MARPOL Annex I Reg 25: hypothetical oil outflow

What Regulation 25 is, and where it sits

Regulation 25 of the consolidated MARPOL Annex I is the deterministic hypothetical oil outflow rule for oil tankers. It calculates how much cargo oil is assumed to spill from a defined damage, not how much spills in a real casualty. The output is two volumes in cubic meters: $O_c$ for side (collision) damage and $O_s$ for bottom (grounding) damage. Those figures are then weighed against the cargo-tank size limit in Regulation 26. The rule lives in Chapter 4 of Annex I, Requirements for the cargo area of oil tankers, alongside the damage-assumption rule (Regulation 24) that fixes the damage extents and the tank-size rule (Regulation 26) that sets the ceiling the outflow must respect.

The three regulations work as one calculation chain. Regulation 24 says where and how big the assumed damage is. Regulation 25 says how much oil that damage releases. Regulation 26 says how large a tank arrangement is allowed to be given that release. A naval architect can’t satisfy Regulation 26 without first running Regulation 25, and can’t run Regulation 25 without the Regulation 24 extents. The whole point is to force a finer cargo-tank subdivision: smaller tanks, protective wing tanks, and a double bottom that together cap the worst-case spill.

A note on numbering, because it trips up surveyors who hold both old and consolidated copies. In the 1973/78 MARPOL text and the editions in force through 2004, the same three rules carried the numbers Regulation 22 (damage assumptions), Regulation 23 (hypothetical outflow of oil), and Regulation 24 (limitations of size and arrangement of cargo tanks). The wholesale revision adopted by resolution MEPC.117(52) on 15 October 2004, in force 1 January 2007, renumbered Annex I and pushed them to 24, 25, and 26. The formulas didn’t change in that renumbering. If a stability booklet cites “Reg. 23 hypothetical outflow,” it predates the 2007 revision; the modern citation is Regulation 25.

Deterministic versus probabilistic: the split with Regulation 23

This is the distinction to fix first, because Regulation 25 and Regulation 23 answer the same environmental question with opposite methods, and they apply to different fleets. Regulation 25 is deterministic. It assumes one specific damage of fixed size in the worst location, assumes a fixed fraction of the breached tanks’ oil escapes, and reports a single outflow volume. There’s no probability anywhere in the calculation. The designer finds the most severe combination of breached compartments within the Regulation 24 extents and reports that one number.

Regulation 23, the accidental oil outflow performance rule, is probabilistic. It runs the full statistical distribution of collision and grounding damages drawn from a casualty database, weights each possible damage by its probability, and reports a non-dimensional mean oil outflow parameter $O_M$. Where Regulation 25 asks “what is the worst single spill this arrangement permits,” Regulation 23 asks “across all credible casualties, what spill is expected on average.” The two never run together on the same hull.

The dividing line is the delivery date. Regulation 25 read with Regulation 26 governs oil tankers delivered before 1 January 2010. Regulation 23 governs oil tankers of 5,000 tonnes deadweight and above delivered on or after that date. So a 2006-built Aframax carries an approved $O_c$ and $O_s$ calculation in its damage-stability documentation, while a 2012-built sister carries an $O_M$ calculation instead. A surveyor checking an older tanker’s loading manual is reading Regulation 25 figures; the probabilistic $O_M$ has no place in that booklet. The deterministic scheme is not retired, it’s grandfathered: it remains the live compliance basis for a large share of the existing tanker fleet, and it stays in force as long as those hulls trade.

The reason the IMO moved on is worth one sentence, because it explains what the deterministic method misses. The Marine Environment Protection Committee found that the deterministic rules “did not properly account for variations in subdivision in general, and longitudinal subdivision in particular,” so two arrangements could report the same $O_c$ yet behave very differently across the real spread of casualties. The probabilistic replacement handles subdivision variation directly. That is a critique of Regulation 25’s coverage, not its arithmetic; for the fleet it governs, the deterministic calculation remains exactly as binding as it was in 1978.

