• Intact Stability: The stability of a sound, undamaged hull structure with all internal compartments, cargo holds, and double bottoms free of sea water flooding under designed cargo, fuel, and ballast conditions;
• Damage Stability: The survival capacity of a compromised hull following underwater breach or compartment flooding, evaluating residual buoyancy, asymmetric heel angles, progressive downflooding, and final waterline equilibrium (to verify draft and trim marks, refer to our operational guide on under keel clearance calculation).

Damage stability scenarios cannot be evaluated without an accurate understanding of intact statics. Correct bridge stability calculations on every commercial voyage determine whether a vessel safely withstands heavy weather, adhering to principles detailed in Basic Ship Theory.

The Four Reference Points of Ship Hydrostatics: K, B, G, and M

The geometric foundation of transverse intact stability relies on the relative vertical positioning of four fundamental points referenced from the molded baseline (keel plate — K):

The Three States of Equilibrium: Righting and Capsizing Moments

Depending on the vertical relationship between the Center of Gravity (G) and the Transverse Metacenter (M), a floating ship demonstrates one of three equilibrium conditions:

1. Stable Equilibrium (GM > 0, Positive Metacentric Height)

Stable equilibrium exists when the Center of Gravity G lies vertically below the transverse metacenter M (KG < KM). When an external moment heels the vessel to an angle θ, the center of buoyancy shifts outward from B to B₁.

Fig. 1. Stable equilibrium: The lateral separation between weight and buoyancy vectors forms positive righting lever GZ.

Because point G is below M, the upward buoyant force acting through B₁ passes to the low side of the downward gravity vector. The horizontal distance separating these opposing vectors is the righting lever (GZ), producing a Righting Moment (M_righting):

This couple acts to rotate the vessel back toward the upright position once the external force ceases. The ship is stable.

2. Neutral Equilibrium (GM = 0, Zero Stability)

Neutral equilibrium occurs when the vertical position of G coincides with metacenter M (KG = KM). As the hull heels, the line of action of the buoyant force passes directly through the center of gravity.

Fig. 2. Neutral equilibrium: The righting lever GZ remains zero throughout small angles of heel.

Because there is no horizontal separation between the vectors, GZ is zero. Neither a righting moment nor an upsetting moment is generated. If heeled by a gust of wind, the ship comes to rest at the new heel angle without attempting to right itself.

Fig. 3. A floating cylindrical log is a textbook example of neutral equilibrium: its center of buoyancy and metacenter coincide with its rotational axis.

3. Unstable Equilibrium (GM < 0, Negative Initial Stability)

Unstable equilibrium occurs when the Center of Gravity G rises above the metacenter M (KG > KM). This hazardous condition can arise from high deck cargo stowage, topside ice accumulation, or cargo shift.

Fig. 4. Unstable equilibrium: An upsetting couple develops, driving the hull toward capsizing.

When heeled, the line of buoyant force passes inside the line of gravity, generating a negative righting arm (capsizing lever −GZ). Rather than righting itself, the ship heels further until the submerged hull flare increases the waterplane area enough to push metacenter M above G (reaching the Angle of Loll), or capsizes entirely.

Stability Hazard: Free Surface Effects and the GZ Curve

Initial metacentric height GM is reliable only for small inclinations (up to 10–12°), where metacenter M remains virtually stationary on the centerline. For larger angles, naval architects evaluate the GZ Curve (Curve of Statical Stability), plotting righting arms across the full range of heel up to the angle of vanishing stability.

IMO 2008 Intact Stability Code Mandatory Criteria:

• Fluid metacentric height (GM_fluid) corrected for free surfaces must not be less than 0.15 m for general cargo ships (and not less than 0.10 m for timber deck cargo carriers);
• The maximum righting arm (GZ_max) must occur at a heel angle preferably exceeding 30°, but never less than 25°;
• The righting lever GZ must be at least 0.20 m at an angle of heel equal to or greater than 30°;
• The area under the GZ curve must be at least 0.055 meter-radians up to 30°, and at least 0.090 meter-radians up to 40°.

Test shipboard parameters dynamically using our online Ship Stability Simulator (GZ Curve).

Longitudinal Stability: Why Vessels Do Not Pitchpole

While the earlier sections focused on transverse stability (rolling around the longitudinal axis), vessels are also subjected to fore-and-aft trimming moments caused by longitudinal weight movements:

Fig. 5. Longitudinal weight shift: Shifting weight aft moves G to G₁, trimming the vessel by the stern and shifting the center of buoyancy from B to B₁.

During pitch motions and trim changes, rotation occurs about the longitudinal metacenter (M_L). The vertical distance between the Center of Gravity and the longitudinal metacenter is the longitudinal metacentric height (GM_L).

Because a ship’s length is 6 to 8 times greater than its breadth, the longitudinal second moment of area of the waterplane is immense. As a result, GM_L is typically 100 to 120 times larger than transverse GM. Under normal operations, commercial vessels cannot capsize end-over-end (pitchpole), which is why shipboard stability control concentrates almost entirely on transverse stability.

Explore how hydrodynamic hull lines affect displacement in our review of the Block Coefficient of a ship, calculate dynamic draft margins using the Ship Squat Calculator, and evaluate freshwater immersion with our DWA / FWA Calculator Online.