PREDICTION OF SHIP MANOEUVRABILITY OF AN 8000 TEU CONTAINERSHIP IN DEEP AND SHALLOW WATER: MATHEMATICAL MODELLING AND CAPTIVE MODEL TESTING

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1 EDICTION OF SHI MANOEUVABILITY OF AN 8000 TEU CONTAINESHI IN DEE AND SHALLOW WATE: MATHEMATICAL MODELLING AND CATIVE MODEL TESTING Katie Eloot (Flades Hydaulics eseach, Belgium) Mac Vatoe (Ghet Uivesity, Belgium) Guillaume Delefotie (Ghet Uivesity, Belgium) Abstact: The Flemish wateways authoities ae pemaetly coceed about safety of avigatio to the Flemish habous i ode to maitai thei peset positio i the Euopea shippig maket. Special attetio is paid to the effect of the costat gowth of ship dimesios, especially i the cotaie tade, o the safety of shippig taffic. Access to ad maoeuvig i habous ae chaacteised by a geat divesity of kiematical ad cotol paametes. I a captive model test pogam has bee executed with a 4.3 m model of a 8000 TEU cotaieship (scale :8) combiig thee distiguished dafts ad thee ude keel cleaaces fom deep to vey shallow wate. This test pogam coveig all possible combiatios of ship velocities ad popelle telegaph positios has bee used to evaluate hull, popelle ad udde foces to be icopoated i a maoeuvig simulatio model applicable i the fou quadats of opeatio. The ifluece of combiatios of daft ad ude keel cleaace o the fist quadat of opeatio (fowad motio, popelle ahead) will be discussed based o the chaacteistic dimesios of a tuig cicle. Sikage ad tim ae emakably iflueced by the ship s daft ad icease geeally with deceasig ude keel cleaace. The iceasig staight-lie stability with deceasig ship s daft, especially obseved i vey shallow wate, is pobably caused by this squat depedece ad the velocity depedet hull foce compoets. Although the udde is ot fully immesed at the smallest daft, diffeeces i udde foces ad coelatio paametes ae cocluded to be small. Fially, as some ucetaities exist about the scale effects, a sesitivity aalysis has to be executed i the futue to give some isight ito the depedece of the mathematical model o idividual foce compoets... BACKGOUND ABOUT CONTAINE TAFFIC TO FLEMISH HABOUS Belgium has fou majo pots of which two of them, the pots of Atwep ad Zeebugge, accommodate impotat hadlig facilities fo cotaieised goods. The pot of Atwep, oe of the most impotat Euopea pots i the Hambug-Le Have age, is accessible though the Weste Scheldt, a tidal estuay equiig sigificat dedgig effots to deepe ad maitai the avigatio chael. I 998, a secod deepeig pogam was completed which guaatees a tide idepedet access fo ships with dafts up to.60 m (38 ft). Duig the ext yeas a ew deepeig pogam will be executed to icease this value to 3.0 m (43 ft). Takig ito accout that the desig daft of the last geeatio of cotaieships is 4.5 m, the tidal age has to be used to guaatee the equied wate depth. The pot of Zeebugge has seveal temials which ca hadle ealy all types of cago ad coespodig taffic lies (LNG, cotaies, cas, oo, passeges). Cotaie taffic is of iceasig impotace; sice ecetly ew shippig lies call at Zeebugge with vessels up to 8500 TEU. Takig accout of the impotat ole of cotaie taffic fo both pots, a thoough kowledge of the behaviou of lage cotaie vessels i shallow ad esticted wates is equied to assess thei safety duig the appoach to ad the maoeuves i the habous. It is of impotace to cove a sufficietly lage age of loadig coditios, as the daft of cotaie vessels may vay sigificatly. Moeove, a lage age of ude keel cleaaces should be coveed, takig