A vessel of constant rectangular cross-section is 7.2 m wide. (a) Draw the metacentric diagram using 0.5 m intervals of draught up to the 4.0 m waterline. (b) If the centre of gravity is 3 m above the keel, determine from the metacentric diagram the limits of draught between which the vessel will be unstable.

A vessel of constant rectangular cross-section is 7.2 m wide.

(a) Draw the metacentric diagram using 0.5 m intervals of draught up to the 4.0 m waterline.

(b) If the centre of gravity is 3 m above the keel, determine from the metacentric diagram the limits of draught between which the vessel will be unstable.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.5

 

Solution:

KB = d/2

BM = B²/12d

       = 7.2²/12d

       = 4.32/4

d	KB	BM	KM
0	0	-	-
0.5	0.25	8.64	8.89
1.0	0.5	4.32	4.82
1.5	0.75	2.88	3.63
2.0	1.0	2.16	3.16
2.5	1.25	1.728	2.998
3.0	1.50	1.440	2.94
3.5	1.75	1.234	2.984
4.0	2.0	1.08	3.08

 

Between draughts of 2.4 m and 3.6 m the vessel will be unstable.