Stability - GZ & GM — Most Asked Questions
33 questions asked about stability - gz & gm across the General and Fn 3 papers, heaviest first. 3 of them are must-master.
Learn the system first
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1 Effects of free surface effect?
Also asked: “What is free surface effect? Causes? How does it cause instability?”
Answer
A slack tank’s liquid runs to the low side as the ship rolls, acting as a virtual rise of G: GM and GZ fall and the roll grows.
- Mechanism: liquid in a partly-full tank moves across with each heel, so the ship behaves as if her GM were reduced — a virtual (imaginary) loss of GM.
- Consequences: centre of gravity effectively shifts, metacentric height and righting lever shrink, angle of heel grows, ship can go unstable.
- Size depends on the free-surface dimensions and the ship’s displacement — wide shallow tanks are the worst.
- Cures: press tanks full, keep slack tanks to a minimum, subdivide wide tanks; near 90% full, pocketing shrinks the effect.
Surveyor follow-up: would you press up a high slack tank or a double-bottom tank first — and why?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
2 Angle of loll
Answer
Angle of loll is the heel a ship with negative GM flops to and stays at — unstable at upright, stable only once heeled.
- With G above M the equilibrium is unstable: any roll grows instead of righting, until buoyancy shifts enough to hold her at the angle of loll.
- She will not return to upright on her own — that fixed heel IS the loll, not a list.
- Cure by lowering G: press up empty double-bottom tanks, pump high slack tanks down, shift weights low, kill free surface first.
- Never start by ballasting the high side or the low side blindly — she can flop violently to the other side mid-correction.
Surveyor follow-up: how do you tell loll from list before you touch a single valve?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
3 Tender and stiff ship
Answer
Stiff means big GM and a violent quick roll; tender means small GM and a slow lazy roll — both still stable while M stays above G.
- Stiff ship: KG too low, GM very large, righting moments huge — she snaps back upright fast with a short roll period.
- Tender ship: KG too high, GM very small, righting moments tiny — she returns sluggishly with a long roll period, but M is still above G so she is stable.
- Period rule: the greater the GMT, the shorter the period — stiff is quick, tender is slow.
- Dangers differ: stiff ships hammer lashings, containers and machinery with acceleration; tender ships sit one bad load from negative GM.
Surveyor follow-up: the roll feels slow and lazy after loading — tender or just comfortable, and which single check settles it?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
4 Static and dynamic stability
Also asked: “What is dynamic stability”, “What is static stability”
Answer
Static stability is the righting lever at an angle; dynamic stability is the energy needed to heel to that angle — the area under the GZ curve.
- Static stability: GZ at a given heel — the ship’s ability to return upright once the heeling moment is removed.
- Dynamic stability: displacement times the area under the GZ curve up to that angle — the work wind and waves must do to heel her there.
- A tall narrow GZ curve can show good initial GM yet poor dynamic stability at large angles — read area to 60°, not just GM.
- Free surface and high KG eat both: less lever and less area, so rolling energy margins collapse together.
Surveyor follow-up: two ships with identical GM — how can one still be dangerously tender in heavy weather?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
5 Angle of contraflexure
Also asked: “Angle of contraflaxture”, “Angle of contrafelxure”, “Angle of contraflacture”
Answer
The contraflexure is the inflection point on the GZ curve where it stops steepening and starts flattening — the lever still grows, but ever more slowly.
- Read it as the knuckle on the curve where curvature flips from concave to convex, usually near deck-edge immersion.
- Up to it each extra degree of heel buys more lever than the last; past it each degree buys less.
- It sits well before the angle of maximum GZ and far before vanishing stability — an early warning of flattening righting energy.
- Free surface, high KG and slack tanks drag it to smaller angles, shrinking the useful stable range.
Surveyor follow-up: contraflexure at 15 degrees with max GZ at 30 — tender ship or just fine, and what proves it?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
6 Gz and gn curves
Also asked: “Kn curve and gz curve”
Answer
Cross curves give levers for any displacement: GZ curves assume a KG, KN curves assume the keel — correct to the true KG.
