Prediction of Speed and Behaviour of a Ship in a Seaway

Transcription

1 ISP, Volum 3, No. 65, 1976 Rprintd: Wbsit: Rpport 047-P, 1976, Dlft Univrsity of Tchnology, Ship Hydromchnics Lbortory, Mklwg, 68 CD Dlft, Th Nthrlnds. Prdiction of Spd nd Bhviour of Ship in Swy J.M.J. Journé Dlft Univrsity of Tchnology Summry A computr progrm hs bn dvlopd to clcult spd nd bhviour of ship in swy. In this stg th progrm is suitbl for sgoing vssls in hd wvs. In dtrmining th spd, two fctors r considrd: th nturl spd rduction du to ddd rsistnc cusd by wind nd wvs nd th voluntry spd rduction by th ship's cptin, in ordr to prvnt svr motions. 1 Introduction For lmost twnty yrs now, ship's cptin cn mk us of routing dviss from wthr routing dprtmnts lik tht from th K.N.M.I. (Royl Nthrlnds Mtorologicl Institut) t D Bilt [1]. With known rough wthr pttrn in th ocn n optimum ship s rout cn b found with minimum trvlling tim, ful consumption or risk of dmg of th ship nd its crgo. Ths routing dviss, r bsd on th momntry nd xpctd wind nd wvs nd th ship s rction to thm. Th forcst of wind nd wvs is mtorologicl problm. Up to now th prdiction of th bhviour of ship in swy - spcilly th ship s spd - is bsd on routing xprinc with th ship considrd or similr ships. Whn routing ship for th first tim routing officr nds rlibl spd loss grphs, to rd th ship s spd s function of wv hight nd mn wv dirction. Dvlopmnts in th lst dcd md it possibl to clcult with sufficint ccurcy th spd in still wtr nd th nturl spd rduction du to ddd rsistnc cusd by wind nd wvs. At this thorticl spd dngrous motions cn ris for th sfty of crw, ship or crgo. Thn th mstr will voluntrily rduc spd in ordr to prvnt svr motions. Svrl critri for this dcision cn b found in litrtur. At th Ship Hydromchnics Lbortory of th Dlft Univrsity of Tchnology mthod hs bn dvlopd to clcult th nturl spd, th voluntry spd rduction nd th bhviour of th ship t 1

2 this spd in swy with hd wvs. This mthod hs bn workd out into n Algol 60 computr progrm, nmd ROUTE, which nbls prcticl us. Clcultion of Spd Aprt from wind nd s conditions, th spd of ship in swy minly dpnds on thr spcts: - dimnsions nd form of th ship's hull nd suprstructur, - dimnsions nd chrctristics of th propllr nd - output nd chrctristics of th propulsiv mchinry. Th nrgy flow of ship in oprtion is givn in th following schm. whr th rltion btwn givn by: = V 1 w V V { ( )} V nd V is At crtin ngin stting ths two qutions r solvd in th progrm ROUTE for vry wind nd s condition s shown in Figur 1. Th propllr bhind ship is considrd s n nrgy trnsformr: torqu with rpm will b trnsformd into thrust with mn spd of dvnc. At crtin stm or ful inlt rtio of th ngin thr will b quilibrium btwn th numbr of rvolutions nd th ship s spd. This quilibrium is in such wy tht two conditions r fulfilld: th torqu ndd by th propllr must b in quilibrium with th torqu dlivrd by th ngin nd th thrust dlivrd by th propllr must b in quilibrium with th totl rsistnc of th ship. Ths two conditions of quilibrium r shown in two coupld qutions s mntiond blow: R T Q ( Q, n, c, n) Q V = η (, n) ( V, V, α, H1/ 3, T, µ ) = T ( V, n) W m W 0 0 m { 1 t( V, n) } Figur 1 Schm of Spd Clcultion For numbr of ship spds th rltions btwn torqu ndd by propllr nd rpm r clcultd from th torqu chrctristics of th propllr bhind th ship nd n dptd wk frction. Th rltion btwn torqu dlivrd by th ngin to th propllr nd rpm is known from ngin chrctristics nd shft losss. Ths rltions giv rltion of quilibrium for spd nd rpm, which togthr with th thrust chrctristics of th propllr bhind th ship nd thrust dduction frction rsults in rsistnc, which cn b chivd by propllr nd ngin, s function of th ship s spd. If th totl rsistnc of th ship for numbr of spds is known by clcultion th ctul spd of th ship cn b found.