accout of the tidal age ad the local depth vaiatios i the access chaels. I the Weste Scheldt, fo istace, the ude keel cleaace may vay fom.5% to moe tha 00%. I a extesive model test pogam has bee executed fo the pot of Zeebugge with a fouth geeatio cotaieship at a daft of 3.5 m to detemie ship maoeuvig chaacteistics. This poject focused o the behaviou of cotaie vessels above ad i mud layes []. Ideed, sice its majo extesio i the 970s, the oute habou of Zeebugge is subject to sedimetatio so that pemaet maiteace dedgig is ecessay to keep the pot accessible fo deep-dafted vessels. As

2 the bottom is coveed with soft mud layes, the bouday betwee wate ad bottom is had to defie ad the ship behaviou above this autical bottom will chage emakably. Although the expeimetal pogam cotaied also tests above a had bottom with diffeet ude keel cleaaces, it was esticted to oe daft, so that questios aose about the ifluece of iceasig dafts ad/o deceasig ude keel cleaaces (UKC) o ship maoeuvability. Theefoe, a eseach pogam was set up by Flades Hydaulics eseach ad pefomed by Ghet Uivesity with the objective to examie the maoeuvig behaviou of a 8000 TEU cotaieship at seveal dafts i deep to vey shallow wate [].. CATIVE MODEL TEST OGAM I a captive model test pogam has bee executed i the Towig Tak fo Maoeuves i Shallow Wate (co-opeatio Flades Hydaulics eseach Ghet Uivesity) with a 4.3 m model of the cotaieship descibed i Table, combiig thee distiguished dafts ad thee ude keel cleaaces (Table ). The ship model was equipped with a six-bladed popelle (/D.0 ad A E /A ) ad a udde with a full scale aea of 83 m. Table. Chaacteistics of a 8000 TEU ship model Model scale Full scale L OA (m) L (m) B (m) T (m) C B scale /80.8 Table Tested combiatios of daft-ukc h/t (UKC).0 (00%).35 (35%).0 (0%) T (m full) h (m full) The test pogam cosisted of followig test types: Statioay model tests: staight-lie tests with positive ad egative fowad speed; oblique towig tests with positive ad egative fowad speed. No-statioay model tests: oscillatoy tests aoud ψ-axis; hamoic sway tests: pue sway; hamoic yaw tests: pue yaw, yaw with dift with positive ad egative fowad speed; multi-modal tests, executed with vayig udde agle, popelle ate o fowad speed, while the othe paametes ae kept at costat values. The test pogam fo the deep wate cases (00% ad 35% UKC) diffes fom the oe fo the shallow wate coditio (0% UKC) i the maximum values applied fo fowad speed ad popelle pm: the ship velocity was vaied betwee -4 ad 6 kots full scale fo 00% ad 35% UKC ad -4 ad 0 kots fo 0% UKC; the popelle ates ahead wee 40, 60 ad 80% of the omial ate 0 ( 00 pm full scale) ad aste -35, -50 ad -80% 0. A popelle pm of 00% 0 o sea full ahead was oly executed duig the deep wate cases. 3. FOU-QUADANT MATHEMATICAL MODEL 3. Oveview Based o the esults of the captive model tests a mathematical model has bee developed fo each combiatio of ude keel cleaace ad daft, cosideig the Foude similaity law. The ship maoeuvig model icopoates the physical backgoud of hydodyamic foces ad has bee based o the model as peseted i []. The hydodyamic foces iduced by hull (H), popelle () ad udde () ae aalysed sepaately ad combied i a modula mathematical model by supepositio: F F + F + F () H The developmet of the mathematical models is based o a egessio aalysis usig the fee ODACK Softwae fo Weighted Othogoal Distace egessio [3]. 3. Hull Foces The logitudial hull foce X H, the lateal hull foce Y H ad the yawig momet N H ae give by: X Y H H ( X ( u) ) u LT m u + mv + mx ( ) ( ) + u + v X' u + ( L) X' ( ) + v + ( L) X' ( ) ( Y m) v + ( Y ( ) - mx ) v LT ( ) ( ) + ( u + v Y' u + L) Y' ( ) + v + ( L) Y' ( ) G G + - mu + () (3)

