ShipCalculators.com

Published · last updated

Trim and list

Trim is the signed difference between a ship’s aft draft and forward draft, expressing the degree and direction of longitudinal inclination in still water. List is the corresponding transverse inclination produced by an off-centre distribution of mass or by an asymmetric wind moment. Both quantities are hydrostatic consequences of where weight is placed relative to the centres of buoyancy and flotation, and both must be monitored continuously throughout loading, discharging, bunkering, and ballasting operations. Uncorrected trim affects propulsive efficiency, hull stress, and compliance with load-line regulations; uncontrolled list endangers stability margins and can initiate capsize in degraded conditions. ShipCalculators.com provides dedicated calculators for every step in the trim and list calculation chain, from moments to change trim through to optimal-trim fuel-savings estimation, covering all commercial vessel types.

Contents

Background and history

The importance of managing a ship’s longitudinal and transverse inclination has been recognised since antiquity. Ancient Mediterranean mariners carried ballast stone to control trim, and early Arab and Chinese navigators documented the relationship between cargo placement and the waterline angle. The systematic mathematical treatment of these phenomena, however, did not emerge until the eighteenth century.

Pierre Bouguer’s Traité du navire (1746) and Leonhard Euler’s Scientia Navalis (1749) established the geometric and hydrostatic theory of metacentric stability - the framework within which both list and trim are now calculated. Bouguer introduced the concept of the metacentre and showed that transverse stability depends on the vertical separation of the metacentre from the centre of gravity. Euler derived the relationship between the second moment of the waterplane area and the metacentric radius, providing the basis for computing both the transverse and the longitudinal metacentric heights that govern list and trim respectively.

The distinction between the longitudinal and transverse hydrostatic problem was first made explicit by French naval architects in the late eighteenth century. The longitudinal metacentric height GML is typically one hundred times larger than the transverse GMT for a conventional cargo vessel, which is why trim - the longitudinal inclination - responds very stiffly to weight shifts while list - the transverse inclination - responds much more sensitively to the same magnitude of off-centre moment.

Through the nineteenth century, the rapid growth of steam-powered iron and steel vessels demanded more formal methods of ensuring that vessels departed port in a safe condition. The loss of HMS Captain in 1870 (the capsizing of an improperly designed turret warship with negative GM) and the Plimsoll agitation in the 1860s and 1870s that led to the UK Merchant Shipping Act of 1876 and the first statutory load-line markings were the two critical regulatory milestones that gave legal force to stability requirements. Samuel Plimsoll’s campaign was explicitly motivated by cases of overloaded and improperly ballasted vessels that left port with dangerously small freeboards and inadequate stability - conditions expressed directly through excessive trim and small GM.

The International Load Line Conference of 1930 established the first internationally agreed freeboard and stability standards, which included limitations on trim relative to the load-line marks. These requirements were progressively codified into IMO instruments through the twentieth century, reaching their current form in SOLAS chapter II-1 (damage stability), the 2008 IMO Intact Stability Code (Resolution MSC.267(85)), and the International Load Line Convention 1966 as amended by the 1988 Protocol. Today, the IMO requires that every vessel’s loading manual and stability booklet be approved by a recognised classification society or flag administration, and that the vessel’s officers verify compliance with trim and stability criteria before each departure.

Definitions and sign conventions

Trim

Trim (t) is defined as the draft aft (dA) minus the draft forward (dF):

t = dA − dF

When the aft draft exceeds the forward draft the vessel is said to be trimmed by the stern, and trim is assigned a positive value. When the forward draft exceeds the aft draft the vessel is trimmed by the head, and trim is negative. The magnitude of trim in commercial practice is normally expressed in metres or centimetres. A vessel on which the forward and aft drafts are equal is said to be on an even keel, a condition that maximises waterplane symmetry and is used as the baseline condition for many hydrostatic tables.

Trim is measured between the perpendiculars of the ship: the forward perpendicular at the intersection of the design waterline with the stem, and the aft perpendicular at the centreline of the rudder stock. The length between perpendiculars (LBP) enters all trim calculations and must not be confused with the length overall (LOA). On most cargo vessels LBP is between 96% and 99% of LOA.

Mean draft and true mean draft

The mean draft dM is the arithmetic average of the forward and aft drafts: dM = (dA + dF) / 2. This gives the draft at the midships point, which lies at the midpoint of LBP. The displacement read from hydrostatic tables corresponds to the draft at the longitudinal centre of flotation (LCF), not at midships. Because the LCF is rarely located exactly amidships, a correction is required to convert the midships mean draft to the true mean draft at the LCF.

The correction is: dLCF = dM + (t × l) / LBP, where l is the distance from midships to the LCF measured positive forward. The mean draft calculator performs this correction automatically from tabulated LCF positions. The resulting true mean draft is the value entered into the hydrostatic table to extract displacement, TPC, MCT1cm, and the other hydrostatic particulars for the loading condition. Neglecting the correction introduces a systematic displacement error that increases with trim and with the distance of the LCF from midships - errors that can reach tens of tonnes on a large bulk carrier with heavy trim by the stern.

List

List is a static transverse heel caused by a permanent asymmetry in the distribution of weight or, in specific circumstances, by a steady wind heeling moment acting on a vessel with inadequate GM. A ship listing to starboard has its port deck edge higher than the starboard deck edge; one listing to port has the starboard edge higher. List is distinguished from dynamic rolling, which is an oscillatory motion, and from loll, which is the condition of a vessel with negative GM that reaches an equilibrium heel angle at which the righting arm GZ is zero.

