447

NOMENCLATURE

BP= baseplane

b= breadthofdoublesides

GM=metacentricheight

GZ=rightinglever



 GM



–initialmetacentricheightoftheintactship

x= transversemomentofinertiaofthefreesurfaceof

floodwater

K= volumetricstiffnessoftheship

l= lengthofcompartment

C= differentialmetacentricradius

w= metacentricradiusoffloodwater

T= draughtoftheintactship

V=volumedisplacement

v= volumeoffloodwater

w= heightofcentreofgravityoffloodwateraboveBP

J= incrementoftransversemomentofinertiaofthe

undamagedwaterplaneduetosinkage

1 INTRODUCTION

Pawłowski & Laskowski (2014) discuss the effect of

various subdivision arrangements of ro‐pax vessels

ondamagestability.Theshipinvestigatedhadtheold

typeofsubdivision,asinFigure1,confinedtospace

below the bulkhead deck (car deck), densely

subdividedbytransversebulkheads.

Mostofthese compa

rtments werevoid,not used

forthecarriage of any cargoorsupplies. Above the

cardeck,therewasnoreservedbuoyancy.Thistype

ofsubdivisionwascommonuntilendofthe1990s.

Nowadays, space below the car deck is frequently

utilised for ro‐ro cargo in the form of a long lower

hold (LLH), stretching for ab

out half of the ship

length(seeFigure2).Ithasdoublesides,subdivided

bytransversebulkheads,usuallyterminatedatthecar

deck,andnotransversebulkheadsincargospace.For

better safety, the double sides should extend above

the car deck; see examples discussed by Pawłowski

(1999),andshowninRINA(2001).

Effect of Watertight Subdivision on Subdivision Index

for Medium Size Ro–Ro Passenger Ferries

M.Pawłowski&A.Laskowski

PolishRegisterofShipping,Gdańsk,Poland

ABSTRACT:Ro‐paxvesselsshouldfulfiltherequirementsofthecurrentharmonisedSOLASConvention.The

studyanalysestheeffectofvariousro‐paxvesselsubdivisionarrangementsonthesubdivisionindex.APolish

ferrywaschosenasagenericshiptoperformthestudy.Forillust

rationofdamagesurvivability,theattained

subdivisionindexAwascalculatedforanumberofmodifiedconfigurations.Thearrangementsincludedsingle

anddoublesidesaboveandbelowthecardeck,withandwithoutadoublebuoyantcardeck.Theconclusions

ofthestudycanbeusedinthedesignofnewro‐pa

xvessels.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 11

Number 3

September 2017

DOI:10.12716/1001.11.03.08

448



Figure1.Watertightsubdivisionofoldro‐roferries



Figure2.Watertightsubdivisionoftheinvestigatedro‐pax



The current study is performed using a Polish

ferryasgenericship,showninFigure2,builtin1990,

still in operation, whose main particulars are as

follows:

 overalllengthLOAm,

 subdivisionlengthLsm,

 lengthbetweenperpendiculars Lppm,

 breathBm,

 depthHm,

 designdraughtTm,

 widthofdoublesidesbB/m,

 heightofdoublebottomhb

B/m,

 heightofCGaboveBPKGm,

 metacentricheightGMm,



blockcoefficientcB,

 numberofpersonsonboard N=314,

 requiredindexofsubdivision R=0.69058.

The ship fulfils the requirements of the IMO

resolutionA.265(1974),thepredecessorofthecurrent

harmonised SOLAS Convention (2009). The said

resolutiondoesnotrequirereservedbuoyancy

above

thecardeck.InthecaseofaLLHbelowthecardeck,

thewidthofthedoublesidesshouldbeequaltob=

0.2B,whiletheheightofthedoublebottomshouldbe

atleasthb=0.1B.Inviewofdamagesafety,theheight

ofthedouble

bottomshouldbeaslowaspossible.A

minimum height of the bottom for the ship

investigatedaccordingtoPRSequalshb=1.025m.

2 NUMERICALEXAMPLES

2.1 Example1

Forillustrationof damage survivability, theattained

subdivisionindexAwillbecalculatedforanumber

of modified configurations.

