The displacement of a ship at draughts of 0, 1, 2, 3 and 4 m are 0, 189, 430, 692 and 977 tonne. Calculate the distance of the centre of buoyancy above the keel when floating at a draught of 4 m, given: VCB below waterline = area between displacement curve and draught axis/ displacement

 The displacement of a ship at draughts of 0, 1, 2, 3 and 4 m are 0, 189, 430, 692 and 977 tonne. Calculate the distance of the centre of buoyancy above the keel when floating at a draught of 4 m, given:

VCB below waterline = area between displacement curve and draught axis/ displacement

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 3.7

 

Solution:

Draft	Displacement	SM	f(M)
0	0	1	0
1	189	4	756
2	430	2	860
3	692	4	2768
4	977	1	977
			∑f(M) = 5361

 

Area of curve  = h/3 * ∑f(M)

                        = 1/3 * 5361

                        = 1787 ton-m

VCB below waterline = area of curve/displacement

                                    = 1787/977

                                    = 1.829 m

KB = 4 – 1.829 = 2.171 m