A ship 180 m long has + widths of waterplane of 1, 7.5, 12, 13.5, 14, 14, 14, 13.5, 12, 7 and 0 m respectively. Calculate: (a) waterplane area (b) TPC (c) waterplane area coefficient.

 A ship 180 m long has + widths of waterplane of 1, 7.5, 12, 13.5, 14, 14, 14, 13.5, 12, 7 and 0 m respectively. Calculate:

(a) waterplane area

(b) TPC

(c) waterplane area coefficient.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 3.1

 

Solution:

a)

½ width	SM	f(A)
1	1	1
7.5	4	30
12	2	24
13.5	4	54
14	2	28
14	4	56
14	2	28
13.5	4	54
12	2	24
7	4	28
0	1	0
		∑f(A) = 327

 

b)

Common interval, h = 180/10 = 18

Waterplane area = 2 * h/3 * ∑f(A)

                             = 2 * 18/3 * 327

                             = 3924 m²

TPC = A_w * 1.025/100

        = 3924*1.025/100

        = 40.22 ton/cm

c)

Breadth = 14*2 = 28 m

Waterplane area coefficient = A_w / L*B

                                                = 3924/180*28

                                                 = 0.778