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RINA’91, International Conference onRo-Ro Safety and Vulnerability the WayAhead, Heathrow Penta Hotel, London,17 - 19 April 1991, Vol. I.

Reprinted: 22-03-2001Website: www.shipmotions.nl

Report 0889-P, September 1991,Delft University of Technology,Ship Hydromechanics Laboratory,Mekelweg 2, 2628 CD Delft,The Netherlands.

Roll Motions of Ships due to Sudden Water Ingress,Calculations and Experiments

A.W. Vredeveldt (TNO) and J.M.J. Journée (DUT)

SUMMARY

Roll-on Roll-off vessels appear to be sensitive to rapid capsizing due to sudden ingress ofwater. Rapid capsizing is caused by a drastic decrease of static stability properties due tofree surfaces, as well as by inertia effects with regard to the roll motion. In this report it isshown that the dynamic behaviour of the ship due to sudden ingress of water cannot beneglected. To this end a calculation model was developed which was verified by ingresstests. For these tests a wing tank cross-duct configuration was chosen. The results arepresented in this report.

1. INTRODUCTION

The safety of ships in general has to beassessed by judging several aspects. Thestability of both the intact ship and thedamaged ship is of major importance.The past has shown the vulnerability ofRo/Ro vessels with regard to stability;see references [l], [2], [3] and [4].

The stability of ships is presentlydetermined by applying quasi-staticmethods. Inertia effects with regard tothe (roll) motions of the ship areneglected. Usually flow calculations arenot carried out either, although there is

one exception, which refers to the designof cross-ducts. When a cross-duct isapplied a flow calculation is carried outin order to establish the minimumrequired cross sectional area. Suchcalculations usually assume a zero heelangle during the period of flooding.

The roll motion of a ship can bedescribed by a second order differentialequation where the angle of roll is usedas the independent variable. On the basisof this equation, it is possible to define anatural roll period TR. The moment ofheel is determined by both the weight ofwater, which has flowed into the ship,

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and the distance of the centre of gravityto the axis of rotation. The flow of thewater into the ship can be described witha first order differential equation. Fromthis equation a time constant TF can bedetermined.

Figure 1 shows the solution of a secondorder differential equation with twodifferent right hand terms. The timeconstants of the response and the “load”terms are indicated. From the figure, itcan be seen that, when a heeling momentis applied to the ship a dynamicamplification is to be expected when thismoment increases from 0 to itsmaximum value within the roll periodTR. When the moment increases muchslower - i.e. from 0 to its maximumvalue during several times TR - then amuch smaller dynamic amplification canbe expected.

Table 1 shows an estimate of bothconstants for an arbitrary chosen ferryand for a damage area with a probabilityof occurrence of 50 % (reference [10]).

Table 1 Estimate of Time Constants TF

(Water Ingress Through a Damage Area) andTR (Roll Period) for an Arbitrary ChosenCase

From this table it can be seen that thetime constant related to the inflow ofwater may equal almost half of the rollperiod. Therefore a dynamicamplification is to be expected. Thisconsideration was the main motive tocarry out this project.

2. PHILOSOPHY

The aim of the work reported here wasto determine whether dynamicconsiderations are required whilejudging the damage stability of shipsduring water ingress. In order to reachthis goal a fairly straightforwardapproach was used. The next paragraphdescribes this approach.

Then on ship motions as well as on flowoff fluids is fairly well developed.Therefore it is feasible to develop acalculation method which can describeboth the roll motion of a ship and theflow of fluid. The method is to beverified with ingress experiments on asimple floating structure in laboratoryconditions, including the effect of rollmotions. Once the calculation method isverified, a systematic parameter studycan be carried out on actual ships. Onthe basis of the parameter study,conclusions may be drawn with regard tothe need to include dynamicconsiderations while judging damagestability. Figure 2 shows this philosophyschematically. This paper covers the firstfour tasks, up to and including theverification.

3. THE CALCULATION METHOD

3.1. EQUATION OF MOTION

Both the vertical immersion and the trimdue to the water ingress are determinedquasi statically, by interpolation basedon the ship’s hydrostatic data. Nodynamics are taken into account.

The roll motion however is determinedincluding dynamic effects. To this endthe following equation of motion with

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one degree of freedom is used. Couplingeffects with sway and yaw motions areneglected as yet.

( ) kxx McbaI =+++ φφφ 444444&&&

Equation 1

where:

xxI mass moment of inertia of the dry ship,

44a hydrodynamic mass moment of inertia due to the presence of water,

φ&& angular acceleration of roll angle,

44b roll damping coefficient,φ& angular velocity of roll motion,

44c righting moment coefficient,φ angle of roll,

kM inclining moment.

