Parallel Sailing

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Because It's Easier To Not Add So Much

Parallel Sailings are very basic as there is no change in latitude, only in longitude. However, as such, they can only be used when sailing either due East or West, which greatly restricts their use. Nonetheless, if you're looking to head straight in either of those directions, here's how you ought to proceed:

If Given Both Positions
If you are given both the starting and final positions and need to find the course and distance between them, start by finding the course, it's easy, trust me. If P2 is farther West than P1, then you are headed in a Westerly direction and your Cn is 270° T. If P2 is farther East than P1, then you are headed in a Easterly direction and your Cn is 090° T. Next solve for DLo in minutes. Simply subtract or add the two longitude values. If P1 and P2 are in the same hemisphere, simply subtract the smaller number from the larger. If P1 is between 0° and 90°East, and P2 is between 0° and 90°West, simply add the two longitude values to get DLo. If P1 and P2 are both between 90° and 180° in opposite hemispheres, add the two values and subtract from 360° to get DLo.
Next, use the value of DLo, and L (in degrees and tenths), and the equation p=DLo cos L to solve for the displacement (p), along the trackline. In this case, this is also the total distance traveled.

If Given The Initial Position, Course, and Distance
If given a position, course, and distance and asked for the final position, begin by finding the DLo by using the equation p=DLo cos L. Your distance is p, and you know your latitude, so simply solve for DLo. The answer you get will be in minutes, which can easily be converted into degrees. Once you know DLo, you can add or subtract appropriately to find l2.

Back to Sailings

Example 1

L1: 23°06'N
λ1: 130°45'E
L2: 23°06'N
λ2: 145°45'W

λ1: 130°45'E
λ2: 145°45'W
DLo = 360-λ12
DLo= 83°30' (E)= 5010' (E)

p= DLo cos L
p = 5010 cos 23.1
p = 4608.3nm

Horizontal Divider 9

Example 2

L1: 23°06'N
λ1: 130°45'E
Cn = 270°T
Dist: 600nm

p = DLo cos L
600 = DLo cos 23.1
DLo = 652.3'(W)= 10°52.3'(W)

λ1: 130°45'E
DLo = 10°52.3'(W)
λ2: 119°52.7'E