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Numerical Simulation for Submerged Body Fitted with Hydrofoil by Boundary Element Method
by Satoshi Masuda, Member, Yoshikazu Kasahara, Member Isao Ashidate, Member
Summary Recently many kinds of high speed boats have been developed. The hydrofoil type is one of them. On considering the hydrofoil type, one important problem is interaction, for example, interaction between the main hull and the hydrofoil, the hydrofoil and the free surface etc. Here we consider the interaction between the free surface and a submerged lifting body by numerical simulation. The submerged lifting body is composed of a submerged body and a hydrofoil adapted to it. The numerical method is the Boundary Element Method (BEM) that was originally developed at Hiroshima Univer sity by Mori and Qi., We have modified the original method and have applied it to this case. We measured the lifting force and the pressure distribution on the hydrofoil in the NKK Tsu' Ship Model Basin, and confirmed that BEM is an effective method for the interaction problem between the free surface and a submerged lifting body. By using this BEM, we considered the depth effect of the lifting force of the submerged lifting body, the optimum location of the adapted hydrofoil and the optimum submerged body shape,
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END Fig. 2 Flow of calculation sswfstae x o MOtotfr 'si'+n'*WE1r 3 £k c Hydrofoil o Sensor position Submerged body Fig. 3 Position of pressure measuring sensors A wmx&g&xsk mm# mesured by load cell (Hydrofoil) mesured by pressure measuring sensor (Hydrofoil) r cal by B.BM / '(Submerged body + Hydrofoil) cal by B£M ___ (Hydrofoil) —■ " __.—' caL bv B£M ^ (Submerged body + Hydrofoil) mesured, by , load cell ; [Submerged body -s + Hydrofoil) mesured by pressure measuring sensor (Submerged body + Hydrofoi) Fig. 4 Cl for each submergence depth thifflwa-vr,Fig. 5 if fcSiSEi,5 EMitKioT**/; #@±©E/7E/F^^f. Fig.6 Ea*^m##©#e© m^©#A& 0 k LT Span;Wd©±®kT®© 8K#©-?-?#, vr*»f£„ ©s§tE± stf^nas^u mmo ©v-^ bthcihi r#*7c-fk $ o , k mnm.b%mm&M?z>b, \iC&EzM###@*#EStttoEttS; < *5KifS±®©E#**;*:§ < *o, cxm^m^vx^-s®^^5„ vi-5, SatoKttth$?iakEASi5)-EJ: 5g*iiJ: <-$$( T@-CttZ§:*^K©^E J;SEAWstittdxS t>„ ## k R# @ %*#E O V^TE A^A©^ &fr ^ w. ztumnm15%mmsm±©aa©*&#*.; % k, *^m#m©^m±®©EA^#^-1s„ _ Fig. 5 ©±5 EH-mSSkSWgm&WBL T> £1t e,fL3. 6akA,s@%mm©m@©#m6m-gk%&. t©a S1 ©ti&kiS^SSa* 0.08 ©i§£-Ctt, ttjo ± %- nfca>e.**E^S®EAIhifflE«:»SERIES 35%ggW>LTt^B kA%^S. o*0&*i$E*VJx _ fc. EE^S®Sf>i,. a%d#R%BSE#L-C S <»5kg6g@-CJ:9*#£z&£#9, f©®fCi #© Ag#m k ir) 9 ®a^ g, ^ f 3 C k &#© 6 vx ■oX^M(omtJ*mT-t^c ttz, ^*8#@&!k#k 3. c exit, ®S©#S8) zm t k> E, #@g©#E *ER#&©«^TH, #Wo Ett, stfflftMl&Eitl.tD^m&XhZtzlbE#£If6»?jgDS e*<$^(cp)^©e®^s & Fig. S <, t©es, gi*©^b/>dt^c»ite'kii?x6H5c 5©4>*E^f *4 JM©50%span©±T®,10.6 W= *E##%©#eE#g^S k, 0.08) Tfroffc, EptfMV-'* y /r-? ktEAB, *©% knsE^SAtg < %51$ k*s^»5/jxs < * -^-c5 - - m, mmxh?>o eiizvmmmmtcx, eme^e (D&frfrZo e ex=frtime£-?xnMCt:WitJ&, E Mt, 5$E[iilia^©Srti©, AD^#, #@J#©gE#%# *SiEUfcE CAUBBVI) Exp. CAL(BEM) Exp. O • d/Lpp=0.06 ------d ■ d/Lpp=0.10 ------a a d/Lpp=0.08 ------d/Lpp=0.13 Inner section mid section Outer section (20%span) (50%span) (80%span) Fig. 5 Pressure distribution (Submerged body+ Hydrofoil) CALfBEM) Exp. CAL(BEM) Exp...... o • d/Lpp=0.06 '— - ° ■ d/Lpp=0.10 ------a a. d/Lpp—0.08 ------o ♦ d/Lpp=0.13 Inner section rrid section Outer section (20%span) (50%span) (80%span) Fig. 6 Pressure distribution (Hydrofoil) u Ltzo am 95%&jg& £ t> , URSS <&-otvi 5o zivpmom (x/C=0.8) Tit CP 3.7%, 4«%*#© 55% LPp x-hz>frt>, i 0.025 ■o 0.08 0.10 C 0.12- o 0.20 -0.025 Fig. 7 Wave profile for each' submergence depth 0.05 z/Lpp ’ y=0.630Lpp x/Lpp Fig. 8 Wave profile (Submerged body with Hydrofoil) 0.8 ClX10» 4.2 U S6SBkJ: 9, C6CkttluSST-Cii£>>k ft-3 fto CC- 0.5 %D#^ft**m©@E&^M^ 3 C k E j: ? T, AR^©^ftv^Rm 9 3 t#KLft. 2£* #g#0.08 Xc/4s> (%) 35, 40, 45, 50, 55, 60% LPP Tvft, 0.0 ' 50.0 100.0 F1g.9 Fig.9^ 6 i v&ynm&tfvztom Fig. 9 Ci for wing positions f, CkA*k^3. L &L 4.1?^Lftj:p E@A&E^@0##E j: 3@A© Fw=0.713 kv^^^Etevi-C, gA*EE#jl3B@ HKJt^-5 k, Ziibc$mt±2 < ft 1^0 Fig. 10 E&** BBsk#*3EEMT&-D, **RE j: 3 @ A*E^©g@ tfr-LvfcEistia, mmo#imm^35%, so%, eo%©# tt/jxi v> k#^.ft„ i o r**m©m v mmm&mEf 5 Z k TWlMA ©M^ftVh S (7 5 C k ftsk, *k\zzim Fig. 10 Wave profile for each wing positions Fig. 11 Pressure distribution for each wing positions I?$ 9 dtfimmzmt, ®rB©BSi£BDk L TES k #g©#P3B^K Vfk 6 © 66SBOffiZT^CJ: 9, W T$a. S:*®S^-Sk LT#x.7z#e, ESmiiS BkA k*EfbV*v> k # A#Bl:^^-#-a##a^g <, ergStfctivMvvk#* iLhilZo m%9#ima^35, SO, 60% LPP ©*§£-©* 6A.&. M±©J:5*3y-te7°h©i)kSS^Covir^ cfIS^B±©JE#:5Mfi£ Fig. 11 tcatf. a-*69Sv)*?S 0.08 EOVxT©jff$?£:fr-oA:o Type A, Type TM<=>tL5»?^OStt/hSV10 r©Ck*^t)PE9#» ffiHEi. -oTfg#^*K k Ak'mtL»WCk #A"©#A & 3 J: 9 If® LfZo 4.3 Fig. 13 ffU 9 #KTi,) a&**©B%©#A^©^@$ mm, m&mmt %k Type b©#A^±#^ck A&KBRt4##K3e^.-rmiLt. a. & A Type A, C, DTK, Type C ©#*A#j: 9 6 ^k»3&*#03B$tK4.2 iFF/J'S <, ft6tit$l®lBSt‘Sa0 Fig. 14 te$m Midship section P totv>*vi45, 5 te&mxjvitt-r z t%*. btiztf±m y-h-ti'i ^mmmkcomt h /hs <%v#. ,1 W#R&K j: SR@j#r#*kiimRm*#E i 3^ Type C eke#*' 1) Jr'D 3?6 6 j: T>*jg* LfcfiSkitE f5ckEj:?T, 1: o k ©%2f#E#T5 '> S i v-*s 3 y b CXWJlTh Type D* 2>bb*y}z>mzl,tz 0 - ' 2) *Wrtm #>© J: 5 ^iS^Efr^ Fig. 12 Types of submerged bodies - -\t -'. •;- -#Wk&»v) k p © #MkWm#0@T&&kw3im@*±ua. p #kf@Ei»%*#BR©aafb» k*69z@i*&#a a Jo measured ,. :5kt$@ST$>5„' W'L, . (a=2deg) ::"p**B%#@a*#$j?p©mt»#@E^»&c t* -ess„ j: ?BsMfwaBWka fr-5 fc»©i£f|-y-;v© loi LT#%T&5k#^. "[ I V 5.0 '!.) ' f I 3) is n T kt± b 6 6§g@ S-tir5A56 gtiia^D,, ?©^#*4»^©#A5 5 ka# ■ Ubrnm^mtcntzo mtz%cm&*'m<-r%bu Type B . Type C Type D Type A 5a^@a%/iv@ <%p, t©ie#@A0^ '. r ... Fig. 13 Cl for submerged body types i'.. ' < %5 C kk&’ISLfco , i 0.025 '”- 10.0 —6 TYPE A —a TYPE ,B ■ . —tOp (TYPE, ,C —« TYPE D • .: "°"025 \: :• i Fig. 14 v Wave iprofile for submerged-body types i. %###%*#&to 9 Qgmu-ff 9 4) ^/f>9^//4 b©SEE i^LifL±tfST. HT^Ij-Lfco a*4#0%9#U(&E& # # X i$ i£ML;fcft&; afiaitlilll, 8SSkV-C*» Mtg Kgk/u insf, 1) Xu Qi and Mori, K., “Numerical simulation of 3-D Nonlinear Water Wave by Boundary Element #AK3&k*:%wkv>56At. oS5 *4# Method —In the case of submerged bodies ”, Jour, of the Soc. of Naval Arch, of Japan, Vol. 165, ftfr-ofZo 1989, pp. 9-15 2) Xu Qi and Mori, K.: “A Boundary Element #*at-%K L-rmmBR Method for the Numerical 3-D Nonlinear Water Waves Created by a Submerged Lifting body ”, 5S4bS-ti:tS*»-eti, #AKKkA,k|B|Uk»a. Jour, of the Soc. of Naval Arch, of Japan, Vol. $*ffi£/J\S < LfcS RSliSAS^AVh§nckA% 167, 1990, pp. 22-34 ifi-otzo L^LUPSti, g*fl:©i*fltl*l!:J:r)t 3) Xu Qi: “Numerical Simulation of 3-D Nonlinear cbus Water Wave by Boundary Element Method ”, »$*9, Doctor Thesis, Hirosima University 1989 4) Ling, Z., Sasaki, Y. and Takahashi, M.: “Analysis #^.eAa. of Three-Dimensional Flow around Marine Pro 6) k S K peller by Direct Formulation of Boundary Ele kt, %*#©#% k f AK Z 3*4'B©@AR^©''<9 ment Method (1st Report : in Uniform Flow) ”, yx2r#£»ttAPft6»vi0 ±^©gg^3:#A&@g% Jour, of the Soc. of Naval Arch, of Japan, Vol. f a zS*^©SP*j2G Z 3 #* k fccpMOWi'tWWl£-E 157, 1985, pp. 85-97 5) Hoyte C. Raven: “Nonlinear Ship Wave Calcula OW-C, Sa»m*^t)4k&WgLTU I J t r Gr%-oj-33^-2. 11 1-2 f yf A*if% 0S/S a.)/—$/a y EM jl| B 3k #* JEM g E 5T %** Simulation of Tandem Hydrofoils by Finite Volume Method with Moving Grid System by Hideki Kawashima, Member, Hideaki Miyata, Member Summary A finite-volume method is applied to a problem of tandem hydrofoil advancing beneath the free surface. The curvilinear grid system is fitted both to the free surface and to the hydrofoil surfaces which moves by the wave motion and ship motion respectively.. It is demonstrated that such simulation technique is useful for understanding of hydrodynamical properties of system with moving boundaries and that it can be practically used for the design of hydrofoils with flaps and associated control system. i. m w i -5 c t c *k "W v >i>:rv 12 mm# 'r'i yosysw, mm, mm f&^mmz i a game ^»9±# taa-te? -n>a„ f ZT, $: mfflMff CFD fSa i^-^s y©fSm©W@S@»M6^ ' K-r S fe 6 K, iESf§^Sri k SEiTiMg^S 16 ie#J@m & '- 5ztic±d , wms&a6&** Fig. 1 Grid system for the tandem hydrofoils. R(B<%g#3/Sai%—ya y tfr-sfk. g?FaS5nti66 mm k Table 1 Conditions of computations Reynolds number 1 1.0x 10* 11 Froude number (baseden chad length} &0 , cooptiutiooal region 1 ," -13.(Xx<20.0- ' -10.0 numberofgrid points (i* j*k)~ 199*50*5 160 * 50 *5 distance between wings (based on cbotd length ) 10 3 ’ . time inclement 1 dt 1 1.0X10-* - - wing section - NACA4412 attack angle of the fote foQ 2.63 attack angle of the aft foil u* , depth of the fore foil ( based cochoni length) IJO depth of the aft foil ( based on chccd length ) - 1.25 number of gnd pants on the fcil surface ' ; ' 35 : , ■ l- : . minimum gnd spacing ‘ v 4.0x10" ' 06 i------1------1------1------1—:—i—-i------i------: | : ? Cfc.of theforefoilj —— o-s : : : t ' CL 61 thfc hit tdnl: —- 1...... i^.A...... !...... 0.4 ** 1 — ■ 1 ' d 03 J<£. 02 ji Ol !______1______i______i______t______i______00 ’ 0 2 4 6 8 10 12 14 16 18 20 Fig. 3 Time histories of CL of fore and aft foils after Fig. 4 Time-sequential development of computed vor- starting. , 1 ticity fields and-wave profiles of free surface ' after starting. Fn—6.0 and f?e=T.0X106, t =4, ~?,yt^§ t, , 6, 8, 10, 12 14, the interval of contour is 0.1, clockwise rotation is drawn in solid lines and v, n-3% anticlockwise rotation is drawn in dotted lines. 3 ©@@© S' s ay - y 3 y - 'I ,, Fig. 3 \mwm distance between wings nondimenaonalized ( based on chord length ) fiequmcy CASEl CASEl 3 1.0 CASE2 10 0.5 CASES 10 1.0 CASE4 10 1.5 CASEl Fig. 6 Comparison of vorticity contour maps in different test conditions (see Table2). F>z=6.0 and /?C=1.0X106, the interval of contour is 0.1, clockwise rotation is drawn in solid lines and anticlockwise rotation is drawn in dotted lines. CASE2 *©3*fcL-C», msmOBO# mmmmx-rztzib, —o tc»5o ■to ______'. . .-._ ... _ CASE4 Fig. 5 Comparison of time histories of CL in different 4. ^ >xA* |t|Sia©zei'> £ o. u-'>3 > test conditions (see Table 2). 4.1" jH)'>5a.V—>3> * ; CFD Ki D{if5.iLfccrL^*6fflvx-c, &fff-£CXf y 7"S zw-ir&mtZo K ± a smssj § ta uj& S < * 5 £ fc *5$!| 3 „ Fig. 6 EC© kg ©am ^SSrET, CFD i'iak-yg y^vjE Sku? SSto d, 2 ifc5E-fk s fLf£*tp^sa©@$b y 5 a y — K#w, d (Dffimvmtimmzti, smmzms yay^tTofco zazzcommmtLx, ±k LT®JfflIC®SLTH5ifeS:li*tp^CoviT^lBbM •&***«., a yo -k x „ &e!l#LfS%m©@#y5 a y-y 3yJffofc 0 ztib 3.3.3 #m (owrtm Fig. 7 ©#»em&# om-rcta r>nt>ti hydrodynamic ^&®5WMffi££Zmmr3 So ______-4,2 -■------H^@®©Mi6Jiz£8St*s bti%7iH-*-*--■?- S jf SIS L mmc Table 3 © i 3 %%ff L, * k&M lx ,mmttzo f kTS„ Table s, (p)mkmmst 4 L^garia#^ -y (PD)m$jmuemm7&o##©m©s#±e*mE*f s s # isii'ciss u is# Fig-8 CScTJ: 3 'F7trflf£E< i tT^&r^io IcffiMK, SDSifok ______- B-D $k)D ?##»*!) D b Its j:3##0M©am 4.3 mm# ______naca 4412-e, #m©a#)s, 2.68 be, mmmaA i i ,28sr*»So $^m#ism*pm c* kv\3, K-y a viTfivi, pitch, heave ® S §r S 6 k U, surge tSEiSk >$4fc^o %*"=F##G.o, Fi /;p L##%1S^©##^5%&ipm7-3 v4/k UT,- ±^ I xkte 1.0 x 10sT$,5o k W71$, -f K5£t -TSC1Q®$.-C©SS^kttSSC^o-T^So -1 wmmmvj? f^-x-y - wcfrmt. i >3^-^k?*f Table 5 CSt„ Jgi&T mmffliZjov>X IS, 1 Table 3 1 Design 1 condition (full scale ship) ' crtAiS^TElSiSzS 4Hr3fc», t %FfO Table 4 ,Ge_pnip|pry of the glpp fpr fpmpptatjfln &:# giWM nondimensionalizedwelghf 0-721 Hi , t', i 1 i _' » . ■ . i') ,: >i if,1 'i ' 1 nondimetgionalized !pomeg( gf ipe^g 27.14 4.5 CL of the fore foil ' ' x! ’: ' 0.454 ' -' CL of the aft foil 0.273 ,: . iv. Table 5 Conditions of computations Ct of. the ship . * 7 ‘ ,0.04 - ' Reyncdds number " "1 ' '- ' " 1.0x10* location of centroid ‘ 1 (x,y) = (- 0.936,1.0) 1 Froode number ' 1 ‘ f — 6j0 ccoputiticnal repco -13.Oct<20.0 -5.25 • number of grid points , . - 199 *50 * 5 207 * 50 *5 ' 0-j*k) " " (wave mating) -tfstributed equivalent weight of the hull distance between wmgs(based co chord length ) 10 - lime increment dt LOXIO-1 ) , .; center of gravity (*0.936,1.0) thrust (y-0.8) -wing section , NACA4412 ' L. | water level (y»0.0)- attack angle cf the fore foil (degree) 268 attack angle of the aft foil (degree) 1.23 forefo3(*S.O,*1.0) depth cf the foie foil ( based on chord length ) IjO ' aftfoa(5.0,-1.25) — -= concentrated equivalent * ! depth of the aft foil ( based co chord length) - - 125 weight of the engine number of grid points on die foil surface 35 „ , i'jh Fig. 8 : Schematic view of the hydrofoil. minimum grid spacing * 4^x10" . . &&&¥%&■? <1 5 9 yfA**B® ys^y-ygy 17 4.5.1 _ mmimA a@TBm#b»n&6, &5@s®mn,&&caz:tK &tpm$t -^r: «tg M£S 4.6 ->ial/->3>iS 4.6.1 'f y/<^f5#MR (.Cml~~ Omshtp) = Cjshtp (15) r®Siiy S ay-y 3 y^®S$3®)5ffle!lkb-t, -f Cmi - K j: 3 ^6'—^ 'y h ®^5cifSR3 /=26 <1 D, Cmehip \ 7\ 7X, h, SfiixFt^ Cl cf the fore fo3 Cl of the aft foil aisesBeBaajgBBBaeBBB pitching moment at center of gravity Fig. 9 Time histories of pitching and heaving motions in impulse response test. Heaving motion is nondimensionalized with respect to chord Fig. 10 Time histories of CL and pitching moment in length. > ; impulse response test. 18 #179# -■ < c teaBfaTt&V zW a5»tiEik6»rvi3c f ZKM ^iS© t 4 ? * 7 =e - K Ux iS $ f a a. i/—y a y ftb t© k # ttit^J(P)ESiJ@ISev^ GP=10 k LTW&. 4.4 B-cmm^-fz Table 6 Initial and desired height i/S a V-—y a y S-fr-ptCo Fig. 13 E pitch A, Fig. 14 C initial height desired height heave £t©B#Fs9®M©^S Sr^"t"o Z©@mTB##&8-©f4y&±@ < T3 k&m*© at the fore foil -1.0 -1.1 < *5„ heave@il©lRmc# at the aft foil A -1.35 -1.25 («M)$J@lL»t)CASEl©# e, pitchAaw&tfa kam±#c ± o Mto-rzizb, Lg63c®K5E5LT ^T#i&F#Bk»3. rtUiSIIS-ctt, B©@m^Eo% Table 7 Wave condition wave height 0.8 wave length , . 20.0 ' Table 8 Values' of feedback gain G, G, - 70 CASE1 o 0 Fig. 11 Time histories of-pitching and heaving" motions . CASE2 : 10 0 . >_ ; under height control, (see Table.6) Heaving 1 CASES 40 0 motion is nondimensionalized with respect to chord length. . . CASE4 40 100 Hap angle of the fore foil flap angle of the aft foil 1 Fig. 121 Time histories of flap angle under height con Fig.' 13 1 Comparison of pitching motions in different trol system. - - ( ( control conditions, (see Table 8) 4 3 ? ^ v-i/3 y 19 -y a y»$7 > f & s c iitza 4-moEEk LT, 3 3. C©A ■ettfflE»fy]E 6 K, c 0#6 CFD &# ■?fcZSby 5 a.y-y 3 y 14, gRmi©3# L»w#fB^ ns®gg^o^»&t*TM*^z-r-5 # # 2t S$ 1) Takai, M. and Zhu, M., Finite-Volume Simula tion of Viscous Flow About Ship with Free-Sur- face by Arbitrary-Lagrange-Euler Method, Proc. CFD Workshop Tokyo 1994, Vol. 1, (1994), 85-94. Fig, 14 Comparison of heaving motions in different 2) #@=P, SB3PJ!, WESS-zSC 4 5 2 '%5zBOf 3 # 3cmjg4t0%@y a a y-y a y, B$m&### control conditions, (see Table 8) Heaving motion is nondimensionalized with respect to KM, #175#, (1994), 11-24. chord length. 3) Rosenfeld, M. and Kwak, D., Time-Dependent Solutions of Viscous Incompressible Flows in Moving Co-ordinates, International Journal for sl»> lb t>mm-bmn§tm Numerical Methods in Fluids, vol. 13, (1991), 1311 CASE 4 <0%&K t4, 6 cm m&OMi©±Tifi -1328. 4) H. Akimoto and H. Miyata, Finite-Volume Simu lation of a Flow about a Moving Body with 4.6.4 shfi® Deformation, Proc. of the 5 th Int. Symp. on Computational Fluid Dynamics, vol. I, (1993). 5) ±mem: 4 &m##y % -pygay-ys X#&t LA**RlBl4, #&#©#L ^y-y 3y, yf AEELAA&E, (1994). 6) #IEK #S3s^, Kn7*4;H 7°k l*:*bs?-4 v b $ @ y y df y v a v'jyf-^wiiai, s a y-y 3 >\z%.frMt£^zb ^^crt^oMSST^, (1989), 75-110. a. & c 7) E-M, #EB5PJ, %*##**#© a±ri4, -5 &@ya 5 y-y 3 y, B$m##&aB8&#l75 #, (1994), 1-10. s) siEfa, mmi, \u±im, WB&MGHLAZRya a y-ya y »fzw, to# 'X7zMmm 21 1-3 ibitiftiMkXc?< S^-fbe J: & zm % # ^ * e ^ m** Determination of the Unknown Wetted Surface of Planing Plates by a Formulation Based on High Aspect Ratio Approximation by Kiyoshige Matsumura, Member Yuuki Mizutani Summary It is intended to solve a problem to determine the unknown wetted surface of free—running planing plate. Efforts from the view point of the perturbation method are paid to analyze both the near and far field of flow around a restrained planing plate with comparably large breadth such a wave-dozer, disregarding gravitational effects. Matching process of each height of water surface leads to a non linear system of integro-differential equations to determine the distributions of both the wetted length and the apparent circulation around the plate. Serious solution of reduced single integral equation, still holding 3-dimensional characteristics but the so-called downwash effects, diverges from the assumed high aspect ratio solution because of the logarithmic non-linearity. The equation gains an insight into static stability in performance and the limitation in height to restrict the plate in exposure above still water. The obtained configuration of wetted surface draws well the behaviour of the spray root line crossing the hard chine, however it is unfortunately rather wide to coincide with the experimental one. Free-running condition is estimated. i. m b s0 v^u Kr=1ECU^viE9, #±*@&{6©%#k L, %%©% ct-c&s. < 3 3. 3 @ J: 5 ii£ si LA'L, D ©%%,&#& 3 M ilifemwfflmz, Wagner 2) O 2 #5cmMA#03gT*8 Sttt, 1 OT& & c & B86 & f, f KMf360T&3. %@0%ec|BL, zk@©S (pileup 3 3 k K J: D 5fyg pile up fc^SUKV^-g-Cffc^vtS 6 kf3 kftvTbS COfStt 5■>„< 3k dead rise angle biSfflSfl, S*@ kf 3H##T& 3kS iLfco L#> L, spray root line (g*@©^%S) k|%#, do3k ti¥se.3,4) ©ni^JFmc-a-iscb* nkLT, ##&* 3 kKJ: mmmsm %*RI@09fLw#&&3;LA. ®6ttgN<.Stf)£@z$E ffiffigm ¥J$8^1H10B ®^C^98 ©EE%Ev >Tvi 5 %%#%© spray ¥$8^5 his , isb root line, 7-/9 »K0#gEA^#, /TV-SEfl^ 22 mm# < is® § nr v > s <, l*»u 9 A# r>0,maiT%%^LTw3t©kf 3. 7cMMw&mB E-C146<, t?L3x7y-©#f(jA%¥A3®EE»?: t E#%e*k#*T*@w rwj$wm?fe5.. ://;■' . 2. s 1 \ m ;\:-::' ! Fig. 1 Etf7 z ibbtiz o fcfc'U a:>0©T5$aSfl-Ktt[F], x<-lw —^.)og \te+lA+*Mx ±lzL}+go(y) (16) h KgfiLfc [F], [S] ©$ a c k SBELTti < „ @M-C, h ii A~i7o +(r+wf) |—x+-2^=ar3'2+• • • | Fig. 2 Flow configuration in near field as x->0+ (17) kMfflZti, *©W*:i£B©S-F&SiLTt>a„ [F]a, mmmmkLTm'Z) iztz±fammmmw.(y) m P, CE§nf£ Kutta © BSCttTlRl§ © downwash) * 3i£C-50 Z. [F] Ai(0; y)=H0 (11) m±T, /«-, Wi &$Ak LA&&, L [S] h\(—lw', y)+wr(~iw)—Ho—v{~lw) (12) *>L, x->±°° Ok §, [L] a@E©5$, [B] a (4) A~(r+w,){-|^log-|i| —^-log-^ [p], [k ] ttsiEu iVhtkfrXh 0, [P] tt Kutta [K] +(1—log 2)-^+ o(~r)} [f] Tkv [s] it, ztiztimim ws, wifi i: is a a msvmm&z^x., am +tio(y)+Hfcx+ — asx-»±oo (19) iSO—BC&#P<&60T&&o ©ip « 2 '%.7trmk LX it, Pili, A, k&AWk^@*[L], [B], [P]&&#&& k a. c /ir k r amnmmvfejMtcfts^ ©###a, IEA?tb3o V ' ^i~Rej^—^^{log(x+i2)+i 7r}J WM^1 (23) + w,-2-f— as z-»0 (33) [P] -^-=0 on 2=0 1 1 1 (24) - [K] " (25) /, +ti"(1™log Sr($,)+l^l"iSrfif4 H 3 ^*^§3. -r*fc-&, g*® (to 4 D ZUi (35) ±Ttt, J ' ■- - '' i ! -e$.3» Vi © l^g©#R@i4%^«i$L, (i zr) 0^(4 $i(x, y, 0-)=—r(y)/2 for— 1 < y .< 1 (27) ^&g@±T© :Kt y ^ i' • b -y y TWf. S mtiW©B*@±-C.ti: [oq] ' 1 2 91 g 14 downwash (#3^## 14 up wash) ©%%&%"4o ^i(x,y,0-)=0 - : . - (28) f %?AC#5f 3&i@*& © 1, 3mgT£.9, (23) (27) (28)at®mf3 - <3” c 4vi4, r(±i)=o «g$ 4v3»&tf, ##toam©m# /^(y) I4*%rc&3©-c, S 3G, h ©A%@©R-@»@*i-3&, :' 1 ' % (38) ©m^@^.(37)^k(38)^&ma$44-C#i4i4, /,(y),r.(y) 3i4f?&D, 47i, i@6© 2%5c Fig. 3 Flow configuration in far field 25 fmoim-bmmzti* »maif, h ©m^ovyf-y c kif4#©m@k u, $s-c ^KJ: Offhtitzifi, 0 courfr^rfcn —©;B1»?*S if, -Wi^fO kiESL, downwash %&&## LT# < C k 6fL%. enttitfu %&^if@n@c©»%n5^e,, # 5#f5. igiofflt^fcfaE, SE©5fy&85miE6f@ < m&msw? yf y^K&5. #icf 5*@&jEf 9 6, f 5@E69*®ES© B*>tf 7/i/- eo^stttt^ibEv^i, %m©^A#g?&5^©f?»)gm#gfL5c L-cm#K&v^T6mAB#&#mf6 5 k -3.1 Downwash U **#^6fL3o r©± 7%#^-, $n5 SC®Wb-C§5„ flo<0 CESS it5© Ko^-C^t 5. Fig. 4 ©Ba#&&&98e,&»a a K, •e, &(y) if &m*r a. ga^tb-c /a K#UT@©#Rk, f©^-y-lf#»5. gar 5 0?if±n5S*SkES!lL, /« k SaKjfiimU /«<0 k»5#^K6, i) /a>0 ©^g : lw k»5.M^8a^6,B>(y), r ©&»^t^0M9KMk6 ■f, /„w A#LV# 9, §*&»* lw(y) 6#LnkV)9##(MU^#^fi'5o Deadrise * ?& <, Bt#*8#8eKB, /,V tt-SIB /a ©»KfR#f 5c Deadrise angle /? &#r 5# o', /a(y)=/a(0)--^r|y| (43) k& 9, /a(0) ©i$»>K, 4) 5 1 O0^’7>7 j8/r(relative deadrise angle kBf.fi) |C tikW-~t5» 00 f.if, ©Sk & 5#m#& 9, -Ho(O) k r§©M© 2 {SitiSSbTi k S, m 2fgk m#*#%K7c©#m k|B|b%^k%5c 3. S7kS©i£®to^S^5tkZcnMm $%m^M@©mm#&t#5A», ^-$ku, E*B©^^@S(41) (42)Se^fjkfSk-r5„ WSif f E?UTmBT$5A*, & 6 5 ## - 0.18 0 k»?TU5. #K(42)^lf UQtt Fig. 4 Property of nonlinear logarithmic equation as *©g?£®5 - k ifmgmmT&5. the first approximate one to determine the un known wetted length AK^XAf °9VA ‘0 31 : (is) ’ MV{(i)tMi+M)?>}-’'z,0;iz= m # i ^ 1^1 u bp~?WFWtJ .- °3-£3G ,' I ‘i ma#25'/ ®S£(Sfr)H M1 3^f9#94^(SS) ‘sa-lj: c-431 °3$i%M^x:.y. J'/»(*a22 °34.:£3l4 * " > **###** 'H3%#® ‘xm (os) [{(i)^-(i+«Wz+(-*^)soi ](/i)“c/-= m®2 ' o $ a 12 3 n (#%0 ® (1=®)3;U0)A\3N e-k-jOfllW33 G ‘'’■few'# T0^»0^B5C«%3W* "H YX ft .c4fZ02 ‘1 3 xctc.2wtgsm*^mim "3^i3ifg$i 3 °3#5#BB®m##i I"-E='9 'TW# \43<£.4 (61) x (/*) “J-V;f=(/?)-”/ Stf'3 4-2:81 > °-/^4l.5S 3(0 9 4T (ES)H%B8 K% °3$i{M,0 a^MS$® Mv K^a^s* M-* 1/ ‘nre-Eputsoo a# os a.#* %@3Taa#V^<*^ I Z E ^ ey a 'n-mama °3 g 3W3%gi °3 (SS) # '«®9k®m# z°3if(mi%*aa>#5^ma3@i m+(Z3oi-i )z+T^z T aoi | m ‘*3 fe®m¥ 1 > %ams > 'fm#®f&2r3«9c3%#3)0Z >PSa?M)3S£K z E • i '943*3 °3*BSi31 * i ^ma:%K3 4- i #B953 {mu\)^\-mi %mm (gp '/Z-=4P(6)l/:g^J f- . ,, %m35m0#a439# zzs , ;!:{(Z80 I-I)Z-^2»0l}^ a39B-EfZ3Jk.4^(ZS )%XVi c#%#M H3£(si)i^.43i °4-SaS® mi ‘xQ>%<$x^wm^\?4 HiS® w.(/-I)^4 *^(ES) ‘5??^.1IBS123 4-a49Sam5###®i% ‘«^®BS®2 °34- ...... %’fef# g3BMa-3%m®5# ‘<5?30 I=(T+)“y 'S3®Wc ' ; ’ 'na-»«*53##3A*a ^=6 ‘H3 3#«mi 0=(I+)^ '141 5^m*0%m*®^(si) ‘«^®r3s®m#0# $1123‘ci$a.m%c.#®^m ■'■ V ■ 034-211 2 3TSlUBri® >PS £Hi2®2 °3sarB3S2ms ‘iii3m¥®i2G':i a##%m#5#m®i$if2 ‘4-9 cf6$a^®$g®M 1 3#n 9 <434-WiSHr '3%%% WB@ ‘Hill* 03C-3149rfl4123gi.4124. ‘H1 2c#3#M#4-’T"033 0='”/ i)?8M4 -”/ °34-mara 55CB® !>'“/ ‘in G 2 °34#S3 12(131*##% 'mm%^a%m^®^(zs) (so %#i S6ZIS W¥E#^8@K*Q 93 biXjSMte&-3< HgjfrfbE J: 27 (D-C&g-tZ „ ±# 80 cm, 52j5 40 cm, JSS 2 cm Fig. 7 Variations of measured spray root lines with trim angles in the case of 7j?=0.3 Fig. 5 Observation of spray root line - 0.155 -0.07 »— 0,1- •- 0.155 -007 Fig, 6 Measured spray root lines corresponding to Fig. 8 Calculated spray root lines corresponding to various restrained still water lines various restrained still water lines 28 8 Ctt, *11© 2 o©7;v=f V XA (52) (55)IRS#© #6/isE% &=-0.155 ©%e©^mt^L?ws. s mn±#**SE^&/»=-0.07(B>=3mm) TSD, 2 fL«±©iS§ cm&E&ESU k*A^rSMSL&#x.r tSS65C KB*L»#7/co JSSK^gg § #SS#, (46)ST-#6tLSE^E6 A=—0.5/e=—0.18 SSL, K im^-LrviS k#^. 6/lS.*S#$/R*2 k KL»^#, relative deadrise angle #*§ uSa', 6$1 E&iSkS/cSC,. 6/i»V^#^-#SS. 2/1 ti, v\-F • yT*%iiL&W#eiz*#Gf 3 k# x 6/i30 i i ' S3i$, mss-ess#, 7n'zf')XM.,r®mm »Lfc^77&SL/c. /h '(O) tt, : <56> 2 l/al ^s. 2/ms i &iK##sm#©*-%©±B kEfc-tf"5C+^-eSS#, k%M6|=|-%* S © C=2cos 2(r/2)• (2 cos r—l)+(/T—r)-sin r *#%©#%%'& 9, t?L3(45)5t© 8/cti, , —2sin2(r/2)-log(sin 2(r/2)) cmgLTv^w fc » k#^ 3©#^3-eS ~2 as z—>0 (57) s„ itifcBL»w% (45) "CSS. r->0 ©@E-eH(45)5tk (56)^1/—gt*S. Fig. Z*3 2 k"CgliHikB^-Sc9l/5o 2/D/4-#©# !10 C(56)AG*is*o r-0 ©#&, %WS#k ^*'s of n i/m*B#©#@-ess« Moe*©-V/i»^©Kaa©ao-ess#, r fmmitw^vpMtfrlm-tzmzmiz &%lx 33d, ©#m#%mikk<#g/i-e^Sk#x6/iSo Sl/j^fPCkS local wave ©IB®AOBf#$ ii 3 *2 6 "C S 4.3 S„ /c/c-L, iSHOgSifigBStofi, *^1±#MC#6/1 iSj$^®c^t/s?i^E©g*S#$$7/c©-e, §6 s#, z/©»K##f s^i±, m^dffy$/f/p©#oam #mmcot)-c##*3o /,v m#c^m#k/sm#86 gg & [K] C%c-CSD-LT fef§6/l*, @AB0#%#lSL /i-et), 77«, mrs©-m## /ci6H®Sifl-8$S^ S £ SSrifflgga LTSSStf/itif/srS 6/IS k#a. 6/ia©T, deadrise ©»v#%©@6#^ »Wo 2/iektm©ffigl#¥;@S /iso ttlSSSSS.____ _!___ ; k,_w.< o*©j%-eg#%a %mm-e©a*fg& ci, b (~xc) it —Sl* ?S5>tL3o S1 C, ffU£kt/c spray root line It, lw »?WEES5SS*©jiS$|vi6E-ti, -r-CMW- (58) Sm##C86/iS/\-F • W-f y&#%S#f kj: < = r-f£/,^y pm>s c krt s. SBtot;: it, - (45)stosrn^Sst# /n-(±l)=0 k%S#R%#o/:S, spray root line fjr,T/,rVy V. Xc(/*)=- (59) F • f’+’W vSSKtS 3 k Ban**, #AT©#@## CUh) &J: Fig. 11 Characteristics in free-running states of plan ing plates with various still water length 3. '$&, mo ) ii h R m ftitm U X is 0, /n-(0)//s=0.48, r/rs=0.73/F„2 k*3 0 Fig. 10 Variations of calculated spray root lines with trim angles in the case of /*=0.3 5. ^ W o ©%-/ > tctzL, momst tl^®©E*S*: 7) Ting, L., Keller, J. B.: Planing of a Flat Plate at High Froude Number, Phys. Fluids, Vol. 17, No. # # 3t SR / i 6 (1974). 1) (t® 2), raamk% 8 ) *3£is#: 2 c o mj (1989). ^x-zcor. wmioim-, 2) Wagner, H.: (jber Stoss-und GleitvorgSnge an 24#, 3 #31987). der Oberflachen von Flussigkeiten, Z. Angew. 9) Shen, Y. T., Ogilvie, T. F.: Nonlinear Math. Mech., 12 (1932). - Hydrodynamic Theory for Finite-Span Planing 3) wmmm: HE Surfaces, J. S. R., Vol. 16 (1972). 208# (1988). H. io) %mm.: (.warn,ism 4) ¥E)i ffi: he 92# (1952). 213# (1990). id > mmiEm: khts bsd ; mm###,54# (1977). zmwSiiz^x, Q*mm##m*m, m# 12) ' : ?S^®cd S*ES^Co t^T, 38 ES¥ (1993). i, ., ,, mm¥##mwsm5#m#%# (1995 ). 6) Wu, T. Y.: A Singular Perturbation Theory for 13) m bhese Nonlinear Free Surface Flow Problems, I. S. P., #A¥#5%#gf# (1984). Vol.14 (1967). 1 1 -1 1; n > .1 j 1 i > 31 1-4 Numerical Study on the Aerodynamic - Characteristics of a Three-Dimensional Power-Augmented Ram Wing in Ground Effect by Nobuyuki Hirata*, Member Summary — — - An investigation through numerical experiments was conducted to determine the aerodynamic characteristics of a power-augmented ram wing in ground effect (PAR-WIG). The Navier-Stokes solver used was a MUSCL-type third-order accurate upwind differencing, finite-volume, pseudo compressibility code based on a multi-block grid approach. In order to understand the mechanism of the power-augmentation effect, two boundary conditions on the ground were considered : (1) a moving belt ground plate condition ; and (2) a fixed ground plate condition corresponding to the wind -tunnel tests. Thrust was represented using prescribed body-force distributions.. The flow arouncLa rectangular wing with end-plates and propellers which were placed forward of the wing and blew under the wing, were computed by the solver with different trailing edge heights. Results were compared with experimental data and the aerodynamic characteristics were discussed. * ---- :— studies2,3'” and theoretical analysis taken forward speed 1. Introduction into consideration 3', have been conducted. Neverthe A wing in ground effect (WIG) vehicle is expected to less, no flow computation has been performed except be one of the promising super high-speed craft in the CFD simulation for two-dimensional PAR-WIGs by next generation, since it has an exceptionally high lift Hirata6,7'. to drag ratio performance at low altitude. However, to In the present study, the aerodynamic characteristics design a full-scale vehicle with an extraordinary perfor of a three-dimensional power-augmented ram wing in mance is very difficult owing to the need for low speed ground effect are examined with CFD procedures and take off and landing on the sea. High speed take off and experimental results. The Navier-Stokes solver used8 ’ landing from water require an excessive structual is based on the MUSCL-type third-order accurate weight and engine power because of the large wave upwind differencing, finite-volume, pseudo-compres impact loads and the water resistance. One of the sibility method with an algebraic turbulence model to possible solutions to this problem is a power-augmented close the system of equations. Because of the geometric ram (PAR) concept, wherein propulsors are placed in complexity of the configuration, a multi-block grid front of the wing and the efflux from the propulsors is approach is introduced. In order to understand the directed under the wing to generate a high lift force at mechanism of the power-augmentation - effect, two low speed. This concept can reduce the take off and boundary conditions on the ground are considered : landing speeds, thus reducing impact loads and also (1) the velocity is equal to the uniform flow ; and (2) allows much higher wing loading. the no slip condition. They correspond to an actual Aerodynamic characteristics of PAR-WIGs have operating condition and a wind-tunnel test with a fixed mostly been studied, using experimental methods. -At ground plate respectively. Propeller effect is represent the David W. Taylor Naval Ship Research and Develop ed by prescribed body-force distributions proposed by ment Centre, from 1975 to 1978, experimental and ana Hough and Ordway 9 ’. Results with different trailing lytical studies were systematically conducted ”. They edge heights are compared with experimental data and measured the PAR performance both statically and at the aerodynamic characteristics are discussed. forward speed, over a solid surface and water in various sea states. They also predicted the static lift and drag 2. Model Shape and Experiments performance using two-dimensional incompressible The principal particulars of the test model used are potential theory. Recently in Japan, some experimental listed in Table 1. The wing, as shown in Fig. 1, has two features. First the aspect ratio is very small compared * Ship Research Institute with that of conventional aeroplanes. The reasons for Received 10th Jan. 1996 such a small aspect ratio are: a large effective aspect Read at the Spring meeting 15, 16th May 1996 ratio can be obtained from the ground effect; and the 32 Journal of The Society of Naval Architects of Japan, Vol. 179 Table 1 Principal particulars - . - - Model. chord length 0.5m span length ~ i - , 0.3m =. wing area , 0.15m2 rwing setting angle L 6?. aspect ratio 0.6 wing section NACA6409 planform rectangular Propeller. propeller radius 90mm Plate 1 View of experimental arrangements in wind hub radius ' 8.5mm i, i ,1, tunnel - . -, number of blades , , ■ 2 ' rotation inward - L - 1 l Hi ' ; Ground plate. '' ’ ' ^ '1 forward plate length 1.23m , , slot width ' ' 40mm 'Propeller slot angle 1 45° rear plate length 2.0m plate thickness , ,, i 36mm , position of L.E. of rear plate x = —0.865m, . Fig. 2 Apparatus of experiments with a ground plate ; tus of the experiments , are shown in Fig. 2, , , . ;-,,,, A ground plate was installed in, the centre, of the wind I tunnel. In order to remove the boundary layer devel oped over the plate, a slotjwas set in the plate upstream of the model 10’, as shown in Fig. 2. The dimensions of the ground plate are listed in Table 1. The flow beneath , the plate was accelerated by a ramp, , hence the slot provided the required suction. However, since we did pot ,use a moving belt, a boundary layer whose thickness Fig. 1 .Wing model and coordinate system ,j ;,was about 25, mm at the wing, still remained on the , plate 8 ’. , i , . , The power-augmentation was simulated by means of PAR performance is,not fully effective with ,a wing,of a, pair of model-aeroplane propellers placed upstream large span. In addition, the model has end-plates so, as of the,wing. The propeller position relative to the to create;-a high pressure region under the wing. The leading edge of the ,wing was kept constant with the base line of the end-plate is parallel to the: ground and changes of the ground height. i the reference, height is equal to that of the wing at the Jbift, drag and pitching moment about the 1/4 chord trailing edge. - ,h ,T , -( . were measured by a six-component force gauge. Forces Experiments were conducted in a wind tunnel at the on; bpth propellers were measured together by a two- Ship Research Institute, as shown in Plate l4’. In order component force gauge and thrust is defined as a resul to simulate the ground, ,effect, two methods, can be tant force in, the xt and zrdirections. Surface-pressure considered 8 ’,an image-wing . method and ra ground on the pressure side of the wing was also, measured. A , plate (board) method. However, the former method is uniform flow of 7.0 m/s was set with a reference pitot- very, difficult, for use with ; PAR, and, in the present tube in the wind-tunnel, however the velocity Uo at the measurements, only a ground plate method was adopt wing was accelerated to! 7.45 m/s, because of the dis ed. L The coordinate system, nomenclature and appara- placement effect, of , the ground plate, apparatus, the Numerical Study on the Aerodynamic Characteristics of a Three-Dimensional Power-Augmented Ram Wing in Ground Effect 33 blockage of the wing and the traverse. The Reynolds a space integration method, the IAF procedure is adopt number based on the chord length and the velocity Uo, ed. was 2.4 X 10s. Aerodynamic forces, thrust and~moment In order to correspond to the flow around the compli are non-dimensionalized by -^pUoSw,-ypGo S„ and cated configuration, a multi-block grid approach is introduced. The approach does not allow the disconti ■^pUdcSw, where p, Sn and c are the density of air, a nuity of grid points on the interface surface, thus the geometric flexibility is restricted. However, sweeps for wing area and a chord length respectively. the IAF procedure through the whole of the solution 3. Computational Method domain are possible and the efficiency of the calculation can be kept to the level of a single grid. The Navier-Stokes solver used in the present study is 3.2 Turbulence Model the upwind finite-volume method with global conserva The closure of the system of equations is achieved by tion and based on a multi-block grid approach because introducing an algebraic two-layer turbulence model of the geometric complexity of the configuration. For proposed by Baldwin - Lomax with a minor details, see Hirata and Kodama 81 . . . modification 111. Because of the geometric complexity of 3.1 Navier-Stokes Solver - - - - the configuration, the model is modified in the region The governing equations are the three-dimensional where multiple turbulent length scales are present, such incompressible Navier-Stokes equations with a pseudo as around the wing, the end-plates and the ground. compressibility method in conservation form. They can Generally, one structured cell has the possibility to be be given as: _ . . affected by a maximum of six boundary surfaces of the Qt+(E+Ep)x+(.F+Fv)i/+(G+Gv)z+H=Q (1) solution domain: in the upstream, downstream, left, where {x, y, z) are the Cartesian coordinates. The right, top and bottom directions. The following formu dependent variables q, the inviscid flux vectors E, F, G, lation is taken as the linear combination of the effects the viscous flux vectors Ev, Fv, Gv and the body force from the multiple surfaces. vector H are written as: 'u ~uz+p vu wu V uv v2+p wv q= , [E F G]= where ffm is the normal distance from the solid wall/ w uw VU) w2+p ground and Vtm is the corresponding kinematic eddy .p. 1 . fiu 0U) . viscosity calculated by a conventional procedure neg 2 Ux Uy+Vx Uz+Wx' lecting the presence of the other solid walls/ground. Uy+Vx 2 Vy Vz+Wy [Ev Fv When the m-th boundary surface of the solution Ux+Wx Vz+Wy 2 Wz domain is not the solid wall/ground, ym and vm is L o o o treated as infinity and zero respectively. : fbx Although this formulation has no physical basis, it fby (2) possess three desirable properties as follows : \ fbz 1) The computation of more complex length scales . 