Angle of vanishing stability

The angle of vanishing stability is the smallest positive angle where the GZ curve crosses the GZ=0 axis with negative slope.

Angle of vanishing stability with heeling arm curve

The angle of vanishing stability with a given heeling arm is the smallest positive angle where the GZ curve crosses the heel arm curve and where the GZ-Heel Arm curve has negative slope.

Downflooding angle

The downflooding angle is the smallest positive angle at which a downflooding point becomes immersed.

Equilibrium angle

The equilibrium angle is the angle closest to zero where the GZ curve crosses the GZ=0 axis with positive slope.

Equilibrium angle with heeling arm curve

The equilibrium angle with a given heeling arm is the angle closest to zero where the GZ curve crosses the heel arm curve where the GZ-Heel Arm curve has positive slope.

First peak in GZ curve

In some cases, the GZ curve may have multiple peaks; this often occurs if the vessel has a large watertight cabin. The angle of the first peak is the lowest positive angle at which a local maximum in the GZ curve occurs.

GM_L or GM_T

Vertical separation of the longitudinal or transverse metacentre and centre of gravity. The location of the metacentre is computed from the water-plane inertia, not the slope of the GZ curve. Note that the centre of gravity used is the upright centre of gravity corrected by the free surface moments of partially filled tanks in their upright condition, rotated to the specified heel (and trim) angle.

GZ Curve

The curve of vessel righting arm (GZ) plotted against vessel heel angle

Heeling arm curve

A curve of heeling lever, which is superimposed on the GZ curve. This is typically used to assess the effects of external heeling moments, which are applied to the vessel. These include the effects of wind, passenger crowding, centripetal effects of tuning, etc. Depending on the moment that they represent, the heeling arm curves will have different shapes.

The heeling arms are never allowed to be negative; if the cos function goes negative, the heeling arm is made zero. If the heeling arm has a power of cos greater than zero, the heeling arm is forced to be zero at heel angles greater than 90° and less than -90°.

Maximum GZ

Positive angle at which the value of GZ is a maximum

Maximum GZ above heeling arm curve

Positive angle at which the value of (GZ - heel arm) is a maximum