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Total System for Prediction of Seakeeping Qualities of Ships
(Prediction of Ship Motions, Wave Loads, etc. and Its Application to Design)
Mt
M ITtRNHl iEC1IL(1. 1-31 LLE 1EN No. 160
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A. rn-A ts" - Acz-(Prediction of Ship Motions, Wave Loads, etc. and Its Application to Design)
TECHNISCHE UNIVERSITET Laboratorium voor Scheepshydromechanica Archief Mekelweg 2, 2628 CD DelftA "Total System for 141144115617g§§arnfinPafitfeFt1)8§§ips" based on the Ordinary Strip Method (0.S.M.) had been devel-oped and completed in 1980. The system has been widely used in our design department for not only the prediction of seakeeping qualities but also the direct calculation of structural strength according to the predicted wave loads.
Although remarkable developments in the strip theory have been achieved in last 10 years and we also have continued the studies in this field, the above mentioned total system based on the O.S.M. is still usefull from the practical point of view.
This paper gives an outline of the system including the general flow of computer programs, the calculation methods, experimental confirmations of prediction method, and the applications to the design of a ship.
Introduction
Ship navigating in ocean is subject to external forces, such as winds and waves. The various qualities related to
the behaviour of a ship in waves are called "seakeeping
qualities", which include ship motions, accelerations, deck wetness, wave loads, slamming, added resistance, speed
loss, propeller racing, weather routings, etc.
To secure the safety of navigation over the long term of a ship's life, the extended considerations should be made at
the initial design stage in order to provide excellent
sea-keeping qualities as well as necessary and sufficient ship structural strength.
The studies on seakeeping qualities has been remarkably
developed with the growth of digital computers and the construction of model test facilities during the last two
decades(' (5'. At present, computer programs for predict-ing seakeeppredict-ing qualities are in use by many organizations through the experimental confirmations.
Mitsubishi Heavy Industries has conducted an extensive study on seakeeping qualities over a long period continu-ously and made the application of the theory to the practi-cal design through the confirmation by model experiments in the Seakeeping and Manoeuvring Basin of Nagasaki
Ex-perimental Tank.
As a result, in 1980 a "Total System for Prediction of Seakeeping Qualities of Ships- based on Ordinary Strip Method (0.S.M.) had been completed and the system is
widely used in design stages of ships, though many further development in this field has been continued after comple-tion of the system.
An outline of the system is presented in this paper,
including general flow of the computer program, calcula-tion methods, experimental confirmacalcula-tions and applicacalcula-tions
to design.
Outline of computation system
The total system for prediction of seakeeping qualities of ships consists of three program modules; input
manage-ment program module, calculation program module and
output management program module. The general flow of computation system is shown in Fig. I. The system is com-posed of many elementary programs and all of the data in
each program are connected through data files.
Dr. Eng., Ship Engineering Department, Shipbuilding & Steel Structures Headquarters
**Ship Engineering Department, Shipbuilding & Steel Structures Headquarters
Ryuichi Nagamoto* Michi Matsuyama**
Kunifumi Hashimoto t* Takeshi Takahashitt,
Calculation program module
of response functions Ship motions
Wave loads Hydrodynamic pressures
Relative motions to wave surface
Accelerations Calculation program of statistical probabilities Data file (C) Table output Graph output
Fig.1 General flow of the computation system
Each program is written in FORTRAN language and the whole system is of the order of about 20 000 steps.
Func-tions of each program module are outlined as follows.
2.1 Input management program module
The input management program module handles the
data on calculation items, principal particulars, hull form, wave conditions and the coordinates of specified points on
hull.
The constitution of the input data is detailed as follows.
Calculation items
The calculation items such as ship motions, wave
loads, hydrodynamic pressures, relative motions to wave
surface, and accelerations are specified. Principal particulars of ship
Principal particulars of the subject ship, such as ship
length (L), breadth (B), depth (D), draft (d), trim (t),
location of the center of gravity (LCG, KG), mass
mo-ments of inertia (IIyy,Izz), etc. are read in.
Hull form data of ship
As described in later chapters, theoretical calculations
aie carried out based on the strip method, in which data
on shapes of 20 equi-spaced sections in longitudinal
direction are needed.
The breadth, draft, and sectional area of every hull
Input management program module
Hull form data
Ou put management program module
Data file (A) Data file (8) I.
<
,form section corresponding to the loaded condition of
the subject ship are read in. As the input program is
connected with standard hull form data file, it is easy to prepare various data on each section by specifying the
mean draft and trim.
Data on weight distribution (optional)
For the calculation of wave loads, the longitudinal
distribution of ship light weight and dead weight, and moment of inertia (ix,r) for rolling at each section are read in. The moments of inertia for pitching and yawing are calculated from the given weight distributions, and
the agreement with the values given in (2) are confirmed. Wave conditions
Wave lengths, wave heights and wave encounter angles are read in.
