A box-shaped vessel 64m 10m 6m floats in salt water on an even keel at 5m draft. A forward compartment 6 metres long and 10 metres wide, extends from the outer bottom to a height of 3.5m, and is full of cargo of permeability 25 per cent. Find the new drafts if this compartment is now bilged.

 A box-shaped vessel 64m 10m 6m floats in salt water on an even keel at 5m draft. A forward compartment 6 metres long and 10 metres wide, extends from the outer bottom to a height of 3.5m, and is full of cargo of permeability 25 per cent. Find the new drafts if this compartment is now bilged.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 22.12

 

Solution:

w = μ*l*B*d*1.025

    = 0.25*6*10*3.5*1.025

    = 53.813 ton

TPC = WPA/97.56

        = L*B/97.56

        = 64*10/97.56

        = 6.56 ton

W = L*B*d*1.025

     = 64*10*5*1.025

      = 3280 ton

BM_L = L²/12d   

          = 64²/12*5

          = 68.27 ton

MCTC = W*BM_L/100L

            = 3280*68.2/100*64

            = 34.99 ton.m/cm

d = 64-6/2 = 29 m

Change of trim = w*BM_L/MCTC

                          = 53.813*29/34.99

                          = 44.60 cm

Now,

x/t = l/L

=> x/44.60 = 32/64

=> x = 0.223 m

And,

y/t = L-l/L

=> y/44.6 = 64-32/64

=> y = 0.223 m

 

New draft AFT = 5 + 0.082 – 0.223 = 4.859 m

New draft FOR = 5 + 0.082 + 0.223 = 5.305 m