Parametric Roll Assessment - VeriSTAR

Parametric Roll Assessment

July 2019

Rule Note NR 667 DT R00 E

Marine & Offshore Le Triangle de l’Arche – 8 cours du Triangle – CS50101

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l Conditions – Edition September 2018

July 2019

RULE NOTE NR 667

NR 667Parametric Roll Assessment

SECTION 1 PARAMETRIC ROLL ASSESSMENT

APPENDIX 1 PHYSICAL BACKGROUND OF PARAMETRIC ROLL

APPENDIX 2 METHODOLOGY FOR SHORT TERM HYDRODYNAMIC CALCULATIONS FOR SHIP MOTIONS RESPONSE

APPENDIX 3 EXAMPLE OF APPLICATION OF PARAMETRIC ROLL CALCULATIONS

2 Bureau Veritas July 2019

Section 1 Parametric Roll Assessment

1 Application 3

1.1 General 1.2 Additional class notation PaRoll1 and PaRoll2 1.3 Documentation to be submitted

2 Loading conditions 4

2.1 Loading conditions for simulations

3 Roll motion assessment 4

3.1 General3.2 Ship operational profile3.3 Computation of maximum roll angle

4 Operational guidance 5

4.1 Criteria4.2 Polar plot4.3 Operation

Appendix 1 Physical Background of Parametric Roll

1 Development of parametric roll 7

1.1

2 Influence of roll damping 8

2.1

3 Influence of speed wave direction 8

3.1

Appendix 2 Methodology for Short Term Hydrodynamic Calculations for Ship Motions Response

1 General 9

1.1 Introduction

2 Wave environment 9

2.1

3 Ship hydrodynamic model 9

3.1 General3.2 Hydrodynamic loads3.3 General modelling considerations3.4 Statistical analysis of ship response in irregular sea state

4 Extreme response 10

4.1 Definition4.2 Short term extreme

July 2019 Bureau Veritas 3

Appendix 3 Example of Application of Parametric Roll Calculations

1 General 12

1.1

2 Roll motions computations 12

2.1 Preliminary check2.2 Roll assessment


NR 667, Sec 1


SECTION 1 PARAMETRIC ROLL ASSESSMENT

1 Application

1.1 General

1.1.1 The requirements of the present Rule Note apply toanalysis criteria and ship motion modeling calculation ofships intended to be granted the additional class notationPaRoll1 and PaRoll2, as defined in NR467 Rules for SteelShips, Pt A, Ch 1, Sec 2, [6.14.48], and detailed in [1.2].

1.1.2 This Rule Note deals with the part of motion analysiswhich aims at performing parametric resonance as pre-sented in App 1 and based on hydrodynamic calculationsincluding ship motions response.

1.1.3 The additional class notations PaRoll1 and PaRoll2may be assigned at the design stage or for vessels in service.

1.2 Additional class notation PaRoll1 and PaRoll2

1.2.1 The additional class notations PaRoll1 or PaRoll2may only be assigned to container ships for which numeri-cal simulations and operational guidance (polar plot) forevaluation of maximum dynamic roll angle (including para-metric roll) in various loading conditions and sea states aredeveloped in compliance with this Rule Note.

• The additional class notation PaRoll1 is granted to shipswithout any anti-rolling devices or to ships using onlybilge keels as anti-rolling devices

• The additional class notation PaRoll2 is granted to shipsusing anti-rolling devices such as anti-roll tank, stabi-lizer fins or any anti-rolling devices different from bilgekeels.

