Question

(a) Explain how the distribution of masses affects rolling and pitching. (6)

(b) A ship turns in a circle of radius 100 metres at a speed of 15 knots. The GM is 2/3 metres and BG is 1 metre. If g=981 cm/sec2 and 1 knot is equal to 1.8532 Km/hour, find the heel due to turning. (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.

Part (b)

$$Radius\:\left(R\right)=100m$$

$$Speed\:\left(v\right)=15\:knots$$

$$GM=\frac23m$$

$$BG=1m$$

$$\tan\the\theta=\frac{v^2\times BG}{g\times r\times GM}$$

$$=\frac{\left(15\times0.514\right)^2\times1\times3}{9.81\times100\times2}$$

$$\theta=5.19\degree$$

✓ 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.