EXERCISE 1– PLANE AND PARALLEL SAILING (Numerical Solution)

In the following cases, find the position arrived:
Starting position
S No.
LATITUDE
LONGITUDE
COURSE
DISTANCE
1.          10˚ 20.0’ N 060˚  20.0’E 155˚ 300 M
2.          10˚ 12.0’ S 120˚  11.0’W 260˚  458 M
3.          00˚ 10.0’ S 179˚  40.0’W 340˚ 510 M
4.          60˚ 11.2’ N 120˚  18.6’E 250˚ 312.4 M
5.          30˚ 14.0’ S 168˚  12.0’W 046˚ 12’ 426.8 M

SOLUTIONS:

  1. COURSE = 155˚ , T = S 25˚ E ,  Dist. = 300 MANS 1

We know that:
D’Lat =(Dist. × Cos Co.)
= 300 × Cos 25˚
= 271.9’
= 4˚ 31.9’ S

 

Lat left= 10˚ 20.0’N
D’LAT  = 04˚ 31.9’ S                             (as calculated above)
LAT ARR’D = 05˚ 48.1’ N

So, M’ LAT = 08˚04.0’N

Again, DEP. =  (D’LAT × Tan Co.)
= 126.79’

Now, D’LONG =( DEP./Cos M’LAT)
= 128.05’ E OR 002˚ 8’ E

LONG LEFT = 060˚ 20’ E
So, LONG ARR’D = 062˚ 28’ E

  1. COURSE = 260˚ ,  T = S 80˚ W ,  Dist. = 458 MANS 2

We know that:
D’Lat = (Dist. × Cos Co.)
= 458 × Cos 80˚
=  79.5’
= 1˚ 19’ S

Lat left            = 10˚ 12.0’ S
D’LAT              = 01˚ 19.0’ S
LAT ARR’D      = 11˚ 31.0’ S

So,  M’ LAT            = 10˚ 51.5’ S

DEP. = (D’LAT × Tan Co.)
= 450.86’

D’LONG =( DEP./Cos M’LAT)
= 459.08’ W OR 007˚ 39’ W

LONG LEFT                               = 120˚ 11.0’ W
LONG ARR’D                            = 127˚ 50.0’ W

  1. COURSE = 340˚, T= N 20˚ W , Dist. = 510 MANS 3

We know that:

D’Lat = (Dist. × Cos Co.)
= (510 × Cos 20˚)
= 479.24’
= 7˚ 59.2’ N

Lat left            = 00˚ 10.0’ S
D’LAT              = 07˚ 59.2’ N
LAT ARR’D      = 07˚ 49.2’ N

So, M’ LAT            = 03˚ 49.6’ N

DEP. =( D’LAT × Tan Co.)
= 174.42’

D’LONG = (DEP./Cos M’LAT)
= 174.42’ E OR 002˚ 54.4’ W

LONG LEFT                               = 179˚ 40.0’ W
LONG ARR’D                            = 177˚ 25.2’ E

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