Significance of area under GZ curve:
The area under the statical stability or GZ curve up to any given angle θ, multiplied by the gravitational weight of the ship (displacement), represents the Dynamic Stability. This is the work done in heeling the ship to the angle θ, and it reflects the ship's ability to absorb the energy imparted by external forces such as waves and wind.
The stability of a ship is directly related to the nature and value of its metacentric height (GM).
- Since GM is closely associated with the Righting Lever (GZ) and the angle of heel, the statical stability curve is plotted between GZ and the angle of heel.
Following information obtained from the curve can be used to assess the stability of the ship:
Angle of Equilibrium
- If the GZ curve intersects the horizontal axis (i.e., no righting lever) at the origin, the ship has inherent positive initial stability.
Maximum GZ
- This represents the ship's largest static heeling moment. The Maximum Righting Lever (GZ), when multiplied by the ship's displacement, gives the maximum heeling moment the ship can sustain without capsizing.
Angle of deck Immersion
- The angle at which the ship’s deck becomes submerged. This is often indicated as the point of inflection on the GZ curve, where the ship’s vulnerability to downflooding increases.
Angle of Vanishing Stability
- The angle at which the GZ curve intersects the horizontal axis, indicating the point where the righting lever becomes zero. Any heel beyond this angle results in negative stability, increasing the risk of capsizing.
Range of Stability
- The range is measured from the origin to the angle of vanishing stability, indicating the range of angles over which the ship has positive stability.
Angle of Contraflexure
- The angle of heel up to which the rate of increase of GZ with heel is rising. Beyond this point, while GZ may continue to increase, the rate of increase begins to diminish.
Angle of Downflooding
- The minimum angle of heel at which an external opening (without a watertight appliance) is submerged, allowing seawater ingress.
- (Downflooding refers to seawater entering the hull or superstructure due to heel or immersion of the vessel.)
Initial Metacentric Height (GM)
- At 57.3 (1 radian), an ordinate is drawn at the origin of the GZ curve. A tangent to the curve is extended to intersect this ordinate, providing the value of the Initial Metacentric Height (GM).