Question

(a) Explain the concept of dynamical stability and describe the effect of an increase in wind pressure when a vessel is at its maximum angle of roll to windward (6)

(b) A ship of 5000 tone displacement has three rectangular double bottom tanks; A 12 m long and 16 m wide; B 14 m long and 15 m wide; C 14 m long and 16 m wide. Calculate the free surface effect for any one tank and state in which order the tanks should be filled when making use of them for correction. (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.

Part (b)

$$Free\:surface\:effect=\frac{\rho_{_{L}_{}\times}i}{\rho_{S}\times\nabla}$$

$$\rho_{L}=density\:of\:liquid\:in\:tank$$

$$\rho_{S}=densituy\:of\:SW$$

In this case, the density of the liquid to be filled is the same as the ship floats.

$$therefore\:\rho_{L}=\rho_{S}$$

$$i \space = \space {{LB^3} \over 12}$$

Part (a)

$$L=12m$$

$$B=16m$$

$$Free \space surface \space effect \space = \space {{{12 \times 16^3} \over 12} \over {{5000} \over 1.025}}$$

$$=\frac{12\times16^3\times1.025}{5000\times12}$$

$$= \space 0.84m$$

Part (b)

$$L=14m$$

$$B=15m$$

$$Free\:surface\:effect\:=\:\frac{\frac{14\times15^3}{12}}{\frac{5000}{1.025}}$$

$$Free\space surface\space effect\space=\frac{14\times15^3\times1.025}{12\times5000}$$

$$= \space 0.807m$$

Part (c)

$$L=14m$$

$$B=16m$$

$$Free \space surface \space effect \space = \space {{{14 \times 16^3} \over 12} \over {{5000} \over 1.025}}$$

$$=\frac{14\times16^3\times1.025}{12\times5000}$$

$$= \space 0.97m$$

Tank with the lowest free surface effect should be filled first, so the tanks should be filled in order of B, A, then C

✓ 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.