3 Som prts ndd for th dtrmintion of th spd r discussd in th following prts of this chptr..1 Rsistnc Th totl rsistnc of ship in swy is dividd into thr prts: V - still wtr rsistnc: R SW ( ) - wind rsistnc: R ( V,, α ) W V W - ddd rsistnc du to wvs: V, H 1/ 3, T, µ R AW ( ) So th rltion btwn rsistnc nd thrust cn b writtn s: R SW ( V ) + R ( V, V, α ) + R = T AW ( V, H 1/ 3, T, µ ) W ( V, n) { 1 t( V, n) } W Th dtrmintion of ths thr componnts of th rsistnc is givn in mor dtil in th following prgrphs..1.1 Still Wtr Rsistnc In litrtur svrl mthods hv bn dscribd to dtrmin th still wtr rsistnc of ship. Ths mthods hv bn bsd on th rsults of lrg numbr of modl xprimnts nd fullscl xprimnts which hv bn systmticlly or sttisticlly trnsformd into grphs, tbls or mpiricl formuls. Up to now in th computr progrm ROUTE, on of th nxt two mthods cn b usd: Th mthod of th Shipbuilding Rsrch Assocition of Jpn []. This mthod hs bn dvlopd for fst slndr ships with blockcofficint btwn 0.55 nd It is grt dvntg of this mthod tht it cn b usd for diffrnt loding conditions of th ship. Th mthod of Lp [3] with n xtnsion of Auf m Kllr [4]. This W W + = mthod cn b usd for most norml nd full ships in full lod condition. With lss ccurcy ship in light lod condition cn b considrd s ship in full lod condition with lrg brdth - drught rtio. Both mthods r vlid for singl-scrw ships with limitd spd rng. For too low spd th rsistnc is xtrpoltd with scond-dgr polynomil nd for too high spd with third dgr polynomil. No llowncs r md for fouling or bulbous bow. In th progrm howvr, it is possibl to multiply th still wtr rsistnc with corrction fctor..1. Wind Rsistnc For continrships nd ships in bllst condition th wind rsistnc oftn is prt of th totl rsistnc which my not b nglctd. Ishrwood [5] hs nlysd th rsults of wind rsistnc xprimnts crrid out t diffrnt lbortoris with modls covring wid rng of mrchnt ships. H givs mpiricl formuls for dtrmining th two horizontl componnts of th wind forc nd th wind-inducd ywing momnt on ny mrchnt ship form for wind from ny dirction. Th formul nd th corrsponding cofficints for th wind rsistnc r usd in th progrm..1.3 Addd Rsistnc du to Wvs To clcult th ddd rsistnc of ship in swy computr progrm, nmd TRIAL, is vilbl t th Dlft Ship Hydromchnics Lbortory. An rlir vrsion of th progrm hs bn dscribd in [6]. Th ship is considrd to trvl in unidirctionl hd wvs nd only pitch nd hv motions r dtrmind. Addd mss nd dmping for th ships crosssctions r clcultd by using Lwis 3

4 conforml trnsformtion. Th rsulting fit to th ctul cross sctionl form is stisfctory for th prsnt purpos [7]. Th incrs of rsistnc in rgulr wvs is clcultd with th mthod of Grritsm nd Buklmn by dtrmining th rditd nrgy of th dmping wvs s dscribd in [8]. Th clcultion in n irrgulr s is bsd on th suprposition principl for th componnts of th wv, motion nd rsistnc spctr s wll s on th ssumption of linrity for th ship s rspons. In rgulr wvs th ddd rsistnc vris s th squr of th wv mplitud. In wv spctrum th mn ddd rsistnc would thn b clcultd from: RAW R AW = ( ω ) ( ) Sζ ω dω 0 ζ Th progrm TRIAL hs bn dptd to this spcil problm in th progrm ROUTE. For th dscription of th s surfc two prmtr Pirson-Moskowitz wv spctr r usd. For ch wv spctrum, th mn ddd rsistnc is clcultd s function of th ship s spd.. Propllr Chrctristics Thrust nd torqu of n opn-wtr propllr r dfind by: 4 T = K ρd n Q = K T Q ρd Th cofficints K T nd K Q r dpnding on th numbr of propllr blds, bld r rtio, pitch rtio nd dvnc cofficint which is dfind by: V J = nd Propllr chrctristics cn b obtind from opn-wtr tst rsults of th Wgningn B-sris propllrs, which r 5 n frquntly usd in prctic. At prsnt bout 10 propllr modls of th B-sris hv bn tstd t th Nthrlnds Ship Modl Bsin. Th thrust nd torqu cofficints r xprssd by Oostrvld nd Vn Oossnn [9] s polynomils in th numbr of propllr blds, bld r rtio, pitch rtio nd dvnc cofficint. With th id of multipl rgrssion nlysis th significnt trms of th polynomils nd th vlus of th corrsponding cofficints r dtrmind. Th polynomils r vlid for opn-wtr propllr modls with Rynolds numbr 6 Rn = 10. Oostrvld nd Vn Oossnn [10] lso giv polynomils to corrct thrust nd torqu cofficints for th ctul Rynolds numbr of th full-siz B-sris opnwtr propllr. Ths polynomils r usd in th progrm. For th propllr bhind ship th clcultd torqu must b corrctd for this bhind condition: η = Q R Q opn wtr bhindship For singl-scrw ships 1.04 is good mn vlu for this rltiv rottiv fficincy, whil for twin-scrw ships 0.97 is dvisd..3 Wk nd Thrust Dduction In th progrm, th wk frction nd th thrust dduction frction cn b stimtd by vry simpl formuls. If on of ths vlus is known, for instnc from modl tsts, it is lso possibl to mk us of this vlu. Wk frction: Tylor [11] singl-scrw ship: w = twin-scrw ship: w = Hrvld [1] C b C b 4

