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Biofouling The Journal of Bioadhesion and Biofilm Research Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713454511 Effects of coating roughness and biofouling on ship resistance and powering Michael P. Schultz a a Department of Naval Architecture and Ocean Engineering, United States Naval Academy, Annapolis, Maryland, USA

Online Publication Date: 01 October 2007 To cite this Article: Schultz, Michael P. (2007) 'Effects of coating roughness and biofouling on ship resistance and powering', Biofouling, 23:5, 331 - 341 To link to this article: DOI: 10.1080/08927010701461974 URL: http://dx.doi.org/10.1080/08927010701461974

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Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 orsodne .P cut,Dprmn fNvlAcietr n ca niern,Uie ttsNvlAaey naoi,M 10,USA. 21402, MD Annapolis, Academy, 10.1080/08927010701461974 online Naval DOI: 1029-2454 States print/ISSN United 0892-7014 Engineering, ISSN Ocean and Architecture Naval a of Department Fax: facing Schultz, P. are M. Correspondence: systems these However, Jelic-Mrcelic 2006). (e.g. minimal al. organisms with et fouling systems control of TBT the fouling settlement that fouling. fact long-term the of to provided effect due the likely with quantifying was This 1992), to Gran- given Grigson, 1981; effort 1989; self-polishing less al. Medhurst, et (e.g. the 1987; Townsin systems ville, of 1981; (TBT) – 1980 tin drag Musker, tributyl (SPC) the copolymer affect surface in changes roughness how this the assessing recently, in on More work focused (1962). research early Lackenby the by given of is on review field A focused this roughness drag. has coating frictional For of work on effect relatively of the 1937). is understanding body on better (Kempf, hull significant drag a the unfouled total reason, when the and of even 90% smooth types, as hull can much some alone as to drag crucial for (Townsin, Frictional is account ships. condition of penalties or coating performance of the speed effect economic The which given of 2003). associated both a power, either input have given maintain in a at results to speed reduced pursuit power this accu- increased a in biofouling as Failure and drag frictional deterioration mulation. in surface coating increase of the (AF) result limit antifouling to ship is a system of role primary The Introduction good show estimates present The speed. powering, cruising layer and at resistance trials. 86% boundary Keywords: speed in power to increases cruising and ship up significant at full-scale to penalties combatant measurements from lead surface powering drag can results naval in films mid-sized with results laboratory-scale slime a agreement fouling that for from calcareous indicate made results heavy results are and The and roughness predictions on speed. of work, maximum range present based near a the with and are In systems coating analysis. estimates antifouling law for similarity The made are conditions. powering and fouling resistance ship full-scale of Predictions Abstract 2007) May USA 15 Maryland, accepted Annapolis, 2007; Academy, March Naval 21 States (Received United Engineering, Ocean and Architecture Naval of Department SCHULTZ P. MICHAEL resistance ship on biofouling powering and and roughness coating of Effects Biofouling þ (1)2321.Emi:[email protected] E-mail: 2219. 293 1(410) 07 35:31–341 – 331 23(5): 2007; , rg oeig eitne ifuig ogns,atfuigcoatings antifouling roughness, biofouling, resistance, powering, Drag, Ó 07Tyo Francis & Taylor 2007 lo ipepeitoso eitneadpowering. and resistance to is of as predictions addressed so simple quantitatively satisfactorily allow coverage be fouling define to to yet how has one resistance, which ship on under- issue fouling on of focused impact research the of standing that body noted large be the on should It despite depends coverage. increase and type the fouling the of that magnitude indicate Bohlander, the drag, frictional studies although in & increase these significant a all to Haslbeck leads of of fouling 1985; results drag The al. the 1992). on et (e.g. conducted fouling been Lewthwaite of also has effect coatings copper-based the & document testing Leer-Andersen ship to Full-scale and 2004). (e.g. Schultz, 2000), 2003; Larsson, Schultz, algae macrofouling 1973; filamentous Unny, calcareous 1999), & of Swain, Kouwen effects (e.g. al. & et the Picologlou Schultz 1969; of 1980; al. et studies Watanabe by (e.g. laboratory reviewed biofilms research is included hydrodynamic work has Subsequent early the (1952). of Anon much 2006; and noted, Efimenko, 1996; & Schultz, Genzer 2006). al. & 2006; et al. Statz Swain et non- (e.g. effective, Carman for alternatives research 2000). active toxic al. spurred et has (Abbott This fouling their controlling and in as not 2003), effective are paints, (Champ, copper-based replacement, 2008 primary in ban worldwide h mato oln nda a ogbeen long has drag on fouling of impact The Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 r h eiur resistance, residuary the are 2 1 C h u ftersdayrssac ofceto the of coefficient resistance residuary model, the of sum the eitnecefiin ftemodel, the of coefficient resistance 332 S hp h oa eitne(rg ftesi model, ship the of full-scale (drag) the resistance R to total similar The geometrically ship. ship a is of that tests tank model towing through requirements made power typically and are resistance ship of Estimates using tests powering model and scale resistance ship of using Prediction (For ship presented. a is of Appendix). laws drag see similarity nomenclature, frictional layer full-scale of boundary method observations the a and to Finally, measurements roughness discussed. laboratory surface are relating of flows impact these the discussed. on and are flows bound- layer turbulent testing of ary model characteristics basic scale some Next, predic- on powering based and resistance tions ship section, this In methods and Materials methodol- hull herein. the described using of ogy scenarios ship impact operational of range and economic a types for the quantified is fouling which and roughness in for planned work Future forms available. is hull are data ship drag and laboratory which conditions fouling hull other single used for be a can here for implemented methodology are (not the form, predictions representative the only and are exhaustive) work this conditions in fouling considered and roughness the While law The similarity analysis. layer speed. boundary and laboratory-scale maximum measurements from drag results near on based and are predictions speed cruising operating conditions at fouling mid-sized and roughness a with of systems range for AF a with made coated combatant are