The angle of list φ for small angles is given by:

tan φ = (w × d) / (Δ × GM)

where w is the transverse off-centre mass, d is its transverse distance from the centreline, Δ is the total displacement, and GM is the effective metacentric height corrected for free surfaces. For angles beyond approximately five to eight degrees the small-angle approximation breaks down and the wall-sided formula or a full GZ curve integration must be used.

Hydrostatic basis of trim calculations

Tonnes per centimetre immersion

The tonnes per centimetre immersion (TPC) quantifies how much vertical bodily sinkage results from adding a small mass. It is derived from the waterplane area Aw and the water density ρ:

TPC = Aw × ρ / 100

where Aw is in m², ρ is in t/m³, and TPC is in t/cm. In salt water (ρ = 1.025 t/m³) this simplifies to TPC = Aw × 1.025 / 100. The TPC calculator and the TPC from Simpson’s Rule calculator both provide this value; the latter derives the waterplane area directly from a set of half-breadths using numerical integration, bypassing the need for tabulated hydrostatics.

Bodily sinkage s (in cm) from adding a mass w (in tonnes) with no change in trim is:

s = w / TPC

The bodily sinkage calculator calculates this directly. In practice, adding weight at the LCF produces pure bodily sinkage without any trim change; adding weight at any other longitudinal position produces both sinkage and a change of trim, and the two effects are superimposed.

Moment to change trim 1 cm

The moment to change trim 1 cm (MCT1cm) is the trimming moment required to produce exactly one centimetre of change in trim between the perpendiculars. It is defined as:

MCT1cm = (Δ × GML) / (100 × LBP)

where Δ is displacement in tonnes, GML is the longitudinal metacentric height in metres, and LBP is the length between perpendiculars in metres. The result is in tonne-metres per centimetre. Values of MCT1cm for a given vessel are tabulated in its stability booklet against draft; the MCT1cm calculator provides the formula-based derivation from first principles.

GML is typically very large compared with the transverse GM - of the order of 90% to 100% of LBP for most cargo vessels - because the longitudinal second moment of the waterplane area vastly exceeds the transverse second moment. This is why it takes substantial trimming moments to change the longitudinal attitude of a large vessel, and why small longitudinal weight shifts, measured in the tens of tonnes, produce trim changes of only a few centimetres on a vessel displacing tens of thousands of tonnes.

Change of trim from weight addition or removal

When a mass w is loaded at a distance d from the LCF, the trimming moment is w × d, and the resulting change of trim Δt (in cm) is:

Δt = (w × d) / MCT1cm

The trim from weight shift calculator and the trim moment calculator perform this calculation. The change of trim is distributed between the fore and aft ends in proportion to the distances from the LCF to the forward and aft perpendiculars. Designating lF and lA as those distances, the change in forward draft is:

ΔdF = −Δt × lF / LBP (negative for trim by stern)

and the change in aft draft is:

ΔdA = +Δt × lA / LBP

The total draft change at each end is the algebraic sum of bodily sinkage and the end-specific trim change. The trim from loading centroid calculator extends this to the combined loading of multiple parcels, placing the resultant at the total loading centre of gravity.

When removing a weight, the sign of the trimming moment reverses: the vessel rises bodily and its trim changes in the direction away from the point of removal relative to the LCF.

Reading draft marks and correcting for geometry

Draft mark positions and reading procedure

All seagoing vessels are required by SOLAS and the International Load Line Convention to carry draft marks at the forward and aft perpendiculars; larger vessels typically also carry midships marks on each side of the hull. Draft marks are calibrated in decimetres or centimetres and are read from the waterline intersection with the marked scale. On vessels with pronounced flare, the observer must position themselves at the correct vantage point to avoid parallax error.

On large vessels such as fully loaded bulk carriers and tankers, drafts are read simultaneously fore and aft, and if possible at midships, by observers equipped with radio communication. The midships reading allows the magnitude of hogging or sagging to be estimated: a vessel that reads less at midships than the mean of fore and aft is sagging (midship deck girder in tension), and one that reads more at midships is hogging (midship deck girder in compression). This distinction matters because the displacement derived from the forward and aft drafts alone will slightly overestimate displacement when the vessel is sagging and underestimate it when hogging. Classification society load-line survey procedures, including those of Lloyd’s Register and DNV, specify corrections for hog and sag when the deviation from the even-keel baseline exceeds prescribed limits.

Correction to the perpendiculars

The draft marks on most vessels are not at the exact location of the forward and aft perpendiculars but are offset by a few decimetres to a few metres. The stability booklet records these offsets, and a perpendicular correction must be applied before using the draft readings in hydrostatic calculations. The correction is:

corrected draft = observed draft ± ((t / LBP) × offset distance)

Applying this correction is mandatory for any draft survey, cargo calculation, or compliance check against load-line marks. Failure to apply it is a common source of systematic displacement errors in cargo surveys.

