Example of composite great circle-limit latitude same with your latitude

Latitude A 18º09’S    Longitude A 178º26’E

Latitude B 33º00’S     Longitude B 71º37’W

Limit latitude 33ºS

Find initial course and total distance?

Latitude  A 18º09’S    Longitude A 178º26’E

Latitude B 33º00’S     Longitude B 71º37’W

-------------------------------------------------------

                                d’long A to B = 109º57’ E

                                d’long B to A = 109º57’ W    

PA = 90º - Lat A

      = 90º - 18º09’

      = 71º51’

PB = 90º - Lat B

      = 90º - 33º

      = 57º

PV1

=90º - 33º

= 57º                                          

Distance AV1

--------------------

sin comp PA = cos AV1 cos PV1

cos PA   = cos AV1 cos PV1

cos AV1 = cos PA / cos PV1

cos AV1 = cos 71º51’ / cos 57º

              = 55.11375°

AV1       = 3306.825 nm .                  

Initial course A

-------------------

sin PV1 = cos comp A . cos comp PA

sin PV1 = sin A . sin PA

sin A     = sin PV1 / sin PA

sin A     = sin 57º / sin 71º51’

A          =  S 61º57.3’ E

T/course= 118°02.7’ (T)                 

d’long P

-----------

sin comp P = tan PV1 tan comp PA

cos P         = tan PV1 cot PA

cos P         = tan PV1 / tan PA

cos P         = tan 57º / tan 71º51’

P               = 59º40.9’ E                         

Longitude A     178º26.0’ E

d’long P             59º40.9’ E

Longitude V1    121º53.1’W

Position V1  Lat 33º00’S  121º53.1’W                     

Distance BV1

-----------------

Long V1          121º53.1’W

Long B             71°37.0’W    

--------------------------------

d’long            50º16.1’ E

                    3016.1                                   

                 

cos lat = dep / d’long

cos 33º = dep / 3016.1’

dep = cos 33º x 3016.1’

dep = 2529.5143’

dist  = dep

dist = 2529.5143 nm                                         

Total distance = 2529.5143 + 3306.825

                     = 5836.3393 nm