What the USCG Exam Tests on Stability
Stability questions appear on every USCG OUPV and Master exam. The National Maritime Center (NMC) draws stability questions from question bank modules covering vessel stability, trim, loading, and load lines. Expect 10-20% of your exam questions to involve stability concepts — many of them requiring calculation.
Transverse Stability
- ✓GM calculation (KM - KG)
- ✓Weight shift formula GG1
- ✓List vs. loll
- ✓Free surface effect
- ✓Passenger heel limits
Longitudinal Stability / Trim
- ✓TPI (tons per inch)
- ✓MCTI (moment to change trim)
- ✓Trim distribution bow/stern
- ✓Draft calculations
- ✓LCF and LCB concepts
Load Lines & Regulations
- ✓Plimsoll mark zones (TF F T S W WNA)
- ✓Stability booklet requirements
- ✓Passenger weight standard (140 lbs)
- ✓Minimum GM requirements
- ✓Range of stability
The Four Stability Points: G, B, M, and GM
Every stability calculation starts with understanding four points. These are not abstractions — each represents a physical force acting on the vessel. Learn them cold before attempting any calculation.
G — Center of Gravity
The point through which the total weight of the vessel acts downward. G is the average location of all weight aboard: hull, machinery, cargo, fuel, water, crew, and passengers.
Key fact: G moves toward any weight added, and away from any weight removed. G rises when weight is added high, falls when weight is added low.
B — Center of Buoyancy
The center of the underwater volume of the hull — the point through which buoyant force acts upward. B is always at the geometric center of the displaced water.
Key fact: Unlike G, B moves when the vessel heels. As the vessel heels, the shape of the underwater volume changes, and B shifts to the low side.
M — Metacenter
The point where the vertical line through B (when heeled) intersects the vessel's centerline. M is treated as a fixed point for small angles of heel (under about 10-15 degrees).
Key fact: M is determined by hull form — specifically the beam of the vessel at the waterline. Wider beam = higher M. M is always above B at small angles.
GM — Metacentric Height
The vertical distance from G to M. GM is the primary measure of initial transverse stability. GM = KM - KG, where K is the keel.
Key fact: Positive GM (G below M): vessel is stable, will right itself. Negative GM (G above M): vessel is unstable, will loll or capsize. Larger GM = stiffer, more snappy roll.
The Most Important Formula
K is the keel. KM is the distance from keel to metacenter. KG is the distance from keel to center of gravity. Positive result: stable. Negative result: loll or capsize risk.
The GZ Curve: Reading Stability at All Angles
GM describes stability only at very small angles of heel. To understand a vessel's behavior at larger angles — including in severe weather — naval architects use the GZ curve (also called the righting arm curve or curve of statical stability). The USCG exam will ask you to read values from a GZ curve and interpret what they mean.
Righting Arm (GZ)
The horizontal distance between the vertical line of gravity through G and the vertical line of buoyancy through B, measured at any angle of heel. GZ represents the lever arm of the righting couple.
Initial Slope
The slope of the GZ curve at the origin (zero heel). Equals GM in the limit as heel approaches zero. A steeper initial slope = larger GM = stiffer vessel.
Maximum GZ
The peak value of the righting arm curve. Represents the maximum righting moment the vessel can generate. Typically occurs at 30-45 degrees of heel for most monohulls.
Angle of Vanishing Stability (AVS)
The angle of heel at which GZ returns to zero after the vessel is heeled past its maximum righting arm. Beyond AVS, the vessel will capsize — there is no righting force.
Range of Stability
The range of heel angles over which GZ is positive — from upright (0 degrees) to AVS. A vessel with a range of stability of 90 degrees can be heeled to 90 degrees before capsizing.
Dynamic Stability
The area under the GZ curve, measured in foot-degrees or metre-degrees. Dynamic stability represents the work done in heeling the vessel — how much energy a wave must deliver to capsize it.
