Parametric Rolling: SGISC Level 1 and Level 2 Criteria

Parametric rolling is resonant roll growth from cyclic GZ variation in waves, screened by the Level 1 and Level 2 vulnerability criteria of IMO MSC.1/Circ.1627.

Updated 1 September 2026

Key facts

Failure mode: Parametric rolling, one of five stability failure modes addressed by the Second Generation Intact Stability Criteria
Governing guidance: IMO MSC.1/Circ.1627, Interim Guidelines on the Second Generation Intact Stability Criteria, dated 10 December 2020
Approved: Maritime Safety Committee, 102nd session, 4 to 11 November 2020
Legal status: Recommendatory interim guidelines. Not mandatory, and they create no carriage or survey requirement.
Mandatory instrument above it: 2008 Intact Stability Code, IMO Resolution MSC.267(85), in force 1 July 2010
Assessment tiers: Level 1 screening, Level 2 checks C1 and C2, direct stability assessment, and operational measures
Level 1 standard value: R_PR, between 0.17 with no bilge keels and 1.87 for a sharp bilge or a full midship section at the area cap
Level 1 design wave: Wavelength equal to the ship length, steepness 0.0167, so a wave height of 0.0167 L
Level 2 standards: C1 not exceeding 0.06, or C2 not exceeding 0.025. Passing either check clears the ship.
Level 2 failure angle: A roll angle exceeding 25 degrees in the C2 simulation
Wave data: 16 wave cases weighted from the North Atlantic scatter of IACS Recommendation No. 34
Direct assessment safety level: Average stability failure rate not exceeding 2.6 x 10 to the minus 3 per ship per year
Operational measures cap: A loading condition is unacceptable if more than 0.2 of operational time would have to be avoided
Ships most exposed: Container ships, car carriers, ro-ro vessels and fine-form fishing vessels with pronounced bow flare and a wide transom stern

Parametric rolling is a resonant roll motion in which a ship’s righting arm varies cyclically as a longitudinal wave passes along the hull, feeding energy into roll until the amplitude grows to dangerous angles in head or following seas without any direct transverse wave force. It is one of five dynamic stability failure modes assessed under the IMO Interim Guidelines on the Second Generation Intact Stability Criteria, MSC.1/Circ.1627, dated 10 December 2020 and approved by the Maritime Safety Committee at its 102nd session. Those guidelines are recommendatory. The mandatory intact stability instrument remains the 2008 Intact Stability Code, Resolution MSC.267(85), whose criteria are evaluated on a calm-water righting lever curve and therefore cannot see the mechanism at all.

Mechanism: righting arm variation in a longitudinal wave

Parametric rolling starts because the transverse second moment of area of the waterplane changes as a wave moves along the hull, and that change transfers directly into metacentric height.

The waterplane inertia about the centreline is

$$I_T = \int_L \frac{1}{12}\,b(x)^3\,\mathrm{d}x$$

with $b(x)$ the local waterline beam in metres. It depends on the cube of the local beam, so a hull with fine underwater sections at the ends and pronounced flare above the waterline changes $I_T$ sharply for a small change in local draught. Since $BM = I_T/\nabla$ and $GM = KB + BM - KG$, a passing wave modulates the metacentric height.

The direction is fixed and is frequently reported backwards. A wave trough amidships gives the maximum GM, because the flared bow and stern are deeply immersed while the wall-sided midship body sits less deep, so the mean instantaneous waterplane is wider than in calm water. A wave crest amidships gives the minimum GM, because the waterplane at the immersed bow and stern is narrower than in calm water.

Writing the metacentric height as a mean plus a harmonic variation at the encounter frequency $\omega_e$,

$$GM(t) = GM_m + \delta GM \cos(\omega_e t)$$

and linearizing the righting lever about the upright position gives the undamped Mathieu equation

$$\ddot{\phi} + \omega_0^{2}\left[1 + \frac{\delta GM}{GM_m}\cos(\omega_e t)\right]\phi = 0$$

where $\phi$ is the roll angle in radians and $\omega_0$ is the natural roll frequency in radians per second. Instability appears in tongues that open from $\omega_0/\omega_e = n/2$. The first and dominant tongue is principal parametric resonance:

$$\omega_e = 2\omega_0 \qquad \Longleftrightarrow \qquad T_e = \tfrac{1}{2}T_\phi$$

The encounter period at principal resonance is half the natural roll period. The ship passes a wave crest amidships twice for every roll cycle. Sources that state the natural roll period is about twice the encounter period are describing the same relation inverted.

Roll damping decides whether the resonance can start. Adding a linear damping term lifts each instability tongue clear of the axis, so parametric rolling requires the stability variation to outrun the damping:

$$\frac{\delta GM}{GM_m} > \frac{4\alpha}{\omega_0}$$

with $\alpha$ the linear roll damping coefficient. That inequality is the physical origin of the Level 1 standard value, and it is why an area of steel welded to the bilge appears in a stability criterion.

Amplitude is bounded by nonlinearity rather than by damping. As heel increases the righting lever departs from $GM\phi$, the effective natural frequency shifts, and the ship detunes itself out of the resonance band. That is why a developed parametric roll settles at a large steady amplitude instead of growing without limit.

Hull forms and loading conditions at risk

The exposed hull has fine underwater sections forward and aft, pronounced bow flare, and a wide flat transom stern, because that combination maximizes the swing in waterplane area as a wave passes.

