A ]] C [SCCCC ^f( `+-6Zwk? Z _ l1_ ` b@ ID DAD<DDD<DB" ` -=_*@  D A ]]CCC[SCCCC ^e'25 `ߚ{? D D D D D D  _ ~a12/ `-s@ DAD<D" `.]fl@ D A ]]CCC[SCCCC CCCCC[CCCCC ]u2M`~%Q`p?7DAbADAbAD D D D D D  n`]]]]]CCCCCCformula1^^]]]CCCCCC ^TanU1'`D D A]]]]]CCCCCC^tan s1!"`:  DD A ]`d^]]]CCCCCCformula2` ]`d^]]]CCCCCC nsinU1 `R|u DAA ]`d^]]]CCCCCC cosU1 `!,sC? DAA ]`d^]]]CCCCCCnsin a "`_GBm6 DD A ~`d^]]]CCCCCCformula3` ~`d^]]]CCCCCC ^AJ`9 %?4D@DD@D^]]]CCCCCCformula4`^]]]CCCCCC ~BF`1IˎP?0DD`DJ/D rr^]]]CCCCCCformula5` `^]]]CCCCCC]2sm &`|ԇDAD&2s1 !0Y:& DA^]]]CCCCCCformula6lBsin s "%HN>$ DD&A^]]]CCCCCC lcos 2sm >}YϿDA^]]]CCCCCC l cos s etc 6p($ D&ADD^]]]CCCCCC l^]]]CCCCCCDlLt`0D >\kLcchLy<Jwe !!!"!#!$!%!&!'!(!)!*w!+w!,w!-!.!/!0!1!2!3!4;!5;!6!7w!8w!9w!:;<=>? l bracket13 Hߏc.D&AD&A ^]]]CCCCCC !l!bracket2-!H%mDD!^]]]CCCCCC "l"^]]]CCCCCC #l#^]]]CCCCCC $~D s$#K_7,DD&ADADD&ADADADDAD&AD&ADADA $~D sG$#K_7&1DDDDDDD D!$^]]]CCCCCC%formula7%` %]`%g^]]]CCCCCC &s*&`B?DD DD$ &s/bA%&`|b?1DD D&gg^]]]CCCCCC'formula8'` ']`' ]]]CCCCCC(top termC(`f*-DAAD&ADAAD&AD A (]`( ]]]CCCCCC) bott term){e+H?*tD DDDAAD&ADAAD&AD ADAAD&ADAAD&AD AA )~`) ]]]CCCCCC*tan f2 *`E D(D)*atan2 f2 !*`], D)D(Aa* ]]]CCCCCC+f2(rad)+]D*A ++ ]]]WCCCCC,f2(deg)",B D+A,(,7B7D*AA, ]]]WCCCCC-formula9- -- ]]]WCCCCC.tan l N.Qځ8D&AD ADD&ADAAD&AD A .. ]]]WCCCCC/l (tan2)P/R;Hف3:DD&ADAAD&AD AD&AD AAa // ]]]WCCCCC0 formula100 00 ]]]WCCCCC 1C]1p /ω@?GD DAbADAbAD DAbADAbA 11 ]]]WCCCCC2 formula112 22 ]]]WCCCCC 3Lv3{8aЁ)`D/D1D DD&D1D&ADAD1D&ADADA 33 ]]]WCCCCC4l2(rad)4[ێ@5 D D3 44 ]]]WCCCCC5l2(deg)J5٥a@4D4 D4AD4AB5(5'٥a@6D4AA5 ]]]WCCCCC6 formula1266l6'٥a@8VD5vf  hD57D5vf@ vD5 $5"B6 ]]]WCCCCC7tan a2 D7p8.DDAAD&ADD&AD A77 ]]]WCCCCC8a2 (rad)8Z\9D7A8@8Z\9*DD&ADD&AD ADAa8 ]]]WCCCCC9a2 (deg)&9N|_@(D8A9&9N|_@/D8A9 ]]]WCCCCC: :: ]]]WCCCCC; ;; ]]]WCCCCC << ]]]WCCCCC == ]]]WCCCCC> ]]]WCCCCC? ]]]WCCCCCDlwq,,@LHcHIIe44**@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]@ ]]]CCCCCCA ]]]CCCCCCB ]]]CCCCJC ]]]CCVPUTWD ]]]CCVPUTWE ]]]CCVPUTWF ]]]CCVPUTW G]^ G^^ GCC H]^ Hef HCC IagIg ICC JCC KCCLCmCChCCCCC LCCMCCCCCCCCCC MCC NCC OCC PCC QCC RCC SCC TCC UCC VCC WCC XCC YCC ZCC [CC \CC ]CC@D**&,,]K':i I-C /@xText 1AINSTRUCTIONS (1)Choose the appropriate ellipsoid parameters on the "Ellipsoids" worksheet. (2) Enter the station names in cells C2,G2 (documentation only). (3) Enter the Latitude of Station 1 in cells C3:E3, Longitude in cells C4:E4. Remember that south latitude and west longitude should be entered as negative values. (4) Enter the azimuth 1-2, in cells G3:I3. (5) Enter the ellipsoidal distance (s) in cell G4. To see the intermediate steps, use the Excel "outlining" features: (i) SHOW the outline symbols, and then (ii) UNGROUP the hidden rows and columns as required. This spreadsheet has been tested for use within the Australian region. While some testing has been done in other parts of the world, the spreadsheet has not been exhaustively tested world-wide. 5 6 6[666@6k6666 6@6A6]d%: C  Picture 16T Equation.3ހldQ . .1   &@ & MathType Times New Roman-2 22 12 12 F 22 F 12 F 12 F 02 W12 O 22 w 02 O22 w02 ON22 w02 kA22 02 0Times New Roman!- 2 / cos 2 / cos 2 sin 2 cos 2 4cos2  )2  12  )( 2 v(tan 2 @tan2 `9)2 `22 `(2  /2 L )2 U(2 '2  )2  12 ( Symbol-2 G -2 F  -Symbol-2 / =2 =2  -2 M=2 `-2 `X=2 9-2 ,=2 -2 =Symbol-2 / a2 / b2 a2 b2 b2 mbTimes New Roman-2 / Lg2 - f2 !B2 `sf2 `f2 `:n2  b2 @b2 a2 4e2 Cf2 'a2 .b & "Systemn-]dBGF  Picture 19 Equation.3DŒˎ  .1  @& & MathType`Times New Roman-2  2 2 cos 2 4cos2  02 t 0 2 tcos 2 t4cos2 . 22 . 1 2 .:sin 2 ..sin2 F 1 2 ~tan 2 @tan 2 Bsec2 ' Times New Roman-2 o22 f 02 k02 22 12 HD12 92Times New Roman- 2 beta 2 Olambda 2  pphi2 S 2 fphi 2 tbeta 2 .nalpha 2 Beta2 f sq 2 eccent 2 Xond2 4e Times New Roman-2  sSymbol-2 v@2 O@2  @2 @2 tr@2 . -2 .@2 :@2 @ Symbol-2 y-Symbol-2 tb2 O4l2  f2 f2 ttb2 .a2 bb & "Systemn-yThis spreadsheet modified 17 May 2002 to give consistent sign convention for lines crossing the equator and 180 east/west=KY.8 > 6   " 7 HއZ  dMbP?_*+%=&C&F&RInverse Solution&L&D&CGDA Technical Mmanual&?'p= ף?(RQ?)Q?M\\ACT-SERVER\Geodesy HP LaserJepS A4ion for lines crossing the eq 4 5''''" P?? EllipsoidsDirect SolutionU} $Col} Col} Col} mCol} Col} Col} ICol} Col} ICol} mol} ol} Iol H  w@ h ; ;  ; ;  !  ;!  ;!  ;!  ;!  ! ! !!!!!!!!!!!!!!!!!H Ellipsoid(H ZGRS80 Station 1y Flinders Peak yy Station 2y Buninyong}z??  Latitude (j1)  KBLL@lxz, @ Latitude (j2)  KBLC@VO$@  ]> Longitude (l1)   Kb@L9@?