OPERATIONAL GUIDANCE TO AVOID PARAMETRIC ROLL

Marc Levadou, Maritime Research Institute Netherlands (MARIN), the NetherlandsGuilhem Gaillarde, Maritime Research Institute Netherlands (MARIN), the Netherlands

SUMMARY

In October 1998, a post-Panamax, Cll class containership encountered extreme weather and sustained extensive lossand damage to deck stowed containers. The motions of the vessel during this storm event were investigated through aseries of model tests and numerical analysis. This confirmed that parametric roll was the most likely cause of theaccident. The results of this study were presented in a technical paper in 2003 [1].The conclusion of the study confirmed the fact that any large container vessels given the right conditions (hull form,loading condition, speed, wave heading and wave condition) can encounter very large roll angles due to parametric roll.The master at that time was not aware of the parametric roll phenomenon and did not know how to correctly react inorder to decrease or avoid the large motions. In this paper we will discuss the tools which can be used to predict theparametric roll phenomenon. A comparison between numerical results and model tests will be made and attention willbe paid to the validity of the numerical results and the consequences of the validity. By making many simulations whereloading condition, speed and wave condition are varied polar diagrams will be presented which could be very valuablefor a master of a container vessel to avoid a situation in which it is likely that parametric roll will occur.

NOMENCLATURE

k ^ - Transverse radius of gyration (m)RMS - Root mean squareT - Period (s)Tp - Peak period (s)Ha - Wave amplitude (m)Hs — Significant wave height (m)Vcaim - Calm water speed (knots)(J. - Relative wave heading (deg)

1. INTRODUCTION

In late October 1998 a laden, post-Panamax, Cll classcontainership, eastbound from Kaohsiung to Seattle, wasovertaken by a violent storm in the North Pacific Ocean.The encounter with the storm continued for some 12hours, mostly at night, during which the master reducedspeed and attempted to steer into increasingly higher seasoff the vessel's starboard bow. Ultimately, the seasbecame completely confused and violent.Significant wave heights steadily increased from 10.9 mwith a TP of 13.5 s at the beginning of the storm to 13.4m and 15.4 s at in the middle. The maximum Hs was14.9 m with a Tp of 16.4 s.

More significant than the violence and magnitude of theseas, however, were reports by experienced engine anddeck officers of unexpectedly extreme and violent shipmotions during the worst of the storm. At times yawangles of 20 deg port and starboard made course keepingalmost impossible. Main engine overspeed trips andshaft vibrations together with pounding reflectedsignificant pitch amplitudes. Port and starboard rolls asgreat as 35 deg to 40 deg were reported to have occurredsimultaneously with the extreme pitching.

Figure 1: Container vessel's aft deck after suffering fromparametric rolling

When the crew surveyed the vessel the followingmorning they found devastation of the cargo. Of thealmost 1300 on-deck containers, one-third, with theircargoes, had been lost overboard. Another one-third,with their cargoes, were in various stages of damage anddestruction. Containers and cargoes hung over both sidesof the vessel.The motions of the vessel during this storm event wereinvestigated through a series of model tests andnumerical analysis. This confirmed that parametric rollwas the most likely cause of the accident. The results ofthis study were presented during SNAME's 2001 annualmeeting and reported in a technical paper [1].

In that paper several recommendations for operationalguidance, design guidance and further research weremade. Following that paper two major actions havebeing taken. The SNAME has established Ad Hoc panelno #13 "Investigation of Head-sea Parametric rolling andresulting Cargo Security Loads". The IMOsubcommittee on "stability, loadlines and on fishingvessel safety" has been asked during the July 2002meeting to consider head-sea parametric roll.

In the present paper we will discuss the tools which canbe used to predict the parametric roll phenomenon andfurther operational guidance will be presented. Acomparison between numerical results and model testswill be made and attention will be paid to the validity ofthe numerical results and the consequences of thevalidity. By making many simulations where loadingcondition, speed and wave condition are varied polardiagrams will be presented which could be very valuablefor a master of a vessel to avoid a situation in which it islikely that parametric roll will occur.