The side-damage outflow Oc

Side damage models a collision: a striking ship’s bow opens the side shell of the struck tanker over the Regulation 24 transverse penetration. The hypothetical outflow from side damage is the sum of all the cargo oil in the wing tanks assumed breached, plus a width-discounted share of the center tanks behind them:

Every symbol has a fixed meaning. $W_i$ is the volume of cargo oil in cubic meters in a wing tank assumed holed by the side damage. $C_i$ is the volume of cargo oil in a center tank assumed holed by the same damage. $K_i$ is a dimensionless coefficient between 0 and 1 that scales how much of the center tank the side damage can reach, set by the protective width of the wing tank in front of it. The summation runs over the tanks breached in the damage case under consideration, and a segregated ballast tank or void counts as zero because it holds no oil: if a wing space adjacent to the damage is a segregated ballast tank, its $W_i$ is taken as zero.

The width coefficient is the heart of the side-damage logic:

Here $b_i$ is the width in meters of the wing tank under consideration, measured inboard from the ship’s side at right angles to the centerline. $t_c$ is the assumed transverse penetration of side damage from Regulation 24. When the wing tank is at least as wide as the assumed penetration, $b_i \geq t_c$, the damage stops inside the wing tank and never reaches the center tank, so $K_i = 0$ and the center tank contributes nothing to $O_c$. A narrow wing tank, $b_i$ small, drives $K_i$ toward 1 and pulls most of the center tank’s oil into the outflow. This single term is why protective wing tanks, the precursor of the double-hull sides that Regulation 19 later mandated, cut hypothetical outflow so sharply. A wing tank wide enough to absorb the full assumed penetration zeroes out the center tank behind it.

For side damage the regulation makes a deliberately harsh assumption about the breached wing tank: all of its oil is treated as lost. There were no reliable data on how much liquid stays aboard a side-holed tank, and theoretical estimation of retained oil was judged impractical, so the method spills 100 percent of $W_i$. A collision is a clean loss of the breached wing tank’s full cargo, discounted only for the center tank behind it through $K_i$. That conservatism is intentional: a side spill reaches the sea surface fast, with little chance for the cargo to stay contained.

Work the summation through term by term, because the per-tank build is where the arithmetic actually lives. The transverse damage box of width $t_c$ is slid to every conceivable position along the length of the ship, and at each position the calculation asks which tanks the box cuts. A wing tank the box reaches contributes its full cargo volume $W_i$ to the first sum. The center tank inboard of that wing tank contributes $K_i C_i$ to the second sum, but only the fraction $K_i = 1 - b_i/t_c$ of the box’s penetration that survives after the wing tank has absorbed its share. If the wing tank in front is itself a segregated ballast tank, its $W_i$ is zero, but it still shields the center tank: a wide enough ballast-filled wing tank carries $b_i \geq t_c$, sets $K_i = 0$, and the center tank drops out entirely. So a single wing space can contribute nothing to the first sum yet zero out a center tank in the second. The governing $O_c$ is the largest value this term-by-term sum reaches across all the box positions, and that worst case is almost always a station where the box catches two opposite wing tanks plus their two center tanks at once.

The units make the dimensional check trivial, which is worth doing once. $W_i$ and $C_i$ are volumes in cubic meters; $K_i$ is the dimensionless ratio of two lengths, $b_i$ and $t_c$, both in meters; so $K_i C_i$ is cubic meters and $O_c$ comes out in cubic meters. There is no density, no mass, no time anywhere in the side-damage formula. It’s a pure volume accounting of how much tank the assumed box opens, which is why it transfers cleanly into the Regulation 26 cubic-meter ceiling without a unit conversion.

