The half-ordinates of a ship’s water-plane, which is 60m long, commencing from forward, are as follows: 0, 3.8, 4.3, 4.6, 4.7, 4.7, 4.5, 4.3 and 1 m, respectively. Find the area of the water-plane, the TPC, the coefficient of fineness of the water-plane area, and the position of the centre of flotation, from amidships.

The half-ordinates of a ship’s water-plane, which is 60m long, commencing from forward, are as follows: 0, 3.8, 4.3, 4.6, 4.7, 4.7, 4.5, 4.3 and 1 m, respectively. Find the area of the water-plane, the TPC, the coefficient of fineness of the water-plane area, and the position of the centre of flotation, from amidships.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 10.2

 

Solution:

	ord	SM	f(A)	Levers	f(M)
FOR	0	1	0	-4	0
	3.8	4	15.2	-3	-45.6
	4.3	2	8.6	-2	-17.2
	4.6	4	18.4	-1	-18.4
	4.7	2	9.4	0	0
	4.7	4	18.8	+1	+18.8
	4.5	2	9	+2	+18
	4.3	4	17.2	+3	+51.6
AFT	0.1	1	0.1	+4	+0.4
			∑ = 96.7		∑ = 7.6

 

Common interval, h = 60/8 = 7.5 m

A_w = 2* h/3 * ∑f(A)

       = 2 * 7.5/3 * 96.7

       = 483.5 m²

TPC = A_w * 1.025/100

        = 483.5 * 1.025/100

        = 5 tons

Center of flotation = ∑ f(m)/∑ f(A) * h

                               = 7.6/96.7 * 7.5

                                  = 0.589 m AFT of midship