Curves of Stat. Stability | List | Free Surface Effetcs | Trim |

**Stability**

*Curves of Statical Stability*

__Load Line requirements for minimum stability
conditions__

The area
under the GZ curve shall not be less than

0.55 m-rad up to an angle of 30°

0.09 m-rad up to an angle of either 40° or the lesser angle at
which the lower edges of any openings which can not be closed weather-tight are
immersed

0.03 m-rad between the angles of heel of 30° and 40° or such
lesser angle as mentioned above

The Righting Lever (GZ) shall be at least
0.20m at an angle of heel equal to or greater than 30°

The maximum
GZ shall occur at an angle of heel of not less than 30°

Initial
transverse metacentric height shall not be less than 0.15m. For ship carrying
timber deck cargo complying with (a), this may be reduced to not less than 0.05
metres.

Curve Of Statical 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 contraflexure – 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).

**GZ Cross Curves of Stability**

To draw the
curve of statical stability, we need GZ values for various angles of heel.

For this we
use the GZ cross curves of stability.

These
curves are provided for an assumed KG, tabulating GZ values for various
displacements and angles of list.

Called
cross curves because the various curves actually ‘cross’ each other.

Since the
curves are plotted for an assumed KG, if the actual KG differs from this a
correction (GG_{1}Sineθ) needs to be applied.

This
correction is positive if the actual KG is less than the assumed KG and
vice-versa.

After
obtaining the GZ values at various angles, the curve of statical stability is
prepared.

KN Cross Curves of Stability

Same as the GZ cross curves and also used to get the GZ values for
making the curve of statical stability.

The only
difference being that here the KG is assumed to be ZERO.

This solves
the problem of a sometimes positive and sometimes negative correction, as now
the correction is always subtracted.

GZ = KN –
KG Sine θ