surface naval powering and resistance and ono,1982). Johnson, resistance, ydvdn yterfrnednmcpressure, dynamic reference express the to the by customary from done dividing is is This arising form. It by non-dimensional hull its fluid. in 1 ship the Equation the of on viscosity tangential stresses to due is wavemak- shear resistance to frictional due the while mainly ing, is resistance residuary The r m Fm Tm ntepeetppr rdcin ffl-cl ship full-scale of predictions paper, present the In m where , U h eiur eitnecefiin fthe of coefficient resistance residuary The . smd po w rmr opnns These components. primary two of up made is , U m 2 m n h etdae ftesi oe hull, model ship the of area wetted the and , C .P Schultz P. M. stesi oe oigsed h total The speed. towing model ship the is Rm r R n h rcinlrssac coefficient, resistance frictional the and , m Fm stefli est o h oe tests model the for density fluid the is ssoni qain1(ile & (Gillmer 1 Equation in shown as , R Tm ¼ R Rm þ R Rm R Fm n h frictional the and , C Tm s therefore, is, , ð 1 Þ oe safnto fteFod number, Froude the of function a Fr is model inalwnei sdt con o ifrne in differences for account to used is allowance tion ofceto h oe s hrfr,gvnas given therefore, is, 1982) model resistance Johnson, total & the The (Gillmer tests. of model the coefficient for fluid the of eiur eitnei ucino h Froude the of function a and is number resistance residuary r ace ssoni qain3: Equation ship in the shown and as model matched the of are in number used the Froude is to the similarity impossible between which dynamic is this incomplete matched Reynolds practice, Instead In be do. the ship. to the and and have accomplish model number to would Froude order number the in both that model. this, illustrates the and 2 ship have Equation the the to desirable between of is similarity resistance it dynamic tests, the model predict with ship accurately full-scale to order In nesodthat understood rcinlrssac coefficient, resistance frictional qain5b substituting by 5 Equation oe safnto fteRyod number, Reynolds the of function a the Re of is coefficient resistance model frictional the Likewise, h TC15 oml Woe l 93 ie as: given 1983) al. et (Woo formula ITTC-1957 the where, coefficient, pescrepnigt ulsaesi pesin below: speeds shown as ship 3, Equation full-scale with model of accordance to range a corresponding at out speeds carried are tests tank Towing qain6(ile ono,1982): Johnson, & (Gillmer 6 Equation ofceto h ship, the of coefficient hr,tesaeratio, scale the where, eitnecefiin fteship, the of coefficient resistance ogaiyand gravity to where, model, the of coefficient C resistance residuary The Rm m m ¼ ste on sn qain2 ic the Since 2. Equation using found then is , ¼ U U U C m m A s ( L gL stesi pe and speed ship the is m stecreainalwne h correla- The allowance. correlation the is C C n m m Tm Tm ) 7 Fr C 7 C 1 smaue tec pe.The speed. each at measured is , U 1/2 Fm ¼ C m Ts L where , m Rm m ¼ C where , p ¼ ¼ ¼ Rm U Fr gL ffiffiffiffiffiffiffiffiffi ¼ Fr stelnt ftemodel. the of length the is ðÞ C m l U log ð s C Rs m m Fr ¼ s r Rs n ntemdltss tis it tests, model the in 10 ¼ ¼ þ C m m L h rcinlresistance frictional The . 0 L ffiffiffiffiffiffi 1 g Þþ L Fs s Re C steknmtcviscosity kinematic the is p Fr / : : m L 075 Re s sas on using found also is , steaclrto due acceleration the is U Fs gL ffiffiffiffiffiffiffi m s m ¼ C C s s h oa resistance total The . þ L Fm s Fm p for U s C 2 stesi length. ship the is sotie using obtained is , l ffiffiffi ð s A C Re 2 Re Ts m sgvnby given is , m Þð h total The . ð ð ð ð 2 3 4 6 5 Þ Þ Þ Þ Þ Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 aa hpv.Fod number, Froude vs. ship naval eaiecnrbto fterssac opnns h correlation The allowance, components. resistance the of contribution relative ono 18) h uli sue ob yruial smooth hydraulically be to assumed is (i.e. hull The (1982). Johnson iue1 rp ftettlrssac coefficient, resistance total the of Graph 1. Figure hull of be term, effect resistance will frictional and the added D separately an in work, with for dealt accounted present the be al. will et the on roughness (Woo In roughness three-dimensionality ship hull 1983). of and the resistance, effect on viscous effect the on scale wake, effect scale characteristics, to due propeller typically resistance ship actual pe yEuto 8: Equation by speed power, speed. high at than would speeds moderate roughness low at to influence greater hull a exert to in expected drag be generally increase the an of importance components, relative aforementioned of because the And, drag. total higher frictional to the leading in resistance increase an cause condi- would coating fouling or through tion roughness resistance. while hull residuary in resistance, the increase on An frictional effect negligible the a a has having on fouling) and influence roughness coating direct (i.e. hull the of C hw nFgr r o yruial mohhull smooth hydraulically a for ( are the 1 results Figure speeds, The in higher shown dominant. At becomes drag. resistance total residuary the of component iue1ilsrtsterltv otiuinof speeds moderate to contribution a low ( At over numbers. relative ship Froude naval of typical range the a for illustrates components resistance 1 Figure D Fr C Ts h hppwrn eurmn ntrso shaft of terms in requirement powering ship The C s Fs ,is: D Fs 5 C otettlrssac ofceto h ship, the of coefficient resistance total the so ¼ Fs .5,tefitoa eitnei h largest the is resistance frictional the 0.25), SP ¼ ) tsol lob oe httecondition the that noted be also should It 0). C 0). A srltdt h oa eitneadship and resistance total the to related is , C stknt e000 ssgetdb ile and Gillmer by suggested as 0.0004 be to taken is Ts ¼ C Rs SP þ ¼ C Fs R Fr PC Ts þ s h ahdlnsso the show lines dashed The . U C S A þ D C Fs C Ts fatypical a of , ð ð 8 7 Þ Þ eemndb h onaylyrthickness, layer boundary U the by determined velocity, nteinrlyr h envelocity, mean law. the the scaling layer, own layers, inner its with the two each In of layer, outer consist and inner to considered generally hull. the travels of one length as the thickness layer. down in boundary grows the layer this called boundary which The is in these exists region gradient to freestream The velocity due its conditions. generated boundary is reaches two gradient velocity velocity from mean A away value. the distance wall, some relative called At no the is its This condition. is by wall. no-slip there the impeded the and wall), fluid is (or the between fluid hull motion the the this In At of underway. viscosity. motion is it the when hull region, ship’s a to to adjacent refer (2000). to Swain and asked Schultz is or more (1979) reader Schlichting For the here. coverage, discussed thorough of be effect will the velocity and