Container ships are the classic case, and large and ultra-large designs most of all. Car carriers, ro-ro vessels, some cruise ships and fine-form fishing vessels are also exposed. Full-form tankers and bulk carriers, with high block coefficients and near wall-sided ends, show very little of the effect.

The loading condition framing has shifted since the phenomenon entered general awareness. The classical case was a head-sea event at moderate metacentric height. The evidence accumulated since 2020 points at least as strongly the other way, toward low metacentric height, a long natural roll period, and following seas. MARIN’s TopTier work advises particular alertness where the roll period exceeds 20 seconds on ships over 250 metres, a condition produced by low GM rather than high.

Free surface corrections apply to the parametric rolling assessment, following chapter 3 of part B of the 2008 IS Code. That is a deliberate contrast with the excessive acceleration failure mode, where MSC.1/Circ.1627 does not apply them.

The SGISC framework and where parametric roll sits in it

The Second Generation Intact Stability Criteria are ship-specific assessments for dynamic stability failure modes, issued as MSC.1/Circ.1627 on 10 December 2020 and covering five modes: parametric rolling, pure loss of stability, surf-riding and broaching, the dead ship condition, and excessive acceleration.

The legal hook is section 1.2 of part A of the 2008 IS Code, which permits an Administration to apply criteria demonstrating that the safety of a particular ship or group of ships is sufficient, having regard to the phenomena the section describes. Section 1.2.1 names righting lever variation as the cause of parametric roll, pure loss of stability, or combinations of the two.

Four routes are treated as equivalent in the regulatory sense: clear Level 1; clear Level 2; pass a direct stability assessment; or accept operational limitations or carry operational guidance. Levels may be skipped, so a designer may go straight to Level 2 or straight to direct assessment, and operational measures may be substituted for the vulnerability criteria altogether.

The guidelines state their own limits plainly. They are not intended to be used in lieu of the mandatory criteria of the 2008 IS Code, and although they were developed envisioning future incorporation into that Code, they record that they require testing before being used as mandatory criteria.

The development record singled out parametric rolling as one of the two modes considered ready. The guidelines note that the dead ship criteria sometimes give non-consistent results between levels, that the excessive acceleration criteria may require further refinement, and that pure loss gives very conservative results for ships with low freeboard, while parametric rolling and surf-riding and broaching “have sufficient scientific background and feasible methods for regulatory use.”

Level 1 vulnerability criterion

Level 1 is a hydrostatic screening test with no speed term and no hydrodynamics. A ship is not vulnerable if both of the following hold:

$$\frac{\delta GM_1}{GM} \le R_{PR} \qquad \text{and} \qquad \frac{\nabla_D - \nabla}{A_W (D - d)} \ge 1.0$$

The second condition is a flare test. It equals exactly 1.0 for a wall-sided hull, exceeds 1.0 where there is flare above the waterline, and falls below 1.0 for tumblehome.

The metacentric height variation amplitude is the difference in transverse waterplane inertia between two parallel waterplanes:

$$\delta GM_1 = \frac{I_{TH} - I_{TL}}{2\nabla}$$

The two draughts come from a standard wave of length equal to the ship length and steepness $S_W = 0.0167$, so a wave height of $0.0167L$:

$$\Delta d_H = \min\left(D - d,\ \tfrac{1}{2}L S_W\right), \qquad \Delta d_L = \min\left(d - 0.25\,d_{full},\ \tfrac{1}{2}L S_W\right)$$

with $d_H = d + \Delta d_H$ and $d_L = d - \Delta d_L$, and $d - 0.25 d_{full}$ not taken below zero. The increments are asymmetric by design: the upward excursion is capped by freeboard and the downward excursion by draught, so only a ship with generous freeboard sees the full half wave height in both directions.

The standard value R_PR

$R_{PR}$ is not a table. It is one constant and three piecewise-linear branches:

$$R_{PR} = \begin{cases} 1.87 & \text{sharp bilge} \\[4pt] 0.17 + 0.425\,\dfrac{100 A_k}{LB} & C_{m,full} > 0.96 \\[6pt] 0.17 + \left(10.625\,C_{m,full} - 9.775\right)\dfrac{100 A_k}{LB} & 0.94 \le C_{m,full} \le 0.96 \\[6pt] 0.17 + 0.2125\,\dfrac{100 A_k}{LB} & C_{m,full} < 0.94 \end{cases}$$

with $100 A_k/(LB)$ capped at 4 in every branch. $A_k$ is the total overall area of the bilge keels and no other appendage, and $C_{m,full}$ is the midship section coefficient of the fully loaded departure condition in calm water.

Three consequences follow from the algebra. A ship with no bilge keels gets $R_{PR} = 0.17$ whatever its midship coefficient. The interpolation branch joins the outer branches exactly, returning 0.2125 at $C_{m,full} = 0.94$ and 0.425 at 0.96, so the function is continuous. And the cap gives a maximum of 1.87 for a full midship section, identical to the sharp-bilge value, against 1.02 for a midship coefficient below 0.94.

$R_{PR}$ is standing in for roll damping. That makes the criterion unusually sensitive to a single drawing-office number, and an error in the bilge keel schedule, such as omitting one side or counting a docking keel, moves the verdict directly.

Level 2 vulnerability criterion

Level 2 carries two independent checks and a disjunctive pass test. A ship is not vulnerable if

$$C_1 \le R_{PR1} = 0.06 \qquad \textbf{or} \qquad C_2 \le R_{PR2} = 0.025$$

Passing either check clears the ship. This inverts the logic of the pure loss of stability Level 2 criterion, where the larger of two indices must satisfy a single standard, so both checks must pass. The parametric rolling section contains no symbol $R_{PR0}$.