1.2.2 The additional class notations PaRoll1 and PaRoll2are not relevant to ship for which all loading conditionsdefined in [2.1] comply with the following condition:

where:

δGM : Amplitude of variation of metacentric height, inm, calculated in accordance with [1.2.3]

GMC : Corrected metacentric height, in m, of the load-ing condition under consideration in calmwater

RPR : Coefficient as defined in Tab 1

Table 1 : Value of RPR

1.2.3 The amplitude of variation of metacentric heightδGM, in m, should be determined according to:

where:

IH : Moment of inertia, in m4, of the waterplane atthe draft TH

IL : Moment of inertia, in m4, of the waterplane atthe draft TL

TH = TLC + δΤH

TL = TLC + δΤL

TLC : Draft amidships corresponding to the loadingcondition under consideration

D : Depth, in m, as defined in NR467 Rules for SteelShips, Pt B, Ch 1, Sec 2

V : Volume, in m3, of displacement of the loadingcondition under consideration

Tfull : Draft, in m, corresponding to the fully loadeddeparture condition

SW = 0,0167

δGMGMC

------------- RPR≤

if the ship has a sharp bilge

if Cm > 0,96

if 0,94 < Cm < 0,96

if Cm < 0,94

Note 1:CM : Coefficient equal to:

Am : Area, in m², of the underwater midship section of the fully loaded condition.

AK : Total overall projected area, in m², of the bilge keels

L : Rule length, in m, as defined in NR467 Rules for Steel Ships, Pt B, Ch 1, Sec 2

B : Moulded breadth, in m, as defined in NR467 Rules for Steel Ships, Pt B, Ch 1, Sec 2

RPR 1 87,=

RPR 0 17, 0 425100AK

L B⋅----------------- ,+=

RPR 0 17, 10 625, Cm⋅ 9 775,–( )+100AK

L B⋅----------------- ⋅=

RPR 0 17, 0 2125100AK

L B⋅----------------- ,+=

CMAm

B Tfull⋅-----------------=

δGM IH IL–2V--------------=

δTH Min D TLC– L SW⋅2

--------------, =

δTL Min TLC 0 25 T, full– L SW⋅2

--------------, =

NR 667, Sec 1


1.3 Documentation to be submitted

1.3.1 The following documents are to be submitted to theSociety:

• ship lines, by submitting a CAD model, or offset table

• necessary loading conditions as required in [2] includ-ing:

- the displacement

- the draft at forward and aft perpendicular

- the three coordinates of center of gravity

- the radius of gyration.

• maximum ship speed

• roll decay or/and forced roll test results, from CFDor/and model test should be provided for:

- several loading conditions so that the roll dampingcan accurately be estimated for all loading conditiondescribed in [2.1]

- several ship speeds so that the roll damping canaccurately be estimated for all ship speeds specifiedin [3.2.3]

• the description of the anti-rolling devices used asdescribed in [3.2.6]

• results of calculations as described in [4.2] (i.e. a set ofpolar plots)

• a description of the means which will be used onboardto display the polar plot corresponding to the operatingloading condition (i.e. in particular the value of GM),the ship speed, the significant wave height, the upcross-ing wave period, the mean wave direction and the shipcourse.

2 Loading conditions

2.1 Loading conditions for simulations

2.1.1 The loading conditions to be considered for applica-tion of [1.2.2] and [3] are to cover the entire range of meta-centric heights from GMmin to GMmax, where:

• GMmax is the maximum GM from the stability booklet,and

• GMmin is the minimum GM from the stability booklet.

2.1.2 The metacentric height is to be incremented fromGMmin and up to GMmax according to the following relation:

where:

GMi : metacentric height of step i with the first stepbeing GM1 = GMmin (as defined in [2.1.1])

GMi+1 : metacentric height of the step i+1

Δf : to be taken not greater than 0,015 s-1

2.1.3 Each metacentric height (GMi) in this range should beassociated a draught.

The draught associated to each GMi may be obtained by lin-ear interpolation between (GMmax, TGMmax) and (GMmin, TGM-

min), where:

• TGMmax is the draught from stability booklet associatedto GMmax, and

• TGMmin is the draught from stability booklet associated toGMmin.

If duly justified, a different GM-Draught curve may be con-sidered.

3 Roll motion assessment

3.1 General

3.1.1 Ship motion simulations are to be computed using anon-linear time domain hydrodynamic code as described inApp 2, [3.2], and should include at least the following threedegrees of freedom: heave, roll and pitch.

3.1.2 The Froude-Krylov forces are to be calculated byapplying the pressure of the undisturbed incoming wave tothe hull on every wet panel at any time step.