5 singl-scrw ship: w = w( Cb, L / B, D / L, hull form ) twin-scrw ship: w = w( Cb, L / B) A givn vlu of th wk frction. Thrust dduction frction: Wingrt: singl-scrw ship: C b t = w C b Cwp twin-scrw ship: C b t = w C b Cwp A givn vlu of thrust dduction frction - wk frction rtio. A givn vlu of th thrust dduction frction. Th bov mntiond vlus r vlid in still wtr. Modl tsts in still wtr showd tht wk frction nd thrust dduction frction r prcticlly indpndnt of spd. It cn b shown from ovrlod tsts in still wtr tht t n incrsing propllr loding nd constnt numbr of rvolutions, th wk frction kps constnt nd th thrust dduction frction is pproximtly linrly dcrsing with th modl spd. Exprimnts t th Dlft Univrsity of Tchnology with modl of fst crgo ship showd no diffrnc btwn still wtr nd rgulr wvs for both frctions t th sm vrg loding of th propllr [8]. In this connction two importnt typs of ngins for ship's propulsion r distinguishd..4.1 Turbin Usully it is ccptd tht t n incrsing ngin loding nd constnt ngin stting th powr rmins constnt. This mns hyprbolic rltion btwn torqu nd numbr of rvolutions: n0 Q = c ηm Q0 n According to som uthors lik Gislr nd Simr [13] nd Goodwin t. l. [14] in prctic thr is linr rltion btwn torqu nd numbr of rvolutions: n Q = c η ( ) m Q0 1 n 0 whr th cofficint dpnds on th typ of th turbin: = If on tks into considrtion tht th numbr of rvolutions of th propllr of ship in s-wy will not rduc mor thn prcnt t constnt stm inlt rtio, th ssumption of constnt powr is sufficintly ccurt for clculting th ship s spd. Th rltions btwn torqu nd rpm mntiond bov r shown in figur..4 Engin Chrctristics For solving th qution btwn th ndd nd dlivrd torqu t th propllr it is ncssry to know th rltion btwn torqu nd rpm of th ngin t crtin stm or ful inlt rtio. Figur 3 Torqu RPM Rltion of Turbin 5

6 .4. Disl Engin For disl ngin it is mostly ccptd tht t n incrsing ngin loding nd constnt ngin stting th torqu rmins constnt. This mns tht =1. 0 in th lst qution nd so: Q = c η m Q 0 In prctic thr is som diffrnc with this ssumption. At constnt ngin stting nd n incrsing ngin loding th torqu will incrs first, thn obtins mximum vlu nd ftrwrds will dcrs gin. This cn b pproximtd by linr rltion btwn torqu nd numbr of rvolutions, providd tht th numbr of rvolutions will not rduc mor thn pr cnt. Thn th linr torqu-rpm rltion cn b usd with for instnc =1. 5. Ths rltions btwn torqu nd numbr of rvolutions r shown in Figur 3. Figur 3 Torqu-RPM Rltion for Disl Engin 3 Clcultion of Motions Th progrm TRIAL, mntiond bfor, clcults vrticl bsolut nd rltiv motions in rgulr wvs for diffrnt ship spds. Ship motions in n irrgulr s r dtrmind by linr suprposition of th ship rsponss to th individul rgulr wv componnts. Figur 4 Symbols nd Dfinitions Lt us considr th hv motion s n xmpl for th clculting mthod. Th dfinitions nd symbols r shown in Figur 4. In complx nottion th hv motion in rgulr wvs cn b writtn s: z ( ) ζ ( ω ε ζ ) ( ω i t+ z t = H ) zζ whr z H zζ ( ω ) = ( ω ) ζ dfins th rspons function of th hv motion. Th suprposition principl nbls th clcultion of th vrinc of th hv motion in known wv spctrum: whr S z m ( ) 0z = S z ω dω 0 ( ω ) = H ( ω ) S ( ω ) zζ dfins th hv spctrum. For most prcticl pplictions it my b ssumd tht motion, vlocity nd cclrtion mplituds follow th Ryligh distribution lw. In this xmpl th probbility tht th hv mplitud * xcds crtin vlu z is givn by: * ( z ) * m0z Pr z > z = { } Th occurrnc rt for this pr hour will b: ζ 6