C1, the susceptibility index

$C_1$ needs hydrostatics in waves and nothing more:

$$C_1 = \sum_{i=1}^{16} W_i C_i$$

$C_i$ is zero if either sub-check is satisfied in wave case $i$, and one if neither is. The first sub-check requires the metacentric height in the wave to stay positive and the variation ratio to fall below $R_{PR}$:

$$GM(H_i, \lambda_i) > 0 \qquad \text{and} \qquad \frac{\delta GM(H_i, \lambda_i)}{GM(H_i, \lambda_i)} < R_{PR}$$

The denominator here is the average GM over the wave series, not the calm-water GM that Level 1 uses. The standard value is reused unchanged from Level 1.

Ten crest positions are evaluated in each wave case: amidships, then 0.1, 0.2, 0.3, 0.4 and 0.5 wavelengths forward, and 0.1, 0.2, 0.3 and 0.4 wavelengths aft, with the ship balanced in sinkage and trim on each. With 16 wave cases that is 160 equilibrium solutions per loading condition.

The second sub-check asks whether the ship can physically reach resonance, and is satisfied when the resonant speed exceeds the service speed:

$$V_{PRi} = \left|\frac{2\lambda_i}{T_r}\sqrt{\frac{GM(H_i,\lambda_i)}{GM}} - \sqrt{\frac{g\lambda_i}{2\pi}}\right|$$

The second term is the deep-water wave celerity and the first is the speed at which the encounter period equals half the roll period, corrected for the change of metacentric height in the wave.

The 16 wave cases

The weights derive from the North Atlantic scatter of IACS Recommendation No. 34 and sum to exactly 1.0.

Case	Weight	Wavelength (m)	Wave height (m)
1	0.000013	22.574	0.350
2	0.001654	37.316	0.495
3	0.020912	55.743	0.857
4	0.092799	77.857	1.295
5	0.199218	103.655	1.732
6	0.248788	133.139	2.205
7	0.208699	166.309	2.697
8	0.128984	203.164	3.176
9	0.062446	243.705	3.625
10	0.024790	287.931	4.040
11	0.008367	335.843	4.421
12	0.002473	387.440	4.769
13	0.000658	442.723	5.097
14	0.000158	501.691	5.370
15	0.000034	564.345	5.621
16	0.000007	630.684	5.950

The wavelengths correspond to a uniform wave-period grid running from 3.802 seconds to 20.098 seconds in constant steps of 1.0864 seconds.

C2, the severity index

$C_2$ requires a nonlinear time-domain roll simulation:

$$C_2 = \frac{1}{25}\left[\sum_{i=1}^{12} C_2(Fn_i,\beta_h)

\tfrac{1}{2}\left{C_2(0,\beta_h) + C_2(0,\beta_f)\right}
\sum_{i=1}^{12} C_2(Fn_i,\beta_f)\right]$$

The 25 conditions are 12 head-sea speeds, 12 following-sea speeds and one zero-speed case taken as the mean of the head and following evaluations, which are physically the same condition. Speeds are the service speed scaled by twelve factors running from 1.0 down to 0.131.

Each term counts sea states in which the maximum roll angle exceeds 25 degrees. Roll amplitude is evaluated with the ship balanced on waves of length equal to the ship length at eleven heights from zero to a tenth of the ship length, by time-domain simulation with the righting lever computed in waves, and the result is interpolated onto the sea-state cells of the scatter table.

Two properties of C2 matter more than the arithmetic. It is evaluated in head and following seas only, with no oblique-sea component. And MSC.1/Circ.1627 specifies no simulation method, no minimum degrees of freedom and no damping model; the damping model reaches the calculation through Appendix 3 of the Explanatory Notes, MSC.1/Circ.1652.

Only principal parametric resonance is addressed. The guidelines state that other types of parametric rolling may occur with much smaller probability and are not covered.

Direct stability assessment

Direct stability assessment replaces the simplified formulae with numerical simulation or model testing of the specific hull, and it sets a quantitative safety level: an average stability failure rate not exceeding 2.6 x 10 to the minus 3 per ship per year.

A stability failure is defined as roll exceeding the lesser of 40 degrees, the calm-water angle of vanishing stability, or the calm-water angle of submergence of unprotected openings; or a lateral acceleration exceeding 9.81 metres per second squared at the highest location along the ship where passengers or crew may be present. For parametric rolling the simulation must include at least heave, roll and pitch.

Note the discontinuity with Level 2, which counts a failure at 25 degrees of roll. The two tiers do not measure the same event.

Three assessment routes are treated as equivalent. The full probabilistic route requires a mean long-term failure rate not exceeding 2.6 x 10 to the minus 8 per second, with wave directions and speeds uniformly distributed. The probabilistic design-situation route works to the upper boundary of the 95 per cent confidence interval against a threshold of one failure every two hours in design sea states, and for parametric rolling it fixes the design situation at head and following waves at zero forward speed. The deterministic design-situation route requires the greatest mean three-hour maximum roll amplitude to stay below half the failure threshold, from at least 15 hours of full-scale-equivalent simulation per situation.

The hard part is rarity. A simulation of realistic length usually contains no failures at all, so the guidelines require statistical extrapolation and make its validation part of the assessment. Extrapolation over wave height uses a model in which the logarithm of the mean time to failure is linear in the reciprocal of the square of significant wave height, needing at least three directly counted rates spanning at least 2 metres of significant wave height, each taken as the upper bound of its 95 per cent confidence interval.

