Ship Stability and Cargo for the OOW

Prerequisites

You should know basic arithmetic with moments (weight × distance), simple trigonometry (sine and tangent), and the parts of a ship. From earlier lessons in this course you should know the OOW's role on the bridge and the duties set out in MGN 315, including the duty to keep a proper deck watch in port. Small-craft stability from the RYA courses (why a yacht heels and comes back up, and why water sloshing below is dangerous) is a useful start, but merchant ship stability is calculated, not felt.

For the Officer of the Watch (Unlimited) certificate (STCW Regulation II/1), stability and cargo work are examined in the MCA Stability and Operations syllabus and in the oral examination (see MSN 1856 and the MCA syllabus documents for the current scope).

Learning Objectives

Define displacement, deadweight and lightship, and use TPC, FWA and DWA.
Locate the centres K, G, B and M, and explain metacentric height (GM).
Calculate a new KG and GM after loading and discharging, including a free surface correction.
Read a GZ curve and state the IMO intact stability criteria.
Explain the free surface effect and how to reduce it.
Tell a list from an angle of loll, and correct each safely.
Calculate list and change of trim from shifting weights.
Read the load line marks and apply the load line rules.
Carry out the OOW's cargo watch and ballast duties in port, and the practical stability checks at sea.

Why the OOW Needs Stability

Stability is usually calculated by the chief officer, with the loading computer, and approved by the master. But the OOW is the one on deck when the ship starts to list unexpectedly during cargo work, who reads the draughts, who watches the ballast pumps, and who is on the bridge when the ship starts rolling slowly and hanging at the end of each roll. Many capsizes and cargo failures started with signs that a watchkeeper could have noticed. You need to understand what the numbers mean so that you can see when reality does not match them.

Displacement and Draught

Basic terms

Displacement (Δ): the total mass of the ship and everything on board, in tonnes. By Archimedes' principle it equals the mass of water displaced: Δ = underwater volume × water density.
Lightship: the ship with no cargo, fuel, water, stores or crew.
Deadweight (DWT): everything the ship carries: cargo, fuel, fresh water, ballast, stores, crew and effects. Deadweight = displacement − lightship.
Density: sea water is taken as 1.025 t/m³ and fresh water as 1.000 t/m³. Dock water lies in between and is measured with a hydrometer.

Tonnes per centimetre (TPC)

TPC is the mass that changes the mean draught by 1 cm:

TPC = waterplane area × density ÷ 100

It is given in the ship's hydrostatic tables against draught. Use it for small changes: loading 300 t on a ship with TPC 30 sinks her 10 cm.

Fresh water allowance (FWA) and dock water allowance (DWA)

A ship floats deeper in fresh water than in sea water because fresh water is less dense. The FWA is the increase in draught, in millimetres, going from salt to fresh water at the summer displacement:

FWA (mm) = Δ ÷ (4 × TPC)

In dock water of density ρ (t/m³, written as kg/m³ in the formula):

DWA (mm) = FWA × (1025 − ρ) ÷ 25

So a ship loading in a river port with dock water of 1010 kg/m³, FWA 150 mm, may submerge her load line by DWA = 150 × 15 ÷ 25 = 90 mm, because she will rise by that amount when she reaches sea water.

The Centres: K, G, B and M

K, the keel: the reference point for vertical heights.
G, the centre of gravity: where the ship's whole weight acts. KG is its height above the keel. It depends on how the ship is loaded, and it is the figure you control.
B, the centre of buoyancy: the centre of the underwater volume, where buoyancy acts upward. KB depends on draught (and hull shape).
M, the transverse metacentre: for small angles of heel, the point where the vertical through the heeled centre of buoyancy cuts the centreline. KM = KB + BM, where BM = I ÷ V (the second moment of the waterplane area about the centreline divided by the underwater volume). KM is read from the hydrostatic tables for the draught.

Metacentric height (GM)

GM = KM − KG

When the ship heels, B moves towards the low side (to B1), because more volume is immersed there. Weight still acts down through G; buoyancy acts up through B1. The horizontal distance between the two lines of action is the righting lever GZ. The diagram below shows the geometry.