7 * * { z > z } = Pr{ z > z } 3600 N m0z π mz in which th scond momnt of th hv spctrum is givn by: m ( ) z = S zζ ω ω dω 0 Th significnt mplitud of th hv motion is givn by: 1/ 3 = m z 0z In this wy th progrm TRIAL clcults th significnt mplituds of hv, pitch, bsolut nd rltiv motions nd cclrtions nd th probbility nd numbr pr hour of xcding crtin vlu by th rltiv motion. 3.1 Rltiv Motions Nglcting th wv disturbnc by th ship th rltiv motion t longitudinl distnc x b from th cntr of grvity is givn by: s ζ z + x θ whr xb = xb b ζ is th vrticl wv displcmnt t position x b. Significnt mplituds nd probbilitis of xcding givn vlu r clcultd s showd for th hv motion. Bcus of bow wvs nd sinkg du to th ship s spd, th ffctiv frbord f t th bow gnrlly diffrs from th gomtric frbord f. Tski [15] givs n mpiricl formul for this sttic swll-up t th bow: L f = f f = 0.75 B Fn L with L is th ship lngth nd L is th lngth of ntrnc of th wtr lin. Exprimnts t th Dlft Ship Hydromchnics Lbortory with modl of fst crgo ship in full lod nd in bllst condition hs shown rmrkbly good grmnt btwn th msurmnts nd this mpiricl formul. For clculting th probbility of dck wtnss t th forwrd prpndiculrs th gomtricl frbord is dcrsd with th sttic swll-up obtind from Tski's formul. Gnrlly, th probbility of slmming will b clcultd t sttion 17 or 18. It is ssumd tht th sttic swll-up t ths sttions is zro t th instnt of r-ntry of th forfoot in th wtr in cs of slmming. Dynmic phnomn incrs th mplitud of th rltiv motion t th bow; thr is dynmic swll-up. Whn th bow immrss, th wtr surfc will ris nd whn th bow mrgs, th wtr surfc will fll. Tski [15] hs crrid out forcd oscilltion tsts with towd ship modl in still wtr to msur th displcmnt of th wtr surfc rltiv to th bow of th modl. From th rsults of ths xprimnts h hs obtind n mpiricl formul to stimt th dynmic swll-up t th bow: s Cb 0.45 L = ω s 3 g with th rstriction: 0.60 < C b < 0.80 So th mplitud of th rltiv motion t th bow is: * s s = + s 1 s This formul is usd in th progrm for clculting th probbility of shipping wtr t th forwrd prpndiculrs. Vn Sluys nd Tn hv crrid out xprimnts in rgulr wvs [16] with compct frigts tht hv shown tht th wv mplitud long th ship s hull is influncd by fctor btwn 0 nd. Th highst dynmic swll-up pprd in th nighbourhood of sttion 17 or 18. Also, xprimnts t th Dlft Ship Hydromchnics Lbortory hv shown 7

8 hr dynmic swll-up of roughly doubl th vlu of th dynmic swll-up t th bow. For clculting th probbility of slmming it is ssumd tht th dynmic swll-up t sttion 17 or 18 is doubl th vlu of Tski t th bow. Mor invstigtions r ncssry to stimt good mn vlu. 3. Acclrtions Th bsolut motion t longitudinl distnc x b from th cntr of grvity cn b xprssd in hv nd pitch motions by: v z x θ = b Th rspons function of th bsolut motion is: v H vζ ( ω, xb ) = ( ω, xb ) ζ which lso cn b usd for clculting th rspons function of th cclrtions t position x by: H v && ζ b ( ω x ) = H ( ω, x ) ω, b vζ b Th vrinc of th cclrtions in wv spctrum nd th Ryligh distribution givs th probbility of xcding crtin vlu by th mplitud of th cclrtion: * ( v && ) * m0 v&& Pr v & > v && = { } It is lso possibl to dtrmin th probbility of xcding crtin vlu by th significnt mplitud of th cclrtion. As Ochi nd Mottr hv shown in [17], th probbility xprssion: Pr { v & 1/ 3 > } b is th sm xprssion s: 1 Pr v & ln b b This xprssion will b usd in chptr 4. 4 Voluntry Spd Rduction Whn ship ncountrs svr storm th ship s cptin will rduc spd in ordr to s svr motions. Th most importnt phnomn for this dcision r th probbility of occurrnc nd svrity of: 1. Dck wtnss Cusd by shipping wtr, this will hppn if th rltiv motion of th bow xcds th ffctiv frbord forwrd. Th probbility of dck wtnss is xprssd by: Pr in which swll-up. f m0 s { dck wtn ss} = m 0 includs th dynmic s. Slmming Slmming is phnomnon ssocitd with xtrm ship motions in wvs. At crtin ship spds in rough ss, th forfoot of th ship mrgs from th wtr s rsult of lrg pitch nd hv motions nd violntly impcts th wtr surfc s it r-ntrs. Th ship's forwrd bottom thrby sustins hvy impulsiv prssur from th wtr nd this impulsiv forc producs shuddr throughout th hull. According to Ochi [18] th probbility of occurrnc of slmming is th joint probbility tht th bow mrgs nd tht th rltiv vlocity xcds crtin mgnitud t th instnt of rntry. H found criticl rltiv vlocity btwn th bow nd wvs, blow which slmming dos not occur nd rcommnds s good thrshold vlu: s & cr = g L Th probbility of slmming is xprssd by: Pr { slmming } = T s& cr + m0s m0s& 8

9 in which m os nd dynmic swll-up. m 0 s & includ th 3. Propllr rcing Th tim-dpndnt immrsion of th propllr rsults in fluctuting torqu nd thrust of th propllr. Although th rpm govrnors grtly rduc possibl dmg to th proplling mchinry du to rcing, lrg torqu nd thrust fluctutions r obsrvd in wvs, vn t constnt rpm. Artssn [19] nlysd lot of fullscl trils nd dfind for propllr rcing: thr is rcing - or th propllr will b clld mrgnt - on vry occsion whn th dcrs of torqu is in xcss of 5 pr cnt. Nglcting sttic nd dynmic swll-up t th strn, Fukud [] hs doptd occurrnc of propllr rcing whn th propllr mrgnc xcds onthird of th dimtr of th propllr. 4. Acclrtions Too high cclrtions cn lso b rson to rduc spd. Th mgnitud of th cclrtions is strongly dpndnt on th ship s lngth. Artssn [0] msurd on th trwlr Blgin Ldy vn cclrtions of.75 g t th forwrd prpndiculrs. Grritsm showd th sm in [1]. In [17] Ochi nd Mottr distinguish, for th stimtion of limit blow which no voluntry spd rduction is xpctd, two loding conditions: 1. Full lod condition In this condition voluntry spd rduction is dpnding on dck wtnss nd cclrtions t th bow: sign. mpl. dck of bow wtnss Pr nd/or cc. will 0.07 t xcd Sttion g. Light lod condition Slmming t sttion 17 nd bow cclrtion r in this condition rsons for voluntry spd rduction. sign. mpl. slm of bow impct Pr nd/or cc. will 0.03 t xcd Sttion g Rltiv motion nd vlocity r both norml rndom procsss, so thy r trtd s sttisticlly indpndnt. For two sttisticl indpndnt vnts A nd B my b writtn: Pr And/or B = { } = 1.0 Pr = 1.0 Pr So th probbility function: Pr And/or B {( not A) nd/or ( not B) } { not A} Pr{ not A} { } c my b writtn s: Pr not A Pr not A 1. 0 { } { } c As mntiond in Sction 3., th probbility xprssion with significnt cclrtion mplitud cn b xprssd in th mplitud of this cclrtion nd th two critri of Ochi nd Mottr cn b xprssd s follows: Full lod condition: f m0s 0 1 m 1 ( g) v& &