2. THEORY

The theory behind parametric roll has been studied anddescribed by many persons. In the references severalpapers and articles are given related to the theory behindparametric roll (Kempf [2], Graff and Heckscher [3],Paulling [4 & 5], Oakley [6], Dunwoody [7 & 8],Dallinga et al [9], Luth [10]). In this paper only theprinciples of parametric roll will be described. Someexamples from model tests will be given.

In "normal" conditions the motions of a vessel are causedby direct wave excitation. Resonant conditions can occurwhen the combination of wave period, vessel speed andheading with respect to the waves lead to an encounterwave period close to the natural roll period of the vessel.These resonant conditions can lead to high motions.

For the roll motion resonant roll conditions can occur inbeam waves and stern quartering waves. In head wavesroll motion caused by direct wave excitation are notpossible. Nevertheless, under certain conditions ofencounter period, a rolling can be excited in head seas.The roll motion, once started, may grow to largeamplitude limited by roll damping and, in extremeconditions, may result in danger to the ship or itscontents. This phenomenon is referred to as "autoparametrically excited motion" which is usuallyshortened to "parametric motion". The term describes astate of motion that results not from direct excitation by atime-varying external force or moment but from theperiodic variation of certain numerical parameters of theoscillating system. For a ship in head or stern seas theuneven wave surface together with the pitch-heavemotion of the ship results in a time-varying underwaterhull geometry. This varying geometry, in turn, results intime-varying changes in the metacentric height, i.e., inthe static roll stability. The variation of the static rollstability can cause instability if it occurs in theappropriate period. The instability can lead to roll whena small excitation, introduced by a rudder movement forexample, causes the vessel to take a small roll angle toone side. The roll angles can become very large if thestability variation and the wave height are large.

From theory and as validated by model tests (Dallinga[9], Luth [10], France et al [1]), parametric roll occurswhen the following requirements are satisfied:

• The natural period of roll is equal to approximatelytwice the wave encounter period.

• The wavelength is on the order of the ship length(between 0.8 and 2 times LBP).

• The wave height exceeds a critical level.• The roll damping is low.

3. RESULTS FROM MODEL TESTS

In the figures below time traces of model tests are givenof the roll motion, pitch motion and wave height during arun in regular head waves.

Figure 2: Time Trace of Roll, Pitch and Wave Heightduring Regular Wave Test

Figure 2 shows that at the start of the test the model waspitching to angles of about 4 deg, with negligible rollresponse. A small excitation, likely introduced by arudder movement, causes the vessel to take a small roll toone side. Quite unexpectedly, roll angles then increasedfrom a few degrees to over 30 degrees in only five rollcycles. This behaviour is parametric rolling. Onceparametric roll was initiated, the model continued to rollviolently. The pitch amplitude remains the same.

Figure 3 shows an expanded view of the roll and pitchresponse in regular waves. Positive pitch values meanthe vessel is pitched down by the böw. It can be seenfrom Figure 3 that there are two pitch cycles for each rollcycle, and that the model is always pitched down by thebow at maximum roll. That is, when the model is atmaximum starboard roll it is pitched down by the bow,when upright at zero heel it is pitched down by the stern,and when at maximum port roll it is pitched down by thebow again. Throughout the test program, thisrelationship between pitch and roll motions existedwhenever parametric roll was induced.

30 -

Figure 3: Expanded View of Roll and Pitch Motionsduring Regular Wave Test

Most of the irregular wave and short-crested sea testsfulfilled the requirements for parametric roll, as well.Figure 4 illustrates the behaviour that was observedduring model tests when parametric roll occurred.

Figure 4: Parametric roll observed in irregularhead seas during model tests

In Figure 5 the roll and pitch motions and the waveheight are shown for a test in irregular seas. The 2:1ratio between roll period and pitch period is againapparent.

When the model encounters a sequence of wavecomponents of a certain period and height, parametricrolling is initiated if the conditions are right. As inregular waves, the roll quickly builds to large amplitudes.When the wave period changes or the wave heightdiminishes, the parametric roll response quicklydissipates.

