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Subdivision and Floodable Length: SOLAS II-1

Contents

The ship subdivision problem is, at its core, a geometry problem: given a hull form, how many watertight compartments of what size are needed so that flooding of some defined number of them doesn’t sink the vessel? The answer has changed considerably over the century since SOLAS was first drafted. The classical method, used from 1929 through 2008, computed a quantity called the floodable length for every point along the ship’s length and then divided it by a regulatory factor to get the permissible length for any one compartment. Bulkheads had to fall within those permissible length limits. That method worked, it was tractable by hand, and it produced the subdivision of virtually every dry cargo vessel built between 1929 and 2008.

From 1 January 2009, following the adoption of Resolution MSC.216(82) in December 2006, the deterministic floodable-length method was superseded for new cargo ships and most passenger ships by the probabilistic attained subdivision index A, which must meet or exceed a required index R set by vessel size. The probabilistic damage stability framework sums the probability-weighted survival probability across all credible damage cases rather than checking only the worst one or two. The sibling article covers the probabilistic method in detail; this article covers the floodable-length method that came before it, why the IMO replaced it, and where deterministic subdivision thinking still appears.

The companion floodable length calculator implements the deterministic geometry numerically; the required subdivision index R calculator covers the probabilistic R formula.

Why compartmentation matters: the physics before the regulation

A floating vessel is in hydrostatic equilibrium. Its displacement equals the weight of water displaced. Flood one compartment and two things happen simultaneously: the vessel gets heavier (mass of water gained) and it loses buoyancy from the flooded space. The net effect is that it settles deeper in the water. If the flooding is asymmetric, it also heels.

The depth it sinks to depends on the volume of water admitted. If the flooded space runs the full beam, the ship sinks by:

δTμlBdwl/T \delta T \approx \frac{\mu \cdot l \cdot B \cdot \overline{d}}{\nabla_{wl} / T}

where μ\mu is permeability of the flooded space, ll is the flooded length, BB is beam, d\overline{d} is mean depth of the compartment, and wl\nabla_{wl} is the waterplane volume (approximately LBTCwL \cdot B \cdot T \cdot C_w for a full-form vessel). The exact calculation uses lost-buoyancy theory on the actual hull offsets, not this approximation, but the proportionality is clear: longer compartments and higher permeability produce larger increases in draft. Longer flooded length also shifts the centre of buoyancy, changing trim.

The margin line is the ceiling on how far the waterline can rise in any of this. Once the margin line is breached at any point on the ship’s length, the regulation treats the vessel as having lost buoyancy access to the deck and as therefore non-survivable. The 76 mm gap between the margin line and the freeboard deck provides allowance for wave action in the damaged condition, for small deck openings, and for the difference between still-water calculations and real-sea conditions.

Freeboard and reserve buoyancy define the external geometric margin: how high above the waterline the freeboard deck sits in the intact condition. Subdivision defines the internal margin: how much of that freeboard is consumed by damage flooding before the margin line is reached.

The deterministic framework: regulatory history

SOLAS 1929 and the foundation

The first SOLAS Convention was signed in 1914 following the Titanic disaster of April 1912. It was not ratified before World War I intervened. A revised convention was signed in 1929 and entered into force in 1933. SOLAS 1929 introduced the framework that would endure for eighty years: the floodable length curve, the factor of subdivision, and the margin line.

The Titanic’s designers understood compartmentation. The ship had 15 transverse watertight bulkheads. What went wrong was a combination of bulkheads that didn’t reach high enough (they stopped at E Deck, not the waterline level), excessive compartment lengths in the forward section, and a collision damage extending across five compartments simultaneously. The bow sank progressively, water overtopped one bulkhead after another, and the ship broke apart before it sank. SOLAS 1929 was specifically designed to address these failure modes: bulkheads had to reach the freeboard deck (later the bulkhead deck), compartment lengths were bounded by the floodable-length calculation, and the two-compartment standard ensured that even adjacent-compartment flooding was survivable.