3.2 Ship operational profile

3.2.1 Sea states

Ship motion simulations are to be computed using all thesea states below the 25 years contour of the wave scatterdiagram for North Atlantic from IACS RecommendationNo. 34. This contour is given in Tab 1.

The sea state are to be modeled by a Pierson-Moskowitz spec-trum as defined in NI 638, Sec 2, [2.2.4] and a "cos n" spread-ing function with n = 8, as defined NI 638, Sec 2, [2.2.7].

3.2.2 Wave heading

Numerical simulations are to be carried out for the range ofwave directions from 0 degrees (following seas) to 180degrees (head seas) with a recommended maximum incre-ment of 15 degrees.

3.2.3 Speed profile

Numerical simulations are to be carried out for the entirerange of service speed including zero speed case, with arecommended maximum increment of 5 knots.

3.2.4 Loading conditions

The ship motion analysis is to be carried out for each of theloading conditions specified in [2.1].

Table 2 : IACS Recommendation No.34 25 years contour

GMi 1+ Δf 0 825, π⋅g

------------------------ B GMi+⋅ ⋅ 2

=

TZ, s 4,5 5,5 6,5 7,5 8,5 9,5 10,5 11,5 12,5 13,5 14,5 15,5 16,5 17,5

HS, m 2,4 5,5 8,4 10,9 12,9 14,4 15,4 15,9 16,1 16,0 15,4 14,6 13,1 10,7

NR 667, Sec 1


3.2.5 Roll damping

The data to be used for roll damping calibration could be:

• roll decay, and/or

• forced roll test, and/or

• CFD computations.

If the wave component of roll damping is already includedin the calculation of radiation forces, measures should betaken to avoid including these effects more than once.

The roll damping is essentially non-linear and may be mod-eled by a linear and quadratic coefficients.

3.2.6 Anti-rolling devices

When a ship is equipped with anti-rolling devices, the fol-lowing information is to be provided to the society accord-ing to the type of anti-rolling devices:

• if the anti-rolling devices are bilge keels, their geometry,sizes and position along the ship should be provided

• if anti-rolling devices are anti-roll tank (ART), the geom-etry and the operational guidance of the ART (filling lev-els according to the loading conditions and the waveperiod) are to be provided. In addition, the loss of stabil-ity due to the reduction of metacentric height is to betaken into account

• if other anti-rolling devices different than bilge keelsand ART are used, the full description of the systemincluding the geometry, installation and operation ofthese devices should be provided.

3.2.7 Reduction of number of simulations

For a given loading condition, wave period, wave headingand ship speed, it is possible to reduce the number of simu-lations by considering that:

• if for a given wave height (Hs), the roll angle assessed asdefined in [3.3.3] is smaller than 5 degrees, it could beconsidered that roll angle for all wave height smallerthan Hs are also smaller than 5 degrees

• if for a given wave height (Hs), the roll angle assessed asdefined in [3.3.3] is greater than the threshold definedin Article [4], it could be considered that the roll anglefor wave height higher than Hs, the vessel will experi-ences roll angle greater than the threshold.

3.3 Computation of maximum roll angle

3.3.1 For each combination of loading condition, waveheight, wave period, wave heading, and ship speed, simula-tions should be repeated at least 20 times with the samespectrum but with different set of initial phase angles.

3.3.2 The duration of each calculation should be at least 1hour, therefore the total time for each combination of load-ing condition, wave height, wave period, wave heading,and ship speed is at least 20 hours.

3.3.3 The maximum roll angle corresponds to one hourmaximum roll angle with a probability of exceedance of0,5.

4 Operational guidance

4.1 Criteria

4.1.1 It is to be checked that the maximum roll angle forany combination of loading condition, wave height, waveperiod, wave heading, and ship speed, is in compliancewith the following formula:

where:

θsh : Maximum roll angle computed in [3.3]θPR : Angle equal to:

• when the ship is granted with the additionalclass notation LASHING or LASHING-WWor LASHING (specific area):

θPR = θlash

with θlash as defined in NR625, Ch 14, Sec 1,[4.3.5]

• for others cases:

θPR = θ with θ as defined in NR625, Ch 4, Sec 3,[2.1.1].