Where the three tiers disagree

The tiers are not a monotone ladder of strictness, and the disagreement runs in both directions.

Level 1 is conservative by construction. ClassNK puts it plainly in its own guidance: Level 1 “may impose significant restrictions on ship operation conditions, as this criterion is based on a large safety margin corresponding to its simplicity.” A Level 1 failure means the cheap filter could not clear the ship, not that the ship is unsafe.

C1 is reproducible and C2 is not. Independent implementations of the criteria by ABS and by Creative Systems on the same benchmark hulls returned C1 values of 0.436 and 0.436 for one container ship and 0.436 and 0.440 for another, agreeing to three decimal places. The C2 values for the same hulls were 0.062 against 0.12, and 0.074 against 0.090. The difference is the simulation: one implementation used a three-dimensional nonlinear panel code, the other a purpose-built three-degree-of-freedom body-exact strip theory solver, and both are compliant readings of a clause that specifies neither.

A higher tier has failed a ship the lower tier cleared. Denmark and the World Shipping Council reported to SDC 10 in November 2023 that for the container ship Maersk Essen in its accident loading condition, a one-degree-of-freedom solver returned a pass against Level 2 C2 while a six-degree-of-freedom nonlinear panel code returned a failure. The ship had rolled beyond 30 degrees and lost 689 containers on 16 January 2021, with parametric resonance identified as the most likely cause. The submission observed that a Level 3 calculation should not fail a ship that Level 2 shows compliant, particularly where an incident actually occurred.

Three structural mismatches sit behind that outcome, and each is checkable against the criteria text:

Threshold. Level 2 counts a failure at 25 degrees. The ship’s own loading program permitted 19.18 degrees before lashing loads exceeded their safe working load, so the regulatory failure angle sat above the commercial one.
Environment. The wave cases and the scatter weights come from the North Atlantic. The casualty occurred in the Pacific in swells of 6 to 8 metres at periods of 15 to 18 seconds, a combination that carries little weight in North Atlantic data.
Method. With no specified simulation, the choice of solver decides the verdict.

The criteria can also clear a vulnerable ship. Finland told SDC 12 in January 2026 that new or existing ships, even where they pass the vulnerability check in the interim guidelines, may still be vulnerable to parametric rolling in unfavourable conditions. That is a Member State asserting false negatives on the record.

SDC 10 concluded that revising the interim guidelines was premature and that more data and practical experience in their application were required.

Worked example: a benchmark container ship at Level 1 and Level 2

The KCS benchmark container ship has a length between perpendiculars of 230.0 metres, breadth 32.2 metres, depth 19.0 metres, design draught 10.8 metres, displacement volume 52,030 cubic metres, midship section coefficient 0.9849 and metacentric height 1.327 metres.

The design wave. $h = 0.0167 \times 230.0 = 3.841$ metres, so half the wave height is 1.9205 metres. The freeboard cap is $19.0 - 10.8 = 8.2$ metres and the lower cap is $10.8 - 2.7 = 8.1$ metres, so neither binds and both draught increments take the wave value. The evaluation draughts are 12.7205 metres and 8.8795 metres.

The stability variation. The published variation amplitude is 0.991 metres, which implies a waterplane inertia difference of $2 \times 52{,}030 \times 0.991 = 1.03 \times 10^{5}$ metres to the fourth across that draught band. Against a calm-water metacentric height of 1.327 metres:

$$\frac{\delta GM_1}{GM} = \frac{0.991}{1.327} = 0.747$$

The standard value. With $C_{m,full} = 0.9849$ the first branch applies. The published $R_{PR}$ of 0.354 corresponds to a bilge keel area ratio of $(0.354 - 0.17)/0.425 = 0.433$, so a total bilge keel area of about 32 square metres.

The Level 1 verdict. $0.747 > 0.354$, so the ship fails the first condition by a factor of 2.1. The flare ratio is 1.004 and clears its threshold, but both conditions must hold, so the ship proceeds to Level 2.

The sensitivity. To clear Level 1 the ship would need $R_{PR} = 0.747$, which requires an area ratio of $(0.747 - 0.17)/0.425 = 1.357$ and therefore a bilge keel area of about 100.5 square metres, roughly 3.1 times the actual area. The ratio sits inside the cap of 4, so the criterion is satisfiable, but nothing else in it can move: the hull, the loading condition and the wave are all fixed.

Level 2 C1. The published index is 0.436, identical in both independent implementations. Because the 16 weights sum to exactly 1.0, that value identifies the failing set: summing the weights from case 7 upward gives 0.436616, which rounds to the published figure. The ship is vulnerable in every wave case from 7 to 16 and clear in cases 1 to 6. Case 7 has a wavelength of 166.309 metres, so the boundary sits at $166.309/230.0 = 0.72$ of the ship length: every wave longer than about 0.72 L scores a failure. This reconstruction is an arithmetic inference from the published index and the published weights.

$C_1 = 0.436$ against a standard of 0.06 is a failure by a factor of 7.3.

Level 2 C2. The published values are 0.062 and 0.12 in the two implementations. Both exceed 0.025, so both fail, and the ship fails Level 2 on both checks in both codes. The verdicts agree while the numbers differ by a factor of 1.94, which is the practical meaning of a method-dependent index.

Operational limitations and operational guidance

Where a ship cannot demonstrate compliance by calculation, MSC.1/Circ.1627 offers two operational routes, and they are not interchangeable.

