Key Stability Terms: K, B, G, M, GM
Stability analysis uses a vertical hierarchy of reference points from keel (K) to metacenter (M). Understanding where each point is and what moves it is the foundation of every exam stability question.
The lowest point of the vessel's hull structure. All vertical measurements in stability calculations are taken from K upward. The keel is the reference baseline.
K is always the lowest reference point. KG = height of center of gravity above keel; KB = height of center of buoyancy above keel.
The geometric center of the underwater volume of the hull. Buoyancy acts upward through B. As the vessel heels, B shifts toward the low side — this shift creates the righting force.
B moves in the direction of heel. When B shifts outboard of G, the vessel has positive righting moment and will return upright.
The point through which all the vessel's weight acts downward. G moves up when weight is added high; G moves down when weight is added low. G is fixed by the loading condition — it does not move when the vessel heels.
Low G = stable. High G = tender (tippy). G is the variable you control through loading decisions.
The point where a vertical line through the shifted center of buoyancy (when heeled at small angles) intersects the vessel's centerline. M is approximately fixed for small angles of heel and is determined by hull geometry.
M is above G in a stable vessel. M is fixed by the hull form — the captain cannot change it through loading.
The vertical distance from G to M. GM = KM − KG. Positive GM means M is above G (stable). Negative GM means G is above M (unstable — vessel will capsize). GM is the primary measure of initial stability.
GM > 0: stable. GM = 0: neutral (barely upright). GM < 0: unstable, will capsize. High GM = stiff. Low GM = tender.
Positive, Neutral & Negative Stability
The sign of GM determines whether a vessel will survive a heel or capsize. This is the single most important stability concept on the exam.
M is above G. When the vessel heels, the upward buoyancy force acts outboard of the downward gravity force, creating a righting moment that returns the vessel to upright.
- • Vessel returns to upright after heel
- • Positive righting arm (GZ > 0)
- • High GM = stiff, snappy roll
- • Low positive GM = tender, slow roll
M and G are at the same point. The vessel has no righting moment — it will remain at whatever angle it is placed. Any perturbation may cause it to take on a list.
- • No righting or capsizing moment
- • Unstable equilibrium — any heel is permanent
- • Dangerous: one wave or wind gust tips it
- • Correct immediately by lowering G
G is above M. When the vessel heels, gravity acts outboard of the buoyancy force, creating a capsizing moment. The vessel will not return upright — it will capsize.
- • Vessel will capsize without intervention
- • Negative righting arm (GZ < 0)
- • Emergency: remove topside weight immediately
- • Caused by overloading high or free surface effect
What Raises G and What Lowers G
The captain controls stability through loading decisions. Every action either raises or lowers the center of gravity. Know this table — the exam builds questions directly from it.
Actions that LOWER G (improve stability)
Actions that RAISE G (reduce stability)
Free Surface Effect
Free surface effect is one of the most heavily tested stability concepts on the OUPV exam. Understand the mechanism — not just the definition.
The Mechanism
In a partially filled tank, liquid can shift freely as the vessel heels. When the vessel heels to starboard, the liquid flows to the low (starboard) side.
This liquid shift acts exactly like moving a weight from the centerline to the starboard side — it raises the effective center of gravity (G) vertically. A raised G means reduced GM.
The mathematics treat free surface effect as a virtual rise in G equal to:GG₁ = (ρ_liquid × i) / (ρ_vessel × V)where i = second moment of area of the tank's free surface, V = vessel displacement volume. For the exam: just know the effect is worst at ~50% fill.
How to Minimize Free Surface Effect
The Stability Curve — GZ Righting Arm
The stability curve (also called the GZ curve or righting lever curve) plots the righting arm (GZ) against the angle of heel. It shows the full stability picture across all heel angles — not just the initial GM at small angles.
Reading the GZ Curve
What the Curve Tells You About Loading
Loading Calculations — Displacement & Weight
The OUPV exam includes basic displacement and weight calculations. Understand the formulas and the difference between salt and fresh water density.
Displacement Formula
Worked Example
Problem
A vessel displaces 350 ft³ of salt water. What is its displacement in long tons?
Displacement (lb) = 350 ft³ × 64 lb/ft³ = 22,400 lb
Convert to long tons: 22,400 ÷ 2,240 = 10 long tons
Fresh Water Caution
In fresh water, the same vessel displaces more volume (sits deeper) because fresh water is less dense. A vessel moving from salt to fresh water sinks deeper — draft increases. This is the freshwater allowance concept.
Trim — Forward and Aft Draft
Trim is the longitudinal (fore-and-aft) inclination of the vessel. It is measured as the difference between the forward and aft drafts.
| Concept | Definition | Effect / Exam Point |
|---|---|---|
| Trim | Difference between aft draft and forward draft (Trim = Aft draft − Fwd draft) | Positive trim = trimmed by stern (deeper aft). Negative trim = trimmed by head (bow down). Even keel = no trim. |
| Trimmed by stern | Aft draft greater than forward draft — vessel is heavier aft | Most vessels are designed to operate trimmed slightly by stern for better steering response and propeller efficiency |
| Trimmed by head (bow down) | Forward draft greater than aft draft — weight is shifted forward | Dangerous — reduces maneuverability, causes bow to plow into waves, increases risk of broaching. Generally undesirable. |
| Shifting weight forward | Moving cargo, fuel, or passengers toward the bow | Reduces aft draft, increases forward draft — trims vessel bow-down. Opposite for shifting weight aft. |
| Moment to Change Trim 1 inch (MCT1) | The weight × distance required to change trim by 1 inch | Used in stability calculations. Shift weight forward of midships to trim bow down; aft to trim bow up. |
Trim rule for the exam
Shifting weight forward trims the vessel bow-down (forward draft increases, aft draft decreases). Shifting weight aft trims the vessel stern-down (aft draft increases, forward draft decreases). The shift in trim is proportional to the weight times the distance shifted, divided by MCT1.