10 Light lod condition: T s& cr + 0 m s m0 s& 0 1 m 1 ( g) v&& 0.97 Ths two conditions r usd in th progrm ROUTE 5 Prcticl Applictions In th following prts of this Chptr dscription of th dt input in th progrm is givn with discussion bout s nd wind conditions. For six ships, clcultion rsults r comprd with fullscl msurmnts. Th tim usd by n IBM 370/158 systm, lik tht of th Mthmticl Cntr of th Dlft Univrsity of Tchnology, for clculting spd nd motions in swy is bout two minuts for on loding condition with mmory us of bout 400 Kbyts. 5.1 Dscription of Dt Input Th progrm nds much informtion bout th ship. To show this, th dt input for fully lodd ship is givn hr: - txt crd with 80 symbols including spcs - lngth t dsign wtrlin - lngth btwn prpndiculrs - distnc from ordint zro until APP - rtio btwn gyrdius nd lngth btwn prpndiculrs - stimtd srvic spd - vn numbr of ordint intrvls - vn numbr of wtrlin distncs - numbr of wv nd wind dirctions - numbr of points for which rltiv motions will b clcultd - numbr of wv spctr nd wind spds - numbr of powr inputs - rry with ordint distncs from ordint zro until forwrd - from ordint zro until forwrd, for vry ordint: - ordint numbr - rry with hlf widths of th sction t th wtrlins from kl until lod wtrlin - rry with wtrlin distncs of th sction from kl until lod wtrlin - rry with positions with rspct to ordint zro of th points for which rltiv motions, shipping wtr, slmming nd cclrtion forwrd will b clcultd - rry with z -vlus for clculting th probbility of xcding, shipping wtr nd slmming (bov lod wtrlin is positiv) - rry with wv dirctions (hd wvs is 180 dgrs) - rry with bsolut wind dirctions (hd wind is 180 dgrs) - rry with significnt wv hights - rry with vrg wv priods - rry with bsolut wind spds - lngth ovrll - ltrl projctd wind r - trnsvrs projctd wind r - lngth of primtr of ltrl projctd wind r xcluding wtrlin nd slndr bodis such s msts nd vntiltors - numbr of distinct groups of msts or king posts sn in ltrl projction - typ of stimtion mthod of th still wtr rsistnc: - 1 = mthod of Lp nd Auf 'm Kllr - = mthod of Shipbuilding Rsrch Assocition of Jpn - multipliction cofficint for corrcting th clcultd still wtr rsistnc for bulbous bow, fouling, tc - typ of stimtion mthod of th wk frction: - 1 = mthod of Tylor - = mthod of Hrvld - 3 = givn vlu of w - if typ = 3 : vlu of w 10

11 - typ of stimtion mthod of th thrust dduction frction: - 1 = mthod of Wingrt - = givn vlu of t / w - 3 = givn vlu of t - if typ = : vlu of t / w - if typ = 3: vlu of t - rltiv rottiv fficincy - numbr of propllrs - numbr of propllr blds - dimtr of propllr - bld r rtio - pitch rtio - booln: English horspowr (1 hp = 76 kg m/sc) - for vry input of powr: - typ of mchin: 1 = powr is constnt = torqu-rpm is linr - stm or ful inlt rtio - mchnicl fficincy of th shft brings - powr in dsign condition - rpm in dsign condition - if typ = : linr cofficint of torqu-rpm rltion - booln: bllst condition - if this booln is tru: - chng of drught t ordint zro - chng of drught forwrd - rtio of gyrdius nd lngth btwn prpndiculrs. Th dimnsions of th diffrnt vlus r: lngth: mtr tim: scond spd: knots powr: horspowr ngl: dgr 5. S nd Wind Conditions Th rcommndtions of th twlfth I.T.T.C., Rom, 1969, r usd for th dscription of s nd wind conditions. Th wv spctr r dfind by: S ζ ( ω ) A = 5 ω B ω 4 in which: ω A, B wv frquncy nd cofficints. If sttisticl informtion is vilbl on th chrctristic wv priod T nd th significnt wv hight H 1/ 3, twoprmtr spctrl formultion cn b usd by dfining: 1/ H 691 A = nd B = 4 5 T T in which: H 1/ 3 = 4 m T = π 0 m m This priod is bsd on th spctrl cntr of grvity nd it cn b tkn s th obsrvd priod. Th spctrl formultion, mntiond bov, is usd in th progrm. If th only informtion vilbl is th significnt wv hight, th 1 th ITTC rcommnds for th cofficints A nd B : 3.11 A = 0.78 nd B = H 1/ 3 This mns in th two-prmtr spctrl formultion rltion btwn significnt wv hight nd chrctristic wv priod: T = 3.86 H 0 / 3 Th 1 th ITTC lso rcommnds rltion btwn wind spd nd significnt wv hight in n opn ocn whn no dt r vilbl: VW H 1/ 3 (kn) (m)