—ROLL—PITCH

WAVE

Figure 5: Expanded view of Roll and Pitch Motions atTime of Largest Roll in Short Crested Sea Test

4. RESULTS FROM SIMULATIONS

Non-linear, time domain seakeeping computer codesbased on potential theory are able to predict thephenomenon of parametric roll. During the investigationof the previous mentioned incident (France et al [1]) twocomputer codes were successfully used to predictparametric roll. SAIC'c LAMP (Large AmplitudeMotion Program, Lin and Salvesen [11], Lin and Yeu [12& 13], Treakle [14]) and MARIN's FREDYN computercode (Hooft [15], de Kat [16 & 17], McTaggart [18])were used to simulate ship motions for comparison withmodel test results.

FREDYN is a non-linear, time domain ship motionsimulation program developed by MARIN over the last10 years for particular use in predicting motions of navalfrigates as part of the Co-operative Research NaviesDynamic Stability project. However, it has also beenutilised for merchant vessel motion predictions.

FREDYN takes into account the external forces on theship due to wind and waves, rudders, bilge keels andactive stabiliser fins and the reaction forces of the shipdue to the motions. The total Froude-Krylov excitingforces are calculated by integration of the hydrostatic anddynamic wave pressures up to the instantaneouswaterline, which makes the program non-linear. SinceFREDYN is a full 6 degrees of freedom model itincludes the couplings between the individual modes ofmotion. Both non-linearity of the excitation forces andcoupling between the 6 motions is required to be able topredict parametric roll motion. The manoeuvring modelis based on frigate type ships; all other routines areindependent of the ship type. Since manoeuvring wasnot a major aspect in this investigation, the FREDYNmodel was applicable.

FREDYN models a ship as a free running vessel inwaves, comparable to a free sailing model in aseakeeping basin. The heading of the vessel is controlledby an autopilot that reacts to the instantaneous motions ofthe ship. The initial speed is set to the desired value and

the RPM of the motor is set such that the ship ispropelled at the desired speed in calm water. Due to thewaves, the speed and course of the ship change duringthe runs.Several studies (France 2003, Luth and Dallinga, 2000)have shown that although FREDYN is capable ofpredicting the occurrence of parametric roll, the accuracypredicted roll amplitudes varies. This is due to thedifficulty to predict the non-linear (viscous) roll dampingcorrectly and the fact that other important effects likespeed loss and speed variations are not modelled.

5. SELECTION OF CASE

5.1 INTRODUCTION

For the study presented in this paper the post-Panamax,Cll containership, which encountered the storm, asdescribed in the introduction was used. It is a logicalstarting point because already FREDYN simulations andmodel tests were performed on the same vessel atMARIN.Three loading conditions were taken into account in thepresent study, with GM values of 1.96 m, 3.0 m and 5.0m, yielding respectively natural roll period of 25.7, 20.8and 16.1 seconds.

5.2 FREDYN SIMULATIONS

The FREDYN computer program was used to generate adatabase containing the probability of parametric roll fora range of speeds, wave heading, wave conditions andloading conditions. Before running the systematic seriesof simulations, representative FREDYN data werecompared to the results of model tests in order to validateour FREDYN model for the calculation of parametricroll for the Cl 1 hull over a wide range of waveconditions.

5.3 AGREEMENT BETWEEN MODEL TESTSAND SIMULATIONS

5.3 (a) Roll decay tests comparison

In Figure 6 the roll decay results from model tests andFREDYN computations for zero knot speed arepresented. Model tests and calculations were performedat the loading condition during the incident thatcorresponds to a natural roll period of 25.7 secondsAs can be seen in the figure the natural roll period aspredicted by FREDYN is not exactly the same as fromthe model test. Also the roll damping (using the IkedaHimeno [19] roll damping method) is somewhat higheras predicted by FREDYN (faster decay).

The FREDYN simulation can be improved by "tuning"the roll model by selecting a value for kxx that results in

good correlation between FREDYN and model test rollperiod and roll damping. In Figure 7 the zero knot rolldecay results from model tests and a FREDYNsimulation with the tuned kxx are presented. The figureshows now a very good comparison between FREDYNand the model tests. The same satisfactory results wereobtained at 5 and 10 knots.

The rest of the FREDYN computations were performedwith a tuned kM value. No other tuning parameters wereused.