Ship speeds
Ship speeds are read in.
Specified points on hull (optional)
In calculating hydrodynamic pressures, relative mo-tions to wave surface and acceleramo-tions, the points on
hull to be made a calculation have to be specified. Wave spectrum and sea route
A type of wave spectrum and a sea route of which
wave statistics are stored in the program are specified
for statistical predictions of ship responses. 2.2 Calculation program module
The calculation program module consists of independent program which corresponds to each calculation item. Each of these program groups can be available as a component of the total system or as an independent program.
(1) Ship motions
This program has the following functions;
to determine two-dimensional hydrodynamic forces
on each strip as Lewis form section,
to determine the coefficients of equations of ship motions by 0.S.M., and
to solve the equations of motions, and to calculate the amplitudes of ship motions and phase difference
to waves.
In usual case, the two-dimensional hydrodynamic forces
are determined through the interpolation of the table of block data in the program, while, if necessary, the
forces can be directly determined by solving two-dimen-sional boundary-value problems based on Ursell-Tasai
method(6)7).
The ship motion program consists of three groups of motion, that is, surging motion, vertical motion (pitch-ing and heav(pitch-ing) and lateral motion (sway(pitch-ing, yaw(pitch-ing
and rolling). Usually all equations of motion with 6
degrees of freedom are solved together, but one arbitrary
group among them can be selected through an external
command.
(2) Wave loads
The wave load program consists of two groups of
calculation program, one for vertical bending moments and vertical shearing forces, and the other for horizontal
bending moments, horizontal shearing forces and tor-sional moments. Wave loads can be calculated at each square station of a ship.
Hydrodynamic pressures Relative motion to wave surface Motion accelerations
Response functions of these items, (3), (4) and (5)
are calculated on the basis of the amplitudes and phase differences of motions obtained in (1).
Statistical probabilities
This program has the functions to determine the energy spectrum and standard deviations of ship
re-sponses based on the linear superposition method, and to make a statistical prediction of the long-term exceed-ing probabilities of ship responses in accordance with the Fukuda's method(8) prevalent in Japan.
The data of wave spectrum and long-term wave
statis-tics is stored in the system. It is also possible for desig-ners to input wave occurrence probabilities of specific
sea areas. A long-term prediction taking account of
nominal speed loss along navigation routes is available.
2.3 Output management program module
All response functions obtained by calculation program
module are stored in the files, and can be printed out in
forms of tables and plotted out in forms of graphs.
In these programs, not only final calculation results but also interim values prepared in the process of calculations (such as hydrodynamic forces, coefficients of motion equa-tions and components of hydrodynamic pressures) can be
printed out in order to facilitate earlier confirmation of
calculations.
2.4 Connection to the structual analysis program
We have already had many systems of the structural analysis programs which are called as "Total System of
Ship Longitudinal Strength(9)", "Total Analysis System of Transverse Strength(10)", "Total Hull Girder System(' 1)",
etc. As an example, the flow chart of the "Total Analysis System of Transverse Strength" is shown in Fig. 2. They
can be connected with this total system for prediction of
sea-keeping qualities through a slight modification.
As the applications of this total system, we have studied the problem how to decide the design value of wave loads
Input data
Calculation o
load vector t each time
Analysis of tank part structure tor unit load
Calculation of structural response amplitude Statistical analysis Load vector Short-term and Long -term probability of stress and deflection
Fig. 2 Flow chart of total analysis system of the transverse
strength(10)
Data file (B) t
which are necessary to the structural strength analysis. By use of a consistent calculation from the response functions to the statistical prediction of wave loads, much considera-tion to the design value was made in comparison with the
1
one given by various classificationsocieties(2 (18 ).
Special features of this total system described so far are
summarized as follows:
Theoretical calculation programs for prediction of
seakeeping qualities have been systemized into a con-sistent continuous calculation.
Each elementary program is available as an
independ-ent program.
Input commands provide the selection of calculation items and the output of interim value in the process of calculations, thus eliminating wasteful calculations and
also facilitating easier confirmation.
The input of hull form data through the offset
pre-pared in hydrostatic calculation program prevent
mis-takes in data writing.
The tabulation of response functions using the line-printer, and the graphic output of them on the plotter
enabled appreciable labor-saving for the arrangement of calculation results, which had required a great amount
of work.
The connection of various data through the files
pro-mises the further growth of easy applications of the
system.
Calculation method
In this system, various calculations on seakeeping quali-ties are carried out by means of the 0.S.M.(2)(3). The cal-culation methods are outlined as follows:
3.1 Coordinate system(19)
The coordinate system is shown in Fig. 3. The space
fixed coordinates
ni,
i are the right-hand system, and the vertical downward direction is a positive direction of i axis. It is assumed that waves advance to the positivedirection of the axis, and that a ship makes motions of
Waves Lee side e' Weather side Waves 71f Hydrodynamic pressure Looking forward
Fig. 3 Coordinate system
and sign convention
Table 1 Nomenclatures
small amplitude around the average position, sailing on a straight line with the angle p to the direction of wave
pro-pagation having advance speed of V.