Sections 3.2, 3.3 and 3.4 give someconsiderations with regard to the left-hand side terms of equation (1). Section3.5 elaborates on the heeling moment.

3.2. SHIP’S MOMENT OF INERTIA

The mass moment of inertia may bedetermined, by extending the ship’smass calculation with a radius for eachmass item. Some approximate methodsare available as well [5]. Thehydrodynamic mass moment of inertiamay be determined in several ways.Some simple estimation methods areavailable [8]. More elaborate methodsare based on two [61 and three-dimensional potential flow methods.However the most accurate way ofdetermining ( )44aI xx + is by performinga roll decay test. The calculated rail

motions as presented in Chapter 5 werebased on the latter approach.

3.3. DAMPING

Because of viscous effects, thedetermination of the damping coefficientis mainly based on empirical methods[7]. Generally, only a small percentagemay be determined by applying potentialflow theory, whereas the largercontribution originates from viscouseffects. In the calculation model thedamping coefficient 44b is assumed toshow a linear relation with the railvelocity. This assumption is acceptablesince most of the damping originatesfrom friction forces, which vary in aquadratic way with the roll velocity.Hence the following formula holds:

φφφ &&& '4444 bb =

Equation 2

Here again a roll decay test will yield themost reliable figures for damping. Itshould be noted that the dependency ofthe damping coefficient 44b on the rollvelocity disturbs the linearity of theequation of motion.

3.4. RIGHTING MOMENT

The righting moment may be determinedin a rather straightforward manner.

( )φρφ

φ sin44 GNgdd

c ∇=

Equation 3

where:

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ρ density of water,g acceleration of gravity,∇ displaced volume of ship,

φGN metacentric above C.o.G. of ship,φ roll angle.

φGN is usually available fromhydrostatic calculations.

It should be noted that the rightingmoment coefficient 44c (in fact a spring“constant”) depends on the roll angle,which disturbs the linearity of theequation of motion.

3.5. HEELING MOMENT

The heeling moment kM may bedetermined by a summation of theheeling moments caused by the weightof the fluid in each compartment.

∑=

=nc

iiik YGVM

1

Equation 4

with:

kM heeling moment,ρ density of water,g acceleration due to gravity,

iv volume of water in each damaged compartment i due to water ingress,

iy heeling lover of water volume in compartment i ,

nc number of compartments.

The volume in each compartment iscalculated by applying Bernoulli’s law

for both the water flow and the airflowthrough each orifice *).However, two adjustments are made:1. The variation of the hydrostatic

water pressure to the height of theorifice is taken into account bysubdividing the orifice intohorizontal strips. The flowcontribution of each strip iscalculated separately followed by asummation of the contributions of allstrips.

2. In order to account for the pressureloss through orifices, a pressure losscoefficient is introduced.

Hence the water flow through each flowstrip is determined with the nextformula.

AK

PQi ⋅

⋅∆⋅

=ρ

2

Equation 5

where:

iQ volume of water flow,P∆ pressure loss through strip,

K pressure loss coefficient,ρ density of water,A sectional area of flow strip.

The airflow through each strip isdetermined with a similar formula. Inorder to cater for the compressibility ofthe air the density is not used any more.The air pressure in each compartmentcan be derived from the theorem ofBoyle - Gay Lussac. Thus the followingformula is derived.

AKPPTRP

Q 221

11 ⋅

⋅+⋅⋅∆

=

Equation 6

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where:

1Q volume of airflow,

1P∆ pressure loss through strip,R specific gas constant of air,T temperature of air,

1P pressure at “front” of strip,

2P pressure at “rear” of strip,K pressure loss coefficient,A flow area of flow strip.

4. MODEL TESTS

4.1. INTRODUCTION

As mentioned in Chapter 2, thecalculation model was verified byexperiments. These experiments werenecessary mainly because of tworeasons:1. The calculation model needed to be

verified.2. Few data were available on pressure

loss coefficients.

Since the trimming motion was expectedto behave quasi statically, this motionwas eliminated by using a test modelwhich was symmetrical about theamidships. In fact this assumptionrequires an experimental justification aswell, however this was not carried out inthis project.

The dynamic behaviour of the test modelhad to be “ship-like” with regard to thefollowing aspects:1. the hydrostatic forces and moments,2. the (hydrodynamic) mass moments

of inertia and hydrodynamicdamping,

3. the flow of water into the damagedcompartments and

4. the flow of water between thecompartments and the cross duct.