The 1948 and 1960 conventions

SOLAS 1948 refined the subdivision framework, tightening the factor-of-subdivision curves and clarifying the permeability tables. The criterion numeral computation became more systematic. SOLAS 1960 extended the framework to cargo ships more explicitly, introduced numerical tables for the factor of subdivision F as a function of the criterion numeral C, and mandated damage stability calculations showing the ship survived the flooding rather than merely that bulkheads were positioned correctly. These are the texts that directly precede the 1974 convention.

SOLAS 1974 and subsequent amendments

SOLAS 1974, which remains the base treaty in force today (as amended), carried over the deterministic subdivision framework from 1960 for cargo ships in Part B of Chapter II-1. For passenger ships, Chapter II-1 Part B-2 provided more stringent requirements including minimum GZ criteria in the damaged condition. Resolution MSC.12(56) in 1988 introduced deterministic damage stability criteria for dry cargo ships, and MSC.19(58) in 1990 adopted the probabilistic method for passenger ships, the first time the A/R index appeared in binding SOLAS text.

The full cargo-ship probabilistic framework arrived with MSC.216(82) in December 2006, entering force on 1 January 2009. The most recent amendment to the framework is Resolution MSC.421(98) adopted by the Maritime Safety Committee in June 2017, which adjusted the required subdivision index R formula and added requirements applicable to ships contracted on or after 1 January 2020.

The floodable-length curve

Definition and construction

The floodable length FL(x)FL(x) at a point xx along the ship’s length is defined as: the maximum length of a compartment, centred on xx, that can be flooded to the design permeability without immersing the margin line at any point along its length.

Constructing the floodable-length curve for a given ship requires the following inputs, all taken from the intact hydrostatics:

  1. The ship’s hull offsets at every station, from which waterplane area AwA_w, second moment of waterplane area ILI_L (longitudinal), and buoyancy volumes can be computed.
  2. The intact draft TT and trim.
  3. The height of the margin line above the keel at each station.
  4. The design permeability μ\mu for the type of space at each location.

The calculation proceeds iteratively. For each assumed centred compartment of length ll at position xx, the lost-buoyancy method computes the new waterplane (excluding the flooded compartment) and finds the equilibrium draft and trim in the flooded condition. If the new waterline exceeds the margin line at any point within the flooded compartment or elsewhere, ll is too long. The maximum ll before margin-line immersion is the floodable length at xx.

Repeat this for all positions xx from bow to stern and you have the floodable-length curve: a continuous function showing how long a flooded compartment can be at each position before the ship fails. The curve typically has its highest values amidships, where freeboard is greatest and the hull is most buoyant, and lower values at the ends, where freeboard diminishes and the hull is finer.

Effect of permeability on the curve

Permeability μ\mu is the proportion of a space’s gross volume that is available for flooding. SOLAS II-1 Regulation 2 defines the design permeability values:

Space typeDesign permeability μ\mu
Stores0.60
Accommodation and service spaces0.95
Machinery spaces0.85
Void spaces, tanks (empty)0.95
Dry cargo holds0.70
Ro-ro cargo spaces0.90

These are regulatory defaults. For the floodable-length calculation, the weighted average permeability over the flooded length is used. The formula for a compartment spanning spaces of different types uses the volume-weighted mean:

μcomp=jμjvjjvj\mu_{comp} = \frac{\sum_j \mu_j \cdot v_j}{\sum_j v_j}

where μj\mu_j and vjv_j are the permeability and gross volume of the jj-th space type within the compartment.

The practical effect: a compartment occupied entirely by dry cargo at μ=0.70\mu = 0.70 can be longer before the margin line is reached than one occupied by accommodation at μ=0.95\mu = 0.95, because less water enters per unit volume. Machinery spaces at μ=0.85\mu = 0.85 fall between. This is why engine rooms, despite their large volume, sometimes allow longer adjacent compartments than pure cargo holds: their lower permeability limits the water ingress. The permeability calculator computes the effective permeability for mixed compartment types.

The permissible length and the factor of subdivision

The factor F

The permissible length PL(x)PL(x) is the floodable length divided by the factor of subdivision FF:

PL(x)=FL(x)FPL(x) = \frac{FL(x)}{F}

Every actual compartment in the ship must have a length no greater than PL(x)PL(x) at its centre. Equivalently, if the floodable-length curve at position xx is FL(x)FL(x), then the largest compartment centred at xx that complies is PL(x)PL(x).

