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OCR for page 157
Prediction of Nonlinear Motions of High-speed Vessels
in Oblique Waves
F-C Clllu,l Y-H Lin ~ C-C Fang,2 S-K Chou2
(iNational Taiwan University, 2United Ship Design and
Development Center, Taiwan)
ABS I RACT
A practical method based on a nonli ear ship
.. fLesis sch me, to calculate the nonlinear motions
of a high speed vessel in oblique waves is p esented
in fLis p per In this method, fLe equations of motions
are described by fLe body fixed comdi ate, rather th m
fLe conventionally used ship carried vertical
coordinate More -: ., the timewarying submerged
hull surface and the coupli g effect between
hmsverse and ve ~i al motions are considered By
using the moment m theory, the flare impact md
dy mic lift are also talcen i to account in the time
dom in simulation, to p went the ~ al
divergence due to the d id of way my or y w
motions, artificial springs in sway md y w modes are
introduced
In order to clarify the validity of fLe pmposed
prediction method, a series of sealceepi g tests i
oblique waves have been carried out in SSPA with a
model of 90 meter patrol vessel, which is designed by
USDDC United Ship Design & D=: elope : Center,
Taiwan) The expedmental results are compared with
the calculation by the present method and some of the
selected results of comparison study are how i this
p per As a practical tool Em predicting fLe nonlinear
motions of high speed vessels in oblique waves, fLe
validity of fLe present method is verified
IN I RODI C I ION
In fLis two dec des, fLe expanding d mmd of
large sized high speed ocean goi g vessels urged fLe
necessity of d : d pi g analytic tools to evaluate fLeir
nonlinear behavim i mugh sea Up to the present,
5=: =:al more sophisticated methods have been
pmposed to predict nonlinear motions and wave lo ds
of a ship at forward speed in head sea Em ex mple, a
th ee dimensional Rim me Pmel Method hi g et al
1996) md a th ee dimensional hansient bee surface
Green Unction source dishibution method (Li & Yue
1990) have proven to be sufficiently useful On fLe
othechmd,apracticaltech iquebai gonanonli ear
ship sy thesis (Chin & Fujino 1929; Chop, Chin &
Lee 1990) ha also pr men to be accurate enough for
practical use
So al years ago, one of the authms Chin and
Li w (1993), followi g the s me nonlinear ship
sy thesis scheme, developed a practical method for
predicting the nonli ear motions of a high speed
vessel i oblique waves Base_ on fLe ~ al
investigation, m existing 60 feet plani g boat had
been how its 6md mental character tics of ve ~i al
md hmsverse m tions in bow/be m sea In this
method, the equations of motions are d scribed by fLe
body fi ed coordinate, rather thm he conventionally
used ship carried ve tical 6 me Moreover, fLe
-i ~~ an. i g submerged hull n -1: e md fLe co pli g
effect between Transverse and ve ~i al motions are
consid red Besid 5, usi g fLe m ment m theory, fLe
flare impact and dy mic lift are also taken into
accomt However, i fLe time d mai simulation,
artificial sp i Es in sway md y w modes are
introduced to pr went the n ~ al divergence due to
the d if t of way md or y w motions
In fLis paper, the dy mic responses of a 90 meter
high speed pahol vessel RD 200, which is d sig ed
by USDDC, havening in oblique waves are predicted
by fLe present method md compared with the result of
experiments carried out by Lmdgren (1997) at SSPA,
in corder to confimm fLe validity of the p esent
method The det iled fommlation of fLe p esent
method was 6 By described in Chin & Li w (1993)
Fm convenience salve, how ver, the basic concept of
the method will be described briefly
I l EORETICAL FORMI LA I ION
Coortfinate System
The fight hand Cartesian comdi ate syst ms and
sig convention used Em following theoretical
fommlation are show i Figure I
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Representative terms from entire chapter:
yaw motions
~/~
~ /~ —~
l
~ - ~ ~.