Cross-section of a heeled ship showing K, G, B, B1, M and the righting lever GZ

If M is above G (GM positive), the couple pushes the ship back upright: stable.
If G and M coincide (GM zero): neutral. The ship stays at whatever angle she is pushed to.
If G is above M (GM negative): unstable when upright. The ship heels over until she finds an angle where she is stable, or capsizes.

For small angles (up to about 10° to 15°):

GZ = GM × sin θ

and the righting moment = Δ × GZ (tonne-metres).

Stiff and tender

A large GM makes a stiff ship: a strong righting moment and a short, quick, jerky roll that is uncomfortable, strains lashings and can shift cargo (container and heavy-lift ships with big GMs suffer this). A small GM makes a tender ship: a long, slow, lazy roll, and less reserve of stability. The ideal is a moderate GM.

The rolling period gives a practical check on GM. A common approximation is:

Roll period T (seconds) ≈ 2 × C × B ÷ √GM

where B is the ship's beam and C is a coefficient usually around 0.37 to 0.42 (the IMO Intact Stability Code gives a formula for it). If the roll period grows noticeably longer during a voyage (fuel burned from double bottoms, ice accretion, water on deck, slack tanks), GM is falling. Report it.

Calculating KG and GM

Method of moments

Each weight's vertical moment about the keel is weight × its own KG (often written Kg). The new KG is the total moment divided by the total displacement:

KG = Σ(weight × Kg) ÷ Σweight

Take discharged weights away as negative weights.

Worked GM calculation

A ship has a displacement of 10,000 t and KG 7.20 m. She loads 500 t of cargo in the lower hold at Kg 2.0 m and discharges 200 t from the 'tween deck at Kg 9.0 m. After the work, the free surface moments of slack tanks total 1,500 t·m. At the final displacement, the hydrostatic tables give KM 7.90 m.

Item	Weight (t)	Kg (m)	Moment (t·m)
Ship	10,000	7.20	72,000
Loaded	+500	2.00	+1,000
Discharged	−200	9.00	−1,800
Total	10,300		71,200

Solid KG = 71,200 ÷ 10,300 = 6.913 m.
Free surface correction (FSC) = 1,500 ÷ 10,300 = 0.146 m.
Fluid KG = 6.913 + 0.146 = 7.059 m.
GM (fluid) = KM − fluid KG = 7.900 − 7.059 = 0.841 m.

The IMO minimum initial GM is 0.15 m, so the ship is well within limits for this criterion. Notice how loading low and discharging high lowered G, increasing GM, while the slack tanks cost almost 15 cm of it.

Free Surface Effect

When a tank is partly full (slack), the liquid flows to the low side as the ship heels. Its centre of gravity moves out to the low side, which reduces the righting lever as if G had risen. This virtual rise of G is the free surface correction:

FSC = free surface moment ÷ Δ

For a rectangular tank, free surface moment (t·m) = (l × b³ ÷ 12) × density of the liquid in the tank

where l is the length and b the breadth of the tank.

Key points:

It depends on the tank's breadth cubed, not on how much liquid is in it. A tank with a few centimetres of water in the bottom has nearly the same effect as a half-full one.
Dividing a tank with a longitudinal bulkhead into two equal halves cuts the free surface effect to a quarter (each half has an eighth of the original b³; two of them make a quarter).
Keep the number of slack tanks to a minimum. Press tanks up full or pump them empty.
Water on deck, in holds, or from firefighting has a large free surface effect. Firefighting water has capsized ships alongside. Pump it out.

Example: a double-bottom tank 20 m long and 10 m wide, slack with sea water. FSM = 20 × 10³ ÷ 12 × 1.025 = 1,708 t·m. On a 10,300 t ship that is an FSC of 0.166 m: one tank alone wipes out about a fifth of the GM in the worked example.

The GZ Curve

For larger angles, GZ is not GM × sin θ, because the waterplane changes shape as the deck edge goes under or the bilge comes out. The ship's stability information gives cross curves (KN curves), and:

GZ = KN − KG × sin θ

(with KG corrected for free surface). Plotting GZ against heel gives the curve of statical stability. The diagram below shows a typical curve and the IMO criteria.