How Loading Changes the GZ Curve
Free Surface Effect: Slack Tanks and GM
Free surface effect is one of the most tested stability topics — and one of the most commonly misunderstood. It has caused real vessel capsizings. The USCG exam tests it repeatedly because it kills ships and people.
What Creates Free Surface
Any slack tank — a tank that is neither empty nor completely full — has a free surface. Fuel tanks, ballast tanks, fresh water tanks, and gray water tanks can all create free surface. Even a small amount of liquid sloshing in a large tank creates significant free surface effect.
How Free Surface Raises G
When the vessel heels, liquid in a slack tank shifts to the low side. This shift increases the heeling moment — acting as if G had risen vertically. The loss of GM due to free surface is called the Free Surface Correction (FSC) and is subtracted from solid GM to get effective GM.
Free Surface Correction Formula
FSC = (i x rho_L) / (V x rho_SW). Where i = second moment of area of the free surface in ft4 or m4, rho_L = density of tank liquid, V = vessel displacement volume, rho_SW = density of seawater. In simplified exam problems: FSC is read from tank tables and subtracted from GM.
Width Cubed Rule
The second moment of area of a rectangular free surface is i = (l x b3) / 12, where l is the tank length and b is the tank breadth (width). Because b is cubed, doubling the tank width multiplies FSC by 8. Subdividing a wide tank with a longitudinal bulkhead dramatically reduces free surface effect.
Two Half Tanks vs. One Full Tank
Two tanks, each half full, have four times the combined free surface of one tank of the same total volume that is half full. This is because each smaller tank has half the width, but its contribution (b3) is only 1/8 — yet you have two of them, giving 2 x (1/8) = 1/4. Wait — actually subdividing reduces FSC. Longitudinal subdivision (adding a centerline bulkhead) reduces i by 75% for each tank half.
Operational Best Practice
Keep tanks either full or empty to eliminate free surface. When consuming fuel or water, transfer from one tank at a time and switch tanks only when one is empty. Never allow multiple large tanks to sit half-full simultaneously before a voyage in heavy weather.
Key Free Surface Rules for the Exam
- ▶ Effective GM = Solid GM − Free Surface Correction (FSC)
- ▶ FSC depends on tank width cubed — wide tanks are far worse than narrow ones
- ▶ Adding a centerline (longitudinal) bulkhead reduces FSC by 75% for that tank
- ▶ FSC is the same regardless of how full or empty the tank is (within the slack range)
- ▶ The only ways to eliminate FSC: fill the tank completely, or empty it completely
- ▶ Never correct loll by flooding a high-side tank — the FSC makes the situation worse
List vs. Loll: The Critical Distinction
This is the most important distinction in practical stability — and the most dangerous to confuse. Applying the wrong corrective action to loll has caused vessels to capsize. Study this until you can identify the difference instantly.
LIST
G is off the centerline — too much weight on one side. The vessel's GM is positive; she is stable in the heeled position.
Symptoms
- •Vessel heels consistently to one side
- •Does not roll back through vertical when heeled away from the list
- •Heeling angle is relatively constant
- •Roll period is short on the listed side, long on the other
Correction
- •Shift weight from the low (listed) side to the high side
- •Add weight to the high side (ballast, cargo)
- •Remove weight from the low side
- •Transfer ballast water to high-side tank
LOLL
G has risen above M — negative GM. The vessel is in unstable equilibrium at centerline and falls to one side, finding a new (lower) equilibrium angle where the curve of statical stability provides a positive righting lever.
