GM and rolling period
GM has a direct relationship with a ship's rolling period. A ship with a small GM will be "tender" - have a long roll period - an excessively low or negative GM increases the risk of a ship capsizing in rough weather (see HMS Captain or the Vasa). It also puts the vessel at risk of potential for large angles of heel if the cargo or ballast shifts (see Cougar Ace). A ship with low GM is less safe if damaged and partially flooded because the lower metacentric height leaves less safety margin. For this reason, maritime regulatory agencies such as the IMO specify minimum safety margins for sea-going vessels. A larger metacentric height, on the other hand can cause a vessel to be too "stiff"; excessive stability is uncomfortable for passengers and crew. This is because the stiff vessel quickly responds to the sea as it attempts to assume the slope of the wave. An overly stiff vessel rolls with a short period and high amplitude which results in high angular acceleration. This increases the risk of damage to the ship as well as the risk cargo may break loose or shift. In contrast a "tender" ship lags behind the motion of the waves and tends to roll at lesser amplitudes. A passenger ship will typically have a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of 6 to 8 seconds.
The period of roll can be estimated from the following equation[2]
Where g is the gravitational constant, k is the radius of gyration about the longitudinal axis through the center of gravity and is the stability index.
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.[2] 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 (see below)
Referrence
1. ^ Ship Stability. Kemp & Young. ISBN 0853090424
2. ^ a b c d Comstock, John (1967). Principles of Naval Architecture. New York: Society of Naval Architects and Marine Engineers. pp. 827. ISBN 670020738.
3. ^ a b Harland, John (1984). Seamanship in the age of sail. London: Conway Maritime Press. pp. 43. ISBN 0851771793.
4. ^ U.S. Coast Guard Technical computer program support accessed 20 December 2006.
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