The coordinate system, o-x, y,z is the right-hand system
fixed to a ship, and the origin is at the cross position of
midship and still water line on ship centerline. The down-ward direction is the positive of z axis. In Fig. 3, sign
con-ventions of motions and wave loads are shown.
The surface elevation of incident wave is expressed as
follows;
= hA cos(kx cosp ky sinp Wet)
27r
where, k
='
X: wave length, o..), = kV cos pX
The nomenclatures which are used in the calculation are
listed in Table 1.
3.2 Calculation method of ship mot ions(3) (1) Heaving and pitching(20)
Let's suppose a strip of a ship cross section with small
length dx. The vertical motion at x cross section can be
expressed as follows:
xG)0 (2)
The force due to the vertical
motion of the strip is expressed as the sum of four kinds of forces.
dFBz dFBzi dFBz2 dFBz3 dFBz4
dx dx dx dx dx
Hydrostatic restoring force
dFBz/
= 2pgy,, 1"
xG)0dx
Wave-making damping force
L, B, D, d, S length, breadth, depth, draft, sectional area
V displacement volume
vertical prismatic coefficient
lxx, lyy, mass moment of inertia
k xx, kyy, kzz radius of gyration fluid density
acceleration of gravity
is lever to shear center
X, hw, h A wave length, wave height, wave amplitude
wave number (k = 27r/X)
surface elevation of incident waves
Tv, Hi, visual wave period, visual wave height
Tw, mean wave period, significant wave height
wave direction
circular frequency of wave
we encounter circular frequency (we= w kVcos,u)
V. Fn ship speed, Froude number (Fn= )
t A, °A, 'PA, OA amplitude of ship motion
q, co, E E ,e phase angle of ship motion
FV, FH, MV, MH, MTG, M TS wave loads
A,
Ay, Az motion acceleration04, space fixed axis
o-xy z body fixed axis
Go, XG, ZG center of gravity of ship
center of gravity of strip
pSz, pSy sectional added mass
pNz, pNy, pNR sectional damping coefficient
iw lever of damping force
lever of added mass for swaying motion pi added mass moment of inertia
a sectional area coefficient (a = S(x)1(B(x),1(x))
w(x) sectional weight
o-,
(1) . V ) nA, et, Go', ZG'dFBz2
pN, (x xG)e. + (5)
dx
Force due to change in kinetic momentum of fluid
= pSz ft
(x x G )6. + 2 Vol d(pSz) (x XG)e + V0,1 (6) dx Inertia force dFBz4 w Q (X G )0 t dxwhere, yw : half breadth of' the waterplane at x cross section.
pSz added mass of the strip, for z direction.. pNz : wave-making damping force of the strip
for z direction.
(F13,2 + FB,3) is called radiation force.
The wave exciting force is calculated as the force act-ing on a restrained ship in waves. The force can be di-vided into two components; one is the hydrostatic force derived from the velocity potential of the waves undis-turbed by the presence of ship (so-called Froude-Kriloff force), and the other is the hydrodynamic force caused by the waves disturbed by the ship (so-called diffraction force). Diffraction force is approximately obtained by
substituting, the radiation force, assuming the motion
equivalent to orbital velocity and acceleration of waves, at a representative point of the ship cross section.
Then, the wave exciting force acting on a strip Is
expressed as the sum of the three following forces.
dF wz
dFi
dF wz2 dFwz3+ _ (8)
dx dx dx dx
dFw, pgh.AC C22yw cbs (kx cosp (Jet) (9)
dx
dF wz2 pArzhAC1C2wsin (kx .cosg
wet) (10) dx
dF wz3
pSzh A Ci C2 W2 cos',(kx cos t..t wet)
dx
pSz)
+ Vd( hAeiC2wsin,(kx cow' Wet) (11)
dx
where, coefficients C1 and C2 are correction factors to
represent effective wave elevation in oblique waves, and are given as follows:
CI = sin (kyw sing)/kyw sing (12)
C2 =e (13)
'The heaving force and pitching moment acting on the 'whole ship generated 'by ship motions are given as
fol-lows; = FE dFBz FE (dFBzi d F Bz2 F Bz fAE dx .dx AE dx dx dFBz3 dFBz4) dx dx dx FE d M
f FE
M Be =dx=
dx AEOn the other hand, wave exciting force and moment
acting on the whole ship are given as follows: FE dF wz Fwz dx SAE
dr
(7) (14) dFBz (x x,G)dx k15) dx =fAFEE dre FE (dFwzi dFwz2 dFzw3 d FxE dFw:X dx (16) xf
Me =
:
S
AE d dx = (x' x,G)dx 1 7) AE dxThus, the coupled equations of motions of heaving'
and pitching are obtained as follows.