The factor FF ranges from 0 (infinitely stringent, unachievable) to 1 (no additional reduction applied beyond the floodable-length geometry). In practice FF lies between 0.5 and 1.0 for cargo vessels. The lower FF, the shorter the permissible compartments, the more bulkheads are needed.

SOLAS II-1 (1960 and 1974 versions) tabulated FF as a function of the criterion numeral CC. The 1974 SOLAS table gave FF values ranging from 1.0 at C=0C = 0 to approximately 0.5 at C=23C = 23 for Type A vessels (oil tankers and bulk carriers), with a separate curve for Type B and passenger ships. The relationship was originally graphical (plotted curves in the convention text) and later expressed as piecewise linear interpolation tables.

The criterion numeral C

The criterion numeral CC was defined in the 1974 SOLAS deterministic framework to reflect the relative exposure of a vessel to loss-of-life consequences from flooding, specifically capturing the ratio of accommodation and machinery space to total ship volume. The 1974 SOLAS formula was:

C=L(B+D)cC = \frac{L \cdot (B + D)}{c}

where LL is the length of the ship (on the subdivision load waterline), BB is the moulded breadth, DD is the moulded depth to the freeboard deck, and cc is a constant (13 for ships with L<131L < 131 m, 3.3 for L131L \geq 131 m). The criterion numeral was then further modified by the number of passengers VV onboard and the ratio of accommodation to total volume, following a prescribed multi-step formula set out in SOLAS II-1 Regulation 11 (pre-2009 text).

The criterion numeral approach was a proxy for risk: a larger ship with more passengers had a higher CC, which drove a lower FF, which demanded shorter compartments, which required more bulkheads. The method worked reasonably well for the ship types of the 1950s and 1960s but became increasingly strained as ships diversified.

Deriving bulkhead positions from the permissible-length curve

The designer’s task is to place bulkheads such that every compartment’s length stays within the permissible length at its centre. This is not simply dividing the ship into equal sections: the permissible-length curve varies continuously, so the bulkhead-position problem is one of fitting rectangles under a curved envelope.

The conventional approach is graphical (or its numerical equivalent): plot the permissible-length curve PL(x)PL(x) over the ship’s profile. Starting at the aft end, step forward the permissible length from that point; that point is where the first bulkhead must fall. Step forward again from the new bulkhead, and so on. The collision bulkhead and afterpeak bulkhead positions are fixed by separate regulation (SOLAS II-1 Regulations 8 and 9 pre-2009, requiring the collision bulkhead between 5% and 8% of the ship’s length aft of the forward perpendicular), so the designer works within those fixed constraints.

The minimum number of transverse bulkheads is determined by how many steps are needed to traverse the ship’s length under the permissible-length envelope. If the permissible length is 40 m amidships on a 180 m ship, roughly four to five compartments cover the mid-body alone. Adding the collision and afterpeak bulkheads and the machinery space boundaries typically gives eight to twelve principal transverse watertight bulkheads on a mid-size cargo vessel.

The bulkhead deck and the margin line: geometry and regulation

The bulkhead deck

The bulkhead deck is the highest deck to which transverse watertight bulkheads are carried. SOLAS II-1 Regulation 3 (pre-2009 text, carried forward in substance) requires that watertight bulkheads extend from the bottom of the ship to the bulkhead deck. The bulkhead deck is at least as high as the freeboard deck. On many vessels they are the same deck; on some (particularly passenger ships with superstructure deck arrangements) the bulkhead deck is a deck below the main freeboard deck.

The bulkhead deck matters because it defines the upper boundary of the watertight envelope. Any opening in a bulkhead above the bulkhead deck is not required to be watertight; below it, every penetration must be controlled by a watertight door capable of remote closure.

The margin line in the stability calculation

In the lost-buoyancy method of computing the flooded condition, the ship’s waterplane in the damaged state excludes the flooded compartment. The remaining waterplane must provide enough upward force to support the vessel’s displacement. The equilibrium waterline is found by iterating until the buoyancy equals the displacement (intact displacement plus the mass of floodwater). The margin line check asks: does this equilibrium waterline, at any point along the ship, rise above the margin line (76 mm below the freeboard deck at side)?