0 . is avoided. where (w, v, w) are the velocity components, p is the 2) As either surface is approached (y«—*0), the pressure, y9 is a positive constant of pseudo-compres - model degenerates to the correct Iimitingiorm of sibility, Re is the Reynolds number, {fbx, fby, fbz) are the the Baldwin-Lomax model. body force components and vt is the kinematic eddy 3) Along the bisector of the included angle between viscosity determined from the turbulence model. the surfaces, the model is affected by both sur The finite-volume method is used for a spatial discret faces equally. ization with the cell-centred layout. Thus, the depen 3.3 Propeller Model dent variables q and the kinematic eddy viscosity vt are The propeller effect is represented using prescribed placed at the centre of each grid cell and the grid cell is body force distributions proposed by Hough and treated as a control volume. Ordway 91 . In order to estimate the flow around the The values of inviscid terms at each cell face are propeller accurately, imposing both'thrust and torque computed using the third-order accurate upwind components is necessary. However,, since the mecha differencing scheme constructed within the flux- nism of the PAR-effect is due to the. increase of the difference splitting framework. The third-order accu pressure under the wing —the efflux from the propulsors racy is attained in the pre-processing (MUSCL) man placed upstream of the wing, is directed under the wing ner. Viscous terms are discretized in the second-order and partially stagnated —,,the: nature of the effect can central differencing scheme based on the Gauss integral be explained by taking only the thrust component into theorem. consideration. Hence, the present computation neglects The Pads time differencing form is used for time the body force distributions in- tangential component as integration with 5=1.0, namely the Euler implicit. As follows : .34 Journal of The Society of Naval Architects of Japan, Vol. 179 fbx=Axr*-l\ —r* :cos Op :' 1 b!..,- - 1 Table 2 Boundary conditions fbp = 0 (4)1 On ground. ftz— —Azr*J\—r* sin Op) , n' • '' '' ' ' numerical simulation '1 experiment where * ;...... case-1 (u,v,w) = (1,0,0) , , case-2 (u;v,w) = (0,0,0) Ground plate method ,71.73 5z/c <2.27 , AS? 105 ' ■ r -rJSs- z-symmetry ,otherwise At-Ctptop Ay ■ 16(4+3 Y^Xl- K) ’ i- Vrpr»p- Cr-^-- zero pressure gradient is implemented. Y-Yh R y= y= 1 ~Yh Rp' I'.i ’. i i.1 (5 ) . Other boundaries. where Op, Ct, Sp, V, R, Rp, Rp is the downward angle of boundary (ti,v,w) ’ P v% the propeller, thrust coefficient, single propeller area, inflow (1,0,0) zero gradient 0 control volume, radial coordinate whose origin, is-the outflow zero gradient ’ 0 zero gradient centre of the propeller, ajhub, radius and, a propeller outer zero gradient zero gradient zero gradient symmetry pi. symmetry , symmetry symmetry radius respectively.,, .it,, 11...... -n body (0,0,0) zero gradient ,.0 3.4, Computational Domain-,and Grid Figure 3 illustrates the computational! grid and the wing configuration at a height of 5%of the chord length. - < Propeller condition. -position of centre > :(xp/c,yF/p,Zp/c)= , 1 To minimize computer resources, symmetry- is assumed (-1.0, ±0.188, zT£./c + 0.31) about the vertical plane at the mid span position. The downward angle 0, = 33° computational grid is body fitted to facilitate the imple coefficient of thrust Ct = 2.9 mentation of boundary conditions. -The mesh contains 75 planes streamwisely, 35 laterally and-55 vertically: grid points are clustered near the wing, the ground and The minimum spacings are 0.005, 0.005 and 0.0001, in the the symmetry plane. . , streamwise, the lateral and the vertical directions. The The solution domain extends 5 chord , lengths up stream from the leading edge of the wing and an equal distance downstream from the trailing edge of the wing. The far-field boundaries in both lateral and vertical directions are 4 chord lengths from the end-plate and the suction side of the wing respectively. In the present scheme, the flow-field consists of 18 blocks of grids. Each block is a rectangular parallele piped in computational coordinates. Figure 4 depicts the schematic view of block topology for the WIG. 3.5 Computational Conditions The computations were carried out with 3 trailing edge heights, h/c of 0.02, 0.05 and 0.10. As a boundary condition on the ground, two methods are considered as slipwn in Table 2. Case-1 is a very common type and similar to an actual operating condition. Case-2 corre sponds to a wind tunnel test with a fixed ground plate. 1 ’ ■ f l - - i * i l 1 i i < | 1 Fig. 3 Computational grid at h/o —0.05 Solid wall condition on the rear plate ^behind the slot) and 2-symmetry condition otherwise are implemented. Thrust was given using, prescribed body force distribu tions from eqs. 4 & 5 and the magnitude, location and downward angle of the propellers are listed in Table 2. The Reynolds number was set at 2.4 X 10s. , i’ ’ 4. Results and Discussions 4.1, Comparison of Computed and Measured r * ( , Results fi ; Prior to the actual test program, a calibration of the ' i " i 1 i i ' , i propellers in a uniform flow was conducted without the wing. The propellers were placed at (xp/c, yp/c, Zp/c)= (—1.0, ±0.188,0.4) and the downward angle Op was 0°, namely paralleled to the ground. The thrust coefficient Fig. 4 Schematic view of block topology for a WIG was set at 2.9. Figure 5 depicts the computed velocity Numerical Study on the Aerodynamic Characteristics of a Three-Dimenaonal Power-Augmented Ram Wing in Ground Effect 35 vectors and pressure contour maps at x/c= —0.8. The flow is sucked into the centre of the propeller and the maximum pressure peak is formed. Comparison of measured and computed u-velocity profile along the horizontal line of (x/c, z/c)=(—0.8,0.4), is shown in Fig. 6. Although the measured data is scattered owing to the computed ----- measured o intensive unsteady state of the wake, the computed 12.0 result shows very good agreement with the experimen 2y7b=0.250 tal data. Figure 7 depicts the comparison of measured and , 0.0 computed surface-pressure distributions on the wing at h/c of 0.05 for case-2. Computed results agree well with the measured data on the pressure side of the wing. The 8.0 =■-- pressure on the pressure side of each section holds a nearly constant high value. This state utilizes the power-augmentation well and can produce a high lift force. The data does not change very much in the spanwise direction. This suggests that the flow is mostly two-dimensional. Thus, the end-plates are found to be quite effective. z/c , -4.0 8.0 2y/b=0.917 0.0 -03 -0.4 -03 -0.2 -O.l 0.0 0.1 02 03 0.4 03 x/c Fig. 5 Velocity vectors and pressure contour maps at x/c=—0.8 (Contour interval is 0.1 Cp) Fig. 7 Comparison of measured and computed surface - pressure distributions oh the wing at /z/c=0.05 for case-2 computed ----- measured o Figure 8 shows the comparison of measured and computed aerodynamic characteristics. Computed results agree very well with corresponding experimen tal data for all characteristics through the whole range of the ground heights. The lift coefficient increases as the wing moves close to the ground. This trend is similar to the results obtained using only the ground effect, however the increase in rate with the addition of PAR is very large and at h/c of 0.02, the lift of PAR- WIG is approximately seven times as large as that of an un-augmented WIG. When the ground height is very y/c small, the difference between case-1 and case-2 is very clear. The possible reasons will be discussed in the next Fig, 6 Comparison of measured and computed u- subsection. velocity profile along the horizontal line of (x/c, The drag coefficient without augmentation is almost z/c)=(-0.8, 0.4) constant with the ground height but that with power- 36— — Journal of The Society of Naval Architects of Japan, Vol. 179 1 10.0 h/o0.02(case-2) measured(casej:CT=0.0) ----- : 8:0 (case-2:CrM).0) V-----. __ _(case-2:Cr=2.9) ...... computed(case-l:CT=0.0) o (case-2:CT=0.Q),i+ " (case-l:CT=2.E>) Q ■. ------(case-2:CT=2-.9) "X: . Fig. 9 Computed velocity vectors ,at y/c=0.188 - ------5- ~t ------h/c-0.02(casc-2) 1 Fig. 8 Comparison of measured and computed ^wPSStrrrrrrKLlF F. MJi aerodynamic characteristics augmentation increases as the' wing approaches the ground, similarly to the lift coefficient. Owing to the increased lift, the pitching 'moment coefficient about thd 1/4 chord tends towards the nose down direction'as the wing ‘moves close to the ground: The lift to drag ratio iricreases as the ground height becomes 1 small, however,' the ratio is inferior to that without augmentation. The position of the centre of pressure shifts forward" as 'the Figj.0 Enlarged view of comput ed veloci ty vectors at ground height decreases. ' ' ’* ' ' 1 ' ' y/c=0.188 v -■ i ; 4.2' Effects on ’Ground Boundary ' Condition 11 and 1 Ground Height - ' ' ' - ‘ pare case-1 and case-2 at h/c of 0.02. The difference Figures 9, 10 & 11 depict the computed velocity can 6'e observed in the flow over the ground: In case-2, vectors arid pressure distributions aty/c'of 0.188, a large flow separation occurs over the plate at x/c of 0. contairiing the centre of the propeller. 1 First we com- 0~0.4, because of an adverse pressure gradient on the Numerical Study on the Aerodynamic Characteristics of a Three-Dimensional Power-Augmented Ram Wing in Ground Effect 37 h/c=0.02(case-l) (case-2) h/c=0.05(case-l) (case-2) h/c=0.10(case-l) (case-2) -2 -1 0 1 - 2 3 4 x/c • — Fig. 12 Computed surface-pressure distributions on the ground at y/c=0.188 h/c=0.02(case-l) — (case-2) --+-- h/c=0.05(case-l) (case-2) ----- h/c=0.10(case-l)------(case-2) ...... 8.0 „ 0.0 Fig. 11 Computed pressure distributions at y/c=0.188 Fig. 13 Computed surface-pressure distributions on (Contour interval is 0.25 Cp. Dotted lines show the wing at y/c=0.188 negative values) buttons on the ground at y/c of 0.188. On the whole, non-slip condition. The velocity under the wing is when the wing is close to the ground, the pressure accelerated on account of this separation. Thus, a high becomes high. At h/c of 0.02, a pressure difference can pressure region between the wing and the ground can be seen because of the large separation over the ground not be observed in case-2. In case-1, owing to the high for case-2. The results for all cases show a small pressure under the wing, the air flows backward over pressure hump, upstream of the leading edge. This is the ground upstream of the wing. However, the flow the impingement point of the efflux from the propulsors. does not separate under the wing and creates a high As the ground height decreases, the position shifts pressure region under the wing. Consequently, lift forward. performance in case-2 is less than that in case-1. Figure 13 depicts the computed surface-pressure dis Secondly, we compare ground height effects. As the tributions on the wing at y/c of 0.188. As the wing wing moves close to the ground, the blockage under the becomes close to the ground, the pressure on the presr wing increases. At higher altitude, the air flows smooth sure side becomes high. The results correspond to the ly under the wing. The flow above the wing does not pressure distribution on the ground (Fig. 12). The change very much with the ground height except in the results of case-1 at h/c of 0.02 indicate that the pressure vicinity of the suction side of the wing. The difference coefficient on the pressure side of the wing is an almost is due to the flow spilling over the wing from the constant high value. This is very close to the ideal propulsors. As the wing is close to the ground, the power-augmentation performance. momentum flux of the flow spilling over the wing Figure 14 shows the velocity vectors on the horizontal increases. Thereby, the pressure of the suction side of plane at z/c=zt.e./c—0.01. For all cases, the tip separa the wing becomes small as the ground height decreases. tion can be easily observed at the leading edge owing to Figure 12 shows the computed surface-pressure distri- the high pressure under the wing. As the ground height 38 ------Journal of- The Society of Naval Architects of Japan, Vol.179 ' ~h/c-0.02(case-2) 15.0 / tmn//////f / / ssssam h/c=0.02(case-l) 1 (case-2) „ . i # z zzflBRW/// s h/c=0.05(case-l) .", »,; / 1 / //0EZ'///f / y ! (case-2) i H ia a 10.0 h/c=0.10(case-l) (case-2) _L’i__!_ j___i__ f_ ? ?sste»?«tt £Ll/Jlars U 300-6—6- ■H~)--- 1- h/<>-0.02(case-l) 5.0 f . . / / //Mm*?// //////^ L i i MSw !*a 0.0 ------'------'------0.0 0.1 , 0/2 0.3 L _ l_LUSBuZj2£fZ LLijii y/c ... h/c-0.05(case-l) Fig. 15 Computed spanwise distributions of lift coefficient ' ----- case-1 (frictional) -o- (pressure ) -+-■ case-2(frictional)--Q- pressure ) -x- G 0.5 : L-E- . . .■- tje-. I - Fig. 14 Computed velocity vectors at z/c =zr. J./c—0.01 becomes larger, the air under the wing flows smoothly. In case-1, at /z/c of 0.02, the air flows backward near the Fig716 Components of computed drag coefficients symmetry plane on account of the high pressure under1 the wing. j ,, ■ .I, Figure 15 depicts the computed spanwise distributions follows : i i of the lift coefficient. Because of the presence of the end 1. Results simulated with different ground heights -plates, high pressure exists under the wing and the flow showed good agreement with experimental data is very similar to the two-dimensional case. Thus, the 1 1 in terms of the aerodynairiic characteristics for end-plates are quite effective. 1 ■ < ‘ r' ' ' ' the ground heights of 0.02~0.10c. Figure' 16 shows' the components of the computed '"2. 1 A further decrease in the ground height raised the drag coefficients. The "frictional component is nearly 1 ' lift coefficient, drag coefficient and lift to drag constant with the ground height, as a result, the increase ' ratio. However, the lift to drag ratio was inferior of the drag is derived only from the pressure drag. ■ to that without augmentation, because of the ' ' ' m 1 I ' * increase of 1 the drag coefficient. 1 ' Conclusions "13. • In the present case, distributions of surface-pres Flows around a three-dimensional power-augmented sure on the pressure bide of a wing and two- ram wing in ground effect with end-plates were comput 1 ' dimensional lift coefficient were a nearly con ed by a Navier-Stokes solver so as to clarify the aer stant high value in the spanwise direction. Thus, odynamic interference between the wing,' the ground r,, mi the'erid-plates were found to be effective, as in arid the propulsors. Because of the geometric complex II the un-augmented condition. ity of the configuration, a multi-block grid approach ^ ■ 4. 1 The lift coefficient of case-2 was less than that of was" introduced. As a ground boundary condition, two "r- case-1, because in very close proximity to the rnethods were examined:1 case-1) the velocity is equal ' '■ grourid, the flow for case-2 has a large separation to the uniform flow ; and case-2) the no slip condition. 11 over the ground under the wing. This velocity They corresponded to an actual operating 1 condition • ' ' under the wirig was accelerated and as a result, and wind-tunnel tests' with a fixed ground plate respec ' ' no high pressure region was found. tively. Propulsors were represented rising prescribed £ In future4 work, flow computation for a PAR-WIG body-force distributions. The reshits obtained were as vehicle with a fuselage and control surfaces will be Numerical Study on the Aerodynamic Characteristics of a Three-Dimensional Power-Augmented Ram Wingin Ground Effect 39 performed with the compressibility effects and total General Meeting of Ship Research Institute, Dec. aerodynamic characteristics of the full-scale vehicle 1994, pp. 153-156 (in Japanese) . will be examined. 5) Murao, R., Hirohama, T. and Hori, T.,“A Momentum Flux Model of PAR-WIG”, Proceed Acknowledgement ings of the 33 rd Aircraft Symposium, Nov. 1995, pp. 439-442 (in Japanese). The author would like to acknowledge the continuing 6) Hirata, N., “Simulation on Viscous Flow around encouragement by Dr. T. Fuwa, Ship Research Institute. Two-Dimensional Power-Augmented Ram Wing The author would also like to express his sincere grati in Ground Effect”, J. of the Soc. of Naval Archi tude to Dr. T. Hino, Ship Research Institute, for his tects of Japan, vol. 174, Dec. 1993, pp. 47-54 (in valuable discussions and suggestions. Japanese). 7) Hirata, N., “Numerical Simulation of Two- References Dimensional PAR-WIG”, Special Publication of National Aerospace Laboratory, SP-27, Dec. 1) Krause, F. H., Gallington, R. W., Rousseau, D. G. 1994, pp. 303-308 (in Japanese). and Kidwell, G. H.,“The Current Level of Power- 8) Hirata, N. and Kodama, Y.,“Flow Computation Augmented-RAM Wing Technology ”, AIAA/ for Three-Dimensional Wing in Ground Effect SNAME Advanced Marine Vehicles Conference, Using Multi-Block Technique ”, J. of the Soc. of San Diego, Apr. 1978. Naval Architects of Japan, vol. 177, Jun. 1995, pp. 2) Matsubara, T., Tashimo, M., Kure, F., Yamagu- 49-57. chi, N. and Ohwaki, T.,“Lift Enhancement of 9) Stem, F., Kim, H. T., Patel, V. C. and Chen, H. C., Ground-Effect Wing (2nd Report, Experimental “A Viscous-Flow Approach to the Computation Investigation of the Power Augmented Ram Wing in Ground Effect through the Wind Tun of Propeller-Hull Interaction ”, J. of Ship nel) ”, J. of the Japan Soc. of Mech. Eng., B-58- Research, vol. 32, No. 4, Dec. 1988, pp. 246-262. 552, Aug. 1992, pp. 2464-2471 (in Japanese). 10) Sowdon, A. and Hori, T.,“An Experimental Tech 3) Nagamatsu, T. and Kure, F.,“Experimental nique for Accurate Simulation of the Flow-Field Study on Aerodynamic Characteristics of PAR- for Wing-In-Surface-Effect Craft”, Accepted for WIG”, J. of the Kansai Soc. of Naval Architects, publication in ‘The Aeronautical Journal ’, 1996. Japan, vol. 222, Sep. 1994, pp. 49-56 (in Japanese) . 11) Huband, G. W., Rizzetta, D. P. and Shang, J. J. S., 4) Hori, T., Hirata, N., Tsukada, Y. and Fuwa, T., “Numerical Simulation of the Navier-Stokes “A Study on the Surface Effect Phenomena and Equations for an F-16A Configuration ”, J. of Characteristics of WISES”, Abstract of the 64 th Aircraft, vol. 26, No. 7, July 1989, pp. 634-640. '.‘.I v/r h . . (t-,v U' . r1 t . 1 ’ ' ' 1 1 ■ ’ ,. - 1 , 1 ' 'i I ! ! ■' :? 1 r 1 i - , v1 1 „r ni-rn , i I- - , < .1 • 1 - ' i 1 I ! ) 1J i :o t I 'I 1 -J'.'LI •1- , t •1 i , ' ' 1 ■! , V> ' !..■ a - ' 1 I 1 i f i 11 | i Y I 1 j' :mr ' ■l ' '1 41 1-5 zl y — y 3 y iHM & # % m* iEM K ffl m** Numerical Simulation of a Bubble Flow by Modified Density Function Method by Akihiro Kanai, Member Hideaki Miyata, Member Summary A new numerical simulation code is developed for elucidating the behavior of a bubble being based on the Navier-Stokes equation. The capturing of the interface between liquid and gas is implemented by the modified density function method significantly suppressing numerical diffusion in the rectangular coordinate system. The density function method, which eliminates the efforts of generating grids fitted to the interface, is shown to capture the complex 3-dimensional deformation of a bubble with sufficient degree of accuracy. Computational results of a rising bubble at high Reynolds number greater than 1000 showed the unsteady motions such as those with zigzag or spiral trajectory and the various deformation of bubble shape like a spherical cap. It is also clarified that the unsteady motion is caused by the asymmetric formulation of longitudinal vortex behind the bubble. This code can be applied to the case of bubbles in a boundary layer to investigate the effects of bubbles on the boundary layer properties. 1. 88 Em 6 & crs c as? v>. msc j: a, a sgc 5 a tx-y 3 y\t, 2 2 fcthSCSffvi, ^ n 6 ©XN«? y -7 E J: 5 ®t6©^-fbSj$^.TVi50 Unverdi & Tryggvason 3’ a, ibu, a#^sa»#A^@a0iokf3 60»if, M 7 D v h h 7 S' * 's'fmM rSo^&^ ’SLTv^vit) <, mnaa, S@r8f£ mu 2 %9 &o?B9 , me#© 2 *.tz, ss, KMK&ibe-e-csfc*, Wl ¥^8¥1^10B %©@T^A-xic^ib^a z 5 ee SeEESCdb'ti-CEE 8 ¥ 5 15, 16 B $UV'5, ZLfia, 3 C k 42 k 3 b^§z.6ti£0 $fc, Sussman, Smere- Fn= UI-JlRg \t7IV— HR, g* B@A^I«]©#@- MS*/n °7y-y-k*-5©», a /pz:2ffl©SSJt, A-P2+®=2WMv(-^)-2to «v(-^)2 (4) jUi/^2: 2 %©%##% Rn=2UR(v : 1/4 y ;>XR, lFe=p,£P(2F)/(r "CCT, Ttt§ 2 ti, fiifwmakma»*6^t©kf3. $ 7k, V, g ZSMUjM&t f S k, 1 (5) TrTfL.p,, p 2 Bs-ti^n, ma#W±K# B smm^- mmam&fsm Lamm©##y 43 m*. mamma, t h^r [email protected]©seRg) -at, B*EE'fbC rising velocity — volume — •a 0.4 easel NondimensfonalTima Nondimensional Time 1 rising velocity —7 volume — ■■ 1 n 0 5 10 15 20 25 5 . 10 15 20 Nondimensional Time Nondimensional Time Fig. 1 Time variations of rising, velocity of a bubble Fig. 2 Time variations of bubble volume for case 1 and for case 1 and case 2 .. v case 2 • k e 4 a glto a# iz&izt9, trajedoiyofabubble — velocity in x-diredion — velocity in y-diredion — •a 0 easel Nondimensional Time trajectory of a bubble — velocity in x-diredion — velocity in y-direction — •a 0 Fig. 4 Bubble trajectories for case 1 and case 2 Nondimensional Time Fig. 3 Time variations of velocities on a horizontal 2 3 4 5 6 8 10 plane for case 1 and case 2 1 o o QQ 2 o ' o * OQQ 5 o o QQO 10 o o 20 o o OQQ 50 o o 100 OOOoc? 200 OOOo Fig.5(a), (b) Bubble shape, pressure contour and velocity vectors on a vertical plane Fig. 5(c) Computed axisymmetric shapes of rising through the volume center of a bubble bubbles as a. function of Reynolds number at T=20 for (a) case 1 and (b) case (R) and Weber number (W) by Ryskin and 2. The contour interval is 0.05 Leal. (ref. 1) ... o o -rv at ■V Nondimensional Velocity con 9+ a R 4 d «x 9+ ym Pt I -A< X' H g # ■<* 4 zv 9+ 0 4 (X 09 1$ !» & P P p p 4* eX Oft Nondimensional V elocity hr 04 £m 9ht 3 EE EE £._ ! tid R (X dr at tX at 8 R m r< ■a tp2 1| © p p r rv % rv £? R ? SB # ro i , o ro Ok ti- as T=15.0 T=52.5 T=17.5 T=30.0 T=42.5 T=55.0 T=57.5 T=35.0 T=47.5 T=60.0 ,v T=25.0 T=37.5 T=50.0 r~Y 48 j it 5 c^3*?, 1 zkn,. ^ - f i U f C3:60T$3 3 k*#&?&. $fc, -<7 tf y^o^nsisk lt ' ##'. ' i>5;ki5&i'vfco r i ' ;:i :' # ' i z I 4) ±#asa#R*m kit^\$ k & ? -c v» a 1 tk£k*, a!A&#v^ IWhSWc-tJ: 5&tz, 4-&0R 1 #1 A @rs % < L------— xT£5-^&vvr-~~ ---1 Z—.. i I 1 , ( *-.V . ' r ; ■ — A " ^ « .. . ; •: i i - . i \ \ - ( "| I 1) Ryskin^G. and Leal, L. G.: “Numerical solution of ' ' i 1 free,-boundary problems in fluid mechanics! Part ''' i * , * i i 2. Buoyancy-driven 1 motion of a gas bubble Fig. 11 Iso-surface of the second derivative of pressure | through a quiescent liquid ”, J„ Fluid Mech., 148, at T=20 for case 3. The iso-surface value is 1.0 i (1984), pp. 19-35. | i 2) iS*, #*,: “KSilS E DMDF n # IE* lii □ __* JE * # S gl** #p * I1 ft* m m tin # , A Numerical Prediction with “DMDF” Model of Pack Ice Motion in the Okhotsk Sea by Takatoshi Matsuzawa, Student Member, Hajime Yamaguchi, Member Chang Kyu Rheem, Member Shinsuke Suzuki Hiroharu Kato, Member Summary The Distributed Mass/Discrete Floe model, DMDF model, is a new numerical model for pack ice motion computation. This model expresses the ice floe collision by dividing the pack ice into many ice floe bunches in which ice floes are distributed uniformly : thus it can express the discrete nature of force transmission between the floes and also can treat a larger number of floes than a discrete element approach. This paper applies the DMDF model to the computation of one-week pack ice motion in the Okhotsk Sea of February 1994, transferring a large amount of data from the Japan Meteorological Agency, and then discusses the characteristics of the model and ice motion in this particular sea area. The main conclusions are: (1) The DMDF model showed rigorous ice motion against the external forces such as wind and current. (2) The ice motion is determined mainly by the wind, but the local behavior is strongly affected by the current. (3) The interaction between the wind, ice and current is important, thus the coupled computation with the current is required to predict the ice motion more precisely. (4) Since the direction of shearing force due to wind is different from the wind direction by the influence of Coriolis force due to the earth rotation, the computed ice motion agrees better with the observation when the shearing force direction is deviated in clockwise direction. (5) The computed ice motion is compared with the buoy observation. The result showed fairly good agreement. It is recognized, however, that more accurate and detailed current data is necessary. -(ifI960 Campbell" 1. U to (C ®##®#f#&g*&%CtK*8S9, Coonetal 2), Thorn dike etaM, Hibier» kgosam, c-fcrp T-il 9 zcfi-MTz t, 5 Tf^k, —o —3 M-mmt Lx&z.zBikommztiZ', modeling t ------bB *’5* -, , —' < □ □ Q !: ■: ., , -V: At: Total ice area in a bunch Ca : Friction coefficient between air and ice bunch Cd ■ Friction coefficient' | ! ; between' II air and water computation grid Ca ■ Friction coefficient between ice and water Fig. 1 Introduction of Ice Bunch to Treat a Large dt: Time step for the computation , Number of Ice Floes Ez : Eddy viscosity in the depth direction /: Coriolis parameter ,, , / - , ,,i. K-psss-r* (Fig. i). e ©###?m ©±% © Ft: Ice interaction force (internal stress) skL, m g : Acceleration of gravity t, ^ ©%#g k bfflkTSo k : Unit vector in the depth direction , 2.2 *P©j$Bl Mt: Total ice mass in a bunch rt+dt Nt: Number of floe rows in a bunch Mi{vi+d‘— Vi) = Ji (Aifa+Aifa ^ lit - Number of floe rows to collide in a bunch —MtgVif —Mifk x Si+Fi)dt Va : Wind velocity dt ®m&®mmmt-ch 9 , &a Vw: Water velocity - ‘ ' ' 1 » T . ‘ I 1 ^ ' !'■ ' 1 ' . ( I I ,r vt. Ice velocity B, Sift© k Mi ■ Ice/ice friction coefficient , , , *S©#^© 5 *>, fa kWcj: V ■ Water surface elevation , ...... J:-5SE/®^"C$>9, f-tibir-k®k 5 \z-5-±t>tiZ0 Pd Density of air , . ^ . fa^PaCaWa— Vi\{Va~ Vi) , (2) Pi: Density of ice...... ' - 1 fa= PaCa\Va~ Vi\(Va~Vi) (3) Pa : Density of water -M,gVy ttig@©®£4ei Sift, ’ -MJk X y, ($3 fa ■ Shear stress acting on a bunch due to the wind v * v ©a, f, t$7ksir=g © ms* v $> 3 o zc-e, msp fa •_ Shear stress acting on a bunch due to the rfe* k <'Asw%© c k current &S5 oDMDF„^r^©mi$ k ©#ZfMBa©a8BC& 09F2ESVgg$§S ivk Distributed Mass / Dis 9 , }±*#©#^©pg©2E#m#t#^ crete Floe Model (DTR DMDF t f;P) H, t jv 'u*>smii fL5o SL< aa$S8)7) S#EStifcvi, *#©SSK )KS©4o 0I0MEJ:o TS 9 kv> 5, mu® x 3 7)81 o 4-$ tE c © ztcmz 5 mk w* ssutes , ##u. nee ?i 9 5„ A me, @9&s©*©m 9 ~©*mf ####??* . ^9I^grtt,DMDF 4-7 S©SSE^fr5o DMDF*=f>vx\t, £©i 5 e*#0 istfiiciiffl U, JtSK^SSHKto*SS-mSC-ov^T V)&. *)©klW-kL, gf 2.3 1* ©n-uc® imimu t ' mE©DMDFtf^/-ca@B*@kMB*@%a^ C k*5-Cg-5„ 5 k, %&&©&*#** . , : zt/2/3"(<1) C * 5 k p 5 o § ?> K*@*%© 2. DMDF Model u AK©@s^mA^m©*mi$%^ -cem ,, 2.1, ;feR©IiE?S , DMDF 5 fckTSk, C©*#©f©*@A*®B&» 6tf, BA7, S *#k«, K#< AK Fiy = Fiy~ 0 (4) A 9.,, f l j '. -' DMDFtf,MC X tmWkMmom.Wfm 51 $ -3 -CEtte?-CS 5 *>', ABt±E®A?BE»72 ©Wi&©& f©72©APtt^a/f*^IS©72 ©Em-#LAf-^3 C k k L72. $fc, #b## #©WNk^l75&m=k LT, mfcltOXffilljRVOlkffi AtSklko A- 7i Wb©##^ 6 imK#AA%AA -5 ©r, CCTktmmf-f ©g#g • ^JP^mffk L (a) Rectangle Roes tCo Fig. 2 Ice Internal Force Acting between Floes nt-mz'&mzmcD?-? is, sajf^5.f§-c^i8L72„ MaifTli 1 0 4 IsJEHSTiaiflE^6 10 m HSS±JH &##fa. ASf-$?-ct±^©®©T-^f vAWLrffl t>TVi?>0 c-AT— J7S ntxFfkicos e-^sin 0) (5) riy— ------4Miz sin d Ftii cos 8 k*a(Fig.2) 0 C CTm Mv hna 6 © f ## $ 4kl2 Wakatsuki & Martin141 (2 Lte t) © £y #T(£ffi L72c SiEgmAXSM k EStSe >x// /1 # 1 A k <* Fig. 4 Ocean Current in the Okhotsk Sea Fig. 3 Computation Domain and Grid (Wakatsuki&Martin, 1991) 52 # 179 Table 1 Physical and Computational Parameters" 3.3 HE4Sg3El$*©$5i' for Calculation C kCJ:3SEfS*©S*C>y-f 3fffflBlRl I Density of Air: p a = 1.293[kg/m 3] - 1 14, 3#ekE#K, 3 9^9A©B#&S» . Density of Water: p„ = 1025.9[kg/m 3] ■ -CUE k ISiFF-ffiSoSHtoCti: 45" &{§?%&, BBC = 910.0[kg/m 3j Density of Ice: p, lii£E©mtiJ:9fi^t$;enJ:9/>§vikSi.e>fL3„ Acceleration of Gravity : g — 9.81 [m/sec2] ' Coriolis Parameter: / — 1.10 x 10-l[sec-‘) 1 $#%T(4RK%E, Mfttt 0°, 22.5°, 45" ©3X?->K (latitude ^ = 45°AT). Friction Coefficient between ^ = 0.001. , ; - the Air and Ice ° B©SEtc*S^14 1 ' Riction Coefficient between > = 0X04 1 ra=P<,C,|K|V„ (9) the Ice and Water £fflv>Ttf-$?U£„ £ £ VSmkW*@B©im« Ca Ice/Ice Friction Coefficient : Pi = 0.3 Ice/Shore Friction Coefficient : p, = 0.1 ,£©(114 Wu‘?> K43 Representative Length of Floe : Ih = 100[mJ ; , ' Ca=(0.8+0.065|Pa|)xiO “3 (10) Number of Layers in the = 5 v . : &8UBL&. Depth Direction Eddy Viscosity in the 3.4 tf-SiSm ^ = 0.03[m2/sec] i ; Depth Direction ' ' 3.4.1 WM&ftkLX 1994 if 2 E 1 B©f-f & 3.2.1 iSS^I=l©li SLhJi©±E (&=1, WzfcB) "C14 1 l}—AiTi + (1 — Af) Ta __ ' ( 8) e>ft3> ez m, t7.amK©mg-c&3. ttz, m#= 111 nzti^n. ;?©g©TEk±m»B#L?^3. ±©S(7")k.S(8) &TE k-±E-K.A?^ 3j5f6rf6# k Ufa 2 ^TcNavier- Stokes^SS k ig*©3Bs5£ E 4S"T, Fig. 5- Observed Jce.Concentration on 1st February, fl3o & jb'SSC $>fc3BT14 non-slip "C$.3 k U, 1994 DMDF ^ef»K i: ?mWkmWs(OmMr?m 53 Table 2 Cases of calculation Direction of Shear Force Current Floe Type Fig.No. due to Wind Interaction between same as the wind Fig.8 the Wind, Ice rectangle 22.5“ right 1 Fig.9 and Current 45° right Fig.10 No rectangle 22.5“ right Fig.ll Interaction disk 22.5“ right Fig.12 Fig. 6 Observed Ice Concentration on 8th February, 1994 1 < i —* I0D bVkc Fig. 8 Calculated Ice Concentration on 8th February, 1994; Rectanglar Floe Model. The direction of shearing force due to wind is the same as that of 1st February, 9am 3rd February, the wind. —* IOjObVk* ^^IftOeVsec 5th February, 9am 7th February, 9am Fig. 7 Variation of Wind during 1 st and 8th February, 1994 ■C, meontti: i pSiLvi»5, ths, wa, ttz, wrwm 3.4.2 2^8B*9Z0#W Table 2 Fig. 9 Calculated Ice Concentration on 8th February, Figs. 8~10 B, 0°, 1994; Rectanglar Floe Model. The direction of 22.5°,45•ftfitli t 2£ 8 0d9*Z%COViT shearing force due to wind is deviated by 22.5° in (D^mw&feZkx-hZo ztibomt-ciz, ms-temm clockwise direction from the wind. 54 Fig. 10 Calculated Ice Concentration on 8th February, Fig. 11 Calculated Ice Concentration on 8th February, 1994; Rectanglar Floe. The direction of shear 1994 ; Rectanglar Floe Model. Stationary Cur ing force due to wind is deviated by 45° in rent (No Interaction between Current, Ice and clockwise direction from the wind. Wind), The direction of shearing force due to ; wind is deviated by 22.5° in clockwise direction from the wind. MMtiiSciill£ ± -5 t.LX, . fcfSLglKit li 22.5° k LTW 5 „ Otfff-Ctt,' i> M-# vtz o Fig. ii Fig. 12 % 3® v ?