Center of Gravity and Buoyancy
The center of gravity and buoyancy are two important concepts in ship stability. The center of gravity (CG) is the point where the weight of the ship is concentrated, while the center of buoyancy (CB) is the point where the buoyant force of the displaced water acts. The difference between CG and CB is that CG depends on the distribution of mass within the ship, while CB depends on the shape and volume of the submerged part of the hull. The position and alignment of these two points determine how a ship behaves at sea, both in still water and in waves. A ship is said to be in equilibrium when the CG and CB are vertically aligned, meaning that the weight and buoyancy forces are balanced. This is also called the upright position. However, when a ship is subjected to an external force, such as wind or waves, it may tilt or heel to one side. This causes the CG to move laterally and the CB to shift to the low side of the hull. The distance between the CG and CB is called the righting arm or lever, and it creates a restoring moment that tends to bring the ship back to equilibrium. The metacentre (M) is another important point in ship stability. It is defined as the point where the vertical line through the CB intersects with the line of action of the buoyant force when the ship is inclined by a small angle. The metacenter can be considered as a pivot point around which the ship rotates when it heels. The distance between the CG and M is called the metacentric height (GM), and it is a measure of the initial stability of a ship. A larger GM means a stiffer ship that resists heeling, while a smaller GM means a more tender ship that heels easily. The metacentric height can be affected by several factors, such as loading, trimming, flooding, or damage. A positive GM indicates that the metacenter is above the CG, and the ship has a stable equilibrium. A negative GM indicates that the metacenter is below the CG, and the ship has an unstable equilibrium. A zero GM indicates that the metacenter coincides with the CG, and the ship has a neutral equilibrium. Ship stability is an essential aspect of naval architecture and ship design, as it ensures the safety and performance of a ship in various sea conditions. Ship stability calculations involve determining the centers of gravity, buoyancy, and metacenter, as well as other parameters such as displacement, draft, trim, heel, freeboard, etc. These calculations require knowledge of hydrostatics, geometry, and physics, as well as empirical data from model testing or computational fluid dynamics.