Question

(a) Explain the concept of dynamical stability (6)

(b) A ship of 12000 tonne displacement has a rudder 15m3 in area, whose centre is 5m below the waterline. The metacentric height of the ship is 0.3m and the centre of buoyancy is 3 3m below the waterline. When travelling at 20 knots the rudder is turned through 30°. Find the initial angle of heel if the force Fn perpendicular to the plane of the rudder is given by Fn = 577 AV2 sin∝ N

Allow 20% for the race effcet. (10)

Answer 1

Part (a)

Dynamical Stability is defined as the amount of energy required to heel a ship from its upright equilibrium position to a specific angle of heel. It provides a measure of the vessel's stability by considering its behaviour in response to dynamic external forces, such as wind or waves.

The concept compares the heeling moment energy (from external forces) and the righting moment energy (from the ship's stability).
The ship will absorb the energy imparted by the heeling moment. If the righting energy is greater than the heeling energy, the ship will stabilize; otherwise, it may capsize.

Areas Under the Curve:

Area A: Represents the region where the heeling moment exceeds the righting moment (external energy > ship's stability).
Area B: Represents the region where the righting moment exceeds the heeling moment (ship's stability > external energy).
The balance of these areas determines whether the ship will right itself or continue to heel.

When exposed to heeling forces such as wind or waves, the vessel inclines and may roll over to a certain angle of heel. If the external force is applied instantaneously, the ship must have enough reserve dynamic stability to absorb the energy and return to an upright position. If the external force is constant, the ship will remain at an equilibrium angle where the righting moment equals the heeling moment.

This refers to the remaining righting energy available to counteract additional external forces. A higher reserve dynamic stability ensures the vessel can handle greater heeling forces without capsizing.

✓ Verified Model Answer (Text Solution)

Dynamical Stability is defined as the amount of energy required to heel a ship from its upright equilibrium position to a specific angle of heel. It provides a measure of the vessel's stability by considering its behaviour in response to dynamic external forces, such as wind or waves.