These aspects called for a fairly largetest model. Moreover the sensitivity ofthe pressure transducers also imposedlower limits to the size of the test model.However on the other hand there werelimitations to the size of the modelbecause of the size of the test basin.

4.2. MODEL DESCRIPTION

Since wing tank – cross-ductconfigurations are used frequently; thisconfiguration was also built into the testmodel. The actual dimensions of thetanks and the duct were scaled downfrom an existing ferry, however somedeviations had to be made because ofpractical reasons.Figure 3 shows the duct configuration.The hull form was chosen rectangular,because no favourable resistancecharacteristics are required and becauseof costs. The actual dimensions aredictated by the dimensions of the testbasin i.e. the width of the towing tank.Further details are shown in Table 2.

Length, L 3.000 mBeam, B 2.100 mDepth, D 1.250 mDraught , T 0.625 mLength of wing tank, tl 1.000 mBreadth of wing tank, tb 0.400 mHeight of wing tank, th 1.250 mLength of cross-duct, dl 1.400 mBreadth of cross-duct, db 0.200 mHeight of cross-duct, dh 0.400 m

Height of CoG, KG 0.750 m

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0.800 mMass of the model(displacement intact), iV 3937.5 m3

Moment of inertia of drytest model (dry), xxI **) 1970 kgm2

Table 2 Characteristics of the Test Pontoon

4.3 VARIABLE AND MEASUREDPARAMETERS

Since several parameters will affect theroll motion due to sudden water ingress,it was considered to be important tocarry out tests where some of theseparameters were varied. Thus the resultsof such measurements could be used tocheck the results obtained bycalculations. Flow calculations throughcross ducts assume a stationary flow.However flow phenomena due to suddenwater ingress are far from stationary. In

order to obtain a preliminary idea of theerror introduced by this assumption,special attention was paid to the flow ofwater into the test model and through thecross-duct.

The following parameters were varied:• size of damage orifice,• height of orifices between wing tank

and duct, height of orifices in theduct,

• size of the air orifices in the top ofthe wing tanks,

• configuration of the cross-duct,• height of the centre of gravity, KG .

By carrying out calculations whilevarying the parameter values, avalidation of the calculation model couldbe accomplished. Table 3 shows areview of the actual parameter values.

Table 3 Review of Parameter Variation (See Figure 4 as well)

Please note that the value of the intactdisplacement, mass moment of inertia,damping and trim ware not varied.

The following parameters weremeasured:• angle of roll,

• water pressure at the bottom of eachcompartment,

• air pressure at the top of eachcompartment and

• water levels in each compartment.

The actual locations of the gauges areshown in Figure 3.

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4.4 EQUIPMENT AND TEST SET UP

Data were recorded both in a digital wayand an analogue way.

Air pressures and water pressures weremeasured with pressure gauges, whichwere in contact with the top of the tankvia small tubes. Thus the gauges couldremain outside the tank.

Water levels wore measured with tworesistance wires per tank as is often usedto measure wave heights at the bowduring sea keeping experiments.Unfortunately these level gauges showeda non linear characteristic.

The angle of roll was measured with aninclinometer, which was very accurate.

Water flows and velocities were notmeasured. They were derived from thewater the level measurements. From thelevel measurements, the increase ofwater volume in each tank could bedetermined. The difference betweenvolume increases yielded the actualwater flow through an orifice.

The time plots of the flow rates showeda rather erratic character. Therefore asmoothing routine was applied on theraw data of the flow rate before theycould be used to derive pressure losscoefficients. Pressure data ware treatedin the same way.

5. RESULTS OF MEASURE-MENTS AND CALCULATIONS

Some of the input data - required tocarry out the calculations - weredetermined experimentally.

This applies in particular to:• mass moment of inertia 44aI xx + ,

• damping coefficient '44b ,

• pressure loss coefficients K .

These properties were determined in thecase where the independent variableswere set as shown below:

centre of gravity above base, KG 0.747 marea of damage orifice, Ai 0.126 m2

cross sectional area comp. 1 0.080 m2

cross sectional area comp. 2 0.055 m2

cross-sectional area comp. 3 0.080 m2

orifice area A, AA 0.027 m2

orifice area B, AB 0.027 m2

orifice area C, AC 0.027 m2

orifice area D, AD 0.027 m2

area of air hole 1, A1 0.001 m2

area of air hole 2, A2 0.001 m2

( )44aI xx + and 44b were determinedfrom the results of a roll decayexperiment. The pressure losscoefficients used were determined bytrial and error in such a way that thecalculated roll motion curve and themeasured roll motion curve fitted best.The height of the centre of gravity, KG ,was determined by incliningexperiments. Once these properties wereestablished they were kept constantthroughout all other calculationscovering other damage orifices, othercross duct dimensions and another KG -value.