Symptoms
- •Vessel heels slowly to one side — or alternates between two sides
- •Sluggish, lazy roll through vertical
- •Rolling to one side feels slower and heavier than rolling to the other
- •Vessel feels tender — any small load shift causes large heel response
Correction
- •Lower G immediately: remove high cargo, use low ballast
- •Fill double-bottom or low ballast tanks
- •Do NOT shift weights from low to high — may momentarily worsen the negative GM
- •Do NOT flood high-side tanks — increases free surface and makes situation worse
| Factor | List | Loll |
|---|---|---|
| GM | Positive | Negative |
| Cause | G off centerline (weight imbalance) | G above M (too much high weight) |
| Roll feel | Normal or stiff to one side | Sluggish, tender, lazy roll |
| Corrective action | Shift weight to high side | Lower G — add low ballast, remove high weight |
| Wrong action | Adding to wrong side worsens heel | Flooding high-side tank — causes capsize |
Weight Shift Calculations: Worked Examples
The weight shift formula GG1 = (w x d) / W underlies every loading calculation. These three worked examples cover the three main scenarios tested on the USCG exam.
A vessel displaces 500 long tons. A 20-ton crane lifts a weight from the centerline and swings it 10 feet to starboard. How far does G shift to starboard?
G moves 0.4 ft to starboard. This creates a listing moment. The vessel will develop a starboard list proportional to the angle whose tangent is GG1 / GM. If GM = 2.0 ft, the list angle = arctan(0.4/2.0) = arctan(0.2) = approximately 11 degrees.
A 500-ton vessel has KG = 12.0 ft. A 10-ton generator is moved from keel level (KG = 1 ft) to the upper deck (KG = 20 ft). What is the new KG?
G rises 0.38 ft. If KM = 13.5 ft, old GM = 13.5 - 12.0 = 1.5 ft. New GM = 13.5 - 12.38 = 1.12 ft. Moving weight upward always reduces GM.
A vessel displaces 400 tons with KG = 10.0 ft and KM = 12.0 ft. You add 50 tons of cargo at a height of 8.0 ft above keel. Find the new KG and GM.
The cargo was loaded below the vessel's G (8.0 ft vs 10.0 ft), so G fell from 10.0 to 9.78 ft and GM improved from 2.0 to 2.22 ft. Loading low cargo always improves stability.
Trim: Longitudinal Stability and Draft
Trim is the difference in draft between bow and stern. A vessel trimmed by the stern (aft draft greater than forward draft) is the normal and desirable condition for most vessels. The USCG exam tests TPI and MCTI calculations frequently.
Trim
The difference between forward and aft drafts. Trim by stern: aft draft greater than forward draft (normal operating condition). Trim by head (or bow): forward draft greater than aft (unusual, often problematic).
Trimming Moment
A weight placed off the longitudinal center of flotation (LCF) creates a trimming moment that changes the fore-and-aft distribution of draft.
Moment to Change Trim 1 Inch (MCTI)
The moment required to change the trim by exactly one inch. MCTI is read from hydrostatic tables at the current displacement/draft. Higher displacement = higher MCTI.
Distribution of Trim Change
The total trim change distributes between bow and stern based on the distance of LCF from amidships. Change at bow = (total trim change x LCF-to-stern distance) / LBP. Change at stern = (total trim change x LCF-to-bow distance) / LBP.
Tons Per Inch Immersion (TPI)
The weight required to change mean draft by one inch. Found in hydrostatic tables. Used to calculate draft change when adding or removing weight uniformly.
Load Line Marks: The Plimsoll Mark
The Plimsoll mark (load line) shows the maximum allowable draft under different sea conditions and seasons. Named for Samuel Plimsoll, who campaigned for its mandatory use after overloaded ships called 'coffin ships' repeatedly sank. Required on all vessels subject to the International Load Line Convention. The USCG exam tests which mark applies in each zone.
Load Line Exam Memory Aid
Reading marks from the top of the load line plate down: TF → F → T → S → W → WNA. The higher the mark on the hull, the more the vessel is permitted to sink — warmer, calmer, less dense water. The lower the mark, the higher the vessel must ride — colder, rougher, denser water.
The Stability Booklet
The stability booklet is the master's operational guide to safe loading. Every inspected commercial vessel is required to have a USCG-approved stability booklet aboard. Before getting underway, the master must complete a loading condition check to verify the vessel meets all criteria in the booklet.
