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Intact stability

Intact stability is the branch of naval architecture and maritime regulation concerned with an undamaged ship’s ability to return to its upright position after an external disturbance such as a wave, wind gust, or cargo shift. The discipline is formalised internationally through the IMO 2008 Intact Stability Code, adopted as Resolution MSC.267(85) on 4 December 2008 and made mandatory for cargo and passenger ships through SOLAS Chapter II-1/2 and the International Convention on Load Lines from 1 July 2010. The Code consolidates more than six decades of accumulated criteria, beginning with the statistical work of Rahola in 1939, and imposes quantitative minimum values for metacentric height, righting lever, area under the righting-lever curve, and a weather-balance energy criterion. A second generation of criteria targeting five dynamic failure modes - parametric roll, surf-riding and broaching, dead ship condition, pure loss of stability, and excessive accelerations - reached interim guidelines stage in 2020 and continues to develop. This article, part of the ShipCalculators.com reference wiki, traces the historical evolution, explains the technical basis of each mandatory criterion, and describes the procedures and software used to verify compliance in practice.

Contents

Background and history

Early statistical foundations

Systematic quantitative criteria for the stability of merchant ships emerged in the first half of the twentieth century, driven by recurring casualties in severe weather rather than by any continuous theoretical programme. The dominant practical measure was metacentric height GM0, the distance from the centre of gravity G to the transverse metacentre M at small angles. High GM0 produces a stiff, quickly-righting ship that recovers rapidly from small heel but generates uncomfortably large rolling accelerations and strains cargo lashings. Low GM0 reduces accelerations but reduces the margin against capsizing.

Rahola’s 1939 doctoral thesis, published by the Finnish Technical University under the title The Judging of Ship Stability from the Basis of Cargo Steamers and Passenger Vessels in Connection with the Requirements of the 1939 International Conference on Safety of Life at Sea, is the direct ancestor of modern criteria. Rahola analysed casualty records for 43 vessels lost in waves and compared the righting-lever curves of casualties with those of survivors. His statistical method identified threshold values for GM0, for the righting lever GZ at 30° of heel, for the area under the GZ curve to 30°, and for the range of positive stability. These thresholds were derived empirically from the observed population and carried no pretence of a deterministic physical derivation. The approach was pragmatic: if all the casualties had curves that fell below a given threshold and most survivors exceeded it, the threshold was a reasonable minimum. The 1939 International Conference on Safety of Life at Sea, held in London, adopted minimum-GM recommendations based partly on Rahola’s work, though a mandatory international instrument did not follow immediately because of the Second World War.

IMO Resolutions A.167(ES.IV) and A.168(ES.IV)

The first IMO instruments to codify intact stability criteria internationally were adopted by the Fourth Extraordinary Session of the Assembly on 28 May 1968 as Resolutions A.167(ES.IV) and A.168(ES.IV). Resolution A.167(ES.IV) set out a recommendation on intact stability for passenger and cargo ships under 100 m in length; A.168(ES.IV) addressed fishing vessels. The 1968 recommendations translated Rahola’s thresholds into quantitative text that flag states were encouraged to adopt through national legislation. The criteria were explicitly recommendatory rather than mandatory: flag state practice varied considerably through the 1970s, and the absence of a uniform binding regime meant that ships registered in states with no implementing legislation could operate without compliance checks.

A series of bulk carrier and general cargo vessel losses through the 1970s and early 1980s kept stability on the IMO agenda. The 1974 SOLAS Convention, which entered force on 25 May 1980, included stability-related provisions for specific ship types but did not universalise the Resolution A.167 criteria. The capsizing of the Gaul (February 1974), a British stern trawler lost in the Barents Sea with 36 lives, demonstrated that fishing vessels were particularly exposed and led to the separate development of criteria for that sector.

Resolution A.749(18) and the 1993 IS Code

IMO Assembly Resolution A.749(18), adopted on 4 November 1993, superseded Resolution A.167(ES.IV) and constituted the first consolidated Intact Stability Code. The 1993 Code was still recommendatory in character; its binding effect depended on the extent to which flag states implemented it through national law or required classification societies to certify compliance as a condition of class maintenance. The text gathered the general criteria from A.167(ES.IV), the weather criterion derived from work by Watanabe (1938) and Yamagata (1959), and criteria for specific vessel categories including passenger ships, cargo ships, high-speed craft, and offshore supply vessels. Several administrations, including the United Kingdom, Japan, and the Nordic states, had already incorporated equivalent criteria into their national statutory instrument surveys.

The 1993 IS Code also introduced the stability information booklet requirement in systematic form, mandating that each ship carry approved documentation of its lightship condition (verified by inclining experiment), hydrostatic tables, KN cross-curves, and sample loaded conditions. Without the booklet, the master had no basis for calculating whether a proposed loading arrangement complied with the criteria.

MSC.267(85) and the 2008 IS Code

Resolution MSC.267(85), adopted by the Maritime Safety Committee on 4 December 2008, replaced A.749(18) with the present 2008 Intact Stability Code. The key change was that Part A of the 2008 Code was made mandatory through concurrent amendments to SOLAS Chapter II-1, Regulation 2, and to the International Convention on Load Lines (ICLL). Both sets of amendments entered force on 1 July 2010, meaning that for vessels to which SOLAS II-1 and the ICLL apply, compliance with IS Code Part A is a legal obligation binding under international law, not merely a recommendation. Part B of the Code, covering recommendatory criteria for special ship categories, retained recommendatory status but is widely applied by flag states and classification societies as part of their survey requirements.