γPR : Conversion factor taken equal to 1,6.

4.2 Polar plot

4.2.1 The final results will be a set of operational guidancepresented in the form of a polar plot. In the polar plot, asshown for example in App 3, Fig 4 to App 3, Fig 7, theradial direction represents the ship speed from zero to themaximum speed and the rotational direction corresponds tothe wave encounter angle.

4.2.2 Polar plot is provided for each case representing aspecific combination of significant wave height, waveperiod and loading condition. The polar plot should be col-ored in two colors for each combination of speed and head-ing corresponding to conditions where the criterion definedin [4.1] is fulfilled or not.

4.2.3 If the ship is granted with more than one additionalclass notation for lashing, a different set of polar plots is tobe provided for each additional class notation. For exampleif a ship is granted with additional class notation LASHINGand LASHING-WW, a set of polar plots should be providedfor the additional class notation LASHING and a differentset of polar plots should be provided for the additional classnotation LASHING-WW.

4.2.4 Alternative ways to display the operational guidanceare possible, provided that all necessary information isincluded.

4.3 Operation

4.3.1 Operational guidance should be provided as easilyaccessible and understandable information in graphicalform, which clearly indicated operational conditions (com-bination of loading conditions, ship speeds and ship course)

θshθPR

ϒPR

--------<

NR 667, Sec 1


that should be avoided for a given sea state. Automatic alertsystems can be used for the cases when operational condi-tions are close to areas of those conditions that should beavoided.

4.3.2 For a given sea state specified by significant waveheight and mean zero up-crossing wave period, operationalconditions that should be avoided are derived from the pre-defined databases of roll angle computed as specified in[3.3], and stored as functions of the ship forward speed andship heading with respect with respect to the mean wavedirection, using as input the actual significant wave height,

mean zero up-crossing wave period, mean wave directionand ship course.

4.3.3 In case where the actual operational conditions (sig-nificant wave height, zero up-crossing wave period) are notin the pre-defined databases, it is recommended to selectthe closest polar plot in GM, mean zero up-crossing waveperiod and significant wave height.

4.3.4 The ship master should ensure that the vessel, at anytime during the voyage and considering the availableweather forecasts, satisfies the operational guidance.

NR 667, App 1


APPENDIX 1 PHYSICAL BACKGROUND OF PARAMETRIC ROLL

1 Development of parametric roll

1.1

1.1.1 Parametric roll (short of parametric roll resonance) isan amplification of roll motions caused by periodic varia-tion of transverse stability in waves. The phenomenon ofparametric roll is predominantly observed in head, follow-ing, bow and stern-quartering seas when ship's encounterfrequency is approximately twice of ship roll natural fre-quency and roll damping of the ship is insufficient to dissi-pate additional energy.

1.1.2 Fig 1 illustrates the development of this phenome-non. If the ship is rolled while on the wave trough,

increased stability provides stronger pushback, or restoringmoment. As the ship returns to the upright position, its rollrate is greater, since there was an additional pushback fromthe increased stability. If at that time the ship has the wavecrest at midship, the stability is decreased and the ship willroll further to the opposite side because of the greater speedof rolling and less resistance to heeling. Then, if the wavetrough reaches the midship section when the ship reachesits maximum amplitude roll, stability increases again andthe cycle starts again. Note that there was one half roll cycleassociated with the passing of an entire wave. So, there aretwo waves that pass during each roll period. That means theroll period is about twice that of the wave encounter periodas illustrated in Fig 2.

Figure 1 : Development of parametric roll resonance

Figure 2 : Example of time series of parametric roll together with wave phase

NR 667, App 1


Figure 3 : Example of decreasing roll amplitude in calm water due to roll damping

2 Influence of roll damping

2.1

2.1.1 When a ship rolls in calm water after being disturbed,the roll amplitude decreases successively due to roll damp-ing as shown in Fig 3. A rolling ship generates waves andeddies, and experiences viscous drag. All these processescontribute to roll damping. Roll damping plays an import-ant role in the development of parametric roll. If the "loss"of energy per cycle caused by damping is more than energy"gain" caused by changing stability in longitudinal seas, theroll angle will not increase and the parametric resonancewill not develop. Once the energy "gain" per cycle is morethan the energy "loss" due to damping, the amplitude of theparametric roll starts to grow.

