Question

(a) Describe how the distribution of mass within the ship affects the rolling period. (6)

(b) The righting moments of a ship at angles of heel of 0, 15°, 30°, 45° and 60° are 0, 1690, 5430, 9360 and 9140 kNm respectively. Calculate the dynamical stability at 60°. (10)

Answer 1

Part (a)

The rolling period is influenced by the ship's metacentric height (GM) and radius of gyration (K), which are determined by the location of the masses onboard.

Masses at the bottom:

The centre of gravity (G) moves down.
Metacentric height (GM) increases, resulting in greater stability.
Rolling period decreases.

Masses at the top:

The centre of gravity (G) moves up.
Metacentric height (GM) decreases, reducing stability.
Rolling period increases.

Masses concentrated at the centre:

The radius of gyration (K) decreases.
Rolling period decreases.

Masses distributed away from the centre:

The radius of gyration (K) increases.
Rolling period increases.

✓ Verified Model Answer (Text Solution)

The rolling period is influenced by the ship's metacentric height (GM) and radius of gyration (K), which are determined by the location of the masses onboard.