The 2008 Code maintained the numerical thresholds from A.749(18) essentially unchanged but rationalised the structure, clarified the scope of application, and added requirements for specific ship categories that had evolved since 1993. It applies to intact loading conditions of cargo ships of 24 m and above and passenger ships, with certain specific provisions extending to smaller vessels.

Principles of righting lever and the GZ curve

Hydrostatic basis

When a ship is displaced from the upright by an angle of heel φ, the submerged volume shifts so that the centre of buoyancy B moves to a new position. The resultant buoyant force, acting vertically upward through the new B, no longer passes through the original G. The perpendicular distance between the line of action of displacement Δ and the vertical through G is the righting lever GZ. When B has moved outboard of G, GZ is positive and a righting moment of Δ × GZ acts to restore the ship to the upright. When the ship has heeled past the angle of vanishing stability, GZ becomes negative and the restoring moment becomes a capsizing moment.

The metacentric height GM governs the initial slope of the GZ curve. At small angles of heel (typically up to 10° to 15° for conventional hulls), the curve rises approximately linearly, with slope equal to GM0 × sin(φ) / φ, which for small φ reduces to simply GM0 in radians notation. A higher GM0 produces a steeper initial slope and greater initial resistance to heel. However, the maximum righting lever and the range of stability depend on the hull form at large angles - in particular on the extent to which the deck edge immerses (reducing the waterplane inertia and hence buoyancy arm) and on the freeboard available before green water enters through openings.

The GZ from KN cross-curve method is the standard computational route. The naval architect tabulates KN values - the righting arm component measured from keel to the perpendicular projection of N (the intersection of the buoyant force line of action with the ship’s centreline) - at a series of heel angles (typically 10°, 20°, 30°, 40°, 50°, 60°, 70°, 80°) and at enough displacement values to span the operating range. For a given loading condition with known displacement Δ and vertical centre of gravity KG, the righting lever at any angle is GZ = KN − KG × sin(φ). The dynamical stability area under the GZ curve integrates these values to give the righting work available against a heeling disturbance.

The wall-sided formula provides an analytical approximation for GZ at moderate angles on geometrically wall-sided hulls: GZ = (GM0 + BM × tan²φ / 2) × sin(φ). This relationship is useful for parametric studies but overestimates GZ significantly once the deck edge immerses, so cross-curve tables derived from the actual hull geometry are used for compliance verification. For a related account of the geometric basis of BM, see hydrostatics and Bonjean curves; the formula for BM from waterplane inertia is covered at the BM geometry formula page.

Free surface effect

Liquids in partly filled tanks reduce effective GM by an amount equal to the free surface moment of the liquid divided by the ship’s displacement. For a rectangular tank of breadth b and length l containing fluid of density ρ_liquid, the free surface moment is ρ_liquid × b³ × l / 12 per unit volume. The correction, denoted FSC or GG1, is added algebraically to KG before computing GZ, effectively raising the apparent KG and reducing the righting lever at every angle. The free surface correction calculator applies this formula. The magnitude of the correction is independent of the actual fill level (for rectangular tanks with the liquid remaining continuous) and depends solely on the breadth of the free surface. Wide tanks therefore impose a disproportionately large penalty. The regulatory background is covered in the companion free surface effect article.

Scope of application and ship categories

Ships covered by Part A

IS Code Part A applies to cargo ships of 24 m in length and above, and to passenger ships, regardless of size. The mandatory requirements reached these vessels through two parallel routes: for cargo ships over 24 m subject to SOLAS Chapter II-1, Regulation 2 references the Code directly; for vessels subject to the 1966 Load Line Convention but not primarily governed by SOLAS (certain non-passenger non-cargo ships), the parallel amendment to the ICLL carried the obligation. Both amendments entered force on 1 July 2010.

The Code uses the term “loading condition” to mean any combination of cargo, ballast, fuel, stores, and personnel that the ship is approved to carry. All loading conditions in the approved stability information booklet must satisfy the Part A criteria; the master must verify that any departure condition matches or is bounded by an approved booklet condition. Conditions must span the full range of intended operation, including the full-load departure, full-load arrival (after fuel and water consumption), ballast departure, ballast arrival, and any intermediate loading states specific to the vessel’s trade. For bulk carriers and tankers that load or discharge at sea, intermediate conditions during the operation must also be evaluated.

Ships exempted or given alternative treatment

Fishing vessels of less than 24 m, vessels in sheltered domestic trade, and certain special-purpose ships may be subject to national regulations that the flag state has determined provide equivalent safety, rather than to Part A directly. High-speed craft subject to the International Code of Safety for High-Speed Craft (HSC Code) have dedicated stability standards derived from performance-based criteria rather than the quasi-static approach of the IS Code; the HSC Code requires demonstration of stability in the dynamic displacement or planing regime as well as at rest.

Dynamically supported craft - including hydrofoils, air-cushion vehicles, and surface-effect ships - present technical challenges to static stability analysis because their restoring moments at operating speeds are dominated by hydrodynamic lift distribution rather than buoyancy. The IS Code Part B Section 12 provides recommendatory guidance for such craft in the displacement mode, with the understanding that foilborne or cushionborne modes require additional type-specific analysis.