The 76 mm offset appears small but carries significant practical weight. The freeboard deck is not perfectly flat athwartships (it has camber) or longitudinally (it has sheer). Deck openings exist. In the real sea, the flooded condition doesn’t occur in flat water. The 76 mm is the convention’s acknowledgment of these practical imperfections.

The damage margin-line calculator computes the clearance between the damaged waterline and the margin line for a given set of hull parameters and damage extent. Negative clearance means the vessel fails the deterministic check at that damage extent.

The two-compartment standard: where F < 1

For cargo ships under the pre-2009 deterministic framework, the one-compartment standard (F=1.0F = 1.0) required survival of flooding any single compartment. The two-compartment standard (F<1.0F < 1.0, sometimes called the “two-compartment ship”) required survival of the simultaneous flooding of any two adjacent compartments.

Passenger ships above certain size thresholds (varying by number of persons onboard, NN) were required to meet the two-compartment standard, meaning each compartment’s permissible length was FL(x)/FFL(x)/F with FF as low as 0.5. In effect the permissible length was halved relative to a one-compartment ship, demanding roughly twice as many bulkheads in the same hull length.

The logic of the two-compartment standard follows from casualty statistics: many collision and grounding events breach two adjacent compartments simultaneously because damage extends beyond one bulkhead spacing. The 1948 and 1960 conventions drew the boundary based on ship size and passenger count: above 400 passengers, two-compartment standard; below 400 passengers (and for cargo ships), one-compartment standard was the default, with the factor FF between 0.5 and 1.0 depending on the criterion numeral.

This is one area where the deterministic method was demonstrably conservative in a way that the probabilistic method addressed more rationally. A two-compartment ship must survive the worst two-compartment case regardless of how improbable that specific damage extent is. The probabilistic method weights each damage case by its likelihood; a low-probability extreme case contributes little to the index.

Permeability in practice: the pre-2009 calculation

The pre-2009 SOLAS II-1 text (Regulation 7) specified that the permeability of machinery spaces was to be taken as μ=0.85\mu = 0.85 for the volume below the inner bottom and 0.85 for the volume above the inner bottom up to the margin line, unless the actual cargo was more dense, in which case a lower value was allowed by the administration. For cargo spaces, μ=0.70\mu = 0.70 was the general default.

The practical consequence for ship design: a vessel with machinery aft (common in the pre-VLCC era) has a lower-permeability engine room compartment near the stern. The afterpeak and engine room together form a relatively short combined length, which the single-compartment standard typically satisfied. The long mid-body cargo holds, with μ=0.70\mu = 0.70, could be somewhat longer than the same space at μ=0.95\mu = 0.95 before the margin line was breached.

Grain carriers were a particular case: bulk grain has a permeability closer to 0.60 to 0.65 because the grain itself occupies significant volume. Ore carriers, with denser cargo, can have permeability as low as 0.40. SOLAS allowed reduced permeability to be demonstrated to the Administration with supporting calculations, which could justify longer cargo compartments and fewer bulkheads (and hence lower construction cost). This was a legitimate regulatory allowance but also a source of gaming: some vessel designs pushed the demonstrated permeability as low as possible to minimize bulkhead count.

The transition to probabilistic subdivision

Why the deterministic method became inadequate

Three interrelated problems drove the IMO to replace the deterministic framework for cargo ships.

First, the criterion numeral and factor-of-subdivision approach did not distinguish between types of damage or their probabilities. A vessel was required to survive flooding of any single compartment, giving equal weight to a 0.5 m graze amidships and a 40 m full-breadth midship flooding. Real collision and grounding damage statistics (compiled by the IMO from accident reports) showed that damage extent follows a probabilistic distribution: short, shallow damage is far more common than long, deep damage. The deterministic method set minimum requirements without rewarding vessel designs that performed well across the probability-weighted damage space.

Second, the method was opaque to trade-offs. A designer who added a second longitudinal bulkhead in the cargo hold improved the vessel’s survivability for asymmetric flooding but received no regulatory credit because the deterministic test only checked transverse flooding across the full beam. The probabilistic method, by summing over all damage cases with their probabilities and survival factors, credits every design improvement that increases expected survivability.