- GZ tables carry an assumed KG; true lever equals table value minus the KG shift times sine of heel.
- KN tables assume G at the keel; true lever equals KN minus actual KG times sine of heel, always subtracted.
- Natural-sine tables printed on the curves supply the correction at each angle.
- Worked check: table 0.73 m at 45 degrees on 7.00 m assumed with 7.54 m actual corrects by 0.38 m to 0.35 m true.
Surveyor follow-up: KN or GZ table in front of you — which correction sign, and is it ever added?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
7 How to find gz
Also asked: “How to find gm in gz”, “What is gz how is it calculated”
Answer
Find GZ from the cross curves corrected to your KG, or from KN minus KG-times-sine — then plot the stability curve.
- Enter GZ tables at displacement and heel, then subtract the KG shift times sine of heel for the true lever.
- KN tables instead subtract actual KG times sine — the correction is always a subtraction.
- Plot levers against heel for the statical-stability curve, reading range, maximum and vanishing angle off it.
- Derive initial GM from the curve’s origin slope as the surveyor’s cross-check.
Surveyor follow-up: table gives 0.73 m at 45 degrees on 7.00 m assumed with 7.54 m actual — true GZ?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
8 What is righting lever?
Also asked: “BWM what is righting lever”, “Define righting lever”
Answer
The righting lever is the horizontal arm between gravity down and buoyancy up — GZ times displacement rights the ship.
- G acting down through the centre of gravity against B acting up through the centre of buoyancy makes the couple.
- The perpendicular distance between those parallel forces at any heel is GZ.
- Righting moment equals displacement times GZ — the number that returns her upright.
- Negative GZ heels her further; zero GZ with zero GM is the loll she sits at.
Surveyor follow-up: displacement up with GZ unchanged — righting moment up, down or same?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
9 Explain why an unstable ship is dangerous. (6) (b) A vessel travelling at 17 knots turns with a radius of 450 m when the rudder is put hard over. The centre of gravity is 7 m above the kecl, the transverse metacentre 7.4
Also asked: “Explain why an unstable ship is dangerous. (6) (b) A vessel travelling at 17 knots turns with a radius of 450 m when the rudder is put hard over. The centre of gravity is 7 m above the kecl, the transverse metacentre 7.45 m above the keel and the centre of buoyancy 4 m above the keel. If the centripetal force is assumed to act at the centre of buoyancy, calculate the angle of heel when turning. Th”
Answer
An unstable ship heels, lolls and can capsize from claimed causes — high cargo, burnt low bunkers, soaked deck loads — then heels outward in the turn.
- Negative GM from high weights, consumed low fuel or waterlogged deck cargo removes the righting arm.
- She lolls to either side on wave action, ships water through side openings and answers helm drunk.
- In the turn centrifugal force heels her outward against a 0.4 m GM with G above B — work the moment against displacement.
- Cure is lower G and kill free surface before sailing; at sea ballast low and full, never slack.
Surveyor follow-up: lolling in a seaway with negative GM — ballast high slack or low full first, and why?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
10 What is the GZ curve?
Answer
The GZ curve plots righting lever against heel: range, maximum and vanishing angle read straight off it.
- Levers from cross curves corrected to true KG at each displacement plotted heel by heel.
- Range is zero to vanishing angle where the lever returns to zero and changes sign.
- Maximum read by tangent to the peak with a perpendicular dropped for the angle.
- Origin slope gives initial GM — the surveyor’s cross-check on every curve.
Surveyor follow-up: range to 86 degrees with max 0.63 m — stable, tender or stiff, and what number proves it?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
11 Significance of metacentric height?
Answer
GM is initial-stability shorthand: positive rights her, negative capsizes her, small means tender and large means stiff.