Sailing vessels, including large training ships and commercial sailing cargo vessels, are subject to IS Code criteria supplemented by additional criteria for the heeling moment produced by wind on sails. The wind pressure on canvas and the lever of the sail plan must be combined with the IS Code weather criterion; flag states that operate sail-training vessels typically apply national codes that reflect this combination.

Interaction with the SOLAS probabilistic subdivision standard

For passenger ships and ro-ro passenger ferries, the intact stability standards of IS Code Part A are a necessary but not sufficient condition for certification. SOLAS Chapter II-1 Part B-1 also requires that these vessels satisfy the probabilistic damage stability standard - the index A must equal or exceed the required subdivision index R, which is a function of ship length and the number of passengers carried. The attained subdivision index is computed by evaluating all possible flooding combinations and their probabilities, weighted by the residual stability available after flooding. This probabilistic analysis is carried out using the methods described in the damage stability article and requires a different software tool set from intact stability. The two analyses must be consistent with each other in their use of the lightship KG; a change to the lightship KG from the inclining experiment invalidates both sets of calculations.

IS Code Part A - mandatory general criteria

Criteria 2.2 - righting lever and area requirements

The general intact stability criteria in IS Code Section 2.2 impose six minimum values on the GZ curve for every loading condition within the operating range. The requirements are:

The area under the righting-lever curve from 0° to 30° must be at least 0.055 m·rad. This is the minimum work available to resist moderate heeling disturbances in the initial to medium-angle range. The dynamical stability area calculator computes this integral from tabulated GZ values by the trapezoidal or Simpson’s rule.

The area under the GZ curve from 0° to 40°, or from 0° to the angle of downflooding φ_f if φ_f is less than 40°, must be at least 0.090 m·rad. Downflooding angle is the angle at which any opening unable to be made watertight is submerged. Companionways, air pipes, ventilation intakes, and side scuttles with non-watertight closures typically govern the downflooding angle. The 0.090 m·rad requirement ensures that sufficient energy absorption capacity exists to withstand larger heeling disturbances.

The area under the GZ curve between 30° and 40°, or between 30° and φ_f if lower, must be at least 0.030 m·rad. This incremental requirement prevents a narrow peak in the GZ curve that satisfies the total area to 30° and to 40° but collapses steeply between those angles.

The righting lever GZ at 30° of heel must be at least 0.20 m. This requirement is distinct from the area requirements: a curve could in principle satisfy the area threshold with a broad shallow shape without meeting the height criterion at 30°.

The maximum GZ must occur at an angle of heel of not less than 25°. The Code states a preference for 30° or above. This requirement prevents designs with a GZ curve that peaks early and falls away rapidly, which would indicate a ship that, once past the peak angle, loses righting capacity quickly.

The initial metacentric height GM0, corrected for free surface effects, must be not less than 0.15 m. This minimum guards against ships that are very tender and susceptible to rapid rolling through zero or to a low-energy capsize in calm conditions. See the IS Code general criteria calculator for a direct compliance check against all six thresholds simultaneously. The KG limit calculator derives the maximum permissible KG for a given displacement from the binding criterion.

Criterion 2.3 - severe weather (wind and rolling) criterion

The weather criterion of IS Code Section 2.3 addresses the combined effect of a steady beam wind and a roll in waves. The method is based on work by Watanabe (Japan, 1938) and refined through subsequent studies published by Yamagata (1959) and further IMO correspondence groups in the 1970s and 1980s. The IS Code severe weather criterion calculator applies the full procedure described below.

The steady wind heeling lever lw1 (m) is the moment per unit displacement from a steady wind pressure applied to the ship’s lateral windage area. The wind pressure for ships on unrestricted service is 504 Pa, applied to the lateral above-waterline area A (m²) at a height Z above the waterplane centroid. The wind heeling lever is lw1 = P × A × Z / (g × Δ), where P is 504 Pa, A is projected lateral area, Z is the vertical arm from the centre of lateral windage area to half-draft, g is 9.81 m/s², and Δ is displacement in tonnes. The value 504 Pa applies to unrestricted service; reduced pressures are permitted for vessels restricted to sheltered waters, subject to flag state agreement.

The ship is assumed to have heeled under the steady wind to angle θ_0, found at the intersection of the upwind part of the GZ curve with lw1. From the heeled position, a roll amplitude θ_1 to windward is applied. The roll amplitude is calculated using the empirical formula: θ_1 = 109 × k × X1 × X2 × sqrt(r) × s (degrees), where k is a factor reflecting bilge keel area (1.0 for no bilge keels, reduced values for proportionally larger bilge keels), X1 is a breadth/draft factor read from a table, X2 is a coefficient accounting for the ratio of block coefficient Cb and B/2d from the same tabulated data, r is the roll gyradius factor, and s is a tabulated factor linked to the metacentric height GM0 and natural roll period. The formula captures the empirical observation that roll amplitude in irregular waves depends on ship geometry, bilge keel suppression, and natural period relative to the wave energy spectrum.

The windward extreme position of the roll is at angle θ_0 − θ_1 below the upright (or zero if that product is negative, meaning the roll does not bring the ship to the upright). The gust wind heeling lever lw2 = 1.5 × lw1 represents the dynamic wind pressure of a sudden squall on a ship already heeled under the steady wind.