=@Longitude (l2)   Ka@LK@w#A@Spheroidal Dist. (S)@,@%D5GGIAA   C Azimuth 1-2 (a12) M s@DAB(NJ@#DAD<B-;q@~@DADD< BOPY User input  Q> Azimuth 2-1(a21)  {_@DA B(|$@,DA D<B-9@DA DD<BZResult]f^^ ]] Dec DegreesRadians ]] ] Latitude (j1)  _ `EvB ID DAD<DDD<DB" `ʗ#2  D A ]] ]Longitude (l1)  _ ` b@ ID DAD<DDD<DB" ` -=_*@  D A ]` ] Latitude (j2)  _ `'ՠB ID DAD<DDD<DB" `]  D A ]] ]Longitude (l2)  _ `D٥a@ ID DAD<DDD<DB" `q}Zێ@ D A ]` ```` ]`]Semi major axis (a)(f@TXAZ_ ^f+f*f$`U$k?DDD ]]^Semi minor axis (b)$f?XADD_^ (f+f*f)/2`U$[?D ]]^Flattening (f)(`+-6Zwk?Z^^(f*f)/2#`)y%> DD ]]]Diff longitude (w) `naЁ D D C(f*f)/8#`)y%> DD ]]^(f*f)/16#`)y%> DD ]] CtanU1'DD A^]]] ]U1`&z$DA^~`]] ]sinU1`R|uDA^~`]] ]cosU1`!,sC?DA^]`]] ]tanU2'R(/jDD A^]`]] ]U2`ddk3DA^]`]] ]sinU2`}DA^]`]] ]cosU2`2!F]?DA^]`]] formula13`^]`]] ~l`naЁD^`hIفD3 `]] formula14`^`]]sin2 s j`GhV? TDDADDADDDDDADDDDDA^j`~x?"TDDADDADDDDDADDDDDA `]] formula15`^^`]]DlLxi B INCFFPCFF+c+   !! !" !# !$ !% !& !' w!( J!) !* !+ !, !- !. !/ !0 !1 !2 !3 !4 !5 !6 !7 w!8 !9 J!: !; !< != !> ;!? ;! Ccos s 3 C* ?"DDDDDA3 CDZ?7DDDDDA ]]! formula16!^^^]]] ! ?> "tan s ""`WR?# DAD "^""`T_? DAD "`"w " ?>  #~s#`5?%D"A#^C#`]B?'-D"A D"AAD"AB#`#w # ?> $ formula17$`^]`$w $ ?> %]sin a J%`y{2'4D  DDDADAB%^J%`Hm614D  DDDADAB%`]]w % ?> & formula18&`^^`]]'C cos 2 s m l'Cd_0Ͽ(VD%AbAD%AbA 0D DDD%AbAD%AbAB'^?'Cx{YϿ@)D DDD%AbAD%AbA ']]] (Cu2K(fh0vp?*5D%AbAD%AbADDDDDD(^K(fBQ`p?*5D%AbAD%AbADDDDDD (]])formula3)`^`]] *]AJ*` b&?,4D(@D(D(@D(*^J*`D %?54D(@D(D(@D( *`]]+formula4+`^]`]] ,]BF,`plT'P?.0D(D(`D(J/D(,^F,`JˎP?.0D(D(`D(J/D( ,`]]-formula6-`^]`]] .~D s.`gۣp'1uD,DAD'D,D D'D'D,D'DD'D'.^.`3C_7?uD,DAD'D,D D'D'D,D'DD'D' .`]]/]`^]`]]0 formula100`l]`]]x0 @ 1C]1`rR@?3GDD%AbAD%AbADD%AbAD%AbA1l]1`Z[7/ω@?3GDD%AbAD%AbADD%AbAD%AbA1`]]x1 @2formula11modified2`l]`]]x2 @ 3lp3`<$ف5ZDD1DD%D AcD1D AcAD'D1D D'D'3lp3hIفZDD1DD%D AcD1D AcAD'D1D D'D'3`]]x3 @4 formula194`l~`]]D4 > 5]sP5`:Y@9:DD samepoint DD*D"AD.B5lM5`@,@7DD samepoint DD*D#D.B5]]]D5 >6 formula206`l`]]]D6 >7]tan a1  7`l?7`6?U>)DD3ADDDDD3A7]]]D7 >8 formula218`l`]]]D8 >9]tan a2  9`l@9`r*/j>*DD3ADDDDD3A9]]]D9 >:]`l`]]D: > ;];`]]D; > <]]<^l]]D< >=Forward azimuth =^=Reverse Azimuth=]]D= >> a12 (radians)>`⦦?D7A> a21 (radians)>`5hP>D9A >]]3>DlM> D D D D AaA3> DqI9^@?D D D D AaA? a12 (degrees)'?`/S-s@@D>Ah? a21 (degrees)'?`v_@? D>A ?]]J?D/S-s@@ 4D> D>AhD>ABJ? v_@@4D>  D>AD>ABDl9?