A vessel of constant rectangular cross-section has a breadth of 12 m and metacentric height of one quarter of the draught. The vertical centre of gravity lies on the waterline. Calculate the draught.

A vessel of constant rectangular cross-section has a breadth of 12 m and metacentric height of one quarter of the draught. The vertical centre of gravity lies on the waterline. Calculate the draught.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.3

 

Solution:

Given,

GM = d/4

KG = d [COG lies on waterline]

 

BM = B²/12d

       = 12²/12d

       = 12/d

KB = d/2

 

KB + GM = KB + BM

=> d + d/4 = d/2 + 12/d

=> 3/4 d = 12/d

=> d² = 4/3 * 12

 => d = 4 m

Draft = 4 m