Allowance for water density

The waterplane-derived TPC and MCT1cm values in hydrostatic tables are computed for salt water at 1.025 t/m³. When the vessel is loading in dock water (fresh water, dock water, or brackish water) both quantities change. The fresh water allowance (FWA) and dock water allowance (DWA) correct the load-line marks; the FWA/DWA calculator and the density-draft calculator provide these corrections. A vessel loading to its full summer load line in dock water of density 1.010 t/m³ will sink to a deeper draft when it reaches open salt water if no FWA correction was applied.

Trim from loading and discharging operations

The superposition principle

The standard method for predicting the final trim of a vessel after a loading or discharging plan has been applied is the superposition of bodily sinkage and change of trim for each parcel of cargo, fuel, or ballast. The calculation proceeds as follows. For each item added, the bodily sinkage at TPC and the trimming moment at the distance from the LCF are computed. All bodily sinkages are summed to give total mean sinkage, and all trimming moments are summed and divided by MCT1cm to give the total change of trim. The change of trim is distributed to fore and aft ends in the proportional manner described above.

This method assumes that TPC and MCT1cm remain substantially constant throughout the loading operation, which is accurate for modest changes in draft. For deep loading operations where drafts change by a metre or more, the calculation should be iterated using updated hydrostatic values at the intermediate draft, or the trim from loading centroid calculator should be used with hydrostatic values at the anticipated final mean draft.

Bulk carrier loading plans

Bulk carriers present some of the most demanding trim management challenges. The grain parcels loaded at each hold must be distributed so that the final trim satisfies the vessel’s trim limits (typically between one-half per cent and one per cent of LBP by the stern for seakeeping and propulsive efficiency), the forward draft does not exceed the forward draft limit derived from the forward load-line, and the shear force and bending moment at every section of the hull remain within the limits specified by the classification society under IACS Unified Requirement S1 for longitudinal strength.

On Panamax and Capesize bulk carriers, typical trim by stern at full departure is between 0.5 m and 2.0 m. Excessive trim by head must be avoided because it raises the stern clear of the water, reducing propeller submergence and causing vibration, and because it increases the bending moment at the midship section. Excessive trim by stern increases squat in shallow water (see below) and can cause the forward accommodation block and navigation equipment to slam in heavy seas.

Reload and restow operations for bulk carriers, which occur when cargo is found to have shifted or when intake ports require redistribution, require re-running the full trim calculation and updating the stability booklet entry before departure.

Container ship loading plans

Container vessels operate with detailed computerised loading plans, produced by dedicated software such as BAPLIE-format planners, that pre-compute trim and stability for every slot. Trim requirements for container ships are stricter than for bulk carriers in one respect: propeller emergence at light ballast conditions can occur easily given the box-shaped underwater form, and the ship operator must ensure that the aft trim at minimum departure conditions provides adequate propeller submergence, typically at least one propeller diameter. Container vessels often finish cargo operations with a controlled stern trim of 0.5 m to 1.5 m achieved by adjusting ballast tanks rather than cargo placement.

Tanker loading and ballasting

On oil tankers and chemical tankers, trim management is integral to the cargo-loading sequence because cargo is pumped into tanks that span the vessel’s breadth. Tanker cargo officers work from a loading manual that specifies the sequence for filling each tank to control trim within limits while maintaining adequate GM at all stages of loading. During simultaneous cargo operations and ballast exchanges, the order in which valves are opened and closed is critical: pressing up a ballast tank before opening a cargo tank maintains the free-surface correction, and the sequencing prevents momentary negative GM that could occur if both a full forward ballast tank and a full forward cargo tank are simultaneously emptied.

Residual cargo in slop tanks, which cannot be discharged and is carried as part of the on-board quantity, shifts the centre of gravity away from the centreline if tank geometry is asymmetric. Tanker operators account for residual slop in the loading calculation. The cargo securing manual is the parallel document governing safe restraint of packaged cargo on Ro-Ro and multi-purpose vessels, and it cross-references similar weight distribution rules.

General cargo and ro-ro vessels

General cargo ships and ro-ro vessels present particular trim and list challenges because cargo is often loaded by wheeled transport - trucks, trailers, and cars - that cannot be repositioned after it leaves the ramp. The chief officer must pre-plan the loading sequence to ensure that each successive deck-tier and each successive cargo batch lands in a position consistent with the evolving trim and GM margin. Deviations from the plan - caused by last-minute cargo changes, shipper substitutions, or late arrivals - require immediate re-assessment of the loading calculation.

On ro-ro vessels, large cargo items such as oversized machinery, industrial equipment, and heavy vehicles must be restrained by lashings dimensioned to withstand the accelerations specified in the vessel’s cargo securing manual. Poor lashing design or installation can allow cargo to slide transversely under rolling, generating a dynamic heeling moment that exceeds the vessel’s intact GM and produces a persistent list. The MV Riverdance and MV Höegh Osaka incidents both illustrate this failure mode, which is discussed below in the section on casualties.

List: causes, calculation, and management

List from transverse weight shift

Moving a mass w transversely a distance d from the centreline shifts the centre of gravity by GG1 = (w × d) / Δ. This transverse GG1 is equivalent to an off-centred heeling moment, and the resulting list angle φ satisfies:

tan φ = GG1 / GM = (w × d) / (Δ × GM)

The list from weight shift calculator and the list angle from transverse weight shift calculator both implement this formula. For a vessel with Δ = 20,000 t, GM = 1.2 m, and a 200 t mass shifted 5 m to starboard, the formula gives tan φ = (200 × 5) / (20,000 × 1.2) = 1,000 / 24,000 = 0.0417, or φ ≈ 2.4°. Corrective action would be to shift ballast water transversely or to move an equivalent weight to port.

