Q6
(a) How the distribution of mass within the ship affects the rolling period?
(6)
(b) A ship of 14000 tonnes displacement is 125 m long and floats at draughts of 7.9 m forward and 8.5 m aft. The TPC is 19, GML 120 m, and LCF 3 m forward of midships. It is required to bring the vessel to an even keel draught of 8.5 m. Calculate the mass which should be added and the distance of the centre of the mass from midships.
(10)
Reference Answer
### Part (a): Effect of Mass Distribution on Rolling Period The distribution of mass within a ship has a profound effect on its rolling period. This relationship is primarily governed by two key parameters: the Metacentric Height (GM) and the Radius of Gyration (k). The formula for the rolling period (T) is: $$ T = \frac{2 \pi k}{\sqrt{g \cdot GM}} $$ Where:
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