2.1.2 During the parametric roll resonance the combina-tion of the variation of transverse stability on wave troughand wave crest, which occur twice during the roll period,makes roll angle grow significantly. The only other condi-tion that has to be met is that the energy loss due to rolldamping is not large enough to completely consume theincrease of energy caused by parametric roll resonance.

3 Influence of speed wave direction

3.1

3.1.1 The frequency of encounter with waves changeswhen a ship is in motion. When a ship is sailing in follow-ing or stern-quartering seas, the direction of waves and shipheading are similar. As a result, the relative speed is smalland a ship encounters fewer waves during the same period(compared to a zero speed case). The encounter period isincreased (and the encounter frequency is decreased) in fol-lowing or stern-quartering waves.

3.1.2 When a ship is sailing in head or bow-quarteringseas, the direction of waves and the ship heading are oppo-site. As a result, the relative speed is large and a shipencounters more waves during the same time (compared toa zero speed case). The encounter period is decreased (andthe encounter frequency is increased) in head or bow-quar-tering waves.

3.1.3 The inception of parametric roll depends on the fre-quency of encounter being in the frequency range wherethe parametric roll is possible. Therefore, the developmentof parametric roll depends on speed and heading. Sinceparametric roll usually occurs when the encounter fre-quency is about twice the roll natural frequency, the follow-ing relation can be written:

where:

VS : ship speed, in m/s

Tθ : natural roll period, in s

TW : wave period, in s

β : wave heading, 0° for following seas, 180° forhead seas.

3.1.4 The excitation is important to trigger parametric roll.In general, the maximum righting lever variation occurswhen the wavelength projected in the longitudinal directionof the ship is nearly the same as the ship length. Therefore,the following relation can be written:

where:

λ : wave length, in m

g : gravity acceleration taken as 9,81 m/s2.

ωe 2ωθ= VS β( )cos→ gTW

2π---------- 1 2– TW

Tθ-------

= =

λ 2L β( )cos⋅= β( )cos→ gTW

2π---------- 1

L--- g

2π-------T

2w⋅= =

NR 667, App 2


APPENDIX 2 METHODOLOGY FOR SHORT TERM HYDRODYNAMIC CALCULATIONS FOR SHIP MOTIONS RESPONSE

1 General

1.1 Introduction

1.1.1 The present Appendix describes methods and tools tobe used for the direct calculation of the hydrodynamicresponse of ships.

1.1.2 The following tools and methods are needed to deter-mine the extreme ship motions corresponding to a givenexposure time:

• a description of the operating conditions during theexposure time, including the wave environment (seeArticle [2]) and the ship operational profile

• a hydrodynamic model of the ship, which is able tocompute the ship response on any type of wave condi-tions (see Article [3])

• a method to derive extreme responses from the results ofthe previous computations (see Article [4]).

2 Wave environment

2.1

2.1.1 In order, to properly describe the sea-states that theship will face over a voyage, the short term description ofwaves as defined in NI 638, Sec 2, [2.2]. Note that the short

term description of waves is used to define one specificwave condition over a short duration (usually 3 hours)where the sea-state is considered as stationary.

3 Ship hydrodynamic model

3.1 General

3.1.1 A good evaluation of the motion response of a ship inwaves needs a proper coupling between a hydrodynamicmodel, which describes the interaction between the shipand the waves. Several levels of assumption can be chosenfor the hydrodynamic model, depending on which physicalbehavior is expected to be reproduced.

Two types of hydrodynamic loads may be considered to beapplied to the ship:

• linear loads (valid only for the smallest sea-state),described in [3.2.1]

• weakly non-linear loads (Froude-Krylov forces), describedin [3.2.2].

3.2 Hydrodynamic loads

3.2.1 Two types of hydrodynamic loads are described, forparametric roll assessment the weakly non-linear loadsmodel described in [3.2.2] is recommended.