List vs Heel — Know the Difference
The exam routinely tests the distinction between list and heel. They look the same (vessel tilted to one side) but have completely different causes and corrections.
| Aspect | List | Heel |
|---|---|---|
| Definition | Permanent static lean caused by off-center weight | Temporary lean caused by an external force |
| Duration | Permanent — persists when external conditions are calm | Temporary — resolves when external force stops |
| Cause | Off-center G: asymmetric cargo, one-sided fuel burn, water ingress in void | Wind, waves, sharp turn, passenger surge to one side |
| Self-correcting? | No — off-center G is still there; vessel stays listed | Yes — stable vessel returns to upright when force stops |
| Correction | Shift weight to the high side; remove or redistribute off-center weight | Reduce speed, change course, reduce sail, brief passengers |
| Exam distinction | List = off-center weight = G is off centerline | Heel = external force = G stays on centerline |
Angle of Loll — a special case
When GM is zero or slightly negative, a vessel rests at an angle of loll rather than upright. Unlike a list, the vessel may loll to either side. Correcting angle of loll requires lowering G — add ballast low, remove topside weight. Do NOT shift cargo to the high side (that can capsize the vessel by aggravating the negative GM).
Critical exam trap
If a vessel develops a list, the instinctive response is to move weight to the high side. That is the right answer if the cause is off-center weight (a true list). But if the cause is negative GM (angle of loll), moving weight to the high side can cause a violent snap to the opposite side and capsize. The exam may present this scenario — identify the cause before choosing the fix.
Practical Stability Guidelines for Captains
Four rules every captain must internalize — not just for the exam, but for every underway operation.
Keep tanks full or empty in rough conditions
Partially filled tanks (especially around 50%) create maximum free surface effect, raising effective G and reducing GM. In a seaway, this can be the difference between a stable vessel and a capsizing one. Monitor fuel burn and cross-flood or top off tanks.
Load heavy gear as low and as centered as possible
Every pound of weight added high raises G. Dive tanks, anchors, and heavy equipment belong in the lowest available stowage — not on the cabin roof or flying bridge. Center heavy items athwartships to avoid inducing a list.
Brief passengers — never let them crowd the rail
Passengers crowding one rail create both an off-center weight (list) and raise effective G. On a 30-foot vessel, 8 passengers on the starboard rail can create a dangerous list. Brief passengers to sit low and distribute evenly.
Never ignore a list — find and fix the cause
A vessel that sits at a permanent angle of heel has a stability problem. Common causes: off-center fuel consumption, asymmetric cargo, water intrusion in a void space, or a flooded compartment. Identify and correct before getting underway in adverse conditions.
Exam Strategy — 3 Cards
GM questions: think cause and effect
Every question about stability can be solved by asking: does this action raise G or lower G? Raising G reduces GM (less stable). Lowering G increases GM (more stable). Free surface effect raises effective G. Loading high raises G. Loading low lowers G.
Free surface = worst at half-full
The exam will give scenarios with tanks at various fill levels. Free surface effect is worst at approximately 50% full — the liquid has maximum freedom to shift. A completely full or completely empty tank has zero free surface effect.
List vs heel: different cause, different fix
List is permanent and caused by off-center weight — fix it by shifting weight. Heel is temporary and caused by external forces — fix it by reducing the force (slow down, change course, reduce sail). The exam tests whether you know which is which.
Frequently Asked Questions
What is metacentric height (GM) and why does it matter for vessel stability?
Metacentric height (GM) is the vertical distance between the center of gravity (G) and the metacenter (M), which is the point where a vertical line through the shifted center of buoyancy intersects the vessel's centerline when heeled. A positive GM (M above G) means the vessel is stable — when heeled, buoyancy acts to return it upright. A negative GM (G above M) means the vessel is unstable and will capsize. A high positive GM produces a stiff, snappy roll; a low positive GM produces a tender, slow roll. The exam typically asks you to identify whether a change in loading raises or lowers G, and therefore increases or decreases GM.
What is free surface effect and how do you minimize it?
Free surface effect is the loss of stability caused by liquid in a partially filled tank. When the vessel heels, the liquid shifts to the low side, effectively raising the vessel's center of gravity (G) and reducing metacentric height (GM). The effect is worst when tanks are approximately 50% full. To minimize free surface effect: keep tanks completely full or completely empty whenever possible; use cross-flooding to equalize tanks; subdivide tanks with longitudinal baffles. In rough conditions, running with half-full tanks significantly increases capsizing risk — especially for smaller vessels.
What is the difference between list and heel?
List is a permanent static lean to one side caused by an off-center weight — cargo loaded asymmetrically, fuel burned from one side only, or improper ballast. List does not self-correct when the external force is removed because the cause (off-center G) persists. Heel is a temporary lean caused by an external force — wind pressure, wave action, or a sharp turn. When the external force stops, a stable vessel returns to upright. The exam distinguishes these because the correction is different: a list requires shifting or removing weight; heel is addressed by reducing speed, changing course, or reducing sail area.
Related Study Guides
Deck General & Safety
Fire classifications, PFD types, EPIRB, MARPOL, distress signals — full Deck General section study guide.
Sea Time Requirements
How to document and qualify your sea service for the OUPV and Master license applications.
OUPV Exam Overview
All four exam sections, passing thresholds, what to expect at the REC, and how to prepare.
Practice Stability & Loading Questions
Drill GM, free surface effect, trim, and displacement calculations with OUPV-style questions and instant answer explanations — free on NailTheTest.
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