3 N H ( N mx ) v + ( N ( ) - I ) v L T G ( ) ( ) + ( u + v N' u + L) N' ( ) + v + ( L) N' ( ) zz - mx G u + (4) The dift agle β, the yaw ate agle γ ad a dift-yaw coelatio agle χ take the velocity effect ito accout ad vay withi the age [-80 ; 80 ]. L β ATAN ( v, u) ; ATAN, u (5) L ATAN, v ATAN(y,x) is a value i [-π;π], defied as: ATAN(y,x) acta(y/x) fo x>0 acta(y/x)+π fo x<0,y>0 acta(y/x) π fo x<0,y<0 ±π/ fo x0 3.3 opelle Iduced Foces 3.3. opelle thust ad toque Captive model tests have bee executed i the fou quadats of opeatio fo the speed u ad popelle ate which ae defied i Table 3. Table 3 Defiitio of the fou quadats of opeatio quadat U ε ( ) Q + + [0,90] Q + - ]90,80[ Q3 - - ]-90,0[ Q4 - + [-80,-90] The thust ad toque coefficiets fo a fou-quadat model ae defied as: T C T ( ε ) (6) ρa 0 [ u + ( 0.7πD ) ] C Q Q ε (7) ρa 0D [ u + ( 0.7πD ) ] ( ) Thust ad toque have bee modelled though the wake facto w, allowig the calculatio of the hydodyamic advace agle ε: ATAN ( u, 0.7 D ) (8) ATAN u w, 0.7 D ( ( ) ) A distictio is made betwee the wake facto detemied accodig to the thust idetity, w T, ad the toque idetity, w Q. These factos ae expessed as fuctio of the appaet hydodyamic advace agle ε*: ε* ATAN u, 0.7πD ATAN J, 0. 7π (9) ( ) ( ) Fig. Lage eddies at the aft body duig a test (T.0 m; 0% UKC) with F 0.07 ad -80% 0 (stoppig, quadat ). Usig equatios (6) to (9) a model fo the thust ad the toque ca be developed: T π ρ D CT (0) 8 ( ε)( + ta ε) Q π ρ D C Q () Logitudial foce ( ε)( + ta ε) The thust yields a logitudial foce give as: X t ε*, ϕ*, γ * T () [ ( )] t beig the thust deductio facto, fomulated as a fuctio of the appaet hydodyamic agles ε*, φ* ad γ*, give i expessios (9) ad (3). ϕ* ATAN( v, 0.7πD ) (3) γ* ATAN 0.5L, 0.7πD ( ) Lateal foce ad yawig momet The asymmety of the flow due to popelle actio iduces a lateal foce ad yawig momet. The latte ae picipally statioay i time i the fist ad thid quadats, but cotai a oscillatig compoet i the secod ad fouth quadat, with a amplitude which is popotioal to the popelle thust, Fig.. Moeove, a additioal effect o the hydodyamic ietia deivatives is obseved. Fomulatios (4) ad (5) wee used to take these effects ito accout. Y K K N 0 ( Y v + Y ) + T ( *) v [ YT (, *) + YT (, *)] + [ ( )][ ( ( ) ( ))] YTA, * cos, * t + ϕ, * 0 ( N v + N ) + L T ( *) v [ N T (, *) + N T (, *)] + [ ( )][ ( ( ) ( ))] N TA, *, K cos, * t + ϕ, *.. (4) (5)

4 K ad K deped o the quadat. K is popotioal to the fowad speed ad is take equal to the Foude umbe F i quadat, ad equals i othe quadats; K i quadats,, 3 ad takes a value betwee 0 ad i quadat 4, depedig o the yaw ate ad yaw acceleatio. 3.4 udde Iduced Foces 3.4. udde dyamics The ship model was equipped with a sigle udde, of which the ope wate lift ad dag chaacteistics had bee detemied i a 360 deg age of agles of attack α. The o-dimesioal dag ad lift coefficiet ae defied as follows: D L C D ( α ) ; C L ( ) (6-7) ρa U ρa U D beig the dag, L the lift foce, A the movable factio of the udde aea ad U the flow velocity. The udde agle δ diffes fom the agle of attack α : α δ + δ + (8) 0 β δ 0, the udde agle whee the omal foce F N vaishes, is a coectio fo flow asymmety, with a typical value of + deg: δ δ 0 (9) ( ) 0 F N I (8), β is the local dift agle at the udde: β ATAN v, u (0) ( ) u, v beig the logitudial