+*,*G7?777$,,`@ ;!A ;!B !C !D !E !F !G @ a12 (degrees):@`/S-s@($D?h  D?h $?B@ a21 (degrees):@`v_@A$D?h  D?h $?B @]]A@D⦦A+DDDDD3ADD3AAaB@ `2A ,DDDDD3ADD3AAaA a12 (degrees)A`/S-s@oDD samepoint SDE northsouth /DF southnorth  $@""BA a21 (degrees)A`v_@DoDD samepoint SDE northsouth /DF southnorth  $@""BA`/S-s@DD samepoint DE northsouth _DF southnorth ;D@ D@AhD@A"""BA `_@ {DD samepoint _DE northsouth ;DF southnorth D@ A""BBBCCritical case testsCRDCE<D D  D D  B$ samepointN.A. @BN.A. DC Same PointOECF9D D  D D  B$ northsouthN.A. BN.A. ECNorth south meridianOFCA9D D  D D  B$ southnorthN.A. BN.A. FCSouth North meridian=Q)w~~]j1GTx /@hText 1INSTRUCTIONS (1) Choose the appropriate ellipsoid on the "Ellipsoids" worksheet. (2) Enter the station names in cells C2,G2 (documentation only). (3) Enter the latitudes in cells (C3:E3 and G3:I3). Remember that south latitude is negative. (4) Enter the longitude in cells (C4:E4 and G4:I4). Remember that west longitude is negative To see the intermediate values, use the Excel "outlining" features: (i) SHOW the outline symbols, and then (ii) UNGROUP the hidden rows and columns as required. This spreadsheet has been tested for use within the Australian region. While some testing has been done in other parts of the world, the spreadsheet has not been exhaustively tested world-wide. 5 6 6R666O6P66666]b6nm   Picture 5 Equation.3wp < .1  4 .&-p4 & MathType "-  "-K"-K*yyy *@*df*f*z Times New Roman-2 q42"12 q422 q412 q4 12 q4 22 q4*12 q4A22 +2K"22 +222 +212 +2 12 +2 22 +222 +2(12 .22 .22 . 22 .+22 n,%22 n,22 n,)22 &) 22 &22 &o22 & 22 &S22 D$+32 D$#22 D$22 D$Q22 D$ 22 D$U22 D$22 !22 !G22 b!22 b?22 b+22 b22 22  22 22 wk 22 02 22 ;$22 G; 22 G@12 G\12 Gi22 ; 22 G 22 q 22 q12 & 22 ]22 12 D12 _12 _$22 02 0Times New Roman- 2 4cos 2 4sin2 4V/2 4) 2 4cos 2 4sin 2 4cos 2 4 cos 2 4R(sin 2 44cot 2 1cos 2 1sin2 1V/2 1) 2 1cos 2 1sin 2 1cos 2 1 cos 2 1R(sin 2 14cot2 /] 2 /cot2 /)2 /N( 2 /cos 2 /sin2 /8)2 /x42 / /2 /: (2 /v)2 /42 //2 /B52 /(2 /b[2 -d] 2 -<cos2 -)2 -T ( 2 -sin2 -t)2 -22 -/2 -v(2 -[2 ) )2 )(2 a'*] 2 a'bcos 2 a'bsin2 a')2 a'22 a'L/2 a'( 2 a' cos2 a')2 a'22 a'0/2 a'"[(2 $v-] 2 $)cos 2 $&sin2 $&)2 $Z%82 $$/2 $."