List from off-centre weight addition

Adding a new mass w at a transverse distance d from the centreline both sinks the vessel bodily and produces a list. The new displacement after addition is Δ1 = Δ + w. The new GM1 must account for the rise of G caused by the mass being added above the keel and for any new free-surface corrections if a tank is partially filled. The resulting list angle satisfies:

tan φ = (w × d) / (Δ1 × GM1)

The list from off-centre weight addition calculator provides this calculation. On completion of bunkering operations, for instance, where the bunker station is located several metres off the centreline, the chief officer calculates the resulting list and corrects it by transferring ballast water or fuel between port and starboard settling tanks.

Wall-sided formula for larger angles

The small-angle approximation for list is accurate to within about 1% for angles up to approximately 5° and to about 5% at 10°. For larger list angles, the wall-sided formula provides a more accurate relationship between GZ and heel angle φ for the range of angles over which the waterplane remains essentially wall-sided (vertical topsides):

GZ = ((GM + BM × tan²φ / 2) × sin φ)

The wall-sided heel calculator solves this equation for the equilibrium heel angle when there is a known transverse heeling moment. The wall-sided formula is particularly relevant for high-sided container vessels and car carriers at moderate load conditions where the initial GM is relatively small and list angles of more than 5° can occur from asymmetric cargo loading.

Free surface and its effect on list

Free surfaces in partially filled tanks reduce effective GM and thus amplify the list produced by any given off-centre moment. The free-surface correction to GM is i × ρL / Δ, where i is the second moment of the tank’s free surface about its own centreline axis and ρL is the density of the liquid. If a vessel simultaneously has a transverse off-centre moment and several large partially filled tanks, the combined effect can produce a list substantially larger than the simple mass-distance/displacement formula would suggest. The free surface effect calculator computes the GM reduction, which feeds into the list and trim calculations.

Pressing up tanks - filling them to 98% or more to eliminate the free surface - is a standard operational measure to restore effective GM before a departure requiring maximum stability margin. The sequencing of pressing-up operations during ballast water exchanges under the Ballast Water Management Convention must be planned to avoid creating large free surfaces simultaneously in multiple tanks, which can transiently reduce GM below acceptable limits.

The relationship between free surfaces and list also affects the free surface effect in damage conditions. When a compartment is flooded following damage, the free surface of the ingressed water contributes to the total free-surface correction. The flooded compartment’s free-surface moment is proportional to the cube of its breadth at the waterplane level, so wide flooding spaces (such as car decks on ro-ro vessels) produce very large free-surface moments even when only partially flooded. This is why unsubdivided car decks are so dangerous from a stability perspective.

Bunkering-induced list and its correction

Bunkering operations - the loading of fuel oil, diesel oil, and lubricating oil into tanks that are frequently located asymmetrically within the vessel’s breadth - routinely produce small lists during and after the operation. On vessels with multiple fuel tanks on port and starboard sides, the loading sequence is planned to maintain symmetry throughout, or at least to limit peak list angles to below 2°. After completing bunkering, the chief officer verifies the final list calculation, and if the residual list exceeds the vessel’s operational limit (typically 1° to 2° for harbour departure, and often 0.5° for crane operations or passenger transfers), corrective ballast water transfer is carried out before departure.

On large tankers and bulk carriers with dedicated heavy fuel oil and marine diesel oil bunker tanks, the transverse offset of the bunker manifold from the centreline means that the mass loaded between manifold connections and the tank itself is briefly in an off-centre position relative to the centrepiece of the ship. This transient effect is small and self-correcting as the fuel distributes within the tank, but it is a reminder that even loading from shore-side pipelines can create momentary list if tank geometry is poorly matched to manifold arrangement.

Grain heel and the IMSBC Code

Grain cargo presents a special list hazard because it can shift transversely in the hold under heeling moments during rolling at sea, reducing the righting moment. IMO Resolution MSC.23(59) and the requirements of the International Grain Code require that the heeling moment from grain shift not exceed the limits defined by the calculated GM and the vessel’s GZ curve. The grain heel calculator computes the volumetric heeling moment from partially filled or trimmed grain holds and checks it against the Code criteria.

The IMSBC Code classifies bulk cargoes into three groups. Group A cargoes - including nickel ore, bauxite, and certain iron ore fines - may liquefy if loaded above their transportable moisture limit, causing a rapid shift of cargo to one side of the hold. Unlike grain, which shifts gradually, a liquefied Group A cargo behaves as a fluid: the entire mass can move to the low side of a rolling vessel within a single roll cycle, producing a catastrophic and potentially irrecoverable list. The angle of repose is a relevant parameter for Group C cargoes (which neither liquefy nor present chemical hazards), defining the static slope at which loose granular material is stable. Group C cargoes can still shift if the angle of repose is exceeded by the dynamic acceleration environment at sea.

Trim, squat, and shallow-water operations

Squat and its trim component

When a ship moves through water, the flow around the hull creates a low-pressure zone that draws the vessel bodily downward - the phenomenon known as squat. In a confined channel or shallow water, the constricted flow amplifies this effect substantially. Total squat has a bodily component and a trim component. The trim component means that a vessel trimmed by the stern tends to squat more at the stern, increasing aft draft, while a vessel trimmed by the head tends to squat more at the bow.