The generic one, treated

asExample1,isshowninFigure2andFigure3.The

shiphas four decks.Deck 1 is theinner bottom and

Deck2isthecardeckataheight7.9m,Deck3ata

height13.2m,andDeck4ataheight

18,2m.Ballast

tanks in the double sides and double bottom are

connected to each other, creating thus a symmetric

space(Figure3),beneficialinthecaseof flooding.It

allows for a rapid cross‐flooding if the tanks in the

double sides are provided with efficient air‐escapes

(vents)

placedatthesides,closetothetopoftanks,to

eliminate detrimental air cushions that may occur

during flooding. The same should apply to cargo

space on Deck 1. To increase further real safety in

damage condition, the car deck should be equipped

with down‐flooding arrangements, thus making the



car deck transparent for floodwater and air. The

449

down‐flooding arrangements prevent the

accumulationofwateroncardeck,whichisthemain

reasonforthecapsizingofdamagedro‐roships.For

thegenericship,accordingtotheoriginaldesign,the

indexofsubdivisionA=0.73015,whichismorethan

therequiredvalueR=0.69058.



Figure3.Cross‐sectionoftheoriginaldesign

2.2 Example2

The ship as above, but with Deck 2 as a pontoon

creatingabuoyant1600mmdoubledeckofthesame

as the height of deck girders, is shown in Figure 4,

dividedlongitudinallyatthePS.SpacesaboveDeck3

are not included in stability calculations, therefore



theywill not be shownfurther down. Atthe design

draught,theundersideofthebuoyantdeckismerely

0,4mabovethewaterline.Theattainedindexvalueis

now A = 0.74574, which is only marginally higher

thaninthepreviouscase.Thisisbecausethebuoyant

deckin

thiscaseremainsunderwaterovermostofits

lengthinthemajorityofdamagescenarios,duetothe

bow trim, thus insignificantly contributing to the

reductionofthefreesurfaceeffect.



Figure4.Cross‐sectionoftheshipinExample2

Theotherreasonisasmallresidualfreeboardand

thelackofreservebuoyancyabovethecardeck.

Ro‐ro ships, in general, have high deck girders

becauseofthelargeunsupporteddeckspans.Inview

oftheproblemofcargohandling,stowageisusually

restrictedtospacesbelowtheflanges

ofthesegirders.

There is an opportunity, therefore, to seal off the

spaceupwardsfromtheflangesofthedeckgirdersto

thedeckplatingtoformachamber(pontoon)thatcan

provide additional buoyancy, and depending on its

location,heightandextent,thatisofsomeadvantage

in terms

of damage survivability. The problem of

locatingthebuoyantdeckisafairlyinvolvedexercise,

discussed by Pawłowski (1999). Adding a pontoon

hardlychangestheweightoftheship.

TheRoroprobEUresearchproject(2000–2003)did

notaccountfortheoptionofabuoyantcardeck.Two

first ro‐pax

 vessels ever built in the world with a

double car deck were built at the Shipyard Nova in

Szczecinin2001,describedinBestShips(2001).They

incorporated the features discussed above. The

double deck appeared to be very effective on these

ships.

2.3 Example3

Ashipasin

Example2,butwithaddedwingtankson

Deck 2 of breadth b = 0.1B, extending to Deck 3

(Figure5).Inthiscasethereisasubstantialincreaseof

the index to the value A = 0.83255. As can be seen,

adding reserved buoyancy above the car deck

significantlyincreases

theindex.Andthisobservation

canbetakenasarule.



Figure5.Cross‐sectionoftheshipinExample3

2.4 Example4

AshipasinExample3,butwithcardeckraisedto8.1

m, resulting in change of deck height by 0,2 m.

Positioningof alltanks adjacenttodeck2is altered.

The height of the buoyancy pontoon changed from

1.60 m to 1.80 m. The subdivision

 index obviously

increasedtoA=0.86729.

2.5 Example5

Changes were introduced similar to those described

inthepreviousexamples,butwith nochangetothe

height of the car deck. They involved introducing a

sheerofthecardeckintheformofasegmentedline,

withknuckles

some⅓ofdecklengthfromtheends,

withariseofthedeckattheendsby1.00m.Alltanks

adjacenttoDeck2changedtheirpositionaccordingly.

ThesubdivisionindexincreasedtoA=0.87804.

450

3 FURTHERNUMERICALEXAMPLES

The study analysed in addition the impact of the

lengthofthelonglowerholdLLHonthesubdivision

indexanddecreasedheightofthedoublebottom.In

examples1a)to5a)computationswereperformedfor

alonglowerholdLLHlengthenedby4.2mtowards



the stern of the generic ship with the closing stern

framemovedfrom39.2mto35.0m.

