The areas of a ship’s water-planes, commencing from the load water-plane and spaced 1 metre apart, are as follows: 800, 760, 700, 600, 450 and 10sq. m, respectively. Midway between the lowest two water-planes the area is 180sq. m. Find the load displacement in salt water, and the height of the centre of buoyancy above the keel.

The areas of a ship’s water-planes, commencing from the load water-plane and spaced 1 metre apart, are as follows:

800, 760, 700, 600, 450 and 10sq. m, respectively.

Midway between the lowest two water-planes the area is 180sq. m. Find the load displacement in salt water, and the height of the centre of buoyancy above the keel.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 10.12

Solution:

Area	SM	f(∇)	Levers(x)	f(m)
800	1	800	5	4000
760	4	3040	4	12160
700	2	1400	3	4200
600	4	2400	2	4800
450	1.5	675	1	675
180	2	360	0.5	180
10	0.5	5	0	0
		∑ = 8680		∑ = 26015

 

Volume = h/3 * f(∇)

                = 1/3 * 8680

                = 2893.33 m³

Displacement = 2893.33 * 1.025 = 2965.667 tons

Center of buoyancy = ∑f(m)/∑f(∇) * h

                                       = 26015/8680 * 1

                                       = 3 m