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Solving Distance By Parallel Sailing



Your vessel receives a distress call from a vessel reporting her position as LAT 35 01’ S; LONG 018 51’ W. Your position is LAT 35 01’ S; LONG 021; 42’ W. Determine what will be your True Course and distance to the vessel in distress by parallel sailing method.

Given:
             λ1 = 021° 42’ W
 λ2 = 018° 51’ W
Lat = 35° 01’ S

What is asked?
           
            True course and distance by parallel sailing

Analysis:

            It is vital to read carefully when answering a question especially when taking a board exam. As of this particular problem we are given a hint of what kind this problem is because it tells us that by parallel sailing method we are to answer it. But even if, supposing, the problem does not mention parallel sailing, we can know it is a parallel sailing by looking the given latitude. From our ship’s latitude of 35 01’ S we go to the vessel in distress’ latitude of 35 01’ S. Our ship’s and the vessel in distress latitude is the same. Therefore, what we have here is a parallel sailing.

Solution:

  •  Solving for the distance.

          Step 1. We have to solve first for the difference of longitude (dlo). This is the rule  in getting Dlo:

                   +  If the longitude are opposite
                   -   If the longitude are the same

             So,

                         λ1 = 021° 42’ W
                      + λ2 = 018° 51’ W
                        Dlo = 002° 51’ E   (The sign of Dlo is east because from
                                                      λ1 to λ2, the direction is eastward)
                                  ×    60           to convert it into miles
                        Dlo = 171 miles

          Step 2. We can now proceed to this formula in getting distance by parallel sailing.

                        Distance = Dlo × Cos Lat
                                      = 171 × Cos 35° 01’
                                = 140 miles
  •   To determine the true course:
            Speaking of a parallel sailing, it is important to note that the true course is either 090° or 270°.  To  determine it is by looking the sign of Dlo. Our dlo here is east, therefore, our true course is 090°.

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