Operational limitations restrict the ship. They may permit operation only in specified areas or routes and, where appropriate, in a specified season, in which case the environment is described by the scatter table for that area and season. Or they may permit operation only up to a maximum significant wave height, in which case the assessment is rerun on the scatter table truncated at that height.

Operational guidance informs the decision. It defines the combinations of ship speed and heading relative to the mean wave direction that are not recommended in each sea state, and it must be provided as easily accessible and understandable information in graphical form, commonly a polar diagram. Automatic alert systems are permitted where the sailing condition approaches an unacceptable region.

The information burden differs sharply. An area and season limitation needs no weather data in service. A wave height limitation needs a forecast. Operational guidance needs a detailed forecast wave spectrum, wind characteristics, and an onboard means of showing the master which speed and heading combinations to avoid.

Two provisions stop this route becoming a way to certify an unsuitable hull. The equivalence standard requires operational measures to provide at least the same level of safety as the vulnerability criteria or the direct assessment. And the practicality cap makes a loading condition unacceptable if the total duration of all situations that should be avoided exceeds 0.2 of total operational time, computed on the full scatter table with uniformly distributed headings and speeds.

The guidelines also warn that guidance may declare conditions safe for roll that are unattainable or dangerous for other reasons, naming parametric rolling in bow waves as the example: roll may fall with increasing speed, but the speed may be unreachable or may cause excessive vertical motions.

Parametric roll against synchronous roll and pure loss of stability

These three are routinely confused, and the confusion has consequences on the bridge.

	Parametric rolling	Synchronous rolling	Pure loss of stability
Driving mechanism	Stability varies as a wave passes	Direct transverse wave force	Stability falls on a single crest
Sea direction	Head, bow, following, quartering, and beam	Beam	Following and quartering
Timing	Encounter period about half the roll period, or about equal to it	Encounter period equal to the roll period	Ship held on one crest
Development	Builds over many encounters	Builds over many encounters	Single event
SGISC status	Failure mode with Level 1, Level 2 and direct assessment	Not a separate SGISC failure mode	Failure mode with its own criteria

Synchronous rolling is what a beam sea does. Parametric rolling is what a longitudinal sea can do while the ship appears to be on the safest heading, which is precisely what makes it dangerous. Pure loss of stability shares the physical cause of parametric rolling, since both come from stability varying as a wave passes, but it fails on one crest rather than accumulating.

MSC.1/Circ.1228 covers the operational side of all three. For parametric rolling it advises selecting course and speed so that the encounter period is not close to the roll period, and not close to half the roll period, in following, quartering, head, bow or beam seas. That circular describes two cases: an encounter ratio near 1 to 1, which produces asymmetric rolling that is larger to one side, and an encounter ratio near 1 to 0.5, which produces symmetric rolling with large amplitudes and can occur in head and bow seas.

Class notations and industry practice

Every major society now offers a notation, and they do not implement the same thing.

Society	Document	Edition	Notation
ABS	Guide for the Assessment of Parametric Roll Resonance in the Design of Container Carriers	August 2024	PARR-C1, PARR-C2
Bureau Veritas	Rule Note NR 667, Parametric Roll Assessment	December 2024	PaRoll1, PaRoll2
DNV	DNV rules for classification of ships	Notation from July 2022	ARCS with PSA or ARD
ClassNK	Guidelines on Preventive Measures against Parametric Rolling	February 2023	PRPM
Lloyd’s Register	Rules and Regulations, Part 3, with the ShipRight roll design assessment procedure	July 2025	RDA

ClassNK binds its notation directly to the IMO criteria, with a functional requirement on complying with the second generation criteria and an appendix outlining the Level 1, Level 2 and direct assessment criteria. The ABS Guide, by contrast, runs a parallel and older track with its own susceptibility and severity criteria and does not reference the IMO guidelines. Lloyd’s Register’s roll design assessment, introduced in 2025, is deliberately broader and addresses resonant parametric or synchronous rolling, a tacit acknowledgment that the two present the same way on a container stack.

IACS UR C6 on lashing software and UR C7 on the approval and certification of container securing systems apply to container ships contracted on or after 1 July 2025.

Onboard implementation and the bridge

Very little of this reaches the ship. The Level 2 checks and any direct assessment are design-office calculations needing a hull model and hours of computation, not something a loading computer runs before departure. What reaches the bridge is the output: an operational limitation in the approved documentation, or a guidance product presented as tables or a polar diagram of safe speed and heading against sea state.

The stability booklet does not model the mechanism. The joint investigation into the MSC Zoe container loss stated the design position directly: the crew is expected to prevent extreme accelerations from parametric oscillation, dynamic loss of stability, resonant oscillation and impulsive loads, and those mechanisms are therefore not included in the design principles. The design assumes the master avoids the phenomenon, and the master is given no instrument with which to do it.

The natural roll period is the input where practice diverges most. The 2008 IS Code gives $T_r = 2CB/\sqrt{GM}$ with $C = 0.373 + 0.023(B/d) - 0.043(L_{WL}/100)$, and MSC.1/Circ.1627 reproduces it. ClassNK uses $0.8B/\sqrt{GM}$. MARIN’s TopTier guidance uses $0.86B/\sqrt{GM}$ and then instructs that the rolling period should be measured after departure, because rules of thumb based on metacentric height are not always accurate. On a large container ship at low metacentric height the spread between these formulations is wide enough to move the ship in or out of the resonance band.