Figure 1 : Typical hydrodynamic mesh for linear (yellow) and non-linear (yellow + green) seakeeping calculations

NR 667, App 2


3.2.2 Linear

The linear part of hydrodynamic loading is calculated byvalidated numerical seakeeping code. The use of codebased on Boundary Element Method (BEM) is recom-mended. A typical hydrodynamic mesh for hydrodynamiccalculation is shown in Fig 1. In the case of linear calcula-tion the mesh contains the mean underwater part only. Themesh size is to be chosen so that the minimal wave length(defined on the basis of encounter frequency) is covered byat least 6 panels. Alternatively, a special treatment of thehigh frequency calculations can be used in order to avoidthe numerical inaccuracies inherent to BEM method. In anycase, the problem of irregular frequencies is to be properlyhandled.

The hydrodynamic problem is solved for the 6 degree offreedom. The equation of motion is then solved in the fre-quency domain for all motions. The outputs of a linearhydrodynamic computation are the Response AmplitudeOperators (RAO). Ship motions RAO are directly computedby the seakeeping software.

3.2.3 Weakly non-linear

The minimum non-linearities that should be included arebased on the so called Froude-Krylov approximation. Thepressure of the undisturbed incoming waves is applied tothe hull on every wet panel, and not only under the meanwaterline as it is done for linear computation. The mesh thatis used to integrate the pressure loading has to include thepart above the mean waterline. The non-linear hydrostaticrestoring forces are also included by taking into account thereal position of the ship in the integration of the hydrody-namic pressure.

The motion equation is solved using a time domain sea-keeping code. The radiation forces are included through thememory functions, whereas the diffraction forces remainlinear. The outputs of a non-linear hydrodynamic computa-tion are time traces. Ship motions are directly computed bythe seakeeping code.

3.3 General modelling considerations

3.3.1 Mass properties

For each loading conditions the following mass propertiesshould be verified according to the values from the trim andstability booklet:

• mass

• radii of gyration

• location of center of gravity.

3.3.2 Hydrostatic balance

For each loading condition, the computed values of dis-placement and trim are to be checked and compared tothose of the trim and stability booklet. The following toler-ances are considered acceptable:

• 2% of the displacement

• 0,1 degree of the trim.

It is also worth checking the following hydrostatic proper-ties:

• location of the center of buoyancy

• transverse metacentric height (GMt).

3.3.3 Roll dampingAdditional damping forces are to be added to the motionequation in order to take into account the viscous dampingand damping due to bilge keels, rudders and other existingappendages. This additional damping is to be added to thewave damping computed by the hydrodynamic program.This damping could be based on experimental dataobtained by roll decay test, or forced roll test performed bya BV recognized facility (normally, a towing tank memberof the International Towing Tank Conference). This dampingcould also be based on Computational Fluid Dynamic com-putations obtained by means of a validated tool. This damp-ing is essentially non-linear and may be modelled by alinear and quadratic damping coefficient.

3.4 Statistical analysis of ship response in irregular sea state

3.4.1 Linear frequency domain simulationsIn case of linear hydrodynamic loads ([3.2.1]) and on agiven irregular sea state the statistic of ship response shouldbe assessed as defined in NI 638, Sec 5, [2.1] and [2.2].

3.4.2 Non-linear time domain simulationsIn case of non-linear hydrodynamic loads (see Sec 1,[3.2.2]), the simulation of ship response is done in timedomain. From a statistical point of view, this time domainsignal can be analyzed with the following counting method.

The up-crossing counting method consists to divide theresponse into cycles (one cycle being defined between twoconsecutive mean up-crossing at a given level), and to iden-tify and keep the maximum and minimum of each cycle.The mean up-crossing period is defined as the mean periodof all the cycles. The maxima and minima are sorted anduse to define an empirical cumulative distribution functionof the response. This distribution may be different from aRayleigh distribution, because of the non-linearities. Theup-crossing counting method is used to define the extremeresponse on a sea state, or a set of sea states.

An analytical function (Weibull distribution for instance)can be fitted to the empirical cumulative distribution func-tion, in order to be able to extrapolate the results to a lowerprobability level. Special care should be taken to the fittingprocedure, and to the possible error introduced by anextrapolation.

