199

1 INTRODUCTION

Oneoftheparametersaffectingshipmaneuveringin

restricted waterways is the influence of quay walls,

channel banks or the stationary or moving ships in

the vicinity. The hydrodynamic forces of ship

interactionwithboundariesinrestrictedwatershave

beenknowntosailorsforyears.Whenashipmoves

along awall the sway force and yawing moment is

producedtha

twouldresulttodynamicinstabilityof

shipsteering.

Thephysicalconceptofinteractionisbasedonthe

transformationofenergyinfamousknownmodified

Bernoulli equation. According to Bernoulli equation

thesummationofpotentialandkineticenergyofflow

part

icles on a streamline remains the same. As the

ship moves in the sea high pressure regions is

induced in the fore and aft part of the ship. It is

obvious that the pressure of the aft is less than the

pressureofforeduetothefrictionalongthehull.The

watertha

tdisplacesintheshipfore,flowstowardthe

aftunderthehull.Thereforethepressuredropsinthe

middle of the hull. If a ship is located in a certain

enoughdistance ofthebank,it feelsnoeffect of the

bank.Butiftheshipmovesal

ittletowardthebank,a

lowpressureregionisproducedamongtheshipand

thewall.

The bank effect phenomena depends on various

parameterssuchasbankshape,waterdepth,distance

of the ship to bank, ship characteristics, ship speed

and propeller performance. There is a limit for ship

navigation in the waterway tha

t this limit could be

obtained by analysis of bank effect. It should be

mentionedthatthebankmaterialcanaffectthebank

effecttoo.Forexamplethebankeffectismoreinthe

sandybanks.

Therehavebeensomanyexperimentalstudiesof

bank effect inthe literature. Fujino 1986studied the

effect of water depth, distance to ba

nk, ship speed,

bank slope, propeller action, drift angle and rudder

Experimental Study of Forces Exerted on Ships Due to

the Vertical Walls of Navigation Channels

M.FathiKazerooni&M.S.Seif

SharifUniversityofTechnology,Iran

ABSTRACT: Ship maneuvering in restricted waters of harbor basins and navigation channels had been the

mainconcerninrecentyearsduetosuddenincreaseofship’ssize.Whentheshipentersanavigationchannel

thelateralboundaryofthechannelexertsatransverseforceandturningmomentontheshiphull.Theseforces

aresoimport

antintheanalysisofsafetyofshipnavigationinthechannels.Shipmodeltestinthetowingtank

is a reliable methodto evaluatethese forces.Therefore systematicmodel testsare held for modeling of the

forces exerted on the tanker ship and dhow model t

raveling alongside a vertical wall. A database of the

interactionforcesisdevelopedandthespecifichydrodynamiceffectsrelatedtothephenomenaarediscussed.

Theresultscanbeusedforsimulationofshipmaneuveringandassessmentofsafetylimitsfornavigationof

shipsalongsidethequaywallsandbreakwaters.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 9

Number 2

June 2015

DOI:10.12716/1001.09.02.06

200

angle on the hydrodynamic loads on the ship

maneuvering in the approach channel through the

model test of tanker and cargo ships. Eda 1971

represented the hydrodynamic coefficients of tanker

ship for three ratios of water depth and distance to

nearestbank.Norrbin1974,1986hadacomprehensive

studyonship

maneuveringingeneralandbankeffect

indetail.Thesetestsarebasedonatankermodeland

empiricalformulaeare presentedforvertical,sloped

and submerged banks. Fuerher and Romisch 1978

discussed hydrodynamic forces, trim, sinkage and

channel reverse flow. Comprehensivemodel testsof

generalcargoshipandcontainercarrier

inperformed

byDand1981.

The result of captive model tests formulates the

forcesexertedonthevesselandtheycanbeusedin

development of maneuvering computer simulations

asindicatedbyGronaz.

In recent years CFD approach is used for

calculationofbankeffects.Zhouetal(2012)proposed

potential

 theory to estimate the forces on ships in

restricted water. However Wang et al (2010)

emphasized that viscous effect should be accounted

for through Reynolds averaged Navier‐Stokes

equations.

SomereferencesasLee2008haveassumedthatthe

freesurfaceisrigidandshownthattheratioofship

draught

toquaywalldepthcaninfluencetheforces.