The energy balance criterion requires that the area b - the area under the GZ curve between the windward roll position (θ_0 − θ_1) and the leeward limit (whichever is lesser of 50°, the downflooding angle φ_f, or the angle at which GZ equals lw2) - must equal or exceed the area a. Area a is the area between the lw2 lever line and the GZ curve from the windward roll angle to θ_0. The physical interpretation is that the ship must have sufficient righting energy in reserve to absorb the gust impulse without capsizing. The criterion is conservative in that it treats the gust as applied at the worst moment of the roll.

IS Code Part B - recommendatory criteria for special ship types

Passenger ships

IS Code Part B Section 2 imposes additional criteria for passenger ships on top of the Part A requirements. The passenger crowding criterion requires that when all passengers on one side of the ship crowd to the rail or to any deck area accessible to passengers, the resulting heel angle does not exceed 10°. The heeling moment from crowd distribution uses 75 kg per person at the rail position. See the passenger crowding heeling moment calculator for the moment calculation.

A turn criterion requires that when turning at full speed with maximum helm angle, the resulting steady heel from centrifugal forces does not exceed 10°. The heeling lever is lTURN = V² × KG / (g × Lpp), where V is service speed, KG is the height of the centre of gravity, g is acceleration due to gravity, and Lpp is ship length between perpendiculars. A third criterion requires a minimum area under the GZ curve of 0.035 m·rad between 0° and 15° (or to the downflooding angle if smaller) for passenger ships. SOLAS Chapter II-1 also imposes the probabilistic subdivision standard for damage stability; the interaction between intact and damage stability requirements is discussed in the damage stability article.

Grain carriers

The International Code for the Safe Carriage of Grain in Bulk (Grain Code), incorporated by reference into IS Code Part B, applies to ships carrying bulk grain in any hold, compartment, or cargo space. The Grain Code requires that after an assumed shift of grain generating a prescribed volumetric heeling moment, the resulting list does not exceed 12°, and the residual GZ curve retains a positive area of at least 0.075 m·rad between the list angle and 40° (or the downflooding angle, if lower). The grain heeling moment calculator and the detailed procedure are described in the IMSBC Code article. Grain carriers must carry a grain loading manual approved by the flag state administration and, for certain configurations, a document of authorisation issued by the administration.

Oil and chemical tankers

Tankers are particularly susceptible to free surface effects because of the large number of slack cargo and ballast tanks at various stages of loading or discharge. IS Code Part B Section 4 requires that tanker loading instruments or manual calculations account for the free surface moments of all tanks with a free surface. The free surface correction calculator handles this calculation. Chemical tankers subject to the IBC Code carry additional requirements; the IBC Code article and the chemical tanker article describe the relationship between cargo compatibility and stability.

Fishing vessels

The Torremolinos International Convention for the Safety of Fishing Vessels, 1977 (and its 1993 Protocol) established stability criteria for fishing vessels of 24 m and above. IMO Resolution A.749(18) and subsequently the 2008 IS Code Part B Section 6 incorporate guidance for fishing vessels, recognising that their high deck equipment, low freeboard, and variable catch weight create a combination of elevated KG and reduced freeboard that makes compliance with general criteria difficult. The relevant criteria set higher minimum GM values and require that the angle of downflooding be related to the minimum reserve buoyancy. The reserve buoyancy calculator quantifies the freeboard margin.

Offshore supply vessels

Offshore supply vessels (OSVs) operate in conditions that include rapid and variable deck cargo changes, deck flooding from wave wash-over, and high-windage superstructures. IS Code Part B Section 7 gives recommendatory criteria for OSVs that address the combination of water on deck (treated as a heeling moment) with the general criteria. Many flag states and classification society rules require compliance with both the IS Code and dedicated OSV codes such as the IMO Code of Safety for Special Purpose Ships.

Icing allowance

For ships operating in high-latitude waters where ice accretion on rigging, superstructures, and deck equipment is a recognised hazard, IS Code Part B Section 8 requires that a mass correction for topside icing be applied before checking stability criteria. The icing allowance calculator applies the IS Code parametric formula, which assigns ice loads of 30 kg/m² on exposed weather decks and 7.5 kg/m² on projected lateral surfaces for vessels on unrestricted service in icing areas. The ice mass is added at its geometric height, increasing KG and reducing GM0. The polar code article addresses the broader context of Arctic and Antarctic operations.

Hull form and its influence on stability

Initial stability and hull parameters

The metacentric height GM0 in the upright condition is determined by KB + BM − KG, where KB is the height of the centre of buoyancy above the keel, BM is the metacentric radius (equal to the waterplane second moment of area divided by displaced volume), and KG is the height of the centre of gravity. For a given displacement, KB is raised by full hull forms with high block coefficients and by flat-bottomed cross-sections. BM is raised by wide waterplane areas and reduced by deep displacement; the governing quantity is the transverse second moment of the waterplane area about the centreline, divided by the displaced volume.

The block coefficient Cb - the ratio of displaced volume to the enclosing rectangular prism of length, breadth, and draft - provides a broad indicator of hull fullness. Vessels with high Cb values (bulk carriers and oil tankers, typically 0.80 to 0.87 in loaded condition) tend to have wide, flat waterplanes that produce a high BM at full load but lose much of that advantage in ballast when the effective waterplane breadth is maintained but draft decreases, raising BM significantly. The waterplane coefficient Cwp - computed by the waterplane area coefficient calculator - determines the waterplane area directly and therefore BM more precisely than Cb alone. The relationship between waterplane form and transverse stability is detailed in the hull form design article.