ad tasvese compoet of the flow velocity ea the udde: V u + v () Usig expessios (6-) the foces o the udde ca be calculated: FX A V [ CL ( ) si + CD ( ) cos ] () F A V C cos C si Y [ ( ) ( ) ] L The aveage o equivalet iflow velocity to the udde depeds o the hull fom, which iduces wake (i the logitudial diectio) ad chage of flow diectio (i tasvese diectio), ad o the popelle which acceleates the logitudial flow, depedig o the udde-popelle distace ad the udde aea affected by the popelle flow. Geeally, the wake at the udde diffes fom the wake at the popelle so that a ew wake facto has to be itoduced. Diffeet wake factos will be deived accodig to the udde foces F X ad F Y to obtai a acceptable accuacy. The wate velocity aft of the popelle ca be appoximated by expessios based o impulse theoy. Oly the expessio fo the fist quadat will be peseted as discussios i the followig chapte will oly be based o the ahead motio: D u w w η ( k) siε + k C + si ε + ( η) [ ( w ) ] [ ] ] u + 0.7πD T (3) si ε I (3), η is the popelle diamete to udde height atio; k is a facto takig accout of the distace udde-popelle. It should be oticed that physically moe coect alteatives ca be fomulated fo (3); evetheless, the peset appoach yields acceptable models. Although a flow ectificatio facto is mostly foud i liteatue to take ito accout the ifluece of dift ad yaw, this facto will be assumed to equal ad the wake facto will be cosideed to deped o the dift ad yaw ate agle i a simila way. The sum of both agles is theefoe cosideed. This assumptio is acceptable fo small dift o yaw ate agles: v v L v + x ta ta ( + ) (4) u u u I this stage, howeve, β+γ is used fo the whole age udde iduced foces ad momet due to coelatio The logitudial udde foce F X yields a icease of esistace X. Usually the icease will be smalle tha F X, which is modelled as follows: X t F (5) ( ) X with t >0. Howeve, the diffeece betwee X ad F X seemed isigificat; settig t to zeo was theefoe acceptable. The asymmetic flow iduced by the udde ot oly esults i a lateal foce F Y o the udde (with applicatio poit x ), but also i a exta lateal foce a H F Y (with applicatio poit x H ) due to a asymmetic flow aoud the hull. This leads to: Y + a F (6) ( H ) Y The coefficiet a H is a fuctio of ε* ad β+γ i the fist quadat. The lateal foce (6) yields a yawig momet which ca be witte as: N x + a x F (7) ( H H ) Y The applicatio poit x H ca be witte as a fuctio of β+γ i the fist quadat. 3.5 Extapolatio fom Model to Full Scale Scale effects have oly bee take ito accout fo the coectio of the fictioal esistace compoet i X (β). No othe coectios have bee pefomed

5 although scale effects will pobably play a pat i all modules of a maoeuvig ship, i.e. hull, popelle ad udde, as has bee ecogized as a esult of a compaative study i [4]. 4. DEIVED MANOEUVING CHAACTEISTICS 4. Chaacteistics of Tuig Cicles The tuig ability of the 8000 TEU cotaie caie duig a motio ahead will be discussed based o the tuig cicle chaacteistics. As this model does ot have a kow full scale equivalet, lies of existig cotaie vessels ot beig available, a diect evaluatio of the simulated maoeuvig chaacteistics is impossible. It is kow that elatively small diffeeces i geomety, e.g. the aft body, ca cause diffeet maoeuvig chaacteistics. O the othe had, a compaiso ca be made with the IMO Stadads fo Ship Maoeuvability [5] ad with full scale tials epoted by ship owes of compaable ships. The simulated chaacteistics of a 35 deg tu pefomed at desig daft with sea full ahead