roughness layer mean surface boundary the turbulent a of in characteristics profile power- basic and some resistance ing, ship on coating fouling of and influence the roughness understand better to order In background layer boundary Turbulent shafting. and propeller the of efficiency overall the where, itnefo h wall, velocity, the friction from distance ftebudr layer, edge boundary outer the the at velocity of the between difference Ka the von layer, outer the For moho og al,i a eepesdas: expressed over be flows can it For walls, walls. rough or smooth smooth for (1938) Millikan by eut nteoelprgo ftetolyr ( layers two the of region profile overlap y velocity the logarithmic matched in a are results 10), profiles velocity and outer 9 and (Equations inner the If al n sgvnb cuae n ce (1961): Tchen and Schubauer by given is and wall’ height, roughness the t h enflwi ubln onaylyris layer boundary turbulent a in flow mean The fluid of region the in forms layer boundary A hsi aldte‘eoiydfc a’ ie as: given law’, ‘velocity-defect the called is This . n / U t PC .Ti scle h lglw n a proposed was and ‘log-law’ the called is This ). U U ¼ tadistance a at , þ rpliecefiin hc represents which coefficient propulsive ¼ U hprssac n powering and resistance Ship U U k 1 U U þ e t ln þ t U h ieai viscosity, kinematic the , ¼ ¼ ðÞþ e U y k fy f þ hsi aldte‘a fthe of ‘law the called is This . U t ðÞ  U þ yU þ U ´rma y n ; ¼ ¼ sdtrie ythe by determined is , B e k t n h oa mean local the and , þ ; g g n(90 hwdthat showed (1930) ´n kU y   : n d d y y D t rmtewl is wall the from U : þ Þð ðÞ k U þ tagiven a at , n d and , ð d 333 and 11 10 ð 9 Þ Þ Þ Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 eteeuvln adruhesheight, roughness sand equivalent the be oe st as onadsit( shift downward a cause to is fore, iue2 rp ftruetbudr ae,ma eoiypolsuiginr(a ftewl)saig h rfie r rmShlzand Schultz from are profiles The scaling. number, wall) Reynolds the roughness of increasing (law of inner effect using profiles the velocity illustrate mean and layer, (2007) boundary Flack turbulent of Graph 2. Figure where, 334 ag nuhs htteda ntewl sentirely is wall the is on roughness drag the the that point, con- so some flow number enough at large rough Reynolds increase, transitionally roughness to tinues the the called As frictional regime. is and function This to roughness roughness drag. the leading in drag the increase pressure an produce increases, to rough- begin number the elements As Reynolds viscosity. small by ness are are out them by elements damped caused completely perturbations roughness any that the so enough regime, regime. smooth this hydraulically In the called is condition nfetdb h ogns and roughness the by unaffected number, of is drag and frictional in roughness increase surface. the the the to to related due directly increased an deficit of indicative momentum is This profile. velocity law ier naruhsraecnitn fdiagonal of consisting height, surface roughness The rough gradient, velo- scratches. a Doppler pressure laser on zero using cimetry a layer in boundary turbulent (2007) obtained Flack and were Schultz of which results recent the in seen mohwl o-a intercept log-law smooth-wall esRyod ubr ( rough- small numbers for (Schlicht- that Reynolds regime shows ness Figure flow The rough 1979). fully roughness ing, the the which in as interest sand function of roughness closely-packed same uniform, the gives of height the ogns ucin(oeta,frsot walls, smooth for that, (note D function roughness U h feto nraigruhesReynolds roughness increasing of effect The þ : .P Schultz P. M. ) h feto ufc ogns,there- roughness, surface of effect The 0). k k ¼ þ ntema eoiypol a be can profile velocity mean the on , o Ka von ´rma nconstant ´n k s þ 5* ¼ k .,and 5.0, shr ae to taken here is , D ) h o is flow the 3), U D U ¼ þ ntelog- the in ) þ 0.41, k ¼ s hsis This . .This 0. D U B þ ¼ ¼ h o vrti yeo ogns shydraulically is roughness ( of type that smooth this shows over Figure The flow flow. taken the pipe roughness developed are of similar fully a results a 2 for the in (2006) are Figure al. shown in et Also Shockling 3. shown Figure profiles in presented velocity mean the regime. flow rough fully elements. the roughness the called on is drag This pressure the to due mohflwand flow smooth ucinehbtn oaihi eedneon dependence logarithmic a exhibiting function esecp o h oeta h ogns ly in plays roughness the ( that velocity role the the setting for except rough- surface ness of independent be to thought generally sand. packed closely uniform, iue4 loicue ntefiuei mohwall in smooth a scaling is ( figure outer the profile in using included Also and presented 4. Schultz Figure are of (2007) profiles velocity Flack mean smooth The and rough surfaces. both usually for is universal be 10) to (Equation considered law velocity-defect the fore, k ag fruhestpsadheights. and types roughness demon- a of for range recently applies law velocity-defect also universal a (2006) that and strated al. type roughness et single Connelly a for height, results are 4 the Figure Although in shown law. velocity-defect universal rough- of a concept the the supporting of thus number, regardless Reynolds ness observed is profiles velocity nteruhestp.Freape Schlichting example, of For limits fully type. suggests degree, and (1979) roughness some to smooth the least at hydraulically on depend, regimes the flow of rough limits The s þ h ogns ucinrslscrepnigto corresponding results function roughness The h ue eino ubln onaylyris layer boundary turbulent a of region outer The 5 h o sflyruhwt h roughness the with rough fully is flow the 25, k s þ k ntelwo h alvlct profile. velocity wall the of law the on , s D þ U þ ¼ ) xeln olpeo h mean the of collapse Excellent 0). )for 0) k s þ U t n egh( length and ) 0frflyruhflwover flow rough fully for 70 k s þ k s þ n ytetime the by and 3 o hydraulically for 5 d cls There- scales. ) k s þ . Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 enlsnumber, Reynolds hw h smttcbhvoro h ogns ucini the in function regime. roughness flow line the rough dashed of fully The behaviour developed (2006). asymptotic al. fully the et and shows Shockling (2007) of experiments Flack flow and pipe Schultz of measurements n lc 20)adilsrt h nestvt fteotrlyrt h ufc roughness. Schultz surface from the are to profiles layer The outer scaling. the law) of (velocity-defect outer insensitivity using the profiles illustrate velocity and mean (2007) layer, Flack boundary and turbulent of Graph 4. Figure function, roughness the of Graph 3. Figure plate a of function roughness and drag the frictional arbitrary of measurements of laboratory-scale plate on This a based of given length drag a procedure. frictional of the impact scaling on to the roughness predict 1987) law to one (1958, allows similarity procedure previous Granville wall a the by in rough develop utilised shown was and was section smooth which layers between boundary similarity The resistance scale frictional ship in at change the of Prediction k s þ aaaefo h onaylayer boundary the from are Data . D U þ s roughness vs. , eghi re omdltecag nfrictional in change the ( model itself to ship to the ship of used of resistance order plate a be in of drag will length frictional in scaling change the law predict similarity work, present Granville’s the In roughness. same the with covered ieto.Tescn ou sln fconstant of line is locus second L The direction. ihteitreto ftolc.Tefis sthe a is by first displaced 12) The of (Equation loci. distance line two friction of smooth intersection the with lt aoaoydt gedwl ihteKa as: given the 1932) with (Schoenherr, smooth line well that friction agreed Schoenherr showed data (2002) resistance laboratory Schultz log( plate frictional of of function a results the as The plate plotting smooth procedure a of The first coefficient 5. of Figure consists in not graphically is illustrated itself roughness. form the hull by dramatically the altered allowance, be of to correlation drag expected the pressure in the embodied and actual is the of hull gradient dimensionality ship pressure three the the of from resulting effect the since assumption relationship: lt aoaoymaueeti hnpotdo the rough on of plotted the then graph for is measurement coefficient laboratory plate resistance frictional The plate rnil’ iiaiylwsaigpoeueis procedure scaling law similarity Granville’s þ ¼ L plate C F D U U esslog( versus Re t þ n 0 k 7 hprssac n powering and resistance Ship p ¼ : [ln(10)] 1 242 C ffiffiffiffiffiffi q F hc aifistefollowing the satisfies which C ffiffiffiffiffi ¼ 2 F  log L Re 1 7 D plate 1 .Ti on coincides point This ). C ðÞ ReC ntepstv log( positive the in Fs k 1 þ q .Ti sareasonable a is This ). F C ffiffiffiffiffi 2 F : : ´rma ð ð Re 335 13 12 Re ´n- ). Þ Þ ) Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 ev lm 030600 10,000 3000 0 150 1000 300 300 10,000 3000 30 1000 0 100 30 100 – 90 80 – 70 60 – 40 0 0 20 – 10 * fouling calcareous Heavy fouling calcareous weed Medium or fouling calcareous Small slime slime Heavy light or coating coating Deteriorated AF applied as Typical surface smooth Hydraulically otn ogns ( roughness coating ecito fcniinNT rating NSTM condition of Description sdb h SNv ae nNvlSis ehia aul(02.Tevle feuvln adruheshih ( height roughness sand index equivalent fouling of a values is The rating (2002). (NSTM) Manual Manual Technical Technical Ships’ Ships’ Naval Naval The on conditions. based fouling Navy and US coating the representative by of used range A I. Table roughness the how illustrates graph The 1987). 1958; (Granville, scaling law similarity Granville’s of function, representation Graphical 5. Figure log( of distance a shifted is determine to order In 336 scale, ifrnebetween difference resistance, yEuto 2frapaeo length, of plate a for 12 Equation by h rtlcsidentifies locus first the log( nices nfitoa eitnei h unfouled the in resistance frictional in exhibited tested increase and coatings an fouled, the unfouled, All the conditions. cleaned in cleaned tested were and biocide-based systems and (2004). AF fouling-release Schultz fouled, both in study, that detailed AF unfouled, In is with work the This coated Hydromechanics conditions. plates Academy in long Naval m coatings 1.52 US on the carried Laboratory measurements at hydrodynamic out on based are SM(2002). NSTM h rsn hpsaefitoa rgpredictions drag frictional ship-scale present The Re D C ieto.Teitreto fti ieand line this of intersection The direction. ) Fs D .P Schultz P. M. . U þ eemndfo h aoaoyhdoyai et srltdt h nraei h rcinlrssac ofceta ship at coefficient resistance frictional the in increase the to related is tests hydrodynamic laboratory the from determined , D C Fs Rt u oteruhesi the is roughness the to due , 50 r ae ntemaueet fShlz(2004). Schultz of measurements the on based are ) C Fs C C Fs n h mohvlegiven value smooth the and Fs h ieo constant of line the , h nraei frictional in increase The . L s / L plate ntepositive the in ) L s . L plate þ * hrfr,b xetdt hrceiealpossible all characterise to and cannot, expected measurements They be (2004). the Schultz therefore, in on given based observations conditions tive ogns n oln odtoswr eeae in generated coating of were of terms conditions range fouling a and for roughness properties cycles, cleaning hydrodynamic and the fouling the more by several drag testing over further author unfouled damage. and frictional and the measurements these deterioration above, From the coating slightly to due but cleaned, condition near, were to When returned fouling. surfaces calcareous increases with the with covered type depended a surfaces fouling for resistance the to frictional condi- on in fouled strongly compared increase the the 7% In – 3 tion, surface. smooth from hydraulically ranging condition h edrsol oeta hs r representa- are these that note should reader The k s hs r hw nTbeI. Table in shown are These . k s ( m m) k s n average and ) 4 Rt 50 100% ( m m) Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 ae nhl uvy sn h M ulRough- Behrends, Hull & 2006). BMT Howell roughness 1990; the (Medhurst, coating using Analyzer of ness surveys mm hull measure 50 on standard of based length a sampling is a which over measured height ifrne nfuigcmuiycmoiinall on composition effect significant a community have could and fouling fouling in and spatial roughness differences example, coating For in conditions. heterogeneity fouling or coating hsppr h orlto loac ( the allowance correlation of The paper. requirements this powering shaft FFG-7 full-scale the (1983). are al. details et Warfare Woo Further Surface in USA. Naval given MD, the Carderock, at Center, model scale 1:20.82 150 vrg ulruhes( roughness hull average ogns n oln ntesatpwrrequire- power shaft the ( coating on ments of fouling impact the and assess roughness to order in work present and drag model Navy class as US the well for as results propeller data powering trial scale visible. is to colour underlying impossible paint the condition, or slime light the difficult the In where is determine. condition colour a paint slime be underlying heavy would and slime light Heavy between layers. drawn be also large distinction should Some of types. coverage multiple heavy of denoting fouling fouling, calcareous 100 calcareous of the rating a of with severity the rating with The increases fouling. calcareous indicates incipient 40 with of surface rating represents a A 30 fouling. of a soft rating of denotes coverage a 0 heavy while of fouling, rating of A free only. surface