A box-shaped vessel 75m X 12m is floating upright in salt water on an even keel at 2.5m draft F and A. The forepeak tank which is 6m long is empty. Find the final drafts if the vessel is now holed forward of the collision bulkhead.

 A box-shaped vessel 75m X 12m is floating upright in salt water on an even keel at 2.5m draft F and A. The forepeak tank which is 6m long is empty. Find the final drafts if the vessel is now holed forward of the collision bulkhead.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 22.8

 

Solution:

Change in draft = (L*B*d*μ)/(L-l) *B

                          = (L*d*μ)/(L-l)

 = (6*2.5)/ (75 – 6)

 = 5/23 m

w = l*B*d*1.025

     = 6*12*2.5*1.025

     = 184.5 ton

W = L*B*d*1.025

     = 75*12*2.5*1.025

     = 2306.255 ton

 

TPC = WPA/97.56

        = (L*B)/97.56

        = (75-6) *12/97.56

        = 8.487 ton/cm

BM_L = (1/12 * L³B) / (L*B*d)

         = (1/12 * (75-6)³*12)/ (75*12*2.5)

         = 146.004 m

MCTC = W*BM_L/100L

            = (2306.25*146.004)/ (100*75)

            = 44.89623 ton.m/cm

Change in trim = w*d/MCTC

                         = 184.5*(75/2)/44.89623

                         = 154.105367

Increase in draft = w/TPC

                            = 184.5/8.487

                            = 21.74 cm

Now,

x/t = l/L

=> x/154.1 = 35/75

=> x = 71.915 cm = 0.719158 m

And,

y/t = L-l/L

=> y/154.1 = 75-35/75

=> y = 82.1895 cm = 0.821895 m

New draft AFT = 2.5 + 5/23 – 0.719 = 2 m

New draft FOR = 2.5 + 5/23 + 0.821 = 3.54 m