ae give i Table 4 fo the deep wate coditio. Accodig to the IMO Stadads the tactical diamete should ot exceed moe tha 5 times the ship legth. Based o Table 4, it could be cocluded that the tuig ability of this ship model is oly magially acceptable ad the atios of tactical diamete to ship legth ae sigificatly highe tha epoted values lyig i the age betwee.5 ad 3.5. This diffeece could patially be explaied based o the lage speed eductio which is obseved duig full scale maoeuves compaed to the pedicted tuig maoeuve. daft. This emakable coclusio will be examied i the ext sectios whee foce compoets will be compaed ad the measued sikage ad tim will be evaluated. Table 5 Ifluece of daft ad h/t atio o the atio of tactical diamete to ship legth at telegaph positio half ahead STBD OT Tactical diamete/l Tact. diamete/ UKC (%) T4.5m T3.5m T.0m Squat: Ifluece of Daft ad UKC The sikage at the foe (F) ad the aft pepedicula (A) duig a fowad motio is peseted i Fig. i pecetages of the ship s daft as fuctio of the o-dimesioal Tuck-paamete, ofte used i empiical fomulae fo the pedictio of squat (e.g. [6]): F h is defied as: h Tuck F (8) F h u F h (9) gh The ifluece of daft ad available wate depth is summaized i Table 5 fo the tactical diamete atio at a telegaph positio "half ahead". This educed popelle pm is chose because of the impotat sikage that occus i vey shallow wate fo the lowest daft (see sectio 4.). The chaacteistic dimesios of the tuig cicle appea to be athe isesitive to the popelle ate. Table 4 Tuig cicle chaacteistics at the desig daft ad deep wate (appoach speed.6 kts) To STBD To OT Advace/L Tasfe/L.3.05 Tact. diamete/ L Time to Time to Accodig to Table 5 the atios oly diffe slightly fo the diffeet ship s dafts at 00% ad 35% UKC, while i vey shallow wate the tactical diamete at m daft is almost twice the diamete at the desig Fig. Sikage at F (black) ad A (white) as fuctio of the Tuck paamete: ifluece of daft T i deep (00% UKC) ad vey shallow wate (0% UKC), 80% 0. Measued sikage at F ad A vay almost liealy with the Tuck-paamete ad although the vaiatio of sikage at the F is almost the same i deep ad vey shallow wate, the sikage at the A iceases cosideably i vey shallow wate, so that at the lagest selected speed the emaiig et UKC has bee halved. The lagest tim is foud fo the smallest daft. Diffeeces i the foce compoets

6 ad maoeuvig chaacteistics could theefoe pobably be explaied based o the diffeeces i et ude keel cleaaces which ae smalle fo the.0 m daft compaed to the desig daft. 4.3 Ifluece of Daft ad UKC o Hull Foce Compoets 4.3. Acceleatio deivatives The most impotat acceleatio deivatives, the added mass due to sway ad the added momet of ietia due to yaw, ae peseted i Fig. 3 ad Fig. 4. These deivatives oly play a pat duig the iitial phase of the tuig maoeuve ad do ot affect the statioay tuig phase. Both deivatives ae made o-dimesioal based o the ship's mass ad peseted as fuctios of the ship legth to ude keel cleaace atio, L/(h-T). It should be boe i mid that the absolute ude keel cleaace h-t deceases ad the paamete L/(h-T) iceases with deceasig daft if the elative ude keel cleaace, expessed as a pecetage of daft, is kept costat. The magitude of the o-dimesioal ietia deivatives iceases as well fo a deceasig daft at costat elative UKC. Fig. 5 Ifluece of daft o o-dimesioal lateal foce due to yaw i deep wate (00% UKC). Y v m Fig. 3 Ifluece of daft ad (h-t) o the added mass due to sway. N ml Fig. 6 Ifluece of daft o o-dimesioal lateal foce ad