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Question From Readers #18: Fresh Water Allowance And Dock Water Allowance Formula

Fresh Water Allowance And Dock Water allowance Formula

A vessel has a mean draft  of 25'-00", her displacement is 10000 tons and the TPI is 42. Find the increase of draft in a water density 1010 kgs/m³.

Given:

 Displacement = 10, 000 tons
Water density = 1010 kgs/m³
                TPI = 42

Solution:

We are going to use two formulas to solve this problem.

1.    Fresh Water Allowance = Displacement
                                              40 x TPI
                                          = 10000   tons
                                              40 x 42 tons per inches immersion
                                          = 5.95 inches

2.                              DWA = FWA x (1025 - New Density)
                                                              25
                                          = 5.95" x (1025-1010)
                                                       25
                                          = 3.57" is our final answer

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Question From Readers #17: Calculate Righting Arm Of A Vessel

Calculate The Righting Arm

Calculate the righting arm of a vessel whose GM is 0.65 m when inclined at an angle of 12°.


Given:

                      GM = 0.65 m
Angle of Inclination = 12°

Solution:

Righting Arm = GM x Sin Angle of Inclination
                    = 0.65 m x Sin 12°
                    = 0.135 meter is the answer

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Question From Readers #16: Calculate Allowable Draft Increase

Allowable Draft Increase

The FWA being 6" for vessel M/V Seafarers. What is the increase of draft allowed in water of RD 1.010?


Given:

Fresh water allowance = 6 inches
         Relative density = 1.010

Solution:

Allowable Draft Increase = FWA ( Change in density)
                                                         25

                                      = 6 inches ( 1025 - 1010)
                                                         25
                                      = 3.6 inches is the answer

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Question From Readers #15: Calculate Time To Empty The Tank

How Long Will It Take To Empty The Tank

A tank measures 3 feet x 32 feet x 40 feet. How long will it take to empty the tank if the pumps discharge rate is 120 gallons per min.

Solution:

1. Calculate the volume of the tank.

               Volume = 3 ft x 32 ft x 40 ft
                           = 3, 840 cubic feet

2. Convert cubic feet into gallons. But how many gallons in 1 cubic foot? It's 7.48 gallons.

              3, 840 ft³
         x       7.48    
              28, 732.2 gallons
        ÷          120      gal/min        to get time to empty the the tank
               239.36 minutes
         ÷      60                        to convert it into hours
              3.98933 hrs or 3 hrs 59 min 21 sec to empty the tank

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Question From Readers #14: Calculate Cargo To Be Loaded


Find The Cargo To Be Loaded


Find the cargo to be loaded if initial draft aft is 10.873m, Trim Corr. = 14.408, TPC = 38.37 and final draft aft = 10.9m.
Ans. 89.19tons

Solution:

1. Subtract final draft and initial draft.
               10.9 m
             - 10.873 m  
                0.027 m 
2. Convert the 0.027 meter difference into centimeter so that we can apply the TPC.
               0.027 m x 100 cm = 2.7 cm 
                              1 m 
3. Multiply the TPC by 2.7 to get tons of cargo.
              38.37 
             x 2.7    
            103.599 tons     
         -   14.408    trim correction
            89.191 tons of cargo to be loaded  
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Question From Readers #13: Sag Correction


Sag Correction

A reader has brought up this question. If you know how to solve this problem, let us know.
Good day, 
Calculate sag correction basis TPC=41.06, MTC=481,LBP=163.6 and estimated sag = 4cm. Ans. 117.2 MT
Ship's hull is sagging 

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Calculate Time For A Star To Rise

Your vessel is at the equator at midnight on 1 January, and a star is observed rising. At what time will this same star rise on 1 February, assuming your vessel's location is still at the equator?


Solution:

One should know how many hours is one sidereal day, and of course a solar day.

             1 solar day = 24hr
         1 sidereal day = 23h 56h 4s   
                                    0h  3m 56s        is the time difference
                                  x            31        since there a 31 days from Jan. 1 to Feb. 1
                                  2h 01m 56s        total difference
       Midnight 1 Jan =  - 24h 00m 00s
                                 21h 58m 04s on 1 February that the star will rise

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Question From Readers #12: Dead Reckoning


Dead Reckoning

gud eve... i need you help with this. SHIP AT 0800 OCT 10 2011 LAT 9 2 N LONG 116 49.5E TRUE COURSE 38 SPEED 16 KTS FIND DEADRECKONING POS. AT 1600 OCT 10 2011


Solution:

Step 1. Get the steaming time.

           Time of arrival = 1600 10 Oct
     Time of departure = 0800 10 Oct 
                                   8 hrs is the steaming time

Step 2. Solve for the distance traveled for 8 hours.

          Distance = Speed x time
                       =  16 kts x 8 hrs
                       = 128 nautical miles

Step 3. Solving for Dlat.

                Dlat = Cos 38° x  128 nm    
                       = 100.86 nm
                           ÷   60          to convert it to degrees and minutes
                Dlat = 1° 40.86' N  North because the ship is northward

Step 4. Add Dlat and your latitude at position 1 to get the latitude of your new position.

                Dlat = 1° 40.86' N
       Latitude 1 = 9°  2' N         (Add because same name)

       Latitude 2 = 10° 42.86' N

Step 5. Solving for the departure and Dlo.

       Departure = Sin 38° x Distance
                       = Sin 38° x 128 nm
                       = 78.80 nautical miles
                          ÷ Cos 10° 42.86'    to get Dlo. But if in equator, Dep = Dlo
                           80.2 nm 
                        ÷ 60                  to convert it to degrees and minutes
                           1° 20.2' E is the Dlo

Step 6. Solving for the new longitude.

          Long 1 = 116° 49.5' E
               Dlo =     1° 20.2' E     same sign; add
          Long 2 = 118° 9.7' E

    So the new position of the ship is 10° 42.86' N, 118° 9.7' E.                                            

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Finding Observed Altitude

At meridian passage, upper passage, the observer's latitude was found to be 43° 34.7' N, Dec. is 1° 46.3' N. Find observed altitude.

 Given:
            Lat = 43° 34.7' N
            Dec = 1° 46.3' N

What is asked?

           Observed altitude (Ho)

Solution:

           Lat = 43° 34.7' N
           Dec = 1° 46.3' N         (Always reverse sign)

            Lat = 43° 34.7' N
           Dec = 1° 46.3'  S      (Subtract because it has different name)
             ZD = 41° 48.4' N
                  - 90°                 (Always minus 90° to get observed altitude)
           Ho = 48° 11.6' N

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