GZ curve showing initial GM tangent, maximum GZ, angle of vanishing stability and the IMO criteria

What to read from it:

Initial slope: the tangent at the origin passes through GM at 57.3° (one radian). A steep start means a large GM.
Maximum GZ and the angle at which it occurs.
Angle of vanishing stability: where GZ falls back to zero. Beyond it the ship capsizes.
Range of stability: from upright to the angle of vanishing stability.
Area under the curve: the dynamic stability, the energy available to resist heeling by wind and waves.

IMO intact stability criteria

The general criteria in the 2008 Intact Stability Code (Part A) are:

Criterion	Minimum
Area under GZ curve up to 30°	0.055 m·rad
Area up to 40° (or the flooding angle, if less)	0.090 m·rad
Area between 30° and 40° (or flooding angle)	0.030 m·rad
GZ at an angle of 30° or more	0.20 m
Angle of maximum GZ	Preferably not less than 25°
Initial GM (corrected for free surface)	0.15 m

There is also a severe wind and rolling (weather) criterion, and special rules for particular ship types (grain cargoes under the International Grain Code, timber deck cargoes, container ships, passenger ships). Every ship must have approved stability information, and the master must make sure the ship complies before sailing. The loading computer checks these criteria for each condition.

List and Loll

A ship lying at an angle in calm water has either a list or an angle of loll. They look the same from the quay, but they have opposite causes and opposite cures, and getting it wrong can capsize the ship. The diagram below compares them.

List

G has moved off the centreline (unequal loading, a full tank on one side, cargo shifted). GM is positive. The ship heels until B1 is vertically below G1, and she always lies to the same side.

tan θ = GG1 ÷ GM, where GG1 = (w × d) ÷ Δ

w is the weight moved (or loaded off-centre) and d the transverse distance.

Example: in the worked GM example (Δ 10,300 t, GM 0.841 m), 80 t of cargo is landed 10 m off the centreline instead of on it. GG1 = 80 × 10 ÷ 10,300 = 0.078 m. tan θ = 0.078 ÷ 0.841 = 0.093, θ = 5.3°.

Cure: move weight back across, or ballast the high side.

Loll

G is on the centreline but above M: GM is negative when upright. The ship cannot stay upright; she flops to one side. As she heels, B moves out far enough that the righting lever becomes positive again, and she hangs at the angle of loll where GZ is zero. She may flop over to the other side in a sea or during a turn, and she has very little reserve of stability.

Signs of loll rather than list:

No reason for a list can be found (tanks and cargo are symmetrical).
The ship flops from one side to the other.
She rolls slowly and hangs at the end of each roll, about the lolled angle rather than about upright.
Typical causes are present: fuel and water burned from double bottoms, high deck cargo (timber, containers) absorbing water, ice accretion, slack tanks.

Cure: lower G. Never try to correct loll by moving weight to the high side: it will make the ship flop over to the other side at a larger angle. The safe sequence is:

Confirm it is loll, not list.
Remove free surface where possible: press up slack tanks or empty them.
Fill low double-bottom tanks, starting with a divided tank on the low side (filling it first adds weight low down and on the side she is already lying, and the free surface of a small tank is small). Then fill the matching tank on the high side.
Remove or lower top weight if possible (jettison deck cargo only as a last resort and with the master's decision).

Trim

Terms

Trim: the difference between the draughts aft and forward. Trim by the stern (deeper aft) is normal for good steering and propeller immersion.
LCF (longitudinal centre of flotation): the point about which the ship trims, the centroid of the waterplane. It is near amidships but moves with draught.
MCTC (moment to change trim 1 cm): the trimming moment (t·m) that changes trim by 1 cm. From the hydrostatic tables.

Change of trim (cm) = trimming moment ÷ MCTC

Worked trim example

A ship 140 m long, Δ 10,300 t, MCTC 160 t·m/cm, LCF at amidships. The OOW is told to transfer 150 t of ballast from the fore peak (centre 60 m forward of amidships) to the after peak (centre 65 m aft of amidships).

Distance moved = 60 + 65 = 125 m aft.
Trimming moment = 150 × 125 = 18,750 t·m by the stern.
Change of trim = 18,750 ÷ 160 = 117 cm by the stern.
With LCF amidships, the change is shared equally: aft draught increases by about 59 cm, forward draught decreases by about 59 cm. (If the LCF is not amidships, share it in proportion to the distances of the perpendiculars from the LCF.)

Check the forward draught does not become so small that the bow slams or the forward bridge visibility rule (SOLAS V/22) is breached, and check the aft draught against the berth or channel depth.

