Mercator sailing

      

      

      Departure position 28°36’S  138°56’W   course 258°(T)  distance 2468 nm.Find arrival position?

Co = 258° = S 78° W     

Dist = d’lat / cos Ɵ

D’lat = dist x cos Ɵ

         = 2468 x cos 78°

         = 513.13’ S

         = 8°33.13’ S        

Lat initial   28°36’S                                              mp   1780.85

D’lat          8°33.13’ S +

Final lat     37°09.13’ S                                        mp   2389.93 –

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

                                                                            Dmp   609.08 

Find the value of  MP Lat  28°36’S

Do interpolation for lat 37°09.13’ S   

Tan Ɵ= d’long / dmp

D’long = tan Ɵ x dmp

             = tan 78° x 609.08

             = 2865.50 W

             = 47°45.5’ W   

Initial longitude     138°56’W

d’long                     47°45.5’ W

Final Longitude     173°18.5’ E