What does GZ represent?

GZ is the righting lever (in metres) — the horizontal distance between the line of action of the ship's weight (through G, the centre of gravity) and the buoyancy force (through B, the centre of buoyancy) when the ship is heeled to a given angle. A positive GZ means the ship tends to return upright; the greater the GZ, the stronger the righting moment. Righting moment = GZ × displacement (t·m).

What are the IMO IS Code 2008 minimum GZ criteria?

Resolution MSC.267(85) requires: (1) area under GZ curve from 0° to 30° ≥ 0.055 m·rad; (2) area from 0° to 40° (or to the angle of downflooding if less) ≥ 0.090 m·rad; (3) area between 30° and 40° ≥ 0.030 m·rad; (4) GZ at 30° heel ≥ 0.200 m; (5) maximum GZ occurs at a heel angle ≥ 25°; (6) initial GM₀ (metacentric height) ≥ 0.150 m.

What is dynamical stability?

Dynamical stability is the work done in heeling the ship to a given angle, equal to the area under the GZ curve up to that angle multiplied by the ship's displacement. It represents the energy that must be removed (by waves, wind, or cargo shift) to capsize the vessel. The IMO criteria for areas under the GZ curve are essentially dynamical stability criteria expressed in m·rad.

What is the severe wind and rolling criterion?

IMO IS Code weather criterion (Resolution MSC.267(85) Reg 2.3): the ship must withstand a combination of beam wind at 26 m/s (wind heeling lever lw2) and rolling from the windward side. The residual area b (between the wind heeling arm and GZ curve, from the static wind heel angle to the angle of downflooding or 50°) must be ≥ area a (from 0° to the angle of roll to windward). This criterion is critical for container ships and vessels with high windage.

GZ curve — intact stability

The GZ righting arm curve (also called the statical stability curve or LS curve) plots the righting lever GZ against the angle of heel from 0° to 90°. It is the fundamental tool for assessing a ship's intact stability under the IMO International Code on Intact Stability 2008 (IS Code), adopted by Resolution MSC.267(85) and made mandatory under SOLAS Chapter II-1.

Key features of the GZ curve

· At small angles, GZ ≈ GM₀ × sin θ; so the initial slope of the curve is determined by the metacentric height GM₀.
· The maximum GZ (GZ max) and the angle at which it occurs define the vessel's peak righting ability.
· The angle of vanishing stability (AVS) is where the GZ curve crosses zero again after the maximum; beyond this the ship cannot self-right.
· Angle of downflooding (θf) is where an opening (hatch, air pipe, ventilator) would submerge; the GZ criteria apply up to θf if θf < 40°.
· Negative GZ at any loading condition indicates loll — the ship heels to a position of false equilibrium; corrective ballasting is required immediately.

IMO IS Code 2008 criteria (MSC.267(85))

· Area 0°–30° ≥ 0.055 m·rad.
· Area 0°–40° (or θf) ≥ 0.090 m·rad.
· Area 30°–40° (or θf) ≥ 0.030 m·rad.
· GZ at 30° ≥ 0.200 m.
· Angle of maximum GZ ≥ 25°.
· GM₀ ≥ 0.150 m (initial metacentric height after free-surface correction).
· All criteria must be met simultaneously at every loading condition in the approved stability booklet.

Severe wind and rolling criterion

· Wind heeling lever lw1 (steady wind, 26 m/s) causes static heel angle θ1; lw2 = 1.5 × lw1 (gust).
· Rolling amplitude θr is calculated from empirical formula based on B (beam), d (draft), GM, and the bilge keel area.
· Area b (residual righting area under wind gust arm from θ2 to θf or 50°) must ≥ Area a (from θ1 − θr to θ1).
· High-windage vessels (car carriers, RoRo, container ships) frequently govern their GM₀ requirement through this criterion rather than the simple area criteria.

Free-surface effect and the stability booklet

· Free surfaces in partially filled tanks reduce the effective GM₀ by the free-surface moment (FSM) / displacement.
· FSM = ρ × l × b³ / 12 for rectangular tanks; tabulated for all tanks in the stability booklet at 10% increments.
· The stability booklet (approved by the flag State) contains GZ curves for all mandatory loading conditions — departure, arrival, ballast, heavy ballast, homogeneous cargo.
· Officers must load to a condition that meets or exceeds booklet criteria; any deviation requires recalculation on the ship's approved loading instrument (stability computer).

Sources: IMO International Code on Intact Stability 2008 (IS Code, Resolution MSC.267(85)); SOLAS Chapter II-1, Part B — Subdivision and stability; IMO IS Code explanatory notes (MSC.1/Circ.1281). See also metacentric height (GM), angle of loll, loading instrument.

GZ curve — intact stability

Key features of the GZ curve

· At small angles, GZ ≈ GM₀ × sin θ; so the initial slope of the curve is determined by the metacentric height GM₀.

· The maximum GZ (GZ max) and the angle at which it occurs define the vessel's peak righting ability.

· The angle of vanishing stability (AVS) is where the GZ curve crosses zero again after the maximum; beyond this the ship cannot self-right.

· Angle of downflooding (θf) is where an opening (hatch, air pipe, ventilator) would submerge; the GZ criteria apply up to θf if θf < 40°.

· Negative GZ at any loading condition indicates loll — the ship heels to a position of false equilibrium; corrective ballasting is required immediately.

IMO IS Code 2008 criteria (MSC.267(85))

· Area 0°–30° ≥ 0.055 m·rad.

· Area 0°–40° (or θf) ≥ 0.090 m·rad.

· Area 30°–40° (or θf) ≥ 0.030 m·rad.

· GZ at 30° ≥ 0.200 m.

· Angle of maximum GZ ≥ 25°.

· GM₀ ≥ 0.150 m (initial metacentric height after free-surface correction).

· All criteria must be met simultaneously at every loading condition in the approved stability booklet.

Severe wind and rolling criterion

· Wind heeling lever lw1 (steady wind, 26 m/s) causes static heel angle θ1; lw2 = 1.5 × lw1 (gust).

· Rolling amplitude θr is calculated from empirical formula based on B (beam), d (draft), GM, and the bilge keel area.

· Area b (residual righting area under wind gust arm from θ2 to θf or 50°) must ≥ Area a (from θ1 − θr to θ1).

· High-windage vessels (car carriers, RoRo, container ships) frequently govern their GM₀ requirement through this criterion rather than the simple area criteria.

Free-surface effect and the stability booklet

· Free surfaces in partially filled tanks reduce the effective GM₀ by the free-surface moment (FSM) / displacement.

· FSM = ρ × l × b³ / 12 for rectangular tanks; tabulated for all tanks in the stability booklet at 10% increments.

· The stability booklet (approved by the flag State) contains GZ curves for all mandatory loading conditions — departure, arrival, ballast, heavy ballast, homogeneous cargo.

· Officers must load to a condition that meets or exceeds booklet criteria; any deviation requires recalculation on the ship's approved loading instrument (stability computer).