Current status

MSC.1/Circ.1627 remains recommendatory. The guidelines record that they were developed envisioning future incorporation into the 2008 IS Code but require testing first, and the Committee agreed to keep them under review in the light of experience gained.

SDC 10, meeting from 22 to 26 January 2024, considered the submission from Denmark and the World Shipping Council on the Maersk Essen calculations and concluded that it was premature to revise the interim guidelines and that more data and practical experience in their application were required. Finland submitted an information paper to SDC 12 in January 2026. As of September 2026 there is no approved IMO output to make the criteria mandatory, and no revision of MSC.1/Circ.1228 has been agreed, so the operational guidance a master actually holds is a circular of 11 January 2007 whose scope paragraph still refers to the superseded Resolution A.749(18).

Limitations

The criteria do not model several things a practitioner should not assume are covered.

Oblique seas are outside the C2 index, which is evaluated in head and following seas only. Real parametric roll casualties have occurred in quartering seas.

The wave environment is North Atlantic. The 16 wave cases and the sea-state weights derive from IACS Recommendation No. 34. For a ship trading a Pacific liner service the scatter data are not representative, and this was one of the mismatches identified in the Maersk Essen submission.

The simulation method is unspecified, so the C2 index is method-dependent. Published independent implementations differ by roughly a factor of two on the same hull. A C2 value quoted without its solver, degrees of freedom, damping model and duration is not a result.

Only principal parametric resonance is addressed. Other resonance regions are explicitly out of scope.

The failure thresholds differ between tiers. Level 2 counts a failure at 25 degrees of roll, while direct assessment uses the lesser of 40 degrees, the angle of vanishing stability or the downflooding angle. A lashing system may be designed to a lower angle than either, in which case the criteria are not protecting the cargo securing arrangement.

Interaction between failure modes is not required to be assessed. MSC.1/Circ.1627 does not require parametric rolling and pure loss of stability to be evaluated together, although both arise from the same physical cause and at least one official casualty investigation has concluded that pure loss of stability on a wave crest may have contributed to the onset of parametric roll resonance.

Green water, cargo shift, wind and directional spread are not modelled in the vulnerability criteria.

The Explanatory Notes carry material this article does not cover. MSC.1/Circ.1652 Appendix 3 holds the roll damping model used in the C2 simulation, and its Part B chapter 2 may address which loading conditions must be assessed.

Frequently Asked Questions (FAQs)

What is parametric rolling?

Parametric rolling is a resonant roll motion caused by cyclic variation in a ship’s righting arm as a wave passes along the hull. With a wave crest amidships the waterplane narrows and stability falls; with a trough amidships the waterplane widens and stability rises. When that variation repeats in step with the roll motion, energy is pumped into roll and the amplitude grows, in head or following seas, with no direct transverse wave force acting on the ship.

Why is it called parametric?

Because the instability comes from a parameter of the system oscillating in time rather than from an external force driving the motion. The parameter is transverse stability, which changes as the wave profile moves along the hull. The governing equation is a damped Mathieu equation, in which a periodic coefficient rather than a forcing term produces the resonance.

Is the encounter period half the natural roll period, or twice it?

At principal parametric resonance the encounter period is half the natural roll period. The metacentric height varies at the encounter frequency and roll responds at half that frequency, so resonance requires the encounter frequency to be twice the natural roll frequency. The ship meets a wave crest amidships twice per roll cycle. Sources that state the natural roll period is approximately twice the encounter period are saying the same thing the other way round.

Does GM rise or fall when a wave crest is amidships?

It falls. A crest amidships narrows the waterplane at the immersed bow and stern of a fine-form hull, cutting the transverse moment of inertia and reducing GM. A trough amidships deeply immerses the flared bow and stern while the wall-sided midship sits less deep, widening the mean waterplane and raising GM above its calm-water value.

Which ships are most exposed to parametric rolling?

Ships with pronounced bow flare, a wide flat transom stern and fine underwater sections forward and aft, because those forms change waterplane area most as a wave passes. Container ships, particularly large and ultra-large designs, are the classic case. Car carriers, ro-ro vessels, some cruise ships and fine-form fishing vessels are also exposed. Full-form tankers and bulk carriers are far less so.

What are the Second Generation Intact Stability Criteria?

They are ship-specific assessments for dynamic stability failure modes that the calm-water criteria of the 2008 Intact Stability Code do not cover. IMO issued them as MSC.1/Circ.1627, the Interim Guidelines on the Second Generation Intact Stability Criteria, dated 10 December 2020. They address five failure modes: parametric rolling, pure loss of stability, surf-riding and broaching, the dead ship condition, and excessive acceleration.

When was MSC.1/Circ.1627 issued?

It is dated 10 December 2020 and was approved by the IMO Maritime Safety Committee at its 102nd session, held from 4 to 11 November 2020.

Are the second generation intact stability criteria mandatory?

No. MSC.1/Circ.1627 is a circular carrying interim guidelines, so it is recommendatory. It creates no carriage requirement, no survey item and no certificate endorsement. The mandatory intact stability instrument remains the 2008 IS Code, Resolution MSC.267(85), made compulsory through SOLAS Chapter II-1 and the 1988 Load Line Protocol. Member States are invited to apply the interim guidelines as complementary measures and to report their experience back to IMO.

Will the criteria become mandatory?

The guidelines say they were developed envisioning future incorporation into the 2008 IS Code but require testing first. SDC 10, meeting from 22 to 26 January 2024, considered a submission from Denmark and the World Shipping Council and concluded that revision was premature and that more data and practical experience were needed. As of September 2026 there is no approved IMO output to make the criteria mandatory.

