How stability is judged, how it is calculated, and why “compliant” is not the same as “safe”
Contents
Use the links below to jump to any section:
- Introduction – Criteria Are Minimums, Not Guarantees
- The Three Questions Stability Criteria Are Trying to Answer
- GM – What It Measures and What It Doesn’t
- Calculating GM (Concept and Method)
- Worked Example: Calculate GM and Interpret It
- GZ Curves – What the Shape Really Means
- Righting Moment and Righting Energy
- Key IMO/Intact Stability “Checks” (What They Mean Operationally)
- Why Ships Can Be Compliant and Still Fail
- Practical Bridge/Deck Use – When Officers Must Care
- Professional Stability Mindset
- Closing Perspective
- Knowledge Check – GM & GZ
- Knowledge Check – Model Answers
1. Introduction – Criteria Are Minimums, Not Guarantees
Stability criteria exist because ships have capsized while appearing “fine” right up to the end.
The criteria most officers learn (GM limits, minimum areas under the GZ curve, minimum maximum GZ, minimum range of stability) are not there to make ships comfortable. They exist to ensure the ship has enough righting capability and enough righting energy to survive a realistic disturbance.
But it is essential to understand what criteria are and what they are not.
Criteria define a minimum acceptable condition under assumed scenarios. They do not account for every real-world hazard, and they do not remove the Master’s responsibility to preserve margin.
2. The Three Questions Stability Criteria Are Trying to Answer
Every stability rule, regardless of how complex it looks, is trying to answer three practical questions:
1) Will the ship try to come back upright after being heeled?
That’s basic restoring tendency.
2) How strongly will it come back at small angles?
That’s initial stability (GM behaviour).
3) Does the ship have enough righting energy to survive a larger heel without “running out” of recovery?
That’s the GZ curve: range and area.
If you keep those three questions in mind, the numbers stop being abstract.
3. GM – What It Measures and What It Doesn’t
GM (metacentric height) is primarily a measure of initial stability at small angles of heel.
- A higher GM generally means the ship generates restoring moment quickly at small angles.
- A low GM means the ship is “tender” and may heel easily.
However, GM does not tell you the whole story.
A ship can have:
- “good” GM but poor stability at larger angles (bad GZ curve shape),
- or “low” GM but still have a long, strong GZ curve (survivable overall).
Key operational truth:
GM mostly tells you what happens early in a heel. It does not tell you what happens when things get serious.
4. Calculating GM (Concept and Method)
In intact stability work, GM is often treated as:
GM = KM − KG
Where:
- KM is the height of the metacentre above the keel (from hydrostatic tables; varies with draft)
- KG is the height of the ship’s centre of gravity above the keel (from loading condition calculations)
So the practical method onboard is:
- Determine the ship’s displacement and draft condition
- Obtain KM from hydrostatic data for that draft/displacement
- Calculate KG from weight distribution (or from the loading computer)
- Subtract to obtain GM
Units
KM, KG, and GM are usually in metres.
Why this works
KM is the ship/hull geometry response for the current draft. KG is how high the ship’s weight is concentrated. Their difference is the margin that determines initial restoring behaviour.
5. Worked Example: Calculate GM and Interpret It
Scenario (typical loading condition)
A general cargo ship is loaded and the loading computer/hydrostatics show:
- Displacement condition gives KM = 8.20 m
- Calculated KG = 7.55 m
Step 1 – Calculate GM
GM = KM − KG
GM = 8.20 − 7.55 = 0.65 m
Interpretation
A GM of 0.65 m suggests the ship has moderate initial stability. This does not automatically mean “safe” or “unsafe” — you must compare it to:
- ship’s stability booklet limits for this condition,
- operational needs (windage, deck cargo, expected weather),
- and the GZ curve (overall stability).
What would raise GM?
Lowering KG (ballast low, reducing high weights, reducing free surface).
What would reduce GM?
Raising KG (loading high, slack tanks/free surface, lifting heavy loads on deck).
This is exactly why stability management is weight management.
6. GZ Curves – What the Shape Really Means
The GZ curve plots the righting lever against angle of heel.
It tells you:
- where righting ability starts,
- how it grows,
- where it peaks,
- how quickly it collapses,
- and at what angle it becomes zero again (loss of stability).
A GZ curve is the ship’s “righting budget”.
Key features you must read from a curve
- Initial slope near zero angle (linked to GM)
- Maximum GZ (how strong peak righting lever is)
- Angle of maximum GZ (where the ship is strongest)
- Range of positive stability (how far the ship can heel before losing restoring lever)
A ship with a long positive range and strong area under the curve generally has better survivability than one with a steep slope but short range.