Tlme(s)

Figure 6: Roll Decay at Zero Knots

Time (5)

Figure 7: Roll Decay at Zero Knots

5.3 (b) Regular wave tests comparison

In Figure 8 the results of FREDYN computations forregular waves are compared to model tests (Ha = 4 m,T=14.1 s, u. = 180 deg and Vcahn = 16 knot). The figureshows time traces of the roll motion, pitch motion andwave amplitude. From the time trace of the waves onecan see that the wave amplitude during the model tests isnot completely constant. The results of this can be seenin the time trace of the pitch motion. There one can seethat the maximum pitch amplitudes are also not constant.The time trace of FREDYN shows constant wave andthus pitch amplitudes

The time traces of the roll motion shows that theFREDYN results are very close to the model tests results.This means that the prediction of the roll damping inFREDYN is very well for this case.Also the pitch amplitudes are very well predicted byFREDYN.

Roll [deg] in Regular Waves Ha = 4 m, T = 14.1 sHeading = 180 deg, Vcalm = 16 knots

Roll motion [deg]

Wave amplitude [m]

Figure 8: Time Trace of Roll, Pitch and Wave Height forModel Test and FREDYN

5.3 (c) Irregular wave tests comparison

The last check on the accuracy of FREDYN is inirregular waves. In the table below the statistical resultsof measurements and calculations in irregular waves isgiven (Hs = 13 m, Tp = 15.1 s, u = 180 deg and Vcalm = 16knot).The RMS value is the root mean square, the Max Ha+roll value is the maximum amplitude to starboard and theMax Ha- roll value is the maximum amplitude to port.

Hs Wave [m]RMS Roll fdeglMax Ha+ Roll [deg]Max Ha-Roll [deg]RMS pitch [deg]

Model tests13.29.8934.74-32.502.18

FREDYN12.969.50

30.57-31.612.14

Table 1: Statistical Results in Irregular Waves

From the table it can be seen that also in irregular wavesthe FREDYN results are very close to the results of themodel tests. The root mean square (RMS or standarddeviation) of roll is within 4 % and the mean of themaximum and minimum values within 8%. Also thepitch motion is very well predicted by FREDYN as canbe expected.Although the maximum values (positive and negative)are quit close, the distribution of the amplitudes of rollangles shows considerable differences betweenFREDYN and the model test results.This can be seen in Figure 9. This figure shows theprobability of exceedance of roll angles of the model testresults and FREDYN simulation results (Hs = 13 m, Tp =15.1 s, u = 180 deg and Vs = 5 knot). The figure showsthat for the lower angles (smaller then 20 degrees) the

probability of exceedance as found by FREDYN ishigher. For high roll amplitudes the probability ofexceedance as found by FREDYN is lower. This meansthat FREDYN predicts less extreme roll amplitudes asfound during the model tests. The differences in theextreme values are however small. Because in this studythe higher roll amplitudes are of importance the resultsshow that FREDYN can be used.

OC(0•ao)<vu

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Model Testo Fredyn

V%&\\

o.. .O. . .V. .• • • < ? v V. . . . . . . V

0..

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;;

10 15 25 30 35

Roll angle [deg]

Figure 9: Comparison of the distribution of Maxima

5.3 (d) Conclusion of comparison between FREDYNand model tests

Results of roll decay, regular wave tests and irregularwave tests have been compared. After "tuning" of thekxx to get the natural roll period correct the FREDYNresults showed good to very good agreement with themodel tests. It is assumed that also in other waveconditions the FREDYN predictions will be good.

6. OCCURENCES OF PARAMETRIC ROLL

6.1 INTRODUCTION

In order to obtain operational guidance to avoidparametric roll the occurrence of parametric roll for anygiven condition must be known. For this purpose a largeamount of FREDYN simulations were performed. Threeloading conditions were investigated, with GM values of1.96 m, 3.0 m and 5.0 m, yielding respectively naturalroll period of 25.7, 20.8 and 16.1 seconds. Calculationswere performed for a matrix of speeds, wave headings,wave periods and wave heights.