What is the difference between the 2008 IS Code and the second generation criteria?

The 2008 IS Code judges a loading condition against a calm-water GZ curve at fixed heel angles, plus a severe wind and rolling weather criterion. It assumes stability stays constant while the ship rolls. The second generation criteria assess what happens when stability itself changes in waves, which is the mechanism behind parametric roll, pure loss of stability and broaching. A ship can pass every 2008 IS Code criterion and still be vulnerable to parametric rolling.

What does the Level 1 parametric roll criterion calculate?

It compares the amplitude of the metacentric height variation in a standard wave against a standard value. The ship is not vulnerable if the ratio of the GM variation amplitude to the calm-water GM is at or below R_PR, and if a second condition on hull flare is also met. The GM variation is computed from the difference in the transverse waterplane moment of inertia at two parallel waterplanes, divided by twice the displacement volume.

What wave does Level 1 use?

A wave of length equal to the ship length with a steepness of 0.0167, so a wave height of 0.0167 times the ship length. For a 230 metre ship that is about 3.84 metres. The two evaluation draughts sit half that wave height above and below the loading draught, capped by the freeboard above and by a quarter of the fully loaded draught below.

What is R_PR and how is it determined?

R_PR is the Level 1 standard value. It is 1.87 for a ship with a sharp bilge. Otherwise it is 0.17 plus a coefficient times the bilge keel area ratio, where the coefficient is 0.425 if the midship section coefficient exceeds 0.96, 0.2125 if it is below 0.94, and a linear interpolation between them in the band from 0.94 to 0.96. The bilge keel area ratio is 100 times the total bilge keel area divided by length times breadth, and it is capped at 4.

Why does bilge keel area appear in a stability criterion?

Because R_PR is a proxy for roll damping. Parametric roll cannot start until the stability variation outruns the damping, and on a conventional merchant hull the bilge keels supply the largest single contribution to roll damping. A ship with no bilge keels gets R_PR of 0.17 whatever its midship coefficient, which makes the criterion extremely sensitive to the accuracy of the bilge keel schedule.

Is there a table of R_PR values?

No. R_PR is one constant plus three formula branches selected by the midship section coefficient. The range from 0.17 to 1.87 that is sometimes presented as a table is simply the floor and ceiling of that expression: 0.17 when there are no bilge keels, and 1.87 for a sharp bilge or for a full midship section at the area cap of 4.

Is there a second condition in Level 1 besides the GM ratio?

Yes. The volume between the loading waterline and the moulded depth, divided by the waterplane area times the freeboard, must be at least 1.0. That ratio equals exactly 1.0 for a wall-sided hull, exceeds 1.0 where there is flare above the waterline, and falls below 1.0 for tumblehome. Both conditions must be satisfied for the ship to clear Level 1.

Does Level 1 check whether the ship can reach the resonant speed?

No. The resonance-speed check is part of Level 2 check C1, not Level 1. Level 1 is purely a hydrostatic comparison and contains no speed term at all.

What does the Level 2 parametric roll criterion calculate?

Level 2 has two checks. C1 is a quasi-static susceptibility index, computed from hydrostatics on 16 weighted regular waves, that counts the waves in which the ship both suffers a large enough GM variation and can physically reach the resonant encounter condition. C2 is a severity index that counts, over 25 combinations of speed and heading, the sea states in which a time-domain simulation predicts a roll angle exceeding 25 degrees.

What are the Level 2 acceptance standards?

A ship is not vulnerable if C1 is at or below 0.06, or if C2 is at or below 0.025. The test is a disjunction: passing either check clears the ship. This inverts the logic of the pure loss of stability Level 2 criterion, where both checks must be satisfied.

Which wave data does Level 2 use?

Sixteen wave cases with weighting factors derived from the North Atlantic wave scatter of IACS Recommendation No. 34. The wavelengths run from 22.574 metres to 630.684 metres with wave heights from 0.350 metres to 5.950 metres, and the weights sum to exactly 1.0. The associated short-term spectrum is the Bretschneider form.

How many hydrostatic calculations does C1 require?

One hundred and sixty per loading condition. Each of the 16 wave cases is evaluated at 10 crest positions: amidships, then 0.1, 0.2, 0.3, 0.4 and 0.5 wavelengths forward, and 0.1, 0.2, 0.3 and 0.4 wavelengths aft. The ship must be balanced in sinkage and trim on each.

Does C1 use the same GM denominator as Level 1?

No, and this is easy to get wrong. Level 1 divides the GM variation amplitude by the calm-water GM. Level 2 C1 divides it by the average GM computed over the wave series for that wave case. The standard value R_PR is reused unchanged from Level 1, but the quantity it is compared against is defined differently.

Does the criteria set cover the second parametric resonance region?

No. Only principal parametric resonance is addressed, where the encounter frequency is about twice the natural roll frequency. MSC.1/Circ.1627 states that other types of parametric rolling may occur with much smaller probability and are not addressed by the second generation intact stability criteria.

Which roll damping model does Level 2 C2 use?

MSC.1/Circ.1627 specifies none. It requires only that the roll angle be evaluated by time-domain simulation with the righting lever computed in waves. The damping model reaches the calculation through the Explanatory Notes, MSC.1/Circ.1652, whose Appendix 3 covers numerical modelling of roll motion in the vulnerability criteria.

Why do two software packages give different C2 values for the same ship?