Load Lines

The marks

The International Convention on Load Lines 1966 (with its 1988 Protocol), applied in the UK by the Merchant Shipping (Load Line) Regulations, sets the minimum freeboard so that the ship has enough reserve buoyancy and a reasonably dry deck. The marks are cut or welded into the ship's side amidships and painted in a contrasting colour. The diagram below shows them.

Load line marks: deck line, Plimsoll disc and the TF, F, T, S, W and WNA lines with typical spacings

Deck line: marks the freeboard deck.
Load line disc (Plimsoll mark): a ring 300 mm across with a horizontal line through it. The upper edge of the line passes through the centre of the disc and is level with the summer load line. The letters either side show the assigning authority (for example L R).
The load lines, each measured to its upper edge:

Mark	Meaning	Position
S	Summer	Level with the centre of the disc
W	Winter	1/48 of the summer draught below S
WNA	Winter North Atlantic	50 mm below W (ships 100 m or less in length)
T	Tropical	1/48 of the summer draught above S
F	Fresh water summer	FWA above S
TF	Tropical fresh water	FWA above T

Timber ships have extra timber load lines marked with an L prefix.

Zones and areas

The Convention divides the oceans into tropical and summer zones and seasonal areas (winter, tropical) shown on a chart in the Convention and on routeing charts. The applicable load line is the one for the zone the ship is in, and the ship must not be loaded so that the appropriate mark is submerged at any stage of the voyage: departure, through each zone, and arrival. A ship leaving a tropical-zone port bound into a summer zone must have burned enough fuel and water by the time she crosses the boundary to bring the summer mark clear.

Loading in dock water

Load until the appropriate mark is submerged by no more than the DWA calculated from the measured dock water density, then allow for fuel and water to be consumed before reaching a new zone. Take the density sample from several depths alongside, away from any outfall.

Overloading is an offence for the master and the owner, and is detained by port State control.

Cargo Watch Duties in Port

When the ship is alongside, the OOW keeps a deck watch for the master and chief officer (STCW Chapter VIII, Part 4-4 sets out the principles of keeping a watch in port). The typical duties are:

Safety of the ship

Moorings: tend them as the ship rises and falls with tide and cargo. Slack lines let the ship range along the berth; overtight lines part or pull bollards out. Never stand in a snap-back zone.
Draught, trim and list: read the draughts regularly and compare them with the loading plan. Any unexpected list is a reason to stop and find out why.
Gangway: safe access with a safety net, lighting, a lifebuoy with line, adjusted as the ship moves.
Weather: watch for wind increase that could break the ship off the berth or stop crane work.
Fire and security: fire rounds, hot work permits, ISPS security level and access control.
Pollution: watch over the side for oil, and keep scuppers plugged during bunkering.

Following the cargo plan

Check the loading or discharging sequence against the stowage plan and the loading computer results, and record progress.
Keep ballast operations in step with cargo so that stresses (shear forces and bending moments) stay within limits at every stage, not just at the end. On bulk carriers the BLU Code requires a loading or unloading plan agreed with the terminal, including ballasting, and the right to stop cargo work if limits will be exceeded.
Watch for the signs of excessive hogging (ends drooping, more draught at the ends than expected) or sagging (middle deeper than the mean of the ends). Compare the midships draught with the mean of forward and aft draughts.
Check that cargo is correctly stowed and secured according to the Cargo Securing Manual (CSS Code), that dangerous goods are segregated and labelled according to the IMDG Code, and that solid bulk cargoes have the right declarations under the IMSBC Code (some cargoes can liquefy and shift if their moisture content is too high).
On tankers, follow the ship-shore safety checklist and ISGOTT procedures, monitor tank levels, inert gas pressure and loading rates, and know how to stop cargo in an emergency.

Stopping cargo work

You have the authority, and the duty, to stop cargo work if you see a danger: an unexpected list, damaged cargo or packaging, a leaking dangerous goods container, stresses approaching limits, mooring failure, or unsafe work by stevedores. Stop first, then inform the chief officer.

Ballast

Why ballast

Ballast gives a light ship enough draught to immerse the propeller and rudder, enough forward draught to reduce slamming, enough stability, acceptable trim and list, and acceptable hull stresses.

