A box-shaped vessel 40m long, 6m beam, is floating at a draft of 2m F and A. She has an amidships compartment 10m long which is empty. If the original GM was 0.6m, find the new GM if this compartment is bilged.

 A box-shaped vessel 40m long, 6m beam, is floating at a draft of 2m F and A. She has an amidships compartment 10m long which is empty. If the original GM was 0.6m, find the new GM if this compartment is bilged.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 22.4

 

Solution:

KM = KB + BM

       = d/2 + b²/12d

       = 2/2 + 6²/12*2

       = 2.5 m

KG = KM – GM = 2.5 – 0.6 = 1.9 m

Increase in draft = (L*B*d)/(L-l) *B

                            = (10*6*2)/ (40-10) *6

                            = 0.67 m

 New draft = 2+0.67 = 2.67 m

New KM = New KB + New BM

               = d/2 + b²/12d

               = 2.67/2 + 6²/12*2.67

               = 2.459 m

New GM = New KM – KG

                = 2.459 – 1.9

                = 0.5559 m