The TPC values of a ship at 1.5 m intervals of draught, commencing at the keel, are 4.0, 6.1, 7.8, 9.1, 10.3, 11.4 and 12.0 m respectively. Calculate at a draught of 9 m: (a) displacement (b) KB

 The TPC values of a ship at 1.5 m intervals of draught, commencing at the keel, are 4.0, 6.1, 7.8, 9.1, 10.3, 11.4 and 12.0 m respectively. Calculate at a draught of 9 m:

(a) displacement

(b) KB

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 3.5

 

Solution:

a)

TPC	SM	f(vol)	Levers	FM
4.0	1	4	0	0
6.1	4	24.4	1	24.4
7.8	2	15.6	2	31.2
9.1	4	36.4	3	109.2
10.3	2	20.6	4	82.4
11.4	4	45.6	5	2280
12	1	12.0	6	720
		∑f(vol) = 158.6		∑f(FM) = 547.2

 

Volume = h/3 * ∑f(vol) * 100/1.025

Displacement = h/3 * ∑f(vol) * 100/1.025 * 1.025

                        = 1.5/3 * 158.6 * 100

                        = 7930 tons

KB = ∑f(FM)/∑f(vol) * h

      = 547.2/158.6 * 1.5

      = 5.175 m