12 5.3 Clcultions nd Full Scl Msurmnts For six ships clcultion rsults of progrm ROUTE r comprd with fullscl msurmnts: 4 ships with disl ngin nd ships with turbin propulsion plnt. Th min dimnsions of ths ships r shown in Tbl 1. Only msurmnts in hd wvs 0 0 ( 150 µ 180 ) r obsrvd to compr thm with clcultions of th bhviour of ths ships in hd wind nd 0 wvs ( 180 ). In clculting th wv spctr th rltion btwn significnt wv hight nd vrg wv priod is dfind by: T = 3.86 H 1/ 3 s mntiond bfor. Th corrsponding wind spd s rcommndd by th twlfth I.T.T.C. is usd. It my b notd tht diffrncs btwn prdictions nd msurmnts, prt from possibl disgrmnts btwn thory nd prctic, cn b cusd by diffrnt rsons. All msurmnts hv crtin rror dpnding on msuring tchniqus nd ccurcy of th msuring quipmnt. Thr is lwys diffrnc btwn th ctul wv spctrum nd th wv spctrum drivd from spctrl formultion with msurd, stimtd or ssumd significnt wv hight nd vrg wv priod. Th input vlus in th progrm, lik ngin stting corrsponding to crtin torqu or powr, wv dirction, wind dirction nd wind spd r mn vlus. Dvitions from ths mn vlus rsult in diffrncs btwn prdictd nd msurd bhviour of th ship. Tbl 1 Min Dimnsions of Compring Ships 1

13 Firstly th clcultion rsults for th four ships with disl propulsion plnt will b discussd nd ftr tht th rsults for th two ships with turbin propulsion plnt. In th lst two dcds, Artssn hs crrid out xprimnts with svrl ships to study th bhviour of ths ships in swy. Th msurmnt rsults of 4 ships r usd to compr thm with th prdictions in hd wvs: m.s. Lukug [3] m.s. Lubumbshi [4, 5] m.s. Jordns [19] m.s. Drt Europ [6]. Th first thr ships r convntionl crgo linrs nd th lst on is continrship, ll ownd by th Compgni Mritim Blg in Antwrp, Blgium. Artssn givs in his pprs much informtion nd dt. Th following r usd to compr thm with th prdictions: powr dlivrd t th propllr, numbr of rvolutions pr minut of th propllr, spd, significnt wv hight nd th significnt mplituds of pitch nd hv motions nd vrticl bow cclrtion. For m.s. Lukug, m.s. Lubumbshi nd m.s. Jordns, th incrs of powr du to fouling is ssumd to b 8 pr cnt of th powr in still wtr t th sm spd. In clculting th still wtr rsistnc of m.s. Drt Europ no llownc is md for th bulbous bow, so it is ssumd tht incrs of powr du to fouling will b nullifid by dcrs of powr du to bulbous bow. In ordr to gt good comprison it is ncssry to us th ctul torqu-rpm rltion in th clcultions. Figur 5 shows ths rltions for th torqu msurd t th propllr. Thos msurmnts r dividd into groups hving brodly th sm torqu. Assuming constnt torqu t constnt ngin stting, this mns groups of constnt ngin stting. For torqu qul to th torqu drivd from th brk horspowr of th ngin nd mximum rpm blonging to it, th ngin stting is ssumd to b 100 pr cnt. Th comprison btwn prdictions nd msurmnts r shown in Figurs 6, 7, 8 nd 9. Th prdictd spds r in rsonbly good until vry good grmnt with th mn vlus of th msurmnts. In rough ss howvr th prdictd spds r littl bit too low, but th msurmnt points scttr mor thn two knots. Th prdictd numbr of rvolutions is somwht too high; in mild wthr conditions vn highr thn th mximum vlu limitd by th govrnor of th ngin. Figur 11 shows tht this cn prtly b cusd by th stimtd wk nd thrust dduction frction. Anothr rson cn b possibl diffrnc btwn th chrctristics of th ctul propllr nd th chrctristics of th Wgningn B-sris propllr usd in th clcultions. Th prdictd significnt mplituds of pitch nd hv motions nd vrticl bow cclrtions r in good grmnt with th msurmnts by Artssn. Th clcultd limits of spd nd significnt wv hight for voluntry spd rduction du to th two critri of Ochi nd Mottr r lso plottd in th Figurs 6, 7, 8 nd 9. Thr ws no bd wthr in hd ss during th xprimnts of m.s. Lukug in full 1od condition nd m.s. Lubumbshi in both loding conditions. Th critri could not b chckd in ths css. Th critrion for full lod condition (in th Figurs mrkd by SH) with mximum probbility of shipping wtr nd xcding 0.4 g by th significnt mplitud of th bow cclrtion of 7 pr cnt, sms to b too low for m.s. Jordns nd m.s. Drt Europ. Th critrion for light lod condition (in th Figurs mrkd by SL) with mximum prmittd probbility of slmming nd xcding 0.4 g by th significnt mplitud of th bow cclrtion of 3 pr cnt, pprs lso to 13