F Bz F wz = 0
(f8)
MBe M we = 0 (19)
These equations can be reduced formally into th
following expressions
+ A 12 +A 13 +A140 +A
150'+A160 =F 42%
"22-+A23+1124°±A'256-1-A26° =M we' (21)
These coefficients such as Av, etc.. are listed in Table 2.,
Surging
Surging is dealt with independently assuming that if
does not couple with other motions, and is formally
expressed as follows. (as for Aii, etc, see Table 2,)
A 31 A 32 t + A 33 = Fw (270
Equations of motions of surging is introduced from
the mass of ship and the Froude-Kriloff force, on the
assumption that the ship is slender and that added mass
and damping force for surging are both negligible. Swaying, yawing, and rolling
The lateral motion at x cross, section are expressed
the same way as vertical motion.
77x =77 +(x xG)V) + ZGct) (23)'
The rotational motion around the x-axis is expressed
as follows-. Cbz =0
Horizontal forces and rolling moments around the
x-axis acting on a strip consist of the following
compo-nents:
dFBy dFByi dFBy2
dx dx dx
dMB15, dMB0,1 dMB02, dM Bey 3 dMB04
dx dx ,dx dx dx
dMB0,5
(26)
Hydrostatic restoring force and moment
dFByl 0
dx
wG6.11,10q5
dx
Wave-making damping force and moment
dFBy2
dx
+ (ZG-w)ti)
=,pNy(ZG +(x _ x0,1,
+ (z G
.10c.b Vi
Force and moment due to kinetic momentum
change of fluid dFBy3 = pS1,117. dx + (x
(ZG 1)0
d(pSy) . 21/+ Vi +
-,dMBoi dFBy3_ dFBy4 dx dx (2,9 (25) dFB,3 dx dM B02 dx (27). (2?) (30) (d) = g : = (C) = 4 FE + + as dx (c)(1) Coupled motion of heave and pitch(A 0, F,, Mwb)
Ai, =
f
(I1j- + pSz)dx, Af
pNzdx VIPSzlA = 2 pgywdx, A14 =
(
+pSs)xbdx= TpSsxbdxA15 =
f
pNzxbdx Vf
pSzdx + V[p.Srx, IA1b =
2f
pgy,,x,dx + Vf
pNzdx V2 [PS,,1A21 = A 14, A22= fpNzxbdx V
f
pSzdx+V[pSzxb] A23 = 2f pgywxbdx, A24 =f + pS.,)4dxA25 = pfNz4dx V[pSzxg]
(2) Surge(Ao,Fw)
w(x)
A31
=i
dx, A32=0, A33=0(3) Coupled motion of sway, yaw androll (ao, Fwy,Mw,b,Mw0) a11 -g +PS)dX a12=f pNydx V[pSy]
=0, .14
=f(
+pSy)xbdx.15 =
f
PNyxbdx V f pSydx V[PSyxb]a16 = -V
f
pNydx + IpSy1 , a12 =f
pSyl;idx a18=fpNylWdx V[1pSy], (119= 0, .21 =a14a22=f PNyxbdx+V f pSydx V[pSyxb], a23 =0 a24
f
+ PS y) xi c 1 x , f pNyxi,dx V[pSyxl,i a26 V f PNyxbdx +1/21 fpSydx + EpSyxhil. a27 =fPSy1x8dxa28 = f PSyldx V[pSyl;ixb]+ fpNylWxbdx
.29 = 0, .31 =a17, a32 1 8 .33 = 0, a34 = a27 a35=f PNylWxbdx V f pSylclx V[PSy1x8]
where
=k cosp, X6 - XG = sin (kyw sinp)/(kyw sing), p = 1.0, p=nir, n = 0, 1, 2, ... C2= e-"d C3= sinp e-"72
Table 2 Coefficient of equation of motion
V
f
pArszbdxV2If
pSzdx [pSzxh11. A26 =2f PgYw4dxFb)
=2pgh,fC,C2yw( kk +hAwwei pSzC,C2( k.x)dx F,,ss sink*x sink*x+ hAL,f pN,C,C2( sin k*x )dx+ cV[pSzCiC2( )1 cos k*x cos k'''`x cos k*x (11.1,"c)='Pgh AfCtC2YwXb(CO5k*x)dx+ hAcaw,fCC2PSzxb( k.x)dx - sin mwt/s sin k*x (sink*x *
+ hAw fCiC2pNzxb )dx+ hA w
f
C1C2PSz (sin kx+hAwV[CIC2PS.,h( :ions kkIrxx )
(F"'c)= pghAi
sin
e cos(k.x ky sinp)dS0
Fws
.36 V
f
PNyldx + V2 ipSyl; a37 = /xx +IPSy12dx a38 a381 + .382 +.383 [ref. Eqs. (63)(66)1, a39 =wGM(FwYc)=
Fwys 2pghA xffe-kzsin (ky sinu)dz (_scinoskZ
s**
k)dx
+ hAwca,, f C3pSy(in kx_cosk.x)dx + hAWfC3PNy (sincos kx)dx+hAVW[C3PSy(C'k)]
-sin k..x
F"c)+2pghA xffe -k2xsin (ky sing)dz(
--coskxk*x dx
XG Fys *
cos k.x).