It is completely obvious that the subject of ship‐

bank interaction is studied in only few research

institutesallaroundtheworldandlittleexperimental

data is published. Empirical expressions that

formulatetheinteractionforcesasafunctionofship

parametersareso

neededinapplication.Therelations

that are presented so far are based on few

experimentsandspecificmodelsaretested.Therefore

the reliability of these expressions is in doubt when

used under different conditions. Therefore the

systematicmodel tests of bankeffectin towing tank

areperformedtodevelopthe

experimentaldatabase.

2 RESEARCHMETHODOLOGY

2.1 Bankeffect

Almost all the sailors have experienced the suction

forceYandyawingmomentNfromthenearbankas

ship navigates in shallow channels (Figure 1). The

forceexertedfrombankhasaninfluencepointthatis

neartheshipsternbecausecommonly

theshipstern

isbluff.



Figure1.forcesexertedonashipmovingalongabank

2.2 ExperimentalFacilities

The towing tank in Sharif University of Technology

has capabilityto perform ship hydrodynamic model

testing. In order to evaluate forces exerted in the

modelinthevicinityofverticalwallinshallowwater

itisessentialtoreducethewaterdepthandship‐bank

distance.

Themain

concernofrestrictedwatertestingisthe

towing tank dimensions that this towing tank has

25mlongand2.5mwide. 

Artificialbottomandsidewallismanufacturedby

plasticplatesthatarefittedonthealuminumframes

toensurethesufficientstrengthasshowninfigure2.



Figure2.themanufacturedrestrictedwaterway

The vertical quay length is 8m and the shallow

wateris extendedin10mlength of the towing tank.

Theshipmodelisattachedtothecarriageunitandis

restrained in all the degrees of freedom except

sinkageandtrimdirections.

2.3 ShipModels

Two types of ship modelsare

 used here inorder to

compare the results and describe the effect of hull

formontheforcesexertedonthevesselinthevicinity

ofverticalwall.Accordingtoabovediscussionfinally

ithadbeendecidedtouseamodeloftankershipas

described in table1 and a

traditional Persian Gulf

cargovesselwhichiscalledDhowasintable2.

Table1.Tanker&modelspecifications

_______________________________________________

Tanker  ModelTanker

_______________________________________________

Length(m)1761

Breadth(m)310.17

Draught(m)  90.05

Displacement  41523tons  7kg

n0.06‐0.27

_______________________________________________



Table2.Dhow&modelspecifications

_______________________________________________

Dhow  Dhowmodel

_______________________________________________

Length(m)280.71

Breadth(m)8.870.225

Draught(m)  1.970.05

Displacement  306.5tons  5kg

n0.06‐0.27

_______________________________________________



201

Figure3andFigure4showsthemodelsthathave

beenused.



Figure3.Tankermodel



Figure4.Dhowmodel

2.4 ModelTestprocedure:

Modeltestsareperformedtoevaluatethebankeffect

ontankeranddhowshipinthetowingtankofSharif

University of Technology. The bank is considered

vertical here and different distances of ship to bank

are studied. Model tests are performed in shallow

watercondition.In

eachcasethewaterdepthistwo

timesofshipdraught.Thechangesofforcesinduced

by vertical bankwould be greater inshallow water.

The magnitude of induced sway force and yawing

momentisafunctionofshipspeedtoo.Figure5and

Figure6showthemodeltest

oftankershipanddhow

respectively.Theratiob/Bisequalto3.



Figure5.Tankermodeltestinvicinityofverticalwall,Left

Moderatespeed,Righthighspeed



Figure6.Dhowmodeltestinvicinity of vertical wall, Left

moderatespeed,Righthighspeed

3 RESULTSANDDISCUSSION

Sway force and yawing moment induced from

vertical bank have a great effect in maneuvering

analysis of ships in confined and laterally restricted

waterways. It is common to express the sway force

and yawing moment in non‐dimensional form Y/m

andN/mLinwhichYisthe

swayforceinkgfandm

isthevesselmassinkg,Nisyawingmomentinkgf‐

mandListhelengthbetweenperpendicularsinm.

The non‐dimensional Sway force exerted on the

tanker ship model in different forward speeds is

plotted in figure 7 for various

distances to vertical

wall. The respected induced yawing moment is

plottedinfigure8.



Figure7.Theswayforceexertedonthetankershipmodel

inthevicinityofverticalwall



Figure8. The yawing moment exerted on the tanker ship

modelinthevicinityofverticalwall

The hydrodynamic forces increase by Froude

number significantly according to diagrams. This

202

behavior is expected logically. The negative sway

force is towards the bank and the negative yawing

moment tends to increase the distance of ship bow

from the bank according to force measuring unit

conventions.