-cwa0dtb&a. LfrLi-ftMEti, *###©#m MStfSti (SEia Ta kS*Ei:a rj A#7k©2E#^l^ E*fLT5EE69"C;ba kv>5 a k65*L-CMa<, £/c, M 3.5 y^rfxy-f ©WlBji k ©itix 0§?»rJ**©f^ffl^lRlSr^x.5k, #E##a©@^*# KOHTf0Ki?I < a&h*. m»a», %Ka0@vi*»"CK*@m©*S0@gSA^6 <, * caf&m*0m@em#f &ms&fz9&*. coma 5. tmm» l©*§& (Fig. s) ©#y@ 9 mt©&m# Or-?Ejcak, 1994 &2MEtiy-fti5,f5 < *5o L*Ljai?»rfS*0fFM^lRlE#m6¥x.a LTSD, #f#kARf 5Ek#3G@ k, ££!&>*}¥$X.ZthXm.fflim-3<. a©ak(i, HE 3 "C$1-3^0 0#*©a#E b C0@A0^@A*^»*)6f#@f 3 a a OJtESff? /c » Ef|-mtam 61*8 E&B L, k6*FL"CV>a kS£5o 2^2 B©y-r ak-en-£?±@ ie^i^sil©® 9 45° kf 5 k=#W6±%t#t)j: 5 y^t ©#^6^©/:. ##&#k u-t& "C$>9, anti#^# —nmmowm&stztm.® HS©ibS S &#*&%# k4BS LA«^©#i gmtzztusz&vrisb-f, ttzmmiz-ijcommMm jjr*a, #%©^#&&Bm±Esay#gkg^Sie* tzfetbtii£m%. 10 A, (1995). 11) Rheem, C. K., H. Yamaguchi and H. Kato : “Drift 7) Rheem, C.K., H. Yamaguchi and H. Kato: “A Tests of Model Floes in a Circulation Water Distributed Mass/Discrete Floe model for Channel” Proc. INSROP ’95, (1995). rheology computation of pack ice consisting of 12) Sverdrop, H. U., M. W. Johnson and R. H Flem disk floes ” Pro. 4 th Int. Conf. 1SOPE, Vol. 2 ing : “The ocean ” Prentice-Hall Inc., Englewood (1994), pp. 458-465. Cliffs, NJ, (1942), pp. 489-503. 8) Rheem, C.K., H. Yamaguchi and H. Kato: 13) Thorndike, A. S., D. A. Rothrock, G. A. Maycut “Numerical simulation of rectangle ice floes and R. Colony : “The thickness distribution of movement using a Distributed Mass/Discrete sea ice”/. Geophys. Res., Vol. 80 (1975), pp. 4501- Floe model ” J. Soc. Naval Archi. Jpn., Vol. 175 4513. (1994), pp. 151-159. 14) Wakatsuki, M. and S. Martin: “Water circula 9 ) tion in the Kuril basin of the Okhotsk sea and its *r;v©w, (1994). relation to eddy formation ” /. Oceanogr. Soc. Jap., 10) Rheem, C.K., H. Yamaguchi and H. Kato: Vol. 47 (1991), pp. 157-168. “Investigation on characteristics of pack ice 15) Wu, J.: “Wind-stress coefficients over sea sur motion with Distributed Mass/Discrete Floe face from breeze to hurricane” /. Geophys. Res., model"/. Soc. Naval Archi. Jpn., Vol. 177 (1994), Vol. 87 (1982), pp. 9704-9706. pp. 131-139. t s 59 1-7 ieji m n m -* earn 75 m m** A Stochastic Model for the Long-Term Prediction ----- Application of the Model to Predicting Ship Responses ----- by Akiji Shinkai, Member Shuntao Wan, Student Member Summary This paper discusses the reconstruction on the algorithm of the long-term prediction by using a stochastic model. ' The model is a rational long-term stochastic model for calculating the long-term statistics of sea waves which was proposed by G. A. Athanassoulis et al. On the basis of the same framework of treating the wave climate as a stochastic model, the algorithm for the long-term stochastic prediction of ship responses in ocean waves is examined and improved for the purpose of using the combination of some long-term wave frequency data which presented with some differences in data format. The long-term predictions of vertical acceleration induced on the bow of a container ship are executed for a few patterns of combination of wave data, and further investigations for reconstruction of the algorithm are discussed. ©©f&CESiiUcaSo* < %mW$t t X-f t-X CSo* < i. m m mmawebeata tins d , ^±¥#©#m%#©f —XX©SSSA?±ESiffV>5o S©±5Cf ®ti+¥ jEgoMtoTifP So ZcDtztbC kt, aimcbt? r$tET s s wa. (#c, SE2&S) £tomc¥i®7S r biWW WbMzftQ@&K, AX®a©fJfflKi:Sir tars. u jss&jsgoEifmngim© V XA ©B*£ff-S Ck&BKkL-CwSo c±anf s c SoBu#©ainS-eSto7^&-ct±, z © smmmsmr-^ es ttmEMMfiWm-rZ Jasper"' ®kLTjE<^fflK#idnrST«D, ^©BUSSli^ k, #mt%^Sk, #%%E^HT, tssttflsesm Eit!) Afi6ATWSo b*b, g eEk^SE^7S@SI@®E^aSgg®/>(Ar, A) ©s }ffl?jffla©7^3-V XAE^TIf, nm&'\ dbiES22’:', ,SB&{S%7'SZkT&So k.©®S® k C,: E^5M@ ©#W(Nlf & 3 60©, 6 30 Wif¥Eiibfc ' 7('o kE5F$?!i sco ©fm©mi#W7-m©fcmmsr Kt*>*>to6-f, 7©^H^\©^EA?+S-CS* 6ii/c k ka-'i^AStve, E^^l©mf#gfEffi-y #, Slffl ttax.*vi 0 tSSS@©E@ 7(0 ©m$M##©##i^$^©J* $#TK, Z$$Eri-T-^©#©m#&T%@LfcSlffl ffl^JkbT, &&%@©K©^@ k &!S©^m$%@ ?#&&^m7s%»E, #rLv^#m©mm%f;y") &# i?$6.5>tirvi5,3>„ c©mmBm%a""*»2' ©mm?#i #E LT63ffl«TfiJffl sns Sjffli6E^SE5F©$S & ' mEmmw^r&s b, x-:^ h ;>###*;, a(0= t&Eu #» s t^a2" vm [kf(0, T(t)](H : #ami& T : ¥iSi6/g?t9) T&SCk SS9?SI©T;vd-vXAE-onTtll-tf" • k^rs^kitt", S^k'3BSOkbT, S 3„ Sti&immi: LTjb±¥#Cg8f SESh©^ £0J ,, s:±, @m&©7A/=f y xa 6 mi#»#^.^© & k eibss k Lxsffl l, n >% f fSkkii-CSSo Sb, fflgjSbfcr^rf.y xa ©;iffl©s#Kovit#^ !, %i%KTs##K&nx, mmzmiDmMmmmz XAr,A)cfA k$to7k§, r ©m%E$ WJA f if, & ?(r; Ar, a) k-tntf, r © 2. ’ f 6ftSo mm (mt, mmkW#) &,s©f7 Wxs wW%' Q(r|AD=f{Ai , Physics space (sea areas) p?=p{s=s?}, Pr'=P{s=sr‘} k#^%k$#K0%K*f3 m©#mm$it, p^=p{s=si} tap, *mt-t3d#m 05§5!WFP(Sn) £5 K^3fi3o Pl=2P(S")P{s=sl|S='} (5) p(s”) a, -mo&mmxmmo&n Sample space k i -p rsis®^sti-o k $»ev ^?, gg^uf, ms&gg ®^a?mi=’ 3. #K, %R©#K**, z6$E9fr-^StLTv^5/Jx & 3#^-E if ^© f 5 a#a.a&*m Fig. 1 Conceptualized diagram of wave data sample space f 3. Fig. 3 K, 'h&M An t\ WMuo ssfi-vm ‘Am Ks-sjsns k §, sn &m. ‘a ” ommM ©s^srattB^toK 'S”={‘sr, is?, -, % •••} ts< r k lx sm={sr, s?, s?, •••} © k**T#3. 'P"=P{s='sT) t jo 5§ II $6 ^ Pn=P{s=s”} : »=1,2, — ; m=l, 2,—,M & It if, /JxB^TiElf-toKiSEkffiSVS 3 k § Ktf, Pf= 30 T)?i=(Hi, Tj)m: z=l, 2, 'pr=-='p nn=- k Ttufm^. •••; y=l,2, -k L, ^7=f3 kg! v>3^s-cif, mm#©m»m Am K&lf3@mS#©g^?aA*(2) Sffl \'XWrUX% 3. Sfc, Sn PCS'”)»? ###&3=). ' BBmT&fwf, rsisM^fra c tv tss. c w#a 3 zmmm-mmmgmm-f-f ©e Sea areas Am = 1 Am + 2Am + *•• j$23> c*'nr$gfflsti^r;>d ivXA-e$)30 ##%&g3TK%f3. *f, *#©##% msHEK 3f,MS tL3 9T$3„' Fig. 2 ©£ 5 k f©#%0 m*4R®0@*3ai«l^@»3k@, km%A"+' KAlf3W&©*^g" k S"+I if, fc5©i7l^i6 ft30 Sample space Sm = 1 Sm + 2Sm + — sm={sr, s?‘, ■■■}, sa*'={sr\s? +l, •••} (3) :;c, Smr)Sm+l= 4. Sea areas 4.i ##&%##*# - ’ / 3±mmmzx\,ix, g#©g#&%mt Am+I m m m S*4 51-11’ fix Vi 3„ Hogben b © GWS (Global Am Wave Statistics)8 ’ OWmmxte, jb*E#, $±?## f 3 104 ®/JxS ^KOV^T, ^jve>®^§ftfrt3lSffi^b0^1130^ Sample space Fa (1854 #—1984 m (DEwmmn^-y (Skm®ffl mmmmfrtt&-%it>biixim-WLmm 9bfc¥#E.-wrti:, OjA siT-^ito 5, 6" ©SSmif 0^(1954 ¥-1963 ¥), SB 6101 ©SEE #&*/<-: LTi? &_©TE0K»#:E » o T V) 3 Ckk rf-0St(1964 ¥-1973 ¥), #36'" 0#SEfH13i(1974 **¥#CiM11-3 tlffi 6,: SB 6, S36 ©HoOSSI ¥—1988 ¥) WfiSdiLTV^o GWS ©H-g- s a: i# 6, sb 6,,s36©mm- osms-^ i&ss-smm©m^s* (^be> f—f^S^E@ALTW3 3 k»?¥§lirv)5„ &mgm) (Dj&x-wr^tix^^o m 9b*¥#©ssmif-ssKov^-c§ 6KWSBE^m- m 6 (D&mmmm-e® 48 bi@, sb6 ©mmm##? 3. ¥#¥T##L7:^±¥#©Am# t kt, %SU)-C$g 0356B@, S36©SSEff-ES©ggE J: 3 fc © T @,LA#KtRDr$9, Fig. 5 C§Lti/>3, GWS Ei> ®m75m-e$>z-0 #K#cof-f%comsmg»%a#- tf 3 Area No. : 6, 7, 112, 13, 14, 18, 19, 20, 21, 22, sfeftK, (#&#, P3) ©mm?m 28, 29^ 30, 31, 40, 41, 42, 43, 44, 45, 46, 52, 53, ST3#%mBia*ET, Fig. 4 KSt. iCB, ##©A 54, 62, 63 © 26 #©/]##& 6#&$ 6#E? ftE, 691-3, Roll 6’©smEm-0# h ©mam#E%fBi-3o 0¥±t# (3.-9 Walden6’ ©SSEfFIl^EO i^T b R#©#^?S-f ¥, ItimMm, S3) S36"'»?rS &©#R&SL-C^3. 3j:D, GWS ©g ufc9b±¥#©m£emi- 3 „ mm6, SB6, S36©mmmmm, ^m-?35¥ FaoS^FSKbTi3EfH5»fcXU9, r-^©7* -vy h ES¥©mm*t&3 & ©©, Bimumss#© b k ES-7 ©#gfkSm**frbfLt, SS©%gSS0 tlX Vi 3 „ #T-f %^L%#mT3 fc ft © EBto^SK-7Vi-CX®23)TBUfiA?, f©3T#*1 k i£&7>vlV Z.XWm\,tco 9b±¥#©A##k 2 0©#%## (GWS ©/J\## Area No. 42 k /hiSiS; Area No. 20) cowt, #sst-7 ©gmR&#gmm#T Fig. 6 Ea^bTV»3o®* i6to*»3 20N 10N 0 10S Fig. 5 Map of calculated sea areas 63 »S$$'Fig.7~9 Izm-To Fig. 7Ett, &±wwo±mm\z^x, ihnbomm ti-mm, R5G0&mmt#K ft SSC Fig. 8 K It, (GWS ©/J## Area No. 20) C Fig. 6 Relationship of different wave data (the North The North Pacific(All sub zones) Pacific) • Yamanouchi et al. 5 1.5 ♦ Takaishi et al. " T Watanabe et al. %# (GWS Area No. 20) E*fUT, ma^kRE^©# O Combined @ GWS(Modified) M03, M04-©^%, Hlft6 ©KB##0&TK4#%## 2,15,16-©efi%&?T9 C kE»3. #E, Ibfl6©z6SE8f@3m± —®C/NSiS *5JE< (if»ilto-WS) ©A*E^atfraieE3.-CR% LA:S^©a-9J©T;pd- y XA 4.2 3 >rxmsgtms kUT, EST-HttBgLAdbkT# OBJ.No. ©±%% Fig. 7 Relative values of long-term prediction of verti Ui„ 3 2=175 m, C„=0.572 cal acceleration at bow, as a function of object ©-WT*3„ ±i?g£ Table 1 Ezfif. m#B#k L numbers (All sub zones) r, mssiiEE^s tizswjfttommzmm u*:,, hs The North P§rcific(40N-50N,150E-170W) 2.0 ■ 1 1 1 1 I 1 I 1 Table 1 Principal dimensions of the container ship Q=10"®, X=180° , Fn==0.30 • Yamanouchi et al. ♦ Takaishi et al. Item SR108 I T Watanabe et al. Container ship O Combined ;K © GWS(Modified) Lpp (Lwp) (m) 175.00 1.0 C? " B (m) : breadth 25.40 D (m) : depth 15.40 d (m) : draught 9.50 A (ton) 24. 742. 00 __ 1___ «___ 1___ !___ Lpp/B 6. 890 4 6 $ 10 B/d 2. 674 OBJ.No. [x10 5] lcbOSLpp) -0. 01417 Fig. 8 Relative values of long-term prediction of verti Cb 0. 572 cal acceleration at bow, as a function of object Cm . 0.970 numbers (Area No. 20) 64 #179# The North Pacific(20N-30N,130E-150E) EifflT-XgU D &jgv>£ kfrSfBrLT, irj$$4i4cT 2.0 T7- I ' |---- ■---- 1---- '---- 1 . , gws Q=10"8 , z=180° , Fn=0.30 -x kso* < cso* < ; , • Yamanouchi et al. § 1.5 ♦ Takaishietal. a - y Watanabe et al. - kiiiESnS. n O Combined GWS(Modified) 1.0 5. A W 0.5 u %##m-s#© f-x wmim, #&&&#©&w= 4 y#m-f-X©ma#»5##E, %##f|-t-X0E 7;i/d-v xAigamibL-c, 0 2 4 ,.6 8 10 ^U&lf 5 EO®¥T^^ y XA£fi$$#U4c. 1fc*¥# OBJ.No. [x10 5] ©swcout, ##©EEmm#%emLT#mf Fig. 9 Relative values of long-term prediction of verti 50us^-rkttK, a #©%#KB88afi,5mm cal acceleration at bow, as a function of object ^mn%s©^8?@#f#t%mLT, tisufir y =f y numbers (Area No. 42) X A E3Eo*§%S#rf-T-X ©#m&fro XcEElfcmiSS &$um-45 £ k K4 y 4 y#mEA:#Lfs#mmg out, UiP3 6©ESgctl-@$, mm*> 4 ©# 4 6 © m*is#©m*Mm©?mT& d , ?am© bs©^si6i± Ho® EiSITcETt—X (combined) ©#X Gffio* <, Eo^T, glfis©r^3-y XA kEEgcfbr-X © jEBlrtlERETlSjS Fw=0.30 ®Jg^-®SS5[Rlinj$S© @©M@^%#it8#Tffr&§titzfc ©ESStiTllsS©^#lc mmmmm t 5 „ £>4c D4#%©*©7/P^y k 14 3. . ' rib±¥#©Ekm (1974— 1988) J ©XV n yf&iSStr T-16B9 u&ab So-® k 14, io- 8 ' —xx —x.©fyffl ceil, Six © rESSHvifc (M) y 7 fi§ GWS ESo* < ^ /•7>F-x-yfy*a©M##©##K@< »L$ ©&m##H@#©mmf-xR©M&k ut ^ltv >5„ L±lf4fo 44c, $WB©mfrR:D18%3 AfH 0e4*Uf, =o©EEmhf-X *¥X^5BSSffliS#yX f 0@© Gws©#%#iE u A ESC&fc -3 fcISffS A,lc#m&#L4 Xo$ir|-#14, SiS^SHECirSr5,tm^$ 4LT^5**, ‘1b*¥#® ±kVT, /n “-Vtwytfa.-X(PC-9821 Xa 10/C 12) A#%©«^R^MTlKia©@aA%¥+eT$5„ 50H @ » 5 & #b##t y X -FACOM M1800/20, OS : MSP-EX Clllfi 6©fix ©i6i^gtlh0$©^#^W^C-nE (com ffl v/co $m%i4%sg###ms5c©mm&§i4T^m@ bined) ©mmEm^5^%T&5 h#m@^5o tL/cT k ztfmLffl{%&&imw$tL£to Fig. 9 1C 14, (GWS ®/J#% AreaNo. 20) K # # 3t m out , m^6©Emmm#m,556©%## E2Z 5. ©%"##tf;0SE©F,3 lll?4 5&0K41/ 1) Has-: m#=isg©m#mi?#, am#i=MX5 yydfyxA, 8¥)mm## (mg). 1 < £416 ©Ho©###!^—X © (combined) ©#X 2) - gfrgpjj-, 5m$) :-EEgtff-r -X ©#M(i k Clo* <, JEBl^ERfiTffii Fw=0.30 ©^©IIUH tSSSliQ?®, @a$)lSS#X|g, S 89 ■§■ (1995) j ih]j!mmE©m%?mi#&^LT^5o 0ci4 mi&mm 3) 11 mm~, 75mm: ib±¥#©EEmm-f-x ©$u io4©mm±mm&_Gws c so* < em?a&ci&L& i ffl kSSQ^SI, s 90 # (1995). 4) ^m, mwm- - s#©e$eh -t-x ©#%# LT5rUTV>5. 0K44U4, =o©%##if-T-X£# ; #178# (1995). ' , , j fS,Cx'®btitzmmmm-3< gws © 5) Roll, H. U.:-Height, length and steepness) of i seawaves in the North Atlantic and dimensions 5L't©#A6, #%©@E^¥+#e& % zowm of: sea waves as functions of wind force (English j Translation) , Technical and Research Bulltin, 14, (AreaNo. 42) tcat45ll#6, 556, E ; No.l~19, SNAME (1958). a6©mm#m-8#©mmif-f%©^-/-^0^ £ t 6) Walden, H.: Die Eigenschafteri der Meerswellen l£&5. L^L»»?6, GWS ©C©4##(Area No. 42) | irh Nordatlantischen Ozean, Deutscher Wetter- ©mmf-fgki4=o©Emmm-f-r-^ %#^C4:##© 1 - -tiienst Seewetteramt,- Einzerveroffentlichungen, g> ©%? u r^com- 65 Nr. 41, Hamburg (1964). 15) E. J. Gumbel: Statistics of Extremes ®(lSnrf^), 7) : &&*©%© Deck Wetness Kit 5 (E^EE),jAJI|ffii£ (1963). mmm, ages), 16) I. M. Yuille: Longitudinal strength of ships, 8) British Maritime Technology (Primary contribu Trans. RINA, Vol. 105 (1963). tors ; Hogben, N., Dacunha, L. F. and Olliver, G. 17) N. NordenstrOm : Calculations of wave-induced F.) : Global wave statistics, Unwin Brothers motions and loads, Progress Report No. 4, A Pilot Limited, London (1986). Study with the Computer Program NV 403, Det 9) Yamanouchi, Y. and Ogawa, A.: Statistical dia Norske Veritas Report No. 66-11-S (1966). gram on the winds and waves on the North 18) @B#c- : > h SS(E©E|6j Pacific Ocean, B!im2# COUT, # 123# (1968). (1970) o 19) 01 x. Hi, J. Fukuda and A. Shinkai: Predicting the io) t r&om-mm longitudinal stress induced on a large oil tanker (1964^-1973 m, m 3 # in sea waves, International Shipbuilding Prog (1980)„ ress, Vol. 25, No. 291 (1978). id mmm, sb^, = ita (1974 20) M. Takaki and Y. Takaishi: Development of ^-1988 # , ^mi4# expression for estimating bow freeboard and (1992)„ assesment of the 1966 Load Line Convention, 12) H. de Sury, M. Olagnon, P. Charriez and P. Journal of the Society of Naval Architects of Lasnier: Contribution of satellite data to Meteo Japan, Vol. 174 (1993). -Oceanic Site characterization : A case study, 2D amo, a a#####©:# Proceedings of the Fourth (1994) International Offshore and Polar Engineering Conference, #,#132# (1972). Osaka, Japan April 10-15 (1994). 22) ±m.~ : @55)1 13) G. A. Athanassoulis, P. B. Vranas and T. H. 5S#*fg, #89# (1995). Soukissian : A new model for long-term stochas 23) mwm~, hes : ameBamamH##©## tic analysis and prediction-Part 1: Theoretical ®©MftE^T,@SEllS#*?g,#91# (1996). background, Journal of Ship Research, Vol. 36, 24) M. St. Denis and W.J. Pierson Jr.: On the No. 1 (1992). motions of ships in confused seas, Trans. 14) N. H. Jasper : Statistical distribution patterns of SNAME, Vol. 61 (1953). ocean waves and of wave-induced ship stresses 25) wm, mm: ^ o ^ and motions, with engineering applications, T,@55)im#^#,#47# (1973). Trans. SNAME, Vol. 64 (1956). •k Q-9 6-01-^44 67 1-8 IEi o' 7G On Statistical Properties of Wave Amplitudes in Stormy Sea ----- Effect of Short-crestedness ----- by Hirofumi Yoshimoto, Member Summary A method to estimate the statistical properties of non-linear short-crested irregular waves without any limitation regarding the directional spreading or the spectral band width is presented which is based on the secondary interaction theory of surface waves. It is shown that the statistical problem can be reduced to that of finding the eigenvalues and the eigenvectors of two real symmetric matrices and the probability density functions of surface elevation can be obtained using the so-called Saddle Points Method. Numerical investigations regarding the effect of shortcrestedness on the statistics of wave amplitudes are performed. And the method is also used to analyze full-scale data measured in stormy sea states and is shown to be a powerful tool for the estimation of the statistical properties of the directional sea. 6, ©f L,. EEti¥J§ i. m m Z:Xti #;©#%?%%& & n a mm fct, D±U3 k^TLbtiZhOXrh ^»c, D, LT@@©@±#kV < %'< Longuet-Higgins 6©^^Tlf, %##©*(& Longuet- Zk-rzumz, Higgins 11 EJ;-p X^jbtltz„ Longuet-Higgins tt, iBSC© ©%±E$K^L<»D, Rice ©mm" C C 5 LfcP9E.SK: S 5>C, Cartwright and #L, S#i6SS26IS¥SI!lE (Long-crested Longuet-Higgins 3’ it, @@©@@^#©E$%aMR© Irregular Waves) t LT%f;HbL, $#2£© 2 ^C©## •—e©#, %e,©a*C3HT$<© B66ESC$tDXnfc¥Sl&:S:5rV7£6>„ ^LT, Cilt m&Tte, #4©figa-m©A# gzSiS-egi-zffl §Il/czSSt-? KlSfflL, *%%#©%$ -mm c t ##%© tbe>ft,z>kz.zk&-or^?>o bp*., fmcmwfcm# L*>L, Longuet-Higgins 6©^jSH, ##%©### K©tfA/kms©#%Tma@fb%m#& t ©mmr& 3. mn©J:5 K9zFg©iS^T*EiffldiL5iS#z6ti, Sz6 if, t 5 ttMkimmam-cit, m M& (Long-crestedWaves) < if£C$l$*5)s < "PUiLfc “Ez&JM (Short-crested,Waves) ” ZLlittSS g $ *Siri^ e> ©pga-#*#% b-6-5 c k (##%©:% fl-ffcffi Cj:^r^U5b©k®$?StLTt>5o fc-C, E$sa ¥i£ 8 ^ 5 M 15, 16 0 t*© ± a s * 70 - B39g&#&m38& mi79# @*>6, ^ftEjitf caseTl T,(4, % Table 1 Simulation condition of surface elevation c 8Ttt, m 2 #-C#6&4SK#F#HUK©t ft> kE, s. case-1 case-2 3.1 , . (, wave-1 wave-2 wave-1 wave-2 (16) 5%&, %©j:9»#EE%»So ' h (m) 300 300 300 ' 300 0.6823 1 (Oj. (rad. /sec) 0.7235 0.6823 0.7235 ?=Re2s;((?;+z>,) su ' 0 0 0 0 +ReSuSs/S/{fftt’(?/+!r/)(?/+ir/)+fli‘,(?/+ir/)(?;-ir;)) 5, (deg.) 0 0 180 0 2 Au (m) 5.0 5.0 ! 5.0 5.0 case -1. case -1 - 0, 20 40 - 60 " 80 0 200 400 600 800 time (sec.) x(m) case - 2- case - 2 , 800 time (sec.) (a) time domain 1 ■ (b) • space domain Fig. 3 Simulation of surface elevations with 2nd order effect.----- sum frequency component. ----- difference frequency component...... results with total 2nd order effect 71 Pi'g © jf&frt(Pi‘qh kSEk-U Xj=(P,‘q)j 0‘=1, •■■. L) XMP^j-l 0"=L+1,-,2L) ku (i9)^©ia®6fijfflrntf,em(2i)^a jg ©2% sa-est-e-So ?=Jj&=Ji&X2+W CCT A=(Pi's)J-, A,=(Ai)j, 7=1, —,L A=0, A,=(A2)j, y=L+l, —, 2L (22) £C E, (A,),- A, © j mSOMnWm^kb-toKac and Siegert 14’ E jcA.B(22)aT&$A.A C ©#### M(d) b, M(* )=&jL-iW*~ vfSSir (23) k*5 o (23)a© FouriergmtfM ikCi t), £©#$ B#&& = k*^C@ 3. A0 $i d n (deg.) P(0=j^J2e-i3:M(d)dd (24) Fig. 4 Behavior of bi-directional quadratic transfer 3,2 KM& function having, eii=0.6823(rad/sce),- S[W/]=S[w;]=y f{K,z)=- ^+z{-ylog(l-^) + 4(fiJ,)} S[»/r/]=0, £[?;?/]=0, £[wv]=0 (/¥=/) (19) (25) Langley' 2’ E* 6 w, (18)^©^ Sr k V % $#< iltKJ;-3t$J!)So Naess and Jhonsen'f It stee pest descent Rgg*&m$K#Rp-CHS E b^MmU frbmS.LXisy, Ztuzm-^X, steepest descent EStoC, ^©EieS^S fir5 EktE4-oT (24) S tiffi^toCWE-f- 5 Eb A?TS' ■So - *>(e)=R e^r^dv 1,1 ■' (27) 5rj=, ^6g©ltfft4, :(26)Sl4-S-S-ttS»d £#‘\ So * 1 I ^■,M^ , , m±5B^7£#SK3So*S, temm. RKt4, %AKx-t^ h )og#^.s& g*;&$o EE-C14, ##©7k»lc^l=l^%M|R**a&R tS#L»vi6©kUT, :' frequency S(f,8)=S(J)-G(8) ;; (28) i ; ;e s(/) t4ki&isrx'^ >;v, G(6) ti^lRl^iMIlScTS O, SiSiSrx^^ h;W; b'T% © Modefied-JONSWAP X K^181 , ' : ' '• ' : ,t Sr 200 :sW=o:l73f%)^^g")z4-W ' EEV- ■-'■■: A , E\: - F=1.323-0.414r+0.105r2-0.015r3+0.001rV : <7=0.07-/<:/p, <7=0.09-/>/p- v ,: , (29) ' GO) E E K, 7f„3 14##W, fP 1417 14 peak, enhancement parameter, s 142j[Sj$ltfv?7^ — & (4 ±:mSrr&So Fig. 5 h ;p k (29)l&TH m=llm, fp=0.053/fe, 7=1.0, (30)SCfc'V^T 3=200/75, 10 k bfcgST&So ##&?E 3=75, 10 kt^#14, £B3E4 5 vteVRtf M^©^696® 5> k"SfVtt>5o ‘: ; Fig: 614, Fig. 5 ©Hi&^X^A b ;v k direction bkc, *m?om ku*F#©*@m#©m$#aWM ig. 5' Frequency wave spectra and directional "func ^S»4cE5ITS 3„ S i K, Fig. 7 kt Fig: 6 @*tiEl)©' tion for numerical simulation , B^sisWB^b, Ui#©#(@©@±# k##J©#m©@ £[S„] (Appendix-A #i® =&$&%E • Fig. 6 4 5,2 %©####%% 5 A4tfeES14, Gauss $T$.5,7ic@#g#©W@m Gauss rith sum : with sum -Higgins ^ total with sum ; with sum \/<7 10000 Fig. 6 Probability density function of surface elevation for input directional wave spectra, ’with sum’: Fig. 7 Expected values of the largest wave amplitudes results when the difference frequency compo of crest and the smallest wave amplitudes of nents are omitted, ’total ’: results with total 2nd trough in N observations, 'with sum’: results order effect when the difference frequency components are omitted, ’total ’: results with total 2nd order - effect • £5 UfcfllRlB, 2 tipZoBIl*,, Fig. 4 KEL*: 2 fczE&msMtffitz 20 #no&& 48 J: 5 K, UfaftWt&tDjvbK-frfrhb-f, SL"0)-5>„ £*l6>©t—^©cfrfr-S 2 v&Lft m=o°) iS^F©r-^i ZMfe Vfm£frO tCo •fSo L^L, < SrSKOftT, n—^ 4.1 ffi&T—i? GiKmfrfa#a#0=F#*%TL, toe*, Fig. 6, 7C^tJ: 572»K3S©z$ii5ESfflv^o mmmmmAB, am# 5o 3 km 5. # # m‘sec/deg r80202 4-0©##% $ k 6wm© J: ^ K»3. • is#i6©^T;vk #&Wf &##&© 2 ^@#SBte£^t8 LAigir©$iW ififlMSLfeo • e©?W&Kj: 9 , ^IqlS-gfctt^SEffl^H-jaK#^. 3 02Hz 0.15 0.1 Bmz&MLAZgm, #c©2%©^e,, m&mm 005 frequency &©©, A*kLTK S®FRilJz&©f£l=r k S t$ k*E6 »V^0 ! m’sec/deg • %B^-CE®S iiAjSSUr-;? ttk K$e&%»SL' 150r, i r81214 Tkmm, 3*&k L-C#%T&3C k ^ * 3' rmmm#©#am®©%&©®mm%j ©- Sk LT, t > f - & 8 C &, B $####, 8 a k (D&mmz t vxmmz titzmm^m^m mm rposEinoNj #Kj=3 mmmmmxm&z titz t© ?$3Ck%^Ei-3o ‘ 1 ■ : ■ - Fig. 10 Input directional wave spectra 75 Table 2 Characteristic values for the analyzed data # # SC it* 1) Longuet-Higgins, M. S: On the statistical distri- r80202 r81214 • . butions of the heights of sea waves, Journal of data lenght(h) 13.5 13.5 Marine Research, Vol. 11, No., pp. 245-265, 1952 2) Rice, S, O.: Mathematical analysis .of random number of ^ A/ 5362 5513 noise, Bell System Technical Journal, Vol. 23, 24 (1994, 1995) 3.08 2.17 3) Cartwright, D.E. and M.S. Longuet-Higgins: *1: standard deviation of surface elevation The statistical distribution of the maxima of a random function, Proc. Royal. Soc. London. Ser. A., Vol. 237, pp. 212-232, 1956 4) tirzRE-, 38808*: AX^SfliJ*z&fflScSto£fEf, gSEiMSSiSB 195#, pp. 1-15, 1984 5) : mmffimwM'&imst j? e, 1984 i . 6) S7C1SS:: AzSmozSSOgcIf-toSeccvi-c, f m 13 '> y df i/* A, pp. 425-432, 1995 7) Hamada, T.: The secondary interactions of sur iff face waves, Report of the Port and Harbour Technical Research Institute, Report No. 10, pp. 1 -28, 1965 8) ttii: 2 ascat? i ® 32 pp. 154-158, 1985 measured 9) m$m, 1W-&, @#JE, : Longuet-Higgins b L 6 with directional effect mmfc^cDMmkfc-o^x, 39 #, pp. 171-175, 1992 without directional effect 10) Sekimoto, T.: Nonlinear Effect on the Estima tion of Directional Wave Spectrum, Wave Gener ation^ pp. 44-59, Yokohama, Japan, 25 Sept, 100 1000 10000 N 1995 11) SacBSi: SEtaStkEiSTMS, 1976 12) Langley, R. S: A statistical analysis of non-lin ear random waves, Ocean Engineering, Vol. 14, No. 5, pp. 389-407, 1987 13) : Bllgctre, 3D Aft, 1984 14) Kac, M. and Siegert, A. J. F: On the theory of noise in radio receivers with square law detector, Journal of Applied Physics, Vol. 18, pp. 383-397, 1947 LU 15) Kato, S and T. Kinoshita : Nonlinear response of moored floating offshore structures in random waves and its stochastic analysis, S27SS4#, pp. 2-143, 1990 16) Naess, A. and Jhonsen, J. M.: An effect numeri measured cal method for calculating the statistical distribu Longuet-Higgins tion of combined first-order and wave drift with directional effect response, Proc. of OMAE, Vol. 2, pp. 59-70, 1991 without directional effect 17) mmtl, £WZ, /J'S* : Fortran 77 K ± £EV7 JtLSfflJK#, 1990 18) Yoshimoto, H.: Characteristics of directional 100 1000 10000 wave spectra measured at Japan sea, Proc. of N OMAE, Vol. 1-A, pp. 35-42, 1992 Fig. 11 Expected values and mean values of the largest, 19 ) e© wave amplitude of crest in N observation 1 gEBoHS, M13#, 76 mi79# 1992 f^,N)=Np P(.m-F^)]N-' (A-l) . 20) W551S5:, : #®SW#S)S •e^xbthZo z :e, MO t©3 #R#%©&^l%X^ 1 ® I I i- "I 1 I *t . t ni :V 1 ' -. ,if 77 1-9 Model Experiments of Ship Capsize in Astern Seas ----- Second Report ----- by Masami Hamamoto*, Member Takashi Enomoto*, Member Wataru Sera**, Student Member James P. Panjaitan**, Student Member Hiroto Ito**, Student Member Yoshifumi Takaishi***, Member' Makoto Kan****, Member Tomihiro Haraguchi****, Member Toshifumi Fujiwara****, Member Summary Capsizing experiments were carried out for both models of container ship and purse seiner running in regular and irregular astern seas. Dangerous situations in ship speed and heading angle of ship to waves are experimentally and analytically investigated for the phenomena which are the so-called harmonic and parametric resonance, pure loss of stability, surf-riding and broaching-to. An analytical approach was attempted to investigate profoundly the dynamics of ship motions and capsizing in severe astern seas. The results of the analytical, approach by making use of computer program are in a good agreement with experiments. ' The main problems here are how to describe and to 1. Introduction solve the equations of motion involved in such phenom The safety against capsizing are concerned with the ena because the ship motion leading to capsizing are stability criteria when designing a ship, the operation of very complicated in the non-linear coupling motion of ship in severe seas and the probability to come across six-degrees of freedom. For this purpose, it will be dangerous situation leading to capsize. Then, the occur reasonable to make the assumption that ’a complete rence of capsizing may be affected by a wide variety of description of ship motion is not attainable, but an causes. The hydrostatic righting arm curve for a acceptable simplification of the problem is useful to smooth water seems to be still the fundamental base to understand a typical feature of phenomena. There are judge the safety against capsize. Even though such two important considerations to be taken into account traditional methods have apparently been successful in for this problem. The first is the fiuctuatioirof righting ensuring adequate stability of conventional ships, it is arm-in severe-seas which affects very sensitively on a expected to establish a new basis to understanding the amplitudes of roll. The second is the encounter fre dynamics of dangerous situations associated with the quency of the ship to waves which becomes much smal operation of ships in severe seas. It is furthermore ler than the natural frequency in heave and pitcti, so expected to relate the dynamics of ship capsize to the that these motions can be approximated to just tracing geometrical characteristics at the design stage and their static equilibria. Accordingly, this approximation operational characteristics at sea. Several dangerous enables us the heel, sinkage,"and trim relating to the situations such as harmonic resonance, parametric reso righting arm to be determined based on their static nance, pure loss of stability, surf-riding and broaching- balance as the ship is -travelling- in--waves. By to have already been pointed out as mentioned in the simplification the righting arm curves for the relative first report 5’. These phenomena exist in the heading position of ship to a wave was estimated and the equa angle from astern to beam seas and in the low encoun tion of rolling" motion of ship running with-constant ter frequency range with severe motion both of ship and speed in severe astern -seas -was described,-so that it waves. becomes possible to obtain a typical feature of har monic and parametric resonance from the numerical * Osaka University. solutions of equation 91 The pure loss of stability seems ** Graduate School, Osaka University. to be a limiting case to occur at the ship speed close to *** Nihon University the waye phase velocity -in waves where the ship **** Ship Research Institute remains almost stationary on the crest for a sufficient Received 10th Jan. 1996 time leading to capsizing. The surf-riding phenomena Read at the Spring meeting 15,16th May 1996 is one of the dangerous situation leading to the broach 78 Journal of The Society of Naval Architects of Japan. Vol. 179 ing-to. The ship is accelerated by the wave excitation another one is an 1/15 scale model of typical 135 GT in the forward direction and travels on the down slope purse seiner which was designed with the current of a wave. If the ship is unstable to course-keeping i% Japanese regulation of hshing vessels and is operating this situation; the ship is forced to swing through almost' f in the East China Sea., The metacentric heights were 90 degrees from a following to beam seas and unable to , adjusted-to satisfy the minimum requirement according regain it original course. to the IMO Resolution A. 167 for the container ship and In order to investigate these dangerous situations, IMO Resolution A. 685 with 19 m/s of wind velocity for free running model experiments of capsize in astern the purse seiner, respectively. Their principal dimen seas have been conducted ,at ,the.,seakeeping and sions-are presented in Table 1 andjTable 2. Figure 1 manoeuvring basin of the National Research Institute and Fig. 2 show the righting arm curves in still water of Fisheries Engineering in 1994 s’ and the square basin of the Ship ‘Research Institute in 1995." ' This' second 'A . paper mainly ,deals with the model experiment conduct ed in 1995. X=0 [deg.f 2. Model Experiments A/L=1.5 Model experiments were carried out in the several combinations of heading angle of model to, waves and the speed of,model in regular and irregular seas. (The , models run at the speeds corresponding to each Froude number of 0.1, 0.2, 0.25, 0.3 and 0.4 for the container 1 ship model and 0.2; 0.25, 0.3, 0.4 and 0.5 for the purse " seiner model in still water, respectively. Both models are controlled with the auto-pilot to keep the heading angle of the model to the waves equal to 0,15,30 and 45 degrees. ; The metacentric heights of each model corre 50 [deg.] spond to 0.15 m and 0.23 m in the full scale container ship and 0.75m in the full scale purse seiner. , , Model particulars |.fI, , . Two models were used for the,experiments. One is an 1/60 scale model of a 15 000 GT container ship ,designed by the Cooperative Association of Japan , Shipbuilders, Fig.l Body plan and GZ curves of container ship -I i : ■ • IK' ' ... . : : V I ■ ' i Jf'l Table 1 Principal dimensions of container ship f i l .1,1 i I I I 1 I . I r , ' 1 , 1 1 , I ‘ 1 1 — r—i GZ Items Ship Model [m] ;V GM=0.75 [m] Length , L(m) , 150.0 2.5 V =H FHonl Breadth. B(m) 27,2; 0.453, A/L—1.5 tro lg'ty i Depth i D(m) . . 13,5 0.225, H/A=1/' 5 r.j t ' , I , i Draft j d/( m) 8.50 . > 0.142 , ’ r ^ "X 1 da(m) 8.50 0.142 T-s; Block Coef. c». ' 0.667 ’ 0.667 still Model Scale T 1/60 J, \ 0 1 ,, ..Table.2 -Principal dimensions of purse,seiner , 0 Items Ship Model st 20 '40 deg.] ' I ' Length - L(m) 34.5,, . 2.3 Breadth ,B(m), 7.6„, 0.507 Depth D(m) i 3.07 0.205 Draft ; d/(m) 2.50 0.167 da(m) 2.80 ! 