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 I M O 1 M 



ff,^ -^^ ^^ <f?^. ^^.y/V ^. T^ /- /y? / /? ^.^S A2 //' ^'^ <y^^ ,^'ao Ay 



sin <h, ^, S"?f ^SrJi/ 2. west of 1. K\ = \.-\, y^a a^^f,S9<^ 



cos <h, /- f/^ ^<^' -^^'^' sin 0, -^.^V^ 9f^C/ sin AA l>^^ f^S- ^ ^ .^^> 9 



tan cK, 't,9^jr .^^ /^^ cos 4>, 7^ ^/^ ^^»V/ cos AA ^^-^^^6^9^/ 



t.n ^^ -f. S'Sf CI 9 9<^ ^ c^^A^ «;n (jS, sin <^2 + COS 01 cos 02 cos A A -/■y<^^f<^^'/<^/ 

 M = cos 0, tan 0, - sin 0, cos AA ^-f^l^ ^fY ^/"<^^ cot u = M/sin AA 7^/ /J^S^^^f^^ 

 N = cos 0, tan 0.- sin 0, cos AA T^ U </ ^^/C> 9.^ X- ^^, , ^ ^/sin AA i^^^MfUpL^ 

 sin d = cos 0, sin AA/sin v = cos ^isin AA /sin u '^' 7 9 S' "^/i '^ ^^ -^ — u 1^ ^f^ •J'^' /f^ 



CSC d 7^/ /?^/9-^^'^ "/ cot d -r^^-^f ^/^9^ V ^^ ^^ ^6' (^9/ 



l^rnsd ^/,^?^f6/V^/ 1-COS d ^LM^^£:Z£_ .in.. . ^ , 6> 6 </ JP 9f ¥^ 



(sin 0,-..;n 0,^ V/ Vf^y/r^/ (sin rA^-sin rA, V Z^^^/ /f^Z/y^ sin V ■^' '^^^ 'P ^ ^ <^ ^^ 

 K. = (sin 0, + sin 0,)^/(l + cos d) /> V^ ^ J^^JVaP- K, = (sin 0,- sin 0,)V(l-cos d) y-.a^^'/'^S^Jl / 



X=V^ +1^^ -^/- ^/J^Si^C-fJ^ Y=K.-K,2^^i^/j^Z^Zf^ XY ^/ ^/^^ /V^9f^ 



x' tV- 9f'i^ 9^3/3 9 Y ^ ^/. 9^9<iV^i^f/ d^ y-/ ^^ /VS'<^S'/ d^ ' ^J.Jif^<sr9. f J^^ ^ 



A = 64d. + 16d = cot d ^^^. 9^<r^S^ .7^^ n = 48 sin d +8d^ esc d -T^C. ^^/ 'P •^ f^^ 



R .-9n ^X/i>^/y^sr^<^/ F-30 sin 9^ -^S.^/^ 79V M^ sin 2d /- > //^ ^^^ /^<^ 



c= -(sod, +8d^ ...A.vi^\ -¥f./9J^/9^V AX -^/Sf, y/'yj/^rs^f 



RY "(f^'^SJ^ ^^^^^ cx^ -f^'/^J^S^V /^^ nxY A/jV^.-r^^ ^V'PJi^ 

 FY' -r4, ^A-r<;/c^;f9<^ S^AX+BY+CX^ + DXY + EY^ 'V- /-^^ ^9 ^^ 



5df=-(f/4)(Xd^-3Ysind)j?^^^f:^^SlZ^^ 5df^ = +(fVl28) 2 .Zl^^ 



d .. p.;\ ^ ^/ -J-/? 9^^f /3 d^ + ;^d^ + ^d I -^/' ^^-^ P ^^ ^^-^ 



s(5df) = a(d^ + h^^)^A£^^^fM^^^I^-^ s(sdf.) = a(d, + sdf + gdf.) %^4''^-;fV^./'^^ ^ 



O / T ^ d/sin d ^A^y'/9r^^-C' ^ , ry 



2u ^-j* ^r- /V^. J^rX 2v f^ £J^ ^/'V/4. 



sin 2u 7-. //J' ^P^^.r' sin 2v ^^ ^^ i^ ^f9^^ 



U = (f/2)cos^0,sin ^. t.t}C>//Jia^^^ V = (f/2) cos V. sin 2v 7^, ^^^ ffV6^^p9 



JT^ /yf'9l?0 UT ^^ ^-'^^^<?.? 



VT 



Su = VT - U 

 + Su 



z^.^'a"^" Sv = -UT + V ^21^ o?^'^^// 



y^/V^^^ + Sv^: r^^ ^^- ^^V 



+180 o . " +180 o I " 



/Jf ^^ VJ^-399^ ^^^-^ ^^ ^^.^^^ 



^ = a^^ = 180°- u + 5u «._, = «vu = 180° + V + Sv 



Line No.lO, See Tables 1 and 2. True distance f? (^^"^^ ^'^ ^^ ^■i"'^ meters. 



135 