In smaller distances to bank the sway force is

towardsthebankanditsdirectionchanges

astheship

speed and distance to vertical bank increases. The

sway force sign changes approximately in a Froude

number equal to 0.15. The test results demonstrate

that this point is delayed as ship distance to bank

increases. In other words the sway force is towards

the bank in narrow

distances and its direction is

reversedasthedistanceincreases.

If we neglect the once positive yawing moment

measured,inalltherangesofspeedanddistance to

bank that is tested in this research, the yawing

moment tends to further the ship bow from the

verticalbank.

The sway force

 is considerable for tanker ship

modeltoo.Inintermediateforwardspeedranges,the

swayforceincreasesasthedistancetobankincrease.

Thisbehavioriscompletelynotexpected.Inthefirst

sightonemaythinkthatthebankeffectdecreasesas

theshipdistancetobankincrease.Itiscompliant

with

ourknowledgeofcommonfluiddynamics.Thisfact

isthrough untilshipwave making invicinity of the

bank is not considered. It should be mentioned that

bankeffectstronglydependsontheinteractionofthe

ship and the reflected waves from the bank. So the

wave making pattern and

 its reflection from nearer

bank and ship‐reflecting wave interaction is an

influential parameter to the forces exerted on the

vessel.Assumethattheshipdistancetobankislarge

enough. When the ship moves forward it makes a

wave pattern that propagates oblique towards the

bank. The waves incise

the bank and reflect.

According to model tests when the ship distance to

bankislargethesereflectingwavesdampbeforethey

reach the vessel. When the ship distance to bank is

smallthewavesdonotgenerateinthegapbetween

shipandbankandtheforcesexertedonthe

vesselare

mainly due to pressure changes and viscous effect.

Themodeltestsdemonstratethatwhenthemodelis

so close to the bank no considerable wave system

generates.

The critical condition occurs in the case that the

shipisinanintermediatedistancetothebank.Inthe

model

tests held in the towing tank for tanker ship

modelthisdistanceisabout4timesshipbreadth.In

this case the ship waves reflect from the bank and

coincide with the ship. If the ship speed is large

enough the vessel moves faster than the reflected

waveandthiswave

patterncannotaffectthevesselso

much.Iftheshipspeedislowwhenthewavesreflects

fromthe bank and comeback towards ofthe vessel

thevesselisnotpresent onthat location.Finallythe

most critical case happens when the ship speed is

medium. In this case

the reflecting wave system

affectsthehullcompletelyandtheamountofinduced

swayforceandyawingmomentisconsiderable.

Themodeltestsarerepeatedforthedhowmodel

andswayforceandyawingmomentmeasuredinthe

testsareplottedinthefigure9and10.



Figure9.TheswayforceexertedontheDhowmodelinthe

vicinityofverticalwall



Figure10.TheyawingmomentexertedontheDhowmodel

inthevicinityofverticalwall

The point that sway force direction changes is

important in this casetoo. For the dhow model this

point is about Froude number 0.1. The sway force

exerted on the tanker ship and dhow model is

comparedinfigure11forbankratio4.



Figure11. comparison of non‐dimensional sway force

exertedontankeranddhowmodelinbankratioof4

Thetanker model bottomisso flat but the dhow

modelhasdeadriseangle.Thereforeitwouldbesome

flowsuctioninthedhowbottomandhydrodynamic

loads would be smaller compared to tanker ship

model.

203



Figure12.comparisonofnon‐dimensionalyawingmoment

exertedontankeranddhowmodelinbankratioof4

4 CONCLUSION

Determination of forces exerted on the ships is so

importantfromthemaneuveringestimationpointof

view.Shipsexperiencedirectionaldynamicinstability

during moving forward alongside banks and quay

walls. In order to analyze these phenomena it is

essential to obtain suitable formulae for the forces

exertedon the

ship hull.These forces areapplied in

the ship maneuvering equations of motion and

dynamic stability of the equations are examined. In

this paper the model test and experimental fluid

dynamicmethodisrecognizedasa powerfultool to

derivetheforcesinducedonthehullduringentering

restricted waterways.

The results of model tests

dependonthemodelsusedtostudytheproblem.The

datameasuredduringthetestsareapplicableonlyif

theshiphullformisclosetohullstestedinthisstudy.

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