4 Extreme response

4.1 Definition

4.1.1 The extreme response associated to a return period Tris the maximum response the ship will see while sailingduring a period Tr with the given environmental conditions.The extreme response is associated to a given exceedanceprobability or risk.

NR 667, App 2


4.2 Short term extreme

4.2.1 For a given short term condition, (sea state and head-ing), the maximum short term response, corresponding to adetermined duration, exceeded with a given risk should beassessed as defined in NI 638, Sec 5, [3].

NR 667, App 3


APPENDIX 3 EXAMPLE OF APPLICATION OF PARAMETRIC ROLL CALCULATIONS

1 General

1.1

1.1.1 Objective

This appendix presents an example of application of para-metric roll calculations. They are only given as a typicalillustration of the methodologies described in Sec 1.

1.1.2 Sample ship

The vessel used in this application is a container ship. Thelines of this vessel are presented in Fig 1, and the details ofthe ship are given in Tab 1.

2 Roll motions computations

2.1 Preliminary check

2.1.1 The loading conditions have been selected using theprocedure defined in Sec 1, [2.1] and assuming that thecurve between the maximum and minimum height is a line.The results are shown in Fig 6, and in this figure the redpoints are loading condition taken in trim and stability

booklet, the blue line is the line between the maximum andminimum metacentric height and the black points aredefined according to Sec 1, [2.1.2].

Applying the requirement defined in Sec 1, [1.2.2] on theloading conditions defined along the blue line (black pointson Fig 2), the results presented in Fig 3 indicate that theadditional class notation PaRoll1, PaRoll2 could be appliedto this ship since there are some loading conditions (blackpoints in Fig 3 above the threshold represented by a greenline in Fig 3) not in compliance with the defined condition.

Table 1 : Characteristics of the sample container ship

Figure 1 : Lines of sample containership

Designation Unit Value

L: ship lentght m 262,0

B: breadth m 40,0

T: draught m 12,0

Tθ: natural roll period s 25,1

GMC: corrected metacentric height in cam water

m 2,75

Lbk: bilge keel lenght m 76,28

Bbk: bilge keel breadth m 0,4

NR 667, App 3


Figure 2 : Example of loading conditions derived from the procedure described in Sec 1, [2.1]

Figure 3 : Preliminary check results

2.2 Roll assessment

2.2.1 Using the procedure described in Sec 1, [3] andapplying the requirement defined in Sec 1, [4.1] andassuming that the ship is complying with the additionalclass notation LASHING, operational guidance in term ofpolar plot have been derived according to Sec 1, [4.2].These calculations have been produced using a non-lineartime domain seakeeping software, namely HydroStar++, for4 sea states having a modal period of 12,5 seconds and15,5 seconds and three different significant wave height: 5,6 and 7 meters. Four sample of polar plots are shown in

Fig 4 to Fig 7. The loading used in these computations is thepresented in Tab 1.These diagrams are created from a series of numerical simu-lations from 0 to 25 knots in 5 knots increments and for aheading from 0 degree (following seas) to 180 degrees(head seas) with 15 degrees increments. All combinationsinside the black region exceed 12,5 degrees roll angledetermined using the requirements in Sec 1, [4.1]. Theregions of higher speed following seas correspond to a reso-nant roll condition where the encounter frequency is nearthe natural roll frequency, while for lower speed, head andfollowing seas are parametric roll induced motions.

0

2

4

6

8

10

12

14

16

18

20

4 6 8 10 12 14

GM

(m

)

T (m)

Curve as def. in Sec 1, [2.1.3]

GM_T&SB

GM as def. in Sec 1, [2.1.2]

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 5 10 15 20

GM

/GM

c

GM (m)

RPR as def. in Sec 1, [1.2.2]

Not in compliance with the conditiondefined in Sec 1, [1.2.2]

GM/GMc as def. in Sec 1, [1.2.3]

NR 667, App 3


Figure 4 : Example of polar plot - Hs = 5.0m, Tp = 12.5 seconds, GM=2.75m


NR 667, App 3




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