7. Righting Moment and Righting Energy
Righting Moment
Righting moment at any heel angle is:
RM = Δ × GZ
Where:
- RM = righting moment (kN·m or tonne·m depending on units)
- Δ = displacement (weight of the ship)
- GZ = righting lever (m)
Operational meaning:
If displacement is large, even a modest GZ generates huge righting moments. This is why large ships can have very strong righting power — but only if GZ remains positive.
Righting Energy (Area Under the Curve)
The area under the GZ curve between angles represents righting energy available to resist capsizing moments.
Practically, criteria often specify minimum area between:
- 0° and 30°
- 0° and 40°
- 30° and 40°
You don’t usually hand-calculate these onboard (the loading computer does), but you must understand what the “area” means:
It is the ship’s capacity to absorb heeling energy without running out of righting ability.
8. Key IMO/Intact Stability “Checks” (What They Mean Operationally)
Most ships’ stability software checks against IMO intact stability-type criteria (exact values vary by ship type and code).
Operationally, the checks usually involve:
- Minimum GM (or equivalent)
Ensures adequate initial stability and resistance to small-angle heeling. - Minimum maximum GZ
Ensures the ship can generate a strong restoring lever. - Minimum range of stability
Ensures the ship remains stable over a meaningful heel range. - Minimum areas under the GZ curve
Ensures enough righting energy across key angle bands.
These criteria are trying to prevent the classic failure modes:
- too tender to recover early,
- too little righting peak to resist continuing heel,
- stability collapsing too early at moderate angles.
9. Why Ships Can Be Compliant and Still Fail
This is the key professional lesson.
A ship can be compliant and still capsize due to:
- cargo shift (the model assumed no shift)
- progressive flooding (intact criteria no longer apply)
- free surface underestimated or not modelled correctly
- wind gusts combined with roll resonance
- human factors: delayed response, poor ballast discipline
The criteria are built on assumptions. When reality violates assumptions, criteria compliance becomes irrelevant.
Compliance is a baseline. Seamanship is what keeps the ship above baseline.
10. Practical Bridge/Deck Use – When Officers Must Care
Officers must care about GM and GZ not only during cargo planning, but when:
- deck cargo is carried (windage and KG rise)
- tanks are slack (free surface)
- heavy lifts are conducted
- ballast operations are restricted
- heavy weather is expected
- the ship has a list or unusual rolling
These are the moments stability stops being an engineering topic and becomes a navigational safety topic.
11. Professional Stability Mindset
A professional officer does not ask:
“Are we compliant?”
They ask:
“If the weather is worse than expected, if a tank is slacker than we think, if cargo shifts slightly — do we still have energy left?”
That is what the GZ curve is really about: reserve.
12. Closing Perspective
GM is about how quickly the ship reacts.
GZ is about how long the ship can keep reacting before it runs out of righting ability.
Criteria are minimum guardrails, not proof of safety. Your job is to preserve margin above those guardrails through correct loading, ballast discipline, and operational judgement.
13. Knowledge Check – GM & GZ
- What does GM describe physically?
- Why does GM mostly apply to small angles of heel?
- What are KM and KG, and where do they come from?
- How do you calculate GM from hydrostatic data?
- What does the GZ curve represent?
- What does the area under a GZ curve mean in real terms?
- How do you calculate righting moment at a given angle?
- Why can high GM still be dangerous?
- Why can low GM still be survivable in some ships?
- What does “range of positive stability” mean?
- Why is compliance not the same as safety?
- In what operations should bridge officers actively care about stability values?
14. Knowledge Check – Model Answers
- Initial restoring tendency: how strongly the ship resists small heels.
- Because GM relates to the initial slope of the righting lever near zero degrees.
- KM is geometry-based from hydrostatics; KG is weight-distribution-based from loading.
- GM = KM − KG.
- The righting lever available at each heel angle.
- The ship’s righting energy reserve over a heel range.
- RM = Δ × GZ.
- It can cause violent rolling and may hide poor large-angle stability or cargo risks.
- Because overall stability depends on the full GZ curve and range/area, not only initial slope.
- The angle band over which GZ remains positive before becoming zero.
- Because criteria assume intact conditions and no shifts/flooding; reality can violate assumptions.
- Heavy weather, slack tanks, deck cargo, heavy lifts, ballast restrictions, abnormal rolling/list.