- Positive GM with G below M gives a righting lever growing as GM times heel angle for the first degrees.
- Negative GM with G above M heels her over — no lever, no return, only ballast or discharge to cure.
- Small GM rolls slow and tender with easy motion but weak margins; large GM snaps back stiff and violent.
- Use GM only to about 10–15 degrees — beyond that read the GZ curve, since the metacentre itself wanders.
Surveyor follow-up: GM positive but tiny with a long slow roll in beam seas — safe, tender or unseaworthy, and what do you move?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
12 Why to carry out inclining experiment
Answer
The inclining experiment finds the lightship’s true weight and centre: without it every loading calculation is fiction.
- Shifting known weights across the deck and reading heel gives GM as inclined for that displacement.
- Hydrostatics supply displacement and KM; subtracting GM yields the as-inclined KG and LCG.
- Correct for weights aboard and missing against build completion to reach true lightweight, VCG and LCG.
- Builders run it near completion with plumb lines on the centreline — the stability book lives on its numbers.
Surveyor follow-up: lightweight up after conversion with the old stability book aboard — valid, void or re-incline?
Full theory: Ship Hydrostatics: Buoyancy, Displacement and Trim -
13 Angle of contraflexion , basically everything abt gz curve
Answer
The GZ curve opens, peaks, comes back to zero and may cross negative: the point after the peak is the contraflexion, or angle of vanishing stability.
- The curve rises through the range of stability, reaches maximum GZ, then falls as the deck edge immerses.
- The contraflexion point is where GZ returns to zero — the angle of vanishing stability — and beyond it the ship will not right.
- Where the curve crosses into negative GZ the ship has lost positive stability even though the mast may still be up.
- Read four things off the curve: initial slope for GM, maximum GZ, angle of vanishing stability and the area under it for dynamical stability.
Surveyor follow-up: GZ curve peak at 40 degrees with vanishing at 62 — is the ship compliant, and against which criterion?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
14 Describe how an inclining experiment is carried out. (6) (b) If the density of seawater is 1.025 t/m} and the density of fresh water is 1.000 t/m3, prove that the statutory fresh water allowance is V /40 TPC cm
Answer
Inclining finds the light condition by shifting known weights; fresh water allowance is then TPC divided by 40 from the density ratio.
- With the ship as near completion as possible, shift known weights and read the heel to obtain GM as inclined.
- Hydrostatics give displacement and KM; subtracting GM yields the as-inclined KG, and trim gives the LCG.
- Correct for weights still to be added and removed to reach the true lightweight, VCG and LCG.
- Proof of the allowance: draught change equals displacement change divided by Aw, and with seawater 1.025 and fresh 1.000 that reduces to TPC divided by 40 cm.
Surveyor follow-up: allowance claimed as TPC divided by 48 — which number, and what draught does that cost the ship?
Full theory: Load Line, Freeboard and Tonnage Measurement -
15 Diff bw list and heel,diff btw stiff vessel and tender vessel?
Answer
List is weight moved off centre with GM still positive; heel is pushed over by a moment. Stiff ships snap back, tender ships roll lazily.
- In a list, G has moved off the centreline from cargo shift or bilging, GM stays positive and the angle is fixed to one side.
- In heel, a moment from wind, sea or helm is balanced by GZ — remove the moment and the ship returns upright.
- A stiff vessel has large GM and short roll periods around 8–10 seconds, jerky and uncomfortable in a seaway.
- A tender vessel has small GM with roll periods of 30–35 seconds, easy motion but a weak margin against cargo shift.
Surveyor follow-up: steady heel to port easing as the wind drops, cargo confirmed centred — list, heel or loll?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
16 Free surface effect , its effect on metacritic height and righting lever
Answer
Free surface takes GM away: slack liquid runs to the low side, so the ship has less metacentric height and a smaller righting lever.
- As the ship heels, liquid in a partly filled tank moves to the lower side, shifting the effective centre of gravity outboard.
