GZ curves of stability

• Graph where GZ is plotted against the angle of heel.
• Drawn for each voyage condition by the ship’s officer.
• This curve is for a particular displacement and KG.

From this curve it is possible to ascertain the following:

• Initial metacentric height – point of intersection of the tangent drawn to the curve at the initial point and a vertical through the angle of heel of 57.3° (1 radian)
• Angle of contra flexure – the angle of heel up to which the rate of increase of GZ with heel is increasing. Though the GZ may increase further, the rate of increase of GZ begins to decrease at this angle.
• The range of stability – where all GZ values are positive.
• The maximum GZ lever & the angle at which it occurs.
• The angle of vanishing stability – beyond which the vessel will capsize.
• The area of negative stability.
• The moment of statical stability at any given angle of heel (GZ x Displacement of the ship).
• The moment of dynamical stability – work done in heeling the ship to a particular angle.

Dynamical stability at è = 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).
 
Assumption:

• The ship's center of gravity does NOT change position as the angle of heel is changed.
• The ship's center of buoyancy is always at thegeometric center of the ship's underwater hull
• The shape of the ship's underwater hull changesas the angle of heel changes.