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Converting Quadrantal Course To True Course

 The course given is S 83° 22' E, find the true course? 

Given:

              S 83° 23' E- quadrantal course

what is asked?

              find the true course


Solution:

   1. " AS IS" if the angle is in the first quadrant

   2. In the second quadrant: 180° minus the angle              given

   3. In the 3rd quadrant: 180° + the angle

   4. In the 4th quadrant: 360° - the angle

   So since the given course is in the second quadrant, we have to subtract the 180°. 

     180° is equal to 179° 60'

                                -   83° 22'  

                                    96° 38' is the answer 

Calculating Ship's Speed

A ship covers a distance of 12 miles in 2 hrs. Find her speed? 

Given:

            Distance = 12 miles

                  Time = 2 hours

What is asked?

              Find the ship's speed 

Solution:

We have to divide distance by time to get the speed. So this is the formula for speed:

                Speed = Distance ÷ Time

                            = 12 miles ÷ 2 hours

                            = 6 miles per hour or 6 knots

So the ship's speed is 6 knots.

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Calculating Ship's Distance Run

For 18 hours, a vessel steamed at an average speed of 10 kts. What was the total distance? 

Given:

            Time = 18 hours

          Speed = 10 knots

What is asked?

            Total distance run for 18 hrs

Solution:

1. We have to multiply ship's speed and the steaming time to get the distance. This is the formula:

        Distance = speed × time

                         = 10 nm/hr × 18 hrs

2. Eliminate the hours

         Distance = 10 nm/ hr   × 18 hrs  

                          = 10 nm × 18

                          = 180 nm is the distance run 

Formula for getting distance 

Converting Ship's Steaming Time Into Days

nullM/V LITE FERRY 20

The steaming time acquired by the vessel is 149. 6 hours, how many days of navigation did she travel?

Given: 

           Steaming time = 149.6 hours

What is asked:

           Convert ship's steaming time into days

Solution:

1.We have to divide 149.6 by 24 to get the number of days.  

                       149.6 ÷ 24 = 6.23333 days 

2. Then subtract 6           - 6                

                                              0.23333 days  

3. Then multiply by 24 to get hours.        

                          0.23333 days × 24 =  5.59992  hours

4. Subtract 5                                      -  5         

                                                               0.59992 hours

5. Multiply it by 60 to get minutes       × 60  

                                                                 36 minutes 

So the final answer is 6 days 5 hours 36  minutes 

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How To Solve For Ship's Steaming Time

 A vessel sailed on a total distance of 120 miles for 10 knots. How many hours did she do for the trip? 

Given:

           Distance = 120 miles

                Speed = 10 knots

What is asked? 

           Solve for the ship's steaming time

Solution:

The formula for solving ship's steaming time is to divide distance by the speed.

Time = Distance ÷ Speed 

          = 120 miles ÷ 10 miles/hour

Now we can can eliminate miles 

          = 120 miles ÷ 10 miles/hour

          = 120 ÷ 10 hours

          = 12 hours is the ship's steaming time 

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How To Solve For DLO ( Difference of Longitude)

 From longitude 155° E thru 155° W, what is the difference of longitude (DLO)?

Given: 

            155° E -  longitude 1

            155° W - longitude 2

What is asked?

             Calculate the difference of longitude (DLO)

Solution:

     longitude 1 =⁷ 155° E

    longitude 2 = 155° W   ( +  because different  sign)

                 DLO = 310° 

                           - 360°   

                               50° E  is difference of longitude    


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How To Solve For Local Hour Angle

 Find the LHA of a star if the GHA of the star is 81° 57.3' and the longitude is 174° 32.9' W.

Given:

          81° 57.3' -  GHA of a star 

   174° 32.9' W -  longitude 

What is asked? 

                Find the LHA of a star

Solution:

1. To get LHA we have to subtract GHA and                     longitude. 

      LHA = GHA - longitude 

       we have to add 360° to the GHA since the longitude is greater. 

                   GHA =  441° 57.3'       

          longitude = 174° 32.9'  W (-)

           LHA Star = 267° 24.4' is the answer 

By the way, Local Hour Angle is the angular distance measured westerly from the Local Celestial Meridian to the body up to 360°.

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How To Solve For Greenwich Mean Time (GMT)

 The LMT of longitude 78° 18' west is 04H 03M. Find the GMT.