Third, the criterion numeral approach, derived in the 1940s and 1950s from the experience of that era’s fleet, did not translate well to very large ships. A 300 m container ship has very different flooding dynamics from the 150 m general cargo vessel the formulae were calibrated on.

The IMO’s Joint Working Group on Subdivision and Damage Stability, active from the 1980s, produced a series of research reports through the 1990s and early 2000s culminating in the text adopted in MSC.216(82).

The A/R index in outline

The probabilistic method is covered in the companion article on probabilistic damage stability. In brief: for each damage zone ii defined along the ship’s length, the probability of damage occurring in that zone is pip_i (from the IMO damage probability distributions). The probability of the vessel surviving given that damage is sis_i (from the GZ curve residual stability in the flooded condition). The attained subdivision index is:

A=ipisiA = \sum_{i} p_i \cdot s_i

This must equal or exceed R. For cargo ships, MSC.421(98) sets:

R=1128Ls+152R = 1 - \frac{128}{L_s + 152}

where LsL_s is the subdivision length in metres. A 200 m cargo ship has R=1128/352=0.636R = 1 - 128/352 = 0.636. A 100 m cargo ship has R=1128/252=0.492R = 1 - 128/252 = 0.492.

For passenger ships, R includes a term for the number of persons onboard NN. The required subdivision index calculator and attained subdivision index calculator implement these calculations. The s-factor survival probability calculator and p-factor damage probability calculator handle the per-zone components.

Cut-off date and transitional provisions

The cut-off applies to the contract date: ships for which the building contract was placed on or after 1 January 2009 must comply with the probabilistic SOLAS II-1. Ships contracted before that date remain subject to the deterministic framework, even if built and delivered after 2009. This creates a mixed fleet: a 25-year-old Panamax bulk carrier built under the deterministic regime will remain in service alongside a new Kamsarmax designed under the probabilistic regime until the older vessel is scrapped.

The practical implication for surveyors and port state control is that the applicable regulatory text depends on the contract date recorded in the IMO ship file, not the year of build. A survey of an older vessel for subdivision compliance should reference the pre-MSC.216(82) SOLAS text, not the current consolidated Chapter II-1.

Where deterministic concepts survive after 2009

The collision bulkhead and the afterpeak bulkhead

SOLAS II-1 Regulation 12 (in the post-2009 consolidated text) retains explicit positional requirements for the collision bulkhead: it must be positioned at a distance not less than 5% of the ship’s length forward of the forward perpendicular and, in general, not more than 3 m + 5% of the ship’s length from it. These limits are deterministic: fixed geometric bounds, not probability-weighted outcomes.

The afterpeak bulkhead (Regulation 11) and the machinery space boundaries similarly have position requirements that are expressed as deterministic minima rather than derived from the probabilistic index. The probabilistic method calculates the A index for the hull as designed; the deterministic bulkhead-position rules set a floor on what designs are acceptable before the probabilistic calculation even runs.

Watertight subdivision of machinery spaces

SOLAS II-1 Regulation 10 (post-2009) requires that the main and auxiliary machinery spaces be enclosed within watertight boundaries. The propeller shaft tunnel, if any, must be watertight. The number and position of these boundaries are subject to the probabilistic calculation, but the existence of the machinery space as a defined watertight volume is a deterministic requirement that predates and survives the 2009 amendment.

Tanker damage stability under MARPOL Annex I

MARPOL Annex I, Regulation 28 (damage stability for oil tankers) sets deterministic survival criteria for collision and stranding damage. An oil tanker must survive flooding of any single transverse section of any cargo tank, any single transverse section of any ballast tank adjacent to a cargo tank, and any single longitudinal section. The survival criteria (maximum heel angle, minimum GZ curve range, minimum residual GM) are deterministic checks on the damaged condition, not contributions to a probabilistic index.

The MARPOL Annex I Regulation 22 (cargo tank size limits) and Regulation 23 (double-hull and double-bottom requirements) similarly impose geometric deterministic constraints. The MARPOL Annex I damage stability article covers these in detail.