- The shift is equivalent to lowering GM, and the righting lever GZ falls with it for the same displacement and KG.
- The effect grows with the free surface dimensions and shrinks with displacement; pocketing near 90% full reduces it.
- Cure it by pressing tanks full or empty, subdividing wide tanks, and treating cargo to remove slack before sailing.
Surveyor follow-up: GM on paper positive with three wide tanks slack and a slow heavy roll — stable, tender or lolling?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
17 Gz curve and x why only 57.3 degree
Answer
The GZ curve is drawn to about 57 degrees because that is the angle at which the deck edge is fully immersed and the freeboard is gone.
- By about 57 degrees the deck edge immerses and the ship is operating with no reserve buoyancy left above her.
- Beyond that the ship is in a damaged or sinking condition, so stability criteria are not written for it.
- That is why the range, maximum GZ and vanishing angle are all quoted inside 0 to about 60 degrees.
- One degree either way of the criterion is the difference between a compliant stability booklet and a detention.
Surveyor follow-up: vanishing angle stated at 62 degrees with the deck edge immersed at 57 — which figure does the surveyor accept?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
18 Gz curve explanation
Answer
The GZ curve is the ship’s righting arm against heel: it shows initial stability, maximum righting, range and where righting ends.
- GZ is plotted against angle of heel for one condition of loading only — loaded arrival, ballast or light condition.
- Its initial slope is GM, the peak is the maximum righting lever, and the return to zero is the angle of vanishing stability.
- The area under the curve measures the work done in returning the ship — its dynamical stability.
- It is the working document for loading: the booklet shows how ballast, cargo shift and free surface bend it.
Surveyor follow-up: GZ curve quoted for laden condition on a ballast voyage — which condition did the surveyor ask for?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
19 Gz curve full
Answer
The full GZ curve gives the surveyor four things at a glance: initial slope, maximum lever, range of stability and area for dynamic stability.
- Initial slope equals GM, so the curve starts steep on a stiff ship and shallow on a tender one.
- Maximum GZ with its angle is the biggest steady heeling moment the ship can carry without capsizing.
- Where GZ returns to zero is the angle of vanishing stability — the largest angle from which she will return unaided.
- The area under the curve to about 60 degrees is the dynamical stability, the energy available to right the ship in a seaway.
Surveyor follow-up: GZ curve with a good peak but the area under it small — which criterion does the book fail?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
20 How to get intial gm from it and why ordinate is taken at 1 radian
Answer
GM is the slope of the curve at the origin; at small angles GZ = GM × sin θ, so one radian gives the value directly.
- For small angles the righting lever is GM multiplied by the sine of the heel, so the curve is a straight line at the origin.
- The ordinate at one radian equals GM in metres, which is why the initial ordinate is read there rather than guessed.
- In practice a tangent at the origin is drawn and its slope gives the same GM by the small-angle relation.
- Beyond roughly 10 to 15 degrees the metacentre wanders and the linear relation fails, so the curve itself must be used.
Surveyor follow-up: GM read at 10 degrees instead of one radian on a loaded ship — how much error, and which way?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
21 Point of contraflexure
Answer
The contraflexion point is where GZ returns to zero: the angle of vanishing stability, past which she will not right herself.
- At the peak of the curve the ship has the greatest righting lever; the contraflexion is on the far side of that peak.
- GZ becomes zero and then negative — beyond it the heeling moment beats the righting moment at any load.
- The range of stability is the whole angle over which GZ stays positive, measured from the origin or from the loll angle.
- If the ship is listed, the range is measured from the list angle; if lolled, from the loll angle — never from zero.
Surveyor follow-up: range quoted from the loll angle on a listed ship — is that number the surveyor’s or the book’s?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
22 Position of metacentre in dead stability
Answer
In dead stability the metacentre sits below G, so GM and GZ are both negative and every small heel makes the ship fall further over.