In examples 1b) to 5b) the double bottom was

lowered from 2.40 m to 1.40 m, and the buoyancy

pontoonheightraisedfrom1.60mto2.00.

Therelationsbetweenparametersin

examples1‐5

weremaintained.However,thesubdivisionindexfor

theexpandedlonglowerholdLLHwassignificantly

lowercomparedtothegenericship.Loweringofthe

doublebottom,inpractice,hadnosignificantimpact.

Thetablesbelowpresenttheindicesofsubdivision

forparticulardesigncases.

Table1.Subdivisionindexforgenericshipparameters.

_______________________________________________

Nr ParameterA

_______________________________________________

1 Generic0.73015

2 Example1,pluspontoon1.6m0.74574

3 Asin2,pluswingtanksoncardeck0.1B 0.83356

4 Asin3,plusdeckraisedby0.2mto8.1m, 0.86729

pontoonheight1.8m

5 Asin3,plus1msheerofcar

deck0.87804

_______________________________________________

Table2.Subdivisionindexfororiginalshipparameterswith

lengthenedLLH.

_______________________________________________

Nr ParameterA

_______________________________________________

1a Genericship0.68307

2a Asin1a,pluspontoon1.6m0.69210

3a Asin2a,pluswingtanksoncardeck0.1B 0.79705

4a Asin3a.,plusdeckraisedby0.2mto8.1m,0.81254

pontoonheight1.8m,

5a Asin3a,sheerofcardeck

1m0.80055

_______________________________________________

Table3.Subdivisionindexfororiginalshipparameterswith

lowereddoublebottom.

_______________________________________________

Nr ParameterA

_______________________________________________

1b Genericship0.72476

2b Asin1b,pluspontoon2.0m0.73277

3b Asin2b,pluswingtanksoncardeck0.1B, 0.83243

4b Asin3b,plusdeckraisedby0.2mto8.1m,0.86086

pontoonheight2.0m

5b Asin3b,sheerofcardeck

1m0.87620

_______________________________________________

4 CONCLUSIONS

Theanalysisoftheindicesofsubdivisionforvarious

configurationsofthegeneralarrangementshowsthe

followingconclusions:

1 The long lower hold LLH under the car deck

contributes positively to the attained subdivision

indexA.Nevertheless,inthecaseofhulldamage,

symmetrical flooding achieved by cross

‐flooding

ofthe opposite sidetanks is recommended along

with an effective air venting system to eliminate

potentialaircushions;

2 An additional buoyancy pontoon under the car

deck slightly increases survivability measured by

thesubdivisionindex;

3 Side tanks of the width b = 0.1B significantly

increasethe subdivision

indexanddoesnotlimit

operationalcapacity of the ferry – space between

deckgirdersandsideframesisanywayuselessfor

thecarriageofro‐rocargo;

4 Another option for increasing the subdivision

indexistoraisetheheightthecardeck.However

suchasolutionisnotalways

feasible;

5 Sheerofaftandforecardeckenhancessafety,but

notasmuchasexpected;

6 ThelengthofthelonglowerholdLLHshouldbe

carefullysetasexcessiveextensioncouldleadtoa

considerabledropofthesubdivisionindex;

7 Theimpactofdoublebottomon

subdivisionindex

is negligible, supported also by work of Sonne

Ravn(2003).

REFERENCES

International Maritime Organisation. 1974. Regulations on

subdivision and stability of passenger ships (as an

equivalent to part B of chapter II of the 1960 SOLAS

Convention).London.

International Maritime Organisation. 2009. SOLAS

Convention,ConsolidatedEdition2009.London.

Pawłowski, M. 1999. Marine Technology, Vol. 36, No. 4,

Subdivisionof RO/ROships

forenhancedsafetyinthe

damagedcondition:194–202.

PawłowskiM.&LaskowskiA.2014.TransRINA,Vol.156,

Part A2, Intl J Maritime Eng, Effect of watertight

subdivisionondamagestabilityofro‐roferries:131–136.

RINA.2001,BestShipsof2001:46‐47.

ROROPROB.2000–2003.EUResearchProject,

FP5,DGXII‐

BRITE,Probabilisticrules‐basedoptimaldesignofro‐ro

passengerships.

Sonne Ravn, E. 2003. PHD Thesis, Probabilistic damage

stabilityofro‐roship.