SOLAS Chapter XII bulk carrier flooding survival

SOLAS Chapter XII, in force from 1 July 2002, introduced a deterministic single-hold flooding criterion for bulk carriers above 150 m in length. The vessel must survive flooding of any single cargo hold to the damaged equilibrium waterline with positive stability margins. This is not part of the Chapter II-1 probabilistic framework; it is a separate deterministic check still in force for all bulk carriers regardless of contract date.

The rationale was the high loss rate for bulk carriers in the late 1980s and 1990s: Derbyshire (1980, 44 lives), Marine Electric (1983, 31 lives), Bulk Jupiter (1984, 37 lives), and numerous others. IMO investigations consistently found inadequate transverse strength and progressive flooding through hatch covers and holds. Chapter XII addressed the survival margin after a hold floods, irrespective of how the flooding started.

Comparison: deterministic floodable-length vs probabilistic A/R index

AttributeDeterministic (floodable length / factor of subdivision)Probabilistic (attained index A vs required index R)
Regulatory basisSOLAS 1929 through pre-2009 Chapter II-1SOLAS Chapter II-1 post-MSC.216(82), in force 2009
Primary outputPermissible compartment length at each stationDimensionless probability-weighted survivability index
Ship types applicableCargo ships pre-2009; some special types stillCargo ships contracted from 2009; passenger ships from 1990
Damage cases consideredAny single (or any two adjacent) compartmentsAll credible damage extents, weighted by probability
Damage probabilityNot modeled; all cases treated equallyExplicitly computed from IMO damage statistics
Survival probabilityBinary pass/fail per caseContinuous 0 to 1 per case, derived from GZ curve
Design flexibilityLow: bulkhead positions constrained geometricallyHigher: compensatory performance across damage cases allowed
Computation methodIterative waterplane / draft calculation; hand-tractableSum over hundreds to thousands of damage cases; software required
ConservatismConservative for low-probability extreme damage; permissive for moderate common damageBalanced: extreme low-probability damage contributes little
TransparencyDirectly verifiable against hull drawingsRequires understanding of p-factor and s-factor methodology
Still relevantVessels pre-dating 2009 contract; collision/afterpeak bulkhead positions; MARPOL tanker rules; SOLAS XII bulk carriersStandard for new cargo and passenger ships

Limitations

The deterministic floodable-length method was not wrong; it was appropriate to its era’s computing resources and fleet composition. Its limitations accumulated as ships grew and diversified.

First, the method cannot account for asymmetric flooding. The floodable-length calculation assumes the flooded compartment spans the full beam: permeability is applied to a full-transverse cross-section. A ship with longitudinal watertight bulkheads (a tanker with center and wing tanks, or a vessel with a centerline trunk) develops a heel in single-wing-tank flooding that the simple lost-buoyancy model ignores. The pre-2009 passenger ship rules partially addressed this with separate heeling-moment criteria, but the cargo ship rules did not.

Second, the factor of subdivision F and the criterion numeral C are empirical proxies for risk, not measurements of it. The calibration was based on the 1940s and 1950s fleet. A 350 m container ship with 20,000 TEU capacity and 20 crew bears no resemblance to the 150 m general cargo vessel that drove the original calibration. The criterion numeral for such a ship gives a value of F that may be either more or less conservative than actual risk would justify, with no systematic way to know which.

Third, the method gives no credit for design choices that reduce flooding consequences without altering compartment lengths. Cross-flooding arrangements, progressive flooding models, bilge pumping capacity, and active damage control all affect survivability in a real flooding event but don’t enter the floodable-length calculation. The probabilistic method credits them indirectly through the s-factor (survival probability), which is computed from the actual residual GZ curve after any cross-flooding equilibrium is reached.

Fourth, the method’s definition of “failure” (margin-line immersion) is a crude proxy for actual loss of the vessel. A ship with its margin line just submerged in a damage scenario might still float and be controllable; a ship whose waterline is well below the margin line but that has lost all residual GZ might capsize. The probabilistic s-factor, computed from the full GZ curve shape, is a better predictor of actual survival.

