Vessel Stability — Metacentric Height, Free Surface, and Intact Righting Energy
TL;DR — A vessel must maintain a minimum initial GM of 1.15 ft (0.35 m) in every condition of loading, and free surface effect in partially filled tanks must be accounted for as a virtual rise in the vessel's center of gravity. The master is legally responsible for verifying compliance before departure. 46 CFR §28.570 46 CFR §28.540 46 CFR §185.315
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What the Rule Says
Metacentric Height (GM) — The Minimum Standard
The metacentric height (GM) is the distance between the vessel's center of gravity (G) and the transverse metacenter (M). A positive GM means the vessel will develop a righting moment when heeled; a negative GM means it will capsize to the angle of loll.
Federal regulations establish hard minimums. In each condition of loading, a vessel must have: 46 CFR §28.570
- An initial GM of at least 1.15 feet (0.35 meters) 46 CFR §28.570
- A righting arm (GZ) of at least 0.66 feet (0.2 meters) at an angle of heel not less than 30° 46 CFR §28.570
- A maximum righting arm occurring at an angle of heel not less than 25° 46 CFR §28.570
- Positive righting arms through 60° of heel, except where the alternate provisions of 46 CFR §28.570(b) apply, in which case positive righting arms must extend to at least 50° 46 CFR §28.570
Area Under the Righting Arm Curve (Righting Energy)
The area under the GZ curve represents the vessel's reserve of dynamic stability — its ability to absorb energy from waves and wind without capsizing. The regulation specifies three separate area requirements: 46 CFR §28.570
| Range of Heel | Minimum Area | |---|---| | 0° to the lesser of 40° or downflooding angle | 16.9 foot-degrees (0.090 m-rad) | | 0° to 30° | 10.3 foot-degrees (0.055 m-rad) | | 30° to the lesser of 40° or downflooding angle | 5.6 foot-degrees (0.030 m-rad) |
All three criteria must be satisfied simultaneously in every loading condition. Note that righting arms must be calculated assuming the vessel trims freely at each angle of heel until the trimming moment is zero. 46 CFR §28.570
Free Surface Effect — The Virtual Rise in G
When a tank is partially filled, the liquid inside shifts as the vessel heels. This shift creates a moment that acts exactly as if the vessel's center of gravity had risen — a phenomenon called the free surface effect. The regulation treats this as a virtual rise in the vessel's vertical center of gravity (VCG). 46 CFR §28.540
The rules for accounting for free surface are specific:
For consumable liquids (fuel, water, lube oil): calculate the maximum free surface effect of the single tank — or transverse pair of tanks — having the greatest free surface effect, plus a correction for service tanks. 46 CFR §28.540
For non-consumable liquids and fish products: calculate the free surface effect of every partially filled tank or hold containing liquid that is not a consumable, or fish/fish products that can shift as the vessel heels. This includes loose water associated with fish processing. 46 CFR §28.540
Cross-connected tanks: if tanks are fitted with cross-connection piping, they must be treated as a single common tank for free surface calculations — unless valves are installed that will be kept closed to prevent liquid transfer as the vessel heels. 46 CFR §28.540
Calculation method: the moment of transference method may be used in lieu of the inertia method. 46 CFR §28.540
The practical consequence: free surface effect reduces effective GM. A vessel with several slack tanks may have a calculated GM that meets the 1.15 ft minimum on paper, but after applying free surface corrections, the corrected GM (GM fluid) may fall below the threshold. 46 CFR §28.570 46 CFR §28.540
Downflooding Angle — A Critical Limiting Factor
The downflooding angle is defined as the static angle from the intersection of the vessel's centerline and the waterline in calm water to the first opening that cannot be closed weathertight and through which downflooding can occur. 46 CFR §28.510
Downflooding itself is defined as the entry of seawater through any opening into the hull or superstructure of an undamaged vessel due to heel, trim, or submergence. 46 CFR §28.510
The downflooding angle caps the range over which righting energy is measured. If a vessel's downflooding angle is, say, 35°, then the area requirements are measured only to 35°, not to 40°. This makes vessels with low freeboard or open hatches more vulnerable to failing the area criteria. 46 CFR §28.570
Icing Allowances
Vessels operating north of 42°N between November 15 and April 15, or south of 42°S between April 15 and November 15, must include ice accumulation in their stability calculations. 46 CFR §28.550
For operations north of 66°30'N or south of 66°S, the assumed ice loading is: 46 CFR §28.550
- 6.14 lb/ft² (30 kg/m²) on horizontal projected areas (equivalent to 1.3 inches / 33 mm thickness)
- 3.07 lb/ft² (15 kg/m²) on vertical projected areas (equivalent to 0.65 inches / 16.5 mm thickness)
For operations between 42° and 66°30'N (or equivalent south), use one-half of those values. 46 CFR §28.550
Small discontinuous surfaces such as rails, spars, and rigging without sail may be accounted for by increasing the calculated projected area by 15 percent. 46 CFR §28.550
Ice accumulation raises the vessel's center of gravity and increases topside weight, both of which reduce GM and righting energy. The weight and location of ice must be included in every loading condition calculation. 46 CFR §28.550
Lifting Gear and Fishing Gear
When a vessel lifts a weight over the side or uses fishing gear (trawls, seines) that can impose an overturning moment, additional stability criteria apply if the maximum heeling moment exceeds the threshold: 0.67 × W × GM × (F/B). 46 CFR §28.545