Given: 

           78° 18' W - longitude 

           04H 03M - LMT

Solution:

1.  We have to convert arc to time, that is we are going to divide the longitude by 15 to get time.

           78° 18' ÷ 15° = 05h 13.2 mins

2. Now we are going to add LMT to our answer in step  1 to get the GMT. 

    As for the rule in getting GMT:

          From LMT to GMT, longitude W (+)   E (-)

          Longitude in time = 05h 13.2 mins

                                  LMT =  04h 03 m    +

                                  GMT = 09h 16.2 mins

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Rules For Solving DLAT (Difference of Latitude)

 From latitude 14 degrees north thru latitude 14 degrees south, what is the DLAT?

Given: 

           Latitude 1 = 14 degrees north 

           Latitude 2 = 14 degrees south 

Solution: 

           This is the rule for solving DLAT ,

            Same name of latitude--we have to subtract 

           Different name of latitude -- we have to add

           Latitude = 14 degrees north

           Latitude = 14 degrees south    

                  Dlat = 28 degrees south is the difference                                  of latitude 

       The sign of the DLAT  is south because that is the direction.

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How To Calculate Earth's Equatorial Radius

 Let us solve to know how much is the equatorial radius of the earth. 

Solution:

1. First we have to calculate how much is the earth's circumference at the equator. Since every minute of an arc at the equator is equavalent to 1 nautical mile, therefore the circumference of the earth at the equator is 21,600 nautical miles. 

2. We can derive from the formula of circumference to get the radius.

    Circumference = 2 π radius

                      Radius = circumference

                                          2 π  

                                      =   21,600 

                                       2 x 3.1416

                                 = 3437.739 nautical miles

3. We have to multiply 3437.739 natical miles by 1.1515 to convert to statute miles.

                      3437.739 nautical miles 

                     X  1.1515

                        3958.6 statute miles is the equatorial radius of the earth. 

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Determine The Area Of Triangle

 Determine the area of a triangle with a base of 3.5 feet and a height of 4 feer.

Given:

            Base = 3.5 feet

            Height = 4 feet

What is asked? 

             Area of a triangle 

Solution:

          1. The formula to getting the area of a                         triangle is 

             Area of triangle = 1/2 bh

                                          = 3.5 ft x 4 ft / 2

                                          = 14 ft² / 2

                                         = 7 ft²

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How To Compute The Ship's Mean Draught If The Compartment Was Bilged

 A vessel whose TPC is 12.3 is drawing 4 meters. A rectangular midship compartment 12 meters long,  10 meters bread, and 6 meters depth has a permeability of 20%. What would be the mean draught if this compartment was bilged?

Given:

TPC = 12.3

Draft = 4 meters

Lenght of the compartment = 12 meters

Breadth of the compartment = 10 meters

Depth of the compartment = 6 meters

Permeability = 20%

What is asked:  

mean draught if this compartment was bilge?

Solution:

1. We have to calculate the displacement. But first we have to convert 4 meters to centimeters. 

     4 m x 100 cm/1m = 400 cm

      Now this  is  the formula to getting displacement:

      Displacement = TPC X draft in centimeters 

                                = 12.3 x 400 cm

                                 = 4,920 tons

2. Then we have to solve for the additional weight added due to flooding. 

       Weight = lenght x bread x draft x density

                     = 12 x 10 x 4 x 1.025

                    = 492 Tons

        But with 20% of permeability,  so 492 tons x 20% = 98.4 tons

3. So now we are going to add the original displacement and the additional weight to get the total displacement. 

        Original displacement = 4 ,920 tons

                Additional weight = 98.4 tons

              Total displacement = 5, 018.4 tons

4. Now the final step which is solving for the ship's draft.

        Draft = displacement / TPC

                  = 5,018.4 tons / 12.3 

                  = 408 cms 

                  = 4.08 meters is the final answer

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Time To Abeam For Ships On Opposite Courses

At 0800H, two ships was observed to be 33 miles apart on opposite courses. One ship was running at 12 knots while the other was making 10 knots. At what time of the day will they be abeam from each other?

Given:

Time : 0800H

Distance: 33 miles

Ship's sppeed of one ship: 12 knots

Ship's speed of the other ship: 10 knots


What is askes in the problem?

At what time of the day the two ships on opposite courses will  be abeam from each other.


Solution: 

1. Add the speed of the two ships.

      12 lnots  + 10 knots = 22 knots

2.  Solve for the steaming time that these two ships on opposite courses will meet to each other. This is the formula in getting time.

     Time = distance / speed

     Time = 33 miles / 22 knots

     Time = 1.5 hours (1 hr 30 minutes)

3. Now we are going to add the answer in step 2 to the time when the two ships are 33 miles from each other which is 0800H.

     0800

+

     0130

     0930H - the final answer 

    So the the time of day when the two ships will be abeam from each other is 0930H.

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