:inns kk:xx )dx+ hAw
f
C3pNyx ax( -cosk..x
+hAcoVfC3pSy scions kk:: dx+ hA Vw [C3pSyx 1
(Mw°5`).ZG( FwYc)+2pgh A ffe-kz sin (ky sing)x(zdz+ydy)( sin k*x )
Øs
dx
Mw Fwys cos k*x
sin k.x cos k.x
+ hAcawef C3pSyln( )dx + hA cafC,pNylw (sin )dx
+ hAVw[C3pSylo( cc's k*x)]sin k.x
=Z 1,, lw
fe
k's sin (kys sing)2Gdzs-
e-kz.sin (kys sinp)Y.rdYs0
(Mw16c MwtYs
+ hAwca,f C3pSyx
Jo sin (kys sing)dzs
=
-a13,-
-= -=--
-cos dx -x sin A
-- VIP +(ZG
-
1r)(1)-
VpSdil 0
(31) - -pSy(ZG - 1,7)11). + (x - xG)111 + (ZG --
2 V + Vd pSy(ZG-
+ (x - x dx VIP + (ZG -Vd IpSy1,7(ZG -194 0. (32) dx (d) Inertia force and momentdFBy4 ..
+(x xG)1.15+Go G0. 5+ Vtl; }
(33)
'60-0177-+(x-xG)0- + VO.
(34)
re) Roll damping moment due to viscosity
dM B05
-
cp.dx pNR
Wave exciting forces are expressed by three
com-ponents as follows, taking Froude-Kriloff force and dif-fraction force into consideration.
dFwy _ dF + wyi dF + 2 dFwy3 dx dx dx dx
dMwq, dill wo 1dMwo2 dMwo 3
+ +
dx dx dx dx
dFwyi
- pghA d e cos (kx cosg
dx o
- kysinp - wet)dz
cohAC3pNyc05 (kxcosp - Wet)
dMwo2 dFwy2 dx dMwo dFwyi dx dx dFwy2 dx dx
dF3
dx dM,,53 dFwy3 (ZG (43) dx dxWhere C3 is correction factor to represent the
in-fluence of oblique waves and is given by the following
formula.
C3 = sinp e-kdI 2 (44) The swaying force, and yawing and rolling moment
acting on the whole ship are given as follows:
FBy = ('FE dFBy
AE dx dx -fAE FE (dFByi dx + dFBy2 dx +dFBy3 + dFBy4) dx dx dx fFE dMB,/, FE dFBy JAE dx
dx -
fAE dx (x_ xG)dx (46) MB, = ('FE (_... dx dxB 91 dMB 02 iFE dMBgy FE (111,1 MB,P= JAE dx dx = dMB03 dMB04 dM B dx dx dx dx (47) dM 1303 dx dx dM8,04 lxx dx= hA W2 C3 pSysin (kxcosbi - Wet)
d(pS VhA dx (35) (ZG -11) (39) (40) (ZG -1w) (41)
cos (kxcosp- Wet) (42)
(45)
The wave exciting force and moments acting on the
whole ship aFreEgidvFen as follows: wy
Fwy-
dx dF + wy2 dFwy3 dx (48) !AE dx .IAFEFEE ddd Fmx + dx wd yxdx -
(x xG)dx fAE dx JFE dF AE dx FE (dMwoi FE dItiwo dx Mwo= JAE dx fAE dx dM w 03) w dx + (50) dx dxThus, the coupled equations of motions of swaying,
yawing and rolling are obtained as follows.
FBy Fwy (51)
MB9 +M9 =
(52)+Mwo = 0 (53)
These equations can be reduced formally into
follow-ing expression.
al 177+a 1277+a 1317+a 141,1, +atsV) +a 16 11/1-a170+a18,:b
+a ,90 = Fwy (54)
a2177+a2277+02371+a24 '1./+6,250-a26 0+a2-7,15+a2e0
+a2,90 "=" Mw4, (55)
a3177+a3277+a3377+a34 4./+a35 036 0+a37(1Y+a38cti
+a390= Mwo (56)
These coefficients such as au are listed also in Table 2.