What the Stability Booklet Contains
Master's Responsibility
The stability booklet is not optional paperwork — it is the go/no-go document for every departure. The master must: (1) record the actual weight and position of every significant load; (2) calculate the departure KG; (3) compare that KG against the limiting KG table at the departure displacement; (4) verify that effective GM (after free surface corrections) meets minimum requirements; and (5) verify the range of stability requirement. Departing with a vessel outside approved stability limits is a violation of federal law and, more importantly, risks the lives of everyone aboard.
Passenger Vessel Stability Requirements
Passenger vessels face unique stability challenges because passengers are a mobile, dynamic load. The USCG applies specific regulatory standards to passenger vessels under 46 CFR Part 170.
Passenger Weight Standard
The USCG standard for passenger weight is 140 pounds per person for stability calculations. This is used to calculate passenger load contribution to displacement and G.
Passenger Crowd Effect
Passengers are treated as a free-moving load. If all passengers move to one side, G shifts transversely. Passenger vessel stability calculations must account for worst-case passenger distribution.
Maximum Heel Limit
During a turn at maximum speed, heel must not exceed 10 degrees for passenger vessels. During passenger crowding (all passengers on one side), heel must not exceed 15 degrees.
Minimum GM
Inspected passenger vessels must maintain GM in accordance with their approved stability booklet. Specific minimum GM values vary by vessel type, but are always positive with margin above zero.
Stability Letter
Passenger vessels must have a USCG-approved stability letter (or equivalent) posted in a visible location. The master must verify departure conditions comply with the letter before each voyage.
Embarking and Debarking
The master must account for passenger movement while boarding and debarking. Large numbers of passengers moving simultaneously to one side of a small vessel can cause dangerous list or capsize.
Small Boat Stability Factors
OUPV candidates often operate small passenger vessels, charter sportfishing boats, and sailing vessels. Understanding how hull design affects stability helps you make better operational decisions — and helps you answer exam questions about specific hull forms.
Beam
Wider beam raises the metacenter (M) and increases initial GM. Wide flat-bottomed boats are initially very stiff but may have poor range of stability — they resist heeling but can capsize suddenly at large angles.
Deadrise
Deadrise is the angle of the hull bottom from horizontal. High deadrise (V-bottom) gives a softer ride in chop but lower initial stability than a flat bottom. Low deadrise (flat bottom) is very stable initially.
Freeboard
Higher freeboard raises the deck edge, which increases the range of stability and delays the point at which waves can wash aboard. Low freeboard vessels can be overwhelmed and swamped in beam seas.
Ballast
External lead or iron ballast bolted to the keel lowers G significantly, improving GM and range of stability. Sailing vessels rely heavily on ballast. Removing ballast (deliberately or through flooding) raises G and is dangerous.
Center of Effort (Sailing Vessels)
The center of effort (CE) is the aerodynamic center of the sail plan — the point through which sail force acts. When CE is too far forward of the center of lateral resistance, the vessel rounds up into the wind (weather helm). Heeling from sail force raises G and reduces effective GM.
Free Surface in Small Craft
A half-full fuel tank in a small boat represents a proportionally much larger free surface effect than in a large ship, because the tank width relative to vessel beam is large. Small boat operators should keep tanks full or empty.
Practice Problems with Full Solutions
Work through each problem before reading the answer. These represent the most common stability calculation formats on the USCG OUPV and Master exams.
A vessel has KM = 15.5 feet and KG = 13.2 feet. What is the GM, and is the vessel stable?
Show Solution
A 600-ton vessel shifts 30 tons of cargo 12 feet to port. How far does G shift to port?
Show Solution
A vessel has KG = 14.0 ft and KM = 13.5 ft. Is she stable? What condition does she have?
Show Solution
A vessel displaces 800 tons with KG = 11.5 ft. A 40-ton piece of deck equipment is removed from a height of 22 ft above keel. Find the new KG.
