The areas of a ship’s water-planes, commencing from the load draft of 24 metres, and taken at equal distances apart, are: 2000, 1950, 1800, 1400, 800, 400 and 100sq. m, respectively. The lower area is that of the ship’s outer bottom. Find the displacement in salt water, the Fresh Water Allowance, and the height of the centre of buoyancy above the keel.

The areas of a ship’s water-planes, commencing from the load draft of 24 metres, and taken at equal distances apart, are: 2000, 1950, 1800, 1400, 800, 400 and 100sq. m, respectively. The lower area is that of the ship’s outer bottom. Find the displacement in salt water, the Fresh Water Allowance, and the height of the centre of buoyancy above the keel.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 10.4

 

Solution:

Aw	SM	f(∇)	Levers	f(m)
2000	1	2000	6	12000
1950	4	7800	5	39000
1800	2	3600	4	14400
1400	4	5600	3	16800
800	2	1600	2	3200
400	4	1600	1	1600
100	1	100	0	0
		∑ = 22300		∑ = 87000

 

Common interval, h = 24/6 = 4 m

Volume = h/3 * ∑f(∇)

               = 4/3 * 22300

               = 29733.33 m³

∆ = 29733.33*1.025 = 30476.67 tons

TPC = A_W*1.025/100

        = 2000*1.025/100

        = 20.5 ton/cm

FWA = ∆/4*TPC

          = 30476.67/4*20.5

          = 371.67 mm

Center of flotation above the keel = ∑ f(m)/∑ f(∇) * h

                                                              = 87000/22300 * 4

                                                              = 15.6 m