yawig momet due to yaw i vey shallow wate (0% UKC). The icease of Y v m ad m L with deceasig daft ca patially be ascibed to the decease of the ship's mass, at least i the vey shallow wate case. I deepe wate, o the cotay, the o-dimesioal acceleatio deivatives emai ealy costat with vayig daft. N 4.3. Velocity depedet tems Fig. 4 Ifluece of daft ad (h-t) o the added momet of ietia due to yaw. The velocity depedet lateal foces ad yawig momets ae diectly liked to the stability leves l v ad l which detemie the staight-lie stability of a

7 ship [7]: N' v N' l' v < l' (30) Y' m'y' + v Due to the iceasig dyamic ste tim with deceasig daft, the leve l v is expected to move aft so that the ship will become moe stable, givig lage values fo tuig cicle chaacteistics such as the tactical diamete. Based o Fig. 5 ad Fig. 6, the followig may be cocluded: Although tuig cicle chaacteistics based o full scale tials show oly a small asymmety betwee a pot ad a staboad tu, lateal foce ad yawig momet due to sway o yaw ae ot ecessaily ati-symmetical. A claificatio fo this asymmety eeds futhe examiatio. The ifluece of the ship s daft o these foces is ot staightfowad fo positive o egative agles β o γ at a costat UKC. Fo 0% UKC as a example, the ifluece of daft o yawig momet N (γ) is limited fo egative yaw ate agles (tu to pot) while it is oticeable fo positive agles. The impotat asymmety betwee a pot ad a staboad tu fo the smallest daft at 0% UKC compaed to the othe dafts, could patially be explaied based o these test esults with a lage N (γ) value fo.0 m daft ad positive yaw ate agles. The eos o the lateal foce due to yaw, Y (γ), ae lage especially i shallow wate ad i deep wate fo lage yaw ate agles. The ifluece of a modificatio of this table based o the ucetaity will be subjected to a sesitivity aalysis as was pefomed i [8]. Fo seveal coditios, the wake facto w T accodig to thust idetity is show i Fig. 7. Fo a costat daft the wake facto deceases with iceasig wate depth as the iflow ito the popelle esembles moe ad moe the fee steam coditio. The ifluece of ship s daft fo diffeet UKCs is ot staightfowad. I deep wate the wake facto at the smallest daft is somewhat lage tha the facto fo the desig daft while at 0% UKC the opposite is foud. I vey shallow wate, the iflow velocity ito the popelle will theefoe be highe fo m daft compaed to 4.5 m daft, givig a smalle popelle thust at the smallest daft. 4.5 Ifluece of Daft ad UKC o udde Iduced Foces At the smallest ship s daft of.0 m the udde aea is ot fully immesed so that smalle udde foces could be expected. A compaiso of measued logitudial ad lateal udde foces shows evetheless that this is ot ecessaily tue. I Fig. 8 the diffeece i F X fo a udde agle to pot (>0) ad both ship s dafts is small while fo a udde agle to staboad the additioal esistace foce F X is smalle i magitude fo the smallest daft. The speed eductio will theefoe be smalle esultig i a tuig cicle with lage chaacteistic dimesios compaed to the desig daft. 4.4 Ifluece of Daft ad UKC o opelle Coefficiets Fo the fist quadat of opeatio the majo cotibutio of the popelle is based o the popelle thust yieldig the popelle iduced logitudial foce X. The popelle iduced lateal foce ad yawig momet ae of mio impotace w T (-) T m; 0% ukc T m, 00% ukc 0. T m; 0% ukc T m; 35% ukc 0. 0 ε* ( ) T m; 00% ukc Fig. 7 Modelled wake factio w T as fuctio of the appaet advace agle ε*. Fig. 8 Compaiso of measued foce F X ad F Y at dafts of.0 ad 4.5 m full scale (F 0.07, 60% 0, 0% UKC).

