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Question From Readers #8: Find The KG


Find the KG

 A ship is inclined by moving a weight of 30 tons a distance of 30 ft. from the centerline. A 28-foot pendulum shows a deflection of 12 inches. Displacement including weight moved is 4,000 tons. KM is 27.64 feet. What is the KG?

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Question From Readers #7: Calculate Ship's New Draft

Calculate Ship's New Draft

A vessel's draft is 14-11 fwd and 14-07 aft. She loads 1,470 tons which is 40 feet aft of the tipping center with a TPI of 60 and a MTI of 1335. What is her new draft?

Solution:

We are going to solve for change of trim. After then we are going to get half trim. What to do with the half trim? Let me proced now.

Step 1. Solving for change of trim.

Trim = (w x D) / MTI
         = (1470 x 40) / 1335
         = 44 inches

Step 2. Parallel sinkage
         
 Parallel sinkage = Wieght ÷ TPI
                                     = 1470 ÷ 60
                                     = 24.5 inches

               24.5 inches ÷ 12 = 2.04166 ft
                0.04166 ft  x 12 = 0.5 inch

So the parallel sinkage is 2' 0.5"                                                
   
Step 3. Get half trim.

            Half trim = 44 /2 = 22 inches
                                          22 inches ÷ 12 = 1.83333 ft
                                            83333 ft x 12 = 10 inches
           Half trim is 1' 10"

Step 3. Add Parallel Sinkage to the original drafts forward and aft. Also apply the half trim. Add it to to the draft aft since we are moving weight aft of the tipping center. And of course, subtract forward draft.

  Forward draft =    14' 11"               Aft draft = 14' 07"
Parallel sinkage = +  2' 0.5"                               + 2' 0.5"  
                              16' 11.5"                              16' 7.5"
Half trim               -  1'  10"                              +  1' 10"    
                              15' 1.5"                                17'  17.5"  
                                                                        + 1  - 12    
                                                                          18'  5.5"
So the final draft is 15' 1.5" forward, 18' 5.5" aft.

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Find The Declination Of The Sun

Find the declination of the sun as it rises and bears 115° 11' at Lat 42° 27' N.

Given:

Azimuth = 115° 11'
Latitude = 42° 27' N

What is asked?

Declination of the sun

Solution:

1. Solve for the amplitude.

                  Azimuth = 115° 11'
                                 -  90°          
               Amplitude = E 25° 11' S

2. With the answer in step 1, we can now solve for the declination.

         Sin Amplitude = Sin Declination
                                   Cos Latitude   (cross-multiply to derive formula for declination)   

        Sin Declination = Sin Amplitude x Cos Latitude
                               = Sin 25° 11' x Cos 42° 27'
                               = 0.42552 x 0.73787
        Sin Declination = 0.31398
              Declination = 0.31398 inv Sin
                               = 18.3 South is the declination

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Question From Readers #6: Change of Draft


What will be her draft in sea water considering there is no change in displacement

A ship has LBP 215 m, TPC 59.05 T, MTC 767.41 T-m, LCB 7.08 m with displacement of 31979 T and floating in a dock water density of 1.022 with draft 4.18 m FWD, 7.69 m AFT. What will be her draft in sea water considering there is no change in displacemet.

 Solution:

 In this kind of problem, we are going to use to two formulae and then a little analysis on what to do with the figure derived from the solution. First formula we are going to use is this:

 DWA = displacement / (4 x TPC)

 The second formula is:

 DWA = FWA x (1025 - new density) / 25

 Ok now let us to answer...

 Step 1.

 DWA = displcement / (4 x TPC) = 31979 / (4 x 59.05) = 31979 / 236.2 = 135.4

 Step 2.

 DWA = 135.4 x (1.025 - 1.022) / 25 =(135.4 x 0.003) / 25 = 0.4062 / 25 = 0.016 m

 Step 3.

A little analysis here. Our ship is originally from a water with density of 1.022 going to the seawater. So there must be a change in draft because there is a change in water density. Your question then is, what will happen to the draft? Will it increase or will it decrease? Since the ship is coming from brackish to sea water, the ship's draft will decrease. So we are going to use our answer in step 2 to subtract the original forward and aft drafts.

 FWD 4.18 m - 0.016 = 4.16 m

AFT 7.69 m - 0.016 =7.67 m

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