10.187 Block" Coef.1 Cb ■' 0:605 '0.605 Model Scale —'' 1/15 .Fig..2 Body"plan and GZ curves of purse seiner Model Experiments of Ship Capsize in Astern Seas 79 and in waves where the wave crest or trough comes purse seiner is the same as that of Beaufort No. 12 for amidships of the container ship and purse seiner, respec container ship in the model scale. The generated wave tively, The models were propelled with D. C. motor profiles were measured during 200 sec. in model scale. whose power was supplied by batteries on board and In these Figures, it is shown that the measured spectrum steered by auto-pilot. The power of the motor has been is slightly higher than the specified one at the peak increased from the model experiments in 1994 frequency. In addition, both models were also run in mentioned in the first report, to achieve higher speed to regular waves of wave height to length ratio 7f/A=l/25 investigate the surf-riding and broaching-to phenom and wave to ship length ratio A/L=1.5 for the container ena. Roll, pitch and yaw angles and their angular ship, and H/A=l/15,1/17.25, A/L=1.5 for the purse velocities were detected by fiber optical gyroscope. seiner. Accelerations of surge, heave and sway were measured Experimental Results by accelerometers. These measured signals were recor A number of runs were performed.with various ship ded on board computer in a digital form. To store the equipment, additional watertight hatches were fitted on Table 3 Wave conditions of the experiments the upper deck. Figure 3 shows the outline of the radio (ship scale) control and measuring system. Wave Characteristics purse seiner container ship In the experiments, regular and irregular waves were H(m)=3.45 H(m)=9.0 used as shown in Table 3. For generating irregular regular T(sec)=5.77 T(sec)=11.9 waves, the ITTC spectrum (1978) was used as follows waves Vb=13 VL=13 ' H(m)=3.00 where a> is the frequency of component waves, Hm the T(sec)=5.77 significant wave height and Tm the mean wave period. X/L=1.5 The significant wave height and mean wave period Beaufort No.6 Beaufort No. 12 were of Beaufort No. 6 and No. 7 for the purse seiner and No. 12 for the container ship, respectively as same irregular Hm(m)=3.44 Hia(m)=13.7 as the experiments in 1994. Figure 4 and Fig. 5 stand for waves Toi(sec)=5.72 Toi(sec)=11.4 the wave spectrum of Beaufort No. 6 and No. 7 in Beaufort No.7 comparison with those of the waves generated by the Hm(m)=4.02 wave maker. The wave spectrum of Beaufort No. 6 for Toi(sec)=6.64 On board equipments Fig. 3 Outline of radio control system • % n- 80 Journal of The Society of Naval Architects of Japan. Vol. 179 S(cufsec) - 1 10 r Pitch angle [deg.] [sec.] :----- SPECIFIED o exp. ■' -.Roll angle ,[deg.], [sec.] LONG CRESTED I\ A I\ f IRREGULAR-WAVE sov "V 60 (MODEL SCALE) ", ih L • Yaw angle [deg.] ' 1 1 [sec.] 30 10 15 ...... " ■ ■ ■ ’* - ’ 1 , i i.1' i ' i' ■ , til (rad/sec) r Rudder angle , [deg.] . , [sec.] Fig. 4- Wave-spectrum for -container- and-purse-seiner ~VA Mfl . i : models'------1^.' ------;------ , Fig. 6 Time histories of parametric , resonance of container model , • ■ ,, - 1 (Fm=0,2, x =30°; GM=0.15 m.B.No. 12) 10 r Pitch angle [deg.] [sec.] o,aA^aA^— + 60 V % : 60 Roll angle [deg.] [sec.] ", 60 V ------10" ------15 -60 70 r Yaw angle [deg.]Ldeg, oi (rad/sec). [sec.] 30, ■+■------d Fig. 5 1 Wave spectrum-for-purse seiner model ------60 -10 40 r Rudder angle [deg.] speed and heading "angle | in long crested irregular^ [sec.] waves. ’ The models started to meet a higher wave 4——d 60 group. If was observed-that "severe motions, unstable -401 ; _ behaviors and capsizing of the models almost happened when the-models encountered aj wave group which Fig. 7 - Time histories of coupling motion of consists of several especially-steep -waves-as -like as - rolling-yawing of purse seiner model regular waves. Theprobability: of capsizing then seems ~ (Fw=0.5,2=30°, GM=0.75 m, B. No. 7) to relate to the probability of the model encountering a wave group having the necessary characteristics which may cause capsizing* ’. - \ r Figure 8 -presents the time histories of surf-riding phe A remarkable difference was measured between the nomena. The results of capsized and surf-riding runs two models on the occurrence of parametric resonance. are presented in Fig. 9 -arid Fig. 10 compared with the During the experiments,- it-was observed that the con dangerous zones indicated by the IMO guidance 1995"". tainer ship model experienced parametric resonance at 3. Equations of-Motion for Numerical the wave encounter period to natural rolling ^period ratio TelTp—\lt as shown in Fig. 6, while i the purse Simulation seiner model did not experience parametric resonance This.section attempts an analytical approach to non at any wave encounter period. The purse seiner model - ^linear dynamics of ship motions and capsizing in travelled with the coupled motions of severe rolling and severe astern seas. For this approach, the horizontal yawing like a snaking walk as presented in Fig. 7. body axes coordinate system as shown in Fig. 11 is used Model Experiments of Ship Capsize in Astern Seas 81 10 Pitch angle [deg.] °, -lo go -10 60 r Roll angle [deg.] °. A- ir 20 -60 40 r Yaw angle [deg.] 0, W 20 -401 40 r Rudder angle [deg.] ", —L-1 2b -40 Fig. 8 Time histories of surf-riding of purse seiner model in regular waves (Fn=0.4, 2=0°, GM=0.75 m, H/A=1/17.25) v=n° '7? Fig. 11 Coordinate System for describing equations of motion in a reasonable combination of manoeuvering and seakeeping motions. This coordinate system is defined to take rotation about the Y axis, and no ( rotations about the y' and x' axes, but a ship can make a rotation about y’ and x' axes. The equations of motion with respect to this coordinate system are described in the following six-degrees of Not capsized case freedom, 1 - for translational motions and forces ■ > Fig. 9 Capsized and not capsized runs plotted with (,m+mx)U—{m+mB)Vii’=X' dangerous zone of IMO guidance (;m-\-m„)V+{m+mx)U4>=Y' (2) 82 Journal of The Society of Naval Architects of Japan, Vol. 179 (m+mz) W = mg +Z'for rotational, motions and moments ’ : (Ixx+Jxx) ] (3) the equations of motion for three-degrees of free (10) 1 X F(x)A(x)cos kUo+x cos x)dx dom are given by, . - - (/zx+/zx)f=/r o -i , Bo= k«(^)c°s 0+ye(a:)sin —pgsin. x JlIzb (x )cos where the coefficients An, Bn calculated as moment (mx—my')UV stand for linearized An='mQi^JL [%WcoS ^+%Wsin (6] hydrodynamic sway force and yaw moment due to sway velocity, yaw rate and rudder angle. XA(z)Fn(a:)cos^-^(5)+x cos z)+&j, S) hydrodynamic surge force correlating to kRoll angle [deg.] forward, sway velocities, yaw rate, and rudder angle, Xv>(x), Yu,{x) and Nw(x) denotes linearized wave excit ing surge force, sway force and yaw moment, respec tively, Y(V, (6, S) and N(V, Experiment .=. Simulation Experiment ° Simulation . Pitch angle [deg.] 1 10 r Pitch angle [deg.] % /ft ' '' [sec.] [sec.] ^ 20 60 -Roll angle . [deg.] , ... -Roll angle [deg.] ' 1 . [sec.] ... 0, 20 -60 , Fig. 13 Harmonic resonance of container model in Fig. 14 Harmonic resonance of purse seiner model in i , regular waves • - v 1 - regular waves , (Fh =0.4, z=30°, GM—0.15 m, H/A=l/25) n - |" (Fn=0.4,2=45°, GM=0.75 m, H/2=l/15) ' 11 - experimental results. In these examples, , the severe ,. ' Experiment , f> , Simulation rolling occurred at the wave encounter period nearly 10 Pitch angle [deg.] equal to the natural tolling period, and the models also [sec.] capsized when the wave crest overtook from astern. 0 ArV> 2b Harmonic resonance for both models running in irregu lar seas do not occurs because the wave encounter “10*- i i - i, . i i , ■, i - i i ii hi i period in random. 60 r Roll angle [deg,] Parametric resonance [sec.] The third example is the parametric resonance of 2b container ship model running with heading angle 15 degrees and Froude number 0.2 in regular waves of the wave height to length ratio H//1=1/25. The pitch arid Fig. 15 Parametric resonance of container model in roll responses are presented in Fig. 15 compared with regular waves , ^e experimental results at the initial roll angle equal to ' (Fm=0.2, 2=15°, GM=0.15 m, H/A=l/25) zero. In this example the severe rolling occurred at Experiment twice the wave encounter period and the roll amplitude 10 Pitch angle [deg.] grew up rapidly 11,21 The first roll to port side with [sec.] amplitude about 10 degrees, and' the last; roll to star board side about 50 degrees. Eventually, ttie model II 20 i (i 1 j ' 1 • 'i ;■ ) . , , > l . 1 - "i "W 1 -10 l capsizes to port side. _ The fourth example is the case of container model 60 r Roll angle [deg.] running in irregular following seas of significant wave height H i/3=13.7 m, mean wave period Tin=11.4 sec. U “l” and Froude number 0.1. The pitch and roll angles are -60L i i ■ - ...... presented in Fig. 16 in comparison between experimen- . 11 i ii. . 'iii.'1.. tal and computed results. It is noted that pitch angle is 10 Pitch angle [deg.] Simulation different from simulation but roll amplitude is almost 0. the same. It is difficult for the simulation to identify the 20 irregular- wave profile used for experiment. In this ~10 example, the severe.Tolling occurs at the wave encounter to the natural rolling period ratio nearly equal to 1/2, 1 6drR°H angl e [deg.] and the model capsizes when the wave crest over takes from astern.. Parametric Tesonance- for purse" seiner running in regular and irregular waves did not occur. Shortly speaking, as the GZ curve of the container ship has a .Fig! 16 Parametric resonance of container model in hardening spring nature, with ah even small irregular waves metacentric height which satisfies the stability criteria , (Fm=0.1, x —0°, GM=0.i5 m, B. No. 12) at the very limit, especially the indices for area of the GZ curve. As a result, the natural roll period can be so a softening spring nature, her metacentric height should significantly large as to induce parametric resonance. be,large to satisfy the IMO criteria A. 685.. As a result, On the contrary, as the GZ curve of the purse seiner has the natural roll period is too small to induce parametric Model Experiments of Ship Capsize in Astern Seas 85 resonance in astern seas. wave velocity Pure loss of stability The fifth example is the case of pure loss of stability for purse seiner model running in irregular sea of significant wave height #1,3=0.272 m, mean wave period 7oi= 1.60 sec., heading angle 30 degrees and Froude number 0.4. The pitch and roll angles are critical ship speed presented in Fig. 17 compared with the experimental results. Because of the high speed, the model capsizes O surf-ridden_ when the wave crest moves into amidships position 3’. (not capsized) Surf-riding A not surf-ridden The critical speed Identic for surf-riding of a ship can (capsized)-" be estimated from the equation proposed by Kan3’ as - (not capsized) follows UamcoBX=c[l-JF‘™X] (23) container ship (11/1=1/25) where Fa is amplitude of wave exciting surge force described by wave velocity ' xsin^^sh#^- (24) critical ship speed (H/ A. = l/17. 25) " and L, B, d, Cp and C„ are the length, breadth, draft, prismatic and midship coefficient of the ship. The critical speed estimated from Eq. (23) are shown in Fig. 18 in comparison with the experiment for the case of the following seas. The surf-riding for both • surf-ridden models occur in higher ship speed than the critical one. (capsized) The critical speed are shown in Figure 19 in comparison with the experiments for the case of heading angle x (not capsized) from 0 to 60 degrees. In this figure, the sign ▲, in the A not surf ridden experimental results meaning “not surf-riding ” but (not capsized) capsizing for the purse seiner running at Fn=0.4 with purse.seiner 10 r Pitch angle [deg.] Experiment [sec.] 1^ Fig. 18 Critical ship speed versus, wave to ship length (i ratio at %=0° -101 60 r Roll angle [deg.] heading angle nearly equal to 15 degrees with wave steepness l/17i 25. This is because of the fact that capsizing occurred just after the model was started before entering the steady surf-riding motion. The critical speed predicted by Eq. (23) seems to be reason 10 Pitch angle [deg.] Simulation able in comparison with most of experimental results. [sec.] Broaching-to , ■ , It would be possible to simulate the broaching-to without capsizing but with the total loss of directional _10 stability and control by making use of Eq. (21) which 60rRoll, angle [deg.] describes the coupled motions of surge, sway* and yaw. [sec.] °. The linear hydrodynamic derivatives for manoeuvering It 10 20 motion in Eq. (21) were obtained from captive model -60 \ tests and the linear wave exciting surge force, sway force, and yaw moment were predicted by making use Fig. 17 Pure loss of stability of purse seiner model in of a strip method 11’. The both models are directionally irregular waves stable in still water. I (Fw=0.4, %=30°, GM=0.75 m, B. No. 7) ' A number of simulations with respect to the surge and 86 Journal of The Society of Naval Architects of Japan, Vol. 179 wave velocity/cos x • exp. (capsized) Fn o exp. (not capsized) * critical ship speed MS"''"""""""""'* 0.2 O surf-ridden (not capsized) Periodic stable ▲not surf-ridden (capsized) 0.0, A riot surf-ridden (not capsized) 0 10 20 30 40 50 %[deg.] 'Container ship . (h/ a=i/25) Fig. 20 Broaching-to zone of container model • exp. (capsized) I .1 . o exp. (not capsized) wave velocity/cos x Periodic stable • (H/ A = 1 /17. 25) • surf-ridden (capsized) O surf-ridden (not capsized) | 0 10 20 30 40 50 ▲ not surf-ridden (capsized) ! %[deg.] A not surf-ridden (not capsized) Fig. 21 Broaching-to zone of purse seiner model the yaw angle is fluctuating around marginal . stable state. Fig. 21 indicates the periodic stable, non-periodic Fig. 19 * Critical ship'speed versus heading angle of ship stable and marginal stable ranges on the heading angle to wave at A/L=1.5 X versus Froude number Fn. , 5. Concluding Remarks sway velocities, and yaw angle can be obtained in the An analytical and experimental study of ship motions specified combinations of Froude number and the head and capsizing has been conducted for the two models of ing angle of ship to , waves. Simulation results for container ship and purse seiner running in severe astern container ship are divided into two categories of mode. seas. The main conclusions are summarized as follows The1 first1 one is the mode that the yaw angle is (1) The capsizing due to harmonic resonance oc exponentially diverging apart from the prescribed curred in higher Froude number than 0.3 for both course. The second one is the mode that yaw angle is models in regular waves. . fluctuating around the prescribed course with the very (2 ) The capsizing due to parametric resonance long, period. Fig. 20 indicates the periodic stable and occurred when the container model is running with unstable ranges for container ship on the heading angle Froude number lower than 0.25 while it did not occur in andithe ship speed. , . , • ’ any Froude number of purse seiner model. i On the other hand; simulation results for purse seiner (3) The capsizing due to pure loss of stability model were divided into three modes. The first mode is occurred in a small heading angle at high Froude num noted when the yawangle is periodically stable with the ber nearly equal to 0.4 for both models. prescribed course. The second mode occurs when the . , (4) The surf-riding occurred at high Froude num yaw angle behaves as non-periodically stable with the ber nearly equal to 0.4 which is in the same range as the prescribed course. " The third modes is identified when pure loss of stability. Model Experiments of Ship Capsize in Astern Seas 87 (5) The broaching-to occurred at the Froude num ence on Stability of Ships and Ocean Vehicles, ber about 0.4 for the container model running in non Tokyo, (1982), pp. 243-253. periodic unstable region and for the purse seiner model 5) Umeda, N., Hamamoto, M., Takaishi, Y., Chiba. running in marginal region. H., Matsuda, A., Sera, W., Suzuki, S., Spyrou, K., Watanabe, K.: Model Experiments of Ship Cap (6) A new analytical approach is presented for size in Astern Seas, Journal of the Society of simulations of ship capsize in regular and long crested Naval Architects of Japan, Vol. 177, (1995), pp. irregular seas. The conclusions mentioned above are 207-217. the derived from both experimental results and numeri 6) Hamamoto, M., Umeda, N., Matsuda, A., Sera, cal simulations by making use of the equations of W.: Analyses on Low Cycle Resonance of Ship in motion for running with the heading angle of ship to Astern Seas, Journal of the Society of Naval Architects of Japan, Vol. 177, (1995), pp. 197-206. waves. It is finally concluded that simulation results 7) Kan, M.,: A Simplified formula to estimate the stand comparison with the experiments. critical speed of surf-riding ofships, Report of This study was carried out under the auspices of Ship Research Institute, Vol. 29, (1992). RR 71 Research panel of Shipbuilding Research Associ 8) Hamamoto, M., Sera, W., Panjaitan, J. P,: Ana ation of Japan. The authors wish to express their lyses on Low Cycle Resonance of Ship in Irregu gratitude to members of the RR 71, chaired by Prof. M. lar Astern Seas, Journal of the Society of Naval Fujino for productive discussions. The authors would Architects of Japan, Vol. 178, (1995), pp. 137-145. 9) Hamamoto, M., Sera, W., Panjaitan, J. P,: Cap also like to thank the assistance of Mr. K. Watanabe size of Ship in Beam and Astern Sea Conditions, (Nihon University) at the model experiments. Technical Report of Faculty of Engineering, References Osaka University, Japan, (1995) (to be publi shed). 1) Grim, 0.: Rollschwingungen, Stabilitat und Si- 10) IMO Sub-committee on Stability, Load Lines and cherheit im Seegang, Schiffstechnik, Vol. 1, Fishing Vessels Safety: IMO Guidance to the (1952), pp. 10-21. Master for Avoiding Dangerous Situations in 2) Kerwin, J. E.: Notes on Rolling in Longitudinal Following and Quartering Seas, draft MSC-circu- Waves, International Shipbuilding Progress, Vol. lars/IMO, (16 March 1995). 2, No. 16, (1955), pp. 597-614. 11) Umeda, N.: Application of Non-linear Dynami 3) Paulling, J. R.: The Transverse Stability of a cal System Approach to Ship Capsize and Broach Ship in a Longitudinal Seaway, Journal of Ship ing-to in Regular Following and Quartering Seas, Research, SNAME, Vol. 4, No. 4, (1961), pp. 37- Report on the Research Supported by a Visiting 49. Research Fellowship of the Engineering and 4) Takaishi, Y.: Consideration on the Dangerous Physical Sciences Research Council, United King Situations Leading to Capsize of Ships in Waves, dom, (30 October 1995). Proceedings of the Second International Confer u ' I f.. ■ I i V A * 'Ui ''I' |i ' 1 ' ■ , 1 ' V -■! -}.U ' rl, -! j' »o i 1 I'M. IL > i. ■. I i I l; rfc . ■ ! , ■ii J . -<) i - i - ‘ ! lii"' I i j ■ It* in i 11 [ <_' t 1)0 lii ' ‘ i, ! ! |. 1 r 1 >i 1 ll ?: .j fi( ii ; III i’1. ' I- - ■ . ij An yfi'i,' 1'« i 1 > i' .. !/l iM'i -.. . i :■ 'i ; 89 1-10 Non-Linear Periodic Motions of a Ship Running in Following and Quartering Seas by Naoya Umeda*, Member Dracos Vassalos**, Overseas Member Summary This paper deals with non-linear periodic motions of a ship running in following and quartering seas with low encounter frequency. It aims at providing a methodology for more comprehensive understand ing of broaching. The motions discussed here include surge, sway, yaw and roll with an auto pilot. A manoeuvring mathematical model in waves is transformed with a mean-velocity inertia axis system and then an averaging method is applied to the transformed model. As a result, local stability and outstructure of periodic motions are discussed with numerical results derived using a purse seiner. These cannot be directly assessed by conventional linear models or purely simulation based approaches. Comparisons with experimental results are also shown. surge and sway, and suggested that they are related to 1. Introduction broaching. However, since their investigation was When a ship travels in following and quartering seas within a linear theory and broaching is a highly non at a relatively high speed, she may suffer broaching. linear phenomenon, they did not clarify the.relationship Since broaching can result in capsizing or grounding, between the large amplitude periodic motions and broa many research efforts have been concentrated on study ching. ■. ing this phenomenon. Recently, occurrence, local stabil In this study, the occurrence, local stability and ity and outstructure of surf-riding equilibrium points outstructure of non-linear periodic motions will be have been intensively investigated'"", because broach investigated for the case of a ship running in regular ing can be explained as one of outstructure for unstable following and quartering seas with low encounter fre equilibria of surf-riding", On the other hand, a dynami quency. A methodology for this investigation has not cal system of a ship in regular quartering seas has other been known because it would appear that non-linear steady states. These are periodic motions at fre vibrations without restoring terms have not yet been quencies equal to the encounter frequency of a ship in treated. Therefore, there is a need to provide a metho waves. Broaching can be regarded as a transition dology first to fill this gap: between periodic motions and equilibria of surf-riding. When a ship runs in following and quartering seas, Therefore, it is necessary to investigate periodic the encounter frequency of the ship in waves becomes motions as well as equilibria of surf-riding. much smaller than the natural frequencies in heave and Nowadays prediction of periodic motions in waves pitch. Therefore, heave and pitch motions can be within a linear strip theory has been well established as approximated by simply tracing their static equilibria. a practical tool. Nevertheless, a linear theory leads to Thus, it is sufficient to examine surge, sway, yaw and infinite amplitudes of surge and sway when the encoun roll motions, whose restoring terms are zero or Small. ter frequency is zero. Thus, it is rather questionable In addition, because of the low encounter frequencies, whether the long-term prediction for surge or sway is hydrodynamic forces due to the shedding of free vor reliable. Ishida and Kan5’ pointed out that the infinite tices are dominant and wave-making effects are almost amplitudes are due to the absence of restoring terms in negligible. Thus, a manoeuvring model is more suitable than a seakeeping model. In this paper, the mathemati cal model used for the investigation of equilibria of surf * National Research Institute of Fisheries Engi -riding will be adopted. Since the model is notjsuitable neering to describe periodic motions, it will be transformed with ** University of Strathclyde a mean-velocity inertia axis system. Then, by using an Recevived 10th Jan. 1996 averaging method, non-linear periodic motions will be Read at the Spring meeting 15, 16th May 1996 investigated. While in averaging methods natural 90 Journal of The Society of Naval Architects of Japan, Vol. 179 vibration due to inertia and restoring terms is usually xh : longitudinal position of centre of interaction regarded as the zero-order solution, it will be attempted force between hull and rudder to use the natural vibration due to inertia and linear , xr : longitudinal position of rudder exciting- terms as the-zero-order solution^ . 1 ‘ - I - -Xu, : wave-induced surge force . Ym : wave-induced sway force 2. Nomenclature ; . . • zh - height of centre of lateral force a : wave amplitude zhr : vertical position of centre of effective rudder Ah : interaction factor between hull and rudder force As : rudder area zr : vertical position of centre of rudder cwave celerity >0, i. - • /, • ! Yr ■ flow-straightening effect coefficient Cb : block coefficient S : rudder angle Cfo ■ frictional resistance in two dimensional flow E* : wake ratio between propeller and hull Ct ■ total residual resistance coefficient II -* da', vanishing angle d : mean draught , i : . p i Km/L : gyro radius in pitch da - aft draught , ; , , Kzz/L : gyro radius in yaw d/ : fore draught • 1 i Kp : interaction factor between propeller and rud Dp : propeller diameter der Fn : nominal Froude number ‘ 1 1 " ‘ '' Kp o : linearlised damping coefficient without for g ■ gravitational acceleration ' 11 ward velocity GM: metacentric height ' . , n , , /i: wave length , GZ : righting arm A : rudder aspect ratio H: wave height fc : longitudinal position of centre of gravity Izx ■ moment of inertia in roll P ■ water density 7zz - moment of inertia in yaw a: eigenvalue J . advance coefficient of propeller (6 : roll angle Jxx '■ added moment of inertia in roll 1 -...... X ■ heading angle i/zz t.added moment-of inertia in yaw ■ 11 -- ’ Xc ■ desired heading angle for auto pilot 1 k: wave number' ' ■ 11 1 co ,;: averaged encounter frequency 1 Kp l rudder gain >’ ^ -■■ 3. Mathematical modelling Kt - thrust coefficient of propeller 1 > Kw :-wave-induced roll-moment - .1 ' 'As can be seen in Fig. 1, two co-ordinate systems are 1. c. b.: longitudinal position of centre of buoyancy used: wave fixed with origin at a wave trough, £ axis In : correction factor for flow-straightening effect'' in the direction of wave travel; upright body fixed with ■ due to yaw rate -,r ■ 11 origin at the centre of ship gravity, the x axis pointing L : ship length between perpendiculars towards the bow, the y axis to starboard and the z axis m: ship mass 1 > 1 ' : - downwards. The latter co-ordinate system is not all- mz • added mass in surge" > . - ■ my : added mass in sway '• 1 6 n '■ propeller revolution number 1 1 ' ' 1 ’ " Nw : wave-induced yaw moment " ’ OG: vertical distance between centre of gravity and ' i "i . ■ waterline ' vn U> . i > ■ - p ■ roll rate • ■ ■ ■ i < ■ ■ • 1 11 ■ ■1 ' i rivyaw rate ru .,'|j •" ■ ■ ■> 1,1 ' -i 1 ' ■ L R l ship resistance ...... 'f Sf - wetted surface'area ■1 1 " i i f t time 1 u11 ''i ' ' '■! 1 ’ 11 ' ' " '' ' wave trough ' &> : thrust deduction factor 1 ■ ' T propeller thrust 1 ■' To': nondimerisional .time constant for differential ' i" -n- control ' I- i . ' '11 ii - -.11 "Tel nondimensional time constant for steering gear Tp '! natural roll period ■ - ’ ■ 1 ' - M : surge velocity' ' ...... > i , ' Uoi' ship cruising velocity '■ y : sway velocity ' ' ii . i n i . Fig. 1 Co-ordinate systems for equilibrium points of ; Wp : effective propeller wake fraction surf-riding 1 Non-Linear Periodic Motions of a Ship Running in Following and Quartering Seas 91 owed to turn about the x axis6’. The symbols are GZ^c/A, xcos (met—kXc cos' z+kYcrsin x) xcos (coct—en) ' ■ - (27) +F2d( U+Xc) cos (aict—kXc cos % 8 = r7 cos (diet—£7) > (28). +Afcsin x)FFze(U+(Xc) ■ ' Then the van del Pol transformation is expressed ■ as Xsin( Here the coefficients, Am, Bm, Cm, Dm, Fm, £f , sm, Cr, are obtained by the coefficients in the right hand side of Eq. (2). (/, m=1, —, 7, a=a, i). For realising caps .1 .111 YFzMc+FcU+FzrU) . , x(uf cos 2 z —2miM2 cos z sin z + mI sin z izing, restoring terms in roll are assumed not to be +3y 2cos z z~6toto.eps z sin z+Suisin2 z) subject to the perturbation principles. | Further, it is assumed that ;l + a (~Fzasin£F+Fzc(oe+FzdU XctK Yc/A=0(v) 1/=0(e2'3) ’ (23). •; I , °(9e^z I, , I / , +F2fU)x( —uiVi cos2 z+mi to. cos z sip z Consequently, higher order terms than e2!/ are ignored. +M2to cos x sin z —M2tosin2 z) (40) This additional assumption means that non-linearities due to surge and sway are nofcso large; -As a result, the 9t(v)=.~\(OeUz--^^ ■ ' _ 1 -' following form of solutions can be expected with fre X(—sin £f +F zcCOe-^- FzdU-b Fz/U) quency equal to the encounter frequency : Xe=ri cos (diet — £1 ) (24) 1 1 .—2ai^Aa (Q)e^22to-h VeBuVt Yg—Tz COS (cOet — £2) (25) — C24 M4 -f- (OeBzGVc, CzgKh— C21U1) }—rt COS (diet —£ a) , 1 - 1 1 1 1 1 v ,/> (26) Non-Linear Periodic Motions of a Ship Running in Following and Quartering Seas 93 + 16£422(-f2‘sinf + m2Mi cos x sin % — U2V2 sin2 x) (44) ffs(M)=-|^M6-2^ +/'sc®* +p2dU+Fz/U) x(m?cos2 x ~2vi V2cos % sin x + mIsin2 % i X(F60 cos EM+FscCOe+FsdU+Fe/U) +3m2 cos 2 x~ 6mim2cos x sin x —2(u X (Fta + Ftc COS £f + FtdCOe+FtgU+F 41U) sin £// + /;66 +F4aU+F,iU)x(—uiVi cos2 x + Mite cos x sin x ~i + m2Mi cos x sin x~M2tesin2 x)+ +Fec + %(!)cA G(v„)=0 ' (48). mx was estimated empirically. For a roll damping Then, G(v) is linearlised at v0, putting v=v0+q to moment, free roll tests were carried out without for obtain the following equation : ward velocity. Forward velocity effects on the roll q=DG{vo)q ■' ' ‘ (49) damping were estimated by Takahashi’s empirical where ; - , , formula 10 A restoring arm curve is fitted with a fifth DG(v)=-£j-(g,(v)) lsSz./rSlO (50). order polynomial which has zero values at 0 degrees, 180 degrees and the vanishing angle, Qo. Forward If an eigenvalue of DG(vo) has a positive real part, the velocity effects on the restoring terms in sway, yaw and local asymptotic behaviour at Vo is unstable. roll were measured with a heeled model, and fitted with bo is a fixeii point of the averaged equation. The functions of the Froude number. On the other hand, averaging thedrem101 indicates that,1 if an averaged coupling hydrodynamic coefficients of sway and yaw equation has a hyperbolic fixed point, Vo, the original due to roll rate are ignored, because of limitations of equation possesses a unique hyperbolic periodic orbit of the experimental capability. All the coefficients for the the same stability type as v0. Therefore, Vo means a mathematical model are presented in the Appendix, in periodic motion with frequency equal to the encounter Tables 1-2 and Figs. 3-5. frequency and its local stability can be examined by Using the above coefficients, the stability di means of eigenvalues. Subharmonic motions can be scriminant D, defined as similarly investigated. D=YvNr+(m+mx—Yr)Nv (51), The Hartman-Grobman theorem and stable manifold has a positive value indicating that the purse seiner is theorem"" indicate that the invariant manifolds re directionally stable in still water. This fact was also presenting all trajectories associated with a fixed point confirmed by examining the eigenvalues of the autono can be obtained by tracing trajectories backwards and mous system in still water, whose fixed point corre forwards in time from the eigenspace spanned by the sponds to a straight-course running with a constant eigenvector at the hyperbolic fixed point. The invariant velocity. manifolds analysis based on this theorem affords us To identify periodic motion in waves, the fixed points understanding of the relationship betvyeen local and of the state equation of the averaged system should be global behaviour associated with periodic motions. determined by using Eq. (48). There are two ways to Thus," invariant manifolds are called outstructure of a fixed point. . v 6. Numerical results for periodic motions Table 2 System parameters used for numerical calculation - Some numerical calculation's were carried out for periodic motions on the basis of Eq. (36). The ship used m/m , 0.0834 8h ' 0.320 here is a 135 GT purse seiner that was designed with the m/m 0.8414 xh /L -0.453 current Japanese regulations of fishing vessels and is JJ1* 0.5424 zim/d 0.266 operating in the East China-Sea. , . Y hv ’ -0.6327 Kp 0.6167 In order to obtain the required .coefficients for the Y ht ’ 0.1396 Sr 0.9577 Nnv’ -0.0858 0.422 mathematical model, the results of captive model tests Y r ' with a 1/17.25 scale model of this purse seiner were Nit’ -0.0804 Ir/L -0.683 zn/d 0.4953 Te’ 0.1 made use of. The tests compose resistance test, self- (at Fn=0.4) propulsion test, circular motion tests and rudder angle I-Wp 0.858 Kp 1.0 tests in still water. These were carried out at the 1-tp 0.853 Td ’ , 0.0 Marine Dynamics Basin of the National Research Insti 11 Kso 0.139 tute of Fisheries Engineering. Since the added mass and moment cannot be obtained from circular motion tests, m„ and Jzz were predicted using a strip method whilst i -if - Table, 1 Principal particulars of the purse i seiner,- " X 34.5 [m] k „/L 0.332 B 7.6 [m] kJL 0.332 - P 3.07 [m] ;GM„ 0.755 [m2] dr 2.84 [m] 0V 40.47 [degrees] d, 3.14 [m] T+ 7.47 [sec] Cb 0.652 ,f Dp i 2.60 [m] " ' l.c.b. (aft)., 1.742 [m] Ar , 3,486 [m2] Sr 391.8 [m2] A 1.838, , . , , Fig. 3 Ship resistance coefficient of'the purse seiner Non-Linear Periodic Motions of a Ship Running in Following and Quartering Seas 95 Ky=-0. 1373J2-0.2283J+0.2244 Surge Amplitude ----- Linear o Nonlinear(A) n Nonlinear(B) Fig. 6 Surge amplitude (surge-sway-roll-yaw-rudder Fig. 4 Propeller thrust coefficient of the purse seiner model ; 72//1=1/15, 2/L=1.5, %=15 degrees, Kp =1.0, Td =0) Y»',W,K»', 135GT Purse seiner 0.04 <|>=15degrees Sway Amplitude 0.02 "4 oq O Y(cxp) 0 P - -c —*■ — M w D N(cxp) 300 * ----- Linear ■ A K(cxp) ! -0.02- &. / 200 - o NonIinear(A) c — Y(fit) / o Nonlinear(B) -0.M- V n 100 - V •- N(fit) '^ -0.06- •a - * K(fil) 0- 0 0.2 0.4 0.6 0.8 •0.08- OG/d=0 0 0.1 0.2 0.3 0.4 0.5 0.6 Fn Fn Fig. 5 Measured manoeuvring derivatives with respect Fig. 7 Sway amplitude (surge-sway-roll-yaw-rudder to heel angle model ; 72/2=1/15, 2/2,=1.5, %=15 degrees, Kp =1.0, 7s=0) solve the equation. One is an algebraic way, in which simultaneous algebraic equations are transformed to a higher order algebraic equation and then solved numeri Roll Amplitude cally. The other is an iteration method with deriva tives, that is, the Newton method. The former can yield all solutions but the transformed equation becomes extremely complicated. The latter is easier but the derived solutions depend on the initial values used for the iteration. In this paper use i is made of the latter way. Provided the results are encouraging, use can then be made of the former way to obtain more comprehen sive understanding in the near future. Firstly, steady periodic motions calculated by using Eq. (48) are shown in Figs. 6-11. Here the amplitudes Fig. 8 Roll amplitude (surge-sway-roll-yaw-rudder are non-dimensionalised as follows :. model ; 72/2=1/15, A/L=1.5, %=15 degrees, Kp n'=n/s (52) =1.0, Td=0) ri=n!a (53) ri=r,/(ak) (54) re=roKak) (55) -linear terms in Eq. (36) and possesses a unique solution ri=r7/(ak) (56) for each control parameter set. On the other hand, a Figs. 12-13 show the maximum of the real part of non-linear solution obtained by an iteration method eigenvalues which represents local stability of periodic depends on the initial values because the non-linear motions. Here the eigenvalues are multiplied by the model can possess co-existing solutions. Here “Non absolute value of the encounter frequency. The linear linear (A) ” means a non-linear solution obtained by the model presented here is obtained by ignoring all the non Newton method whose initial value is the non-linear 96 11 Journal of The Society of Naval Architects of Japan, Vol. 179 1 Yaw Amplitude Maximum of Real Part ofEgenvalues 400- 100 - Fig. 12 Maximum of real part of nondimensional eigenvalues multiplied by the absolute value of Fig. 9 Yaw amplitude (surge-sway-roll-yaw-rudder the encounter frequency (surge-sway-roll-yaw .