5.1. ROLL MOTION

Table 4 gives a review of some of thecharacteristics of the roll versus timecurves.

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Table 4 Comparison of Calculated andMeasured Characteristics of Roll VersusTime (M refers to measured and C refers tocalculated).

Figure 4 up to and including Figure 8present some plots of both the calculatedand the measured roll motions as afunction of time. Moreover Figure 9shows the influence of the area of thedamage orifice area on the maximumroll angle.

5.2. PRESSURE LOSSCOEFFICIENTS

From the measurements, pressure losscoefficients were determined as well.This was carried out for run 53 onlywhere:

KG : 0.750 miD : 0.400 m

duct height SB: 0.275 mduct height at CL: 0.400 mduct height PS: 0.275 morifice height A: 0.225 morifice height B: 0.225 m

orifice height C: 0.225 morifice height D: 0.225 marea airvent SB: 0.002513 m2

area airvent PS: 0.002513 m2

Some results are shown in Figure 10 andFigure 11.

It was found that the pressure losscoefficients depended upon the flowspeed. This dependency is not mentionedin literature.

Table 5 presents both the values of thelower asymptotes of the K - flow speedcurves and the values as used in thecalculations.

Table 5 Pressure Loss Coefficients, Values asUsed in Calculations (Air Loss Coefficientfrom [9])

The values as used in the calculations,were determined by trial and error untilin the case of run 53 the calculatedmaximum roll angle and the levelingtime agreed with the measurement.During all other calculations thesevalues were kept constant.

6. CONCLUSION

6.1. MATHEMATICAL MODEL

The mathematical description of the rolland flow phenomena seems appropriate.Figure 4 to Figure 8 show bothcalculated and measured roll responsecurves, while Table 4 gives a review.

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Please note that the coefficients, as usedin the calculations were determined insuch a way that the roll motion of run 53was described best. Subsequent thecoefficients were kept constant.

6.2. PRESSURE LOSSCOEFFICIENTS

Pressure loss coefficients, as measured,show a strong flow speed dependency.Current literature ([8], [9] and [10]) doesnot mention this dependency. Probablythe dependency is due to the fact thatduring the tests the flow of water is farfrom stationary, which is a requirementfor applying the concept of pressure losscoefficients. Moreover inertia effects inthe fluids are neglected. The actualfigures vary within a large range (0.6 -40.0).

6.3. OVERSHOOT

From the measurements as well as fromthe calculations it can be concluded thatthere is a significant overshoot in theinitial roll angle just after the wateringress has started. This overshoot isentirely due to inertia effects associatedwith the roll motion. Thus it can bestated that the dynamics of the rollmotion cannot be neglected whenjudging the damage stability of ships. Across duct does not seem to affect thisovershoot significantly (see Table 4).

6.4. FURTHER RESEARCH

During discussions about this project, itwas brought up that sway and yawmotions could be of significantimportance. In the calculation model as

reported here these motions areneglected. Some justification may befound in the reasonable agreementbetween calculated and measuredresults. However a systematicverification should be carried out.The choice of the pressure losscoefficients is of importance for both themaximum roll angle and the timerequired to level out. Unfortunately themeasured coefficients are not in linewith literature. Moreover measurementsshow that these coefficients vary withflow speed, which is not reported inliterature either. Therefore it is proposedto investigate this matter moreextensively. It should be noted that onlyone of twelve measuring runs wasanalysed with regard to this aspect dueto budget limits.

The results of the measurements and thecalculations refer to a rectangularpontoon. It is essential to use thecalculation method on actual ships. Oncethis has been done final conclusions maybe drawn with regard to dynamic effects.

It seems useful to link the computerprogram as described here with existingprograms on hydrostatic data and cross-curves. It is also useful to extend thecurrent program with subroutines, whichdetermine added moment of inertia anddamping or establish a link withhydrodynamic programs, which cancalculate such parameters.

*) Apart from the air flow calculations,this approach is taken from the IMCOrecommendations for the determinationof minimum cross-duct areas [101.

**) Calculated with: ( )22

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1DBiVxxI += .