8 shallow wate ca patially be explaied based o the educed leve x H. Fig. 9 Flow at the udde at 00% (left) ad 0% (ight) UKC fo a full scale daft of m. Fo the lateal udde foce F Y, diffeeces ae also moe poouced fo a staboad tha fo a pot udde commad. Especially fo egative udde agles, the magitude of the udde foce F Y depeds o the applied udde agle: at smalle udde agles (δ -0 ), highe udde foces ae measued fo the smallest daft, while at had staboad udde, the udde foce appeas to be slightly highe if the ship is loaded at he desig daft. Despite of the diffeece i immesed udde aea fo the thee dafts, the small diffeece i foces at the udde positio could be explaied based o the impotat icease of the flow iduced by the wake ad the popelle slipsteam fo the ship model loaded at the smallest daft as show i Fig. 9. Fig. 0 Compaiso of measued foce F Y at dafts of.0 ad 4.5 m full scale (F 0.08, 60% 0, 0% UKC). Lateal foces F Y measued duig low speed model tests, chaacteized by lage ages of dift agles, ae peseted i Fig. 0. The ifluece of ship s daft is small with somewhat lage values fo the.0 m daft at high udde agles. Diffeeces i the coelatio coefficiets due to udde actio ae examied fo the hull coefficiet a H (Fig. ) ad the applicatio poit x H (Fig. ). Depedig o the appaet advace agle, a icease of daft may lead to eithe smalle o lage values fo the hull coefficiet a H. The ship self-populsio poit coespods to a advace agle ε* of appoximately 0 deg so that highe a H values ae foud fo the desig daft compaed to the smalle dafts; fo lowe advace agles o highe popelle loadig the additioal hull cotibutio is lage fo the smallest daft compaed to the othes. Some doubt may aise about the accuacy of this coefficiet fo advace agles ε* highe tha 5 deg: these values ae domiatig the simulatio us i Table 5 while they ca oly be obtaied duig the model tests i vey shallow wate usig low popelle ates due to the limited model speed. Geeally, a highe hull coefficiet a H causes a iceased tuig ability. The applicatio poit x H of the additioal hull cotibutio to the udde actio is show as fuctio of the wate depth to daft atio i Fig. fo a staight ahead motio. This poit moves towads midships with deceasig UKC. The ifluece of ship s daft is ot clea, although the diffeeces fo each UKC ae limited. The educed tuig ability i Fig. Ifluece of ship s daft o coelatio facto a H (staight ahead, 0% UKC) Fig. Ifluece of ship s daft ad UKC o the applicatio poit x H (staight ahead) 5. CONCLUSION A clea ifluece of ship s daft o loadig coditio o ship maoeuvability i both deep ad vey shallow wate is seldom foud i liteatue. Full scale

9 tials at the delivey ofte povide maoeuvig chaacteistics i a timmed ballast coditio o eve keel desig coditio, with mostly oly deep wate. This eseach was set up to meet this lack of kowledge. Thaks to the extesive pogam of captive model tests, available i the fou quadats of opeatio, a mathematical maoeuvig model is developed with a wide applicability. Oly the tuig ability i the fist quadat is discussed hee ad the coclusios ae: affected the deived mathematical model. As some ucetaities still exist about the scale effects that must be take ito accout i deep ad shallow wate, a sesitivity aalysis of idividual model compoets could give moe isight ito the elatioship betwee math model ad esultat full scale maoeuvig chaacteistics. Sikage ad tim ae emakably iflueced by the ship s daft. Geeally, squat iceases with