fouling soft of coverage of condition fouling I the hull Table evaluate the to in divers underwater shown by on used ratings are guidance NSTM for The case. document uses cleaning. each the hull Navy is in US (2002) fouling the NSTM that the the of of 081 height maximum Chapter likely trough the these to represent for peak I given Table values in the conditions therefore, surface; fouled oNvlSis ehia aul(SM2002). (NSTM Manual Technical Rt Ships’ according Naval rating fouling to Navy US the and conditions D okwe h ulsaetil eecnutd and conducted, ( roughness were hull trials average the made dry full-scale of the out also when recently was dock were ship The herein conditions. these for predictions full-scale The ulsaetil eecridoti ewtrwith The seawater in tonnes. out of metric beam carried 3779 a r were with displaces trials m full-scale 124.4 and of m length 14.3 waterline a has C ¼ 50 h aafo h oe et eeue opredict to used were tests model the from data The h ae fWoe l 18)poie ohfull both provides (1983) al. et Woo of paper The Fs 023k m kg 1022.3 m losoni al r h estimated the are I Table in shown Also . rgt ( frigate stemxmmpa otog roughness trough to peak maximum the is .Tesi oe et eecnutdo a on conducted were tests model ship The m. Rt sn h rcdrspeiul ulndin outlined previously procedures the using nsitu in SP 50 )ofan sntgnrlyue ocaatrs a characterise to used generally not is FFG-7 aig f3 rls r sdt denote to used are less or 30 of Ratings . 7 3 .Teedt eeue nthe in used were data These ). FFG-7 and Rt Rt n ulfr.The form. hull ¼ 50 50 8.97 a siae obe to estimated was ) o h different the for ) lvrHzr Perry Hazard Oliver k s n h resulting the and 6 C 10 A 7 a taken was ) 7 m FFG-7 2 s 7 1 . odtos h rcdr o calculating roughness Schultz for fouling procedure and this roughness The of coating conditions. with of range results well a flow for function reasonably the rough agree 1992), transitionally all (2004) the (Grigson, for known universal in is regime not it types is While function 3. roughness roughness Figure Shockling the in and shown that (2007) (2006) Flack al. and et the Schultz follows function of roughness results the that presented paper, ones this subsequent in the as well as calculation, C ieto;vi)tecrepnigvleof value corresponding the viii) direction; lt flength, of plate eetdbsdo al ;i)a nta au of value initial an ii) I; Table on based selected 18)frasmlrhl om h hnei the in change The form. ( Johnson hull coefficient and resistance similar Gillmer frictional a by for suggested as (1982) 0.0004 be to sue n tp i iiaerpae.If repeated. are viii – iii steps and used is is second the by (b) offset 13; 12 Equation Equation satisfying v step from h rcdr scmlt.I ti o o,alarger a low, too is it If complete. is procedure the rmmdlts eut eemd o hpspeeds ship for s made m were 7.7 results of test model from the of powering full-scale the of predictions The discussion and Results resulting the predict to 8 eghsae( scale length au of value ih smaller a high, eitnecefiin ( coefficient resistance log( eetd x h nraei rcinlresistance, frictional in increase the D ix) repeated; cut,20) i h w oio Granville’s of loci of line a two is first The the (a) located. vi) are procedure 2004); Schultz, ino h eodlcsadtefis ou hfe a shifted locus log( first the of and locus distance second the of tion cln rcdr Gavle 98 97 for 1987) 1958; (Granville, Rt procedure law similarity using scaling calculated was roughness hull the olw:i h au of value The i) follows: al .Teeaesoni al Ifrasi speed ship a for II Table in in shown shown are the These conditions of I. all fouling Table for and speeds ship roughness two coating same the is for out results carried trials full-scale speeds). both at the between 1.5% (within agreement and excellent The predictions 6. (1983) al. Figure the et in Woo of presented trials are full-scale the of with results along the predictions These respectively. speed, full nearly and speed cruising typical a to correspond which icu eghsae( scale length viscous bandfo h rp.If graph. the from obtained function roughness corresponding ( the iii) assumed; D C Fs 50 rdcin ftecag nttlrssac were resistance total in change the of Predictions U Fs Re n h mohvlegvnb qain1 o a for 12 Equation by given value smooth the and þ ¼ u oteruhesi h ifrnebetween difference the is roughness the to due , sdtrie rmFgr ;i)teviscous the iv) 3; Figure from determined is ) ieto;vi h hpsaefrictional scale ship the vii) direction; ) 150 L plate 7 m 1 m( þ 1 nt)ad1. s m 15.4 and knots) (15 n / L sdtrie as determined is U k s hprssac n powering and resistance Ship k s ;x) L t ¼ s sdtrie as determined is ) þ s / L 30 D sue n tp i iiare viii – iii steps and used is plate D L C C U k plate m Fs Fs s ntepstv log( positive the in ) ) twsasmdfrthis for assumed was It m). þ slctdb h intersec- the by located is ) o ie ulcniinis condition hull given a for SP k sue nEutos7and 7 Equations in used is ¼ [ln(10)] Re . .2mi h td of study the in m 1.52 s D stevledesired, value the is L C plate Fs 7 eutn from resulting ) 1 7 iie ythe by divided ntepositive the in k 1 s / k 3 knots), (30 s D Re þ C ;v)the s FFG Fs L Re stoo is k plate sas is s 337 þ s Re k -7 s þ is is þ ) Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 k ev lm 120% 41 calcareous Heavy calcareous Medium calcareous Small slime Heavy coating Deteriorated an ersnaiecaigadfuigcniin tasedof speed a at conditions fouling s m and 7.7 class coating Perry representative Hazard Oliver cln o yia sapidA otn ( coating AF applied as typical a for scaling f77ms m 7.7 of applied as Typical Hydraulically ( resistance total in change the of Predictions II. Table ( power shaft required of Graph 6. Figure 338 condition of Description hpsedo 54ms m 15.4 of speed ship a ulruhesadfuigrne rm4–55%. – 4 from ranges fouling and roughness to due hull resistance in increase percentage The III. Table otn eeirto ralgtsielyr the significant layer, become coating slime to With AF begins light hull. ( resistance a applied on smooth or impact as hydraulically deterioration typical, a coating to a compared from ( result penalty resistance small a only ae ntepeetmto sn h oe etdt fWoo of data test predictions model the the with are using (1983) circles method al. filled et present The the (1983). on al. based et Woo of trials eitnei erydulda riigsed( fouling in speed cruising total increase at of the doubled fouling, nearly severity calcareous is of resistance layer the heavy a with for until, increase to continues * s ¼ fouling fouling weed or fouling slime light or Fcoating AF surface smooth h rdcin ftecag nttlrssac for resistance total in change the of predictions The FFG-7 1 nraein increase 11% 30 m 7 m). 1 .P Schultz P. M. rgt.Tesldln hw h eut ftefull-scale the of results the shows line solid The frigate. 