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ACKNOWLEDGEMENT

The authors wish to record theirappreciation of the work carried out bystaff members of the Shiphydro-mechanics Laboratory of the DelftUniversity of Technology. A specialword of thanks is addressed to Mr. E.Vossnack (former head of designdepartment of Nedlloyd Fleet Services),Mr. H. Vermeer (NetherlandsDirectorate General of Shipping andMaritime Affairs), Mr. D. Spanjer andMr. J. Uwland (TNO). Finally, theauthors like to thank Mr. A. van Strien(Delft University of Technology), whohas been a great help with theperformance of the experiments.

REFERENCES

1. Spouge, J.R., “The TechnicalInvestigation of the Sinking of theRO/RO Ferry EUROPEANGATEWAY”, RINA Mar., No. 3,1986.

2. Boilwood, D.T., “Ro/Ro Ship Sur-vivability; Comments on DamageStability Modelling”, Ro/Ro-88,Gothenburg, 7-9 June 1988.

3. Braund, N.A., “Damage Stability;Research for the Future”, SafeShip/Safe Cargo Conference,London, 1978.

4. Dand, I.W., “Hydrodynamic Aspectsof the Sinking of the Ferry HERALDOF FREE ENTERPRISE”, TheNaval Architect, May 1989.

5. Peach, et al, “The Radii of Gyrationof Merchant Ships”, North-EastCoast of Engineers and ShipbuildingTransactions, June 1987, Page 155 -117.

6. Journée, J.M.J., “Seaway-Delft, UserManual and Theoretical Backgroundof Release 3.0”, ShipHydrodynamics Laboratory, DelftUniversity of Technology, ReportNo. 849, January 1990.

7. lkeda Y. et al, “Prediction Methodfor Ship Rolling”, Department ofNaval Architecture, University ofOsaka Prefecture, Japan, Report No.00405, 1978.

8. Blevins R.O., “Applied FluidDynamics Handbook”, von NostrandReinhold Company, New York,1984.

9. Ireland N., “Damage Stability ModelTests”, Project No. 34620, BritishMaritime Technology, May 1988.

10. IMCO, “Explanatory Notes to theRegulations on Subdivision andDamage Stability of Passenger Shipsas Equivalent to Part B of Chapter 11of the International Convention forSafety of life at Sea, 1960”, ANNEXII, STAB XV/11.

11. Delft University of Technology,“Numerical Analysis C1”, LectureNotes (in Dutch).

NOMENCLATURE

A flow area, m2

44a hydrodynamic moment of inertia, kgm2

B beam, m

44b hydrodynamic damping coeff., Nms/rad'

44b hydrodyn. damping factor, Nms 2/rad2

db breadth of duct, m

tb breadth of wing tank, m

44c spring coefficient, Nm/ rad

CoG centre of gravityD depth, m

P∆ pressure loss, N/m2

iD diameter of damage orifice, m

g acceleration of gravity (9.81), m/s2

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φGN metacentric height, m

( varying with angle of heel)

th height of wing tank, m

xxI ridgid moment of inertia of ship, kgm2

K pressure loss coefficient, N/m2

KG height of CoG above base, mL length of ship, m

dl length of duct, m

tl length of tank, m

kM heeling moment, Nm

nc number of compartments

φ&& angular roll acceleration, rad/s2

φ& angular roll velocity, rad/s

φ roll angle, rad

Q water flow, m3/s

R gas constant, J/(kgK)ρ density of water, kg/m3

T draught, m

iu approximative value by Euler

integrationV volume of displacement, m3

iv2 approximative value by Euler

integration

iv approximative value by Euler

integration

iy exact value

dh height of duct, m

Figure 1 Rough Estimates of Roll response to Sudden Water Ingress

A: TG = 10 s, B: TF = 40 s

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Figure 2 Schematic Representation of the Philosophy

(* indicates tasks covered in this paper)

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Figure 3 Cross-Section and Top View of Testmodel

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Figure 4 Roll Motion Run 43 (Decreased Duct Area)

Figure 5 Roll Motion Run 51 (Area of Vent. Holes Increased)

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Figure 6 Roll Motion Run 53 (Initial Configuration)

Figure 7 Roll Motion Run 59 (Damaged Orifice Decreased)

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Figure 8 Roll Motion Run 120 (Height of CoG Increased)

Figure 9 Maximum Roll Angle Versus Area of Damage Orifice

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Figure 10 Pressure Loss Coefficient as Function of Flow Velocity, Damage Orifice

Figure 11 Pressure Loss Coefficient as Function of Flow Velocity, Orifice C

(see Figure 3)