The speed range used was from 2.5 knots to 20 knotswith a 2.5 knots increment, three ship headings wereused (two bow-quartering waves 120 deg and 150 degand head waves 180 deg). Cases with following seaswere not investigated in the present study. It is however

obvious that parametric roll can also occur for thisheadings at low or zero speed.The wave periods (Tp) varied from 3.5 s to 17.5 sec withone second increment and the wave height range takenvaried from Hs = 0.5 to Hs = 14.5 m with one meterincrement.

By eliminating all unrealistic combinations of waveheight and wave period the total amount of calculationscould be reduced to 3165 simulations. Each simulationwas performed for three hours real time.

6.2 IDENTIFICATION OF PARAMETRIC ROLL

The result of each individual calculation is a three hourstime trace of the motions, position of the vessel, speedetc. as presented in the earlier sections. The programgives also statistical results (RMS, minimum, maximumetc.), which however cannot be used to determine if thevessel suffered from parametric roll in that particularcondition. The vessel could indeed be in parametric rollconditions only for a small period of time, whichwouldn't influence the statistical results but still a fewlarge roll angles are sufficient to cause large damage tothe vessel. So, to analyse the probability of parametricroll in each condition the individual time traces wereused.

In order to see if parametric roll occurred in onesimulation a special analysis was made on the results.For each time step the roll angle was compared to athreshold level. If two subsequent roll amplitudes(negative or positive) are higher than that threshold thegroup of roll angles is marked as parametric roll (seeFigure 10). For each simulation the number of thesegroups was determined as well as the total duration of allgroups in one simulation. The total group time is a goodindicator to evaluate the probability and seriousness ofparametric roll events in a particular sea state. Todetermine the group time a threshold of 10 degrees rollamplitude was used.

Several different criteria were tried to determine if in asea state the vessel suffers from parametric roll. The firstone was the number of groups with parametric roll per 3hours simulation. It was expected that the number ofgroups would increase with the wave height. It turnedout that above a certain wave height the number ofgroups decreases because the vessel is continuallysubject to parametric roll. Finally, the mean of l/lO01

highest roll amplitudes was used to determine if in a seastate the vessel suffered from parametric roll. If thatvalue was above 10 degrees the sea state was marked asone in which the vessel could have parametric roll.

WW

Group time (sec)

/!\tli üL

—/

V1 A A ^ „v V v

Figure 10: Determination of Group Time of Subsequent(Parametric) Roll Angles

7. ROLL OCCURENCES

7.1 INTRODUCTION

First order resonant roll can also occur in stern-quartering seas and around beam seas at speeds close tozero. As the main goal of the present study is to presentan example of useful operational guidance by means ofpolar plots, extreme roll behaviour should be predictedfor all headings, what ever cause they originate from. Itwould not be wise to propose to change heading to avoidone problem and encounter another one.

7.2 IDENTIFICATION OF ROLL

For the identification of resonant roll conditions the shipmotions were calculated with MARTN's traditional 2D-strip theory frequency domain program SHTPMO. Theresults are presented in contour plots of roll response fordifferent speeds. These plots can indicate the headings atwhich resonant roll will occur. In addition, operabilityplots were made, showing the significant doubleamplitude (SDA) of roll for different combinations ofsignificant wave heights and headings.

As calculations were performed in the frequency domain,the choice of criteria among calculated quantities waseasier than for parametric roll with time domainsimulations. A criterion of 15 deg Significant DoubleAmplitude (SDA) was chosen to represent cases wereroll would be a problem for the vessel.

8. LOSS OF STABILITY OCCURENCES

A third mechanism that yields large roll angles is loss ofstability in case of lower metacentric height.Unfortunatly there was no time to cover this aspect in thepresent work. Risk of loss of stability in following andstern-quartering seas in cases of very low encounterfrequency could also be investigated in the future inorder to provide a complete picture of the operationalrisk related to extreme roll behaviour. Exactly as forparametric roll, non-linear time domain simulations willnecessary to investigate this item.

9. OPERATIONAL GUIDANCE

With the results from the simulations, one can nowpresent the reuslts in polar plots that can be used asguidance and support for onboard decision or during shiploading or even ship design. A problem in thepresentation of the results is that the occurrence ofexperiencing extreme behaviour is determined by manyparameters. The results could be presented in many waysand the following figures are just examples of what canbe done for this particular hull form.