■ model; H/A=1/15, A/L=1.5, %=15 degrees, KP - rudder model ; 77/2=l/l5, A/L= 1.5, %=15 =1.0, Td=0) 1 degrees, KP=1.0, To =0) i Phase of Surge \ ■ Maximum ofReal Part of Eigenvalues Linear o Nonlinear(A) i 0.2 -• □ Nonlinear(B) Fig. 13 Maximum of real part of nondimensional Fig. 10 Phase of surge (surge-sway-roll-yaw-rudder , eigenvalues multiplied by the absolute value model ; 77/2=1/15, A/L=1.5', %=15 degrees, of the encounter frequency (surge-sway-roll- KP=1.0, Td=0) yaw - rudder model ; 77/2=1/15, 2/L=1.5, %= 15 degrees, KP—1.0, To =0) Phase of Sway motions become infinity; This is due to the absence of restoring forces in surge and sway. Since restoring Linear ' moments exist in roll and yaw, amplitudes of linear roll arid; yaw are finite. However, they are very large -because coupling terms due to sway become large. The restoring moment in yaw is due to the stability deriva tive, Mi,' which rhairily consists of the Munk moment. If non-linear terms are taken into account, some terms proportional to surge and sway displacement emerge and thus the amplitudes are finite even when the encounter frequency is1 zero. 1 These virtual restoring Fig. 11 Phase of sway (surge-sway-roll-yaw-rudder 1 " model ; 77/2=1/15, A/ll= 1.5, 'Jr=15 " degrees, terms exist because a' wave is described with a %=1.0, rD=0)v 11 " l ; sinusoidal function of displacement as well as time. i. , i However, a linear theory ignores the contributions from periodic displacement as higher order. solution for slightly lower Froude numbers. Thus the Although amplitudes of surge and sway are finite solutions are determined in 'sequence; from F„=0.05 to with the non-linear prediction, they are still too large. .Fi=0.7. The step of increasing the Froude -'number is That is, they are from 70 to 200 times larger than'wave lO.OI. , “Nonlinear (B)” on the other hand refers to height or from '4 to 14 times larger than wave length. solutions determined in sequence from Fn—0.7 to F„— -Thus it is necessary to examine their stability. Fig. 12 0.05. ; 1 - i -ih 111 L 'i: j i, and its part-enlargement, Fig. 13, show that the linear When the encounter frequency is zero, that is, Fn— solution is stable except in the neighbourhood of a>e=0. 0.506 in this case, amplitudes of linear surge and sway 'The instability of linear solution can be excluded by Non-Linear Periodic Motions of a Ship Running in Following and Quartering Seas 97 fixing the rudder amidships, as shown in Fig. 14. Obvi normal resonance in roll is also shown at Fn~0.1 but is ously, the linear model cannot be justified because not significant because of the relatively large roll damp stable and extremely large amplitude does not satisfy ing momenta . ______the assumption of small amplitude. In Fig. 13, the The periodic motions obtained by Eq. (48) were Nonlinear (A) solution is stable when F„<0.41 and checked against model experiments undertaken by unstable elsewhere. Contrary, the Nonlinear (B) solu Umeda et al.12) with a free running model of the ship tion is always unstable. Therefore, stable and unstable used in this paper. The comparison between calcula periodic motions co-exist when Fn < 0.41. The ampli tions and experiments are shown in Figs. 16~17. Here tudes of stable surge and sway motions remain about 5 the non-linear calculation means the “Nonlinear (A)” times larger than the wave amplitude or about one third defined above and only a stable periodic motion can be of the wave length. The roll is dominant for the insta observed in the model experiments with these control bility of non-linear periodic motion, as the eigenvector parameters. The calculated results compare fairly well indicates in Fig. 15. The unstable roll amplitude is with the experimental results. almost constant and about 16 times larger than the With the control parameter used here two distinct maximum wave slope. This implies that the unstable cases are found as shown in Figs. 6-11: one refers to the periodic roll motion has a single amplitude of about 196 co-existence of stable and unstable periodic motions degrees. This can be regarded as capsizing in practice. and the other to co-existence of two unstable periodic The unstable periodic yaw motion can be large when oi c motions. To explore the relationship between co-exist >0 while it decreases when aie<0. ing , fixed points, trajectories forming the invariant At o>e=0, there is a discontinuity of phase in surge manifolds were calculated. Fig. 18 shows an example and sway. This can be helpful in understanding the for the former, that is, part of the invariant manifolds divergence of linear periodic motion at Maximum of Real Part of Eigenvalues (ReCoOjmax Roll Amplitude ——Linear . ^ o Non!ineai(A) 0.2 o$r (Wtato 0 o NonlinearfB) Calc. (Nonlinear) 8 -0.5 ■ Exp. (Umeda ct Fn , aL) , ; Fig. 14 Maximum of real part of nondimensional eigenvalues multiplied by the absolute value of Fig. 16 Roll amplitude (surge-sway-roll-yaw-rudder encounter, frequency (surge-sway-roll-yaw- model ; H/A=l/15, AjL—1.5, *=25 degrees, ' rudder model ; H/A=1/15, A/L=1.5, x=15 Ap=1.0, To=0) degrees, A},=0.0, 7o=0.0) Eigenvector at an unstable periodic motion ■— Calc. (Linear) 0.8 ------Calc. 0.6 (Nonlinear) 0.4 ■ Exp. (Umeda et 0.2 ul vl u2 v2 u4 v4 u6 - v6 u7 v7 Fig. 15 Eigenvector at an unstable periodic motion Fig. 17 Yaw amplitude (surge-sway-roll-yaw-rudder (.HI,1=1/15, A/L=1.5, %=15 degrees, F„=0.4, 1 " model; H/A=1/15, zl/L=1.5, %=25 degrees, A,=1.0, To =0) 1 Ap=1.0, Td=0) ' ' -98 Journal of The Society of Naval Architects of Japan. Vol. 179 Fn=0.40 Surge Amplitude ' 120 I 100 - " 11 > ' , 80 r ---- Linear 60- o Nonlinear(A) 40- □ Nonlinear(B) 20- -10 0 0.2 : 0.4 0.6 0.8 U4/(ak) Fn Fig. 18 Part of invariant manifolds of unstable peri Fig, 19 Surge amplitude (surge - sway - yaw - rudder odic motions . (surge-sway-roll-yaw-rudder model ; 7f/A=l/15, A/L—1.5, %=15 degrees, | model ; 7f/A=l/15, A/L=1.5, %=15 degrees, lc Kp—\Si, Td =0.0) n iv=D.40) Here the diamond symbol indicates , , ' - 1 i - ' '« ' . * i stable periodic motion i' *! ' ! ...... i 1 > ., i ; Sway Amplitude' tories can be 10-dimensional, only projection's of them on 2-dimensional planes are provided. However, one distinct saddle is found on the ut~vt plane because ■?—-Linear instability in roll is dominant and its index is one. Other ,200 " o Nonlinear(A) projections of the invariant manifolds on the Ui-Vi, uz~ □ NonlineaifB) to, ue-Vs and tir-Vr planes are omitted because they show little movements. The stable fixed point is plotted with a diamond symbol. It is found that the unstable fixed point is a saddle and the invariant manifolds from it do not reach the stable fixed point. This means that, only when the initial roll angle or roll-rate is very large, Fig. 20 Sway amplitude , . (surge - sway - yaw - rudder the ship will suffer unstable periodic motions, j model ; 77/A=l/15, A/L= 1.5, *=15 degrees, With the above calculation the coupling effect has not ' 70=1.0, To =0.0) I yet been clarified because instability in the periodic roll motion is dominant. Thus,-similar calculations were carried out ignoring the roll motion and coupling due to roll. The calculated results are shown in Figs. 19-25. In Yaw Amplitude contrast with the calculations including roll, a stable non-linear periodic motion is found by the calculation without roll,even when ... Maximum of Real Part ofEigenvalues Phase of Surge {ReCoOJmax 'X ''' 0.5 ■ -Linear —"Linear " , . o Nonllnear(A) ^ 02 Qy 0 8 o NonHnear(B) □ Nonlinear(B) -0.5 jr ------■ ■ - Fn Fig. 25 Maximum of real part of nondimensional Fig. 22 Phase Of surge (surge - sway - yaw - rudder eigenvalues multiplied by the absolute value of model ; Hi/1—1/15, A/L=1.5, %=15 degrees, encounter frequency (surge-sway-yaw-rudder Kp=l.Q, Td=0.0) model; Hb1=1/15, A/L=1.5, 2=15 degrees, Kp=1.0, Tz>—0.0) Phase of Sway Fn=0.45 (without Roll Coupling) -Linear ------15 - o NonBnear(A) 10- o Nonlinear(B) : C- o -5‘ ------16- Ul/a Fig. 23 Phase of sway (surge - sway - yaw - rudder model ; #//1=1/15, A/L=1.5, 2=15 degrees, Fig. 26 Part of invariant manifolds of unstable peri- Kp=1.0, Tfl=0.0) ' 1 odie motions (surge-sway-yaw-rudder model ; 1 77/4=1/15, A/L=1.5, 2=15 degrees, F„=0.45) Maximum of Real Part ofEigenvalues Fn=0.45 (without Roll Coupling) -10 Fig. 24 Maximum of real part of nondimensional eigenvalues multiplied by the absolute value of 1 encounter frequency (surge-sway-yaw-rudder ' model; H//1=1/15, A/L= 1.5, 2=15 degrees, Fig. 27 Part of invariant manifolds of unstable peri Kp —1.0, Td =0.0) 1 odic motions (surge-sway-yaw-rudder model ; H/A=l/15, A/L=1.5, 2=15 degrees, F„=0.45) induce the maximum rudder angle at least under this applicable to these combinations. That is, the region parameter set. It should be remarked that the possibil where no stable periodic motion is found exists only in ity of reaching the maximum rudder angle still remains the vicinity of the zero encounter frequency. However, in transient states. because of non-linear nature of this problem, more To obtain more general features of periodic motions, intensive surveys are expected for different combina Fig. 29 is provided for the combinations of heading tions of parameter set. angle and ship speed. The above discussion is generally 100 ,, Journal of The Society of Naval Architects of Japan, VoL 179 Critical Conditions ' Fn=0.45 (without Roll Coupling) HA=1/15, X/L=1.5, Kp=1.0,To=0 0.6 -Lower limit of c- __stable periodic solutions 02 ; ' 1 0.1 ~ Upper limit of l ...... siaoie periodic ) 20 ------40 - - ; 60------solutions Ultras) ' U6/(ak) Fig. 29 Critical conditions for stable periodic motions Fig. 28. Part of invariants manifolds I of unstable peri- ; (surge-sway-yaw-rudder model; H/A=l/15, ■y-,odic motions (surge-swayryawmidder model ; -, , A/L=1.5,~ Kp=1.0, To =0.0) i , H/A=l/15,A/L=l.5, %—15 degre'es, F'n=0.45) Waves”, Schiffstechnik, Bd. 42, (1994), 103-112. 4) Spyrou, K. J. and N. Umeda: “From Surf-Riding 7. Conclusions to Loss of Control and. Capsize : A Model of The main conclusions from this work are summarised Dynamic Behaviour of Ships in Following/Quar tering Seas”,-Eroceedings.of-the^th International as follows : Symposium on Practical Design of Ships, and (1) ATrianoeuvrmgmathemafical model in waves ,' Mobile Units, Seoul, 1, (1995) , 494-505. | ' was transformed with a mean-velocity inertia 5) , Ishida, S. and M. Kan: “Motions in Quartering axis system. - " ! • i , Seas arid | Broaching ”, Japan Marine Dynamics (2) A method to assess occurrenceTlocalj stability Committee, SK-8-5, (1985), (in Japanese.) 0 and outstructure of periodiclnotions ‘was for 6) Hamamoto, —M.-et-al.-:-“Dynamic-Stability of a Ship in Quartering Seas”, Proceedings of the 5 th mulated by. using an averaging method. International Conference on Stability of Ships (3) While1inear~periodic"solutioris"for "surge and and Ocean Vehicles, Melbourne, 4, (1994). sway are unbounded at the zero encounter 7) Umeda, N., et al.: “Experimental Study for frequency, an analysis including the non-linear- • Wave Forces on a Ship Running in Quartering , , ity of waves due to horizontal displacements Seas with." Very Low Encounter Frequency ”, i .1( provides finite amplitudes of periodic motions, Proceedings of the International Symposium on i (4) If this non-linearity, is considered, unstable and Ship Safety in a Seaway : Stability, Manoeuvrability, Nonlinear Approach, Kalinin stable periodic motions may co-exist. When grad, 1, 14, (1995), 1-18. the encounter frequency approaches zero, a I 8) Fujino, M, et al.: “On the Stability Derivatives of stable periodic motion may become unstable. a Ship Travelling in the Following Waves”, Jour (5) Further numerical surveys by using the present nal of the Society of Naval Architects of Japan, method are expected to provide more general ! 152, (1983), 167-179, (in Japanese.) j features of periodic motions. ; 9) Fuwa, T., et al.: “An Experimental Study on | i! ’' Broaching of a:Small High Speed Craft”, Papers The work described'in this paper_\vas carried out at !' !•-: of Ship Research Institute; 66, (1982), 1-40. the University of-Strathclyde duringjthe first author ’s 10) Guckenheimer, J. and P. Holmes: Nonlinear stay as a visiting research fellow) This was Supported Oscillations, -Dynamical-Systems, and-Bifurcations by the Engineering and Physical Sciences Research of Vector Field Spring-Verlag, (New York), Council in United Kingdom, to whom the| authors (1983). 1 express their gratitude? " 11) Himeno, Y.: “Roll Damping Moment ”, Proceed- 1 ings of the12 nd Seakeeping Syfnposium, Tokyo, References . ' ' (1977), 199-208,' (in Japanese.) ' . 1) Umeda, N. and M;,R.,,Renilson: “Broaching-A 21) Umeda, N., M. Hamamoto, et al.: “Model Exper- ( Dynamic Analysis of Yaw Behaviour, of a Vessel iments of Ship Capsize in Astern Seas”, Journal in a Following Sea”, Manoeuvring and Control of the Society of Naval Architects of Japan, 177, ofMarine''Craft ! (Wilson, 1 P. A. eds.), (1995), 207-217. Computational Mechanics Publications (South Appendix ampton), (1992), 553-543. ( , 12) Umeda, N. and M. R. Renilson : ‘‘Broaching of a The coefficients shown in Eos) (3-9) are defined as 1 ' Fishing- Vessel - in' Following and Quartering follows: 1 ’ 1 ' J lj'r...... 1 ■ - Seas”; Proceedings of the 5th International Con- T=lX~tp)pimKrU) ' ' " (All) • ' fererice on Stability of Ships and Ocean Vehicles, , R^piFSpCriFn) , , ...... (A.2) . Melbourne, 3, i(1994); 115-132. n 3) Spyrou, K. J.: “Surf-Riding, Yaw Instability and Large Heeling of Ships in Following/Quartering yy=-^-pL6fY;/o« —(l+ (Z;/)-^-pA«/«£j?(l — top) " ; Non-Linear Periodic Motions of a Ship Running in Following and Quartering Seas 101 X Jr (A. 3) x{e%l-wp)'(l+fp-^ |zz2+2e*(l —zvp) Yr —^pt} dYnrll — (1 + a»)ypAp/„Ep(l — Wp) X y 1 + /fp ^y 2 Z<«iwj (A. 9) X yrIr y 1+Kp^^ru (A. 4) Aj = — (xp+zz,m,)ypAp/« Nv=^£pUdN'mu - (xff—auXu^pAnfaeti x|d(l wp)^l+Kp-^r )zz2+2e*(l —ivp) X (1 - «;P) y 1+Kp^^-n (A. 5) X y 1+ATp- _^J2 IIUtroj (A. 10) Nr—^pUdN'm u—(xr +anXiD^-pARf„ER Aj=(l+zz«)a«pypApA X (1—wp) YrIr^ 1+Kp-^jru (A. 6) x |d(l zvp)2(l+ )zz2+2ep(1-zvp ) Ad = —^-pLdzit Ylia zz + (1+an)znR-^-pARfi£r X y 1 + ATp _^y 2 ZZZZlWfJ (A. 11) X(l-Wp)r»yi+K^^p-M (A.7) where r (1 Wp)u J~ nDp (A. 12) Kr=—pi? dzu Y'ht z<+(1+a^ZHR^pAuf i£r , 6.13A /a_ 2.25+A (A. 13) X (1—wp) r*/* y 1+Kp^pru (A. 8) uwR=aw cos % exp (—kzs) cos (2/TgclA+kxR cos %) (A. 14). y»=—(1+zz/^ypAp/i 'itj. 1 - f , tv . F I , ! ) I 103 1-11 mm* ^ # # & Ro-Ro ^ 3E* E Be I t* II s 1 iem m M E* zm /Jn /II jEl 1 Jl t X* Study on Damge Stability with Water on Deck of a RO-RO Passenger Ship in Waves by Shigesuke Ishida, Member Sunao Murashige, Member Iwao Watanabe, Member Yoshitaka Ogawa, Member Toshifumi Fujiwara, Member Summary RO-RO passenger vessel has a wide non-separated car deck. Once free flooded water is piled up.on it, the large heel moment could be the cause of capsize because of this feature. The stability standard of RO-RO passenger vessels was deliberated at IMO commission from 1994 to 1995 in order to prevent capsizing disaster like the one of ESTONIA in 1994. The authors, one of which was a member of the IMO expert panel, conducted an experiment on the stability of this type of ship ' because few papers have been published on this problem. The experiment was carried out in beam seas using a model ship with a side damage hole which is prescribed by the SOLAS regulation. After the duration time of the experiment (30 minutes in ship scale) in irregular waves the ship survived with a constant mean heel angle 1994 1995 gM### i. ti u *> e Hi (IMO) K33HT RO-RO 1994 WcK RO-RO ffli; h-7 *§■<*)&%[ tffrbtiko SHS^*^©Si£Ea, ##©— L&.900 &kn3A#©#@ t, HffiOS Lfc. ZLX, 1995118 cRO-RO tt, 0 solas C cfoti, -7© J: -5 SEEttOfSHi - fc A § 3:11311 k LT® D±tf 6-iLfco RO- ¥/& 8 *F U110 B - Rosnsa, 8 ^ 5 b 15, ig b 104f m 179 h, & ;sk, ^m©*A*pE±#KM 2. s » * a a(#§##&D, fjtKj:aM#t-/>hEj:?T mm-rz&at#154:if&, C, w&o ;,T2ri , SOLAS kw? ©*t #RRmm»0iM0®$ Fig. 1 k Table 1 C ©SAT&^A. "r:';''i|%,A *l&T-i£s|^x a a k k>a„68#©SSi$gBli, SOLAS #MU 8.4 CSo*§ME a EH,D ©3%y* V d-*$A6fia.| , (3.0+LPPX 3/100)=6.03 m, ®^|6] B/5=3.2 m, SE -oliiX Y-7W'%Z^\t%it\z?GiL-0'y:7)V F*Z ^IrJ ttSS^±±ai kU, mfW*0 2 EE»>*S*T a 7 v-iy>-y5-i'x#©#%”- j: 5 ciitin v, K, Sig^SEfr-fcmiiS^EiiL, Xm©W*A%X ' (§E ®*i£b"'>$EPE$-e©iSS) §^a z ktf? ■tzm^rebZo intact * $&S*A#±T a a._ 0§a„ ttz’, $M^e±©^gpKti, SjflffinJfig* center kifi^wxha„ a©*- K0ig*SfEA©f§£EOv>Ttt, casing * 5ISiH Sb-TVia0 &®@*S 3), e J: O T9f§5§ *vcv> <5 „,, . t£&, £ '"■| ■ - -’J " 1,15: - ., .,,. iShip- . i m - , . Model (scale ratio:l/23.5) Intact Damaged Intact ' 1 Damaged ' Length Lpp 101.0m 4.3m Breadth 5 16.0m ' 0.681m Depth D 1 ' -5.7m 0.236m Draft d - • 4.37m- 5.22m 0.186m 0l222m Freeboard / 1 1 "■ '- T.17m 1 0.33m ' 0.050m 0.014m Ro-Ro deck height ; 4.84m 0.206m ' Displacement W~ 3821.15t J 272.69kg Height of center of gravity KG o.87m “ 0.25m Metacentric height GM 1.62m 3.12m 0.069m 0.133m Natural period of roll motion Tr 9.40sec. 8.43sec. , 1.94sec. 1.74sec. 105 StiSSkt GMrf=3.12m (## $®) *'€> 1.27m S-C551D Kms-ftTSo 2.2 nWife 5E@m, MaSE@f%filfOW*®(LxSxD=50X8 X4.5 m) -eff^Tio h 18.75 m ©{£EK, gmfra & a a 5 cihel^o smte ±©?$g?7kffi:ti:, ®g^|6jc 50 cm 1 IS tmwTgmuA (Fig .i#®„ :©* {Sff-cJ; p#®f®©¥^ffi©5fc* i5©'C, a ckEJ:D $Pa9 E±0i#@*m & c k»$-CS5„ SSC, ^#%7#$B9E±©*&dfyX Angular frequency (radAsec.) Fig. 2 Incident wave spectrum %@kA<^-oTWA. &%, SWEBfiC^b’ri-* X9&BAEL, ?E±©*©mil&#gLt. GMd(m) M4lf-CJ:OEi$2:«&, ilSIHa D±T@k&6%%MILA. £fc, 2 S© b*r**X9E %l-c=mwo> mmKum-ewmvKc 2.3 AJJ$ JONS WAP Ex ^ h;V-eW5Si6H77„3=4.0m, b°- 0 -0.5 7^=8 sec. ©?mUK6A#mk U-cm^A. Fig. 2 », ^©AS’MX^X b yvoitms k %## £i£E L T VI 5o $ fc, fc * -5 J: -5 K, T,[sec.]= -50 -40 -30 -20 -10 0 10 20 30 40 50 . 4/fWm] ©&(£©*> kk#9!i■Z^Lx.k-m.h'fi Heel angle (deg.) ■otzo sac, in]gg$ascov>rsi^57c©K, ^nozST 1 Fig' 3 GZ Curves and amount of water on deck in ©S8@IkfiX>-Ci>a„ ; 1 -damaged condition j 2.4 EEX jWI mitmmz* omwM | BJRSFig.SKiSTo ffliJW(;MI4L7c!f#S ' /d y iufc„ cne»«tD, ## tGS© GMrf=3.12m TI4,- P t)S5 1 1.5 ?sc*v>it*?to^5o $%, / 5; E##U, GM„ S.ViSt’fc'MMMfi14/hS < %30 - *, S@*jakg*@Sl4 GM„ k k i> C*§ < *5„ C© 0. 0.5 r k i4%©4 5. ciftHj-es s„ ax-L^K^ kmatREA^ /j\g^©r, m#i4KT#E±# a. ?©*&#, *mo©@m*!@<»D, g*vc< <*5„ -^, ffi-c.' twmmiM v^©-c,. aa#Ri% k A,km^» Vi» f©A», mmaE*V^ Heel angle (deg.) f <%3. 3.2 center casing ©K2W GMdf2.02m Fig. 8 14, center casing center casing I4$M?^|% ©*©%#]# [Rl©##&%lf, 8*t4iB(8®iK# < 3 ©T, §8# 14 center casing A%^%ekR*©m±@l (SltE-tffl) KWM-3. GMd A? 0 0.5 %2mMT"C, kS*5E6EA ?center casing ViS£- k It^ry # Vi© 14, #±0J5 ©? T&3. GMj »t/h$ViSk*y§ <(E < (®IrJI4, center casing * ?%Vii§-B-k IH D"C£> 2>o 44c, 20 ! 30 Heel angle (deg.) ##R® (GMd=3.12 m) TI4, center casing *t%Vilg o' kUSC, ±& ^ 4l 6 "4" 5 S-L'iS $, center casing © -®K, #%*K:AVi-catWI©lE:BMkMSV)k#4) WM, $zMZS$, 41/TVi5©l4##im#K®r & P, #m@#MUK6Z:©# 3.1 S/C.'iS$©g5S . . . .. X.^»?s^stvt;vi5„' b*ik, Fig. 7 14 center casing *t%.Vi#^©, @%#© !X^ -by ©#*©#% 14, ^ y ^ fi© S 62k©HE (x □ y yy) yiSS.GM, ©g^S^u-rviS. Eli^MEo^T-e & ©»?#<, $&, % m a a * % - a oh oh Fig. 5 Time evolutions of roll angle 4> and amount of water on deck w (no center casing) 108 i- " Roll angle (deg.) i f Roll-angle (deg.)—^ ;—Roll angle (deg.)—j —Rollangle (dog.) — _ Roll angle (dog.) — — -40- ' -20 ! 20 40 -40 -20 0 40 20 , 0 i 0 \i4 . - « pi 1 - - , [• 5. t wl T n*T ,, : 10 • Capslz^ <1 Time Time Time Time "J Fig. fj i 15 (min.) ! 1 1 - (min.) (min.) (min.) • 6 <(■ water, Time I 20 ? 6Md=2.89m i SMd-1 - ' - 1 ■ , - * - * i 1 evolutions n 25 on t 1 , 34m, r deck . 30 , w i of, (with ;li roll ; iu center angle : mi?9 ' in S 8 , 4> in casing) . ? 20 and 20 - 0 .. 0 i- amount . : ,5 i 5 ( '' _____ r. -/ 110 of .10 . .Capsize. ' 'Time Time Time Time Time '15 15 (min.) (min.) (min.) (min.) (min.) 20 20 25 25 30 30 W ater.cn th e deck (96) 3 W ater Ingress rate (% /sec.) .W ater on d eck (%) H eel an g le (deg.) g. 7, 0 0 0 - — Experimental (no □ O ! 1 center — , : : fd»1.50m, fd-0.33m, 1 1 2 1 ' : casing) results GM GMd , Fig. 2 2 i r™ 4 I (m) i (m) 9 in irregular amount Effects 5 3 3 O 6 of of waves water freeboard 7 4 4 on deck on Fig. 2 © o> 2 i O) © w . . heel 8 (no 10 Experimental (with 0 center — angle O □ 1 center 1 lfd=1.50m, casing) : 4>t> fd=0.33m, 1 i ------O D and casing) results 1 GMd GMd(m] GMd=1 H GMd-1 ------i GMd v3 2 (m) in (m) (m) 1 1 3 ) . 79 -a irrengular m — & 3 O waves - 4 109 110 mm# ommmm a ro-ro it mnxu z * •e#.x.6iT5o-Tr k&GMd E3:^f— ®, RO-RO K-t-a-Ek % kj uTS/h-il&K * D ikmc'mxu-th 3 (/c=7.42 #B#R@ m)J tt omtit&iotitez- o-R-cmm§ u3 z. t•&%>& (GM - 40 f" "1 ! GMd=2|02m 1 20 .— sr’ 0 Oi g k I -20 H SBR " FfPfF To! 0 10,-----.15-'- 20.., 25 30 Time (min.) j , L 40 il 1 GMd=1.27m- 20 . ti. A O B 0 U>- ' * apslze -20 V s 1\ -40 ____ i____ 0 5 10 15 20 25 30' Time (min.) ‘ s Time (min.) Fig. 10 Effects of initial heel on roll angle 4> and amount of water on deck u/ (no center casing) 0.7 :------1 0.6 O damaaed . .... A Intact v , " __15. 0.5 0.4 ---- 1------0.3 O . O -----mean line 0.2 ■-■■■oeo" -O damaged. 0 -- A Intact 61 A 0 0 12 3 4 GMd(m) ,GMd(m) Fig. 11 Natural period Tr and damping coefficient BeW of roll motion in 4.2 Mwm^oimmgm 3) ffiJ:M*kj8#0Ml@©gS IIWOsI*^ Fig. 12 EET„ XMi&iDmm -#E, k»&B&&B, mam&Ej: MJtB 1/25T—Sk LTt>S0 ##Btuning factor = 9 S-fkT s 3 kA#3 iirv^So ;;tb, oulcor T, A#K©A^K& 0 o oa 1.79 I □ □ 2.44 1 g. (deg.) (deg.) > .. > 2.89 « < X *» amplitude : amplitude amplitude o P* ro c Roll .Roll O e cn I'd In e ' 1 e~ s B £ 7 (m) (m) o >□ amplitude water water,amplitude Relative Relative (%) (%) D deck deck on on . Water ' Water t? 1 o o o _ Do (%/sec.) (%/sec.) rate rate X> o Ingress Ingress 6 Water Water - (deg.) (deg.) O' 6o angle angle Heel Heel x> 2 1 0 -Fig. 12 Frequency responses in regular waves Sq Water on deck (%) Water on deck (%) Water on deck (%) 8 I! ll > m ^ § l r< ^ sr I a t* r» r a I S3 «P w Height of water on deck (rri) g g (Y :-v" 3 $ ' -! 4 eX g) !* ir " •dS-i jf!' “I I'S 9+ . E5S W 'S a- m§ o* CO n S S gt Ak W ’ g . & fcc tit a R ,d ' £ > £ X"° =6 > % * $tl to X' 9r St & R ,~r\ Ofr Vlv -CO r\ . 4" * (X «X e a 3 St a- (Y n .% ' 9t ti- n d 9- n> 2 E #i- s 3: U« Si 9% ft 8- -II e R #c o % a 8 n ttf ti- .H» -v5v .-B- @ % r\ t-r 54 Af M- B \JV X- 4, d E fa <7 vJ*- -% s T 1 o :S # » X- p ^9+ ~ 4- r 0< R ; Ft 00 x- Q R :ta (X 0 * Oft . S' 1. iT to '•(X M St ,a * ° % R ci ~x * % 4 rr 8 f r * >. as -B-dS ,r <4 4- xi id, r* St 9r >. V 5 IS -M n 'X -7t oi -« S i 4; 8 C' a ^ 4 1 M )r "4 s O SLg < 3 CL CO ICD CD ?r Is r :l # > I ro -ro 3gf% 115 RBtRCEB, *M, *SS*^OSE*%*§ < L, WSlOfii Sfcha* 0 Cf sugars 3. . mm^r-a f*LE iHd range ftfis?3£ffUL, Fig. 4 fees c k**rs s. ua>u Ad *@3emr%4tf & k@t,fL, &A, #@*©#KB#E t*B@$*i3©r, £k bsst6h „ v . &L, ±E^L6T##BE j: 3#%e&B, #%»#(-# 0 , % k»?r§5or, emm^e©#i^c#m6 tiokStotiSo ^mo*mmrB, 0 E666wku56,^AE^g6#k Lr G% §1.79 m k OO g?ck ft D ^ ? T® 5„ 6. # m . RO-ROMSg@lC SOLAS MW1E#^ § *L6Mm® ttz, OT*S-$kL7ciI*tIk, $W¥ERO¥ ±a*EiSs k^o#±*@k o# & > (i) &m&#r# 30 mi l* Fig. 17 Stability and instability in Hd—fi diagram G% vM$k*^se #4)iB/J'S <, §V^|q]E £ 3 . GAfdA^S B#iB, *BBS*LT LW2L%t\, mst, BBI3r-t?n©gr &-5o Hd (2) center casing #©#^B, BkA k*Stt®|CM B^fiSSSS (0.33 m) Kl$18^Wv (6=0% % 'I'So center casing #©#0 B, )S Ez&T®J Cl@£4T 3 . =0.33 m »$^r©ytiI©X:?- h;5R:63.Fig. 16 Ear ±# < ML6#0TB, center casing #©^a#* L^ L6 GMd -CB^jaoM*-C^MEA»^ 1450 f"Vi„ r, L?E63. %Ka%< &-±ei (3) mug*o^m%fT?Ae*, CM ITU < k, E Hd K , < B3MAf#@*a6 k*c & B-)£©fi(0.4—0.8 m) £k3©T, ABXf-1A^6 tfM.Ztitco ttz, 'S@*tffi#k®3 *tcj®nrv)< Fig.l5a>6;ba>3J:5E, # am@b& k*fflg6#CJ: 9, ##©E#Aa^f6-3 C ktfto 6 BMk k b E Hd *?{STL, E*L^f fr-otZo <&%. sfc, 3 kMa*#^f 3. % (4) SM¥EfiO¥i^*EiSdtt, -ist^©f±* orji8«, r®f4J-rao@TJ-rm*j-r% ®@ejk E8 9 t^t)(&Er/<7>xT3 C kA%*^A. HOC HyillSfcSDjSl^*^, Fig.4©#EAE#©?6# k B, OT*SOii*akSEAO®TC*S 6##^%. @*SO^V»t> O^x kSBLTfr < CkE63. 3. eur, GM„=2.44 mffli) C^E$egBa?£f±*; 9 ©# (5) mm%3@mm<, *6m±#jEm#Lr^< ^Cli, ¥EEEti-tirm*?k $ 9 BSt«iE63. $ #mrB,%B is. B-SOEOEBR Kt3.a&BCO$i 6, GM,=1.79mOJ:5 E?##Ba##E?fT6#eE ' m=Tr%4 K##k#@*m&mn#-tiru <■„ B, @36^*7 yx^ErSSfc®C63o 6*:L, ®E*ffl|g©iE©EB» ?/l\§ <69, #@©3i?vt/f-A: mamok'owmr/;? >x-f 3*>b, ^E%E^Emm tn^®x.36 5 K63 kEErsSOk^x.6*1-3. &k 6Mmf 3%K6M@6or,: 4-&Ot#m@k L6 (6) S?@*ja-Sife©(SE*EI8@S3fffL, Hd~4> ti0 g%E, g&S'L'Opgjvi GMd=1.27 m TB Hd=0.4 m (@#A)mE±©T##B6^»CkKj:^r, #%6Et tL#&Lr&, ¥ ' #/fBrmB@#m&63e#Herf3 c k®?rs 3. 966 tt^gcS^^fSC L^6 66wo CZtrB, SE*fflE6 k*Bto6j3:%ffl^r^IZE^ r, 3EfkB±S66v). %?r, %#Rl@&#EL6a:, J{iME@©ifi^$giKS5§ 6 k*C i vMffi-rzK-3tix¥W$&Wfrmii; ffiwikstomtob 3 Hd ©Eib, BSSSfiSl^OE-fbOffi ktK%EA@m*WbL, a&Ke@T3m*k63. S&6Y, @%^#ms6B@a%?r^3. $6, # ■' 116 .Wmm& , 1) The Joint Accident Investigation Commission of Estonia, Finland and Sweden : Part-Report Cov- mmotzib, Fig.A.icu:-? 1 ering Technical Issues on the Capsizing on v 28 its#'&§X6„ isis ©*©itiA 9 tt 1 ' - September 1994 in the Baltic Sea of the RO-RO S(vao Heave, Sway ^|6j©@Eili Roll )5lRl©ii!l!bE,Hzt i Passenger .VesselMV ESTONIA, 1995 J T/J'S S5>C, W±©*©66S 7 2) - I. W. Band: Hydrodynamic Aspects of the Sink ing of the Ferry , ‘Herald of Free Enterprise ’, (M-s-nych <-© k-§ Trans, of R. I. N. A., 1988 ©*©S'C,'fim Gi Xoyo ic A 3) N. Shimizu, K. Roby, Y: Ikeda: An Experimental (&, J?o) li^-e^X. ^fL^c, ' ~ 1 Study on Flooding into the Car Deck of a RORO 5>(A £2)=h tan Q cos 4> 11 ■ Ferryvthrough Damaged- Bow. Boor; ijbumal of I tan212 j sin <6 j the Kansai Society of Navi Architects, Vol.225, . . , 1996 (to be published). 7?o(& 42)= — A tan 12 sin 4> (A.l) 4) H. Bird,*R.P. Browne ; Damage Stability Model ^^(^T-f+fTtaH2 J2) cos <6 J Experiments, Trans, of R. I.N; A., 1973 " K 5) S. VelschouJ -M.'1 Schindler-: RO-RO Passenger . ; j Ferry Damage Stability Studies -A Continuation cc-e, r kdffyy i if 'i ’ . i, ' - -16^ U2 ' / 1 1 Mm .*> 11 ' i: i nl' '. i , of Model Tests for a Typical Ferry; Symp. on RO -RO Ships ’ Survivability, 1994 . / ; ,. - , - 6) I.W. Dand : Factors Affecting the Capsize of T=y^ 2+y/»(fo 2+ vl) ; Damaged RO-RO Vessels in Waves, Symp. on RO -RO Ships’Survivability, 1994 , Jjr 1 1 v *'f/=Afff{(o+-y- —fifo)(l —cos (6) .7) D. Vassalos: Capsizal Resistance Prediction of a v. >! •. . 6 i/ ’ 'I l ; Damaged Ship in a Random Sea, Symp. on RO- : +T/,fehL_C0S RO Ships ’ Survivability, 1994 , , - / :, ,, , ;,, , . ^ ^ 8) Some Results of Medel Test, IMO RORO/ISWG/ ' 1/3/5,1995 ’ 1- f' ;l; 1 1 1 ' i. ‘ 1 - ' ■ ' • ' - ‘ - , 2 - 9) tfffi, -Effl, mm, /Nil: RO-RO JtSSWffiSOE* ;,ccr, ±tf K v b ' =d/dt, i:f&W -i-i1 / T7'":'-r-rlf^T7“ i .. t1 1 i r? I No water , M) .. : ;Fig.- A. 11 Rolling motion of a box-shaped floating body , with water on deck in beam seas - - - ro -ro 117 %(#)-#=»- L~T~U (A-3) a+oz/2 K2 f>3= , f>«= {!+&) G0M0 Go A/o ■t vi§ztiz («= or q\ mmm. (A. 7) Edb’tfaffiS A(=0), &=a-^K^L, (A.l), (A.2) (a .6)S:t-s=o k»aA*#ma-c&a. 9 S$-(A.3)SC{tXra0 @6K, A, & KfKd'Tta k L xumt-rz’t'm.znzo Fig.A. 2 «%#© Roll A w/i^a+-^-+/ij 61+mli A+»zyAA=0 (A.4.2) p-0.05 ZZ.X, ■g —tf.fcmtD A sin i ■ l / 4 r ( 119 1-12 : IE* - S Position and Motion Measurement of a Free-Running Model Ship Using Template Matching and Error Detection with Encoding Human Judgment by Shinji Ninomiya, Member Summary A new image analysis system for a motion measurement of a free-running model ship is developed. In the present system, a target is traced through template matching procedure, and error identification is distinguished by using some characteristic parameters. The tracking procedure by a human judg ment is supported in the system. The change in the mutual correlation coefficient of the image and the contrast of the image are used as characteristic parameters. The characteristic parameters are projected on a characteristic vector field and the error identification is judged on the characteristic vector field. For the verification of the present system, a target on a rotating disk with a constant speed was traced. The error of the rotating radius remained less than 2% and the mean tangential velocity remained less than 0.5% respectively. The measurement of a free running model ship succeeded with satisfactory results. Moreover, it was confirmed that the judging error identification of the present system was very effective. 1. Sff H ##b 14, (High-speed semi-sub- ’ mersible Vehicle with wings; JifTBSUT HSV EST y^X0^#SS14C usimkto btiz »>*, io b is, isb Fig. 1 Free-running HSV model used for experiments 120 mm# з. Analog recording Taking VTR images by CCD camera ia, - m * ##mota©mw#fyxf AkLt, Digital recording / ? r*B a at a#& s am a at t 6 * *A^j:Tf##^@t*^f3%&**LTw3". L Decision of &L, *#%T**kf3 HSV Fig. 1 initial parameters fj:'!)K:*#^B%Tt5±, ^faRcia^^xh^y TF Decision of location I'#W#0lB#©A##*%kf 31 *, #@P#R^ by correlation method @MK@m&#&i-3Zkim#Tt3. $t, #±*0 ? Database of auc&&t±9*#*%i,vt&, ^a-tAaa©?-*- Judgment by characteristic characteristic vector vector field &RmT3Ck6#Lw. 1 *#%na, ** •THRESHOLD LEVEL Radi us (m) Fig. 3 Schematic image of characteristic vector field L t A, f >yy- h Us (3)^K:a;f. ^=l-W(f)-A(f-l)|/g (l) Ry=l-\V(t)-V(t + l)\/B (2) P* 1 o+l Rs=1 9xBc(f,Q) nr czTA(f), y(f) Fig. 5 Measured radius of trajectory of target on ##g, a KM*CUktm. Bc(A ,) (f, rotating disk (i), (2)gu±@#0 3>h9Xhiq$A;t*L, (3)5t#M# Speed (m/s) kLTmw6. m'CX6Ko3E 3. liiimaro^E -maaTBgf >f-y/l/±KHSVK@iNL^%#tRmL, 9 (deg) n y h u*: t @ & Fig. 4 c, m&qig&meimmaorHR f flf ft Fig. 5, Fig. 6 . %#Af* / ? 6 Fig. 6 Measured forward speed of target on rotating #6m^&@m»0deg disk Stt 0.12 m trjfrfLT 0.118 m, 1fc®m& e* § < * 9 , imm©##©& -kVt-kvf ?d 3 7h?a-^Ei DIHl-WSfL5o ik^&L < »?7272&T;b3 kSfcnSo $@BBTKi@JZ m^oH-SI^PSte-r 5 k ®B#E$M/®±i3$EJK 9 *W A CCD */7 (/=3.6 mm) £fHMBE*f LXXS < ## 7c7>v&An@-e%;kEio, wwsm-cmmawz mW#©f-f &i5im Ck«T@&H. (4), § -tirPoCin^ ©##^ 6 me% e^b®® sw® l 72 *?, ©?## «#%-#- 3» X= .2 flsxV kce-eme##Ek&&. ## i+^=0 (4) iffl-Ctt*EEEES*LX^ 3 g+SJi?SSBfSJfSi$AT*S% AT Y=jlbijX'y’ (5) ##L, H-I^$±©«§g|iSkITfflWc. ::t(x, y ) «@m©m##, (x, y> 3.2 iSBfcES Zo'-miN 3 c kT-mtoKSffllKii mmmET©#m#8©m#m# (@s±rmss©&E t#IEf 3 £ k*i-C§ 5„ #=3 k UT, l/nyl- L/C t©) & Fig. 8 EiS-To iSF«7i@©@E SIDE VIEW CCD CONTROL /- CAMERA UNIT/iZ<- 1 SHIP I (a) low-speed turning TOP VIEW CARRIAGE 22mp MEASUREMENT (b) high-speed turning Fig. 8. Sample picture of tracked path and photo Fig. 7 Schematic view of experimental facility graphic plane 123 tif&fr oTV>3im£tt^ftSk*^v>k^?WIi«Sfr£ V>„ h;>©^«V)f3i© wm& 20-30 ea?$ 9 , jt#%^%v^gEgrr#^T Fig. 10 Measured path of high-speed left turning stfrctilebit^y 3y^mv^c*?, 1 xr (model speed: 1.5m/s) vTh-fz'O 8@>@g-CS3c UnLZLOftSWEiSSih. y- h y y f- y y' 3 #@g »**§ < &3iSiS®EireJ: 9#<5§£LTV>5„ T&S. itum-e«, mmaiiA#* § titzm^ izxMvmmzm 4,3 8HHeS m-*i\ w{mwmz.tikxmmm^mz.\t, afsc Fig. o, Fig. io c, {mm.®# xvismmmzis vznm j: small kf yyy- ivyfy/eJ: smail©F=geSE ■TS yx-r g^mssomiiSFiffl cmm mmo *EC 3s 5 k*©y-f xa#*# L f i) ? 1 -! M • |-, j (!-.,:■) 125 1-13 (SHfg SS^E^©^*#) ie a ;*: S E -&* i I I ff IE r # m %*** iE it in fa H: 5:-** IE I f ffl f %** A Study on Flow Field Around Full Ship Forms in Maneuvering Motion (3rd Report : Flow Field around Ship ’s Hull in Steady Turning Condition) by Takuya Ohmori, Member Masataka Fujino, Member Keiji Tatsumi, Student Member Takafumi Kawamura, Member Hideaki Miyata, Member Summary A continuous effort has been made to investigate flow field around two full ships in maneuvring motion by means of numerical and experimental methods. Following the previous reports a finite- volume simulation method based on the Navier-Stokes equation is applied to the ships in steady turning motion, and the flow field is thoroughly studied and compared with measured results in the present paper. The degree of accuracy in predicting hydrodynamic forces and moments is improved by revising the numerical method. Detailed measurement of the flow field on the vertical plane at A. > P. is carried out in the steady turning motion and the results agree well with numerical solutions. The typical characteristics of the flow field in steady turning condition is revealed by the numerical simulation and the relations between hull form, flow field and forces are clarified. »©*k , i. m w m < m&ti a %%©#?&% e i'tafco % tc, x ttlf CSSEcotx-C-SSSIIllcpOlS^SEEjjOrhSlSfT X, IMO G J: vi, 71S—A.7 it. 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P.efBfiCoviTfT-DTSoH-HEfflttzEfL ' 31 v >-c S'®® L T V > 5 o ** —#E*?* k#BrT@ 3 location o f meaHtroneni Fig. 2 Schematic sketch of velocity correction in flow Fig. 1 Locations of flow measurement , measurement 127 #E@}£§ o-x lx2x3 Sfx5„ E.5 o K8B* t-f, M*©SKontfi5„ 0E»Jx3®fcHC *^©^*#±T, a:1, x\ x3 [%#©#a-, 6k ft-gSE-t^E k 5> tLT v> 5 k L, o-x'xV^O- -pVaiX(fflXr)=pf(s)Xr)Xffl X‘X2X3 ±T#B rc, nmtift ;9 9 £IE =pFtu2i—pF(wr) TBEZB^fT^ A P(Xi‘, X,2, ssfrssE X,3) ©#EM? h;v r=X.‘/‘+X?/2+A?