14 b too low. Th critrion vlid in full lod condition sms to b bttr hr. Mor invstigtions r ncssry to gt good mn vlus for ths prcntgs usd in th progrm. Th prdictions of this computing mthod r lso comprd with msurmnts on turbin ships. In 197 Buklmn nd Buitnhk crrid out xprimnts on th continrship Atlntic Crown [7]. In th clcultions it is ssumd tht th still wtr rsistnc of this twin-scrw ship with bulbous bow, including fouling, is qul to th still wtr rsistnc clcultd by th mthod of th Shipbuilding Rsrch Assocition of Jpn for singl-scrw ships with convntionl bow, xcluding fouling. Th grmnts btwn prdictions nd msurmnts of spd, numbr of rvolutions nd pitch nd hv motions r vry good s is shown in Figur 10. Th routing offic of th Royl Nthrlnds Mtorologicl Institut md spd loss grphs vilbl for group of turbin ships. For on of ths ships, t.s. Kllti, prdictions r md in full lod condition. Th incrs of powr du to fouling is ssumd to b 8 pr cnt of th powr in still wtr t th sm spd. Th prdictions nd obsrvtions r shown in Figur 10. Mximum obsrvd spds r in good grmnt with th prdictd spds t 7500 horspowr. Th mximum continuous numbr of rvolutions of th propllr, 100 rpm, is in vry good grmnt with th prdictd vlu. 6 Finl Rmrks Th clcultion of th thr componnts of th totl rsistnc nd th spd of ship, t constnt ngin stting in swy, shows in Figur 1 for m.s. Lubumbshi tht ddd rsistnc du to wvs cn b considrbl prt of th totl rsistnc. At significnt wv hight corrsponding with Bufort 6 th ddd rsistnc is qul to th still wtr rsistnc. Of cours this is dpnding on th ship s lngth. In dsigning ship, much ttntion will b pid to th still wtr rsistnc in rltion to bull form nd xpnsiv bulbous bows. On th North Atlntic howvr, s stt of Bufort 6 is xcdd in 70 pr cnt of th tim during th wintr sson. In th summr sson this prcntg is 45 [1]. Considring this, it is worth whil to py mor ttntion to ddd rsistnc nd motions in swy. Th progrm ROUTE cn b n xpdint for invstigting this problm. This progrm cn b md suitbl for clculting th ful consumption of ship in swy ftr which it cn b usd for routing ship with minimum us of ful, prdictions of ful consumption, tc. Excpt for routing purposs, this progrm cn b usd for th dtrmintion of ndd mchin powr t srvic spd in crtin stt nd choic of propllr in th rgulr dsign procdur of ship, in lngthning of ships, tc. In th nr futur this progrm will lso b md suitbl for following wvs. 7 Acknowldgmnt Th uthor wishs to thnk Prof. ir. J. Grritsm nd Mr. W. Buklmn for thir stimulting ttntion pid to this work nd thir vlubl dviss nd rmrks. Th convrstions with Ir. D. Mons of th Royl Nthrlnds Mtorologicl Institut bout routing problms r vry much pprcitd. Lst but not lst th prprtion of th grphs by Mr. P. d Hr is grtfully cknowldgd. 8 Rfrncs [1] W. D. Mons, Mtorologicl Routing (in Dutch). 14