Figu~e I Co xdi ate sy tem
The space fixed cooldi ate system O X Z
(heleafix Fo fi me) is defined so fhat fLe
X Y plme coincides with fLe undstu~bed watel
sulface md the Z xis is vxtically dow wa~d The
incident waves plopagate towa~d positive
X dilection Ship ca~ied v xtical coold nate syst m
o xyz (hxcafielFv f me) is moving at hip speed
U in x di ection and k eping z xis veltically
dow wa~d x xis is I id on fLe mdst bed watel
sulface The mgle between x di ection md
X xis is denoted with j A othel coxdnate
system o yz is hip fixed hxcafiel Fo f me)
with oligin located at fLe centx of glavity of fLe hip
md x xis pa~allels to fLe bae line of the hip The
ship is ass med to be steady I mning in calm wate
md let fLe moment just encount xi g with the wave a
sta~ti g time t = 0 At fLis moment, the cent x of fLe
watelline at fLe mid hip is set to be o md coincides
with O. A d the cooldnates of o i Fv fi me ale
(x~,y~ t;,) T~and ;,a~ethei clementsofLim
md si k ge due to ste dy lunni g i calm wate
espectively, while ¢,t,: md (,O,l/r dnote
sulge, way, heave displacement md loll, pitch, y w
mgle of Fo fi me lelative to Fv fi me lespectively
due to waves if we define ~ = T~ + O then the
Eulel mgles of Fo fi me lelative to Fv fi me fol a
ship nmning in w es cm be descfibed a (,r,yr,
md fLe lelation hips between the Fv cooldi ates md
Fo cooldnates a~e
X'1 Fx XO +4
y't=Lv`, jy + yO +rl
z'J ~z Zo + (;s + (;
whxethchansfolmationmaUx LVII isdfi edas
(1)
cos ~ cos ~ sin ~ sin ~ cos ~ cos ~ sin
LVD= cosTsin~ sin~sinTsin~+cos~cos~
sinT sin~cosT
cos~sinTcosi,v+singsinYs1
cos~sinTsini,V sin~cosl,V (Z)
Cos ~ Cos ~
Mxewel, fLe lelation hips between fLe
K cooldi ates md Fv cooldinates a~e
Ix
(3)
as equation (2) but just substituti g the Eulel mgles
(~)by(x~o~o)
Then, substituting equation (1) i to fLe 1ight hand
side of equation (3) ,fLe 1elationships between fLe
Fo cooldi ates md Fo cooldi ates c m be obtained as
x X1 Fxo +4 +(lt1
Y = Lov Lv`, y ~ + ~ yO + rl ~ (4)
z zJ ~zo+
I singtEnr cos~tinr
R '= O cos; sin;
O singsecr cos~secr
LEV = L ~ The first term of the fight hand side of
equation (8)
Fu Ccos~cos~ 1
Lzv] O = U(singsinTcosl,v cos~sin1,vt
O U(cos (sinr cosyr + sin; sinyrJ
(9)
denotes fLe velocity component related to fLe steady
forward speed, while fLe second term denotes the
velocity component related to fLe oscillatory motion
speed md c m be defi ed a
IVI=L8VI11I
w ~
(10)
Furthermore, we cm substitute ¢=;~=0,
~ = T~ into equation (9) md d fine the velocity
c mponent of a hip ~ mning in ca m water as
[uol [UCosrsl
wO UsinrS
Incident Wnves
The i cident wave ;~ md fLe subsuzfa~
incident wave (~ aze d scfibed as follow in fLe
space fixed Foft me
(1 1)
;~ = ;~ CoS(l`.X tO t)
(7) :~ = :~e cos(tX t f)
(IZ)
(13)
where (~ is fLe wave mplit de, IS the wave
n mber, t fLe wave frequency, X and Z cm be
exp essed by equation (4) By defi i g
X= X Utcos/, equation (12) md (13)become
~w =
OCR for page 160
The plessuze of
Bemoulli's equation
P=P~ZIPLUtW(UtW1~1
~ p[(v~w)2 (V¢w)z-]
= PZ(Z <~)+ Z pm <~ (l e ) (ZI)
wh xc p is fLe density of watel
Transformaidon of Elydrodynamic Coefficient
Mntrix
The fight hmd Caztesim coxdinate systems md
sign convention used fol fLe hansfommation of
sectional hyd ody mic coefficient mah x aze how
in Figuze 2 The i xis of fLe ve tical co xdi ate
system i yZ hele ftel FV fi me) is I id on fLe
still watel suzface Point b is fLe i telsection of the
x xis of Fo f me and fLe hull section Anothe
vxtical cooldi ate system b yZ heleafiel
FV f me) is palallel to F* fi me Cooldi ate
system b yz hele ftx Fbfi me)isfixedinthe