Container ships, which carry cargo at elevated positions in above-deck tiers, present the opposite challenge: high KG from stacked containers on deck reduces GM0, and the pronounced bow flare that gives them a rising GZ characteristic at large angles also increases the variation of waterplane area in waves (making them susceptible to parametric roll, as described in the second-generation criteria section). Achieving a positive GM0 while stacking containers eight or nine tiers high requires careful management of the below-deck cargo distribution, strategic use of ballast, and recognition that the limiting criterion may change from the general GM0 threshold to the weather criterion or to the parametric roll susceptibility check depending on the vessel’s proportions and route.

Large-angle stability and hull form interaction

The shape of the GZ curve at angles above 30° is dominated by the rate at which the deck edge submerges and free-board is consumed. A vessel with high freeboard and a wall-sided hull (vertical topsides) retains a rising GZ curve to relatively large angles. A vessel with pronounced tumblehome (hull sides inclining inboard above the waterline) experiences early loss of waterplane inertia as the deck submerges and a falling GZ curve that violates the IS Code preference for maximum GZ at or above 30°.

Flare - hull sides inclining outboard above the waterline - increases the effective waterplane breadth as the vessel heels, temporarily sustaining or increasing BM and maintaining the rise of the GZ curve past angles at which a wall-sided vessel would begin to decline. This flare effect explains why many container ships and car ferries appear to have favourable large-angle GZ values despite high KG values; it also explains their susceptibility to the parametric roll failure mode, since the same flare that sustains GZ also produces the greatest variation in effective waterplane area as waves pass along the hull.

Bilge keels reduce roll amplitude in service but do not alter the static GZ curve. Their effect enters the IS Code weather criterion through the k factor in the roll amplitude formula: the ratio of the bilge keel area to the ship’s length-breadth product determines the value of k, which ranges from approximately 0.75 for well-equipped bilge keels to 1.0 for none. Reducing roll amplitude through bilge keels reduces the energy demanded of the righting work term, making the weather criterion easier to satisfy without changing the fundamental static stability of the vessel.

Trim, list, and their effects on stability assessment

Effect of list on the GZ curve

A vessel with a steady list to starboard, produced by off-centre cargo, a flooded compartment, or asymmetric ballast distribution, has a displaced GZ curve relative to the upright. The peak GZ to the low (starboard) side is reached at a smaller heel angle and the range of positive stability to that side is reduced. The area requirement between 30° and 40° is applied from the listed position, not from the upright, if the list exceeds 0.5°. The IS Code requires that any steady list at the departure or arrival condition be within the limits at which the Part A criteria remain satisfied when evaluated from the listed heel angle. The list from weight shift calculator computes the list angle from a transverse moment imbalance.

For practical compliance verification, the stability software applies the list correction by evaluating the GZ curve at the actual KG and listing moment, reporting the effective GZ values referenced to the listing angle. A vessel that satisfies the general GM0 criterion in the upright but that lists four degrees to port by virtue of off-centre fuel consumption still has a reduced margin on the weather-side GZ area that must be verified. The IS Code specifies that the list angle at departure or arrival conditions should not exceed 10° and, where practicable, should be less than five degrees.

Effect of trim on hydrostatic tables

Hydrostatic tables are typically calculated for the vessel on an even keel; a trim changes the waterplane area, KB, and BM relative to the even-keel values at the same mean draft. For small trims the corrections are typically minor and within the accuracy of the KN cross-curve method. For large trims - common in bulk carriers departing in ballast with heavy stern trim - the corrections may be significant and require that the hydrostatics be re-evaluated at the trimmed waterplane rather than interpolated from the even-keel tables. The IS Code requires that the stability calculations use hydrostatics appropriate to the actual trim condition. The trim from weight shift calculator provides the basic trim computation. A more detailed discussion is in the trim and list article.

Inclining experiment

Purpose and regulatory basis

The inclining experiment is the only direct empirical method of determining a ship’s lightship displacement and the height of its centre of gravity KG0 in the lightship condition. Every ship must undergo an inclining experiment, or have a reliable inclining experiment transferred to it from a sister ship under the conditions specified by the flag state administration, before the stability information booklet can be approved. IS Code Section 7.3 and the 2019 Revised Guidelines for the Inclining Test (MSC.1/Circ.1667) specify the procedure.

Procedure

The experiment is conducted with the ship as close to the lightship condition as possible. All tanks should be pressed full or empty; slack tanks introduce free surface moments that mask the true centre of gravity. All portable equipment, tools, consumable stores, and personnel not involved in the test are removed or their masses and positions precisely recorded so that corrections can be made. Gangways and cranes are positioned to eliminate any external forces on the hull.

A known mass w (typically of the order of 1% to 2% of the lightship displacement, placed in several increments for reliability) is shifted transversely a measured distance d across the deck, generating a heeling moment w × d. The resulting heel angle φ is measured with a pendulum (plumb bob and batten or digital inclinometer) at a minimum of two stations. The experiment criterion requires that the heel angle at each weight shift does not exceed approximately four degrees, to remain within the small-angle approximation for which GM0 = w × d / (Δ × tan(φ)).

