Question

Damaged Stability

If a ship floods, the loss of stability is due to the increase in B, the Center of Buoyancy, and the loss of waterplane area - thus a loss of the waterplane moment of inertia - which decreases the metacentric height.

This additional mass will also reduce freeboard (distance from water to the deck) and the ship's angle of down flooding (minimum angle of heel at which water will be able to flow into the hull).

The range of positive stability will be reduced to the angle of down flooding resulting in a reduced righting lever.

When the vessel is inclined, the fluid in the flooded volume will move to the lower side, shifting its center of gravity toward the list, further extending the heeling force. This is known as the free surface effect.

Free surface effect.

In tanks or spaces that are partially filled with a fluid or semi-fluid (fish, ice or grain for example) as the tank is inclined the surface of the liquid, or semi-fluid, stays level. This results in a displacement of the centre of gravity of the tank or space relative to the overall center of gravity. The effect is similar to that of carrying a large flat tray of water. When an edge is tipped, the water rushes to that side which exacerbates the tip even further.

The significance of this effect is proportional to the square of the width of the tank or compartment, so two baffles separating the area into thirds will reduce the displacement of the centre of gravity of the fluid by a factor of 9.

This is always of significance in ship fuel tanks or ballast tanks, tanker cargo tanks, and in flooded or partially flooded compartments of damaged ships. Another worrying feature of free surface effect is that a positive feedback loop can be established, in which the period of the roll is equal or almost equal to the period of the motion of the centre of gravity in the fluid, resulting in each roll increasing in magnitude until the loop is broken or the ship capsizes.

The metacentric height (GM) is the distance between the center of gravity of a ship and its metacenter. The GM is used to calculate the stability of a ship and this must be done before it proceeds to sea. The GM must equal or exceed the minimum required GM for that ship for the duration of the forthcoming voyage. This is to ensure that the ship has adequate stability.