-
y
Figuze 2 Cooldi ate system fol d fining sectional
hyd ody mic coefficients
hull section We denote the sectional added mass
matfix f x oscillat xy motion with Lm ~ i fLe
F* f me, Lm ~ i the FV f me, [m] i the
~fi me ie
rm~ m~ m°~ 1
° ] m~ m~ m>
m~ m~ m~
m~ m~ m~
[mb ] = m>~ m~ m~
m~ m~ m~
m~ m~ m~
[m ]= m~ m~ m~
m~ m~ m~
(zz)
Denoti g fLe hanslational velocity of a hull section
in FV f me with v i y xis, w i Z xis,
md with p fol mg laz velocity, the sectional
velocity and ang lal velocity in F* f me is
deschbed a v + ZbP , W YbP and
p lespectively Fuzfhxmole, fLe sectional fl id
moment m descfibed in FV fi me can be explessed
in telms of which descfibed in F* f me as
tP ~ P P'
[mb ]] v = [m ] ~ V + ZbP + O (z3)
tw ~ YbP O
whele
P = Lm>~P +m,y(v +Zbp)+m~(w YbP)]Zb
Lm~P + m~v K + ZbP) + m~ (w YbP)] Yb
. Yb. Zb is the co xdi ates of b i I
Considxi g fLe sy meLv of
substituti g the equation
Lm°~. Lm5]and
~mb m~ 1 Em,y m~ 1
Lmb m 1=Lm~ m~4
into equation (23), the mtation related 3 el ments of
sy mehicalmatrix Lm ~ cmbe xpressedi txms
of the elements of Lm ~ as
m7=m7+m7Zb m~yb
m =m°~+m~zb
m = m~°~ + (m 7 + m 7 )Zb (m~z + m Yb
(Z5)
The sectional velocity md mgular velocity i
P
Fb ft me is described a 1~, v Mmeovx, the
w
sectional fluid m ment m described in F~f~ me cm
be xpressed in term of which d scfibed in
Fv f~ me as
[m ]| | = [Vb [m] [bv | |
W W
md then,
[m ] tvb[m]tbv
[m] tbvLm ]lvb
can beobtai ed hxe
F! o o 1
[vb = O COS; sin;
O sin; cos;
md
[bv [vb
(3o)
Substituting equation (29) md (30) i to equation
(25), fLe relation hips between the 6 el ments of
symmehical matrix Lm ~ md those of Lm ~cm be
obt ined a foll ws
m~ = m
m, = m cos ~ + m sin
m~r= m sin¢+m cos~
m~v = m~ coss ~ + m sinS ~ + zm~ sin ~ cos
m' =m (coss~ sin2~)+(m m~ )cos~sin~
mr=m cos2~+m sin2~+zm sin~cos~
(3 1)
Finally, substit ti g equation (24) and (25) into
equation (31), the sectional added mass maUx
Lm ~ d scfibed in Fb 6 me can be t msfxmed 6 m
the sectional dded mas maUx [m ] descfibed i
Fv f~ me ln a mmner similar to the above stated
derivation of the hmsfmmation of sectional add d
mas matrix, d noti g the sectional d mpi g
coefficient matrx with LN° ~ in the F* f~ me,
LN jin the Fv f~ me, [N] i the Fb 6 me, fLen
the equation (24), (25) md (31) are also effective fm
(Z6) the hansfommation of sectional d mping coefficient
mahix
Seddonal Force Components
(Z7)
(Z8)
Since u,v,w md p,q,r are denoted as fLe
hanslational velocity md mgular velocity of the ship
deschbed in Fo f~ me, then the avxage relative
velocity md relative angular velocity to the water at
section x described in Fo f~ me, denoti g with
i7,,v,,w and p,,cmbegivena
i',=u V~ _ 1
v,=v+xr v
(Z9) w = w xq K
P.=P P J
(3Z)
where the velocity of the point y = z = 0 is d fined
as fLe avxage velocity at section x, and
7, V>. K denote fLe sectional aver ge of the mbital
velocity of wave particles given by equation (20)
~e
R = I | Rdc
Vy =—iVydc
K = I iKdc
(33)
md W=Ucos~sinTcos;~+w ~q vespectively
The effects of suzge to fLe othev motion modes sve
as med to be negligible, snd the smge mod is
decoupled in fLe subsequent formulation of fLe
equations of motions
seedimal foreeF znd mom~mt M dm to dhe
eh~mge of fluid momenh~m The sectionsl
hyd ody mic fome snd m ment due to the time
vsziation of fluidm ment cm be descfibed a
where | me ms fLe integ ation slong the hull section M~ d ~ (P Pw
contouz pwdenotes the equivalent avevage sngulaz Fym dt ~ V V
velocity of fLe orbital motion of wave pszticles F. ~ P V,
velative to fLe poi t y = z = 0 at section x, snd is t~. ~.