Multiple weight moves are conducted: typically four moves with four masses, generating eight heel measurements that are plotted as a pendulum deflection versus heeling moment. The slope of the best-fit line through the plotted points gives GM0. The lightship KG0 is then KM − GM0, where KM is taken from the hydrostatic tables at the observed mean draft. The GM from inclining experiment calculator applies this formula. The inclining check formula page provides the verification procedure for assessing whether the scatter in the measurements meets the acceptance criteria.

Lightweight survey and periodic updates

A lightweight survey, verifying the mass and centre of gravity by visual inspection and comparison with previous records rather than by heeling experiment, is required at five-year intervals or whenever the lightship mass is estimated to have changed by more than 2% or the lightship KG by more than 1%. Classification society rules and flag state guidance specify the conditions under which a new inclining experiment is required - for example after major conversion or following an accumulation of small modifications whose combined effect has reached the threshold.

Stability information and loading software

Stability information booklet

IS Code Section 2.4 requires that every ship carry an approved stability information booklet. The booklet must contain the results of the inclining experiment (or the lightship details transferred from a sister vessel inclining), the hydrostatic curves or tables, the cross-curves of stability (KN values), and a series of approved loading conditions spanning the range of operation. Each sample condition illustrates the displacement, KG, GM0, the corrected GM for free surfaces, the GZ curve at key angles, and a confirmation that the Part A criteria are satisfied. The master must verify that any proposed actual loading condition satisfies the same criteria before departure.

Loading instruments and software

Class rules and flag state requirements for many ships above a certain size require an approved loading instrument - either a mechanical computer or, in modern practice, an approved software application. Such instruments calculate the current KG, GM, and GZ curve from the reported masses and positions of cargo, ballast, fuel, and stores. The leading commercial packages used for ship stability calculation include NAPA (developed by NAPA Group, Finland), GHS (General HydroStatics, Creative Systems Inc., USA), Maxsurf (Bentley Systems), and AVEVA Marine (formerly Tribon). Classification societies maintain lists of approved instruments; class approval certifies that the software correctly reproduces the approved stability data for the individual ship and gives results consistent with the inclining experiment baseline. The ShipCalculators.com calculator catalogue provides web-based access to the core stability calculations used in the booklet and loading checks.

GM from rolling period

In the absence of a recent inclining experiment, an approximate value of GM0 can be estimated from the natural roll period Tr measured at sea. The empirical relationship is GM0 = (C × B)² / Tr², where B is ship breadth and C is a coefficient that depends on ship type and load distribution (approximately 0.77 to 0.82 for typical cargo ships). The GM from rolling period calculator applies this formula. The method is unreliable in heavy weather or when the rolling is not free from external forcing. It provides a sanity check on the booklet value but cannot substitute for the inclining experiment for certification purposes. The natural roll period is also computed independently by the seakeeping roll period formula page.

Second-generation intact stability criteria

Background and motivation

The 2008 IS Code criteria are semi-empirical static or quasi-static checks derived from population statistics of casualties and survivors. They do not explicitly address the dynamic failure modes that have been identified from detailed analysis of casualties and from numerical seakeeping research since the 1990s. Five categories of dynamic failure mode were identified through IMO correspondence group work coordinated under the Sub-Committee on Ship Design and Construction (SDC): parametric rolling, surf-riding and broaching, dead ship condition, pure loss of stability, and excessive accelerations.

The Intercessional Correspondence Group on Second Generation Intact Stability Criteria (SGISC) began work in 2007 and produced a series of reports to the SDC. MSC.1/Circ.1627, issued in December 2020, provides interim guidelines for the first two levels of assessment (Level 1 susceptibility checks and Level 2 simplified dynamic checks) for parametric roll, pure loss of stability, and surf-riding/broaching. A Level 3 direct stability assessment using time-domain numerical simulation is defined in principle but the acceptance criteria and the required verification standards for simulation models remain under development. Industry implementation guidelines were published as MSC.1/Circ.1652 in 2022.

Parametric roll

Parametric rolling occurs when the restoring moment varies periodically at close to twice the natural roll frequency, which happens when a ship is running in longitudinal waves of wavelength approximately equal to ship length. As the wave crest passes amidships, the waterplane narrows (reducing GM0 and reducing the restoring moment), while the crest at the bow and stern simultaneously increases the effective waterplane area. This periodic variation in GM0 drives a resonant oscillation that can grow to very large amplitudes - roll angles exceeding 30° in a matter of seconds - without any initial transverse disturbance. Container ships with large bow flare and flat stern sections are particularly susceptible because of their pronounced fore-and-aft variation in waterplane area. The APL China incident of October 1998, in which a C11-class container ship lost hundreds of containers in parametric rolling in the North Pacific, was a turning point in industry awareness.

The Cougar Ace casualty of August 2006 is related: the ro-ro vehicle carrier was conducting a ballast water exchange procedure that required asymmetric partial filling of ballast tanks, which reduced GM0 to an abnormally low value. The ship experienced a rapid roll to about 60° in the North Pacific and remained listed, losing one crew member. While the immediate cause was the ballast management procedure rather than parametric resonance, the incident highlighted the vulnerability of large ro-ro vessels to rapid heel when GM0 is compromised by operational decisions. The parametric roll susceptibility calculator implements the Level 1 and Level 2 SGISC checks for this mode.