There is one structural allowance worth stating, because it shapes how designers lay out the cargo block. Where a void space or segregated ballast tank of a length less than the assumed longitudinal side-damage extent $l_c$ sits between two wing oil tanks, $O_c$ may be computed using the volume of one such wing tank, the actual volume where the two are equal or the smaller where they differ, multiplied by a length factor:

where $l_i$ is the length in meters of the intervening void or segregated ballast tank and $l_c$ is the assumed longitudinal side-damage extent from Regulation 24. The wider that protective gap, the smaller $S_i$, and the less of the adjacent wing tank counts toward the outflow; all other wing tanks caught in the same collision still enter at full volume. The allowance rewards interleaving ballast spaces and voids between cargo wing tanks, which is the layout that segregated-ballast and protective-location rules were pushing tankers toward in the same era.

The bottom-damage outflow Os

Bottom damage models a grounding: the ship’s bottom is torn open over the Regulation 24 vertical penetration $v_s$. The hypothetical outflow from bottom damage is one third of a depth-weighted sum over the wing and center tanks above the damage:

Read the formula exactly. Both the wing-tank term and the center-tank term carry the same coefficient $Z_i$. This is the point the most casual summaries get wrong: bottom damage does not reuse the side-damage width factor $K_i$ on the wing tanks. A grounding tears the bottom shell, so what protects a tank from a grounding is the depth of the double bottom beneath it, not the width of the wing tank outboard of it. Every cargo tank over the assumed bottom damage, wing or center alike, is discounted by the same $Z_i$, and the volumes $W_i$ and $C_i$ are the same wing-tank and center-tank cargo volumes used in the side-damage formula.

The leading factor of one third is the grounding analogue of the side-damage 100 percent loss. A grounded tanker that holds bottom on a rising or falling tide doesn’t empty the breached tank cleanly: hydrostatic balance, the relative density of oil against seawater, and the partial penetration all leave a large share of the cargo aboard. The 1973/78 drafters fixed that retained fraction at two thirds, so one third of the depth-weighted tank volume is assumed to outflow. That single fraction stands in for a messy real-grounding physics the deterministic method declines to model in detail.

The depth coefficient mirrors the side-damage width coefficient, one deck below:

$h_i$ is the minimum depth in meters of the double bottom under the tank in question; where no double bottom is fitted under a tank, $h_i$ is taken as zero, which forces $Z_i = 1$ and spills a full third of that tank. $v_s$ is the assumed vertical extent of bottom damage from Regulation 24, $B/15$ or 6 m, whichever is less. When the double bottom is at least as deep as the assumed vertical penetration, $h_i \geq v_s$, the grounding damage stops in the double-bottom space below the cargo and never breaches the cargo tank, so $Z_i = 0$ and that tank contributes nothing to $O_s$. A shallow or absent double bottom, $h_i$ small, drives $Z_i$ toward 1 and exposes the full tank. This is the deterministic forerunner of the Regulation 19 double-bottom height requirement: a double bottom deep enough to absorb the assumed grounding penetration zeroes out the cargo tank above it, just as a wide enough wing tank does for side damage.

There is a four-tank special case worth stating, because it changes the leading factor. Where bottom damage simultaneously involves four center tanks, Regulation 25 allows the outflow to be computed with a one-quarter factor instead of one third:

The reasoning is that spreading the same grounding across four center tanks raises the chance that the cargo redistributes and is retained, so the assumed escaped fraction drops from one third to one quarter. The same one-quarter factor is the ceiling an approved emergency cargo-transfer system can earn: an installed high-suction arrangement able to move oil from a breached tank to segregated ballast or spare cargo space within two hours, transferring at least half the largest breached tank’s volume, lets the designer calculate $O_s$ on the one-quarter basis. That credit is administrative, granted by the flag Administration, and the transfer pipe suctions must sit at least the bottom-damage height $v_s$ above the keel so the grounding does not sever them.

The credit rules on the double bottom itself are strict, and they constrain how a designer claims a low $Z_i$. Credit is given only for double-bottom tanks that are empty or carrying clean water while cargo sits above them. Where the double bottom does not run the full length and width of the tank above, it is treated as non-existent: the full tank volume enters the $O_s$ sum even though a partial double bottom is fitted, because a partial floor does not reliably stop the assumed penetration. Suction wells may be ignored in setting $h_i$ only if they are shallow, no deeper than half the double-bottom height; a deeper well reduces the effective $h_i$ to the double-bottom height minus the well depth, raising $Z_i$ for that tank. These clauses stop a designer from earning the $Z_i = 0$ credit on paper while leaving a real grounding path open.

