C L DUBEY – EXERCISE – 02 : Simpson’s Rule

• Geometric centre between first two = 4156.67/387

                                                                       = 10.74m

• Geometric centre between last two = 5263.335/553

                                                                      = 9.518m

Q14. The TPC values for a ship at 1.2 meters intervals of draught commencing at the keel, are 8.2, 16.5, 18.7, 19.4, 20.0, 20.5, 21.1 respectively. Calculate her displacement at 7.2 metres draught.

Solution –

TPC	Ordinate	SM	Product of volume
8.2	8.2x	1	8.2x
16.5	16.5x	4	66x
18.7	18.7x	2	37.4x
19.4	19.4x	4	77.6x
20.0	20.0x	2	40.0x
20.5	20.5x	4	82.0x
21.1	21.1x	1	21.1x
			332.2x

TPC = (A/100) x density
A = TPC ⨯ (100/density)
X = 100/1.025

V/W volume = (1.2/3) ⨯ 332.3 ⨯ 100/1.025
= 12967.804