/3 Eov^t:, ® *© H5 * ©Zi® (oi, 02,0)=(ro cos ( r =-frt‘ & r ©@E©RW\#m©m*©a#^^H /oF-^pr=.F —2loViaX-|j- —,oViaX(a>Xr) —(rPsin 111 i _-i '-,- '-csttto©»* i) %ck& Tabel 2 Condition of computation ^LTt^o £fc,~ luE©tf$?(Sk±fc®tVr b, its®® tt*&©%m©% Reynolds Number Re — 2.835 X 10® Number of grid points 19099IK 1 X i2 X(3 = 101 X 31X61) m&#L,TV)3, , Computational region (xl-dir. before ship) 0.5 x Lpp Computational region (x'-dir. after ship) 0.75 x Lpp \ - 4,2 ^©s&k ^iri&s ,; Computational region (£J-dir.) 0SxLpp l v . v mWtmEAa k, m*©emm Mimnimum grid spacing (z'-dir.) Sx I0~3 X Lpp Mimnimum grid spacing (<2-dir. at midship) 1 x 10-1 X lpp K# .SR221A. SR221A v 0.06 Prev. cal. Prev. Cal. Drift Angle (deg) Drift Angle (deg) SR221B 0.02 *: Prev. Cal. 3 6 i o 3 6 9 Drift Angle (deg) Drift Angle (deg) Fig73 Comparison of measured and computed hydrodynamic lateral -force ’ Y' and yawing moment N' of SR221A and SR221B, horizontal axis is yS 129 SR221A - SR221B Prev.CaL i Prev.CaL * 0.1 • (a) r=0.2, /S=0deg SR221A SR221B Prev.CaL (b) r*-0 A, /$=0deg 'i Prev.CaL " SR221A SR221B (c) r=05, p =9deg Fig. 4 Comparison of measured and computed longitu dinal distribution of sectional lateral force Fig. 4 fc3s?-„ Kffi iE0, ma$T-ftcD^|6] • sfitoc-stLTfc'd, ,130 -•—'— --- —i— — —----SR221A— ----- tV'50 tctih, B USS© (r't yS)=(0.2, 0) © S. S. 1 W$t£ brjoD, $l»>u 6© k ft#T3 k, ± 9?miEE56 ka% ^5o #Em*#SB© S. S.3&S S.S. 1 K »>tfTOgfcE ?©%#«#&<, tssto c-srra »gBT&3k#%.^^5. **>, aS#m#T©@Tm#A ©EA*W*i < m-5.El=]A?S5Ai, ^©ESkLTii, SR221B H31iti-55©*7-tey b»H- (b) 1=0.4, =Odeg | SR221A k:©yjftgttA^tf6iL-5o **, 5«Ji?A?d H k‘$STt£^fr *B+SffiM©P411i 6 § & I -at o vW#@A!&5. I _____ OJ !§ 6Ki®*> < Ar»C, fc&WiStoE Iffisan —Fig. 5 1 SR221B ijtm Fig. 6 A#miET&a. 3 >? (c) r=0.2, p=9deg Cp T 0.1, ##EHA©EA%m@ • E©EA?*S-eSd ft Fig. 5 Distribution of computed lateral force SR221A. SR221B. (b) (r\/?M0.4,0) "^-o.i 0.0 (c) (r',/J)=(0.2,9° ) Fig. 6 Distribution of measured lateral force 131 rv>a„ £A, l, yotymGsome#-?*a rnsj ©@^©ggg ^nmtfcmmonm\±m-e, cftsstva. ttz,vmy y-^oAmmaum? y- BR@aA$r%^.rnack$a;Lrvia. AOB ®ECifc^T*Efl-)£-rj£ < yntyMi&fRV) f^%»$caa. < k rssj \z%mvm Kft, #%W!&5#eEE0A*#^LTW5A;, SB lss^a ± 5 a^c^siyrMcmrao mm ifi< 'CttiS»#^C*-3-tViSo WtBrkimJtiE^a *?o < kiDx.TM!l©*Bffi< KSS^^fona. rn ^#r$D, && D*#aAH%$Lrviavi. SHI^g 5 ©mt*-r^r tror &nrv>5*?, r§Ej©gp ©/J\$V:> r'=0.4 CDS^-ttffiOS^-J: 9^:# fl-OgBfOil^ FBEJ 0&EAk*£»>< jiak#^0 TW3A%, fiSjStfifirtt*a^®L&a. ##§P (i~-p07*n y^C^HtSftao *E5£< OnPfl-r ti:^© %K%@e$tma k, /ISJlgKSOMBifctrn^B A&gS&L, ©Sflflrti:IE©:A£5§£Lrv>ao ti"5£©—Stf©£S@i® kj&ftc $ k k> 9 rurvia—*f© f&fc&^x-mtHDfrintm^ tr-^a k' SR221B Fig: 7 Contours of measured and computed wake, (>", j8)=(0.2, 0 deg) Fig. 8 Contours of measured and computed wake, (r', £)=(0.4,0 deg) 133 Z(cm) SR221A - 0.2 SR221B Fig. 9 Contours of measured and computed wake, (r',/S)=( 0.2,9 deg) Cal. -30 -20 -10 SR221A 10 20 30 40 Y (cm) Z(cm) 1 V 1 1 j 1 Cal. -30 -20 -10 SR221B 10 20 30 40 Y (cm) Fig. 10 Vorticity distribution of measured and comput ed longitudinal vortex on, (r', £)=(0.2,0 deg) E7v-A© B tiaE©J#£ti:@B©ito*3£v>o &A, ## Kb < „ e, mm-' t, me®®®t & o, mwmttm&momm< vi7 y-A© AVmfficom&ffi <, u LtzT&X' Fig. 16~Fig. 18 C7St"0 HICSt© (i helicity 134. — __ SR221AJ ---- SR221B Y (cm) Fig. 11 Vorticity distribution of, measured and comput ed longitudinal vortex wi, (r', /S)=(0.4, 0 deg) c> : SR221A SR221B "" Fig. 12 Vorticity distribution of measured and comput ed longitudinal vortex (S&B Lamb Scalar) LDf VHfacDMZmto '?%£>% Ls=u SS^BU^SPriin-fiLCDS^HUttHOgtS-CS.5>„ X S.S.1/2 Ia .e. ■■ SR221A SR221A SR221B Fig. 13 Computed vorticity distribution of longitudinal Fig. 15 Computed vorticity distribution of longitudinal vortex oil, (r', /?)=(0.2,0 deg) vortex w\, (r', /9)=(0.2, 9 deg) *B56< KS5 6 9-o©#«#@B S k*©3SS SSB^ 6©IM® Big® < tss sisirik * v, (r', j3)=(0.2,9 deg) ©#&% fc* J:oT@l ®S?A^§ < vr n5o S*tocBfiSS© t*;pygi$ 5 ffi b #WFfi#®%%& & 5S®-o (r', yS)=(0.2, 9 deg) ©S^li-O A.3 6©©, (/, /S)=(0.4,0 deg) Tti t*9, (rz,/S)=(0.2,0deg)-Cttfrtf© ®L^EBK^t)fL&V20 ftnxT, 6SEC '5>ii9A ?SE69k :&-p"Cvi5o 6. # S ' a © 3. fct, SSIt k$Eti:tg©MS£#x.it, Fig. 14 Computed vorticity distribution of longitudinal z:k&<, vortex o)i, (r', y9)=(0.4, 0 deg) C ktf*SgT-^So JU±® ±5 »B%K±-3-C, $S"Cti, o k ©R% t u-caamka (r', /?) #k©MmE0V2-c#^&)m^3. • - =(0.2,9 deg) OfS-6-tiWflJomB VE7V-AOA6SEl$*Bti"55"ed-;V <, u m.y u-j^ , Fig. 16 Computed helicity isosurfaces, ,, Xr', j8)=(0.2, 0 deg) i i - i| 5owst**«s sk • mm o a., ^ mwft^Wssfrbmik-rzmt v m. Fig. 18 Computed helicity isosurfaces, (r',/8)=(0.2,9deg) m±© $ 5 c, mm^omm^m < sm# ' k k , j®»J5S@SW k r7°D^7Efd'3fi§jio XWifcWV #&fTci72o $72, Navier-Stokes%rES©^cilrh$?C$ Xty < o 3©%o0#0{aEHf7x?7x±@i©^©A©# ?XgWB©y 5 a i%- y a Vtfz?72. M#©ifgS£ifci£ ^kTffll©lE©A©^cyj£LTv^„ $72, #A©% ##L72W& MT©$ 5 »%#*?#&7x72o * -XA*>fiJ»C$ SE*@T*?#* 1. SE^O^gK^WScH-EL, ^©mSSV72„ &gg&L?w 3k#^.wf, mfi!i]©®tt^fii]T-5$<, mis 2. ^&mea < # omzfomxm^z-tfrb, ±m©m#?m©^E, t® ;gr#3Ck&#L, *H5:-efflvi72Mffms*? ©#%TE©^|=l© A &#± L X W 3 *S* k LTU awm##©mmk Lxwjix-^iz. t *mm\, 3. S3C, Z:?©mm&jtRLTt, VI71/-A0A 72 o D , eb#k ±®j©^©*© 3. #mkMi%©K*&#eLX%mSE4:©%#m D k^5 taxis # # 3t K 5.0#%, j: 9 m-mmpg , 1) - *sm ekeb , sa%m &#m: m%mo# 3 itorgSSElfcfijffl ESifi^osEScggrsEgs (s-18 $mw,m, •eS5WIE&S'#oTVi5kvi5 c:k»i-c§ J:5» 8^:^###%#, m 176 -#- (1994) c om%m##i5]#K %) 2) RKEEB, *SEtil, lEPM!A, Sfflsf ' ‘ BJ3: Rtm©#EmW©8E#KB8fam32 (S- 221 LTfrbfia: 6 OTt„D, M## # kEAtMi), B^i© mm i i i i I 139 1-14 3EJ —* 2EM 0U JH % A Component-type Mathematical Model of Hydrodynamic Forces in Steering Motion Derived by Simplified Vortex Model by Keiichi Karasuno, Member Kazuyoshi Maekawa, Member Summary One of the authors presented the component-type mathematical model of hydrodynamic forces in steering motion on the basis of kinematic forces acting upon the both ends of the hull. The mathemati cal model can describe well the forces X, Y and N with large drift angles and tough turning motion. The rotative coefficients in the model are estimated from the static coefficients at oblique motion. The rotative coefficients thus derived are, however, somewhat different from the ones delivered from the experimental data of turning motion. 1 In order to improve this point, the authors will now break up the hydrodynamic forces into the following components, i. e., ideal flow force, viscous force, induced drag, cross flow drag, cross flow lift and frictional resistance in the normal sense. Then a simplified vortex theory is called upon to evaluate the ideal flow force, viscous lift and induced drag. - - As the results, the present mathematical model can describe the hydrodynamic forces acting upon a hull in tuming/drifting motion with a fair accuracy. The model also provides a sensible insight on the mechanism of hydrodynamic forces appearing in steering motion. . ffcS tiSo i. m w iptti, -rw-MMWi±^^-nwBz ©assmx * 1 i®i^T 3 fits x, y, n &mm? t±tb z, Ziumb a$rt£c tZo L*V, *WM EilFtif UT § cf-C, Yf} k ds vmmtriti KM¥-r a t MffigW. 10 B ak»^joT%fco zmt, mmmm^^zmm ¥/&8¥5H is, is b gE@©?8:< %a k*§ 140 #179# {m&vwwixit *& X ##©##& Sfr^-Cn a ©T, f©RgK SEkSrSo f CT, SAAKKWl© ts^xl- a: 7077 9-m*©$#m@©'3 tc ft&k#t}*w®iiai It ZtiZ K fci^J*Lfc§g|ggg£g&fT^&T»:„ %r;v-ei$fflLfcMtrjt 2 AT-ffi4> • ^-gf • 2. 61 ’ " " ' ##t%E*j&f 3###t 7T » 3 C k CT • ; no ’- ' '. 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' #? -c?gm#©m*A kt, m#%,. imrsms*? SSSSB1/2-L,, (65^**) ©tiE§®55$S Ar,r ©MB mm#©-*©m%Tm#^;L6:h'5 (Big. 2). . . £ii£*¥E (1-2M m-r©#a-#-cga-f k (Fig. 2), , . : "'. , , " ■ a#@K ■ - 'Mi . . -■_ ~ rif.r=ma/{p-L Pp‘d)‘(.2/2'Xfr) ,_ =l/2-Lpp-(m'p)-(.2/2-Xf r) ■ „ 1/2-Lpp C /W. r= — rripKp • Lpp ■ d)-(2/3 • zy r-)------, =l/2'Lpp'(.- im'u)-(.2l2-x/-r) j Fig. 3 Vortex model of a flat plate in turning motion (ideal flow) in-lpp jc ______r__..._____L riaa.T=myl(p-Lpp-d) ‘(2l2’Xa'r) j 1: =1/2 • Lpp • (»iy) • (2/3 • z„ • r) i ! - | =mJ(p-Lpp-d)-(.2l3'Xa'r) ffiSHe ' " 1" - * _ _=T/2 ' (2/3 • Xa-r) r,a,r=—my/(.p-Lpp-d) ‘(.2l3'Xa'r) Lla —Lla, o ~h Pla, r =l/2-Lpp-(-»z£M2/3-zyr)j (2) < =my/(.p-Lpp-d)-(v+2/3-Xa ‘r) ! ©#^&a. * is, _c ©Mc±i, mgEgt^A © X, F, ! =l/2'Lpp'( —My)-(v+2/3-Xa-r) (3) k*5o **, C ilK j: o TAfa%E%#A H X,.r=0 Xi=my- r-v- --■ - ~ - — K.r=0 y,=o ' Ni = — my’vu I k 5 g — .—.- i- - ■— -' —— —.—1 k»a. a >mta#KjSB kcs-c, c©ms i±msE¥g&m? tzbox$> a*?, , ■t a mtfm d*. %E k®h-t a rte, r ©m &-€-©#EE@#(0,0, ©#A6, Egmmiciaaf a c©#%-ee@%j(.3 c k*^c@ z tt±Sk*5„ ,------1 ,------i $ > c&a**, &K%#t#iBLT%m*piSafaB# C) S @ ______’______i_ __J______!_ ifcb $• a e css k » a „ , ; fiUt, $mmh(u7v, 0),t 5¥Sib’ <£ ImScEaE!® (m, 3.21 i 0, r) ■t5¥Ecovit$B^C (u,-v, r) ©#^&#^.a k, rtUi^EZSb(m>,0) kEK2Eli k, c >THKatwf2%: (0,0, r) k©mia^b*k#xTS^©T*, ©¥®, SHL6S^*-L'@©¥E (Lppxo') k»«I© x a¥mE±c&fa—o©### k @ec x a##-* ¥# (Bxrf) t'tfMbtaikSfiS (Fig. 4). ©#R%%kT#R$A3 (Fig. 3)0 L ©m^-a-2 m©¥m#E^im («, t,, r) f a#&, G#T©^©^@ STITT (2 )5» 9 Hu5E©^®¥®©S**?iJffl-ta k»tif®Wi /V=/V.o+/V, r (m, y, r) "C®E@ L, SS^ci]^@©¥Ett (-.y, «, r) T^E =mJ(p-Lpp-d)-(v+2/3-x/-r) ■ta„ C©3g#Ki-DT^#**E©&68&Kk)*:oT± =1/2-Lpp-(m'y)-(v +2/3• zyr) . fask #4®;K. F/flV = 0+T/jV. r y gE ± a-*f©^fe®^ r,y.r=mxKp-B-d)-(2/3-yr) = — ms/(/o • Lpp • rf)-(2/3 • zy r) -mmmtiz (Fig. 5)0 a#©0i =l/2'Lpp'(-m',,)'(2/3-Xf,r) , t*f i. J-' ,59. : . r,ma=0 + Lima, t , i 143 Fig. 4 Modeling and vortex model of a ship in oblique motion (ideal flow) -ti) 1 ls,0 v+xr Fig. 5 Vortex model of a ship in pure-turning and turning motion (ideal flow) rlP-r,P,o+r,P.r flmp — 0+Pimp, t =1/2 • LPP • (LPP/B) • ( m'x)-(it—2/3-yp-r) =i/2'LPP-(Lp P/B)-(—m$-(—2/3-yP\r) SEgfil/2-BK 1/2-B K 144 m 179 -ij- rI ns — 0 "1" JTlms, t f ' c ©#, as nr m s -c & -r s m m st * z>zx \t, =l/2‘ Lpp ‘(Lpp/B) ‘(mrx)'(—2/3*y s*r) p-rx-ri-cDLxT#^3Cka*m$3. ;^es:$##) — V------!- _ ©aa, /;ama«©aa, c^ //s=//s,o + //s,r | J 1 ar, c * ?as<@©& 3as^%%%m#4''r% 9 #-$ E =1/2 • Lpp • (Lpp/By-( — mx) -(zz.—;2/3 iy s • rX_._ n^x, m#K##©#s% ©6k > Kutta 9, #3 Ztib Kutta ©m;gmm#:T©#E/mk)3 k#S#m %5%^©6k > » 3 6 © g A@®%m, ic^n -e©m#m A. kt, ztizti X 7 D -£ k* © 2 ^TcMfr^SSE aoneKutta ©#ta£-r an* (tmmtj tv?#) a, + Ccio ,(—TMy+Clo'COS yg) 2}*y 2 (12) %ti?n k»a. J:^TB@£toMca Lv/,o=l/2'P'Lpp ’d'(.CLrcos yg)-y U CDi=(Lpp/2d)-{C'Du'(m'y +C'u-cos yg) 2 Lva,o z=l/2'p-Lpp'd-(.Cla-COS &)-v U + CoLa'i,—m'v+ CLa'Cos yg) 2}-sin2 yg (13) T&3. k%D, $fcSlS}J±DiolLo (=Cd,/Cl =tana; a H§}£lk 3) mm# ^•*kO%1-ft) &*5k (Lpp/2d) • {Cdu• (m'y+ Cir cos ft)2 tan J— + Cpia-(-m' v+ CLa'cos yg) 2} ^e.®#mmtt*v»o l^l, %#m#ia%akg*^E tan (14) nmm^x&Zo ®my-m.mw-x COS /So = m/7«2,+ (xa • r)2 uakca&e,©m%m^%_65%a.is#ai©m »mt, 61 ft? M±© Kutta ©,#EAQt» 5 k, SSSS «WSatfx^5ia, U^L, 53 J: 14, m#m#-e©is# //, r—jTl/t r^~Pv/,r , r * ’ ‘ -• i =l/2-Lpp*(wy+Clf-cos &f)-(2/3-xs-r) 14#;Uiv>= %?-C$m@©##, #©mflj 14 Kutta ©# I'm/, r —Flmf* r *f" 0 ' L-cismm^ammTa t#x.a (Fig. =l/2’Lpp*( —W2y)*(2/3*a:/*r) 7)= r . /»ia, r—//Ha. r H" 0 i©e, am@©a@ rj.r«Kutta ©%©a@?&a 11 =ll2-Lpp ‘{m'y)-{2ji-Xa-r) ^sismjioimasists Pa. r —Pla. r H~Pva. r Pj.r~Paf.T =\l2-Lpp ‘{—m'y+C'La’Cos 0a)-(2l3-xa-r) =1/2 • Lpp • ( C£/ • cos /S/) • (2/3 • xr• r) \ (17) , Pa.r^Pva.r bis: a „ *53, @EZ@6 (0,0, r) ©##E 14 TV. r=Ka. r= =l/2'Lpp'(Ct a'Cos 0a)-(2/3'Xa-r) (18) ok*a„ 1 ' ' k*a. 2) ' , , " ' '' ' 4) s§i@i/to ism mu i 6 (i8)^©%%m c#? -cew%mm© a?) S0m»C^fflLTE9£t*§&5fL»ao IStMT© L/,r=l/2'p-L}pp-d-(m'y+CLrcos /?/) ' S#@%Ai4, ^etvenogttoc^Pfre •(2/3 • Xf r)-J uz+(xf r)2 Dif,r = p ‘Pf.T’T/.r’ C'dl/ L»y,r=l/2* p-Lpp-d-(-m'y) 1 — Z/2’p ’Lpp'd'(.Lpp/2d')'Cbu •(2/3-x/-r)*w • (m'y+ Cif • cos j9/) • ( Cl/ • cos /Sy) t Lma.r=l/2-p-Lpp-d'(m'y ) •(2/3*xyr) 2 •(2/3-Xa‘r)‘u Dia, r=P’Pa,r'Pa.r’ CoLa La.r=l/2-p-Lpp'd-( — my+Cla-C0S /So) = l/2* P * Lpp • • Kutta k V 'C f) k T) k 'kTS/lI V fe©k-ra0 -c^a* 5, a k 5) 3 frfiX.Y.N 3*oT, ms.®-Ct>mLt\elVZvte]E v+xr - Fig. 7 Vortex model of a flat plate in pure-turning and ' turning motion (viscous flow) 147 X=l/2-p- Lpp- d-{Cts+ Cla) ^iRicssr •cos A'(2/3 -ay r)-(ay r) L/=ll2' p-Lpp-d-im'u+Clrcos A) —1/2 • p' Lpp • d • (Lpp/2d) •(y+2/3*ay rWw2+(y+ay r)2 • { Cdis •(m'y+ Cir • cos f3/)'Ci/ Lmf=\l2‘ p-Lpp ’ d-(—m’y) + Cota • ( — W»+ CL • COS A) • CL} •(2/3-ay r)-M •cos 2 A--(2/3 -ayr) 2 (19-1) Lma=ll2-p-Lpp-d-(tn'y) Y=-ll2-p-Lpp-d-(Ci,-C'La) •(2/3 -xa-r)-u •cos 0/-(2/3-x/-r)-u La=ll2-p-L Pp-d-(—my+Cia-cos A) —1/2 • p • Lpp • • (Lppl2d ) •(y+2/3-ayr) ;i/w2+(y+ay r)2 •{C'Dif(m'p+ Cpf cos A)* CL k*a„ — Cota •(—?»»+ CL • cos A) • CL}, 3) mm# ' •cos A‘(2/3-ay r)2-(-sin A) (19-2) a vi t©k-#-ak,4.1.2 1V= — 1 / 2 • p • L%p • d • m'y• v •« ciaa ©#mm « & <, 4.1.1 —1 /2 • p • Lpp • fi? • £/• (CL + CL) •esE^fcsm-e©w#©a.»^ivc#S(£i5r a „ •cos A'(2/3-ay ?-)•% Kutta 0# & k UTlSSMAi 6 g 6#£Mir a —1/2 • p • Lpp • d • (Lpp/2d) k#^_S (Fig. 7). -x}-{C'du’(.m'y+ CL/• cos A)* CL £ © i a cuts?#© 5 *i, #mr©mm + Com • (—wz»+ CL • cos A)' CL} %#©# km@r© Kutta ©#**g 6#%mmr a©T, •cos A'(2/3-ay r)2-(—sin A) (19-3) t A-e,mm#©a@ « fcftSo r/=1/2-lpp £ > C •{wzi-y+CL'Cos A-(y+2/3*ay r)} sin A= —ay r//tt2+(ay r)2 Fi=H2-Lpp cos A=“//w2+(ayr) 2 •{—m'y’ V+Cla’COS 0a‘(v + 2/3•Xa’r)} (22) •C$5, k&&. 4.1.3 %#m#r©m@ 4) 4.1.1 (m, V, 0) k 4.1.2 Oisez® (0,0, r) (2i)^;c^fm##k(22)^;catf&m#ci-3T&# 1) Kutta •&#©# Dif—p’FfFf• Cozy (y+z-r) c ± ^ am =1/2 • p • Lpp • d - (Lp P/2d) • Cow @0 Kutta ©# A* fct, (6), (16) 9 •((?%(+CL'Cos A)‘(y+2/3-zyr)} rv/=rVf, o + Fv/,r •{wLy+CL ’Cos A’(y+2/3*ayr)} =l/2'LPp-(CL,cos A)‘(y+2/3-ay r) Dta = P'Fa‘Fa'CbLa Fva = Fva, o ■{" Fva,r =1/2 • p • Lpp • d • (Lpp/2d ) • Cota =l/2-Lpp-(CLrcos0sHv+2/2-Xa-r) (20) •{(—w^+CL-cos A),(t,+2/3iXair)} k&ao-e, ^«, (?), d?) •{ —wLy+CL-COS 0a-(.V+2/3‘Xa'r)} amtK(3), (20)^i D k»a. F/—Fi/-i- Fv/ £ v k =l/2'Lpp'(m'u+ Cl/’cos A)-(y+2/3-ay r) cos A=%/•fuz+(v+x/-r)2 —T*m/ “i" 0 COS @a = ulJu 2+(v + Xa- r)2 =1/2-Lpp-( —m$-(2l2-x/-r) -C, mfW:*a©#-*KB9%A&±C»Vik^a. Fma—Fima 4" 0 5) 3 ftt!X,Y,N =1/2 • Z./v> • (w*t) • (2/3 • Xa • r) wM —l/2-p-Lpp-d-(Lppl2d) • [C'du•(m'p+ CL/• cos 0/)‘(v+2l3-X/-r) 1 •{?«»• y+Cl/ 1 cos yS/-(y+2/3:Z/-r)}-cos /?/ + Cota •(—>»»+ Cta• COS /9a)"(v + 2/3"Za’ 7") •{—wt»-y+Cta’cos ySe ,,(y+2/3-Ze-r)} •cos /9a] i (23-1) Y=-\l2-p-L Pp-d •{Ct/-cos/8/-(y+2/3-z/-,r) ; + Cta'COS /9i'(y + 2/31Za,7')}1tt, . —l/2'p'Lpp ‘d-{Lppl2d) •[ Cot/ •( Wy + Ct/• cos/8/) •( y +2/3 • z/• r) . •{TTz^-y+Ct/.-cos /8r(y+2/3 iz/-7-)} ■ : : •(—sin/9/) , + Cota • ( — 7?z(,+ Cta1 COS /9a) "( y + 2/3 - Za1 r) 1 /s,0 V -■( •{ — »?»• y+Cta'COS /8a-(y+2/3'Za ir)}, | Fig. 8 Vortex model of a ship in turning motion •(-sin/9a)] ■; ,,i (23-2) (viscous flow) N=—1/2-p-lJpp-d'm'p'vu ■ , —1/2 •p-lfpprd, , | ■ •z>{Ct/-cos jS/-(y+2/3 ,z/ir) ; (##Lv) &z.T}wmmi iw&Di) \zftwxm-t, — Cta'COS 0a-(v+2/3’Xa‘r)}-U , X=X,+X l v+XDi (25-1) —l/2-p-L 2pp-d-(Lpp/2d) , ; CICT • z/• [Cot/ • (?«»+ Ct/• cos /9/) • (y +,2/3•z/• r) Xi=ll2-p-L%p-d ’tn'v'r’v /{wi-y+Ctt'COS /9/-(y+2/3-zy r)} j. XL<>==\12' P’Lpp ’d ,v •(—sin/9/) •{Cz/'cos /9/-(y+2/3'Z/'r)-(y+Z/-r) — Cota • ( — 7?Zy+ Cta • COS /8a M V+2/3 • Za • 7") + Cta-COS/8a 1(y + 2/3-Za*7')'(y + Zair)} • { — y + Cta • COS /9a • (y j+2/3 *,Za • r)} ,, , , Xdi=—l/2-P‘Lpp-d-(Lpp/2d) •(-sin/9a)] . / (23-3) • [C'du'(w'v+Circos fi/)-(v+2/3-x/-r) ■bn'p'V+CLr cos /9/-(y +2/3 •z/-r)}-cos /8/ - + Cota '( — 77^+Cta-COS /9a) *(y + 2/3 •Za'T') • { — m'y-V + Cta• COS /9a ‘(y+2/3-Za ‘ r)} •COS /9a] 4.2 *5tt3S(*;T'(7)6m$(Z);@^7 r;iz* , • _ F=F/+Vta+Fo,- ,, , ,, . (25-2) ®0¥&©.ffiK 3.2 -cf J: 5 Kffi/hUGKj-am#* Yi=-l/2-p-L%p'd'mx'r ‘U :i j: V) (Pig. 8). c ^-e, ss :|, Ylv=—l/2\p'LPp'd LT#x.5 •{Ct/’cos/8/ ‘(y+2/3-z/’r) iCffififrTfxfe Kutta + Cta'COS /9a'(y + 2/3-Za'7-))'« v>„ 3.2 -exB^fc J: 5 CSS8K Km=—1/2 • p • Lpp • d • (,LPp/2d) > CUTisvi-r lot 4.1.3 Kx!+< •[Cot/'Wo+Ct/'Cos jS/)'(y+2/3"Z/-r) Afgm*0#ty/I/0(21), (22)^m^k LX, Ztl •{wo-y+Ctycos /9/*(y+2/3-Z/-r)} z z t K%a„ sn%, & •(-sin /9/) LTfct(4)5$©6©*5/iilfc 5o *33, + Cota •(—»?»+ Cta• COS /8a) • (y + 2/3• Za• z) c e.< 1 , 1 • { — »Zy" y + Cta• COS /Sa*(y + 2/3*Za* 7*)} rt=nP=r£s=n= o . , (24) •(-sin &)] , . . . , T&&„ iV=M+M.v+M>,- (25-3) i-oX 4.1.3 CSaU*gSft:^ij>®©¥St ^©SS#^ CCT B©¥Et K:»>-5S-aio-ti: 5 tMi*A#©A 16 , Ni=ll2-p'L 2pp'd ’(ntx—nip)-vu 9 , f©33-#x, y,n(#¥/), NLv=—ll2‘P'L2pp'd 149 •x /-{C'l/-cos ftr(v+2/3'Xfr) J:i&f n%7n -Sib (Xc) M — CL"COS f}a‘(v+2/2’Xa'r)}'U KmiSiSS* (XF) Xh 9 ' NDi=—1/2-p‘Vpp'd ’(,Lppl2d) Xc=l/2’P’Lpp-d •x'r[ Cbu • (CL" cos /8» • { Clasp •(v+xrr)z- C'lasa '(v+xa’ r)2] •(y+2/3"zyr) Xp——\l2-p-Lpp-d.-Cp ‘\u\‘U •{m’y'V+Clrcos P/'(v+2/3'X/-r)} Xsr: •(-sin fi/) Yc=—l/2'P'JCD’\v+x-r\-(v+x-r)‘d-dx C'dlh • ( «i+ CL • cos /So) •(v+2/3-Xa'r) Nc=—1/2’P' JCD-\v+x-r\’(v+x'r)'X'd-dx "{ — m'y-V+Cia'COS Pa'(v+2l2’Xa'r)} (26) •(-sin &,)] TlB-r^fc^-r^-So k&&. x, 3 frti x, y, n #, (25), (26)5SJ:D*4)#C»&0 X=Xi +Xlv +Xdi+(Xc+Xf +Xsr) • 4.2 • msfttitimzm-j < m^wtKom Y=Y,+ YLv+Ym+(Yc) K, ztizt ± s «&%*:& o , N=N1+Nlv +NdMNc) 1 (27) i -5 PCC9 ’ SSS k Lfc£4E, itoS@ ^nx7n— {ft# (y c), (AM & Figs. 9~10 KShho X' o exp. o tap. tJ—6 -0.2- oeap. Fig. 9 Analysed results of hydrodynamic forces Fig. 10 Estimated results of hydrodynamic forces (X', Y' and N') in oblique motion (X', Y' and AD in pure-turning motion 150 ' m 179 m* x\ y', x x, y, n com%Km-c, • Cia • COS/9a • (2/3 • Za • r) mY . • {m'y-v + Cif • cos (if • (y +2/3 • x/ • r)} *'**, >:+T+r-ti, (%&=eTn' GffiftO #WSfSfAk65 k,_*©fE*5„ _ —*l/2-p'Lpp'dj(Lppl2d)sC'Dis ------1) mBrnw-camm («, y, 0) • (m'y+ C'l/Y• cos 2 /Sy(y+2/3-z/-r) 2 . ^gp-css-r 5 s^s©m®-c$Lfc„ 2) (%, 0, z-) f 5W&m# x, gsm#©mm#K i a#ma & , 5 -*©#K*m©m&i#-;b-e-c#% H2-p-Lpp-d-{Lppl2d)-.Cka r'~X''K' t*o- ' •(—m’y+Cia-COS @a)'(v_+2/3•Xa-r) - - 3) i. 5^%«StMSC«W-5JgBS^® •{ —TMp-y+Cia'COS fla‘(v + 2/3'Xa'r)} '«(Kutta ©m r Wfln-r 5 c k-cs ■ (}]&*T)U -c»/k#e, 4#, ^tf;i/&^MC-C^ax7o-BtA©3% 1/2 • p • Lpp • d- (Lpp/2d)-Coi/ • (»C+G/ • cos &•) ; •CV'Cos fir (2/3-z/-r)2 ‘ ' , •c, a 4#, r ©T-cmt^j:.tfm#l5im#A©A-#^a&M*L, Mr —►1/2 • p-Lpp • o' • {Lppjld) ■ Cdu (m'y+ C'lsY A j:36 9 -C$,5. #9 KftiW '• cos 2 j8/ • (2/3 • Z/ • r)2 ±#%#gp rjggj fiO-6 g /^W+Oz) &fc$fc9SBitL$t. kL-,;£-fc -- -j,,— — - < r> ■" ' " : # # x $* mms-ctommtfitnt 1/2 ’ P'Lpp • d • {Lppf2d) • Cola • ( — »Zy+ Cia * COS y?a) i) #pmm: o ©snfcmmrn S195# (1984) 151 2) Nonaka, K.: Estimation of Hydrodynamic 10) Karasuno, K., Igarashi, K.: A physical-mathe Forces Acting on a Ship in Manoeuvring Motion, matical model of hydrodynamic forces and Proc. of MARSIM’93, Vol. 11(1993) moment acting on a hull during large drifting and 3) fflcp m, : Cross Flow tSK turning motion under the conditions of slow s i?6 speed, Proc. of MARSIM' 93, (1993) # (1994) id /]#=%%, mam®, mmm, 4) #mm, ssm, mmt ■■ ui ±jis : mss iv; tt-t.fr*) ®m%t\mtKDstn, ©» s 721 # (1989 ) S88# (1994) 12) SFJE-, KE-fin, z+miz: 5) Fujino, M., Ohmori, T., Usami, S., Eguchi, S., fctKDmm&imfrfrMiz 1(S2ig), ICanai, M. and Miyata, H.: Longitudinal Distri B9mBda#&#i64# (1991 ) bution of Hydrodynamic Lateral Force Acting on 13) SSS-, f&F-BP, S+MSI3:: a Ship in Manoeuvring Motion, Proc. Symposium K % # 3 aESSftigfffiStffct; ©SrL t>v C on Ship Manoeuvrability, Fukuoka (1995) (s 2 #)-am#0#&-, 6) asm mmmx -m^-s: i&m-e #217# (1992) 14) mu im#: c ± s 153# (1984) »• a 7) 4fcm-, wm; a 37 f/pcmf a-##, S195 # MC 37-5 (1993) (1984) 15) /NHE&, 8) W-Mt&mt %aymv& 25$, t, s ieo # U986) ytf5??AT*x h (1981) 9 ) f (# 16) f-ps-, sme@: t 2#-@m#g8#, ±®fc\m < ffifcti c vi t, w®s 2 e, Kgsimmm#0,S2io# (i988) W35SSSS4@yyd<^VAT*x h (1987) I fl } r- -'M1 i , u .! - 1 i i I \ I I 496-0/- 354-5" 153 2-1 IE * III ^ s* .III #* es** Response Characteristics of a Long Life Type Floating Offshore Airport in Waves (3rd report : Response due to Short Waves and an Attempt of Active Inclination Control). by Tsugukiyo Hirayama, Member Ning Ma, Member Flavio Ossamu Nishio, Student member, Naoaki Sato, Student member Summary The hydroelastic responses of a semisubmersible type floating airport, which consists of multiple removable units supported by column-footings in head sea are discussed. The emphases are placed on the response characteristics in short wave length range and the influence of lacking of units in this third report. Active inclination control by using air pressure in underwater columns is attempted for the case of unit lacking supposing replacement of the corroded or damaged units. Numerical analyses are performed based on the mode superposition method which combining the 3-D analyses of hydrodynamic forces (source distribution method) and mode analyses (FEM). In this report, the calculated added mass and wave exciting force of each column are shown for understanding the interactions among columns especially in high frequency range. The calculated deflections and bending moments including higher elastic deformation modes are compared with the experimental results obtained from high frequency excitation tests. Also the responses in regular waves are calculated and compared with experiments for different conditions including unit lacking, with and without air pressure control. Finally, the influence of unit lacking on response and the effect of air pressure control are investigated consequently. L ** -- : " tVr s-tfu Lgmm t stm-r »gl ¥688^1^9 B 3. $6E#m©^-y fas^sB is, ie b V mm. • $J(iP£fTV\ f©K© 154 H^Sfe©, gS#E^©^-y b (A 2, B2, Fig. 10M) Zmyfl-lsXiDkMtfMmmbfT^, ^©E, a-7 b& m&o&mmp%fifc Air Column ; AooP Probe / / SF4M1 P4P3 P8P7 P6P5 \ MOORING . ■ 2 AirColutm \ MOORING P8P7 \|P6P5 X F?4P3 Fig. 1 Floating airport model, arrangement of mea surements and underwater air-columns 1 Mmimffi&tmi&maigi&'Pi&giim 155 7-KSiBStl, zmov^-i F (106g, @E¥g7.5cm) SZviCKM^l6|C|B|S8lHlEd'ti:fclWO^C,*K i. 9-Z ®©»©jgEA6iSWjto;iatfia&i;:*x>'tV>a 0 ## CSn^.72i!lDiE»t4iaE^OTS5C® 9 Fm*f£Mt n-so 1 Measurement |* Target + - ,------, Command ,------, ,------, StLTa^O/E^ttllDEAk kfcC7-Vx®tfrLJlEIS( ------»&~H ControEer |— »| Valve I—H Actuator I—»* » nuktSiZZ t ,oL-.o»..Hoioi Draft—const. | Factor | 2.3 • $WHi£ I Disturbance 1 Fig. 4 Block diagram for control of air pressure SSmMtet/T-tt^ifeSlSChSESt°X F >0±TEi actuator 9 ±Tffitioim :&mmft6>, 9±mh., a. * 1= pd ©7-i 9 * ? v 7 a -1 x-mmzmffiz * a w %b*m&&#mb*. 32"*$a@gr$a„ ##*Am#i:*at^E®ftg* $9f32ttSHtoC im# fa*, 4-@{©smw*%g#k L-c^aEKj: am#* x OEE'fbS’B-pTviSo : (3), (4mopm.mkftttm'x, 3.1 3 ft3o SSEtozUD Pd, Pr btf-CM 3. ibZH'&h LtiSSSft,' if *®&& < S$-e 3.2 Lfcmiiits-a @5j:i)K:»?,-CS-CW3o iCTS, Bishop. 5>91 ES-s . Mth$?i2,,3) r-tt, (6) T^toBS^ffliASB^igTS L fcSS-fb §®i}i 3 „ ,* HVTUMbtlS ©Tib.5»*, WJ - me zftifg*©m#mm tf©±® ^ B&6#*#©# o') — ^ . z, y, «t-5 KIbVs £ i; nr(x,y,z)=nr(x,—y,z) r=1,3,5 1 (7) »?-CS5„ • ' ' “■ ~ ,zzr(x, y, z)r=~«r(x, -y, z) r=2,4,6. j:! . ' - u(x, y, z,t)=’2ur(x,y, z)p T{t) 450oD3£■?©"!?, %© =k 5 (Composite Func ' 1 / m ; i ,— -- tion) - v(x, y,z, t)='Zvr(x, y, z)pr(t) •(1 ) : ' Po=Po(x, y, z)±pt,(x, -y, z)' - p3=Pd(x, y, z)±p d{x, — y,z) (8 ) w(x, y, z, t)=llwr(x, y, z)pr(t) , p$=pr(,x,y,z)±pr(x,—y,z) C C C, pr(t)=pre ““‘ ti r F©±®@T,«r, Vr, Wr &#AU f6r B r h'0(D x,.y, r= ■ I i ■, * i i 1 1 • 11. ’ ' i ' > k^© .: "^(x,y>4=y £(*>y. 2)+4^r_//j 0(%,yj,z,) . Fr = ipCOJJ g nT‘Uri.Pt+pd)dS, a , ' _ , ' *■ , ; r=l, 2, •••, zzz . - (15) x_^G(z, y, z; xi, yi,~Zi)<7S fc± k*5-e§50 [ - 1 j 1 1 l | ' 11 ! I _i r (6),, , Haskind ©MHS,4) yy 157 VJy'frbhMafflfttfffUSftSo 66*#%©$Sg# Full Model (144col. x 32 panels) 4608 panels COUTH: FV= ~pffs,(*^~*^)^ ’ r—1,2, —, >« (16) k*s„ $#TKctizm'XM&fflfitDmmumm Z?*'y?Ltz±, (16) SC £ StflMISfiEffl LtzJ 3.3 Sffflz^mu -met 5 -tfy#©###m%©#^, 3 %yc©am% m%ibLt@m©^ss&m&#< -0.5 Hm mW&) k^{i©@Wt- F SS/ELEm^©^ &,*&&#% (t- FSO ^SS**, ##©, R#mm6 Two units removed, 16 air-columns------Efizoisw^- k ©±ssp(7) cMf sarnies no trim (air controlled) 5248 panels BTEk»S„ ())/+A)p(<)+(6+B)p(<)+(c+ C)p{t)=Fe ,M (17) c c c, ji/, 6, c BffLfwm, mm? t v yxx-r, a , b,c B^fL^w#nna, mwo @ZMA? h V y 7XT, mXmOT h V y yx^-S&So F tt-mtbSMriSmb'-t? h^T, (15)SCiS. # ftOPMtfcllEX Bffig£ C H B 5 mat (17) SC Full Single —-A2&B2 removed (no ctl) ----- A2&B2 removed (air ctl) oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo #00000oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo 20 25 30 oo (rad / s) 1 »(M,6) pgVZ/d 0.7 Full single, 4 oooooo oooooo oooooc saaaaa o o o o o o o o o o o o o o o o o o o o o o o o o o o o •o oooooo oooooo oooooc ji—-A2&B2 removed (no ctl) 3.5 oooooo oooooo oooooc oooooo oooooo oooooc oooooo oooooo oooooc J— —A2&B2 removed (air ctl) 3 oooooo oooooo oooooc oooooo oooooo oooooo ooooo# oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo 25 oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo oooooo booooo oooooo oooooo 2 j 1.5 Full single 1 —-A2&B2 removed (no ctl) 0.5 __J\2&B2 removed (air ctl) 0 20 25 30 10 15 20 25 30 oo {rad Is) (a (rad /s) Fig. 6 Wave exciting force on column in heave • Fig. 7 Added mass of column in heave direction in high direction in high frequency range frequency range. _ • > - 1 I - I I K#L Full Model -10 rad/s 0.76 — 0:72 — ■ A2&B2 units removed (air control) 0.78 — -I — — r-i I i I, I. I , , , , , . 0.74--- 0.66,— 0.62 - pgvyd A2&B2 units removed (no control) 0.72 — 0.68 — 0.64 --- 0.6 - 0.56 — I Fig. 9 Wave exciting force on column in heave direc- - Fig. 10 Added mass of column in heave direction at tion at frequency £U=10 rad/s (head sea, no air - , frequency 0=10 rad/s (head sea, no air-col -column) umn) . i tzckfrb, EzSS©z$cslt v>2>**, MLWiWtJK16titc3 9 AluSOffiiS* 1!< Wwai.i.ncj: *>'&?> *o, tavyacj:s%mzfflt)i$if*§ F $ (5g©#^*s R# C * 3 k# <*t>£k *>*#•*> So z.ztiz0 4.1.2 4.2 3.-V F%#Stf##l@J@l©B# (a--7 h L2, Fig. 1 #S3) #@#©#@%©—O 1±, h) (EiigffKJ:5jiE65»®S) & f©#^-3.-v F3m#©lS@##&-h&E@L'Cl3 < £> Fig. 11 g*©±T#, mm-/ > F ©vi-fn B*5^3.#@PT&mi3L-y h©m#&g&#, m pts/f -•?■% tf- / *?!. e> n, ^%©mm- f (2 %: ®k 3 0©{£SK0ViT^Mb, f©S^»KML'CA 6)2=10.5rad/s, 3% : 03=20rad/s, 4% : 04=34rad/s) 5#^*5-@B#*S:t# w C k*5#c *5@JiBS *VC V> 3 £ kimm-C§ 5„ *13, l^CSLft *o Miai/cti-T-* < -9-rx ^-;Wi^SScS©J±r, L/A=15~150 ©jASSffl (2^37 FM±) Cov^T^ifU $*mjlEFig .8 ©Jt-5 aiig+JJtt(B5ip.©fc*, hu P, 2 3-^.y F*HX0 #;c^s *^#Efb*5?i®S1L5©-C, S$CE$#PCJ:S mm# g§mE©3$$*k*CoviTkKltf3„ h©4 3 9AC|aIcmiE**5f^ffl-f5kLT 4.2.1 ^Ag*©fS@ ff-otzo y F Co^tttlSfekfto lE@im*^^4:©^±##©## (3:7 3 9 A#L) © -CW3*5, ±T®/tt@W/gi6»y :@W/9E^^l3 #3# ±T# mm, Fig.l#E)kffiif t-/ v F {Mi, M2, Mz : 6St, Fig. 1 mm) *13, t- D#)Sl/ & Fig. 12 Kflfco H^K^rT J: o C##fizfcRl± (L/A) *5 1~20 ©jtR%#&B©& (S.S9ESI-C A=91 m~l 818 160 1 mi79 # EXCITER (Unit L2) EXCITER (UnitiL2) •cal. . £0.6- n O.2 TO: -—cal £0.6- N0.2 , Zs cal. . n 0.2- 40 10 20 50 100 150185 10 20 50 100 150185 - . : UX ' ■ - : ' . UX Fig. 11 ^-displacements (left) and -bending moments (right) due to one point sinusoidal vertical excitation on L2 unit in high frequency range (Zi,Z6, Z8 : fore, midship, aft; Mi,M2, M3: fore, midship, aft; o>2 :2nd bending nat.freq.; ah: 3rd bending nat.freq.; m: 4th bending nat. freq.) . , 1 Ot, Heave 0@WM$® ( g±TSS®T®J, Z8 ) k*:© ttMtSfO® ®aE»E ± D (I^LfcffifXyXX T#6 T-fc #%9U©-g!l £ Fig. 13 KiWc. S/c’ffifcfT—X y b E-onTS, 1 *6tf©@WJ=l -y'b (A3) ©±E 4 kg 09x—b SitCi O 2%m ##E b V A t t—;u§4i:§*fctK^ECi SMTHESfir^TuSo @^6^3i5 CfiSlfZyx 161 Full model Full model exp . —cal. exp. . exp. . UX _ . U-X Fig. 12 ^-displacements (left) and bending moments (right) of full model in head sea condition (no air ' -column ; Zi, Z6, Z8 : fore, midship, aft; Mi, Mz, M3: fore, midship, aft; (Oh : heave nat. freq. ; oh : 1st bending nat. freq. ; coz: 2nd bending nat. freq.) 7 v open/ ■So b 9 A&9 k b 9 ffilTfclS close/hold Sr y gTS$S©Z$(e)<4 rad/s, L/A<1.84) E#CiSg©® *fir, iSi©m>aiM&a, (Fig. 12, xr-37-A »sn, Z7X^Mmo±T®i(Zi,z4)b m w Kifc-t, 1 xmfmgmmst ( Weight (4kg) on A3 unit F, fgV^/d A2&B2 unitslremoved (air control) ° ® 5 rad/s hold dose rnrmn nr rElectro magnetic vplve (Unit A1) hold 1111 Electro magnetic valve (Unit A3) "'ii A2&B2 units removed (air control) hold p v ' 5'rad/s, ^Electro Ji agnelic vplve (Unit C1) dose open hold dose Electro magneticyplye (UnilC3) Relative still water Wei l Fig. 15 Wave exciting force and added mass of column Inclination (0,,(y in heave direction at first bending mode fre quency with air pressure control in head sea (unit A 2, B 2-removed ; with air-column) s * a *§£-,_ imfemmccmxt a c t tac -9 a mmtct'z+frmi -rzi&mtf&Zo ztiz^i5[a©isiSft;11 c, #ggKLTW@AW. , 5. m ' m , SEtmic j: 9 msf asfr.-a a. mmm-# t mlau-cf# 6 iL/c±»Siai±MT(D® DTSSo 'i. 3 ees ©±TtitnEta* k ata**, $L, ±T^mi©m Fig. 13 An example of records from air pressure con trol test (Static load 4 kgf on A 3 unit) AKSfL3< ASKOAfOB Wd'S < is 5 a k *5HJ 6 #> k * o A. r 2. JSA*t;v , ZL-y hXMBLTfx--y^g. '£§§■ A^@ ©3 ?kmmBSbPk 6 Kf@*L, # W0MlEov>t, 3##%3W LA 3 Ki£gsS!l#14ffi©3.-7 A i 9 Ltna t-K^SCJ: 9i£ c ao mttsr^ESijgpc± 9 %*0±E#kaWt-^ v h fcftJJU mcj: 9#E mw.im-Tzm&omm'pib a *?, ommt v A) .LAB*, 4t0#A 6w-m*# 6 4tA. * LA#tt-Cfct 1:11603 7A0R*a**B<&9, w® A,a a. $a, cccam 3»&cA#, i7-^37A5;fifltfc^i'E7tl'-CB) a. t 3. mmwimoijMmmzm', a _7i-3 7 (2 6 LA. $ a i < A o A**, j®gO t^UK 14 $ * 9#i@k4M 6 fici aam#t-#i4*m k & ft, mmmi tit£ip^>tZo . , .;; » k* ©mkbm^asfmm <%ftA ma. aO J: 5 J: aBto^teSSmESJffllC'J: 9 EHS • 4. a.z:y h^@Ej:9±fa#e%e&ti5MS$^aA 163 A2,B2 removed (no control) A2.B2 removed (air control) exp. . exp. . exp. . exp. . exp. . co(rad/sec) co(rad/sec) U7L U1 Fig. 14 ^-displacements with/without air pressure control in head sea (unit A 2, B 2 removed; with air -column ; Zt, Zc, Z%: fore, midship, aft; oih : heave nat. freq. ; tui: 1st bending nat. freq. ; (Oz: 2nd bending nat. freq.) A, 3 7AT8PCfWn b mmmm, tmikvm BfffigcESE£, Effl^owsc® ALtmwz. 7-3 7AK±5OWT - h L-aivif20MS#©^Ctt@ St # # # SC i£ feme, i) ?u>70-h#mm#: msa^#n%x$g tiv£)S±£8®$l$, 1994 iS|lj@S-SWcD^AKft 5 £ t && <, • h+ 164 #179 # 2) to; 9) Bishop, " R. E. D., Price, W. G. & Wu, Y. S.: A m; No. 794, 1995 ¥ 8 H, pp. 7-12 - - ~ ~ - . ~ ~ general linear hydroelasticity theory of floating 3) Mamidipudi, P. & Webster, W. C.: The motions " structures moving in a seaway. Phil; Trans. Roy. performance of a matlike floating airport, Proc. i ! Soc.-London, A 316, 1986, pp. 375-426 Int. Conf. on Hydroelasticity in Marine Technol 10) Wu, Y. S., Wang, D. Y., Riggs, H. R. & Ertekin, ogy, 1994, pp. 363-375 , ' i ! R. C.: Composite singularity distribution method 4) f with application to hydroelasticity, Marine Struc i m s$#$$u3 z ture, 6 (1993), pp. 143-163 !. m nj #, 1995 sse a, ; 11) Wehausen, J. V. & Laitone, E. jV.: Surface pp. 219-230 , 1 ' waves, In handbuch der Phisik, Vol. 9, Berlin: 5) frnrn, s % mm79 5 Springer-Verlag, 1960, pp. 445-778 ■ ^S±S@©z&SIPfSl:#&—S? 2 # ~ iRi^vizScp 12) Hess, J. L. & Smith, A. M. O.: Calculation of non ©zBkwttisscov.T-, lifting potential flow about arbitrary three - S, # 178 #, 1995 ¥ 12 fl, pp. 225-236 - j " dimensional bodies, Journal Ship Research, No. 8- 6) liiT^m: mfctD&mmmftmcD-mm, % 11 j 2, 1964, pp. 22-44 i 1992^7 H, pp. 271-277 - j 13) Hirayama, T., Tuzcuoglu, S. A. & Chen, G.: 7) %M®£:: 1CA 5 s„ i Estimation of motions of semisubmersibles in 66 1995,^11 . i combined heel and trim condition by the applica- i , pp. 248-249 ' ! l_ tion of boundary element method) Journal of 8 ) Patel, M. H. and Witz, J. A. :■ On active control of 1 Society of Naval Architects of Japan, Vol. 176, marine vehicles with pneumatic compliances, 1994. 12, pp. 153-162 ! -International Shipbuilding Progress, Vol. 34, No. 14) Newman, J.N.: Marine -hydrodynamics, The '"395,1987 - r MIT Pressr Cambridge, 1978 - : < i ! ! i :• i. Gj-cjb- 0(-%4-6 165 2-2 ie* # ±, m ?f* ie* m* m # m Feasibility Design of a Floating Airport and Estimation of Environmental Forces on it. by Yoshiyuki Inoue, Member Shigeru Tabeta, Member Yasumasa Takei, Member Summary Kansai international airport was newly constructed and opened in 1994 at the site of offshore in Osaka bay. This airport was built on the newly reclaimed land. Although similar airport concepts are recently discussed in Japan, yet newly reclaimed land in the deeper sea is very difficult from the points of view of necessity of huge volume of sand for land filling, long period for construction and environ mental impacts. On the contrary, concepts of a floating land for the airport are recently discussed again. These concepts were discussed more than a decade ago, even though that was not realized because of no experience of the construction of such huge floating body for the mankind before. After these concepts were proposed, huge floating oil storage bases with million ton capacities were realized in Japan. Therefore, a floating airport should be discussed more and deeper to realize it. The authors wish to show one of the concept designs of floating airport and to discuss the estimates of the environmental forces. j: ; 1. n W t mmx b m&comm^m-ch a m ESSgfd" ¥fiU¥ljnO0 15, 16 0 CSA' 9, Fig. 1 esxf 5 Passengers in a year (xl()4 people) 166 3000 5000 4000 2000 1000 -Nagoy.