The contrast between the two formulas tells the design story. Side damage spills the wing tanks at full value and discounts only the center through $K_i$; bottom damage discounts everything by the one-third retention factor and by the protective depth $Z_i$, but reaches both wings and center because a grounding runs the full breadth of the bottom. A tanker built with both protective wing tanks, high $b_i$, and a deep double bottom, high $h_i$, drives $K_i$ and $Z_i$ toward zero across both formulas and collapses $O_c$ and $O_s$ together. That coupling is the engineering logic the deterministic scheme was built to force.

The Regulation 24 damage assumptions

Regulation 25 can’t be evaluated without the damage extents from Regulation 24, Damage assumptions. The rule fixes the size and shape of the assumed damage as a parallelepiped on the side and on the bottom of the hull, and the calculation places that parallelepiped in the worst position along the ship to maximize the outflow. The extents enter Regulation 25 directly as $t_c$ and $v_s$.

For side damage the assumed extents are a longitudinal extent $l_c$ equal to one third of $L^{2/3}$ or 14.5 meters, whichever is less; a transverse extent $t_c$, measured inboard from the ship’s side at right angles to the centerline at the level of the summer load line, equal to $B/5$ or 11.5 meters, whichever is less; and a vertical extent $v_c$ from the baseline upward without limit. The transverse figure $t_c$ is the one that feeds $K_i$: it is the penetration depth that a wing tank must match or exceed to protect the center tank behind it.

Bottom damage is split into two zones along the hull, because a grounding forward differs from one amidships or aft. For the forward $0.3L$ measured from the forward perpendicular, the longitudinal extent $l_s$ is $L/10$; the transverse extent $t_s$ is $B/6$ or 10 meters, whichever is less, but not less than 5 meters. Anywhere else along the ship the longitudinal extent $l_s$ is $L/10$ or 5 meters, whichever is less, and the transverse extent $t_s$ is a flat 5 meters. The vertical extent $v_s$, measured from the baseline, is the same $B/15$ or 6 meters, whichever is less, over the whole length. That $v_s$ is the depth that feeds $Z_i$: the double bottom must match or exceed it to protect the cargo tank above. The forward zone gets the larger longitudinal and transverse box because groundings concentrate at the forefoot where the ship first touches the bottom; the rest of the hull carries the smaller box.

These extents are why $B$ and $L$ govern the protective dimensions a tanker needs. A wider ship has a larger $t_c$ ceiling and a larger $v_s$ ceiling, so it needs wider wing tanks and a deeper double bottom to hold $K_i$ and $Z_i$ at zero. The 11.5 meter side cap and the 6 meter bottom cap mean that above a certain breadth the protective dimensions stop growing: a tanker beyond about $B = 57.5$ meters is held to the 11.5 meter side penetration rather than $B/5$, and beyond $B = 90$ meters to the 6 meter bottom penetration rather than $B/15$.

The Regulation 26 limit the outflow must satisfy

Regulation 26, Limitations of size and arrangement of cargo tanks, is the ceiling that turns the Regulation 25 outflow into a pass-or-fail test. The governing limit is a single inequality on both outflow figures:

$DW$ is the deadweight of the ship in tonnes. The limit is the greater of 30,000 cubic meters and 400 times the cube root of the deadweight, but it is never allowed above 40,000 cubic meters. For a small tanker the 30,000 floor governs. The cube-root term overtakes the floor at $400\sqrt[3]{DW} = 30{,}000$, that is at $DW = (75)^3 = 421{,}875$ tonnes, so in practice the 30,000 floor binds for essentially the entire conventional tanker fleet and the cube-root and 40,000 ceiling matter only for the largest crude carriers. Both $O_c$ and $O_s$ must clear the same limit; the design fails if either the side or the bottom case exceeds it.