Show Solution
A vessel has TPI = 20 long tons per inch. You load 100 tons of cargo evenly distributed. How much does the mean draft increase?
Show Solution
A vessel has MCTI = 80 ft-tons per inch. You load 10 tons at a point 24 feet forward of the LCF. How much does trim change?
Show Solution
Which load line mark allows the deepest loading draft? Which requires the greatest freeboard?
Show Solution
USCG Exam High-Yield Callouts
These are the stability concepts most frequently tested on USCG OUPV and Master exams. If you know these cold, you will answer the majority of stability questions correctly.
GM = KM - KG — the single most tested formula
USCG stability questions almost always give you KM (metacentric height above keel) and KG (center of gravity above keel) and ask you to find GM. The formula is simply GM = KM - KG. If the result is negative, the vessel has a stability problem (loll or capsize risk). Positive GM means stable. All other stability concepts build on this one calculation.
List vs. Loll — the most dangerous mix-up on the exam
List: positive GM, G off centerline, correct by shifting weight to high side. Loll: negative GM, G above M, correct by lowering G. The wrong treatment for loll — shifting a weight to the high side — can capsize a vessel that is already on the edge. The exam will test whether you know which condition exists and which action is correct. If the vessel is rolling slowly and feels tender, suspect loll.
Free surface always reduces GM — fill or empty tanks
Every slack tank reduces effective GM. The examiner will ask: what happens to GM when you have a slack tank? It decreases. What reduces free surface effect? Filling the tank completely or emptying it. What worsens free surface effect? Widening a tank (effect goes as width cubed). Adding a centerline longitudinal bulkhead to a tank cuts its free surface contribution by 75%.
Weight shift formula: GG1 = (w x d) / W
This formula applies to all weight movements — transverse shifts, vertical shifts, adding weight, removing weight. The shift of G is proportional to the weight moved and the distance moved, and inversely proportional to the total displacement. Memorize this: GG1 = w times d divided by W. It is the foundation of all loading calculations.
Plimsoll mark S is the center of the disc — marks go up for warm/fresh water
S (Summer Salt Water) is the baseline mark at the center of the load line disc. TF and F are above S (warmer, less dense water allows deeper loading). W and WNA are below S (rougher conditions require more freeboard). The vessel must not be loaded past the applicable mark. On the exam: which mark allows the deepest loading? TF. Which requires the most freeboard? WNA.
USCG passenger weight standard is 140 lbs per person
For stability calculations on inspected passenger vessels, every passenger is assumed to weigh 140 pounds. This standardized weight is used to calculate the contribution of passengers to displacement and to determine worst-case heel scenarios when passengers crowd to one side. The maximum heel from passenger crowding is 15 degrees.
Angle of vanishing stability — beyond it, no righting force
The angle of vanishing stability (AVS) is the point on the GZ curve where the righting arm returns to zero. Past AVS, the vessel will capsize — the GZ curve goes negative. USCG regulations require inspected vessels to have AVS of at least 60 degrees (passenger vessels). When loading raises G, the GZ curve flattens and AVS decreases. A vessel with reduced AVS is more vulnerable to capsizing in unexpected waves.
Pro Tips for Stability Questions on the USCG Exam
Continue Your Stability Studies
Stability is a broad subject. These related NailTheTest guides cover topics that build on the foundations in this article.
Cargo and Stability
Loading plans, cargo securing, stowage factors, broken stowage, and stability impact of cargo operations.
Vessel Stability Advanced
Advanced GZ curve analysis, damaged stability, flooding calculations, and inclining experiments.
Ship Stability Advanced
IMO intact stability code, dynamic stability, parametric rolling, and stability in severe weather.
Test Your Stability Knowledge
Reading about stability is the first step. The second step is doing actual exam problems under timed conditions. NailTheTest gives you adaptive practice questions drawn from the official USCG question bank — including stability calculations, GZ curve interpretation, and load line questions.