1 knots). (15 7 R 1 T ). 1 nt) h eut niaethat indicate results The knots). (15 C A ¼ .0.Tepeito sdsmlrt law similarity used prediction The 0.004. U s ¼ R rgt ( frigate T . s m 7.7 7 .Terssac penalty resistance The ). D 1 R 6 80% 52% 162 105 . 2% 4.6 T 934% 11% 69 23 –– 3 nt)aesonin shown are knots) (30 @ 7 FFG 1 * SP (kN) % sepce to expected is 2%) 7 iharneof range a with -7) ) vs hpsed( speed ship U Rt s % 50 ¼ D ¼ . s m 7.7 D R * R T 150 o an for ) T U 89% @ s )for m m; 7 1 ersnaiecaigadfuigcniin tasedof speed a at conditions fouling s m and 15.4 class coating Perry representative Hazard Oliver h yruial mohflwrgm tcruise at regime flow AF in applied smooth nearly ( as operating hydraulically typical, from goes the the surface is This speed. the coating. exception high to at lone due resistance The residuary resistance is the frictional This to of compared speed. contribution cruising relative are smaller at speed this than at increases lower percentage the general, In condition of Description power. shaft fixed a for speed in eiea ihsed( speed high at regime ev lm 9 16% 192 calcareous Heavy calcareous Medium calcareous Small slime Heavy eeirtdcoating Deteriorated yia sapplied as Typical Hydraulically ( resistance total in change the of Predictions III. Table lm ae,teipc npwrn eisto begins powering on ( light impact significant a hydraulically the or become a deterioration layer, coating to slime With compared hull. small coating smooth a The AF only (1983). applied that al. indicate et ( penalty again Woo propeller results in water powering presented open the results fouling on efficiency test based heavier propulsive calculated in the were changes for hull These in increased the reduction coefficient conditions. significant to the propulsive a due to for the speed lead can given also which a fouling, but at loading in resistance increase propeller the hull for power only shaft total not required accounts in here change presented the that note should atclrcniin tsol entdta the that ( noted height roughness be this sand for should equivalent speed maximum It high at condition. penalty particular resistance total in rise o hpsedo . s IV m Table 7.7 in of shown speed are ship a These for out. carried speed. also ship were with decreases it and length, ship with * is conditions smooth edo h yeo hpadissed o the For speed. its and ship of de- type does FFG-7 the surface on smooth pend hydraulically a maintain k fouling fouling weed or fouling rlgtslime light or Fcoating AF mohsurface smooth s 7 rdcin ftecag nrqie hf power shaft required in change the of Predictions þ m * t3 nt.Ti au ed oincrease to tends value This knots. 30 at m h aiu au of value maximum the , )t elit h rniinlyruhflow rough transitionally the into well to 7) 7 1 * 3 nt) lopeetdi h ecnaedecrease percentage the is presented Also knots). (30 % sepce orsl rmatpcl as typical, a from result to expected is 2%) U s ¼ * * 54ms m 15.4 rgt ( frigate k 1 nraein increase 11% 13.5 s D þ R 7 55% 36% 25% 677 447 305 1 10% 118 7 * T 64% 46 –– 1 @ m 4.Ti xlisthe explains This 14). 1 nt) h reader The knots). (15 7 FFG t1 nt n is and knots 15 at m 1 (kN) k s 7 iharneof range a with -7) o hydraulically for U s ¼ % SP 54ms m 15.4 D D R R .The ). T T o an for ) k @ s )to 7 1 Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 ev lm 311%4.0% 10.7% 7.5% 5.8% – 0.9% 2.7% 16% 59% 38% 26% – 4% 10% 4311 16,043 10,329 6934 1004 2618 – fouling calcareous Heavy fouling calcareous weed Medium or fouling calcareous Small slime slime Heavy light or coating coating Deteriorated AF applied as Typical surface smooth Hydraulically ecito fcondition of Description power. shaft fixed . 07.Ti orsod oasedls of loss speed a to s from m corresponds ranges 0.14 This speed in 10.7%. – reduction 0.9 percentage the that al .Peitoso h hnei eurdsatpwr( s power m 15.4 shaft 21% of required speed a in at change conditions fouling the and coating of representative Predictions V. Table 458 calcareous Heavy calcareous Medium calcareous Small slime Heavy coating Deteriorated applied as Typical Hydraulically of speed a at conditions fouling s m and 7.7 coating ( representative power shaft required an in change for the of Predictions IV. Table s m 15.4 of of speed ship layer a for power heavy a increased is for power the 86%. required by until, with the fouling, fouling increase calcareous of to continues severity penalty powering condition of Description pe tafie nu hf oe f2.7 of power shaft in input reduction fixed percentage a the at is speed V same Also Table results. the in this resistance for the presented speed in at discussed cruising was increases at as reason – than percentage 4 lower from the are ranges speed general, fouling In and roughness 59%. penalty hull powering to percentage The due V. Table in shown ula 54ms m 15.4 smooth at hydraulically the hull for power shaft required the xs n h rsn rdcin ilb made. be will predictions present the the and to similar exist forms hull for FFG literature the in results fouling fouling weed or fouling slime light or coating AF surface smooth h rdcin ftecag nrqie shaft required in change the of predictions The lhuhteeaerltvl e ulsaetrial full-scale few relatively are there Although 7 oecmaiosbtenteoe that ones the between comparisons some -7, lvrHzr er class Perry Hazard Oliver 7 1 1 knots). (15 7 1 o16ms m 1.6 to 7 1 U 3 nt) h nlssshows analysis The knots). (30 s ¼ 7 . s m 7.7 1 D 02 . knots). 3.2 – (0.28 9886% 54% 1908 1200 rgt ( frigate SP 8 35% 11% 781 250 –– 02% 50 @ 7 1 (kW) FFG 7 1 7 iharneof range a with -7) U 3 nt)are knots) (30 s ¼ U 54ms m 15.4 6 s % ¼ D 10 . s m 7.7 D SP SP 4 @ kW, D 7 @ SP 1 7 (kW) 1 D ) SP 7 o an for ) 1 3 nt) lopeetdi h ecnaedces nsedfra for speed in decrease percentage the is presented Also knots). (30 nwihtesatpwradsi pe were cleaning, speed After ( roughness again. ship hull average and performed the and cleaned were was trials power ship power the shaft Subsequently, the conducted measured. were to which little trials with Power in film fouling. indicated slime calcareous heavy inspection fairly no hull a of initial presence Hawaii An the Harbor, months. Pearl in and 22 fouling TBT for to and subject oxide been cuprous had both containing paint trials power class the study, on their slime conducted of In were effect powering. the ship quantify on to layers order in trials sea scale of increase form. hull measured similar the a on with is 24% which agreement method, good present by in predicted is fouling the iey hrfr,a2 2 nraein increase 32% – 22 respec- kW, a coating’ 2457 in Therefore, and kW tively. requirements ‘deteriorated 2258 as are power conditions and ‘typical these predicted the The coating’ between conditions. been AF have applied to expected the be on