A ship’s load water-plane is 60m long. The lengths of the half-ordinates commencing from forward are as follows: 0.1, 3.5, 4.6, 5.1, 5.2, 5.1, 4.9, 4.3 and 0.1 m, respectively. Calculate the area of the water-plane, the TPC in salt water, and the position of the center of flotation, from amidships.

 

A ship’s load water-plane is 60m long. The lengths of the half-ordinates commencing from forward are as follows:

0.1, 3.5, 4.6, 5.1, 5.2, 5.1, 4.9, 4.3 and 0.1 m, respectively.

Calculate the area of the water-plane, the TPC in salt water, and the position of the center of flotation, from amidships.

Reference: Ship Stability for Masters & Mates (6^th edition), Exercise – 10.1

Solution:

	Ordinates	SM	F(A)	Levers	F(M) FOR
FOR	0.1	1	0.1	-4	-0.4
	3.5	4	14	-3	-42
	4.6	2	9.2	-2	-18.4
	5.1	4	20.4	-1	-20.4
	5.2	2	10.4	0	0
	5.1	4	20.4	+1	+20.4
	4.9	2	9.8	+2	+18.4
	4.3	4	17.2	+3	+51.6
	0.1	1	0.1	+4	+0.4
AFT			∑f(A) = 101.6		∑f(M) = +9.56

Common interval, h = 60/8

Waterplane area, A_W  = (h/3) * ∑f(A)

     = (60/8) * (1/3) * 101.6 * 2

     = 508 m²

 

TPC = (Aw*1.025)/100 = (508*1.025)/100  = 5.2 tons

 

Center of Flotation = (∑f(M))/(∑f(A)) * h 

                                = (9.56/101.6) * (60/8)

                                = 0.8 m AFT of amidship