Surf-riding and broaching

Surf-riding occurs when a ship running in following seas is accelerated by a wave to a speed equal to the wave phase speed and then rides the crest without being overtaken. In this captured state, the hydrodynamic forces on the hull can produce a large yawing moment that overcomes the corrective torque from the rudder, driving the ship beam-on to the seas in a violent uncontrolled turn. This event - broaching - exposes the ship’s full beam to wave action and is a principal cause of capsizing in following seas. The phenomenon is strongly speed- and course-dependent; reducing speed in following seas (consistent with the general advice in slow steaming and CII in its context of rough weather passage) eliminates the surf-riding hazard. The broaching risk calculator evaluates susceptibility using the Froude-number and wave-steepness parameters specified in MSC.1/Circ.1627.

Pure loss of stability

Pure loss of stability is the condition in which a ship on a wave crest experiences a reduction in GM0 large enough that the restoring moment at moderate heel angles falls to zero or below. The ship then heels rapidly to the angle at which wave-induced waterplane geometry restores positive buoyancy, a process that may be violent enough to cause injury, cargo shift, or capsize. The Level 1 check in MSC.1/Circ.1627 evaluates the minimum GM0 on a wave crest (denoted GMW) relative to the required GM from Part A criteria; if GMW falls below a threshold based on ship type and proportions, a Level 2 assessment is required.

Dead ship condition

The dead ship condition is defined as the state in which the main propulsion and steering are inoperative and the ship lies beam-on to wind and waves with no corrective action available. A ship in this condition relies entirely on its righting energy to resist the combination of steady wind and irregular wave-induced rolling. The criterion for this mode draws on the same energy-balance framework as the weather criterion in IS Code Section 2.3 but uses long-crested irregular wave statistics rather than the parametric roll formula of the deterministic criterion. The dead ship assessment is particularly relevant to vessels that may experience propulsion failure in severe weather, including older general cargo ships and bulk carriers.

Excessive accelerations

The excessive accelerations mode addresses vessels in which high GM0 produces roll periods short enough that transverse accelerations at deck level and at the bridge exceed the values at which personnel can operate effectively, cargo lashings are overloaded, or portable equipment is displaced. The threshold is typically expressed in terms of the product of the roll amplitude and the square of the roll frequency; the SGISC Level 1 check uses a GM0 upper bound derived from the ship’s breadth and an assumed metacentric height limit. The mode is relevant to small craft and fishing vessels with heavy fishing gear aloft, and to offshore supply vessels in ballast.

Notable casualties and their lessons

Gaul (1974)

The British stern trawler Gaul disappeared on 8 February 1974 in severe weather in the Barents Sea with all 36 crew. A 1974 formal investigation concluded she was lost in heavy weather without determining a specific cause. A 1997 discovery of the wreck and a 2004 re-opened inquiry concluded that flooding through open non-return valves and possibly the factory deck entrance was the most probable cause of sinking. The casualty contributed to the programme that produced IMO Resolution A.168(ES.IV) criteria for fishing vessels.

Derbyshire (1980)

The MV Derbyshire was a British bulk carrier lost on 9 September 1980 in Typhoon Orchid in the North Pacific with 44 crew. The casualty is primarily attributed to hull-girder overloading and progressive structural failure rather than to a stability failure in the intact stability sense. A 1987 formal investigation and the 2000 re-opened inquiry with wreck survey concluded that wave-induced flooding through vent pipes and hatch covers caused structural overloading amidships. The case is a reference point for the SOLAS convention bulk carrier structural requirements and hatch cover standards rather than for intact stability criteria per se.

MSC Napoli (2007)

The container ship MSC Napoli suffered progressive structural failure in a North Atlantic storm on 18 January 2007. The ship was intentionally beached off Branscombe, Devon, and subsequently broke in two. The casualty is relevant to intact stability insofar as the investigation revealed misdeclared cargo masses causing an unforeseen change in hull-girder loading. The relationship between actual loading, stability booklet data, and structural strength margins is a recurring theme in incidents involving heavy or dense cargo in containers.

Cougar Ace (2006)

The ro-ro vehicle carrier Cougar Ace heeled approximately 60° to port in the Aleutian Islands on 24 August 2006 during a mandated ballast water exchange. The exchange procedure under IMO ballast water management guidance required filling new seawater before discharging the existing ballast, but the simultaneous partial flooding of all ballast tanks reduced GM0 to a critically low value during the transition. The incident resulted in the loss of one salvage worker and the total loss of approximately 4,700 vehicles. It prompted revisions to IMO guidance on ballast exchange procedures and strengthened the case for the mandatory adoption of ballast water treatment systems under the Ballast Water Management Convention. It also demonstrated the importance of checking GM0 at each intermediate stage of a ballast operation, not only at the start and end conditions specified in the stability booklet.

Hyundai Fortune (2006)

The container ship Hyundai Fortune suffered an explosion in the engine room on 21 March 2006 in the Gulf of Aden, losing approximately 1,200 containers overboard. While the immediate cause was the cargo fire rather than a stability failure, the incident is often cited alongside parametric roll studies because the sudden loss of deck cargo changed the ship’s KG and influenced the subsequent behaviour of the floating hull. Analysis of the post-incident condition required recalculation of stability with the changed loading state.