The rule then constrains individual tank volumes so that no single tank dominates the cargo block. The volume of any one wing cargo oil tank must not exceed 75 percent of the hypothetical outflow limit above. The volume of any one center cargo oil tank is capped at 50,000 cubic meters, though in segregated-ballast tankers built with protective wing-tank arrangements a center tank may be larger where the protective location is demonstrated. There are also limits on cargo-tank length tied to the presence and spacing of longitudinal bulkheads. The combined effect is to break a large cargo deadweight into many moderate tanks rather than a few enormous ones, because the hypothetical outflow scales with the size of the breached tank.

Regulation 26 is where the outflow calculation meets the rest of the construction code. The wing-tank width that zeroes $K_i$ is the same dimension that protective-location and segregated-ballast rules want, so a tanker designed to Regulation 18 segregated ballast tends to pass the side-damage case with margin. The double-bottom depth that zeroes $Z_i$ is the same dimension that later became the explicit Regulation 19 double-hull requirement. So Regulations 24, 25, and 26 don’t sit alone: they are the outflow half of a construction package whose other half is the segregated-ballast and protective-location regime, and whose endpoint is the damage stability the tanker must retain after the same assumed casualty.

A worked example

Take a 70,000 tonne deadweight product tanker with a conventional six-across cargo arrangement: two rows of wing tanks port and starboard and a row of center tanks, plus segregated ballast in protective positions. Work one representative midship damage station with these stated cargo volumes and dimensions, and follow the arithmetic by hand.

For the side-damage case, suppose the two wing tanks at the damage station each hold $W_i = 7{,}481$ m³ of cargo oil, and the two adjacent center tanks hold $C_i = 7{,}495$ m³ each. The wing-tank width is $b_i = 3.6$ m and the assumed side penetration from Regulation 24 is $t_c = B/5$. For a 70,000 DWT tanker of beam near 32 m, $t_c = 32/5 = 6.4$ m, so the penetration exceeds the wing-tank width and the center tank is reachable. The width coefficient is $K_i = 1 - b_i/t_c = 1 - 3.6/6.4 = 0.438$. Applying the formula across the breached tanks:

For the bottom-damage case at the same station, the double bottom under the cargo tanks is $h_i = 2.0$ m deep and the assumed vertical penetration is $v_s = B/15 = 32/15 = 2.13$ m, just deeper than the double bottom, so the cargo tanks are reached. The depth coefficient is the same for both wing and center tanks, $Z_i = 1 - h_i/v_s = 1 - 2.0/2.13 = 0.061$, and both terms in the bottom formula carry it:

Now the Regulation 26 limit. For $DW = 70{,}000$ t, the cube-root term is $400 \times \sqrt[3]{70{,}000} = 400 \times 41.2 = 16{,}480$ m³, which is below the 30,000 floor, so the limit is 30,000 m³. Both outflows clear it: $O_c \approx 21{,}528$ m³ and $O_s \approx 609$ m³ are each under 30,000 m³, so the tank arrangement satisfies the hypothetical-outflow ceiling. The wing-tank volume check also passes, since $7{,}481$ m³ is far under $0.75 \times 30{,}000 = 22{,}500$ m³.

Two design lessons fall straight out of the numbers. First, the side case dominates: $O_c$ is more than thirty times $O_s$, because side damage spills the wing tanks at full value while bottom damage carries the one-third retention factor and a near-zero $Z_i$ from a double bottom only just shallower than $v_s$. Side protection is where the outflow margin is won or lost. Second, widening the wing tank pays off fast. Push $b_i$ from 3.6 m to 6.4 m and $K_i$ falls to zero, dropping the center-tank contribution out of $O_c$ entirely and cutting the side outflow to 14,962 m³, the two wing tanks alone. A naval architect tuning a layout to Regulation 25 spends the effort on wing-tank width and on splitting the center tanks, not on the double bottom, which is usually already deep enough to keep $Z_i$ small. A purpose-built hypothetical oil outflow calculator runs every damage station this way and reports the governing worst case.