Where W is displacement including the lifted weight, GM is the metacentric height with that weight included, F is freeboard to the lowest weather deck at amidships, and B is maximum beam. 46 CFR §28.545
When this threshold is exceeded, the vessel must have at least 15 foot-degrees (0.080 m-rad) of area under the corrected righting arm curve (reduced to 10 foot-degrees / 0.053 m-rad for protected waters operations). The angle of intersection of the heeling arm curve and the righting arm curve must not exceed 10°. 46 CFR §28.545
The weight of a suspended load is assumed to act at the tip of the boom unless transverse movement is restricted (e.g., by sideboards). 46 CFR §28.545
Master's Responsibility Before Departure
The master bears direct legal responsibility for stability compliance. After loading and prior to departure — and at all other times necessary to assure safety — the master must determine that the vessel complies with all applicable stability requirements in the trim and stability book, stability letter, Certificate of Inspection, and Load Line Certificate. The vessel may not depart until it is in compliance. 46 CFR §185.315
In making this determination, the master must account for the total weight of passengers, crew, and all variable loads. 46 CFR §185.315
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Why It Matters on the Exam
Exam questions on this topic typically test three things:
1. Numerical thresholds. Know the minimum GM (1.15 ft / 0.35 m), the minimum GZ at 30° (0.66 ft / 0.2 m), the angle at which maximum GZ must occur (not less than 25°), and the three area-under-the-curve values. These numbers appear directly in multiple-choice questions. 46 CFR §28.570
2. Free surface mechanics. Questions will ask what happens to GM when tanks are slack, what happens when cross-connected tanks are not valved off, and which tanks must be included in the calculation. The key concept: free surface acts as a virtual rise in G, reducing effective GM. 46 CFR §28.540
3. Master's duty. Questions about who is responsible for verifying stability before departure, and what documents govern that determination, point directly to 46 CFR §185.315. 46 CFR §185.315
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Common Pitfalls
Confusing GM with GZ. GM is the initial metacentric height — a measure of initial stability. GZ is the righting arm at a specific angle of heel — a measure of stability at that angle. The exam tests both, and they are not interchangeable.
Forgetting the downflooding angle cap. Candidates often apply the 40° cutoff to the area calculations without checking whether the vessel's downflooding angle is less than 40°. The rule uses the lesser of 40° or the downflooding angle. 46 CFR §28.570
Treating all tanks the same for free surface. For consumables, only the worst-case tank (or pair) is used. For non-consumables and fish products, every partially filled tank must be included. Cross-connected tanks without closed valves are treated as one large tank — a significant penalty. 46 CFR §28.540
Ignoring icing season and latitude thresholds. The icing requirement triggers at 42°N (or 42°S), not at the Arctic Circle. The full ice loading applies above 66°30'N; half-loading applies between 42°N and 66°30'N. 46 CFR §28.550
Assuming the boom tip rule does not apply. When a load is suspended from a boom, its weight is assumed to act at the boom tip — not at the hook or the deck — unless transverse movement is restricted. This raises the effective heeling moment significantly. 46 CFR §28.545
Overlooking the master's pre-departure obligation. The master cannot delegate the responsibility to verify stability compliance. The vessel may not depart until compliance is confirmed. 46 CFR §185.315
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Quick Check
What is the minimum initial GM required in each condition of loading?
1.15 feet (0.35 meters). 46 CFR §28.570
What is the minimum righting arm (GZ) required at 30° of heel?
At least 0.66 feet (0.2 meters). 46 CFR §28.570
At what minimum angle of heel must the maximum righting arm occur?
Not less than 25° (0.44 radians). 46 CFR §28.570
What is the minimum area under the righting arm curve from 0° to the lesser of 40° or the downflooding angle?
16.9 foot-degrees (0.090 meter-radians). 46 CFR §28.570
How does free surface effect change a vessel's stability, and what is the regulatory treatment?
Free surface effect causes a virtual rise in the vessel's vertical center of gravity, reducing effective GM. Regulations require this to be calculated as a correction to VCG in all loading conditions. For consumables, use the worst-case tank or pair; for non-consumables and fish products, include every partially filled tank. Cross-connected tanks without closed valves are treated as one common tank. 46 CFR §28.540
A vessel operates north of 42°N but south of 66°30'N in winter. What ice loading must be assumed on horizontal surfaces?
One-half of the full value, which equals 3.07 lb/ft² (15 kg/m²) on horizontal projected areas. 46 CFR §28.550
Who is responsible for verifying stability compliance before departure, and what is the consequence of non-compliance?
The master is responsible. The vessel may not depart until it is in compliance with all applicable stability requirements in the trim and stability book, stability letter, Certificate of Inspection, and Load Line Certificate. 46 CFR §185.315
When a weight is suspended from a boom, where is its weight assumed to act for stability calculations?
At the tip of the boom, unless the suspended load's transverse movement is restricted (e.g., by sideboards). 46 CFR §28.545