(4) Solutions of motion
A ship is assumed to make harmonic motion of
6-degrees of freedom in accordance with encounter fre-quency of waves, and solutions of equations of motion
can be expressed as follows.
surging : = cos (Wet + el) (57)
heaving : =A cos (Wet + (58)
pitching : 0 = OA cos (Wet + ee) (59) swaying : 77 = rlA cos (Wet + ,7) (60) yawing : J1= 111 A cos (wet + e4, ) (61)
rolling : 0OA cos (wet + eo) (62)
The origin of time is taken at the time when the wave trough passes midship, and the phase lead to waves is
taken to give the positive maximum value of response.
However, as for roll damping coefficient a38 in Eq. (56), the following modifications are introduced based on the results of forced rolling model tests, from view
point of practical use(21)(22).
a38 = a381 + a382 + a383 (63)
a382 = (kvN10° +NBK) 77
(d
4V a383 = kulthZG)
(1.1 2 weN/13/2g)fFE pSydx AE (66) (49) a381 = kwf
pNy(ZG -1w)2dx (64) 200 a37 (65) where,a381 Coefficient corresponding to the damping
due to wave-making calculated by potential
theory
--
-0-R382 : Coefficient corresponding to the viscous damping which is a part of N coefficient
a383 Coefficient representing the effect of
advance speed
Nwo: N coefficient for bare hull estimated from
Watanabe-Inoue's formula(23)
N coefficient for bilge keels estimated from
Watanabe-lnoue's formula
=
pS(ZG
)2 dx/ pSydx1/2ku, k, k w : Correction factor
Coupled equations(54)(56) are nonlinear, therefore,
they have to be solved by iteration method.
3.3 Calculation method of wave loads(24)(25)
The calculation of wave loads are carried out on the
basis of the solution of ship motions. Using the same co-ordinate system and notations as those in the calculation of ship motions, the equations of wave loads acting on the
section at x1 section are obtained as follows:
Fv(xi) =
fxdFB,
cix dFAE(
w2.) dx dx M V(x 1) =fxi
AE dx ( dFdF ,z)
(xx
dxi)dx
dFwy xi cIP By + dx F H(x 1 / =1 dx dx AErx i (dF
By dFwy , M H(x 1) =J
AE dx dx txi)dx
di 1 I Bo"
dx A 1 TG(x1) =ix 'AE dx dx M TS(x1) = M TG(x1)+ 1sF H(xi) (73)The coefficients, A1, ao, and wave exciting term F, M in the equations of motion are all used as the same expression,
but the integral range is from the aft end of hull (AE) to
xl. Their components are obtained as follows:
Vertical wave shearing force
Fv = F vA cos (wet + Fv) (74) Vertical wave bending moment
Mv=MvA COS (wet + e my) (75)
Horizontal wave shearing force
FH = FHA cos (wet + eFH) (76)
Horizontal wave bending moment
MH=MHA COS (Wet + emH) (77)
Wave torsional moment (around center of gravity)
MTG = MTGA cos (wet MTG) (78)
Wave torsional moment (around shear center)
MTS = MTSA COS (Wet + MTS) (79)
3.4 Calculation method of wave hydrodynamic
pres-sures
The hydrodynamic pressures acting on the hull surface are obtained by O.S.M. and are expressed in the same way
as ship motions as follows( 19)(26):
Hydrodynamic pressure : P = PA cos (Wet + ep) = P, cos Wet Ps sin Wet
(80)
The pressure which acts on the hull surface from outside
to inside of ship is taken as positive. The hydrodynamic pressure can be resolved into four components and
ex-NBK:
(67)
pressed as follows respectively.
(1) Hydrodynamic pressure due to vertical motion PVC1.= A [(I + Pa'H) 1 cosc
sinq-P VS hA sine
q
1t. COSE-(xx G)
[(I +P)
hA (COSEB) Q4 i since 1 i sincecosee
r2pa,H, since t hA L 1 --cosfe , COSE0 11 + 1G1H . sineeHydrodynamic pressure due to horizontal motion
PHC 1. 77A [pll cosen P HS hA L aS sine, P dS 1
coser
sine,/ Li + (X G) ="11 [ns hA pas sincv, COSE,p J +(VIGie) hA P'cis,y)
cose sine PZIS ( sinco COSE0I]
Hydrodynamic pressure due to rolling
PRC
Ys i0
COSE0 t+yw 0,4 cosePRS hA sinco hA L sine,
cosco
Hydrodynamic pressure due to wave
P wc
-= ''sJ cos (kxcosp
kysini.)1
PwS sin (kxcosp kysinp) I
[ c,) 2 cos (kxcosp) t ( ) Pali
We sin (kxcosp) I
co ( sin (kxcosp) 1
iwecos (kxcosp)
,d
CO 2 sin (kx cosp) 1+e-'T sing () Pas
We cos (kxcosp) 1
co cos (kx cosp) 11
PdS (84)
We sin (kxcosp) I J
Detailed expression of P aH" , PdH", PaS" , PdS", PaR",
and P dR", are given in reference (26). These equations are
reduced into the following expressions.