A contrasting case: wing-tank damage versus center-tank damage

The first example put the worst damage at a station with both wing and center tanks present. A sharper way to see how arrangement drives the result is to fix one ship and ask what changes when the same side damage lands on a tank row laid out two different ways. Keep the 70,000 DWT hull, beam 32 m, so $t_c = 6.4$ m and $v_s = 2.13$ m throughout.

Take Arrangement A, the conventional layout: a narrow wing tank of width $b_i = 3.0$ m holding $W_i = 9{,}000$ m³, with a center tank of $C_i = 12{,}000$ m³ inboard of it. Side damage at this station breaches the wing tank fully and reaches the center tank with $K_i = 1 - 3.0/6.4 = 0.531$:

Now Arrangement B, the same cargo deadweight redistributed: a wide protective wing tank of width $b_i = 6.5$ m holding the same $W_i = 9{,}000$ m³, with the center tank reduced to $C_i = 12{,}000$ m³ behind it. Because $b_i = 6.5$ m now exceeds $t_c = 6.4$ m, $K_i = 0$ and the center tank drops out of the side-damage sum entirely:

The same striking-ship damage, the same volumes of oil aboard, but Arrangement B reports a side outflow 41 percent lower, 9,000 m³ against 15,375 m³, purely because 3.5 extra meters of wing-tank width carried the assumed penetration short of the center tank. That is the entire argument for the protective wing tank in one pair of numbers. The center tank is not safer because it holds less oil; it is safer because the damage box can no longer reach it. A designer who cannot widen the wing tank gets the same effect by filling that wing space with segregated ballast instead of cargo, which sets $W_i = 0$ for the wing while keeping $b_i \geq t_c$ to zero $K_i$, dropping both terms at that station to zero. The deterministic formula rewards moving oil away from the shell, not merely moving it around.

History: the 1973/78 origin and the path to Regulation 23

The deterministic hypothetical outflow scheme is original MARPOL machinery. It entered the 1973 International Convention for the Prevention of Pollution from Ships and survived into the 1978 Protocol that gave the convention its working form, MARPOL 73/78. Through the 1970s, 1980s, and 1990s, the $O_c$ and $O_s$ calculation was the only outflow logic in Annex I: every oil tanker designed in that era sized its cargo tanks to the hypothetical-outflow limit, and the wing-tank-width and double-bottom-depth coefficients shaped tanker cross-sections long before “double hull” was a regulatory term.

The scheme tightened over time without changing its arithmetic. The segregated-ballast and protective-location amendments of the late 1970s and 1980s pushed ballast tanks into the wing and bottom positions that the $K_i$ and $Z_i$ coefficients reward, so a compliant tanker increasingly looked like a proto double-hull. After the Exxon Valdez grounding in 1989, the United States Oil Pollution Act of 1990 and the IMO’s 1992 amendments adding the double-hull Regulation 13F (later renumbered Regulation 19) made the protective wing and double bottom mandatory rather than merely advantageous. The hypothetical-outflow calculation didn’t go away; it sat alongside the new prescriptive double-hull dimensions, with the outflow limit confirming what the prescribed clearances were already delivering.

The deterministic method finally yielded its place for newbuildings in 2004. The Marine Environment Protection Committee adopted resolution MEPC.117(52) on 15 October 2004, revising and renumbering Annex I and introducing the probabilistic accidental oil outflow performance rule, Regulation 23, in force 1 January 2007 and applicable to oil tankers delivered on or after 1 January 2010. The companion resolution MEPC.122(52), adopted the same day, set out the explanatory notes for the probabilistic method. From the 2010 delivery cutoff, newbuildings compute $O_M$, not $O_c$ and $O_s$. But the renumbered Regulations 24, 25, and 26 stayed in the book precisely because the existing fleet was designed to them and remains certified against them, so a Regulation 25 calculation is still a live document for a 2008-built tanker, checked at every renewal survey and at port state control inspection of the loading and stability documentation.