Because the criteria do not specify the simulation method, the degrees of freedom, or the duration. Published independent implementations of C2 for the same benchmark container ship differ by roughly a factor of two, while C1 for the same hulls agrees to three decimal places. C1 is a deterministic hydrostatic calculation; C2 is whatever solver the analyst brings to it.

What is a direct stability assessment?

It is the tier that replaces the simplified formulae with numerical simulation or model testing of the specific hull in irregular waves. MSC.1/Circ.1627 sets its safety level as an average stability failure rate not exceeding 2.6 x 10 to the minus 3 per ship per year, and defines a failure as roll exceeding the lesser of 40 degrees, the angle of vanishing stability, or the downflooding angle, or a lateral acceleration exceeding 9.81 metres per second squared where people may be present.

How does a direct assessment handle events that are too rare to simulate?

By statistical extrapolation, which the guidelines treat as the core of the problem. Direct counting must report the upper boundary of the 95 per cent confidence interval of the failure rate. Extrapolation over wave height uses a model in which the logarithm of the mean time to failure is linear in the reciprocal of the square of significant wave height, requiring at least three directly counted rates spanning at least 2 metres of significant wave height.

Can a ship pass Level 2 but fail a direct stability assessment?

Yes, and it has happened on a ship that suffered a real casualty. Denmark and the World Shipping Council reported to SDC 10 that for Maersk Essen in its accident loading condition a one-degree-of-freedom solver returned a pass for Level 2 C2 while a six-degree-of-freedom nonlinear panel code returned a failure. Their submission observed that a higher tier should not fail a ship the lower tier has cleared, particularly where an incident actually occurred.

Is Level 1 conservative?

Yes, by design, and measurably so. It is a screening filter meant to clear most hulls cheaply while catching everything genuinely vulnerable, so it fails ships a fuller assessment would clear. A Level 1 failure is a finding that the cheap test could not rule vulnerability out, not a finding that the ship is dangerous. Treating a Level 1 failure as a design defect is the most common misreading of the framework.

What are operational limitations and operational guidance?

Operational limitations restrict the ship: by area, route and season, or by a maximum significant wave height written into the approved documentation. Operational guidance informs the decision, defining the combinations of speed and heading relative to the sea that should be avoided in each sea state, presented graphically and often as a polar diagram. For parametric rolling either route is available.

Can a ship be certified purely on operational restrictions?

Not without limit. MSC.1/Circ.1627 sets a practicality cap: a loading condition cannot be considered acceptable if the ratio of the total duration of all situations that should be avoided to total operational time exceeds 0.2. If more than a fifth of the ship’s operating time would have to be avoided, the loading condition is rejected rather than restricted.

How does parametric roll differ from synchronous roll?

Synchronous roll happens in beam seas when the encounter period matches the natural roll period, and the waves push the ship transversely once per roll cycle. Parametric roll needs no transverse force: it occurs in head and following seas where the wave passing along the hull changes the ship’s stability, typically twice per roll cycle. On the bridge the distinction is that synchronous roll is what a beam sea does, and parametric roll is what a longitudinal sea can do while the ship appears to be on the safest heading.

How does parametric roll differ from pure loss of stability?

Pure loss of stability is a single-event failure in which the ship sits on a wave crest long enough for the reduced righting arm to let it heel or capsize on that one crest, typically in following or quartering seas at a speed close to the wave celerity. Parametric roll accumulates over many wave encounters until the amplitude reaches a dangerous angle. Both arise from stability varying as a wave passes, but one fails on a single crest and the other builds.

Do bilge keels and stabilizers prevent parametric roll?

Roll damping raises the wave height needed to start parametric roll and limits the amplitude it reaches, which is why bilge keel area enters the Level 1 criterion directly. It does not remove the mechanism. The criteria are assessed with active anti-roll fins and anti-roll tanks inactive or retracted, and operational measures must be developed and accepted both with active devices operating and with them off.

What should a master do when parametric roll starts?

Break the resonance by changing the encounter period, which means changing course, changing speed, or both. MSC.1/Circ.1228 advises selecting course and speed so the encounter period is not close to the roll period or to half the roll period, and it covers following, quartering, head, bow and beam seas. Which lever to use depends on the sea state, the lashing condition and the sea room available, and any ship-specific operational guidance is what tells the bridge which direction to move in.

Does a surveyor check parametric roll vulnerability at survey?

Not under any statutory instrument, because MSC.1/Circ.1627 is recommendatory. Where a ship carries a class notation for parametric roll the society surveys against its own rule: ABS, Bureau Veritas, DNV, ClassNK and Lloyd’s Register each offer one, and the annual survey typically confirms that approved operational guidance is aboard and that any onboard system displays it correctly.

Do the class notations implement the IMO criteria?

Not uniformly. ClassNK’s Guidelines on Preventive Measures against Parametric Rolling of February 2023 bind their notation directly to the IMO criteria, with a clause on complying with the second generation criteria and an appendix outlining them. The ABS Guide for the Assessment of Parametric Roll Resonance in the Design of Container Carriers, in its August 2024 edition, runs a parallel and older track with its own susceptibility and severity criteria and does not reference the IMO guidelines at all.

What does the criteria set not model?

Oblique seas in the C2 index, which is evaluated in head and following seas only. Wave environments outside the North Atlantic scatter data the weights are drawn from. Cargo shift, green water on deck, wind, and the directional spread of a real sea. The second parametric resonance region. And the interaction with pure loss of stability, which MSC.1/Circ.1627 does not require to be assessed together with parametric rolling.