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Middle Latitude Sailing: Solving For True Course And Distance

A vessel at Lat. 28° 00' N, Long. 116° 00'W heads for a destination at Lat. 34° 00' N, Long. 123° 40' W. Determine the true course and distance by Middle Latitude Sailing.

Given

L1 = 28° 00' N
L2 = 34° 00' N
λ1 = 116° 00' W
λ2 = 123° 40' W

What is asked?

True course and distance by Middle Latitude Sailing.

Solution

1.  Find for DLAT:

            L2 = 34° 00' N
            L1 = 28° 00' N  
       DLAT = 06° 00' N   (Sign of DLAT is north because ship's direction is going north)
                       x  60        (to convert DLAT into miles)
                     360 miles

2. Find for DLO:

            λ2 = 123° 40' W
            λ1 = 116° 00' W   
        DLO =     7° 40' W  (Sign of DLO is west because ship's direction is going west)
                    x 60              (multiply 7° by 60 to convert into miles)
                     420
                    + 40  
        DLO = 460 miles

3. Solving for MLAT. We are going to add the latitudes and then divide it by 2.

            L2 = 34° 00' N
            L1 = 28° 00' N 
                     62° 00'
                   ÷  2            
      MLAT = 31°

4. Solving for true course by Middle Latitude Sailing.

Tan Course = Cos MLAT x DLO      
                             DLAT   
                   = Cos 31° x 460 miles  
                             360 miles
                   = 1.09526
       Course = Inv Tan 1.09526
       Course = N 47.6° W       (N-W because: DLAT is North; DLO is West)
                                         To covert this course angle into True Course, we have to subtract it to 360°.
                       360°
                     -  47.6° 
True Course = 312.4°

5. Solving now for the distance:

     Distance = DLAT    
                      Cos Co
                   = 360 miles  
                      Cos 47.6°
    Distance = 533.88 miles

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8 comments:

  1. AnonymousJuly 12, 2018 at 2:09 PM

    How did INV Tan 1.0956 become 47.6 west? What is INV pelase help

    ReplyDelete
    Replies
    1. UnknownJuly 15, 2018 at 8:37 PM

      Shift Tan to 1.0956 and the answer would be 47.6

      Delete
  2. UnknownSeptember 28, 2019 at 10:46 AM

    When a longitude is same how can i get a dlo in mercator sailing? Or there is other way exept of mercator? Thankyou in advance


    Ex.

    Wp7- wp8
    Lat¹: 21° 17.00° long¹: 088° 12.20°
    Lat²: 21° 03.00° long²: 088° 12.20°

    Btw im a student

    ReplyDelete
    Replies
    1. Serge BailliuMarch 9, 2021 at 7:24 PM

      Dan vaar je pal oost 90 graden of pal west 270 graden.

      Delete
  3. UnknownJanuary 11, 2022 at 3:14 PM

    hi i just want to ask why it add 40 miles at the d'long when converted to distance/?

    ReplyDelete
    Replies
    1. AnonymousJanuary 18, 2022 at 6:51 PM

      The dlo is 7 degrees 40 minutes.
      The author is converting the dlo into miles. So 7 degrees x 60. Then just add 40 miles because 1 minute = 1 miles.

      Delete
  4. AnonymousJanuary 27, 2023 at 11:15 AM

    i,am very confuse how to get the exact computation icant get the answer of 1.09526 always wrong my computation even i follow the formula..=cos (31 degree x 460 different answer not the same 1,09526
    kindly help me sir how to calculate to correct..

    ReplyDelete
    Replies
    1. New Age GadgetsFebruary 18, 2023 at 8:52 PM

      maybe you are computing both directly.
      compute cos 31 first

      then the answer multiply it by 460 and

      again once done divided it by 360

      Delete