Topic - 10 INTACT STABILITY

Intact stability

Illustration of the stability of bottom-heavy (left) and top-heavy (right) ships with respect to the positions of their centers of buoyancy (CB) and gravity (CG)

Intact stability calculations are relatively straightforward and involve taking all the centers of mass of objects on the vessel which are then computed to identify the center of gravity of the vessel, and the center of buoyancy of the hull. Cargo arrangements and loadings, crane operations, and the design sea states are usually taken into account.

GZ = KN - KG×sinθ

Statical Stability

Statical stability is a measure of the tendency of a ship to return to the upright position if inclined by an external force.

For stability to be adequate, the righting lever (GZ) resulting from the heeling of a loaded barge is required to be greater than zero (positive) for all angles of heel up to a certain minimum heel angle. 35° is a recommended minimum heel value.

When the ship is heeled by an external force by an angle θ, the centre of gravity of the ship remains in the same position but the centre of buoyancy moves from B to B₁.

The buoyancy, therefore acts through B₁, while the weight still acts downwards through G, creating a moment ∆g×GZ which tends to return the ship to the upright. ∆g×GZ is known as righting moment and GZ is known as righting lever.

For small angles of heel, (up to about 10°)

GZ = GM×sinθ

Where, GZ is the righting lever, GM is the transverse meta-centric height.

For large angles of heel, (>10°):

When the ship heels to an angle greater than 10^°,the position of centre of gravity of the ship changes.

Let, G is the assumed position of centre of gravity

G₁ is the actual position of centre of gravity

If G₁ lies below G, then the ship is more stable and

G₁Z = GZ+GG₁sinθ

If G₁ lies above G, then the ship is less stable and

G₁Z = GZ-GG₁sinθ

Dynamical Stability

The area under the GZ curve (and above the horizontal (0) axis), is a product of meters and degrees, and is also an important measure of the stability of a vessel. The larger this area the greater the capacity of the vessel to right itself as it rolls from side to side. This is known as righting energy.

A recommended minimum value for the area under the GZ curve is 5.73 meter x degrees.

The size of this area is determined by the initial GM (which gives the starting slope of the curve), the heel angle at which maximum GZ occurs (which gives the height of the curve) and the rangeof heel angles for which GZ is positive (which gives the length of the curve).

The moment of dynamical stability is the work done in heeling the ship to a particular angle.

Dynamical stability = W x A (in t-m-rad)

W = Displacement (in tonnes)

A = area between the curve and the baseline up to the given angle of heel (in metre radians).

Statical stability curve:The righting levers arising from different angles of heel are best understood when plotted on a curve.  Each vessel will have a unique curve depending on displacement, weight distribution and hull shape.