The lineage matters for anyone reading older class and flag approvals. A stability booklet stamped before 2007 cites the hypothetical outflow under the old Regulation 23 number; a booklet from 2007 onward cites Regulation 25; a booklet for a 2010-or-later delivery cites Regulation 23 in its new probabilistic sense. Three different things wearing two numbers across one decade is a genuine source of confusion, and the delivery date plus the formula form, deterministic $O_c$ and $O_s$ versus probabilistic $O_M$, is the only reliable way to tell which regime a given calculation belongs to.

How Oc and Os feed the wider construction code

The hypothetical-outflow figures don’t end at Regulation 26. They are inputs to the tanker’s whole protective-construction logic, and they couple to the rules a surveyor checks alongside them. The wing-tank width $b_i$ that drives $K_i$ is the same dimension that the segregated ballast tank protective-location rule wants ballast to occupy: putting segregated ballast in the wings simultaneously zeroes the wing-tank oil volume in the outflow sum and satisfies the protective-location requirement. One arrangement decision answers two rules.

The segregated-ballast credit is worth tracing in detail, because it is the most direct way an arrangement buys down $O_c$ and $O_s$. Regulation 18 requires tankers above defined sizes to carry their ballast in tanks wholly separate from the cargo and fuel systems, and for the larger crude carriers it adds a protective-location requirement: those segregated ballast tanks must sit in the wing and bottom positions, the spaces a collision or grounding hits first. Regulation 25 reads that arrangement through two doors. A segregated ballast tank holds no oil, so its $W_i$ or $C_i$ is taken as zero in the sums, removing it from the outflow directly. And because it occupies the outboard wing space, its width counts toward the protective $b_i$ that zeros $K_i$ on the cargo tank inboard of it, and its depth counts toward the $h_i$ that zeros $Z_i$ on the cargo tank above it. So a wing ballast tank subtracts twice: once as a zero-volume term, once as a protective barrier. The protective-location math in Regulation 18 specifies how much of the side and bottom shell those ballast spaces must cover, expressed as area fractions $PA_c$ and $PA_s$; a tanker that meets those fractions is by construction holding $b_i$ and $h_i$ at the values that drive the outflow coefficients toward zero. The two rules were written to converge on the same cross-section.

The double-bottom depth $h_i$ behind $Z_i$ runs the same way into the double-hull rule, Regulation 19. Regulation 19 prescribes a minimum double-bottom height as an explicit dimension, $B/15$ or 2.0 m, whichever is less, with a 1.0 m floor, and a minimum wing-tank width set by deadweight, $0.5 + DW/20{,}000$ m or 2.0 m, whichever is less, with a 1.0 m floor. Compare those prescribed clearances against the Regulation 24 penetrations the outflow coefficients use. The double-hull bottom height tracks $v_s = B/15$ closely, and the double-hull wing width is sized to carry a collision short of the cargo. So a double-hull tanker built to Regulation 19 reports a low $O_s$ almost by construction: the prescribed double bottom already approaches or exceeds the $v_s$ penetration over most of the cargo block, holding $Z_i$ near zero, and the prescribed wing void holds $K_i$ near zero for the side case. The deterministic outflow check and the prescriptive double-hull check are two views of the same protective geometry, which is why a Regulation 19 hull rarely fails Regulation 26: the dimensions that satisfy one were chosen to satisfy the other. The difference is that Regulation 19 states the answer as a dimension a surveyor can measure with a tape, while Regulation 25 derives it as an outflow volume; on a double-hull tanker the two are consistent by design rather than by coincidence.

The outflow calculation also sits next to the damage-stability rule, Regulation 28, though they test different things. Regulation 25 asks how much oil escapes a defined damage; Regulation 28 asks whether the tanker stays afloat and upright after the same kind of damage, against survival criteria for damage stability. A tank arrangement has to pass both: a layout that minimizes outflow by subdividing into many small tanks can complicate the damaged-condition floodable-length and residual-stability picture, so the naval architect balances the outflow optimum against the stability optimum. The two calculations share the same damage assumptions from Regulation 24, which is why they’re usually run together in the same stability software pass.