The Barrass formula for maximum squat at the stern or bow (whichever is applicable) is:

squat (m) = (Cb × Vs²) / 100

where Cb is the block coefficient and Vs is the ship speed in knots. The squat calculator and the tuck effect calculator implement Barrass and Tuck formulations. For a laden Capesize with Cb = 0.84 at 5 knots in a confined channel, maximum squat is approximately 0.84 × 25 / 100 = 0.21 m, which must be added to the static draft before checking under-keel clearance limits.

Pre-arrival trim optimisation in shallow-water ports therefore involves minimising the aft draft at departure to ensure that after-squat does not breach the permitted under-keel clearance. Port authorities such as those of Rotterdam, Hamburg, and Singapore publish maximum permissible aft drafts for specific channels at specific tidal states, and these limits effectively constrain the allowable trim at sea.

Influence of trim on under-keel clearance

Trim by the stern increases the aft static draft but decreases the forward draft. In channels with uniform depth, a stern-trimmed vessel may safely pass a shoal that would ground a level-keel vessel of the same displacement, because the forward draft is reduced. Conversely, trimming by the head could ground the bow in a stern-deep channel even though the displacement is within load-line limits. For vessels navigating through approach channels with shoals at specific locations, some port authorities specify maximum permissible bow-down trim to ensure adequate forward under-keel clearance.

Dynamic under-keel clearance (DUKC) is a port authority methodology that integrates squat, wave-induced vessel motion (heave and pitch), water level prediction, and tide gauge data to compute a real-time or predicted minimum clearance between the deepest point of the keel and the seabed. Ports such as the Port of Brisbane and the Port Hedland iron ore terminal in Western Australia use DUKC systems that allow fully laden Cape-size bulk carriers to pass with clearances of 0.2 m or less under specific tidal and weather windows. In these operations, trim is a managed variable in the DUKC calculation: a one-centimetre change in aft trim can translate directly into a one-centimetre change in the limiting constraint, affecting the maximum permissible departure displacement.

Optimal trim for fuel efficiency

Mechanism of fuel saving from trim adjustment

The resistance of a ship hull at a given displacement is not minimised at zero trim. The hull form is designed with a specific design waterline at which the wave-making, viscous pressure, and frictional components of resistance combine to give the lowest total resistance. When the vessel trims away from this design waterline, the effective underwater hull shape changes: the bow and stern wave systems interact differently, and the pressure distribution around the hull shifts. Depending on the direction of trim, resistance can increase or decrease relative to the even-keel condition at the same displacement.

The fuel saving from operating at the resistance-minimising trim rather than at the zero-trim condition is typically in the range of 1% to 3% of fuel consumption for most vessel types. For a large tanker burning 60 tonnes of fuel per day, a two per cent trim-optimisation saving amounts to 1.2 t/day, or approximately 440 t/year - a commercially significant figure against contemporary bunker prices.

The trim optimisation fuel savings calculator implements a parametric model for estimating this fuel-saving potential from vessel particulars and speed. The calculation draws on the same hydrodynamic principles as the energy-saving device assessments provided by dedicated ESD calculators such as those for pre-swirl stators and Mewis ducts.

Trim sensitivity by ship type

Trim sensitivity - the rate of change of resistance with trim angle - varies substantially by ship type. Bulk carriers are moderately sensitive: they are designed for a specific ballast and laden waterline, and operating at the design trim typically saves 1% to 2% relative to a flat-keel condition. At full load, most Panamaxes and Capesizes benefit from a slight stern trim of 0.5 m to 1.0 m.

Container ships exhibit greater trim sensitivity than bulk carriers because their block coefficient is lower and their hull form is finer. Published model test results and full-scale trials for large ultra-large container vessels show trim optima that vary with displacement: at ballast draught the optimum trim is often 1.0 m to 2.5 m by the stern, while at design draught it may be less than 0.5 m. Maersk Line, working with Nautilus International and DNV GL (now DNV), was among the first operators to deploy real-time trim optimisation software fleet-wide, reporting average fuel savings of approximately 1.5% across their triple-E class vessels.

Tankers are less trim-sensitive than container ships at full-load conditions because of their high block coefficient, but at ballast they can benefit from adjusting ballast distribution to place the hull at its resistance minimum, often between 0.3 m and 1.5 m by the stern depending on vessel size.

Software and operational implementation

Commercial trim optimisation tools include NAPA’s Onboard stability and trim module, GHS (General HydroStatics by Creative Systems), Bureau Veritas TrimOptimizer, and the proprietary Maersk Trim Guide. All operate on the same principle: they compare the hull resistance (derived from model test data or CFD calculations supplied by the shipbuilder) at a range of trim conditions at the operating speed and displacement, identify the resistance minimum, and recommend a ballast tank configuration to achieve that trim. The captain and chief officer must balance the trim optimisation recommendation against the constraints of the next port’s under-keel clearance, the permitted bending moment and shear force limits, and the stability margin.

The IMO Data Collection System (DCS) and EU MRV (Monitoring, Reporting and Verification) frameworks both require records of fuel consumption per voyage; the IMO DCS vs EU MRV article explains these reporting obligations. Trim optimisation is recognised in the IMO Carbon Intensity Indicator (CII) guidelines as a technical and operational measure contributing to CII improvement, alongside slow steaming and hull cleaning. For a full treatment of CII, see what is CII and slow steaming and CII.