( 2 $cot2 $)2 $22 $./2 $( 2 $6cos 2 $6sin2 $)2 $162 $ /2 $ (2 $6)2 $162 $2/2 $$[(2 "] 2 " cos 2 "sin2 "6)2 "v22 "/2 "8(2 "[2  $] 2  !cot2  )2  22  /2  ( 2  cos 2  sin2  :22  /2  )2  (2   22  T /2  )2  (2  b[2 ] 2 cos2 F)2 22 /2 H ( 2 sin2 h)2 [(2 #n ]2 # )2 #12 #[(2 #Z/2 1 2 A,sin2 A/2 A) 2 Asin2 Az(2 *$) 2  !cos 2 cos 2 Nsin 2 :cos 2 (sin2 2 ) 2 P cos 2 (sin 2 .sin 2 Wcos 2 W4cos 2 hcos 2 cos2 )2 12 )( 2 (tan 2 @tan2 Eo )2 EW 12 Ey )( 2 El(tan 2 E@tan2 )2 (2 )2 22 /(2 v)2 v12 v(Symbol-2 <4P!b2 4l2 4b2 4b2 4l2 4 b2 4b2 4&a2 1P!b2 1l2 1b2 1b2 1l2 1 b2 1b2 1&a2 /f2 /f2 /f2 /f2 /f2 -tf2 -f2 - f2 ), f2 )4l2 a':f2 a'Hf2 a'd f2 a' f2 $,f2 $(f2 $f2 $f2 $Lf2 $f2 $f2 " f2 " f2  #f2  f2  4f2  f2  f2  f2 f2  f2 #~ f2 A f2 @b2 ^b2 zb2 nb2  b2 f2 WJf2 b2 b2 bb2 EbbSymbol-2 4-2 4 =2 1-2 1 =2 /.+2 / +2 /-2 /:+2 -: -2 --2 -:+2 )+2 )=2 )l-2 a'+2 a':+2 $!-2 $-2 $ +2 $:+2 "`-2 ":+2  l+2  +2  -2  +2  -2  :+2 . -2 r+2 :+2 # +2 #+2 #=2 -2 =2 AH=2 :-2 +2 d=2 W+2 W=2 T=2 f=2 -2 d=2 EA -2 E:=2 -2 =2 -2 `=2 v-2 v= Symbol-2 q4-2 +2-Times New Roman-2 / f2 / f2 /Jf2 /`m<D2 -$ec2 -& f2 -Hf2 -`a2 )8f2 )f2 )L2 a'f2 a' ec2 a'rf2 a'`am2 $#f2 $pf2 $ f2 $tf2 $`m2 " f2 "`a2  ^f2  Jf2  f2  f2  f2  `m2 ec2  f2 f2 df2 `a2 # f2 #f2 #b2 #@S2 c2 :m2 AL2 Ab2 A4c2 L#L2 (L2 W0 L2 Wb2 Wa2 .b2 c2 :a2 f2 6B2 E f2 E B2 ?L2 LL2 FL2 Bf2 f2 :n2 vNf2 v(a2 v.b Times New Roman-2 +c & "Systemn-]bGG   Picture 6 Equation.3QaPHw̏   .1   &` r & MathTypeTimes New Roman9-2 12 22 22 12 t22 t 1 Times New Roman-2 & 12 & 122 22 12 A22 (1Symbol-2 -2 =2 -2 =2 @=2 l=2 H=2 t= Symbol-2 & -2 -Times New Roman9- 2 Halpha 2 Halpha 2 @lambda 2 phi 2 tbeta 2 tJbetaSymbol-2 a2 a2 @4l2 f2 Fb2 tFb & "Systemn-=KY.8 > 6 LLL" 7   dMbP?_*+%=&C&F&RTest Data&L&D&CGDA Technical Manual&?'?(?)?M\\print\m3-g280-2a-qnual 4dXXA4   RPCSRC1DE170.ini01.0001.00RCOMMON`? priv4XXf`ddf`ddHddC17E1us.HLPArial " C17E1us.HLPC17E1us.HLP&6&6C17E1us.HLPC17E1us.HLPd" YXX??Direct SolutionInverse SolutioncU} $So} So} So} $So} $ So} tSo}  So} So     h     rrr@@s@@@@@s Ellipsoid GRS80AAAA Station 1y Flinders Peak CC Station 2y Buninyong CF Latitude (j1)  " KBLL@lxz, @ Latitude (j2)  " KBLC@VO$@Longitude (l1)  " Kb@L9@?=@Longitude (l2)  " Ka@LK@w#A@Spheroidal Dist. (S)'1@CCF Azimuth 1-2 (a12) "K s@LJ@3-~@CCFAzimuth 2-1(a21)  "_@$@s9@<tH^=KY.8 >   " ՜.+,00 8@ H   EllipsoidsDirect SolutionInverse Solution Test Data'Direct Solution'!Print_Area'Inverse Solution'!Print_Area  Worksheets Named Ranges FMicrosoft Excel 2003 WorksheetBiff8Excel.Sheet.89qCompObj~k