Limitations

The deterministic method has known blind spots, and the IMO’s own move to Regulation 23 names the chief one. It treats subdivision crudely. Two arrangements can report identical $O_c$ and $O_s$ yet spill very differently across the real range of casualties, because the method evaluates one worst-case damage of fixed size rather than the full distribution of damage locations and extents. The MEPC found the deterministic rules “did not properly account for variations in subdivision in general, and longitudinal subdivision in particular,” which is precisely the gap the probabilistic $O_M$ was built to close. For the fleet Regulation 25 governs, the calculation is still binding, but it is a coarser instrument than its replacement.

The fixed-fraction outflow assumptions are conservative simplifications, not physics. Side damage spills 100 percent of the breached wing tank because the drafters had no reliable retained-liquid data, and bottom damage retains exactly two thirds regardless of the actual relative density of the cargo, the trim and heel after grounding, or the tide state. A real grounding outflow depends on hydrostatic balance and on how the tank sits on the ground; the flat one-third factor can over- or under-state the spill for a specific cargo and casualty. The method trades realism for a calculable single number, which is the right trade for a design ceiling but the wrong basis for predicting a real incident.

The damage extents are themselves bounded and dated. The 14.5 meter and 11.5 meter side caps and the 6 meter bottom cap mean the assumed damage stops growing above a certain hull size, so a very large crude carrier is checked against the same absolute penetration as a much smaller ship even though a real striking vessel scales with traffic. The extents derive from casualty experience of the 1960s and 1970s and were never re-derived for the deterministic rule; the probabilistic method re-based its distributions on a 1980 to 1990 casualty set instead. So the Regulation 25 extents reflect an older view of how tankers are damaged.

The calculation is also silent on everything outside the cargo block. It addresses cargo oil outflow only, not bunker fuel-oil spills, not slop-tank residues, and not the consequences of cargo released into the engine room or pump room. Bunker-tank protection comes from a separate later rule, Regulation 12A on fuel oil tank protection, and pump-room bottom protection from its own regulation; a tanker can have a low $O_c$ and $O_s$ and still carry poorly protected bunkers. Reading the hypothetical-outflow figure as a complete measure of a tanker’s pollution risk overstates what the calculation covers.

Finally, Regulation 25 is a design and survey check, not an operational one. It assumes the cargo tanks are loaded to the volumes in the approved booklet and that the as-built dimensions match the drawings. A tanker that has had tanks modified, a double bottom corroded thin, or that loads outside its approved conditions can carry an outflow figure that no longer reflects the hull. The figure is only as good as the verification behind it, which is why class and port state control confirm the loading and stability documentation against the actual ship rather than trusting the calculated number alone.

See also

• MARPOL Annex I: the full oil-pollution annex within which Chapter 4 sets the tanker construction rules.
• MARPOL Convention: the parent 1973/78 convention and its protocols.
• MARPOL Annex I Regulation 24: damage assumptions: the parallelepiped damage box whose extents $t_c$ and $v_s$ feed this calculation.
• MARPOL Annex I Regulation 26: cargo tank size limits: the ceiling the $O_c$ and $O_s$ figures must satisfy.
• MARPOL Annex I Regulation 23: accidental oil outflow: the probabilistic mean-outflow rule that replaced this deterministic scheme for tankers delivered from 2010.
• MARPOL Annex I Regulation 19: double hull: the prescriptive wing-tank and double-bottom clearances that this calculation’s coefficients reward.
• MARPOL Annex I Regulation 18: segregated ballast tanks: the protective-location regime that shares the wing and bottom dimensions.
• MARPOL Annex I Regulation 28: damage stability: the survival check run against the same Regulation 24 damage assumptions.
• Damage stability: the general naval-architecture treatment of the survival-after-damage problem.
• Port state control: the inspection regime that verifies the loading and stability documentation carrying the outflow figures.