Trim guides and operational limits

Trim limits in the stability booklet

Every vessel subject to SOLAS chapter II-1 stability requirements carries a stability booklet (also called a loading manual) approved by the flag administration or a recognised classification society. The stability booklet records the maximum and minimum permissible drafts at each perpendicular for each loading condition, the corresponding permissible trim range, and the limiting GM (or minimum GM corrected for free surfaces) for each condition. The trim limits derive from three sources: structural limits on longitudinal bending moment at the section of minimum hull modulus; propeller immersion requirements; and forward draft limits from the load-line marks.

Where trim limits are stated as a range, operating outside that range - even if the displacement is within the load-line envelope - constitutes a non-compliance with the approved loading conditions and can be treated as a detainable deficiency by port state control. Under the Paris MOU concentrated inspection campaigns and flag state targeting lists, stability-related deficiencies are a persistent finding category, and several detentions each year cite non-compliance with approved trim conditions.

Trim guides for specific loading conditions

For vessels that frequently operate at a small number of standard loading conditions (departure full load, intermediate, ballast departure, ballast arrival), the stability booklet typically includes a pre-computed trim guide in tabular form, showing the tank configuration needed to achieve the target trim at each fuel, water, and cargo combination. Tankers additionally use cargo-specific trim tables that account for the density of the specific cargo being loaded, since the density affects the actual volumes required at each draft.

Bulk carriers loading at multiple ports on a partial cargo voyage must recalculate trim at each intermediate port. The current loading plan is compared against the hydrostatic tables for the expected draft at the next port, and ballast tanks are adjusted in advance to achieve a trim consistent with the port’s channel limits.

Damaged condition list and counterflooding

List in damage conditions

When flooding occurs following damage - collision, grounding, or structural failure - the ingress of water into asymmetric compartments produces both a list and a change of trim. The list in a damaged condition is more complex to analyse than the intact-condition list, because the flooded compartment contributes to displacement and its free surface reduces the effective GM dramatically. SOLAS chapter II-1, part B, requires probabilistic damage stability calculations using the s-factor formulation, and SOLAS chapter II-1, part B-1, governs Ro-Ro vessels under the Stockholm Agreement.

At an operational level, the ship’s damage control plan specifies the sequence of counterflooding operations to restore the vessel to an upright attitude after flooding. Counterflooding means deliberately admitting seawater to an undamaged tank on the opposite side of the vessel from the flooded compartment, reducing the transverse asymmetry and thereby reducing list. The standard approach is to counterfloood to an upright attitude rather than to compensate exactly - partially corrected list is preferred to a condition that overshoots to the opposite side, which could destabilise the vessel in a different direction. Counterflooding in damaged conditions is addressed in the damage stability article.

MS Estonia (1994)

The loss of the passenger ro-ro vessel MS Estonia on 28 September 1994 in the Baltic Sea resulted in 852 deaths, the worst peacetime maritime disaster in European waters in the late twentieth century. The immediate cause was the failure of the forward visor lock and the subsequent flooding of the car deck. Once the car deck was flooded, the ship developed a rapid and progressive list to starboard. The free water on the car deck - a large unsubdivided space with substantial free-surface effect - catastrophically reduced the effective GM, and the vessel capsized and sank within 32 minutes of the initial flooding. The disaster was a direct driver of the Stockholm Agreement (1996), which imposed enhanced stability requirements for Ro-Ro passenger vessels operating in the North Atlantic and Baltic regions, and contributed to the subsequent revision of IMO’s damage stability framework that became SOLAS 2009.

MV Erika (1999)

The double-hull single-skin tanker MV Erika broke in two and sank off the coast of Brittany on 12 December 1999, releasing approximately 20,000 tonnes of heavy fuel oil. The structural failure was preceded by progressive flooding that created an asymmetric flooding pattern and a developing list, combined with severe longitudinal bending in heavy weather. The Erika disaster prompted the EU to accelerate the phase-out of single-hull tankers, a process that was completed by 2010 under MARPOL Annex I regulation 20, as discussed in the MARPOL convention article. The sequence of list-then-bending-failure illustrates the coupling between transverse stability and longitudinal structural integrity in damaged conditions.

MV Riverdance (2008)

The ro-ro cargo vessel MV Riverdance developed a severe list of approximately 45° in heavy seas in the Irish Sea on 31 January 2008 and was driven aground on Cleveleys beach near Blackpool. The initial list was caused by a combination of poor cargo securing, cargo shift, and free surfaces in ballast tanks that were not fully pressed up. This casualty reinforced Maritime and Coastguard Agency (MCA) guidance on pre-departure stability checks and the mandatory requirement to press up ballast tanks before entering the intended sea area. The cargo securing manual requirements that followed tightened standards for ro-ro cargo lashing assessments.