descfibed by
w C |. w
V,y Vyz
where Pw = z + zZ
(34)
In fLe subsequent formulation of fLe equations of
motions fov a high speed vessel, which sze defived by
followi g fLe Ovdi szy Ship Method sy fLesis, md
like Fujino & Chiu (1933), the state of steady mning
in calm watev is consideved as fLe initisl veference
state fmm which fLe hip motions sze veckoned
Therefove, both the velative velocity md the
hyd ody mic coefficients sze d composed i to fLe
oscillatovy motion velated component md the steady
forward motion velated c mponent By usi g equation
(3)~(11), fLe equation (32) bec mes
i =UcosTcosw+i V<~UcosTcosw
v~= Ucospsinw+v+xr Vy=V Vy
w = (w wO )+ wO
=(UcospsinTcosw+w ~q V~ wO)+wO
_ = (~/ _V~ wO )+ wO
Pr=P Pw
(35)
where the term of si ~ on the flght hmd side of
equation (9) is neglected by considefi g that it is
mmch maller fhm the temm of Cos; Moveovev,
T',IV sve d fi cd as V= Ucos~simyr+t +xr,
m~, m=,o
+ my, m>, o wO (36)
mm mm,O
wheve " ~ " denotes fLe sectional add d mass fov
steady vmning i cam water, snd fLose at infinite
frequency sze used under the ass mption of high
speed mning condition Subscfipt " O " denotes fLe
sectionsl dded mass which is waluated fov fLe
submerged po tion md v the mdistuzbed water
suzface while ste dy vunning i still watev Due to the
symmehy of hull section, m~ 0 = m= 0 = 0 can be
substit ted i to equation (36)
Seetmmml damptng force F znd moment M
_ Similaz to F md M ,fLe sectionsl d mpi g
fome md m ment sze decomposed into the oscillatovy
motion velated component snd the ste dy forward
motion velated component, md is descflbed as
(37)
wheve " ~ " md " O " have the s me mesni g
mentioned sbove Then the second temm of fifht hand
side ha no conhibution fLevefove
Seetmmml resh rtng znd Iromdmlfrytov force
F zmd momem M Denoti g fLe sutmerged
po tion md v fLe mdistuzbed water smface while
steady vunni g i still w tev with CO, pressuze acti g
on it with PO, md the submecged p xtion undx the
mdist bed incid nt wave smface while mnni g in
wave with C, pcessuce acti g on it with P ,the
sectional cest xi g and Fmude F ylov fxce and
moment ace descfibed a
F~ = |Pdz
F~ = |Pdz | PodY
· , ., , (38)
9~ = l p ydy + zdx ) + ml ~ (ze zO )sin ~
+mg(3/c yO)({ COS¢)
wh xc | me ms the integ ation along fLe contom of
sut mecged po tion f om p xt to starboard Ye ~ Zc
denote the co xdinates of sectional cent x of gcavity i
Fv f me m is sectional mas PO cm be obtai cd
f om equation (4) md is expcessed as
Po = P Z. = Plf(Zo + (;s Xsin7S
while P is given a equation (21)
(ZCOS7S)
Seealmal imr&e force F and momem Ml _
The sectional i xtia fmce and moment are expcessed
as
F~ = m(v + xr )
F.' = m(w x1)
M' = i~P
(4o)
celative to o x xis
Equnidons of Moldons
T ing the mation of all fLe sectional fmce md
moment stated above, fLen integ ati g fLe total
sectional fxce and mom nt fmm fLe afimost
watec hull i tecsection A to the f x most wat x hull
intxsection F yields fLe equations of motions in
Fo f me a follows ln which fLe state of ste dy
mnni g in cam watx is considxed a fLe i itial
cefxence state fmm which fLe ship motions are
ceckmned
sway | (F,m + F. + F. + F. )dx = 0
heave | (F~m + F.' + F,~ + F.' dx = 0
rall | (M~ + M~ + Ml +M' dx = 0
pitch | K x) (F~m + F.' + F,l + F,')dx = 0
y w | x (F>m + F~ + F~ + F~ )dx = 0
(41)
Substit ting equation (35) i to equation
(36~(35) ,(40) md then substituting these equations
into equation (41), the cesultmt equations of 5 D
coupled motions are expressed in a mah x fmm a
~-1 ~W1
[mjj]|pl+[\`j]lPl+{Ri}+{Li}
= {F}+ {D;}
whece fLe d tailed xpressions of the vacious cl ments
incl ded in fLe coefficient matfices and fLe fmce
vectms can be cef xced i Chiu & Li w (1993)
Nl MERICALALGORITHM
Seddonal Elydrodynamic Coeflmients
The pmcedme to calculate fLe i stmtmeous
sectional hyd ody mic coefficient matfices
[ml[N] and [dm/dt] i Fb fc me dmi g
n mefical integ ation of equations of motions can be