15 [] Dsign Chrts for th Propulsiv Prformncs of High Spd Crgo Linrs, Th Shipbuilding Rsrch Assocition of Jpn, [3] A. J. W. Lp, Digrms for Dtrmining th Rsistnc of Singl Scrw Ships, Intrntionl Shipbuilding Progrss, Vol. 1, No. 4, [4] W.H. Auf m Kllr, Extndd Digrms for Dtrmining th Rsistnc nd Rquird Powr for Singl Scrw Ships, Intrntionl Shipbuilding Progrss, Vol. 0, No. 5, [5] W. Buklmn nd E.F. Bijlsm, Dscription of Progrm to Clcult th Bhviour of Ship in Swy (nmd TRIAL), Rport 383, Dlft Univrsity of Tchnology, Ship Hydromchnics Lbortory. [7] J. Grritsm nd W. Buklmn, Anlysis of th Modifid Strip Thory for th Clcultion of Ship Motions nd Wv Bnding Momnts, Nthrlnds Ship Rsrch Cntr TNO, Shipbuilding Dprtmnt, Rport 96-S. [8] J. Grritsm nd W. Buklmn, Anlysis of th Rsistnc Incrs in Wvs of Fst Crgo Ship, Intrntionl Shipbuilding Progrss, Vol. 19, No. 17, 197. [9] M.W.C. Oostrvld nd P. vn Oossnn, Rcnt Dvlopmnts in Mrin Propllr Hydrodynmics, Intrntionl Jubil Mting 197, NSMB, Wgningn. [10] M.W.G. Oostrvld nd P. vn Oossnn, Rprsnttion of Propllr Chrctristics Suitbl for Prliminry Ship Dsign Studis, Intrntionl Confrnc on Computr Applictions in th Automtion of Shipyrd Oprtion nd Ship Dsign, Tokyo, [11] W. J. Luk, Exprimntl Invstigtion on Wk nd Thrust Dduction Vlus, Trns. of th Inst. of Nvl Arch., 1910, 1914, [1] S.A. Hrvld, Wk of Mrchnt Ships, Doctor's Thsis, Th Dnish Tchnicl Prss, Copnhgn, [13] 0. Gislr nd G. Simr, Dynmisch Blstung von Schiffsdmpfturbinnnlgn bi Umstur-Mnövrn, Schiff und Hfn, Hft 3, [14] A.J.H. Goodwin, t. l., Th Prcticl Appliction of Computrs in Mrin Enginring. [15] Shipmnt of Wtr in Wvs, Th Socity of Nvl Architcts of Jpn, 60 th Annivrsry Sris, Vol. 8, Pr. 6.4, [16] M.F. vn Sluys nd Tn Sng Gi, Bhviour nd Prformnc of Compct Frigts in Hd Ss, Intrntionl Shipbuilding Progrss, Vol. 19, No. 10, Fbrury 197. [17] M.K. Ochi nd E. Mottr, Prdiction of Extrm Ship Rsponss in Rough Ss of th North Atlntic, Intrntionl Symposium on th Dynmics of Mrin Vhicls nd Structurs in Wvs. London, 1974, Ppr 0. [18] M.K. Ochi, Prdiction of Occurrnc nd Svrity of Ship Slmming t S, 5 th Symposium on Nvl Hydrodynmics, Brgn, Norwy, [19] G. Artssn, Srvic Prformnc nd Skping Trils on m.v. Jordns, [0] G. Artssn, Lboring of Ships in Rough Ss, SNAME, Dimond Jubil Intrntionl Mting, Nw York, [1] J. Grritsm, Sustind S Spd, 1 th ITTC, Rom,

16 [] J. Fukud, Y. Ono nd G. Ogt, Dtrmintion of For nd Aftr Drught of Bllstd Bulk Crrirs Associtd with th Critri of Slmming nd Propllr Rcing, 11 th ITTC, Tokyo, [3] G. Artssn, Srvic Prformnc nd Skping Trils on m.v. Lukug. [4] G. Artssn, S Trils on 9500 Ton Ddwight Motor Crgo Linr. [5] G. Artssn, Furthr S Trils on th Lubumbshi. [6] G. Artssn nd M.F. vn Sluys, Srvic Prformnc nd Skping Trils on Lrg Continrship, TRINA, Vol. 114, 197. [7] W. Buklmn nd M. Buitnhk, Full Scl Msurmnts nd Prdictd Skping Prformnc of th Continrship Atlntic Crown, TNO Rport 185S. [8] J.M.J. Journé, Motions, Rsistnc nd Propulsion of Ship in Longitudinl Rgulr Wvs, Rport 48, Dlft Univrsity of Tchnology, Ship Hydromchnics Lbortory, Fbrury List of Symbols RSW R W R R T Q AW T Qm Q n n 0 0 still wtr rsistnc wind rsistnc ddd rsistnc du to wvs totl rsistnc trust of th propllr torqu t th propllr torqu t th ngin torqu t th ngin (dsign mximum) numbr of rvolutions numbr of rvolutions (dsign mximum) cofficint for th torqu-rpm rltion P V V t w V α W W powr spd of dvnc ship s spd thrust dduction frction wk frction tru wind spd tru wind dirction H 1/ 3 significnt wv hight T vrg wv priod µ wv dirction c stm or ful inlt rtio ηm mchnicl fficincy of th shft brings KT thrust cofficint KQ torqu cofficint ρ dnsity of wtr D dimtr of propllr J dvnc cofficint ηr rltiv rottiv fficincy L lngth B brdth T drught C block cofficint C θ z v v& & s x b b ζ ω S wp.. m f f.. Pr g ω { } wtr pln cofficint pitch motion hv motion bsolut vrticl motion vrticl cclrtion rltiv vrticl motion longitudinl distnc to cntr of grvity wv mplitud frquncy of ncountr spctrl vlu vrinc or spctrl momnt gomtric frbord ffctiv frbord probbility cclrtion of grvity circulr wv frquncy 16

17 Figur 5 Msurd nd Assumd Torqu-RPM Rltion for Disl Proplld Ships 17

18 Figur 6 Prdictd nd Msurd Bhviour of m.s. Lukug in Swy (Hd Wvs) 18

19 Figur 7 Prdictd nd Msurd Bhviour of m.s. Lubumbshi in Swy (Hd Wvs) 19

20 Figur 8 Prdictd nd Msurd Bhviour of m.s. Jordns in Swy (Hd Wvs) 0

21 Figur 9 Prdictd nd Msurd Bhviour of m.s. Drt Europ in Swy (Hd Wvs) 1

22 Figur 10 Prdictd nd Msurd Bhviour of Turbin Ships in Swy (Hd Wvs)

23 Figur 11 Influnc of Estimtd Wk nd Thrust Dduction Frction on Clcultd Spd nd RPM 3

24 Figur 1 Division of th 3 Componnts of Totl Rsistnc t Constnt Engin Stting of Ship in Swy (Hd Wvs) 4