9.1 EFFECT OF THE HEADING

9.1 (a) Parametric roll

The following figure 11 shows the influence of theheading on the occurrence of parametric rolling at aspeed of 5 knots in a sea state with a peak period Tp =13.5 s. The radial scale shows the significant waveheight. The following results were obtained for a GM of1.96 m.

" Roll A. 1/lOth-10.0

É'50 [deg]

Figure 11: Mean of 1/10th highest roll amplitudes fordifferent wave headings and Hs, 5 knots, Tp = 13.5 s

In this particular case only a rather drastic change in shipheading could allow the vessel to stay away from asituation with large risk of parametric roll.

9.1 (b) Resonant roll

For all loading conditions at very low speeds themaximum roll response will be observed in beam seas.As soon as the vessel will sail with a forward speed themaximum roll response will be observed in stern-quartering seas. This is due to the fact that the encounterfrequency is then tuned to the natural roll frequency ofthe vessel. This is shown in the following figure of thecontour of roll response, presented as a function ofheading and wave frequency at a speed of 20 knots.

most unfavourableheading (30 deg)

\N W E FREQUENCY In ratjrt

Figure 12: Contour plot of roll at 20 knots,for a GM of 1.96 m (25.7 s natural roll period)

The figure 12 shows however that range of the headingsat which resonance will occur is rather narrow. At agiven speed a slight change in course can "detune" thenatural roll frequency of the vessel and the encounterfrequency. A change in speed will have also the sameeffect.

9.2 EFFECT OF THE LOADING CONDITION

9.2 (a) Parametric roll

Figure 13 shows the effect of the loading condition onthe occurrence of parametric rolling, at a fixed speed of 5knots and a peak period of 13.5 sec. The bold line inFigure 13 shows the limiting significant wave heightabove which the criteria of 10 deg SA l/10th will beexceeded.

W5.0 Roll A. l/10th 345hk 10.0 r , ,

• 15-° [ gl

GM = 3.0 m GM = 1.96 m

Figure 13: Mean of l/10th highest roll amplitudes fordifferent wave headings and Hs, 5 knots, Tp = 13.5 s

A change in the GM value affects the natural roll period,which is one of the main parameters that will influencethe risk of parametric roll (together with the encounterwave period, wave length, speed and roll damping). Inthe example above the increase of GM value changes thenatural roll period from 25.7 s. down to 20.8 s. In thesimulated peak period of 13.5 s., the lowest GM value isindeed more inclined to yield parametric roll then theothers do. A different case with a peak period of 10 s.would have created a more unfavourable situation for thehigher GM condition. However, from a statistical pointof view, this lower peak period is associated with lowersignificant wave height than a peak period of 13.5 s.As the significant wave height is also one of the rulingparameters that will unleash parametric roll, adopting aGM value that will yield natural roll period below 20 s. iscertainly a rather efficient way to reduce the risk ofencountering unfavourable wave conditions.

9.2 (b) Resonant roll

The following Figure 14 represents the contour plot ofroll when the GM is equal to 5.0 m. This figure is to becompared with the Figure 12, where the mostunfavourable heading is closer to 30 deg heading.

most unfavourableheading (60 deg)

WAVE FREQUENCY In rad/s

Figure 14: Contour plot of roll at 20 knots,for a GM of 5.0 m (16.1 s natural roll period)

The following figures present the result of theworkability analysis for a GM of 1.96 m and 5.0 m, eachfor their most unfavourable heading and at differentspeeds. As the most unfavourable heading depends onthe tuning between encounter frequency and natural rollfrequency, it will differ from one loading condition toanother.

The lines in Figures 15 and 16 show in a scatter diagramthe wave conditions at which a criterion of 15 degSignificant Double Amplitude is reached.

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Figure 15: Limiting wave conditions for a criterion of 15deg SDA, for a GM of 1.96 m and different speeds

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Figure 16: Limiting wave conditions for a criterion of 15deg SDA, for a GM of 5.0 m and different speeds

These scatter plots are the most complete way toinvestigate resonant roll behaviour. In many followingplots, especially polar plots where headings and Hs andship speed are shown as parameters, a choice on thewave period was always made. It should be kept in mindhowever that this parameter is one of the most importantones.