was roughness hull cleaning we h w oe ras hsi otappro- the most between is difference This the trials. by power represented priately two the tween acrosfuigo ed odto.I this In condition. s m weed’ 7.7 fouling the or condition, The fouling 24%. calcareous coincides pre-cleaning is best the that paper with fouling present the the from condition be to can that power attributed required in increase the Therefore, The f‘niin uewr rwh,terqie shaft required the coverage growth’, ( 20% – worm power 10 tube and ‘incipient grass’ a of ‘light and propeller with clean fouled a hull with operating When ship frigate. of on series a trials conducted powering (1980) Tate and Hundley ifrnei eurdsatpwro %a ship a at s 9% m 8.2 of power of shaft speed required in difference 264 alekadBhadr(92 odce full- conducted (1992) Bohlander and Haslbeck m lvrHzr er class Perry Hazard Oliver rgt.Tesi a otdwt naltv AF ablative an with coated was ship The frigate. SP sn h M ulRuhesAaye.A Analyzer. Roughness Hull BMT the using m U 7 SP s 1 fe h ulwscendws35 kW. 3650 was cleaned was hull the after ¼ % )at7.7ms 1 nt) ti o scerwa h post- the what clear as not is It knots). (15 54ms m 15.4 D SP SP @ hprssac n powering and resistance Ship 7 7 S aodE Holt E. Harold USS 1 1 speitdt e28 Wat kW 2989 be to predicted is 1 nt)wsmaue be- measured was knots) (16 Holt 7 S Brewton USS 1 rgt ( frigate 1 nt)ws42 kW. 4525 was knots) (15 Rt oe ra ste‘small the is trial power o fixed for 50 a esrdt be to measured was ) FFG euto nspeed in reduction % Holt 7 iharneof range a with -7) SP another , ,a u twould it but , ¼ 2.7 SP nxclass Knox 6 u to due 10 Knox 4 339 kW Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 eeoeet nruhesadfuigmysreto serve this. may elucidate fouling not further and significant is roughness with in Hydro- surfaces it heterogeneity have. on will present, measurements this significant At dynamic influence and the observed. case, clear often altogether the not is entire typically the variation is over This distribution homogeneous hull. a have assumed the was to In fouling and penalties. roughness powering the work, and present drag have resulting composition the community and on fouling fouling in and differences roughness spatial coating that role in the address heterogeneity area better Another to fleet. is work Navy future roughness US for hull entire the of to impact fouling economic and the methodol- assess this to utilise ogy to are plans good Future show of literature agreement. the trials in full-scale reported forms with hull Com- results similar present speed. the cruising of at parisons hull to smooth to compared hydraulically as predicted 86% a by is power this fouling shaft required for calcareous increase power Heavy shaft form. required hull a in deterio- cause to increase A predicted is speed. significant film slime top light coating or near coating rated and AF speed applied at cruising power shaft as both required in typical, penalties small a fairly suffers that show results illustrated was an method for The resistance. on frictional condition surface the law the of similarity impact the layer assess to boundary scaling with along and ship tests laboratory-scale resistance model from The results presented. frictional on been relies has the prediction ship full-scale on a of fouling powering rough- coating and of impact ness the predicting of method A Conclusions predictions. present the to similar are in ntepeetwr.A riigspeed cruising At work. present s the condi- m (7.7 coating’ in ‘deteriorated the tions and slime’ ‘heavy 340 oe a esrdfrteehl om.A maximum a forms. with the destroyer to hull for similar power speed observed input these was fixed shaft a 9% required at for of speed in maximum measured in 110% – reduction 60 was of power increase makes era an This cruising speed at frigate. 1930s However, – 1920 impractical. present differ comparisons battleship) direct the (two era from II War on significantly World a reported and destroyers forms hull Prevention in Its presented and are agreement fouling good calcareous very in is trials. full-scale from This the resulting 8%. the with power is required Given fouling in the kW. increase 2666 the coat- ing’, ‘deteriorated is the for condition prediction aforementioned slime’ ‘heavy ulsaetil ouetn h feto heavy of effect the documenting trials Full-scale lvrHzr er class Perry Hazard Oliver .P Schultz P. M. 7 1 r1 nt) h rdce Pi the in SP predicted the knots), 15 or Ao,15) notntl,the Unfortunately, 1952). (Anon, FFG-7 hs eut,therefore, results, These . rgt ( frigate aieFouling Marine FFG 7.The -7). rZeezyadt h eeesfrtermany Note their for referees Naval the suggestions. of and to comments Office and helpful and Beaver the Bill Zseleczky Mr by to Mr due also financial research are Thanks the this Research. acknowledges of gratefully support author The Acknowledgements .A lentv praht hprssac n powering and resistance ship to approach alternative An 1. ude L aeC.18.Hl-oln tde n ship and studies Hull-fouling 1980. CW. Tate LL, in Hundley roughness surface of review A 2006. B. Behrends D, Howell on effects biofilm hull Microbial by 1992. G. caused Bohlander ships EG, new drag Haslbeck of losses the Drag for 1992. CWB. methods Grigson indirect turbulent Three and 1987. resistance PS. frictional Granville The 1958. PS. Granville architecture. naval to Introduction 1982. B. super- Johnson TC, in Gillmer developments Recent 2006. K. Efimenko J, Genzer scaling Velocity-defect 2006. KA. Flack MP, Schultz JS, Connelly port on impacts environmental and Economic 2003. MA. Champ Wilkerson JF, Schumacher AW, Feinberg TG, Estes MD: ML, Annapolis, Carman prevention. its and fouling Marine Cost-benefit 1952. Anon. 2000. A. Milne DW, Arnold PD, Abel A, Abbott References aa hpRsac eeomn etrRpr # Report Center Development & p. Research 111 Taylor DTNSRDC-80/027. DW ships. Ship class 1052 FF Naval seven on results trial powering 410. length. – cutoff 22:401 of Biofouling importance the Symp. illustrating coatings Production antifouling Ship SNAME p. Proc 7 field. 