^p - • m o o «« — Kagoshima Kansai Fig. Narita 500 □ ■ ------^ □ o Haneda o 1 1000 1 ------London Heathrow ^ Scale o o 0 - 1500 .V » Site ° ' ------O ^ of o O area 2000 in J.F.Kennedy major 0 T7 . cw o — o (ha) * rorjc , 2500 -' , ------airports Charles , — 3000 Paris ° o • o • r- <9 % Airports 'of Model in 'airports Airports de — floating Japan 3500 Gaulle ' ), ------ r,- 4000 j,a:h,s@&#KBcfsR#L&g#ag;& „ iELfi. Fig. iinik § ::1 2.2 6 * • mm# ¥r«9@S-ElHl^:i^7^l5l tc, 3. 2 K, fiffifBS %© J: : 2,800 ^ .- 2,800mX60m 300 m k X LT©±SB£ ^ : 3,000 mx800 y^V-BlZ: i-f3„ 5 Table h &3S&&. m ffifemRVW 1 t LTffi -a- 3 . 167 Table 1 Principal particulars of the floating airport Co it, w@r, iu±# #0#mE##&$f l.om±E(t»6»V)k#^e,ftS LXBXD (m) 3000X800X4.5 c„=o.9 k vfi„ mmvuj&M Cf It, SE4,5> kUSO^TS.F. Hoemer ©g#"' % draft (m) 1.6 7 f) tE*ftfc 0 f©#*, £@±B© O tt^Ifi]*tC/ t= Deck Area (ha) 2 1 9.0 2.5X10"3, 0=3.0 xlO"3, #ftTB© Cf It CJL =1.5xl0"3, 0=1.6 X10"3 b^tzo displacement (t f) 3 7 5.OX 1 0 4 Ztz, © SBEE E fEffl * 5 MES It, Peter Sachs ©3tE,y Zbt Ef Table 2 Weight estimation of the floating airport tfco Wa? - s *;kRtfSm&WEov>-c its @©@mwit#ieLt. ccr, suioiSE^SEit 1/ Airport buildings 1 0 0 k t f Pavement of runway,taxiway,etc 1, 1 00k t f TSMUSfflvitco Steel for structure 1, 1 00 k t f (2) #&% Greenbelts (soil and grass) 1 0 0 k t f #EAIt, Y^fi/^Wf^EtS&@*#Etot Fuel and water 1, 3 5 0k t f Rmwcit, ®=fS© k § k|H]SE##E® Total 3, 7 5 0 k t f E££tokS$g£to© 2 -doj &EEWT# x.o eas :* itue* sir 5 Table 3 Enviromental conditions ckEt^-cm-#L, mmmAit^mm&m^TTit0 Wind Significant wave ©##©* <*T©®©88lA^^»t: 13,o Co* B*56S-CW±SS»iSE§tL5W6gtt»?iS^m®#, <*> Accumulative 70% 6 $ 0.5 ±m##©mm©*3Fx*-;t/itm+ km ©*- 0.6 Openiiml probib i 1 11 90% 9 5 3.9 1 1.0 1.0 4.2 condition C CTlt#±@#& Fig. 3 © t Miifavn sidewind 1 6 0 1.3 5 0 Ooeyearstorm 250 2 7 5 *S§ 40 km, iff 20 km, *E 20 m ©SS^ETEEEU lOOyears storm 5.0 9.6 Earthquake 1 1 0 1.0 4.2 condition Tsunami 1 1 0 1.0 4.2 fkk@©M,a»Ej:iSEEIt 6 Jg-C, *?^B©#T(@lt 400 m#©m#^B) X500 m (@g©@Ei%) r&a. mstmjim [email protected] fliSSlfco Table 2 m, JIB 12 #M©a»$A^^a-k LT^x., 5 HIM (60 %&**= n-s^frvi, a#©i 2.3 m&m. etco & t:, @ ± 9 6&5A* t*o *#E:Bv>R©*?(tWE%?&^B&3-S k#t.6ti 3©T, iiTlt##g#B©#%EtSSIEcblt&tif) zmz&n-woim* fa20m, #* 10m ©kLTrPffSfr-ctc, •CgS^S^-COV>-CCi^lif&fT5„ Fig. 4 lt#±@#^@5M©##» 6 20 km Hfttr&E 2.4 EibSkS®, ®SE|fi]^'5S|6l»?E) LTOMSiBSi&tNi Table 3 ESvTt? ©Efii/to, SSi/to, Aa%A©^RI^kT$3. E* E, #©9F%3,,,5> EJt^TiFFS L L,Ar"»„ IS E%SB, *81 20m k L, %@±R^EM3LAM@lt% El'RU&VX, ' 3.1 sismt ioo tt&imvm*, m o * /iL^to©^[=l (4WffLt, m^Eit tZo (i) smm Fig. 3 The rectangular basin and positions of the float imzMimijffitj tmmtati t E#»-tti-$?u*:„ e* ing airport used for calculation of current force 168 t mmtm-e%> zmmatKD 1500 e^k^oT^SOtt, ##*:#&L%^k#©igB£j 1000 iaci5#w** wmrnhmmms): *?e*Si*g D±#^C kKj:3. hilSKSi^Ki5 SE^JEti^SC/JxSvi©;C, ®jSW»?/Jx§utscu? ©BBSjEE zmmLzffim&KDmzfc ± fa i C LfrLM±&£ 3©TC©ia »#^E3 k#£ 3 ------PRESSURE FORCE n, i Dma©m^#%& ------FRICTIONAL FORCE m»3^BA*63. , ------TOtAL FORCE' (3) , _ 48 51 54 - 57 , 60 TIMEfhour] 1 1 ( ’ ' ®tsto&li£“> £MWtt©mcffiEU17>, - - 111 ! " ■' ‘ 1' . , ' #^UT##SEz6W?$.3J®-6-k»nS6-Cov>x, f Fig. 4 Time variation of tidal current force acting on ? ©#miK*T0&ma%A l the floating airport ' ' \.< :>_■ ■ - - . <1 ’ v - • .i_v i ,1 . A. £©ne, ##kimm#k© 300 mmeiOrnkL, g#©a#IRK I k Lfc„ Fig. 7 » 3 © 1 *3KLT#6:h,&@#omm#*T©*#m%%e -B -FRESSUF E FORCE . -A-FRICTIO NAL FORCE ______. -• -TOTAL FORCE * J f ' ; w?2/2 T-M^Tcft 7?( P : W*©8?S (=1,025/m3) ,, ff : IRAmm (=9.8/s2) -*.10 .—20- _.J . -30- DISTANCE [km] 6>«( Table 4 Enviromental forces in the transverse direction of the floating airport Survival —-—— "Operational condition (kN) corofition(kN) W1thout 3.0X1 03 2.9X1 04 b r ea kwater b u 1 1 d i n 8 * Wl th 1.SX103 1.5X104 Wind breakwater force Pressure 1.3X1 03 1.2X1 04 without Breakwater floating resistance Frictional with Breakwater 1.1 XI o3 1.1 XI o4 res 1 stance Cu r r e n t Floating 0.8X1 0 3 .6.0X1 0 3 force body Period (sec) Without Wave 4.1 XI 03 7.5X1 04 Floating b r ea kwater drift Fig. 7 The drift force of floating airport in regular body With 2.0X1 03 6.8X1 04 wave b r e akwa ter Wl thout 1 0.3X1 O3 1 3.3X1 04 breakwater Toa 1 With 6.7X1 03 1 1.2X1 04 breakwater S$BE#Sl0%C5lhS^3KAJ^TCfll£3©*?5i g'% kw?##&6kE, L %#eiz:7WT#'g»BE#©Sgk&$&3 k, without Breakwater I) with Breakwater #^ii% 13 3 ® 60 m R8B) SWFrJ 38 3 (19 80 m FSE) II) B##&mmL72#A- -~ - Period (sec) #^i% 11 3 (%70mMIB) Fig, 8 mean drift forces of floating airport in irregular mu fa 32 s m 95 m mg) wave k»3. 'c©mm, iis^ossm^-Ac± 3s*Etit$ 3.7 t lzthto mmc&o-3zsn cm k>» < a@mecMaa<, $ 72###-c & 23.5 EifQiSiSO2t>(D-e&Zo cm kS^±f=91S%v :ikSk)iL3o sun k $ » 3 %.%m 4. 3 th m 13 z. k EJ: D ###©&&$#?#) 50%, ###©&# z6SC#Ltt$S*-e, @R*jtkL-C« w%i$Lfem%Lt) c t &£>&%<, @a#!k»726, mm©z 5 o** w ib tz f 3#^ k^ig§ti3»?, #ft©5SCjt-tBS»?^SK^H72© Table 4 B#me&&a872##f#BBk»3. CCTR@%e#l 3,2 IS'^rA ;. kill #©^m-cRv\ &72# ©F/i/7-fy-7xy^-ffiSrs, wcosmimmistco mT2 %7CTfrH, Z tfgg##&Fig.\9 K^-r wvh (El=0) (El=0) (El = 0) (EI=1.0E11) Fig. 10 Heaving amplitudes of each body and rigid body 7) :%Bm###ey?-: =7#- h -/\y FX"y?, ^TOIniSa, (1986) 8) ±3##: m 4 y F yy ? N ii, ms S, (1989) k»3AA, SSCJ:o -5J:5*H!l 9 ) b s mm-mm), &#, (1981) k o#m^ns, utl -*? 10) B$)igs^# ? x, 4-ES 6 at^oEtf^-f k , B*aam##8K #67i#, (1985) 3 k®k>n-5o 11) S. F. Hoemer: Fluid Dynamic Drag, (1965) **k> d c, mmt$c 12) PETER SACHS: Wind Forces in Engineering, B) Z&fXftbtitz£k £*L^sx.o PERGAMON PRESS, (1972) 13) S. Tabeta and Y. Inoue: Interaction of ocean # # £ SX current and a huge floating structure in restricted 1) : @@m#k^g#r|f, (1993) sea, MARIENV ’ 95, (1995) 2) uiffl&s: (T-wAxxazmtons 14) #&a±: 6 J: S 8 8 VoL5, (1991) mm, s is (1971 ) 3) B$imm%m# akssammms# mw 15) m## mftmmmmmte&mmmmizty? 6: MBgBSmmSKRt) 6g#I&©$±% k -: (igae^s^) iggfttCOUT, (1979) 16) : ##ommos#±og# • ngm 4) smm&m: B$mm6, (1979 ¥3 fl) xx y ho-gij (^oi~io), 17) Y. Inoue, X. Zhang : A study on Malti-body (1982-1983) Floating System in Finite Water Depth by Sepa s) emem, s, ±s? rate Region Method, OMAE ’ 96 i&mmmm&mmotcibomiwmmft ,» is) #$#, bifiee : $4#, (i983) ###m©#%&K-2^T-d?yy-ymg#@# 6) Y. Inoue, et al: Dynamic Behaviors of a Floating A—, i?s # 0995 ) p2is- Airport and its Effects on Ocean Current, ISOPE, p 224 (1995) n ') i -0 0 ( I V m i. I I ' r i -v 4%-o|-3%4-l 173 2-3 7* e m # m ie * On the Estimation Method of Hydrodynamic Forces Acting on a Huge Floating Structure by Hiroshi Kagemoto, Member Masataka Fujino, Member Tingyao Zhu, Member Summary The floating structures that may be used for such purposes as an international airport or an offshore city are expected to be as large as several kilometers long and wide. For the estimation of hydrodynamic forces due to waves or body motions that will act on such huge; structures, a direct application of conventional numerical methods is practically prohibitive, because the required computational burden is enormous. In order to get rid of this difficulty, an approximate numerical method is proposed in which computational time is drastically reduced without appreciable loss of accuracy. Although a direct application of conventional methods is difficult for the reason that the corresponding structure is so large, the method proposed in this paper exploits the very fact that a structure is huge to simplify the calculation. The effectiveness of the new method is demonstrated in comparison with results obtained without any approximations. i 5 k-rzmm&$>z>o lx ® 1. m m »Ktt, #&tES®©gS 14^6 < kfe 5,000miE'g-CS) m±®m^mmxn, a < &z 9, i@b 1,000s5®U*:ip ©%&©mm©m#d#A,K%frc#m K, Ztl£X®&*:mWk®i&m*400mES©SSVS <, Mii&KAza&msL, ^#»k-©mm 9, xh&K10ISEL < e,a*, ¥/$ 6 X 100f>%Z£m®M$i®&#tfra,, ##Ej)0k>a HFsrrSStt (Dfmtzm-eh a „ naAzs© H, g£tl, k'E J: 2>?]&±tz a b ©T aaKtAoTH, g*a©A%8b# UZ(i$CJ:5^5:E6il"C^50 x-iSii, Sd 400 m T, S5 m & A rtK^ESfLT, affcSk otascis* WM& < ss-t ack »5SE-e$> a „ »*a«DA%a *tm? a k, 20—30 m iPK »a t, ##%© & ## c % a ksnri? fl-sr* < & fiTSTlot), o , * kwsm&e,*, #####»?$tas;h,Tv>a„ k #ima & 9 , sk ^-siu smut ^ ©%#A i #&ft a»$, § ttiV©3£$ tt- $k-rak, -m Jimga ¥ffK8¥l^lOE S(z io@m©ama%ar&a k@frt^a. $goT, s ¥^8¥5^ is, ie a § 5,000 m, # 1,000 m ©@#©##^±^^©##1= 174 mm# a%5#©& (ES39m) T14 (@g* &*# <«^$-&5Ckd4Wger&3k#^e,fL6. -©Ckt^RK&mM;rm*'A3A6E, SS 1000 k LXi>) SS;£|r]E 1250Esli, <@:SIrIE250BS©tb m, 2.1 ...... < ms X . 0.5 '- 3 ' x=9o: XbIOObi i (a) Panel subdivision of a very long structure into • -1.0 500 panels - 1 10 20 30— 40 —50 - 60 70 80 90 100 ( 105 S56 ) 1 (b) Panel subdivision of a very long structure into (b) The lengthwise distribution of the singularity 105 panels ., tJ strength obtained by 105 panels in beam waves Fig. 1 - • . - . i r, , « , ,; , Fig. 2 175 rtffyS'i ’MOiitirakAzk* —$ CES^Sira^Ett^<, 1 )S tz'&ixmttz kiSSLT, ^#%g#T{t#$-eac kE-toT,, Sm&iS^S-tka r k»i-e§ £„ SS 1000 m, i® 50 m ©##E, %=80°, 2=100 m ©#%%^A#f a#eKov^7, SOOESitEtfSILT;^ »6>S©SS^iRl(x^l9)k , WBSB® # io g#&m sirens s-s-t 105 g ^itELT, Fig.4(a), (b)KTjkto 500gSTH-2 ?$tl (a) The lengthwise distribution of the singularity tcmwz k 105 a#TM#a iT,&emB*#ica < -scut strength obtained by 500 panels in oblique waves wa% Fig.5(a), (b)cs-r y (105 g£) (b) The lengthwise distribution of the singularity strength obtained by 105 panels in oblique waves (*=80 deg.). Fig. 3 A very long structure in oblique waves Fig. 4 176 m 179 # j- ■ 90 100 i-.. j . ( 500 (a) 1 The lengthwise distribution of the singularity strength (devided by emxj~y)C0S>L) obtained by 500 (a) The lengthwise distribution of the singularity - panels in oblique waves (z=80 deg) , , , strength obtained by 500 panels in head waves. ! : ! ■ 1 r~1 r ' ! 0.5 ( 205 BK) (b) The lengthwise" distribution of the singularity (b) strength (devided by e ■*<*■>-»>< ”«)- obtained by 105 strength obtained by 205 panels in head waves. panels in oblique waves (*=80 deg.). ': . ! i . Flg "7 . ci' Ffg- '5 ( - i r( _ ' ' .■ i ' , ‘ n ' ' . ■ : ' X=100. 6mji?#rP;gS»s£V)k i, n'x. 5„ LfrLK&b, M X“°° x-'l2xmu-tzctnxz»&e., c© Fig. 6 Panel subdivision of a very long structure in 3£$tt . - '• ' head waves. (205 panels) / j *■ ; \ ’ ‘ 1 " • . ■ o^G«\xj-Xi\-lK-emxrxi) ■ (2) . _. _ v \ ) Lv ' " \ \ 1 ' C ki^iLZo $£^>X, 6, am# < m&mtea^ks#* z.tiz 500 k?£-?x ® f>, g*©±% rtSB0=&?!|-Ctt 2osW#E j: zi&wpty&z ®(S5&6> ££ktz®5tL6u0 ktt, T -ti-.SZ kASarfigZ-fek kjgx.5. „ K* ruCBfrVTV)< cofLT, w< K, SS 1000m, "#50 m ©i?{$©^&41 (ifcg 100 m) © a#&, Wo esc^-sjLxsj-nvtzm KMznxLUvtmuzn, ztDmMkLx&mjmz Mb, Fig. 8 X -5 K, ^JO±WS% 20 gSfE# itTffiXitf&miiv9 :t>© kltSStvz* ' @jl, t©m©ma#%» i # 105 g 6, li-trncW:* m) ^©±T*a(2 )SKf-3T#M®S*'mt5 k® )£LTlfffU;fcs£SiB6#;ELT Fig.9(aJ i • %m±i •Af=100i Table 1 Comparisons of the heave force and the pitch moment obtained by 500, 105, 55 and. 30 X-o° panels. Fig. 8 Panel subdivision of a very long structure in Heave F.fpgCaBL Pitch M.f^pgCiBL 2 **# kc.d/a kc.d/a head waves. (105 panels) 500 a 1.13E-02 1.18E-02 105 b 1.12E-02 I.22E-02 a 988 ' 1.036 55 c 1.15E-02 1.19E-02 1.018 1.007 30 d 1.24E-02 1.06E-02 1.097 a 898 real '(,105 33 9, lx , TMiESvigfcS-1> hifrh, Tmatm* Fig. 8 CSrLfcJ: 5 ■ i . 1 10 20 30 40 50 60 70 80 90 100 Efc, LX, &Pl(D±ms&>* 10g#E^#!IL^#e (55 g#, 5B^K^@LA#e (a) Comparisons of the lengthwise singularity (30 ss) omwm 500 mx-mz l tzm&tsm. l x , , strength distribution in head waves obtained by 500 panels and those obtained by 105 panels. Fig. 9(b), (c)KW. $7i, heave force, (y ®$;b 9 ©)pitch moment 500, 105, 55, 30 tlzmZimVT Table 1 Ka* real £ 55 ■to mm 55 T6B^K500 ©##© 2%tiT, mm 30 LTiiESirsoo ©#a-© io%gg©E z h&iofrio : 3. 3.1 ...... ' HuS-Cli, V>;EgVi#f£ -1,0 »ti I i I l tli I i I * 1 10 20 30 40 50 60 70 80 90 100 (b) Comparisons of the lengthwise singularity (@:b266CJt^T^:§V3j:#£5>tL5o C strength distribution in head waves obtained by ©3:5 »g#©MkLT, 6S 1500 mX300 500 panels and those obtained by 55 panels. m e. StS 100 m (DMWM&XMt Z m&ZMfeLX, Fig. 10 EahhJ: 5 E 1800 m S (150X12) Kfl-SI L Tbf U§ ftS Soft, is© l9lk#&S 6 911 S ©##A^@©m@ (x ^IrI)^ Fig. 11(a), (b)Ear$-0 C©G#»6i l%IBk 6 ack**6^S. BPS, ^-i§C@L72:l?!JB-ett, Mg# ©#e k erne, k n v{m-QMmL-o-oTmzfafr?ximvx''\< % 5.ftSJKAo 7i 6 ^jg-ct*iEE-fr-fSBCMSu ±m k, S «13: k A, k*-tr n 1C 30 (0 =5roT, S©BRWKkA,(fgmLT Z: k t (c) Compariosons of the lengthwise singularity ^LTUSo strength distribution in head waves obtained by 500 panels and those obtained by 30 panels. Fig. 12 KarTi 5 E, ±a5«i?#Elot Fig. 9 m&$3rc^9, SSBSiSSSCJ: T E59 S ftT v> a* 178 mm# 6, f >^^(m BASlzS® J: -5 E #Ba. 2/^—0 at —h^z^d 1 (3) Fig.-lO- Panel subdivision of a very long and-viery wide -|^=0 at z=—d (4) ! "structure! (1800 panels) __ ■______I -§f-=0 at z=-h . -■ -■ ; (5) ^ h x, h B*g& d imfcovgfrzmi- b (6) ! (>2=0,1,2, •••) kWaii-t'-C, (3)5U9 /B, | W-4Z=0- iK* mT=d) (7) ------f— e±M (8 ) 105 120v 135 150 ■0=(i4je‘"r4-yl;h _';’,x)-cos fcn(z+h) 1 (9) £*U:9, (a) The lengthwise distribution of the singularity 9 ,-Fig. 11 (b) Kibfei 5 immv-fizm strength obtained by 1800 panels in head waves. (1st column of panels) istfiucffimi-zmm&mi-es, *© e-** xh acktfSTga. mm, m±mm 2.0 r—i | i j i j r^—i jj i 1 j • i | 1 r* —i 1 rr-j1 i j i #%E±#»#*E, t b, — Bg#^MlE x~U2eikx X%L — f.... !..... j...... !..... =..... f—frailrea ...... {'..... 1.0 -...... I.....i...... i.....|..... |.."q.A!!38iiaag ...... j...... i&u tz.^m\ -cb, #^^§Bse^i=ic e-'^-cmmizmk-rz t — — ...... - | V | I j" | | I I | ; - #x.6#L3o Fig. 10 E*r L fc J: 5 E##jgm^l@-E r 1800 Fig. is K^-rtv ...... - ui I I . ..I, I I I | j I... ; E, ^J®±MEifiV>gS:9-£ 30 SSESOAK ^SJL, % fU: 9 TmiEisu-c B,' 2 9UTB% . -1-5:.....I.....j....1...... |:.... I..... i...... j.....f...... I '"” <- Si® s a? x- ,,2eitz xmt-rt ktesb, xh,wYoni$& .-2.0 ■ i ■ i ' i ■ ii . 1 I1 ■ I ■ i—i .i. ■—i—i—I ©motb, ##A®$*5 e-',x-cE-fhfa kisk-ra a ' 751 766 781 736 ' 811 826 841' 856 1 87V 886 ' 900 ' tKivt, 372 : ( 1800 E-58 6 PJB ) m^WcUVtzmgkttimLx Fig. 14(a) (1>JB), Fig. (b) The lengthwise distribution of the singularity 14'(b)(6?lJi)E^„ 372 SST*. 1800B%T#WLA 1 1 strength obtained by 1800 panels in head waves! (6th column of panels) : igS k B tLT 5 „ mxa, ##A®$^ e-"x -c^ib-r a kiESfa*^ 9 Fig. 11 ' e, 6 $ aigp$M±iin7^T$rtai-eb, ##A® g'B-tfo k®$LT f) s6ffl±Fn1® * ^ t S! S fL 5 *5, m. m£% 1800 ®Sf (a) 372 (b) b/a Heave F-lpgCaBL 5.93E-03 5.87E-03 a 989 Pitch M./Lptf'BL* Fig. 13 Panel subdivision of a very long and very wide 5.81E-03 5.89E-03 1.015 structure. (372 panels) real t 1800 Fig. 15 Panel subdivision of a very long and very wide structure in head waves. (155 panels) 1800 BIB, 6%lgKO^?&4 Fig. 16(a), (b)E#f. 155B&?6, '$ C fc % < Sim^fiSX&Z Z. bifitofrZ o t-tz k, (155/1800)'= 1 15 30 45 60 75 90 105 120 135 150 0.0074 E $ S#3Ck 5 0 - © Jt 5 (mu) ms 5000m, ®1000m kv^fcg (a) Comparisons of the lengthwise singularity strength distribution in head waves obtained by A#m0mm#%##Emmsfts c t 40 m m 1800 panels and those obtained by 372 panels. (1st column of panels) mutism k-rsk, «E4ms (1/10mm) ©gmc kf" ft# 312,500 5*?, $ wix.#Fig. 17 ± 5 E 341SS?H-WWtg?S5 k#x.6ft50 HrS0E$ real ( 372| &*&*:&&&&$ (/mWTMmPT I ' ' | real : woo ' ■' ioag real (151 ass > JB3£. ----- : - - — & M - ifWAl %-8 0 vji\ — X=100m i. - Fig. 19 Panel subdivision of a 1500 m X 300 m structure L___ 1 r 1 . . ~iL_t_ Ji_V_! 1 IS 30 45 60 75 90 105 120 135 150 i in oblique-waves. (612 panels) i ■ 1 ■ (mg > ■ ! ■ 1 ■1 ' (a) Comparisons of the lengthwise singularity strength distribution in head waves obtained by 1800 panels and those obtained by 155 panels. (1st real I( 612 j_,_L 90 105 ' 120 135 150 < i m) (a,)—Comparisons* of the lengthwise singularity L strength distribution in oblique waves (%=80°) j- obtained by 1800 panels and those obtained by ! 612 panels. (1st column of panels) I (b) Comparisons of the lengthwise singularity strength distribution in head waves obtained by , 0.010 1800 panels and those obtained by 155 panels. ■ , (6th column,of panels) ' 1 ‘ . 1 Fig. 16 ' " -0.005 v -o.oio i 1 i Fig. 17 Panel subdivision of a 5000 mX 1000 m struc ture in head waves. (341 panels) ( 6 Mg > , (b) Comparisons of the lengthwise singularity strength distribution in 'oblique waves (%=80°) 0 0 01 002 0 03 0 04 0 05 0 06 0 07 QOS 009 obtained by 1800 panels and those obtained by § 612 panels. (6th column of panels) Fig. 20 § -2500 -1250 . 0 1250 2500 ^(D^coMu^it, Fig. 18 Singularity- strength distribution, 6 commit ± v, e-** ’-* (n»=/iwS7) t&s i' U(real part) 2+(imaginary part) 2 of ;a 5000 m X1000 m structure in head waves (3=40 m). CjsuTgtf-Sifcb fflMTrC it, 181 Fig. 24 Panel subdivision for thd analysis of a_ radia- ; tion problem due to heave motions. _____ ' 361 362 363 364 365 366 367 368 369 370 371 372 Fig. 21 The beamwise distribution of the singularity strength in oblique waves (%=80°). . i . 1 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800 (a) Comparisons of the singularity strength distribu X=100m tion (real part) due to forced heave motions obtained by 1800 panels and those obtained by 369 panels. Fig. 22 Panel subdivision of a 5000 mX 1000 m struc ture in oblique waves. (1681 panels) 0 01 02 0.3 0 4 oa 0 6 0.7 0.8 •2500 .1250 0 1250 2500 Fig. 23 Singularity strength distribution U(real part) 2-(-(imaginary part) 2) of a 5000 mXIOOO m structure in oblique waves (%=80°, 1 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800 -1=100 m). (b) Comparisons of the singularity strength distribu tion (imaginary part) due to forced heave Fig. 22 ESrjhJ:5"C$,55 k motions obtained by 1800 panels and those Fig.22SS 5000m• (a 1000m obtained by 369 panels. 1681 4. 3fE # * a A'6, Fig. 24 E 5hh.t5E, & 1 SBRTfSaae, ?©±TB 4.1 ii-SkfSS-ta£kA$r§a„ C©j:5»B SS-SJ (369 B%) Eio Ttf-HS flfcSS 1500 m, Table 3 -Comparisons of added_mass (added mass I"' 5. *'■■ moment of inertia) and wave making damp ing coefficient due to forced' heave* motions ZtiSTtt, mf#&k c k "obtained-by 1800; 369 panels. ’ SSEk LTEzBUTS/c*?, 1800 3%, (a) 369 (b) b/a 6 HSCiSffl-e§ 5„ $*• %#=A©#HT&k LX A33f%pgB 2Z 2.352 , i ' 2.332 i .h 0.991 ■®33/wfpgB 2L tt; #SMS&Of6c, k"* ? 0.121 0.123 1.016 fflv^itSo g*T@©@%&% (7/7X®S) k@ S,1~ES150) 12?IJ (ES1651~SS1800) $X #TaiAxmjgx©%#&#^&#^xM%#©mBme tRLTv ©!,,) $ $> C, k L.XigsXo- #k LX,. %Kf©mgV)g*K# cos titix • e-““'=^-(e‘"”T+ie-“,”z) • e~ia - (10) ...... : I ^ 2 » ©J: -5 E51fTZ$©Sto^;b-tirV3Hi:ti:, #6%f©KA© , 1) Odd Faltinsen: Wave forces on a restrained ship mfk|##WA^EX D , % cos &z » in head-sea waves, 9th ONR, 1972, 1763-1843. S^&XS C k»?¥ilXS 3. 6 9 k@%0t- FXkt, 2) H. Kagemoto and D. K. P. Yue: Wave forces on wmmofcMimmi-tik t mmsm*-?-1 » s© a platform supported on a large number of float X, ^ tL $ Tm L fc j:, -5 ;& mMfr til®ffl "C % ing legs, Proc. 5th Inti. Offshore and Arctic Engi neering Symp., Vol. 1, 1986, 206-211. SA?SHiU4", ##:&#© 1/10 @g©Xt£©ESEfl-S!l LX#{-#XS C k**qI#ST&%a o 'I in r ,- 183 2-4 Prediction of Wave Drift Damping by a Higher Order BEM by B. Teng*, Member S. Kato*, Member K. Hoshino*, Member Summary The paper develops a numerical method for predicting wave drift damping of three dimensional bodies. The first order potentials are calculated by a new integral equation method, which removes the second derivatives of the steady potential from the integration on the free surface. The second order mean potential is calculated by an integral equation method which is first developed. Comparison is made with analytic solution for a uniform cylinder. Numerical examinations are made oh the convergence with radius of the mesh on the free surface, and magnitude of each component of wave drift damping. Timman-Newman relation is also used to check the correction of the first order potentials. Comparison with experimental results are made on an array of four cylinders which are restrained and freely moving respectively. It was found that good agreements exist between the present calculation and experimental results and negative wave damping may occur at some wave frequency. The present research examines the wave damping of 1. Introduction floating bodies by a higher order boundary element Tension leg platforms (TLPs) are semi-submersible method based on perturbation with respect, to wave structures moored to seabed with a number of preten slope and current velocity. The oscillating wave poten sioned vertical cables (tethers). The response motion tials are resolved by a new developed integral equation of upper structure with wave exciting induces tethers (Teng and Kato"') . Comparing with some widely used vibrating continuously, which will break when their ones, the present one removes second derivatives of fatigue life has been reached. Damping can decrease steady potential from the integral on the free surface. amplitudes of response of structures. Thus, accurately Thus, the present integral equation can be dealt with predicting damping is important for the prediction of more accurately. Cauchy principal value (CPV) inte fatigue life of tethers. Usually damping of a compli grals on the body surface and the free surface are dealt ment structure can be divided into the viscous damping, with by direct and indirect methods respectively. The the radiation damping and the wave drift damping. The present work also derived an integral equation for the wave drift damping, defined by Wichers and Sluijs", is calculation of second order steady potential, which will due to the increase of drift force with forward moving give rise to some contribution to wave drift damping speed of a floating body. Its calculation needs the (Grue and Palm9 ). The second order drift forces on nonlinear knowledge on wave diffraction and radiation forward moving bodies are calculated both by a near in a steady flow. field and a far field method. The wave damping is In this respect, significant progress has been made obtained by numerical differentiation of second order recently. Matsui, Lee and Sano 9 and Emmerhoff and mean drift forces in current. Sclavounos 9 have derived analytic solutions for uni Numerical test is made on the convergence of drift form cylinders in finite and infinite water depth. Bao force with radius of the mesh on the free surface, and and Kinoshita 9 expended to truncated cylinders. For the examination of the contribution of the second order 3D arbitrary bodies, integral equation method had been steady potential on drift force. The comparison developed by Nossen, Grue and Palm9 , Grue and Palm9 , between the far field and near field method is made upon Zhao et al7), Huijsmans and Hermans9 and Eatock horizontal , modes at restrained case. The Timman- Taylor and Teng 9 , Newman* 9 , among others. Newman relationship is also used to certify the correc tion of the present method. Comparison is made with Kinoshita, Sunahara and Bao ’s19 experimental results * Ship Research Institute on an array of four cylinders which are restrained and Received 9th Jan. 1996 freely moving respectively. - It was found that good Read at the Spring meeting 15, 16th May 1996 agreements exist between the present calculation and 184 Journal of The Society of Naval Architects of Japan. Vol. 179 experimental results and negative wave drift damping pm is the hydrostatic pressure and p iw) the linear may occur at some wave frequency. oscillating pressure. The remaining components are defined by the relations 2. Perturbation expansion j ° 2.1 Velocity potential and wave surface The fluid is assumed to be homogenous and incom 1 ^)=-/3[^-i|P-+-lv(Z) -=0. (22) —vofap —2h~ dx dz -GfalXx)-V2z(x)]ds The body condition can be written as fa'Kxo) for + d ing transforms are used . ' // ...... JJSf ni - i - - : =ffs/m(.x)^Go-V2^im(x)ds (38) 4" for#' '' jjs Gmnjds for/=l, 6 ; 1 for the zero order terms in r; and - for the integral on the free surface, where Cj is a [l-ffSivGmdxdi/]ftlV{xo) | contour at outer boundary of the mesh on the free surface, and _ ‘ r +ffjt +ffs(vGm-2iGl?Wmds ,i . , l- j „ W0’*• n)-Go(aw>Xn)• V#'*]rfc ' G,(V#'*x5,,0'W/ +ifc G +2rsin2 0)\H(d)\2d6 +2Cg (kh)cos y9 7?e[S]j (C.W)sin6 Fig. 1 Examination on the convergence with radius of —2rsin 6 cos 8)\H(8)\ 2dd . the mesh on the free surface for second order +2Cg (kti)sm yS MS]} • drift force on a truncated cylinder at Fr—— 0.10 and ka=1.5. 188 Journal of The Society of-Naval-Architects of Japan. VoL 179 second mean drift force. It can be seen that the domi at Froude numbers of ±0.1. The reason we chosen nant contribution comes from the water-line integral ; these. values is that, they are zero, in the still water and the body integral of the first order potential. At low problem and only come from the, disturbance of the frequency, the term from the second order mean poten steady flow, so the calculation of those values are very tial is very small; but it Increases with the increase of sensible to the methods used, and can show their availa wave frequency and is not negligible at high frequency. bility more clearly. From Figs. 3 and, 4 it can be seen Figures 3 and 4 are the cross coupling surge and heave that the added mass and damping coefficients an(U) added mass and damping coefficients of an hemisphere and bn(U) in the following current is close to the added mass and damping coefficients «3i(— U) and bn{— U) in o . " 1 ' c< a corresponding reverse current. Timman and Newman relationship is satisfied very well. Figure 5 shows the comparison of the second order drift forces on the fixed hemisphere by the near field and the far field method at Fr=— 0.1. It can be seen from t the comparison that the good agreement exists between the two methods. Figure 6 shows the comparison of "the first order exciting force on a uniform circular cylinder of radius a in a Xvater depth of h/a—1 with Matsui et al’s2,18) ana lytic solution. In the calculation, a mesh of 16 (4 ,1.4 ! , ,1.6 , [ (circumferentially) x 41 (depthwise)) elements on a quaclrant of body surface, and 32 (4 (circumferentially) Fig. 2 Examination on the contribution of each term x8 (radially) ) elements'on a quadrant of free surface of the wave damping of the truncated cylinder. . i 1 _i i _ i . ■ 1 i . i - • . 111 1 ■ • are applied. The comparison shows that the agreement r with’ Matsui’s analytic solution is very good. Fig. 7 ‘ M , I 0.4 • • 11 i i i >" i i 0.35 - • F? «pK0-3 - li ' 0.25 1 ...» mM . . J 1 - 1 . 1 1 .0.04 0.2 1' 1 'll 1 1 ' 0.02 ‘•t 1 if 0.15 : , far field...... , / near field o ' ' ‘ 0.1 i ' -i - 0.2 0.4 0.6' 0.8 1.2" 1.4 1.6 -i.8 0.05 'a > o ----- 1-----1---- 1——I— _1___ I___ 1___ I___ Fig. 3 Cross coupling surge-heave added mass of an' 0.2 0.4 0.6 - 0.8 1 1.2 1.4 1.6 1.8 2 hemisphere of radius a in a water depth of h/a—2 Fig* 5 Comparison of second order! drift iorce on the ffi . hemisphere by the near and far field methods 0.35 - ' i gpAa : Fr=4>.05 — Fr= 0.00 — Fi=0.05 — Matsui o 0.2 0.4 0.6 0.6 1.2 1.4 1.< 1 1.2 , Fig. 4 . Cross coupling . surge-heave damping i =■ X coefficients of an hemisphere of radius Fig. 6 Surge exciting forces on a uniform cylinder of a in a water depth of h/a=2 . I - radius s in a water depth of hja=1. Prediction of Wave Drift Damping by a Higher Order BEM 189 shows the comparison of the second order mean drift Figures 9-lTshow the comparison of the mean drift force at different Fronde number. The comparison with forces of-present calculation by the far field method Matsui’s analytic solution shows that at low frequency with Kinoshita et al’s® experimental results of an array the two results agree very well, but at high frequency a of four restrained cylinders. The cylinders are with little difference exists. It seems that the difference radii "of a and draft T\a=2, and are located at comers comes from the methods used in the calculation of wave of a square with side length of 5a. Figs. 12-14 show the forces. Matsui’s method is to get them by the Taylor ’s comparison with Kinoshita et al’s8) freely moving exper expansion with the forces and its derivatives at zero iments. The geometric factors of the cylinders are the current speed, but ours is to compute them directly at a same as the restrained case, and the inertia factors used given speed. Due to the nonlinearity of the dispersion in the present calculation are the same as Kinoshita et equation with.current speed and relatively stronger effect of current at high frequency, especially in an opposing current, our results diverge from Matsui et al’s at high wave frequency and are not symmetric about the one in still water. From Figs. 6 and 7, it can also be seen that the current effect on the second order drift force is significant, but the effect on the first order Calculated —. H=4cm o exciting forces is relatively weak. _ - - H=7cm + Figure 8 is the wave damping of the cylinder, which is H=10cm o obtained by the numerical differentiation of the mean drift forces at Fr=± 0.05 with respect to body moving speed. It can be seen that the wave damping reaches its maximum at about ka=0.7, and then oscillates with the increase of wave frequency. Fig. 9 Comparison of wave drift force on four restrained cylinders at F>=0.05. Calculated------H=4cm » H=7cm + . - H=10cm □ 0.6 - Ff=4).05 — 0.4 - Fn* 0.00----- . Fr= 0.05----- Matsui o Fig. 7 Second order mean drift forces on a uniform cylinder of radius a in a water depth of h/a=1. 10 Comparison of wave drift force on four -----restrained cylinders at FV=0.00. Calculated------H=4cm » H=7cm + . H=10cm □ •, 1,5 Fig. 8 Wave damping of a uniform cylinder of radius a in a water depth of h/a=l, obtained by numeri cal differentiation of the mean drift forces at Fr Fig. 11 Comparison of wave drift force on four =+/—0.05. restrained cylinders at Fr=—0.05. ' 190 Journal of The Society of Naval Architects of Japan, Vol. 179 Calculated —- H= 4 cm o - H-7cm + 1 H=10cm o , H=15cm x > 15 - Calculated — H= 4 cm * H- 7 cm + H=10cm o -20 Fig. 12 Comparison of wave drift force on four freely Fig. 15 Comparison of wave drift damping of four moving cylinders at Fr=0.05. | _ ■ ( restrained cylinders. . _ 30------1------1------1—i------1------1------Calculated------" "b, 25;'■ ; H=4cm * H=7cm + . fgA2aJga 20 HrIOcm o s H=15cm x . 15 r', 19 - i J 6 + ------< . * . * > ' ' ii. ° -5 0 □ Calculated -rrr H=4cm ❖ -10 H= 7 cm + H=10cm 0 ------15 r - H=15cm x - i -20 ______1______1______1______1______1______0.2 0.4 - 0.6 0.8 1 1.2 1.4 Fig. 13 Comparison of wave drift force* on four freely :—moving cylinders at Fr=0.00. Fig. 16 Comparison of wave drift damping of four h— - freely moving cylinder^. j - - 3.5 S Conclusions 1.; All components of second order drift forces con verge quickly with the increase of the radius of the mesh on the free surface. Truncating errors can be neglected When R/a>is larger than 4. 12.' When wave frequency is not very high, the contri 0.5 - ■ I bution from the second order mean velocity potential is very -small for the hear field method^ However, at high frequency, it is not negligible. , Fig. 14 Comparison of-wave drift force-on [four freely 3.} Timman-Newman relationship is satisfied very _ moving cylinders at Fr=— 0.05. | well and good agreement is found from thecomparison ! of the first order exciting force with Matsui’s analytic I ■ ; J. solution. It states that the method for the first order al’s experiment. It can be seen that the present calcula potential is correct and accurate. 1 tion has a good agreement with the experiments no 4: Good agreements are found between* the present matterjn the restrained or freely moving cases. calculation and the experimental results on} an array of Figures T5 and 16 show the wave drift; damping, four" restrained and freely moving cylinders. It vali- obtained by numerical differentiation of the mean drift dates-the application -of-the -present -theory. Negative force} at Fr= ±0.05. It again shows that gbod agree wave damping is again found at some wave frequency. ment! exists between the present calculation and the It may induce big response of the system. Special experimental results,'and negative waveUrift; damping concern is suggested to be paid for complex structures. appears at about ka=0.8 both in experimental and calculated results. ,The negative damping may induce a , , References big response of the system. ■ • 11 ,1 1) Wichers, J. E. W. and Sluijs, M. F., 1979, The Prediction of Wave Drift Damping by a Higher Order BEM 191 Influence of Waves on the Low Frequency 10) Newman, J. N., 1993, Wave-drift Damping of Hydrodynamic Coefficients of Moored Vessels, Floating Bodies, J. Fluid Mech., Vol. 249, pp. 241 Proc. Offshore Technology Conf., Houston, -259. OTC3625. 