87.NA February 2020 Q.6(b)

A box-shaped vessel 65 m x 12 m x 8 m has KG 4 m, and is floating in salt water upright on even keel at 4 m draft F and A. Calculate the moment of statical stability at (a) 5 degrees and (b) 25 degrees heel.

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GIVEN

L = 65 m

B = 12 m

D = 8 m
d = 4 m

KG = 4 m

TO FIND 

a) moment of statical stability at 5 degrees heel
b) moment of statical stability at 25 degrees heel.

SOLUTION

 Displacement, W = L x B x draft x 1.025   

                             = 65 x 12 x 4 x 1.025      

                             = 3198 tonnes

 As it is box shaped vessel KB = ½ draft
                                           KB = 2 m

 BM = B²/12d

        = (12 x 12) / 12 x 4

        = 3 m

   

 KM = KB + BM 
       = 2 + 3 
       = 5 m

KG = 4 m

     
GM = KM – KG

       = 5 – 4

       = 1 m

a) at 5^o heel          
    
    GZ = GM x sin q

          = 1 x sin 5^o

          = 0.0872 m

    
     Moment of statical stability = W x GZ

                                                = 3198 x 0.0872

                                                = 278.9 tonnes m

b) at 25^o heel    GZ = (GM + ½ BM tan²q) sinq

                                = (1 + ½ x 3 x tan²25^o) sin25^o

                                = (1 + 0.3262)sin25^o

                                = 1.3262 sin25^o

                                = 0.56 m

            
Moment of statical stability = W x GZ

                                           = 3198 x 0.56

                                           = 1790.9 tonnes m