3A-1. No. and Paper lab – drag 196. – 36:182 Res Ship plates. J finish. flat on 77. – surfaces 31:70 Res rough Ship J arbitrarily of 74. – 2:52 characterization Res Ship J surfaces. rough of layer boundary Institute. Naval US MD: Annapolis, a fouling: marine 360. – to 22:339 Biofouling relevance review. their and surfaces hydrophobic 195. roughness. – 40:188 relative of Fluids range Exp a with layers boundary turbulent for anti- 940. – marine 46:935 Bull harmful Pollut ban Mar to systems. convention fouling the from harbors and 21. – 22:11 2006. Biofouling wett- attachment. AB. cell correlating Brennan with – JA, ability microtopographies Callow ME, antifouling Callow Engineered LH, Wilson W, Institute. Naval US approach. treatment a for 19. – case 258:5 the Environ TBT: Total of Sci use the of analysis h eitneadpwrn rdcin rmtetomethods that two noted comparable. residuary the be generally from should the predictions are It powering the in used. and is 1983), resistance for frictional factor the al. US form accounted et no the the implicitly and Woo resistance, by is by 1982; Johnson, employed resistance multiplied & form procedure Gillmer form factor present (e.g. the Navy the form for In a accounts resistance. resistance. as explicitly form or due procedure resistance pressure be ITTC-78 to and assumed resistance The method. is frictional [ITTC], ITTC-78 component both the viscous to as the Conference to method, this referred Tank In generally compo- is total viscous Towing This the and 1978). that (International wavemaking assume of to nents comprised is is tests model resistance scale from prediction Downloaded By: [Us Naval Academy] At: 12:03 13 September 2007 oni L 03 h hphl oln eat.Biofouling penalty. fouling hull ship The 2003. RL. non- Townsin of evaluation and testing The 1996. MP. Schultz GW, Swain PB. Messersmith JA, Callow in M, Callow effects J, Dalsin Roughness J, Finlay 2006. A, Statz AJ. Smits JJ, Allen MA, Shockling boundary turbulent rough-wall The 2007. KA. skin Flack on MP, biofilms Schultz of influence The 2000. GW. Swain MP, turbulent Schultz on biofilms of effect coating The 1999. antifouling GW. Swain of MP, Schultz resistance Frictional 2004. MP. Schultz resistance frictional between relationship The 2002. MP. Schultz covered surfaces on layers boundary Jersey, Turbulent 2000. New MP. flow. Schultz Turbulent 1961. CM. Tchen GB, Schubauer through moving surfaces flat of Resistances York: 1932. New KE. Schoenherr ed. 7th theory. Boundary-layer 1979. H. Schlichting growth Biofilm 1980. WG. Characklis N, Zelver BF, Picologlou for underwater Waterbourne functions 2002. Manual. roughness Technical Ships’ Universal Naval 1981. – 1980 AJ. Musker for standard international draft a of Outline 1990. JS. Medhurst correlation and measurement systematic The 1989. in JS. flows Medhurst turbulent of discussion critical A 1938. CM. Millikan investigation An 1985. KW. Thomas AF, Molland JC, Lewthwaite experimental/numerical An 2003. L. Larsson M, Leer-Andersen to reference special with ships, of Resistance 1962. H. Lackenby channels. open in of roughness resistance Flexible 1973. the TE. on Unny N, roughness Kouwen of Biofouling effect the 2006. On 1937. G. B. Kempf Antolic M, Sliskovic G, Jelic-Mrcelic 15th Proc 1978. (ITTC) Conference Tank Towing International 9Spl)9–16. – 19(Suppl.):9 197. – 10:187 Biofouling coatings. antifouling mussels. toxic marine by inspired polymer 399. – 22:391 a Biofouling metal with of properties coated fouling-release surfaces and antifouling Algal 2006. 285. – 564:267 Mech Fluid J flow. pipe turbulent regime. rough 405. fully – 580:381 the Mech to Fluid smooth J hydraulically the from layer 139. – 15:129 Biofouling drag. friction 746. – 121:733 Eng Fluids J ASME layers. boundary 1047. – 126:1039 Eng Fluids J J ASME ASME systems. sanding. by 499. smoothed – 124:492 surfaces Eng Fluids for roughness 363. and – 122:357 Eng Fluids J ASME algae. filamentous with Press. University Princeton USA: 313. – 40:279 SNAME Trans fluid. a McGraw-Hill. – 106:733 Div Hydraulics 746. J ASCE performance. hydraulic and p. S9086-CQ-STM- 31 # Command. Systems Publication Sea ships. Naval Navy 010/CH-081R4. of cleaning hull 6. – 1:1 Eng Mech Soc Can Architects. Trans surfaces. Naval naturally-occurring of Institute p. Royal 9 London: 1990. March flow. fluid topography roughness in of characterisation and measurement the Thesis, PhD UK. Newcastle-upon-Tyne, antifoulings. of ablative Appl University coatings, to hull reference Congr ship particular of topography with Int and resistance frictional 5th the of Proc 392. – 386 tubes. pp MA. circular Cambridge, Mechanics, and channels 284. – 127:269 fouling. Architects with resistance Naval frictional Inst skin R ship Trans of variation the with into 36. – ships 8:26 Technol full-scale Sci on Mar friction J roughness. skin surface evaluating for approach Eng Mechl Inst Proc condition. 1014. surface – 176:981 hull and friction skin 728. – 99:713 Division Hydraulics J ASCE 119. – 79:109 INA Trans ships. TBT-free and 302. TBT – 22:293 with Biofouling paints. coated antifouling panels copper-based test on communities Hague. performance The of committee. report Conference: Tank Towing International SP smooth s S L l d rough t U D Re þ¼ Superscript PC length sampling mm 50 L k R experiment C y U R Fr roughness/fouling hull to due R k k g D C C C Appendix m Subscripts r n U D Rt D o L aaahG od .18.Si-oe orlto of correlation Ship-model 1983. G. Borda G, Karafiath EL, Woo The 1969. Y. Kawakami K, Yokoo N, Nagamatsu S, Watanabe o Ka von Estimating 1981. A. Milne TE, Svensen D, Byrne RL, Townsin w ¼ s ¼ ¼ ¼ plate ¼ ¼ R C SP U ¼ ¼ T R F A T R F ¼ ¼ t e ¼ ¼ ¼ ¼ 50 ah e isGo Wiss Ges Nachr oeigpromneo S lvrHzr er,FFG-7 Perry, 52. – Hazard 20:35 Technol Oliver Mar USS class. on performance powering Soc 51. Kansai – J 131:45 slime. Architects to Naval due resistance frictional in augmentation h ehia n cnmcpnliso uladpropeller and hull of 318. – penalties 89:295 SNAME economic Trans roughness. and technical the ¼ ¼ ¼ ¼ ¼ ¼ ¼ F ¼ T ¼ ¼ ¼ ¼ ¼ ship þ ¼ udknmtcviscosity kinematic fluid rvttoa acceleration gravitational itnefo h wall the from distance cl ratio scale thickness layer boundary ogns height roughness ogns height roughness uddensity fluid etdsraeae ftehull the of area surface wetted aeln length waterline qiaetsn ogns height roughness sand equivalent model velocity omlsdby normalised ¼ ¼ ¼ ¼ alserstress shear wall ruenumber Froude eoiya ue deo h onaylayer boundary the of edge outer at velocity enlsnumber Reynolds ¼ rcinvelocity friction ¼ rcinlrssac coefficient resistance frictional rcinlresistance frictional oa eitnecoefficient resistance total oa resistance total hf power shaft eiur eitnecoefficient resistance residuary eiur resistance residuary orlto allowance correlation ´rma rpliecoefficient propulsive ¼ aiu ekt ruhhih vra over height trough to peak maximum hnei h rcinlrssac coefficient resistance frictional the in change ¼ hnei oa resistance total in change SP ogns function roughness egho a lt sdi laboratory in used plate flat of length o culsraecondition surface actual for nT 90 ehnseahlcki n turbulenz. and aehnlichkeit Mechanishe 1930. T. ´n o yruial mohsraecondition surface smooth hydraulically for rough ¼ 7 L L hprssac n powering and resistance Ship ¼ m SP s tign5 76. – 58 ¨ttingen U R PC smooth T ¼ t ¼ U or q ¼ p U gL ffiffiffiffi UL n ffiffiffiffi t r w n / U t ¼ 2 1 r R U ¼ T ¼ 2 S 2 1 2 1 r r R U R U F R 2 2 S S 341