Q7
(a) Explain how an increase of draught and of displacement influence rolling.
(6)
(b) A pontoon has a constant cross-section as shown in Fig. Given below. The metacentric height is 2.5 m. Find the height of the centre of gravity above the keel.
(10)
Reference Answer
### Part (a): Influence of Draught and Displacement on Rolling An increase in a vessel's draught and displacement, typically by loading cargo, has a profound and multi-faceted effect on its rolling characteristics. These effects are primarily governed by changes in the metacentric height (GM), the radius of gyration (K), and the damping forces. The natural rolling period (T) of a ship is given by the formula: $$ T = \frac{2 \pi K}{\sqrt{g \cdot GM}} $$
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