Page 104 - statbility for masters and mates

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Ship Stability for Masters and Mates
Exercise 10
1 A ship's load water-plane is 60 m 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 centre of ¯otation, from amidships.
2 Thehalf-ordinatesofaship'swater-plane,whichis60mlong,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 coef®cient of ®neness of the water-plane area, and the position of the centre of ¯otation, from amid- ships.
3 The breadths at the load water-plane of a ship 90 metres long, measured at equal intervals from forward, are as follows:
0, 3.96, 8.53, 11.58, 12.19, 12.5, 11.58, 5.18, 3.44, and 0.30 m respectively.
If the load draft is 5 metres, and the block coef®cient is 0.6, ®nd the FWA
and the position of the centre of ¯otation, from amidships.
4 The areas of a ship's water-planes, commencing from the load draft of 24
metres, and taken at equal distances apart, are:
2000, 1950, 1800, 1400, 800, 400, and 100 sq m respectively.
The lower area is that of the ship's outer bottom. Find the displacement in salt water, the Fresh Water Allowance, and the height of the centre of buoyancy above the keel.
5 The areas of vertical transverse sections of a forward hold, spaced equidistantly between bulkheads, are as follows:
800, 960, 1100, and 1120 sq m respectively.
The length of the hold is 20 m. Find how many tonnes of coal (stowing at
4 cu. m per tonne) it will hold.
6 A ship 90 metres long is ¯oating on an even keel at 6 m draft. The half-
ordinates, commencing from forward, are as follows:
0, 4.88, 6.71, 7.31, 7.01, 6.40, and 0.9 m respectively.
The half-ordinates 7.5 metres from bow and stern are 2.13 m. and 3.35 m respectively. Find the area of the water-plane and the change in draft if 153 tonnes of cargo is loaded with its centre of gravity vertically over the centre of ¯otation. Find also the position of the centre of ¯otation.
7 The areas of a ship's water-planes commencing from the load water-plane and spaced at equidistant intervals down to the inner bottom, are:
2500, 2000, 1850, 1550, 1250, 900 and 800 sq m respectively.