- M above G means positive GM and GZ — stable; M at G means both zero — neutral; M below G means both negative — unstable.
- The dead-stable case is the loll condition: the ship flops to a fixed angle either side and stays there.
- Metacentric height cannot be used beyond about 15 degrees, since the metacentre itself ceases to exist there.
- KM is the height of M above the keel and must never be confused with GM, the distance from G to M.
Surveyor follow-up: heeled either side with M below G — stable, neutral or dead, and what number proves it?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
23 Significance of gz
Answer
GZ is the ship’s actual righting effort at any angle — the number that decides whether a gust, a wave or a shift ends in recovery.
- GZ multiplied by displacement gives the largest steady heeling moment the ship can bear without capsizing.
- Its peak and the angle at which it occurs matter as much as its size — a small early peak is a fragile ship.
- The value at which GZ vanishes is the largest angle from which the ship returns once the disturbance is removed.
- Wind heeling, turning, list and loll are all judged against the GZ curve, not against GM alone.
Surveyor follow-up: adequate GM but the GZ peak falling early — safe in still water, or unsafe the moment a gust hits?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
24 Stiff and tender ship What will happen if metacentre goes lower than g
Also asked: “What will happen if metacentre goes lower than g”
Answer
M below G is dead stability: the ship will not right from a small heel, it will fall away — that is the loll condition.
- With the metacentre lower than the centre of gravity, GM and GZ are both negative for small angles of heel.
- Any disturbance drives her further over until a new equilibrium or the capsize, and she may sit at a fixed angle either side.
- The remedy is to lower G symmetrically — ballast low, discharge high — never to list-correct across.
- Filling a tank to cure it first costs GM to free surface, so the cure must be a full tank in one move.
Surveyor follow-up: lolled with slack tanks each side and a high ballast tank offered — press up, transfer or discharge?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
25 Tender ship , stiff ship ... So many ×××
Answer
Tender or stiff is set by roll period: large GM and short period is stiff, small GM and long period is tender.
- Stiff ship: large GM, short roll period around 8 to 10 seconds, jerky motion but the best margin against shifting cargo.
- Tender ship: small GM, long roll period around 30 to 35 seconds, easy motion but a weak margin she must not waste.
- A comfortable ship rolls in roughly 20 to 25 seconds — the band that survives both the surveyor and the crew.
- Trim and heel also change the picture: raising G or adding free surface converts a stiff ship into a tender one.
Surveyor follow-up: tender ship with heavy weather damage claims — GM, free surface or the sea state first to blame?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
26 What gz curves gives
Answer
A GZ curve gives the ship’s behaviour in words: how she rights, how hard, over what range, and where she stops righting altogether.
- It shows the maximum steady heeling moment the ship can withstand without capsizing, and the angle at which it occurs.
- It gives the range of stability — the total angle over which she will return to upright unaided.
- It gives the area under the curve, which is the energy available for dynamical stability in a seaway.
- It is the only stability statement that holds beyond small angles, because the metacentre itself wanders there.
Surveyor follow-up: GZ curve consulted for a 5-degree roll question — is the curve needed, or is GM enough?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
27 What happend in end of gz curve
Answer
At the end of the curve GZ reaches zero: beyond the contraflexion the heeling moment wins and the ship goes over and stays over.
- The curve ends at the angle of vanishing stability, where the righting lever has fallen to nothing.
- Past that angle a steady heeling moment smaller than before still leaves the ship unable to return.
- The curve then turns negative, meaning the ship actively heels further away from upright as weight is shifted.
- That is why the criteria are written to 0 to 30, 40 and 60 degrees — the region where the ship is still recoverable.
Surveyor follow-up: GZ negative at 45 degrees with the ship upright — loll, list or a calculated condition, and which?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
28 What is gm?
Answer
GM is the distance from the centre of gravity to the metacentre: positive when G is below M, negative when it is above.
- It measures initial stability and relates directly to GZ for small angles, being easier to find than the full curve.