Hoegh Osaka (2015)

The pure car and truck carrier MV Höegh Osaka developed a list approaching 52° after departing Southampton on 3 January 2015. The vessel’s master took the decision to deliberately beach the ship on Bramble Bank in the Solent rather than risk capsize and loss of the vessel with possible environmental consequences. Investigation by the UK Marine Accident Investigation Branch (MAIB) found that the vessel had departed with an effective GM of approximately 0.18 m, substantially below the minimum permitted value of 0.30 m, due to errors in the cargo loading calculation (incorrect solid ballast assumptions and a tank configuration that had not been updated after pre-departure ballasting). The low GM combined with multiple partially filled ballast tanks produced free-surface corrections that brought the actual effective GM to a marginally positive or possibly negative value, causing the vessel to develop a heel from which she could not self-recover. The deliberate grounding prevented capsizing and allowed the cargo to be removed and the vessel refloated. The MAIB report highlighted deficiencies in stability data management software and recommended improvements to loading computer type-approval standards.

Longitudinal bending moment and trim optimality

Relationship between trim and bending moment

For any given displacement, the distribution of buoyancy along the hull depends on the trim. When the vessel is trimmed by the stern, the buoyancy centre moves aft, the bow section is less immersed, and the distribution of buoyancy force is altered relative to the distribution of weight. The difference between the weight distribution curve and the buoyancy distribution curve at each section defines the load curve, whose integral over the ship length gives the shear force distribution and whose double integral gives the bending moment distribution.

At even keel at the design displacement, most commercial vessels are designed to have a bending moment distribution that places the worst hogging or sagging moment near the midship section, roughly matching the hull’s minimum section modulus. Trimming the vessel away from this condition by large amounts redistributes buoyancy and can either increase or decrease the midship bending moment. Classification societies (Lloyd’s Register Rule 3.1, DNV Rules Pt.3 Ch.1) require the ship’s loading computer to check the bending moment and shear force at each section against the structural limits for both seagoing and harbour conditions before each departure.

On large bulk carriers, trimming by the stern typically reduces the sagging bending moment at midships, because it transfers buoyancy aft and reduces the forward overhanging weight relative to buoyancy. This is one reason why bulk carrier operators prefer a moderate stern trim at sea: it simultaneously improves propulsive efficiency and reduces the structural load at the critical midship section.

Minimum stress trim

The trim condition at which the worst-case section bending moment is minimised is sometimes called the minimum-stress trim or the structural-optimal trim. For most loaded cargo vessels it lies within one to two per cent of LBP of the even-keel condition. This coincides approximately with the resistance-optimal trim for most vessel types, providing a convergence between structural and propulsive objectives that experienced loading officers can exploit in voyage planning.

The structural limits are enforced by the loading computer, which is a type-approved software system interfaced with tank gauge sensors and cargo weight inputs. Classification society type-approval requirements - for example, Lloyd’s Register Rules for the Classification of Ships Part 3, and DNV Rules for Ships Part 3 Chapter 1 - mandate that the loading computer provide real-time or near-real-time bending moment and shear force diagrams at the required sections, with alarms when calculated values approach 90% of the permissible limits. These systems make it impractical to depart with a trim that violates structural limits, even if the hull’s draft compliance and stability margins are satisfied.

The relationship between trim and propulsive performance is also reflected in the CII (Carbon Intensity Indicator) assigned to each voyage under IMO Resolution MEPC.337(76). Vessels that habitually operate at a non-optimal trim will show a higher fuel consumption per unit of transport work, resulting in a worse CII rating. The what is CII article describes how CII is calculated and how operational measures including trim management are assessed against the required annual rating improvement trajectory.

Trim and ice loading

Vessels operating in ice-covered waters under the IMO Polar Code (in force from 1 January 2017 under SOLAS chapter XIV and MARPOL Annex I/II) must carry out additional stability calculations that account for ice accretion on exposed horizontal and vertical surfaces. The icing allowance adds a mass at an elevated KG, reducing the effective metacentric height. For a typical Arctic supply vessel, the icing allowance specified in the Polar Code for Category A vessels can add approximately 10 kg/m² to horizontal and 7.5 kg/m² to vertical exposed surfaces, raising KG by several centimetres depending on superstructure area.

This increased KG tightens the minimum GM margin available for off-centre loading. A vessel that meets its trim and list limits in temperate waters with a comfortable GM margin may find that ice accretion in the Arctic reduces that margin below the minimum required. The operational response is to reduce the allowable list angle target during polar operations, to carry additional ballast, and to prefer loading plans that place cargo centred on the vessel’s centreline.

Polar operations also affect trim through ice resistance. A vessel pushing through level ice experiences a greater bow resistance than a stern-trimmed vessel of the same displacement. Some polar-class vessels are specifically designed with a slight bow-down trim at their ice-operating draft to ensure the hull breaks ice cleanly rather than riding up on it. The Polar Code and the guidelines published by the Arctic Council’s Protection of the Arctic Marine Environment (PAME) working group specify minimum manoeuvrability criteria that implicitly constrain the range of trim conditions permitted.

Interaction with other stability quantities

Trim affects the effective GM indirectly. When a vessel trims, the centroid of the waterplane area shifts longitudinally, moving the LCF. The transverse second moment of the waterplane about the new axis changes slightly, altering BMT and hence KMT. For small trims this effect is negligible, but for vessels with a pronounced flare or tuck in the underwater sections, the variation of KMT with trim can be significant. High-quality stability booklets published by classification societies such as those accredited under SOLAS regulation II-1/5 present KMT as a function of both mean draft and trim, and loading computers interpolate within this two-dimensional table.