= PghA (Pvc + PHC + PRC + PWC) (85) Ps = PghA (V'S + PHS + P RS +PWS) (86)
3.5 Calculation method of relative motions to wave
surface
When the ship motions are determined as the solutions
of Eqs. (57) through (62), the relative motion to wave
surface Zr at an arbitrary point (x, y) on ship's hull is
cal-culated as fOHOWS(27)(28): 1 sinco cose,o1 1 }] (81) (83) :
(
+ (68) ,(6.9) (70) (71) (72) (3) (2) sine, cosev, ,hA (4) I dH I 1.sineoZr = (x x G )0 +yØ (87)
Zr = ZrA cos (Wet + e) 13/2
= Z cos Wet Z, sin Wet (88)
The relative motion is taken as positive when hull sinks below the average draft. In the calculation of relative
mo-tion, the dynamic swell-up due to disturbance on wave surface by ship motion is not taken into account in this
prediction system.
3.6 Calculation method of motion accelerations The accelerations at an arbitrary point P(x, y, z) on ship
are calculated as follows. (1) Vertical acceleration
A z = (x G)e. + y (89)
= AzA cos (wet + eAz)
= A z, cos Wet A. sin Wet (90)
where, A _We2k.A cosq-A sinq. j coseol sinco 1 (2) Lateral acceleration YOA Ay =
+ (x - xolp - (z
-z)0..-= A yA cos (wet + eAy)
=A ye cos Wet - A ys sin Wet
(x xG)0 A
COSE6
I sine, 1
The positive direction of each acceleration is defined as coinciding with the negative direction of the coordinates
shown in Fig. 3.
Components of accelerations include the lateral and
longitudinal components of gravity due to rolling and
pitch-ing, considering the relation with the structural strength
analysis.
3.7 Calculation method of added resistance and
nomi-nal speed loss in waves
If a ship goes on relatively moderate sea under a
con-stant engine output, the ship speed will drop inevitably
because of added resistance due to waves and wind. This is
called nominal speed loss.
When navigating in rough sea, to avoid occurence of
shipping of water, slamming, propeller racing, etc., ship's operator will deliberately lower the power and reduce the ship speed. This is called deliberate speed loss. In this
pre-diction system, only the nominal speed loss is considered.
The ship resistance in a seaway is supposed to be
ex-RAH
B 2
Bluntness coefficient slag= +3I sin,fidy
2 Total added resistance RAw=RA,(0),RAw(i) due to ship motion RAW(.1 due to bow, ,reflection RAMO 0 0.5 1 0 1.5
Fig. 4 Definition of bluntness coefficient and components of added resistance for a full ship(31)
pressed as the sum of the resistance in still water, the added
resistance due to waves, the added air resistance due to
winds, the added resistance due to steering, etc. To simplify the problem, two main components, the added resistance
due to waves and the added resistance due to winds are
treated as resistance increase in a seaway.
(1) Added resistance in waves
The added resistance due to waves can be divided into
two components as illustrated in Fig. 4, from the view point of practical application(29).
RAW = AW(0)÷ AW(1) (98)
where,
RAW : Added resistance due to waves
RA w(0) : Added resistance due to ship motions
R Aw( 1) : Added resistance due to wave reflection
from bow
R A W(0 ) is given by Maruo as follows(30):
R A w(o) =4.11)9[-f
a
a2 (m + K0E2)2(m kcos,u) Hi(m) I2dm .\/(m 1-K0cz)4 _K02m2 where, k = 2n/K, Ko = gIV2, E2 = Vwelg, We = k(C V cosil) C2 = g lk a, } Ko a2 2HI (m) can be approximately expressed as follows,
provided that the ship body is slender and sources
in-tensity a(x) is proportional to the vertical relative
velo-city to surrounding water at each section of the ship,
and is concentrated at a constant depth Zo = Cypd(31).
(m + K0E2)2
Hi (m) =
f
(a, ad exp Z + imx1 dxIn the case of full ships, the added resistance due to wave reflection from the bow is remarkable in the short-er wave length range. It is approximately expressed as follows(29), on the basis of Havelock's formula for wave
drifting force.
(1 + 2E2 ± -\,/ 1 +42) where,
Ay, _we2r,
cose
ilA cose A sine, YS (Z ZG)(PA COSE0 sinco (3) Longitudinal acceleration.. OA I coseot sinco (94) we2 A x -=+(z zG)e ytIr +gt9 (95)
=A ,A cos (wet + cAx)
=A
Wet A sin Wet
where, Ax, _cje,[ s jCOSEt A cosce xs inet since (96) COSEvj 0A (97) cosee t sine, I We l ViA 1 .