Ballast water management

The IMO Ballast Water Management Convention (in force since 2017) aims to stop the transfer of harmful aquatic organisms in ballast water. Ships carry an approved Ballast Water Management Plan and a Ballast Water Record Book, and must meet:

the D-1 standard (ballast water exchange): at least 95% volumetric exchange, where possible at least 200 nautical miles from the nearest land in water at least 200 m deep (if not possible, at least 50 miles from land in 200 m depth). This standard has now been replaced by D-2 for almost all ships.
the D-2 standard (performance): treatment by an approved ballast water management system to limit the number of viable organisms discharged.

Every ballast operation (taking in, discharging, transferring, treating) must be recorded with times, positions, quantities and tanks. Check the requirements of each port State, which may be stricter.

OOW ballast duties

Know which tanks are being worked, the planned quantities, and the order.
Sound tanks or monitor the remote gauges regularly, and check the ship's draught and list respond as expected.
Watch for overflow from air pipes, which means a tank is pressed up or a valve is wrong.
Remember sequential exchange at sea briefly affects stability and stress: follow the approved sequence exactly.
Record everything.

Practical Stability Checks for the OOW at Sea

Watch the roll. A long, slow roll that hangs at the end suggests small or negative GM. A sudden change in roll period is a warning.
Watch for unexpected list. It may mean cargo shift, flooding, a tank valve left open, or loll.
Bilge and tank soundings. Unexplained increases in a hold bilge or a ballast tank can mean flooding.
Deck cargo and lashings. Check after heavy weather, and report anything slack or damaged.
Ice accretion and water on deck. Both raise G. Arrange removal of ice early.
Fuel and water consumption. Burning from double bottoms raises G and adds free surface. The chief officer will have planned the sequence; know it.
Heavy weather. Avoid conditions that cause synchronous or parametric rolling, and remember stability is reduced when a wave crest is amidships.
Damage. In flooding, the order is: stop the inflow if possible, report, close watertight doors, and use the damage stability information. Free surface and loss of buoyancy both act at once.

Worked Example: An Unexpected List During Loading

A general cargo ship is loading steel products at night. You are on deck watch. The ship is planned to be upright throughout. At 0200 you notice a list of about 3.5° to port, and the gangway is starting to bind.

Stop and assess. Ask the stevedore foreman to stop loading on the port side. Read the draughts both sides amidships: port 8.26 m, starboard 7.04 m. On a 20 m beam that difference of 1.22 m confirms a list of about 3.5° (tan θ = 1.22 ÷ 20).
Check the obvious causes. The last three lifts went into the port wing of No. 3 hold. Tank soundings show No. 2 double-bottom port is 30 t fuller than the plan. Someone has been filling it.
Is it a list or loll? The ship lies steadily to port, does not flop, and the causes found are asymmetric: list, with positive GM.
Estimate. Δ 12,000 t and GM 0.65 m (from the loading computer). The extra 30 t in the port tank is 6 m off the centreline (180 t·m), and about 60 t more cargo than planned has gone into the port wing at 5 m (300 t·m). Total 480 t·m. GG1 = 480 ÷ 12,000 = 0.040 m. tan θ = 0.040 ÷ 0.65 = 0.062, θ = 3.5°. The calculated list matches the observed one, so the cause is understood.
Correct and report. Call the chief officer. The pump on No. 2 port is stopped and the valve found open; the tank is transferred back to plan. The stevedores load the next lifts to starboard. The ship comes upright. Record the event in the log.

The point: an unexpected list is information. Find the cause before correcting it, because the wrong correction on a lolling ship is dangerous.

Common Mistakes

Forgetting the free surface correction, or thinking a nearly empty tank has no free surface effect.
Using GZ = GM sin θ at large angles. Use KN curves.
Correcting loll by shifting weight to the high side. Lower G instead, starting with the low side.
Treating a list as unimportant. It always has a cause, and the cause may be flooding.
Ignoring the midships draught, so missing hogging or sagging.
Deballasting ahead of cargo, letting stresses exceed limits during the operation.
Loading to the mark in dock water without the DWA calculation, or forgetting a zone change during the voyage.
Not recording ballast operations in the Ballast Water Record Book.
Allowing firefighting water to accumulate in a ship alongside.

