Statical stability curve. (GZ curve)

Minimum stability requirements (as to the date)

Having a positive GM value alone is not sufficient.

 The minimum stability criteria for cargo ships as per the Load Line Convention

1. The area under the curve of righting lever (GZ curve) shall be not less than, 
1. 0.055 meter radians up to an angle of 30°
2. 0.09 meter radians up to an angle of 40° or the angle at which lower edges of any openings in the hull,superstructure or deck house which cannot be closed watertight, are immersed if that angle be less
3. 0.03 meter radians between 30° and 40° or the angle referred above

  2. The righting lever (GZ) should be 0.20m at an angle of heel equal to greater than 30°.
  3. The maximum righting lever (GZ) should occur at an angle of heel not less than 30°.
  4. The transverse meta-centric (GM) height should not be less than 0.15m.

IMO recommended general criteria for cargo ships  (IS code 2008)

(The only difference from the Load line rules above is that the maximum righting lever should occur at angle of heel not less than 25°. Others are the same.)

1. The area under the curve of righting lever (GZ curve) shall be not less than, 
1. 0.055 meter radians up to an angle of 30°
2. 0.09 meter radians up to an angle of 40° or the angle of down flooding if that angle be less
3. 0.03 meter radians between 30° and 40° or the angle referred above
   

  2. The righting lever (GZ) should be 0.20m at an angle of heel equal to greater than 30°.
  3. The maximum righting lever (GZ) should occur at an angle of heel not less than 25°. If this is not practicable, an alternative criteria based on an equalant level of safety may be applied to the approval of the administaration.
  4. The transverse meta-centric (GM) height should not be less than 0.15m.

 

 

 

Statical stability curve. (GZ curve)

Introduction

The Statical stability curve or the GZ curve is drawn by plotting the GZ values against the angle of heel. It is drawn for each voyage condition for a particular displacement and KG.

Illustration 1: GZ curve - Source - http://thenauticalsite.com/NauticalNotes/Stability/MyStability-Lesson06-CurvesofStatStab.htm

 Following data can be extracted from a GZ curve,

1. Initial metacentric height (GM). Its the point of intersection when a tangent drawn at the origin and the purpendicular at 57.3° or 1 radian meets. The scale on the GZ shows the value of initial GM.
2. Point of contra fexture. Point of Contra flexture means the point on the curve where the direction of bending. Angle of heel at this point represents the angle of deck edge immersion (DEI).
3. Maximum GZ and the angle of heel it occurs.
4. The range of piositive stability.
5. Angle of of vanishing stabitlity.
6. The moment of stability for a given angle of heel. (GZ x Displacement = FLM)
7. The dynamical stability for a given angle of heel. (Dynamical stability at Ɵ° = Ship's displacement in tonnes (W) x Area between the GZ curve and the baseline upto the angle of heel in im meter-radians. (A))