The interaction between trim and intact stability is addressed in detail in the intact stability and metacentric height articles. The relationship between waterplane geometry, block coefficient, and form stability is covered in hydrostatics and Bonjean curves and block coefficient. For vessels in ice, the Polar Code specifies additional stability margins that effectively constrain the minimum permissible GM and restrict the range of permissible loading conditions, limiting trim flexibility in polar waters. The icing allowance - an increment to KG to account for ice accretion on superstructure and deck equipment - reduces effective GM and may require the operator to reduce stern trim to keep deck flooding from raising the roll inertia further.

Practical workflow for trim and list calculation

Step-by-step procedure for a cargo loading condition

A complete trim and list calculation for a loaded departure condition follows this sequence. First, the officer determines the total displacement from the sum of lightship weight, all cargo, fuel, fresh water, ballast, and stores. The mean draft is derived from hydrostatic tables at this displacement, correcting for water density using the density-draft calculator if loading in non-salt water.

Second, the longitudinal centre of gravity (LCG) is calculated as the weighted mean of all items’ positions relative to the aft perpendicular. The difference between the LCG and the LCB at the anticipated mean draft gives the trimming lever, and the trimming moment is Δ × (LCG − LCB). Dividing by MCT1cm gives the change of trim from even keel.

Third, the transverse centre of gravity (TCG) is calculated as the weighted mean of all items’ transverse positions. If the TCG departs from zero, the resulting list angle is calculated using the formula above with the effective GM corrected for all free surfaces.

Fourth, the drafts at the perpendiculars are computed by applying the bodily sinkage, the trim distribution, and the perpendicular corrections. These are checked against the vessel’s load-line marks, the port’s draft restriction, the channel’s under-keel clearance, and the stability booklet’s trim limits.

Fifth, the shear force and bending moment at critical sections are verified against classification society limits. If any limit is exceeded, cargo or ballast is redistributed and the calculation iterated. The ShipCalculators.com calculator catalogue provides individual calculators for each step in this chain, allowing verification of intermediate results or standalone calculation of specific quantities.

Ballast water management and trim during ballast exchanges

Under the Ballast Water Management Convention and IMO Resolution MEPC.325(75), vessels are required to manage ballast water to prevent the transfer of invasive aquatic species. The two standard compliance methods - sequential exchange and flow-through exchange - both temporarily alter the ballast distribution and hence the trim and stability of the vessel.

Sequential exchange empties and then refills each ballast tank in turn. During the emptying phase, the vessel may lose significant ballast volume, reducing displacement and altering trim. If a large aft peak tank is emptied first, the bow-down trim may increase sharply, raising the aft draft reduction and potentially reducing propeller submergence below operational limits. The exchange plan must be pre-computed to keep trim within limits and to ensure that GM remains positive throughout. The ballast D-2 compliance check calculator verifies compliance with the D-2 numerical standard for treated ballast.

Flow-through exchange maintains displacement more stably but involves large tank volumes at 98% filling level, maximising free-surface corrections if the overflow is not carefully managed. Pressing tanks beyond the overflow point is illegal (it constitutes overboard discharge) but failing to fill fully leaves a free surface. The standard operational procedure is to calculate the maximum acceptable free-surface loss of GM before beginning the exchange and to plan the sequence so that the sum of free-surface corrections at no point during the exchange exceeds the available GM margin.

See also

References

  1. IMO Resolution MSC.267(85) - International Code on Intact Stability, 2008 (2008 IS Code). International Maritime Organization, London, 2009.
  2. IMO Resolution MSC.23(59) - International Grain Code, as amended. International Maritime Organization, London.
  3. SOLAS Chapter II-1 - Construction, subdivision and stability. International Maritime Organization (consolidated edition).
  4. IACS Unified Requirement S1 - Longitudinal strength standard. International Association of Classification Societies, rev. 4.
  5. International Load Line Convention 1966, as amended by the 1988 Protocol. International Maritime Organization.
  6. IMO Resolution MEPC.325(75) - 2021 Guidelines for ballast water exchange. International Maritime Organization.
  7. MAIB Report No. 19/2015 - Report on the investigation of the listing, flooding and grounding of Höegh Osaka, Marine Accident Investigation Branch, United Kingdom, 2015.
  8. UK Marine Accident Investigation Branch - Report on MV Riverdance, 2009.
  9. Joint Investigation Commission Estonia Final Report, 1997 - Government Commissions of Estonia, Finland and Sweden.
  10. Barras, C.B. - Ship Squat and Interaction. Witherby Seamanship International, 2009.
  11. Barras, C.B. - Ship Stability for Masters and Mates. 7th edition. Butterworth-Heinemann, 2012.
  12. Derrett, D.J. (revised Barras, C.B.) - Ship Stability for Masters and Mates. Elsevier, 2006.
  13. Molland, A.F. (ed.) - The Maritime Engineering Reference Book. Butterworth-Heinemann, 2008.

Further reading

  • Brown, D.K. - Warrior to Dreadnought: Warship Development 1860-1905. Chatham Publishing, 1997. (Historical context for stability regulation following HMS Captain.)
  • Papanikolaou, A. (ed.) - Risk-Based Ship Design. Springer, 2009. (Probabilistic damage stability and flooding risk.)
  • NAPA Ltd. - NAPA Stability User Manual. Current edition. (Description of commercial trim and stability software.)