descfibed bciefly as follows
The sectional hyd odyn mic coefficients i
Fv f me at swecal diffecent pcescfibed d fts and
heel angles of a section at an enco mtec f equency, i e
[m 1 [N ], and fLose at i finite fcequency, i e
Lm ], ace computed i advmce by Fcank close fit
method (Fcmk & Salvesen, 1970) fm each hmsvxse
section Mmeovx, Ldm /dd,] . Ldm /dd, j,
Ldm /d¢,] md Ldm /d¢,] cm be calculated
then h xc d, md ¢, d note fLe sectional d afi md
heel mgle of a section celative to mdistmbed w e
smface cespectively The obt ined cesults ace saved as
a database. Making use of such a database, the
sectional hydrodynamic coefficients are evaluated by
interpolation at each time step during numerical
integration of equations of motions. tamb /0t~as
well as tamb /3t~can be calculated by
amb amb aa7r + am 3¢,r ¢
at fair at Oar at
Then the instantaneous sectional hydrodynamic
coefficient matrices [ml [N] and [3m / at] in Fb
frame can be obtained following the transformation
described in the previous section.
Time Integration
For the numerical integration of the equations of
motions described in ship-fixed FB frame, i.e.
equation (42), the Newmark- ,B method with ,B =1/4
is used from the viewpoint of the stability and the
accuracy of numerical integration. The discrete time
interval At adopted for time integration is 1/60 of the
encounter period.
Viscous Roll Damping
In order to take into account the viscous effect in
roll motion, the equivalent roll damping coefficient
N44 is expressed as N44 = 2m44~e ~ where
m44 is the virtual moment of inertia in roll, and
He denotes the roll damping factor which is evaluated
from roll decay test results according to
In '¢~° = He n · 24
(44)
where ¢0 denotes the initial roll amplitude used,
n the number of swings, ¢~ the roll amplitude of nth
swing, and T4 denotes the natural rollperiod.
Artificial Spring
In general, to solve the 5 degrees coupled motions
in time domain, the stability of solution will be
affected by sway and/or yaw motions due to no
restoring force and moment in these two modes.
Therefore, to prevent the numerical divergence due to
the numerical drift of sway and/or yaw motions,
artificial springs in sway and yaw modes are
introduced. Other methods such as introducing rudder
force with auto-pilot or introducing a numerical filter
may be considered, however making use of artificial
springs seems to be the simplest way to meet this
purpose. The strength of the artificial springs is
decided by a trade-off, that is to say it has to be strong
enough to keep the drifts small, and weak enough not
to affect the motions significantly.
In this paper, the artificial spring constant is given
by K (me 12)2 M, where M denotes the mass for
sway mode, and the longitudinal moment of inertia for
yaw mode respectively. while K is a factor for tuning,
K=10.0 is adopted to carry out the numerical
computation .
COMPARISON OF PREDICTION AND
EXPERIMENTAL RESULTS
In order to verify the validity of the present
nonlinear prediction method, the model test results of
a free-running 1:25 scale hull model carried out in
S SPA Maritime Dynamics Laboratory are used for
comparison. The model is self-propelled, autopilot
steered and free to move in all six degrees of freedom.
There are over 120 runs performed in this test project.
They covered investigation of the seakeeping
performance of the vessel, which is designed by
USDDC, in both regular and irregular waves. This
paper describes some of the selected results of the
comparison study. Solid model of the RD-200 is
shown in Figure 3. Some of its principal particulars
are shown in Table 1.
Figure 3 Solid model of the RD-200
Table 1 Principal particulars of the RD-200
Length between perpendiculars, L
Breadth of Water Line, B
Draft
Displacement
Vertical position of CG
Longitudinal position of CG
Radius of gyration in roll
Radius of gyration in pitch
90.0 m
12.2 m
3.55 m
1840 tonnes
5.59 m abv B.L.
