EXERCISE 3 — MERCATOR SAILING (Numerical Solution)

SOLUTION:

6. Course = 241˚ = S 61˚ W

We know that:
D’Lat   = (Distance × Cos Co.)
= (1897 × Cos 61˚)
= 919.68’ S
= 15˚ 19.7’ S

Lat Left = 36˚ 48.0’ N                 MP for Lat Left           2363.60 N
D’Lat = 15˚ 19.7’ S                       MP for  Lat Arrived     1310.70 N
Lat Arrived = 21˚ 28.3’ N                                     DMP       1052.90

D’Long = (DMP × Tan Co.)
D’Long = 1899.5’ or 31˚ 39.5’ W

Long Left  085 ˚ 53.0’ W
D’long     031 ˚ 39.5’ W
Long Arrived       117 ˚ 32.5’ W

POSITION ARRIVED   :-     LAT 21˚ 28.3’ N        LONG 117˚ 32.5’ W

7. Course = 333˚ = N27˚ W

We know that:
D’Lat   = (Distance × Cos Co.)
= (4450 × Cos 27˚)
= 3965’ N
= 66˚ 05.0’ N

Lat Left           = 06˚ 10.0’ S             MP for Lat Left            0368.20
D’Lat                = 66˚ 05.0’ N         MP for Lat Arrived      4497.11 N
Lat Arrived     = 59˚ 55.0’ N                                   DMP        4865.31

D’Long  = (DMP × Tan Co.)
D’Long  = 2479’ or 41˚ 19’ W

Long Left               176 ˚ 47.0’ W
D’long                   041˚ 19.0’ W
Long Arrived        141 ˚ 54.1’ E

POSITION ARRIVED   :-     LAT 59˚ 55.0’ N        LONG 141˚ 54.1’ E

8. Course = 124˚ = S56˚ E

We know that:
D’Lat   = ( Distance  × Cos Co.)
= (3256 × Cos 56˚)
= 1820.73’ S
= 30˚ 20.7’ S

Lat Left           = 38˚ 18.0’ S                 MP for Lat Left            2476.64 S
D’Lat                = 30˚ 20.7’ S               MP for Lat Arrived      5712.16S
Lat Arrived     = 68˚ 38.7’ S                                   DMP             3235.52

D’Long = (DMP × Tan Co.)
D’Long = 4796.85’
= 79˚ 56.8’ E

Long Left               005˚ 11.0’ W
D’long                    079˚ 56.8’ E
Long Arrived        074 ˚ 45.8’ E

POSITION ARRIVED   :-     LAT 68˚ 38.7’ S        LONG 074˚ 45.8’ E

9. Course = 056˚ = N56˚ E

We know that:
D’Lat   = (Distance × Cos Co.)
= (2222× Cos 56˚)
= 1242.52’ N
= 20˚ 42.5’ N

Lat Left           = 44˚ 11.0’ N                      MP for Lat Left      2944.81 N
D’Lat                = 20˚ 42.5’ N               MP for Lat Arrived     5141.25 N
Lat Arrived = 64˚ 53.5’ N                                              DMP    2196.44

D’Long = (DMP × Tan Co.)
D’Long = 3256.3’
=  54˚ 16.3’ E

Long Left               140 ˚ 20.0’ W
D’long                      054˚ 16.3’ E
Long Arrived        086 ˚ 03.7’ W

POSITION ARRIVED   :-     LAT  64˚ 53.5’ N        LONG 086 ˚ 03.7’ W

10. Course = 265˚ = S85˚ W

We know that :
D’Lat   = (Distance × Cos Co.)
= (7126 × Cos 85˚)
= 621.07’ S
= 10˚ 21.0’ S

Lat Left           = 18˚ 58.0’ N             MP for Lat Left       1151.77 N
D’Lat         = 10˚ 21.0’ S             MP for Lat Arrived     0515.50 N
Lat Arrived  = 08˚ 37.0’ N                                  DMP    0636.27

D’Long = (DMP × Tan Co.)
D’Long = 7272.60
= 121˚ 12.6’ W

Long Left               072 ˚ 52.0’ E
D’long                    121˚ 12.6’ W
Long Arrived        048 ˚ 20.6’ W

POSITION ARRIVED   :-     LAT 08˚ 37.0’ N        LONG 048˚ 20.6’ W