Summary

Displacement = underwater volume × density. Deadweight = displacement − lightship. TPC, FWA = Δ ÷ (4 × TPC), DWA = FWA × (1025 − ρ) ÷ 25.
GM = KM − KG. Positive GM: stable. For small angles GZ = GM sin θ; for large angles GZ = KN − KG sin θ.
New KG by moments; add the free surface correction (FSM ÷ Δ) to get fluid KG.
Free surface effect depends on tank breadth cubed; a centreline bulkhead cuts it to a quarter.
IMO criteria: areas 0.055, 0.090 and 0.030 m·rad; GZ 0.20 m at 30° or more; maximum GZ at 25° or more; GM at least 0.15 m.
List: G off the centreline, GM positive, always the same side; tan θ = GG1 ÷ GM. Loll: GM negative upright, flops either side; lower G, low side first.
Change of trim = trimming moment ÷ MCTC.
Load lines: S at the disc centre, T and W at 1/48 of summer draught above and below, WNA 50 mm below W, F and TF one FWA above S and T.
On cargo watch, keep ballast in step with cargo, watch draughts, list and moorings, and stop work when something is wrong.
At sea, watch the roll period, lists, soundings and anything that raises G.

Check Your Understanding

A ship has KM 8.20 m and KG 7.60 m, with free surface moments of 900 t·m at a displacement of 15,000 t. What is her fluid GM?

Answer: FSC = 900 ÷ 15,000 = 0.06 m. Fluid KG = 7.66 m. GM = 8.20 − 7.66 = 0.54 m.

Why does dividing a slack tank with a centreline bulkhead reduce the free surface effect to a quarter?

Answer: Free surface moment depends on the tank breadth cubed. Each half has half the breadth, so one-eighth of the moment; two halves give one-quarter of the original.

A ship of Δ 8,000 t and GM 0.40 m has 50 t moved 12 m across the deck. What list results?

Answer: GG1 = 50 × 12 ÷ 8,000 = 0.075 m. tan θ = 0.075 ÷ 0.40 = 0.1875, θ = 10.6°.

How do you tell a list from an angle of loll, and why does it matter?

Answer: A list lies steadily to one side with an asymmetric cause found and positive GM. A lolling ship has no asymmetric cause, may flop to either side, and rolls slowly about the lolled angle. It matters because the cure for a list (moving weight to the high side) can make a lolling ship flop over to a larger angle on the other side.

State four of the IMO intact stability criteria from the 2008 IS Code.

Answer: Any four of: area to 30° at least 0.055 m·rad; area to 40° (or flooding angle) at least 0.090 m·rad; area 30° to 40° at least 0.030 m·rad; GZ at least 0.20 m at 30° or more; maximum GZ preferably at 25° or more; initial GM at least 0.15 m.

Summer draught 12.00 m, TPC 40, summer displacement 40,000 t. Where are the T, W and F marks relative to S?

Answer: 1/48 of 12.00 m = 250 mm, so T is 250 mm above S and W 250 mm below S. FWA = 40,000 ÷ (4 × 40) = 250 mm, so F is 250 mm above S.

The ship in question 6 loads in dock water of density 1,005 kg/m³. By how much may she submerge the summer mark?

Answer: DWA = 250 × (1,025 − 1,005) ÷ 25 = 200 mm, assuming she is in a summer zone and no further allowance for consumption is needed.

A ship with MCTC 200 t·m/cm shifts 120 t of cargo 50 m forward. What is the change of trim, and how is it shared if the LCF is amidships?

Answer: Trimming moment 6,000 t·m. Change of trim = 30 cm by the head. Forward draught increases by 15 cm and aft draught decreases by 15 cm.

During cargo work you find the midships draught is much deeper than the mean of the forward and aft draughts. What does this suggest, and what should you do?

Answer: The ship is sagging (heavy weight concentrated amidships). Check the loading computer stresses against the actual condition, inform the chief officer, and stop or adjust cargo and ballast work if limits may be exceeded.

On passage the roll period has become noticeably longer and the ship hangs at the end of each roll. What may be happening, and what checks would you make?

Answer: GM is decreasing, possibly towards zero or negative. Check for slack tanks and fuel burn from double bottoms, water on deck or in holds, ice accretion, and shifting cargo; take soundings; inform the master.