These limitations don’t mean every pre-2009 vessel is unsafe. They mean the probabilistic method produces a more accurate characterization of subdivision adequacy and provides cleaner incentives for safer design. A designer under the probabilistic framework knows that improving survivability in any damage case improves the attained index A; under the deterministic framework, improvements beyond the minimum required for pass/fail brought no regulatory reward.

Operational significance of subdivision for the ship’s crew

The ISM Code requires every ship to have a damage control booklet: a document showing the subdivision plan, the identities of all watertight doors and their normal operating state, and the procedures to be followed in a flooding emergency. The officer responsible for damage control must know not just where the bulkheads are but how long the vessel can tolerate progressive flooding before a second compartment is threatened.

For the ship’s stability officer, the marine stability booklet and loading computer typically contains the damage stability information in simplified form: pre-computed damage cases showing which loading conditions keep the vessel within the damage stability criteria for the defined damage scenarios. This doesn’t mean the officer can compute the full A/R index on watch; it means the booklet tells them whether, given the current loading and trim, the vessel meets its subdivision requirement.

The damage stability article covers the operational side: what happens after damage occurs, how stability criteria are applied in the real damaged condition, and how cross-flooding and progressive flooding affect the vessel’s response. The GZ curve and righting arm article covers the stability geometry that underpins both the deterministic survival check and the probabilistic s-factor.

The floodable-length curve in modern practice

Design software has replaced graphical floodable-length construction, but the calculation itself is unchanged. Maxsurf Stability, NAPA, Hydromax, and comparable packages compute the floodable-length curve automatically from the hull model. For ships within the probabilistic regime, the software then uses the same hull model and compartment definitions to run the full A/R index calculation. The floodable-length output is still available and many designers retain it as a design intuition check: if the permissible length at some station falls below the proposed compartment length under the probabilistic regime, the probabilistic index will almost certainly be deficient at that location too.

For vessels subject to deterministic rules (pre-2009 contract dates, tankers under MARPOL Annex I, bulk carriers under SOLAS XII), the floodable-length curve retains direct regulatory significance. Classification society plan approval for such vessels requires submission of the floodable-length table and permissible-length comparison, together with the bulkhead arrangement drawing showing that every compartment falls within the permissible length at its centre.

The SOLAS II-1 Regulation 16 framework (construction of watertight subdivision, intact and in damaged conditions) is the primary regulatory checkpoint; the SOLAS II-1/16 calculator implements the associated numerical checks. The damage-stab A-index calculator provides a cross-check on the probabilistic side for ships subject to the post-2009 regime.

See also

Related wiki articles:

Related calculators:

Frequently asked questions

What is floodable length in ship subdivision?
Floodable length at any point along a ship's length is the maximum length of compartment, centred on that point, that can be flooded to the design permeability without immersing the margin line. It is determined by the ship's hull form, freeboard, and permeability of the spaces involved.
What is the margin line?
The margin line is a reference line drawn 76 mm below the upper surface of the freeboard deck at side. In the deterministic subdivision method, flooded waterplane calculations must not breach this line; if they do, the vessel fails the subdivision check for that compartment length.
What is the factor of subdivision?
The factor of subdivision F is a number between 0 and 1 that divides the floodable length to give the permissible length. It depends on the criterion numeral C, which is derived from the ship's size and the proportion of machinery and accommodation space. Lower F (more stringent) applies to passenger ships with large onboard populations.
When did probabilistic subdivision replace the deterministic method?
SOLAS Chapter II-1 was revised by Resolution MSC.216(82) adopted in December 2006 and entering into force on 1 January 2009. Ships contracted on or after 1 January 2009 must use the probabilistic A/R index method for cargo ships and most passenger ships. The deterministic floodable-length method was retained only for ships contracted before that date and for specific ship types where SOLAS still references it explicitly.
How does permeability affect the floodable length calculation?
Permeability is the fraction of a compartment volume that floodwater can actually occupy. Higher permeability (approaching 1.0 for empty spaces) means more water enters per unit length, which means the vessel sinks deeper for a given flooded length, which means the maximum flooded length before the margin line is breached is shorter. Standard permeability values are set in SOLAS II-1 Regulations 2 and 7 and typically range from 0.60 for machinery spaces to 0.95 for accommodation.