46.92 m aft F.P.
4.43 m
22.5 m
The comparisons between experimental results md
present predictions for the cases in regular b w sea
( X = 135 deg) with various wavelengths at the
forward speed corresponding to fLe Em de n mber in
ship 1=::=. h of 0 416 ate selected to be how i fLis
p per The wavelength to ship length ratio ( ~ / ~ ) md
wave steep ess (He 17) ate show i Table 2, varied
60m 0 476 to 4 gg5 md 1/29 9 to 1/136 5 respectively
The corresponding data used i prediction for
c mpamison are also how i Table 2 The Heave, roll
md pitch motions a well a : -i al accelerations at
mai deck of FF, LCG stations and at helicopter
platform were measured and compared The steady
mni g him md CG rise meauled at fLe ab we
mentioned fo ward speed i ca m water are
approximately 0 39 degree md 0 33 m respectively
The roll d mping factor Eli and natural period
T4Obtai ed 60m fLe mll decay test at fLe forward
speed correspondi g to 24 mot of fLe 6 11 scale hip
ate O I 5 md 5 I second respectively
71L
0 476
0 623
0 6g7
O 848
I 073
1 401
1 909
2 271
2 747
3 393
4 292
4 EE5
Table 2 Wave length md steepness
Rend meats r
Halt
1/29 9
1/39 0
1/30 0
1/29 9
1/37 9
1/39 1
1/53 3
1/63 4
1/76 7
1/94 g
1/1199
1/136 5
A/L
r
06 1
_ OS I
lo 1
_ 125
_ 15 1
175 1
_ 20
_ 25
So r
35 r
40
_ 450
H 1
1/30
1/30
1/40
1/40
1 1/40
1 1/60
1/60
1/90
1/90
1/120
1/120
1/120
Figures 4 fnrough 9 illustrate the wavelength
d pend ace of responses of :' 200 havelli g i b w
seas at fLe fo wand speed corresponding to the Fmude
n mber of 0416 In these ~~ .5 the
nondimensionalixed mplit d s of I order md the
phase male, which is related to when the wave Cough
is at the ship's CG, of heave 5/5, roll
y/~ and pitch 0/~ as well as :~~i al
accelerations at mai deck of FF station
OF. /~5~, of LCG station ;~CG/~5~ md at
helicopter platfomm I,, /a(5~ are plotted together
with predicted responses obt ined by the present
computation The abscissa of the fig es denotes fLe
wavelength to ship length ratios ~ /
414~
~U'~
l
~Present
O Exp
180 ~
1
of of
0~0 10 20 30 40 50 i/1
Figure 4 Heave response in b w sea atFn 0416
¢1~
24q
20~
.2 _
os
on
moo ~
for
o ~
Con
ang e (deg )
,~ i N°
As seen in these fig es file present calculations
tend to somewhat Underestimate the pitch md vertical
acceleration responses in file wage of longer
wavelength, while the agre ment between file
responses predicted by file present calculation and the
experimental results se ms satisfactory it is especially
evident that the pe k location by file calculation agrees
k bly well with file experimental results
O/1c(~
7_ ._
o
~ T r r T 1 ~ T r I
Phase ang e (deg )
o
to
270
(~ / 9De
r r r 1 ~ T r j
Fig e 7 Response of : hi al acceleration at
main d ckof FFstationi b ~ sea as F- 0416
CLOG / °Se C
dew ~
Figure 3 Response of ve tical acceleration at
m in d Ok of LCG station i b w sea at Fn 0 416
0~_- _ ~
HEP / °)e
Lo
lo
0
ange (deg )
_ _ ~ O
270 J
350 OK
450
O /L
Figure 9 Response of vertical acceleration at
helicopter peal -= in bow sea at Fn 0 416
he recorded time histories of m tions together
with calculated results of two test runs of //L
1 073 and 1 909 ate show in Figure I O and Figure I I
respectively in these figures wave as well a sway
md heave motions ace nondmensionalized by wave
mplit de, while All, pitch md y w motions are
nondimensionalized by the mplit de of wave slop
F themmore, fLe calculated heave motion is k pt in
phase with fLe mended heave motion, md it can be
f md that fLe relative phase angles between motions
obtai ed by present calculation ag ee well with that of
experiment results
, Exp
l T
C_'5
20~
00: .
