A cargo planner does not need to be a naval architect, but should understand how every container, deck cargo item or tonne of ballast changes a ship's stability. This guide explains intact stability in practical terms, from displacement and centre of gravity to the GZ curve and the general criteria of the IS Code 2008. GM gets its own deep dive in metacentric height (GM) explained.
The terms you need
| Term | Meaning | Where the number comes from |
|---|---|---|
| Displacement (Δ) | Total weight of the ship and everything on board, equal to the weight of water displaced | Lightship + cargo + tanks |
| K | Keel point, the datum for heights | Ship's baseline |
| G, KG | Centre of gravity and its height above the keel | Moment calculation |
| B | Centre of buoyancy, the centre of the underwater volume | Hull form and draft |
| M, KM | Metacentre and its height above the keel | Hydrostatic tables at the draft |
| GM | Metacentric height, GM = KM − KG | Calculation |
| GZ | Righting lever at a given heel angle | Cross curves (KN) and KG |
Weight acts down through G and buoyancy acts up through B. When the ship heels, B moves towards the immersed side. The horizontal distance between the two lines of force is GZ, and the righting moment is Δ × GZ. When M is above G (positive GM), that moment brings the ship back upright.
Building a loading condition step by step
Every loading condition is worked out in the same order, whether by the ship's loading computer or by shore-side planning software:
- Lightship weight and centre of gravity from the stability booklet.
- Constants and tanks: fuel, fresh water, ballast, lube oil, stores and crew.
- Cargo: each container or item with its weight and vertical (VCG), longitudinal (LCG) and transverse (TCG) centre of gravity.
- Sum up: Δ = Σw and KG = Σ(w × VCG) / Σw. The same for LCG and TCG.
- Read the hydrostatics at that displacement: drafts, KM, LCB, LCF, TPC and MTC.
- Work out GM, trim and drafts, then the GZ curve with GZ = KN − KG × sin θ.
- Compare with the stability criteria and the longitudinal strength limits.
Conditions are calculated for departure, arrival and the worst intermediate stage, because fuel and water are consumed on passage and free surface changes. Trim and drafts are covered in ship trim and draft.
Worked example: a loading condition
Illustrative feeder, not a real ship. Hydrostatic values are assumed to come from its stability booklet.
| Item | Weight (t) | VCG (m) | Moment (t·m) |
|---|---|---|---|
| Lightship | 6,500 | 7.20 | 46,800 |
| Fuel and fresh water | 900 | 3.00 | 2,700 |
| Ballast | 1,600 | 1.50 | 2,400 |
| Containers in holds | 5,000 | 5.40 | 27,000 |
| Containers on deck | 4,000 | 14.50 | 58,000 |
| Total | 18,000 | 136,900 |
- KG = 136,900 / 18,000 = 7.61 m.
- From the hydrostatic tables at Δ 18,000 t: KM = 8.90 m.
- Solid GM = 8.90 − 7.61 = 1.29 m.
- Total free surface moments are 2,700 t·m, so the free surface correction (FSC) = 2,700 / 18,000 = 0.15 m.
- Fluid GM = 1.29 − 0.15 = 1.14 m.
At small angles GZ ≈ GM × sin θ. At 5°, GZ ≈ 1.14 × 0.087 = 0.10 m, so the righting moment is about 18,000 × 0.10 = 1,800 t·m. That shortcut fails at larger angles, where cross curves are used. At 30°, for example, with KN 4.55 m from the cross curves and a corrected KG of 7.76 m, GZ = 4.55 − 7.76 × 0.5 = 0.67 m.
You can repeat the combined KG calculation with the combined centre of gravity tool and the basic GM check with the GM calculator.
Free surface: the invisible enemy
In a partly filled tank the liquid flows to the low side as the ship heels. The effect is the same as raising the centre of gravity. It is calculated from each tank's free surface moment (FSM), which is the moment of inertia of the liquid surface times the liquid density, divided by displacement.
For a rectangular tank the transverse moment of inertia is length × breadth³ / 12. Breadth is cubed, so wide tanks matter far more than narrow ones. Example: a 15 m × 10 m fuel tank with density 0.95 t/m³ gives FSM = 15 × 1,000 / 12 × 0.95 ≈ 1,190 t·m, roughly 0.07 m off GM at Δ 18,000 t. Full or empty tanks have almost no free surface.
Good practice: keep the number of slack tanks low, and allow for the largest free surface expected during the voyage, not only the one at departure.
IS Code 2008 intact stability criteria
SOLAS Chapter II-1 requires approved stability information on board, and Part A of the IS Code 2008 sets the mandatory criteria. Conceptually the general criteria judge the shape of the GZ curve, not a single number:
| General criterion (concept summary) | Minimum |
|---|---|
| Area under the GZ curve up to 30° | 0.055 m·rad |
| Area up to 40° (or the downflooding angle if smaller) | 0.090 m·rad |
| Area between 30° and 40° (or the downflooding angle) | 0.030 m·rad |
| GZ at an angle of 30° or more | 0.20 m |
| Angle of maximum GZ | not less than 25° |
| Initial GM after free surface correction | 0.15 m |
There is also a weather criterion (severe wind and rolling) and additional provisions for certain ship types. This summary is for understanding the concept; the official text is the IMO IS Code, and the limits that apply to your ship are in its stability booklet, often presented as a minimum GM or maximum KG curve against draft.
Common mistakes in stability work
- Using KM for the wrong draft. KM changes with draft; any large change in loading means reading the hydrostatic tables again.
- Forgetting the free surface correction. Solid GM may look comfortable, but fluid GM is what is judged against the criteria.
- Relying on GM alone. Adequate GM does not guarantee the GZ curve meets the minimum areas, especially on ships with low freeboard or a low downflooding angle.
- Careless container VCGs. Many systems assume a container's centre of gravity at mid-height or at a fixed fraction of it. Heavy cargo concentrated on the container floor makes reality slightly different.
- Checking departure only. The arrival condition, with fuel tanks nearly empty and ballast moved, can be the worst case.
- Too much GM. Excess stability makes the ship roll quickly and violently, which raises lashing forces on deck containers. The upper end deserves attention too.
The planner, the loading computer and shore software
A planner should meet the criteria with a sensible margin, not right at the limit. VGM errors, assumed container VCGs and unrecorded tank contents can move KG by several centimetres. Besides stability, every condition must also stay within the shear force and bending moment limits; see shear force and bending moment.
STOWAGE.ID Vessel Stowage calculates loading conditions and GZ curves from shore as planning and decision support. The vessel's class-approved loading computer (see IACS UR L5) and stability booklet remain the official reference. How the two fit together is explained in loading computer vs shore-side planning.