9.3 EFFECT OF SUSTAINED SPEED ANDSIGNIFICANT WAVE HEIGHT

9.3 (a) Parametric roll

In figures 17 and 18 below the mean of l/lO"1 highest rollamplitudes is plotted against the significant wave heightfor a few different conditions.The significant wave height and ship speed can not reallybe dissociated, as the first one together with the waveperiod will rule the maximum sustainable speed at whichthe vessel will be able to sail with use of full power.

Figure 17 shows the risk of parametric roll in head seaswith the most unfavourable wave period tuning, both foradded resistance and parametric rolling.The maximum sustained speed line represents the lowestsustained speed for each given significant wave height.This means that higher sustained speed could be reachedin more favourable wave periods at the same significantwave height. Also, the occurence of paramtric roll foreach significant wave height is taken for the mostunfavourable wave period.This figure should be taken as relatively conservative butgives a good indication on the situations where risk canbe present.

O results of FREDYN simulations J maximum sustained speed at worst period

5 10

Significant wave height Hs [m]

: no risk of parametric roll due to highsustained speed and low significant waveheight.

: potential risk of parametric roll, avoidedthanks to the possibility to maintain highsustained speed. Problems may beencountered when speed is reducedvoluntary.

): parametric roll will occur due to low speedbut can be avoided by increasing sustainedspeed

) : parametric roll can not be avoided for thisheading as speed can not be increased.

Figure 17: Risk of parametric as a function of significantwave height and sustained speed

The previous figure shows clearly that high sustainedspeed reduces the risk of parametric roll. This is alsoillustrated in Figure 18, where one can see that thethreshold significant wave height (wave height for whichparametric roll will start) increases with increasing shipspeed.

,.

-•—Speed s S kn

JlOt —•

3t5

- £ - Speed »7.5 knots...;*;... Speed = 10 knots —-3K- Speed =* 12.5 knots

- • -Speed «15knots

-•—m- • 9~

r11I /

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Figure 18: Mean of 1/10th highest roll amplitudes fordifferent speeds, head waves, Tp = 13.5 s

9.3 (b) Resonant roll

The relation between encounter frequency and shipnatural roll frequency is highly dependent on the shipspeed. Ship speed will have obviously a clear effect instern-quartering in being in resonant case or not.

9.4 EFFECT OF WAVE HEIGHT AND PERIOD

9.4 (a) Parametric roll

In the table below a sample of the FREDYN results isgiven. The table shows the mean of l/10th highest rollamplitudes for a speed of 5 knots in head waves for arange of wave heights and wave peak periods, for theloading condition yielding the longest natural roll period.

14.513.512.511.510.59.58.57.56.55.54.53.52.51.50.5

Hs(m

0.100000

8.5Tp(s)

0.10.100000

9.5

0.20.10.1000000

10.5

3.35.18

8.10.60.20.10000

11.5

29.6

ÉBISSi4.30.30.1000

12.5

'WSk

ÜÜ1

Bf1.30.30.100

13.5

ipim

Hin1.90.40.2000

14.5

nm

gjpÜË1.3

0.40.30.20.10000

15.5

4.41.60.70.40.30.20.10.10000

16.5

SUM!8.33.44.43.75.65.85.20.10.10.10000

17.5

Table 2: Mean of 1/10* highest roll amplitudes, speed=5knots, head waves

The shadowed area shows the sea states where theparamtric roll criterion is reached. These sea states arethus denoted as ones where the vessel will suffer fromparametric roll. As can be seen the occurrence ofparametric roll depends on wave height and wave period(at constant speed and wave heading).

9.4 (b) Resonant roll

At a given ship speed and heading, the wave period willhave the obvious effect of tuning or not the encounterperiod on the natural roll period. Concerning thesignificant wave height, even if resonant roll has arelatively non-linear character as parametric rolling, itwill be react in an opposite way. While a clear thresholdHs must be reached before parametric roll increasesdrastically, the roll response will tend to reduce relativelyto the wave height with increasing Hs.