20
~/~a
00: ~
~O-
2 0
005~
20
4/~a
00~ ~
JO
~ ~ rat,
Cal
~ / L=1 073
Hw/ ~ = 1/37 9
ooze
'° ~ 1
20
00 ~ ~
20
JO—
ooze \AAAAI
JO
~ 0
002~
~ JO
DO ~ ~
us 1
so t(sec) Co 90 100
~,~ 1 073atFn 0416
I Exp
°] /VW
° 1
o:
to
2 0
001~
20 1 1 20 t
Coca
00 ~~ 1,, :~ 20
to MALI sol JJv ~
ViK(B
20 20
TV
1 r 1
~ taco 110
Cal
1/ L=1 909
Hw/ 1 =1/53 3
° 1 1
.o
°° ~ ~AAI
oo —~ ~ oo
20 1 1 20
~ 10 20 30 ~ (sac) 50
1 r 1
Figure 11 Comparison of time hi t Dies of
motionsinbowseawith //L 1909 at En 0416
CONCLt SION
A prediction method, basi g on a nonlinear ship
.. thesis sch me, to calculate the nonlinear motions
of a high speed vessel in oblique waves is presented
md pplied to a high speed patml vessel :' 200
havening i b w sea The present results of ship
motions and v xtical accel nations at th ee different
positions, have been validated by a pmp X comparison
with experimental data A d fLe following conclusion
may be d awn
Through fLe comparison between fLe dy mic
responses predicted by the p esent nonli ear
calculation and UP ximental results, it is confimmed
that fLe present method can be applied to estimate fLe
ship motions and v xtical accel nations along ship
length of a high speed vessel i oblique waves with
accuracy enough for practical use F th Am Be, it can
be xpected that oth X dy mic responses for
instance, wave load and p essure on hull pa :=l
c m be p en cted by extend ng the present method
ACKNO~tEDGEMENTS
This research wa 6mded by the National Science
Comcil T iwm under Grmt N mbers
NSC80 0403 E 002 01, NSC88 2611 E 002 01, md
the Mi ishy of Economic Affairs Taiwm md r Grant
N mber 5891030
REFERENCES
F.C. Chhu & M. Fujino,'Nonli ear p ediction of
vectical motions and wave loads of high speed crads
in head sea', lnternational Shipb ilding Prog ess,
Vol. 36, No 406, 1989
F.C. Chiu & Y.C. Linw,'A practical method for
estimating ship motions of high speed cr fts i
oblique waves', Journal of fLe Society of Naval
A chitects of Jap m, Vol. 1 74, 1 993
S.K. Chou, F.C. Chiu, Y.J. Lee,'Nonli ear motions
md whipping lo ds of high speed crads i he d sea',
18 ONR Symposi m on Naval Hyd ody mics, A n
A bor, 1990
W. Frank & N. Sntvesen,'The Frmk close fit ship
motion c mputer p og m', NSRDC Repo t No 3289,
Bethesda, Md, 1 970
M. Fujino & F.C. Chiu,'Vectical motions of
high speed boats in head sea md wave lo ds', Jo mal
of the Society of Naval A chitects of J pan, Vol. 154,
1983
D. Krtng, Y.-F. Hunng, P. Sclavounos, T. Vndn, A.
Branthen,'Nonlinear ship motions and wave i duced
lo ds by a Ranki e method'21 ONR Symposi m on
Naval Hyd ody mics, Tmndheim, 1 996
W.-M. Lin & D. Yue, 'N merical solutions for
large mplit de hip motions in fLe time domai ', I 8
ONR Symposi m on Naval Hyd ody mics, A n
A bor, 1990
J. Lundgren,'USDDC OPV Seake ping tests in
regu ar md megular waves', SSPA Report 97 4256 1,
DISCUSSION
T. Ful~sa~
Kanaza..s institute of Techmo I ogy, Jcp m
let the time domain simulation of ship motion
in oblique waves, it is most impo tmt to secure
the mmmericcl stability in simulation, bee mse
there is no restoring force md moment in sway
md yaw motions The absence of the ~estormg
force md moment ceases the mmmericcl d fftmg
md diverging of ship motions in the simulation
The mthors adopted the artificial prings to
remove She mmmericcl d if ing in sway md yaw
motions How ver, it is not easy to determine the
adequate sprmg constmt, with which She d fftmg
of motions c m be controlled, so Nat the motion
amplitude md phase mgle are not effected by She
sprmgs The discusser, on the of her hand, hr.