Verification of compliance

Loading condition check sequence

For a typical loading condition, the compliance check proceeds as follows. The naval architect or ship’s officer records the mass and vertical centre of each item on board: cargo (by hold or bay, referencing the bill of lading or container weight certificates), ballast water (by tank sounding), fuel oil (by ullage), fresh water, stores, and the lightship baseline from the approved booklet. The displacement Δ and KG are computed by the moment summation method. The free surface correction is applied using the measured fill levels and tank geometries. The corrected KG is used with the KN tables at the computed displacement to calculate the GZ curve at standard heel angles. The six Part A criteria are checked numerically. The weather criterion calculation then uses the computed GM0 and the ship’s geometry to determine whether the energy balance is satisfied. If any criterion fails, the loading must be adjusted - typically by adding ballast, redistributing cargo vertically, or modifying the tank arrangement to reduce free surface moments.

Role of classification societies and port state control

Classification societies - organisations such as Lloyd’s Register, DNV, Bureau Veritas, ClassNK, ABS, and RINA - survey ships against their own rules, which incorporate the IS Code criteria as a minimum. The stability booklet is submitted to the relevant flag state administration or its authorised recognition for approval; in practice this approval function is delegated to the classification society in most flag states. Port state control officers, working under the Paris MOU, Tokyo MOU, and other regional agreements, inspect ships in port and may detain a vessel if the stability booklet is absent or not being applied. The port state control article describes the inspection framework; the classification society article covers the role of recognised organisations in IS Code implementation.

Interaction with load line requirements

The International Convention on Load Lines interacts with intact stability through the concept of reserve buoyancy. The freeboard assigned to a ship limits the minimum hydrostatic reserve buoyancy; the IS Code criteria additionally require that the downflooding angle φ_f be high enough to allow the GZ curve to reach its required area thresholds. Ships assigned a reduced freeboard must demonstrate that their stability curves retain sufficient extent and area. The load line article describes the freeboard assignment process; the reserve buoyancy calculator quantifies the relationship between freeboard and the minimum reserve hydrostatic volume.

The ShipCalculators.com calculator catalogue includes the following tools directly relevant to intact stability compliance:

The IS Code general criteria calculator checks all six Part A criteria simultaneously for a given loading condition defined by displacement, KG, and tabulated GZ values. The IS Code severe weather criterion calculator performs the full wind-heeling and energy-balance computation. The GZ from KN cross-curve calculator converts KN table data and KG into the righting-lever array at standard angles. The GM from inclining experiment calculator derives GM0 from weight shift, distance, displacement, and pendulum deflection data. The KG limit from intact criteria calculator inverts the Part A criteria to find the maximum permissible KG at each displacement.

For the individual correction calculations: free surface correction, list from weight shift, new KG after weight addition, icing allowance, grain heeling moment, and passenger crowding heeling moment.

For second-generation criteria: parametric roll susceptibility and broaching risk in following seas. For damage stability, see the residual GM check.

See also

References

  1. International Maritime Organization. Code on Intact Stability for All Types of Ships, Resolution MSC.267(85), adopted 4 December 2008. IMO, London, 2009.
  2. International Maritime Organization. Recommendation on a Severe Wind and Rolling Criterion (Weather Criterion) for the Intact Stability of Passenger and Cargo Ships of 24 Metres in Length and Over, Resolution A.749(18), adopted 4 November 1993, incorporating A.167(ES.IV) (1968). IMO, London, 1993.
  3. International Maritime Organization. MSC.1/Circ.1627, Interim Guidelines on the Second Generation Intact Stability Criteria, 9 December 2020. IMO, London, 2020.
  4. International Maritime Organization. MSC.1/Circ.1652, Explanatory Notes to the Interim Guidelines on the Second Generation Intact Stability Criteria, 5 January 2022. IMO, London, 2022.
  5. International Maritime Organization. MSC.1/Circ.1667, 2019 Revised Guidelines for the Inclining Test, 5 June 2020. IMO, London, 2020.
  6. Rahola, J. The Judging of Ship Stability from the Basis of Cargo Steamers and Passenger Vessels in Connection with the Requirements of the 1939 International Conference on Safety of Life at Sea. Finnish Technical University, Helsinki, 1939.
  7. Yamagata, M. “Standard of Stability Adopted in Japan.” Transactions of the Institution of Naval Architects, vol. 101, 1959, pp. 417–443.
  8. International Maritime Organization. International Convention on Load Lines, 1966, as amended by the 1988 Protocol. IMO, London, consolidated edition 2002.
  9. International Maritime Organization. International Code for the Safe Carriage of Grain in Bulk (Grain Code). IMO, London, 1991.
  10. United Kingdom Marine Accident Investigation Branch. Report of the Re-Opened Formal Investigation into the Loss of MV Derbyshire, 2000.
  11. Papanikolaou, A. (ed.). Ship Design: Methodologies of Preliminary Design. Springer, 2014, chapter on intact stability.
  12. Kobylinski, L. and Kastner, S. Stability and Safety of Ships: Regulation and Operation. Elsevier, 2003.

Further reading

  • Molyneux, D. and Rousseau, J. Prediction of Parametric Roll Resonance, National Research Council of Canada, Institute for Ocean Technology, 2002.
  • Belenky, V. L. and Sevastianov, N. B. Stability and Safety of Ships: Risk of Capsizing, 2nd edition. Society of Naval Architects and Marine Engineers, 2007.
  • International Maritime Organization. Intact Stability Criteria for Passenger and Cargo Ships of 24 Metres in Length and Over, MSC Circulars and Unified Interpretations series.