deceasig UKC while the sikage at the aft pepedicula is much lage fo a itemediate daft compaed to the desig daft. The chaacteistic dimesios of a tuig cicle diffe oly slightly fo all dafts i deep (00% UKC) ad shallow wate (35% UKC). I vey shallow wate, the tactical diamete atio fo.0 m daft is almost twice the atio fo the desig daft. I additio, diffeeces betwee a pot ad a staboad tu icease with deceasig UKC. The o-dimesioal added mass due to sway Y v m ad the added momet of ietia due to yaw N m L ae ealy costat i deep wate while these o-dimesioal deivatives icease with deceasig daft i vey shallow wate. This icease ca patially be ascibed to the decease of the ship s mass. The iceasig staight-lie stability with deceasig ship s daft ca be explaied by the evolutio of the velocity depedet hull foce compoets. As a example, the yawig momet due to yaw N (γ) iceases with deceasig daft fo positive yaw ate agles i vey shallow wate. The lage asymmety betwee a pot ad staboad tu at 0% UKC ad.0 m daft could be explaied based o this diffeece. The lack of ati-symmety of the modeled velocity depedet lateal foce ad yawig momet as fuctios of dift agle o yaw ate agle eeds futhe examiatio. Although the udde is ot fully immesed at.0 m daft the foces measued at the udde oly diffe slightly fo the diffeet dafts. Eve the diffeece fo the coelatio paametes a H ad x H is small so that the deceasig tuig ability with deceasig daft i vey shallow wate caot be explaied based o these esults. Due to the diffeece i squat, especially i vey shallow wate, the test pogam fo the smallest daft ad the othe dafts was ot idetical. Some tests could ot be executed, which could have EFEENCES [] Delefotie G., Vatoe M., Eloot K. Modellig avigatio i muddy aeas though captive model tests, Joual of Maie Sciece ad Techology, Vol. 0 (4), pp. 88-0, 005 [] Vatoe M., Eloot K. et al Weteschappelijke bijstad voo het uitvoee va poeve e het opstelle va wiskudige maoeuveemodelle voo 8000 TEU cotaieschepe voo de toegag tot de Vlaamse haves, oveeekomst 6EB/04/0, 004 [3] Boggs.T., Byd.H., oges J.E., Schabel.B. Use s efeece Guide fo ODACK Vesio.0 Softwae fo Othogoal Distace egessio, Cete fo Computig ad Applied Mathematics, U.S. Depatmet of Commece, 99 [4] 4 th Iteatioal Towig Tak Cofeece, The Maoeuvig Committee Fial epot ad ecommedatios to the 4 th ITTC, Southampto, 005 [5] Iteatioal Maitime Ogaizatio, Maitime Safety Committee Explaatoy otes to the Stadads fo ship maoeuvability, esolutio MSC.37(76), 00 [6] Akudiov V., Daggett L.L., Hewlett J.C., Jakobse B.K. ototype measuemet of ship sikage i cofied wate oceedigs of MASIM000, Olado, pp , 000 [7] 3 d Iteatioal Towig Tak Cofeece, The Maoeuvig Committee Fial epot ad ecommedatios to the 3 d ITTC, Veice, 00 [8] Matiusse K., ige E. Maoeuvig edicitio Duig Desig Stage Iteatioal Wokshop o Ship Maoeuvability at the Hambug Ship Model Basi, pape No. 8, 000 AUTHO S BIOGAHY Katie Eloot obtaied a Maste s degee i Naval Achitectue fom Ghet Uivesity Belgium i 995. She woked as a academic assistat at the uivesity fom 995 util 000. Thee she stated he picipal eseach coceig mathematical modelig of ship maoeuves i shallow wate ad captive model testig. I 00 she eteed he peset post at Flades Hydaulics eseach, a laboatoy of the Flemish Commuity. As study-egiee she caies out eseach cotacts o eal-time ad fast-time maoeuvig simulatio fo the public ad the pivate secto.

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