DISTANCE COMPUTING FORM — ANDOYER-LAMBERT 



TYPE APPROXIMATION WITH SECOND ORDER TERMS 



(No conversion to parametric latitudes) 



Clarke Spheroid 1866, a = 6,378,206.4 meters 



f/2 = 0.00169503765, f/4 = 0.000847518825, fVl28 = 0.0897860195 x 10"' 



O t M , O I M 



sin./.. -^'^^^ U^fJ 2. west of 1. A A = A,-A . r^i^ S"-^ ^ /' ^^ f 



cos ch^ ' ^^^ ^^^^ ^ sin </,, y^^rSr<i9-^^^ sin KX T^^fff 7f3/J^ 



tan ^, '^S-/ ^^^/^ cos </., A J'^^ ^^^/j/ cos AA ^. ^^^ ^ j' ^V;^ 



tan (^2 ■=^' '^r y V_7_2_y^z. cos d = sin (/>. sin <j!>2 + cos cf)iCos4>2 cos A A 7 ^- "'^T^Y^ 7^ 



M = cos 0. tan 02 - sin 0, cos AA ^'=^" ^"^^ S^^ ^ f ^S^ cot u = M/sin A X Vv=^' ^VJ/J" ^J'-S^ ^J^ 



N = cos 02 tan 0.- sin 02 cos AA - - ^<^/ ^ S'^f 9f/ cot v = N/sin AA — - ^^/^jT^ J'c^^/ 



sin d = cos 0i sin AA/sin v = cos ^jsin AA /sin u 7^' y/^Y 7 J /V „ •^'^ ^^ S /. (^ ^ / 



CSC d^il^l^ cot d r^ ^>^^^f^^ Y.'f V ?"^ ^^-' ^/.>(^j^ 



1 + cos A -f-A^^S-^ rY(?7S^ 1-cos d ^- $"^^^ /<r;^^ ^ sin u -t^. -i'^^ y<^^^^ 



(sin .^, -. sin ^,^^ ^ 9f/V^y/'^7 (.sin .^,- sin .A^) ^ A 7f9'S3/9s^ gin v y. 99999X6. ? 



K. = (sin0, + sin02)V(l + cos X\ '/--9:?a J? ^:S'd)S3 R-^ = fsin 0.-sin 0^1Vn-rns d> 'f--^Sr<i,S' 99^^ 



X =y. +K, ^/ 9U<^^s-^ S'/ Y^K^-k^ ^.^>^/^^^ir<^ XY y-, /^,7^rf7'P 



A = 64d^ + 16d^cot d y-/'.!?^ ^Jff.-r/^^^ n = 48 's in d +8d/ CSC d ^U^S3fl^7S'V^ 



B = -9n -/oP-?- ^ ^9r^^^jr V = ^n sin 9d y,f^. .>?.f^r V^^r^ sin 9d -y^. /^9^/6s-^ 



c= -(30d^ +8d/ c.td.F/9^ -Vir'/jo-3/<^ r'7 AX 7V^^> y^^'^^^-^^i^ 



RY -x^, ^-^f^r/O'Sy cx^ -xs^. ///r'.^/ ^^ J^ nxY ^y/. ^fl7rff ^36- 



fV2 7-- ^f^r^jr^-^J <9 S=AX + RY4-rX^ + DXY + F,Y' ^^--?- ^-S^ 97/9^^ 



^dj^-rf/dUxd^-^Ysin xs ~.,^<^c2.<:>^f¥?3^ ?^a^ = ^(^v^')9^^. -h. d>^^o<:)^c^9a^ S^ 

 d ^ ;id ^ yy .<y.^ ^ 9 ^ s-~? ^ a ^ ka^ ^ ;;d / y- /' S-Af ^^/ ^^/ 



r I _ r t t 



S(Sdf) = a(d^ + F><\^) ^ ^'^^.9^S, a-S3 ^^^ S{8df2) = a(dr + Sdf + 8df2).^^^S^^^9£Z^2£^^ 



sin 2u 7*^^ ^ 9^S ^"yj^S^L. sin 2v — , (PC?S^^ /-^ <^ -3 



U = (f/2) cosVi sin 2n -^/,^f79V'///^~^ ^ =tf/2) cos^cA. sin 2v - & - -C6 ^3 j^ X' /d9 " '^ 



VT - 9> 99a /S? X y^ - ^ TIT ^/.6^/7J(^<^X /^ ^-^ 



;;„ . VT - Ti - ^ ^d^/^rr? ¥/ 8. ^-TiT + v -- ^^/^-r.>2 -t;^i?^/ 



+ su _j= ^^ y/ <^/^^ + sv_^^ ^r V'^'!r^9 



+180 o . M +180 o , M 



y^i^^ ^r^ -/;"- ^i^ ^70 ^^ ^O'^// 



a._2 = a^^ = 180°- u + Su a^_^ = a^„ = 180° + v + 5v 



Line No.ll,See Tables 1 and 2. True ^\'<■>7^r^cf^ '9, <!^S^S^7 7 / r /^ J ^^^^^s. 



136 