proposed c procedure to remove the mmmericcl
d if ing of ship motions with the use of c
mmmericcl filter [I ] in this procedme, There is no
messy probl m Ike She detemmirution of the
sprmg constmt, md She ship motion cmplit de is
not effected et all
he She Figmes 10 md 11, the predicted
swaying md yawing amplitude hr. not enough
accmacy comparing with the of her motions Does
this mean that the artificial sprmg constmt using
in She paper is not adequate? A d, if it is difficult
to choose She adequate sprmg constmt, isot it
better to use such c procedme es the mmmericcl
filter to remove She mmmericcl d if ting?
On She otherhmd, the actual d if ting in sway
md yaw motions is inevitable in the experiments
in the case where c f rumming model is used
The d fftmg m yawing motion, in particular,
closes the shift of attack mgle of ship to wave,
md She mean encounter mgle between ship md
wave differs from the expected one
I would like to hear the mthors' comment on
the comparison of He d if tmg in sway md yaw
motions m the experiments md m the simulations
How cm we predict She actual d if ing in sway
md yaw motions, avoiding the mmmericcl d fftmg
in These motion ? A d also, m case the d fftmg in
the simulation is removed, how do we consider
the encounter mgle shift in the experiment ?
I Fukasa~, T. "On She Numerical Time
Integration Method of Nonlinear Equations
for Ship Motions md Wave Loads in Oblique
Waves," Joumcl of She Society of Naval
A chitects of Ji purrs Vol. 167, June 1990, pp
69-79 (in Japanese)
AUTHOR'S REPLY
Th predicted lateral moti ms me relatively
sensitive to the values of artificial sprmg
constmts, md the predicted sway md yaw
amplitude is not satisfactory The mthors agree
withthe discussor's opinion that it's better to use
c mmmericcl filter to avoid the mmmericcl
instability it requites et lea t N times of the
computer time, where N denotes the order of the
mmmericcl li lter, which values m ight be, say, 50 or
60 Basing on results show in this paper, She
futme study on the employing of c mmmericcl
filter into She present model is undergoing
The physical d ffting in sway md yaw
motions are not considered in the present method
As show in the experimental records of Figures
I O md I I, the overall yaw d if are no more f m
3 degrees The effect of the d fits on She
encounter mgle seems to be little
DISCUSSION
D Yue
Massachusetts Instit te of Tech olo :, USA
In the presser model for the prediction of
nonlinear motions of high-speed vessels, artificial
sprmgs are employed to suppress the mmmericcl
instability associated with the d if t of sway md
yaw motions How sensitive is the overall
solution to f he choice of the spring c or at mts?
Since the d if of sway md yaw motions is
physical md should be considered es part of the
solution, it is probably more recsorurble to include
physical damping (ouches She wave-d if
damping) rather th m artfficicHestormg t:3rces to
retain She stability of the scheme Could the
mthors comment on His?
AUTHOR'S REPLY
The following is c t piccl example, Figme A
shows the sensitivity of ship motions to the spring
constants The vertical motions em not be
effected significmtly, while She t msverse
motions are quite sensitive to the spring constmt
This sensitivity may be considered es m
importmt factor that results in unsatisfactory
lateral motion predictions The mfhors would
suggest that c mmmericcl treatment may be needed
to obtain c stable solution The mfhors also agree
to the discussor's viewpoint that it may offer c
mme recsorurble solution to take into account She
physically exi ti g d if ing force which was not
considered in the present model
0 _
—
_ Heaved ~ . ~ ~ ~ I
vU_ Vow ~
00 05 lO ~ ~ 20 091f
Figme A E fects of artificial Spring Constmts on
ship motions ( ~ I L =1 0 et Fn=0 416)
DISCUSSION
J xia
The University of We tem Aushalic,
Aushalic
Could the mthors please comment on She
i duence of neglecting memo y effects on Heir
mod hng of hyd odynamic forces md vessel
motions
AUTHOR'S REPLY
Since we just take into account the effects of
noncimulatory part of dynamic Ifft on the ship
motions, so Here is no need to consider She
memory effects However, the reduced fiequency
of c plarming vessel rumming in heed se seems
not to be smell enough to neglect the memory
effects if the circulatory part of dynamic lift is
taken mto account The mfhors thirJc Nat it needs
further study to clarify She influence of neglecting
the circulatory part of dynamic lif on ship
motions