- Easier to calculate than GZ, so it is used to express initial stability — but only up to about 10 to 15 degrees.
- Positive GM with G below M is stable; negative GM with G above M is unstable and leads to the loll condition.
- KM is the height of M above the keel — a different figure, and the two are confused in half the oral failures.
Surveyor follow-up: KM quoted when the question asked for GM — which is which, and how do you tell them apart on the drawing?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
29 What is gz cure , how will you get gz, gm,
Answer
GZ is the righting lever at that angle; get both from the hydrostatic data: KM and displacement from the tables, GM from the slope.
- From hydrostatics read displacement and KM for the loading condition, then subtract the actual KG to get GM.
- GZ at each angle is then the horizontal distance between the weight line through G and the buoyancy line through B.
- Plot those GZ values against heel to build the curve, and check its area and peak against the criteria.
- Both figures are condition-specific — re-derive them for every loading, not once for the ship.
Surveyor follow-up: GZ taken from a curve drawn for the wrong displacement — how much error, and which way does it run?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
30 Why 57.3 degree angle
Answer
57.3 degrees is where the deck edge goes under: the ship has spent all her reserve buoyancy and no stability criterion is written beyond it.
- At about 57 degrees the deck edge immerses completely and the freeboard reserve above the waterline is gone.
- Beyond that the ship is in a sinking or damaged condition, so no criterion can require her to right from there.
- This is why the criteria run to 30, 40 and 60 degrees and why the curves are drawn to about that limit.
- The 57.3 figure is geometry, not convention — it is the angle the deck edge reaches, not a number chosen by rule.
Surveyor follow-up: vanishing angle of 62 degrees claimed with the deck edge immersed at 57 — accept the claim or the geometry?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
31 Why static stability curve explain
Answer
The static curve is the working reference: it shows righting at every angle, not just upright, for that exact loading.
- Static stability treats the ship as heeled by a steady moment and released, so the curve is righting arm against heel.
- It is drawn for one loading condition only — loaded arrival, medium ballast or light ballast — and re-drawn for each.
- It gives initial stability, the range, the maximum righting lever and the area for dynamic stability in one picture.
- Its shape changes with KG, free surface and trim, which is why the loading computer works in curves rather than single numbers.
Surveyor follow-up: static curve drawn for loaded arrival and used for a ballast departure condition — valid, or which curve applies?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
32 Why stiff ship has large gm
Answer
A stiff ship has large GM because the righting lever builds fast with heel — the ship snaps back hard and rolls in a short period.
- The greater the GM, the shorter the natural roll period, which is exactly the definition of a stiff ship.
- A stiff ship returns quickly to upright from a disturbance, which is safe against cargo shift and stiff in a seaway.
- Stiff vessels include container ships and ro-ros, running about 1.5 m GM, where the ride is accepted for that safety.
- Tender ships roll slowly and comfortably but have a weak margin, which is why they need a careful watch on free surface.
Surveyor follow-up: high GM for safety with a complaining crew on a long voyage — is that a stability fault or a design choice?
Full theory: Ship Stability: GM, Righting Levers and Free Surface -
33 life boat regulations Angle of loll
Also asked: “Life boat safety Angle of loll”
Answer
Two unrelated rules in one oral question: the lifeboat list angle for launching, and the angle of loll for stability.
- Davits must launch a lifeboat at a list of 20° and a trim of 10°, with a limit switch preventing the falls running out.
- The angle of loll is where a ship with negative GM settles and stays — the surveyor will test both in the same breath.
- A boat that will not launch at 20° list is outside the SOLAS requirement, whatever the ship’s stability is doing.
- Keep them separate in the answer: one is a boat requirement, the other a stability condition, and neither is proved by the other.
Surveyor follow-up: davit proved at 10° list and the ship shown to have GM positive — which of the two answers is right?
Full theory: LSA Chapter 5: Lifeboats — Types, Engine, Davit & Drills
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