9.5 ONBOARD GUIDANCE

At all parameters detailed up to now, only a few can beinfluenced by the master when the vessel is loaded andsailing. Heading and ship speed to some extent can bechosen by the master, or modified, in order to avoidcritical conditions. Figure 17 clearly shows that thechoice of the sustained speed can be heavily reduceddepending on the encountered wave conditions.In order to show what could be a useful onboardguidance, it was decided to place the vessel in one givensea state and demonstrate the master the options.

Figures 19 and 20 show this example for a vessel sailingin a given wave climate: Hs = 7.0 m & Tp = 13.5 s. Theexample is shown for two different loading conditions: aGM of 1.96 m in Figure 19 and a GM of 3.0 m in Figure20. The radial scale represents the ship speed in knots.

Two important limitations in the results presented in thetwo following figures should be reminded:

• the risk of parametric roll in following seas was notcalculated.

• the risk of loss of stability was not calculated.

The latter point is however not of concern for the type ofloading conditions used in the present study. However itdefinitly becomes an issue for lower stability levels.

speed that cannot beachieved in that sea state

max sustainedspeed

lOdeg SAl/lO*

15deg SDA

,,] 5.0

110.0 Roll(degl115.0

Figure 19: Roll as a function of heading and speed inknots, in Hs=7.0m and Tp=13.5 s, GM = 1.96 m.

speed that cannot beachieved in that sea state

max sustainedspeed

10 deg SA 1/10*

15deg SDA

5.010.0 Roll [deg]15.0

Figure 20: Roll as a function of heading and speed inknots, in Hs=7.0m and Tp=13.5 s, GM = 3.0 m.

12. REFERENCES10. CONCLUSIONS

This paper explores various ways to visualise operationalguidance in order to avoid extreme behaviour.

• Because a (container) vessel will sail with differentloading conditions and encounter different waveconditions at different speeds the amount ofinformation which is needed for a reliableoperational guidance is rather large.

• With actual knowledge of the different phenomenonyielding large roll motions and possibilities to usereliable numerical models and/or model testsdatabases, the identification of cases when large rollmotions will occur can be made.

• The most efficient way to present this informationonboard would be to put the (ship specific) motionsand roll databases on a PC where the user only hasto choose loading condition and wave condition.

• When encountered weather can be gathered in areliable way from onboard radar for example, theinformation could be used automatically andefficiently to inform the captain on potential risk (orrisk build up with weather forecast when weatherdeteriorates). The system would then provide acontourpiot showing which headings and speeds toavoid, or which options are left to avoid problems.

11. RECOMMANDATION FOR FURTHERRESEARCH

The present paper demonstrates the capability ofpredicting roll behaviour of large container vessel, bothresonant roll and parametric roll. For practical reasonssome limitations were taken. For further research thefollowing items could be taken into account or evaluated:

• Cover the effects of loss of stability in followingseas.

• Take into account more variations in loadingconditions.

• Evaluate the influence of design changes (stern, bowflare, bilge keel, fin stabilisers, etc.) on theprobability of roll.

• Evaluate the influence of routes and area ofoperations.

• Establish the risk of encountering critical conditionsbased on scenario simulations on given routes ofoperations.

• Variation in used or installed power.

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Guilhem Gaillarde holds the current position of projectmanager in the seakeeping department of the MaritimeResearch Institute Netherlands. He joined MARIN in1997 after he received a Master of Science degree inmarine engineering from the Institut des Sciences del'Ingénieur de Toulon et du Var (ISITV) in France in1996. He is responsible for contract research undertakenon behalf of the maritime and offshore industry as wellas research of a more fundamental character. Bothinvolve model testing and numerical work.

13. AUTHORS BIOGRAPHY

Marc Levadou holds the current position of projectmanager in the seakeeping department of the MaritimeResearch Institute Netherlands (MARIN). He received aMaster of Science degree in marine engineering from theDelft University of Technology in 1995. Before joiningMARIN he worked on a 6 months project for the RoyalHuisman Shipyard in Vollenhoven (Netherlands). Hejoined MARIN in 1996 were he first worked in thesoftware department. In 2000 he joined the seakeepingdepartment were he is responsible for contract research,for maritime and offshore industry, as well as research ofa more fundamental character. Both involve modeltesting and numerical work.