11) Teng, B. and Kato, S., 1995, A New Integral 2) Matsui, T., Lee, S. Y. and Sano, K., (1991), Equation for Wave Action on Body in Waves Hydrodynamic Forces on a Vertical Cylinder in with Small Forward Speed, Proc. of General Current and Waves, Jour, of the Society of Naval Meeting of Ship Research Institute, Japan, Vol. Architects of Japan, Vol. 170, pp. 277-287. 66, pp. 258-265. 3) Emmerhoff O. J. and Sclavounos, P. D., 1992, The 12) Kinoshita, K., Sunahara, S. and Bao, W., 1995, slow-drift motion of arrays of vertical cylinders, Wave Drift Damping Action on Multiple Circular J. Fluid Mech., Vol. 242, pp. 31-50. Cylinders (Model Tests), Proc. OMAE, Vol. 1-A, 4) Bao, W. and Kinoshita, T., 1993, Hydrodynamic pp. 443-454. Interaction among Multiple Floating Cylinders in 13) Ogilvie, T. F. and Tuck, E. O., 1969, A rational both Waves and Slow Current, J. Soc. of Naval strip theory of ship motions: part 1, Report No. Arch, of Japan, Vol. 174, pp. 193-203. 013, The Department of Naval Architecture and 5) Nossen, J., Grue, J. and Palm E., 1991, Wave Marian Engineering, The University of Michigan, Forces on Three-Dimensional Floating Bodies College of Engineering. with Small Forward Speed, J. Fluid Mech., Vol. 14) Eatock Taylor, R. and Chau, F. P., 1992, Wave 227, pp. 135-160. Diffraction-Some Developments in Linear and 6) Grue, J. and Palm, E., 1993, The Mean Drift Force NonLinear Theory, J. of Offshore Mech. and and Yaw Moment on Marine Structures in Arctic Eng. , Vol. 114, pp. 185-194. Waves and Current, J. Fluid Mech., Vol. 250,121— 15) Teng, B. and Eatock Taylor, R, 1992, Effects of 142. Combined Waves and Currents in an Ideal Flow, 7) Zhao, R, Faltinsen, O.M., Krokstad, J. R., and Final Report on Project FLU 79, MTD Managed Aanesland, V., 1988, Wave-Current Interaction Programme on Behaviour of Fixed and Compli Effects on Large-Volume Structures, Proc. ant Offshore Structures. BOSS, pp. 623-638. 16) Wu, G. X. and Eatock Taylor, R., 1990, The 8) Huijsmans, R. H. M., and Hermans, A. J., 1989, hydrodynamic force on an oscillating ship with The Effect of the Steady Perturbation Potential low forward speed, J. Fluid Mech. Vol. 211, pp. on the Motions of a Ship Sailing in Random Seas, 333-353. Proc. 5 th Int. Conf. Numerical Ship 17) Grue, J. and Biberg, D., 1993, Wave Forces on Hydrodynamics, Hiroshima, Japan. Marine Structures with Small Speed in Water of 9) Eatock Taylor, R. and Teng, B., 1993, The Effect Restricted Depth, J. Fluid Mech., Vol. 250, pp. 121 of Comers on Diffraction/Radiation Forces and -142. Wave Drift Damping, Proc. Offshore Technology 18) Matsui, T., 1994, Private communication. Conference, Paper 7187, Vol. 2, pp. 571-581. Gf 9 b o/- 3S4-^ 193 2-5 «n t}n y h [FLYING FISHJ (D EM /Jv#Uj h.* EM ill □ EM t|3 # I r EM # % # A** Development of an Observation Robot ("Flying FishJ for Comprehensive Measurements of Ocean Environment by Wataru Koterayama, Member Satoru Yamaguchi, Member Masahiko Nakamura, Member, Taketo Akamatu, Member Summary A pitch, roll and depth controllable towed vehicle has been developed and named as “FLYING FISH”. The towed vehicle equips with an acoustic Doppler current profiler (ADCP), COz analyzer and sensors for measuring temperature, salinity, dissolved oxygen, PH, turbidity, chlorophyll. Flying Fish enables us to obtain the space continuous data of physical and chemical properties in the ocean upper mixed layer efficiently. Its maximum submerged depth is 200 m. The length is 3.84 m, breadth 2.26 m, height 1.4 m, weight in air 1400 kg and weight in water is about 0 kg. Numerical simulations were carried out in order to design mechanical parts of the control system and estimate the accuracy of motion control of Flying Fish. The simulations are based on the six degree freedom motion equations for underwater vehicle and lumped mass method for the towing cable. Field experiments were conducted to confirm the performance of Flying Fish and accuracy of numerical simulations. Results of field experiments and numerical simulations are compared. lx , 1. m w kDT, & s Kbaamae-caa • tix § 6-c^©Kjy-vr,E#($m©@fin:¥ziSc$ew-B, WblfSF3ECSg Sivrsft KiItf ewaw* s ©S^SjlS fc#, +a-c& 9& i>tzb-rtz&,. &mx 11> c, LT#±L zti&x, aki T5jEft= ?S#gTifflS@EKT-E>IEBk L-Ui, AR9©±@ MtpximwizmfB^&k vxmz%^kkmmfbti xftf^x$m\sX%fcz.hkm -eso, @#«iE@ y©y-f yxxA^E# ena. & Ama©*sm^ ztix&tzo ###&, S#®=ErPSMSBX'fy*r a * * ©i@#mma#N5M-mw@6» e-A#a a 'i srXt>2>» k*ogi%c#MVfc»i, | f ©. »?40Qm t$Sfc.fe, &##©#^E 5 a H-A$fc6S©jE 4>"C, y-i n$vj\s < tsk^Eii, t©g^%#A^BTta. @&-c#m-c&a#, w^K^iscoy'f ^xrAiS-sM , sXe, ±wj:mmx$>m^m»mnts a c t u, /j#©y Wf 3@#g - as%©3@&t©psaEWf a©-c, & -f i/XTA^ircttSSI^yD y b»k*@J:5 E, £m m*©mm^ §n#^Ek»a. ctte, CE k#m©im##Hm&BKk L%, ###&?^ 4 GJ>-S- w:__», Mother thip ma - *?S6:k*©t/ssf-iiEinxTS*^ffl(b#ti$r$'r 5iSaSESS#tia • fb^BSIn * 7 K Fly ing Fish SEU^-CSa5’, u O^XtACJ: t>, W#-^© xno7 ^ ;t/-PH S|5]iWE, ^RET, ^oSPiflffi^tocEi-liys #mr#Bk»a. - CO: analyzer Acoustic Dopier current profiler - Flying Fish E± 5 ©S6E5l=l©yn 7 -t ;i/»*Sgk & a „ ^©fcfel 6@i/ffc Fig. 1 Conceptual view of Flying Fish system F [FLYING FISHJ. ®R%mg 195 mtf&v, ?oifts$M5;iE±p, CgSrgfSti, ##HigSgA#r&5. MESHIX jeuse.k, o e-ts± 5 k ^®gfi^»r;y s®y v-a k frp ®MSil6S$ k l 8Sihr3We§s„ #tyf— r-M+ffl$tifcfitt, &E %±@#I#EE TEgM8f5. GPS (Global Positioning System) YjrHffl UfciES-fuE k (1) y-y-y-9-- - Si® • yyy-y k b • EB5HZ* kam#k ®##, T-yoesfUiry 2.1 **WE y-y-^LTff5o 8fWmSE'ADCP-#l&&*mt Flying Fish OS^ttlESiMTC^-to «m#m±#emEK • mm® • (1) iUEUE 2 y y F-10 y y F EA#W#E®$J@iit Fig. 3 csti 5 e y-y y»- (2) 0-200 m 0*IO-y'Cv>5o j (3) 60 tsi®i±sa±^e>&®ty -^y$f£t> Tjgssns «&t ^-#x, Ki&m 3839.5 325.5 229.5 30199.5 Water intake 'Water leakage 6-port EMV sensor ------Water sampling pump TOC-5000 Gas / Telemeter Gas cylinder | Pressure Y. regulator J\ " ADCP Standard reagent J Stabilized power unit/I; Pressure hull Rubber fender Transformer, Fig. 2 Vertical view of Flying Fish 196 #179# System Block Diagram S±Sl^cJ:oT, t - 7 A#: % & C k tf&Z-^>tz®X, 6 K 4 SMSJt&fSLT, 1/2032 Mother Ship ±^e-7©##At±#V)©K, ©i|£E y bE^©tiEA> 6M-ATw Towed Vehicle RM@©A»©#^@K#*A • EISA- #M@©%KK0 Telemeter AD CP ■a has o tiznmsmomz. ag@;@*gea. 6As#c Water analyzer ©», ^ em @ A s. ti@^xrAi:pv> rti, iiciiy5a.y-y 3 y© k z: sr, #L ' Water C02 Pressure ± 9 5 z: k c * 9 , m. leak control watcher analyzer system m£Efite£?>B®&ia; ##%7S z: k «z: © y x f 3 ©TAKE i@%©X$HS k mEtbSI L7£*i&-i£:9- • PH SfvT? %fflvarSEt-5o igEtfxiSKttiSzkejg-jrsS mE©KE**X^EpC02 ©I-Cffi^EMT S„ Fig. 5 k ^ ©SEEET*. 5 SkjtiSSE • EA#J# »7D-ft-nst. ^KE^rriH' Fig. 4 Mechanics of wing actuators NS*&#*6fsa© t ©?$ 9 , EAmmmm, im. X A E#b A.& * + 9 7#X&#E#^e»%& 1/508, *¥ $^S&©6©T$S. f 9 7#X(N2 mm®1/254 c? ■' #x) UTti 9, 2EScB+lJ 617 x. tf BESSsft ©E A^A35m/sec, 70%/sec-C$>508S(iasf 5 a y ;0-#rE+© Weil%©S50 k & S „ k©fc»S ©gsc iAfcf 10 %/sec C k HfloE*&:kiEfcimrS ©»?, c©#E?&S. E aasadKE&Lkr&AK, kvryyyficis i 5 t * 5 k k C Pressure hull Water intake 2-port electromagnetic valve Check valve 6-port electromagnetic Small capacity valve j/ Water exhaust port 3-port electromagnetic valve t Water course 10 liter C02 analyzer 3-port electromagnetic TOC - 5000 valve 10 liter Standard reagent Decompression Water pump tank Water intake Pressure governor Stainless tube ------1/16 inch ------1/4 inch 1/2 inch Fig. 5 Flow line of sampling water and carrier gas 5o zomm-c, y^mc Table 1 Characteristics of sensors gtXLr < /jsEdfyrti:/7 y y> - ? -r 7°-p;b 9, Acoustic Doppler current profiler Depth sensor Acoustic frequency 1S0XHZ Type Electrostatic capacity Sfl 200 W BBEA 35 kg/cm 2 "P? y 7 ©SB: 14^5 V No. of acoustic beam 4 0-20Cta 250m/400m 0.3% of full range Velocity range (MOm/sec Time response 7 F/yp&S. 1:* -r 1) 7*'X 14 2 Rater of depth cell 128 Dissolved oxygen smsor Direction accuracy Type Polargraphic ©f/X dt y-t (10 L, 150 kg/cm 2) U 0-20ppm CO- analyzer Accuracy O.Jpf* 150 kg/cm 2 ^6 5~6 kg/cm 2 Ci$E4i3.2$© Measuring object Dissolved Time response Type San-Dispersive EH yrx di c fc c j; d **j 60 s. Infra-Gas Glass electrode AnalyzerIKDIR) 4-14EH Range 4ppb-5000n* 0.D5PH (5) mimFyyy-ammf 1% of range Time response lOsec Time response EWE F 7 7° 7 —SffiBU- (Acoustic Doppler Current Temperature sensor Type Infrared bedtscattering Type Pt resitance Range (MOOppe Profiler; ADCP) !4mE©%m©ma##&«Sf 5. $ Range -5 - 45*C 2% o.ofc Time response O.ZSsec y X r A -CEffl -f 5 f> © 14 4 $© 150 kHz ©EWE tf- Time response 0.25sec Conductivity sensor Chlorophyll sensor Type Induction cell Fluorescence analysis %mh©@E^ 6 400 m & T©%@ & T& Range NOmho/a Range 0.5-fiO g/iltter- ' O.OSnho/cm 0.1% Time response Time response ** Maxlum allowable submerged depth of all @a%gyyy (soom) mm c & sensors is set at 200a 3C k fp@ 3. 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IS '■p 71. - -ti E c •P Cl D. a a c_ - p — b S3 3- O 3r Qj >,0- 4U o § m u g ou. ^ 20------v ■ UwVW— V ”* „ , ' ■ 3 >s 280; 01 40 3 A B , C , D E Fig. 12 ' Chemical properties ‘between Hokkaido and Russia obtained using-Flying Fish giilE*:?*:,,. £ © J: 5 E# < ©*&Kg^m©mK#ia c©m©ie#Km©#Hm@«d E»3 ©T^XTA ' v *, AT#©#mk|B|#Emib&^L'C^3^3 @CB5>n€. j:5E, f*@© D A&agT DE^r* 3 A?, V©itE daCffio*< EUftT, 3c 3ft aw5asg&ic@TLT^3. im#Ema-©@Ttm# I^nu7-(^k »AS*t*3 EKOfBM mm ■ 5SS©ti5n»?B5.tL5o-99,e>^ED5/-TS^etttf3 A?*3-±-3lcli-3. -U/cA?oTig#KiC7)V'tBg|!il 6 B$%#EA4j-T©6 © k KBU©##©*#**# %»%ib k>un7^i'kIlU BJi$©Bem»Seib SUTVi^ c. t&bi'Zo C©3b^^6 &#e#0 k®x_3'A?, 3 ©SEOti-CSIa-hitf3 E tt, ©m@S%«*mwTB##A*EfT#%3 3 kTB*m § 6ET-^©WSl$i2'Ek-t3c $fc®7®©^EAfx ?nu-7 J MtCtpb bhtcZMfa* ®stt¥®s©±A^ • ph t SbO'5i5?ut37^1/1±@#%7°7y-X h y©T^Sl tBgg^cAS, ES&M3 k, ©ffifiISSt6©?S5©T,- S^®ISr«g^bE;i3 i; M&*?-C^3. ?#A©±A»* B PH ©§g@Ase6B ©»i*SV)0 Ltztf-zX? n n 7 -f !«,©%# »#*gE^M: u„PH ©SISSiSASfi© b ©EtiyvC, +a-T6V)©T^ #=#k.JE,3Z kllTM*vv;ft 3A»?>^SBA^5>ny71; EA/-X$iS©iffl$SlSSEi:UTWcA?, s^PSEtt PH © a##ess-t a*#k * & m#$saa/F@w©r, it^ft/syyxok^fc, SJSf/i *m KmmwE,%%AEB «• ©em&gEf %.!k # %. SE&oTv>3„ ^EAfxiSgtt^EiSSi^SSlbAS* # 3c StifcgBEWt) ©*a©*S • &9-ASJ±ftm <, * <, $fcigkS*voV 3„ icr," Flying Fish Ej: Dm m^m©##A!&3kfc’Sf £feft3AS, C©AK0W-n± S^i[6j©tbSI6%iS-T3ft:* E, Jtt£fWv>mvMiW ttiESSMiE 5 ^U5o*vi-c,ESlf ny <^-fbg-&3^gAS±U3c iOfeAEB, re®® as b ^sfi-cEiffl-r 3 h z kAs T^3#gBe@AA©?"n ^9 £ y/E mwwm-&mmvX'y f tflying fishj mm¥m 203 Depth (m) 1 (m/sec) 42 I r pC0 2 in Surface Sea Water (Depth = 5 m) - Measured with Flying Fish 5.7 m : pC0 2 in Air ^ Fig. 13 Velocity distribution measured with ADCP of Flying Fish July, 1994 (days) Fig. 14 Comparison of dissolved C02 obtained with Flying Fish system and direct measurements 5$E4a k * a o F v 7°?-S®SU-E & 5. m m Fig. 13 izmto Z S I' » : u • ' ' ' 1 J X . i 1 205 2-6 Water Entry Simulation of Free-fall Lifeboat —Second Report: 'Effects of Acceleration on the Occupants— by Makoto Aral*, M. Reaz H. Khondoker** Yoshiyuki Inoue* Summary Free-fall lifeboats provide significant advances in the maritime lifesaving systems. Much of the danger associated with conventional lifeboat systems can be eliminated by this, new evacuation method if the boat is launched selecting suitable launching parameters. A primary consideration in the free- fall lifeboat system is the acceleration field to which the occupants are subjected during water entry. The international regulation, therefore, requires that a lifeboat for free-fall launching shall be capable of ensuring protection against harmful accelerations when it is launched with its full complement of persons and equipment from at least the maximum designed height. When the lifeboat enters the water, the acceleration forces exerted upon the boat due to impact are - very high. According to the basic study upon the human body response, tolerance level for acceleration is different for each axis of the human body. Therefore, the safe seats in a free-fall lifeboat are usually reclined relative to the axes of the lifeboat to reduce the effect of high accelerations. In this paper, the authors introduce a new and probably the simplest concept to evaluate the acceleration field of the free 1 -fall lifeboat and apply it to the analysis of the safe seat orientation for the occupants. The results have been compared with those of the SRSS acceleration criteria and the dynamic response criteria, both of which are recommended by the IMO, and good agreement has been found. domain of safe acceleration forces can be defined by an 1. Introduction ellipsoidal envelope bounded in the direction of each Free fall lifeboats are becoming common lifesaving axis of the human body by some value. Injury should appliances in the ocean environment. These are now not occur as long as the acceleration forces are within widely used for tankers, cargo ships, mobile offshore the envelope. Although the SRSS criteria is very drilling units and fixed oil production platforms. For straightforward, this method for evaluating accelera these lifeboats to be certified by maritime authorities, tion forces has a weakness. It considers only the the occupants must be protected from harmful accelera magnitude of the acceleration force and the duration of tions during the launching procedure especially when the force is not taken into account. The dynamic the boats impact the water. The accelerations may response criteria that evaluates the injury potential of become extreme, if the fall height is high or the boats an acceleration field by introducing a displacement are used in high wind and rough seas. approach overcomes this shortcoming. It assumes that To evaluate the response of human body to the high the human body response in each coordinate direction accelerations, some methods are proposed ; the square- can be characterized as an independent, single degree of root-sum-of-the-squares (SRSS) acceleration criteria, freedom mass-spring system subjected to the accelera the dynamic response criteria, application of the Hybrid tion field. III human surrogate, etc. The first two methods have In this paper, the authors introduce an alternative been accepted by the International Maritime Organiza concept of “polar diagram of acceleration ” and show tion (IMO)”. the effectiveness of it to the study of the acceleration The SRSS criteria is based on the assumption that the field in free-fall lifeboat. We also show the application of the method to the determination of the safe seat * Faculty of Engineering, Yokohama National orientation for the occupants. The results obtained University, . from this method are compared with the results by the **' Graduate School, Yokohama National Univer- SRSS acceleration criteria and the dynamic response , sity. 1 criteria. The comparison shows good agreement on the Received 9th Jap. 1996 - - - - seat angles that minimize the risk of injury of the Read at the Spring meeting 15, 16th May 1996 occupants. 206 Journal of The Society of Naval Architects of Japan, Vol. 179 2. Numerical Computation of Lifeboat Motion 3. Analysis of the Computed Data by Other and the Introduction of ’’Polar Diagram of Methods Acceleration ” . 3.1 ■, Application of SRSS Acceleration Criteria During the water entry of the lifeboat, the/accelera ' The square-root-sum-of-the-squares (SRSS) accel tion of the centre of gravity of the boat can be comput-, eration, criteria11 is based upon the assumption that the ed from the following equations 21: domain of safe acceleration forces for human body can Mx=Fmn sin 6—Fma cos d+Fdn sin Q—Fda cos 8 be defined by an ellipsoidal envelope bounded in each (1 a) coordinate direction by some value. Such an envelope Mz=Fmn COS tf + FmtSin d+Fdn cos 8 , for acceleration forces in the £ — f plane (see Fig. 1) is +FdaSm'B-Mg+F„' ‘ (lb) shown in Fig. 2. Injury should not occur as long as the 10= Mmn Mdn Mb (1 c) acceleration forces are within the shaded region of the In Equation (1), x and z represent the position of the envelope. The combined acceleration response (CAR) centre of gravity of the boat in the global coordinate is computed as an interaction equation of the form : system, and 8 is the instantaneous angle of the axis of' at ___ (3) the boat with horizontal (see Fig.' 1). M is the mass of (A>y 1 va ?/ 1 VAf> I'M'1' 1 . ‘ , i , ' , ‘ ; i the lifeboat and I is the rotational moment of inertia , where, At, At, At are the limiting values of accelera for pitching. Furthermore, F„„ is the force due to : tions in the £, rj and f directions and the recommend momentum transfer in the normal direction to the boat ed, values by the.IMO have been shown in Table 1. axis, Fma, the force due to momentum transfer in the The CAR index is the peak of the CAR time, histories axial direction, Fan, normal drag force, Fda, axial drag ' measured or computed in the axes of the seat. Injury force, Ft, buoyancy force, Mg, gravity force, should not occur if the CAR index is less than unity. moment due to momentum transfer in the. normal direc 'The advantage of the SRSS criteria is that it is very tion, Mdn, drag,moment and Mb, buoyancy moment. simple to,use but it considers only the magnitude of the The derivation of these-fluid forces has been discussed acceleration force. The duration of the force is not extensively in our first report 21. <• 1 taken into account. ;. -...... These accelerations of the centre of gravity of the In Equation (3), at, at and at are the acceleration lifeboat in global coordinate system can be used to time histories for a particular seat angle Occupant —j, Fig. 2 Ellipsoidal safety envelope for SRSS criteria Table 1 Allowable accelerations for the SRSS acceleration criteria , t 1 l Coordinate axis . '■ S.W.L > Allowable accelerations (A) f (eyeballs in/out) 15g 77 (eyeballs left/right) ?g - Fig. 1 Coordinate systems and seat angle f;. £" (eyeballs up/down) . r , ■ ,?e Water Entry Simulation of Free-fall Lifeboat 207 at a particular seat foundation in the lifeboat and can ' mb t + CtSt+kiSf^—mai (5 b) be obtained from our numerical simulation using Equa Here cf, kf, cf and kt are the damping and stiffness tion (2). Effect in rj direction (i. e., lateral direction) coefficients in $ and f directions as defined in Table 2°. has been neglected in this paper due to the two dimen The relative velocity (5) can be obtained by integrating sional analysis. Now, substituting these values of Equation (5) and further integration will provide rela accelerations in Equation (3), time history of the CAR tive displacement (8). Newmark-# method has been for a particular position can be obtained, which can used for the numerical integration of Equation (5). further be used to evaluate the safe seat orientations for To evaluate the acceptability of the acceleration field the occupants. with this displacement approach, the effect of multi 3.2 Application of Dynamic Response Criteria axis accelerations can now be combined to give the Brinkley 31 have introduced the concept of dynamic combined dynamic response (CDR) ratio for every seat response to evaluate the potential of injury to human position and orientation as: bodies. According to this concept each body axis can be idealized as an independent single degree of freedom ■ «» mass-spring system that is subjected to known seat where, St, St, Sf are the allowable displacements in acceleration. The model was originally developed for the f, 9 and K directions for a particular risk level and evaluating the effects of acceleration along the spine, are shown in Table 3 as proposed by the IMO”. These but it has been expanded to evaluate the effects of allowable displacements are for a 50 th percentile of 28 acceleration perpendicular to the chest and parallel to year old male in a fully restrained seat and harness, and the shoulders as well. Through research carried out at they were obtained from the research conducted at the United States Air Force Aerospace Medical AFAMRL3’. “Training condition ” is said to be corre Research Laboratory (AFAMRL)3’, values for the natu sponding to 0.5% possibility of injury and “Emergency ral frequencies and damping ratios in each coordinate condition ” to 5% possibility 5’. axis have been investigated. The peak value of the CDR time history is called the In order to analyse the risk of injury of occupants by CDR index. If the CDR index of a certain seat position our numerical simulation method together with the and orientation is smaller than 1.0 during the launch dynamic response model, the following four steps are and impact time span, then the level of risk of injury required : associated with the allowable displacements, is not (1) calculation of the acceleration of the centre of exceeded. The combined dynamic response as calcu gravity of the lifeboat at water impact, lated from Equation (6) can also be used for the (2) calculation of accelerations at the seat founda evaluation of the safe seat orientation for a particular tion for a number of seat positions, position in the lifeboat. (3) calculation of relative displacements between occupant body and seat, and 4. Results and Discussions (4) combining these displacements with allowable In order to study the effects of acceleration on the displacements to find combined dynamic occupants of a lifeboat, numerical simulations have response (CDR) ratio. been conducted to obtain the accelerations at positions The accelerations of the centre of gravity of the boat 5Z./6 from the aft end of the boat (we call the position can be obtained from Equation (1) and the calculation as “Bow ” in this paper), L/2 from the aft end (“Mid of acceleration field at the seat foundation in local ship") and L/6 from the aft end (“Stem”). (Here, L coordinate system can be carried out through Equation means the length of the lifeboat.) Accelerations at these (2). Using Equation (4), the accelerations in seat positions are measured during model experiments 3’. coordinate system (i. e., the coordinate system for an Polar diagrams of acceleration using measured and inclined seat) can be obtained, which will be used to computed data have been drawn for all these positions evaluate the relative displacement between body and to see how the safe seat angle changes along the longitu- seat. The system of equations for the body-seat spring mass system are as follows : m b't+ ce'S i+kiSe—ma t (5 a) Table 3 Allowable displacements for the dynamic response model Allowable displacement (S) Table 2 Coefficients of the dynamic response model Coordinate axis Training cond. Emergency cond. Coordinate Axis Stiffness (N/m) Damping (kg/sec.) £ (eyeballs in/out) 0.070 (m) 0.087 (m) £ (eyeballs in/out) 942 30xl04 - 7? (eyeballs lefl/right) 0.041 (m) 0.050 (m) Jj (eyeballs lefl/right) 25xl04 783 £ (eyeballs up) 0.032 (m) 0.042 (m) £ (eyeballs up/down) 21xl04 1,777 £ (eyeballs down) 0.053 (m) 0.063 (m) 208 Journal of The Society of Naval Architects of Japan, Vol. 179 dinalaxis of the lifeboat. The combined acceleration couple which causes the angular, motion of the boat in response (CAR) index and combined dynamic response anti-clockwise direction. This rotating motion then (CDR) index have also been, calculated, at the same leads to the. second impact (i. e., stem impact) . After positions from the acceleration time histories , during these; two impacts, buoyancy force .increases and the water entry. The results of the numerical simulations impact force, or the force due to the momentum trans and model experiments have been shown in,Jug. 3 to fer,reduces as long as the boat goes into water until it .,,, . i , u I .■ _,n un - - 1 i I' reaches to its maximum immersion. At that time, the Fig. 3 shows the calculated trajectory of the axis of axis of the lifeboat disappears fully inside the water and the Tree-fall lifeboat model, (longitudinal line through a large buoyancy force pushes it up. The boat then the center of gravity of the boat) falling at an initial comes out of the water and falls down again into water angle 0=30° and from, a height H=1.$L. As we can see with, already forwarding some distance.- This process from this figure, at the beginning of the launching continues till the boat stops. , , process, the boat slides along the skid with a sliding .Fig. 4 and,pig. 5 show the computed and measured length Leo-=0.8L. 1 (Here, Lgi'i means the distance polar diagrams of accelerations at three positions between the centre of gravity of the boat and lower end (Bow, Midship and Stem) for the same falling case. of the skid.) Then the boat rotates in, clockwise direc The agreement between the computed and measured tion and falls freely until if touches the water surface. accelerations is good. , The vertical axes in the polar As the boat enters the water, high impact force is diagrams show the accelerations, in normal (or vertical) exerted on the bow of the boat. The impact force, the direction, of the boat and the horizontal axes present the buoyancy force and the weight of the lifeboat form a accelerations in the axial (or: longitudinal) direction. ,, 2-5 i, (.5 . 1-0 . -1.0 -i i i" , J L 1 - 1 ■ X/L Fig. 3 Simulated trajectory of free-fall lifeboat u't tttt '■A rnrr Ste : Mil Ishij - : Bow, cd'* ■ \ i 11 4 l : j Bqw . - - : Impact i listen 1 3 1 -5 -4 -3-2-1 0 1 [ Unit in g] Fig. 5 Polar diagram of measured accelerations (0=30°, ti/L=1.40, WL=0.80) The time increment used to plot the data is kept con stant in these diagrams. Therefore the distance between the adjacent two points in the diagrams shows the rate of change of the phenomenon. For example, the part corresponds to the bow impact seems lighter in these diagrams due to the rapid change of the accelera tion magnitude. It is found from the diagram at the bow, that both bow and stem impact generate the acceleration almost in the same angular direction, As shown in Table 1, the acceptable acceleration for human body is different in each axis of the body and the tolerance level along the axis of the spine is the lowest. Therefore, it is rather easy to decide the optimum reclining angle of the seat for the bow position, and it is the angle that the back of the seat (or the axis along the (a) SRSS acceleration criteria spine of the occupant) to be in perpendicular to, this maximum acceleration direction. According to Fig. 4 and Fig. 5, optimum seat angle (p) is about 55-65 degrees, From the polar diagram of acceleration at midship, it is seen that there exists some angular difference between the directions pf the accelerations due to the bow impact and that of the stem impact. Yet it is not very difficult to decide the optimum orientation of the seat there, i, e., the reclining angle of 40-50 degrees. However, from the diagram at the stem, it is seen that there exists a remarkable angular difference between the directions of the accelerations due to bow and stem impact (i. e., almost 90 degrees) , and it is very difficult to determine the best seat orientation. There fore, it can be said that the designer of the lifeboat should be careful about the acceleration field for the ' (b) Dynamic response criteria (training condition) occupants in the stem seats. Fig. 6 CAR and CDR indexes vs. seat angle Fig. 6 shows the distributions of combined accelera (0=30°, H/L=1.40 and Leo-lL=0.80) tion response (CAR) and combined dynamic response (CDR) indexes with respect to seat angles. It is seen that there are two clear crests and troughs of the CAR degrees (or to —120 degrees), the harmful effects of index for the bow position with" a phase difference of accelerations are minimized according to the SRSS 180 degrees. The maximum values are at about 30 i acceleration criteria. Similarly, by reclining the seat degrees and at +150 degrees and the minimum values angles to 45 degrees (or to —135 degrees) at midship are at about —120 degrees and +60 degrees. It means positions, the harmful effects of acceleration can be that if the seat axis for the bow seats are reclined to 60 minimized. These are also seen in the polar diagrams of 210 Journal of The Society of Naval Architects of Japan, Vol. 179 acceleration, (Fig. 4). However, the difference between evacuation cases. _ However, if we change the water the maximum and minimum CAR- indexes of the stem lentry parameters such as initial skid angle, falling seats are very less. Therefore, for the stem seats, the height, sliding length, etc., we will obtain different boat risk of injury can not be reduced so much by changing motions. Fig. 7 shows one of such different motions. the seat angle. This figure also shows the combined The conditions for this second simulation" are initial dynamic response (CDR) index in different positions angle 0=30°, falling height H=IAL and sliding length with various seat angles. The computation was done £(m>~0.15L. The falling process of this pas ’e is similar with the allowable values for training condition shown to the previous one up to water touching, however, the in Table 3. Unlike the CAR index curve, there is only boat travels in different path after the water entry. one crest for the 360 degree~range of seat angles for a This is one of the unfavourable motions for a lifeboat particular (longitudinal position... This is because the- because the boat may collide with the parent vessel if it dynamic response criteria has different values;of toler ) .moves backward after water entry. We are going to ances for two directions along spine (i. e., eyeballs up discuss the boat motions in detail in our third report. and eyeballs down directions) . However! the reclining Fig. 8 presents the polar diagrams of acceleration at angles which minimize the effect of accelerations are 1 three positions (i. e., Bow, Midship and Stem) comput almost the same to those obtained by the SRSS criteria ed for the case shown in Fig. 7. For the bow position, it in all three longitudinal positions. It is also seen that is seen that there is a small angular difference between the safe seat anglesevaluated from tfiepolar diagrams the acceleration curves of the bow impact and the stern of acceleration for different positions provide good fits impact. However, it is not difficult to decide the opti to the ones from the SRSS acceleration criteria and the mum reclining angle of the seat for the bow position dynamic response criteria. , arid the optimum reclinirig of the back of the seat (p), The boat motion shown in Fig: 3 is one of the smooth which assurried to be parallel to the spine, is about 55- 65 degrees. From the polar diagram of acceleration at 2-0 .. midship, it is seen that maximum accelerations due to the bow impact and the' stem irnpact are almost in the ,1.5 . same directions. This makes it easier to decide the reclinirig angle of the seat there and the optimum angle is 40-50 degrees. Again, it is also difficult to determine the optimum seat angle at the stem position, since there is a clear difference in the angular direction between the bow and the stem impacts for this position. It is also seen from the comparison of Fig. 4 and Fig. 8 that the S.W.L magriifude of accelerations iri normal directions are very less in the second case than the first one especially -0-5 . for the stem seats. ' ” ' Fig. 9 shows the CAR and the CDR indexes with -1.0 different seat angles for this second case. It is seen that for three positions of the seat (i. e., Bow, Midship, and Stem), the safe seat angle evaluated from the polar ' Fig. 7 Simulated trajectory of free-fall lifeboat - diagrams of acceleration agrees reasonably well with (0=30°, fl/L=l,40, L„o-/Z.=0.15) those obtained from 1 the SRSS and the dynamic : Stem -Midship £—Stem Impact Impact * ,01.-5 -4 , t3 -2,-1 0,1 -3 ' Axial Acceleration (a^) - Fig. 8 - Polar diagram of computed accelerations (6)=30°, HjL=1.40; and L8 o-/L=0.15) Water Entry Simulation of Free-fall Lifeboat 211 evaluated. From the results shown in the paper, the following remarks have been obtained : 1. The proposed polar diagram of acceleration is a simple and effective method for evaluating the safe seat orientations for the occupants at different longitudinal positions of free-fall lifeboat. It gives useful informa tion to understand the impact phenomena as well. 2. The stem of the free-fall lifeboat experiences Midship- two distinct impacts (i. e., bow and stem impact) in two different directions during its water entry. On the other hand, at the bow position, the acceleration caused by the two impacts has almost the same angular direction. These phenomena are shown very clearly by the polar Seat angle (- d cv r ZS- cE Sr St 8 8 #K m % 09 8 8 9- 0< Xi u a #tX 3 % O' Si V % pi 8 04 #0 R Q 4 Gr n St 04 ? 3 R % 4 # 3ft I N n #i1 m k : 9? o 1 1 a™ &K m 4 8- 04 X' a 4 ot Hi 09 d ts- 4 tt u d % £ «x 4 Pt F r6t XI 5 £• m K rv -if f4 4 a » m * ri eX R /v £8 1$ % l$ 04 ag