Kneel
--
-= -cos Surface Reflected waves; Incident ayes : : , -K (100) (99)-
-(.91) (92) (93)R = (1 + a2) 1 pghA 2B sin2k3
2 (101)
Air resist.
Thrust deduction factor
Advance speed of propeller
Prop. open characteristics
Relative rotative characteristics
Hull efficiency
Stern tube friction loss
* Principal particulars of ship * Ship speed instill water * Wave condition
Resist, instill water
Total resist, in waves
Thrust in waves
1.17,7J=7.nTI/VD
.4Or J, ep
Propulsive efficiency
Delivered horse power
Shaft horse power
IP const. P in wave = P in still water
Effect, horse power
Nconst.
Qconst
where,
ka : Wind direction effect coefficient : Wind resistance coefficient in head wind
Pa : Air density
AT : Frontal projected area of ship above water
line
V, : Relative wind speed
The wind direction effect coefficient is given in the
standard analysis method of speed trial results
devel-oped by Japan Towing Tank Conference, and the ahead
wind resistance coefficient Cx0 is derived from Wagner's graph(32).
(3) Propeller characteristics and self-propulsion factors in
waves
Propeller characteristics and self-propulsion factors in
waves is said to be not always the same in still water
when ship motion is larger. However, nominal speed loss
in moderate sea condition can be calculated under the
Ship motion in regular waves
Resist, increase in regular waves
No, of revolution
RAA = kaCx0 paATV,2
2
Resist, increase in irregular waves
Resist, increase in wave
Q in wave =
Q in still water Yes
Fig. 5 Calculation procedure of nominal speedloss(33)
Irregular wave spectrum
Nin wave =
Nin still water No Yes
(103)
where,
al Correction factor for finite draft
a2 Experimental correction factor for the effect
of advance speed.
sin213 : Bluntness coefficient as defined in Fig. 4
According to Maruo("), the resistance increase in irregular waves can be obtained by the following
for-mula, by superposing the response function of the added
resistance and the wave spectrum of irregular waves.
f R A w(W)
R Aw = 2 (6))12 d (102)
o hA
where:
R Aw : Mean added resistance in irregular waves'
'Circular frequency of waves
[f(co)} 2 Wave spectrum
(2) Added resistance due to wind
Added resistance due to wind can be estimated from
the following formula.
1..Yes Nominal speed loss
:
W(1)
=
following assumptions and conditions.
Propeller characteristics in waves are the same as
those in still water.
Self-propulsion factors in waves are the same as
those in still water.
Ship-Model correlation factors on propulsive per-formance in waves have the same values as those in
calm sea trial.
(4) Calculation method of speed loss
For the estimation of the ship speed loss in waves, the characteristics of main engine should be taken into con-sideration. Three cases of basic characteristics; constant horsepower, constant torque, and constant rpm can be taken into consideration.
As shown in Fig. 5, the estimation of shaft
horse-power of a ship in waves is performed essentially in the same manner as the horsepower estimation in calm sea by use of the thrust identity method(33). The ship speed
in waves can be determined by iteration method
cor-responding to the given main engine characteristics.
3.8 Statistical prediction of ship responses (Short-term
and long-term prediction)(8)
For the safety of ships which sail in ocean over a long term, it is necessary to predict the various ship responses in irregular waves statistically taking account of occurrence
frequency of waves.
Statistical prediction is carried out as follows.
10
1. Ship response function in regular waves
2 Ship response spectrum in irregular waves
Short-term prediction of ship response in
irregular waves
Long-term prediction of ship response
-Tr 0
A Assumption of ocean wave spectrum
Assumption of short-term
probability distribution
Long-term occurrence frequency of waves
The short-term prediction is concerned with response
over a short period (say 20 to 30 minutes) when no
signifi-cant change in the sea conditions occurs, while the
long-term prediction is concerned with the response over a long
period such as a voyage or the life of a ship. (1) Short-term prediction
If the response function of the ship is known, the
variance of response amplitude R2 is obtained from the
following formula based on the linear superposition
method, when ships sailing on a constant course to an
average direction of waves with a constant advance
speed. R2
=i 7
[A (w, 6 + ii)]2 [f (w, 012 dwo =f
IT [A (w, 5+)12 [f (w)] 2 COS2 P dwdil 2 2 (104) [f (w)] 2 = 0.11H,2 WT-1 (w/WT)-5 exp [ 0.44(w/WT)-4 (105) where,R : Standard deviation of a ship
response in short crested irregular wave from the direction of 8
[A (co, 5 +II)] : Response amplitude operator of a
ship in regular wave from the direction of (8 +
[f(co, pt)] 2 : Directional wave spectrum
[f(co)] 2 : Wave spectrum
8 : Average heading angle against
average wave direction
: Visual average wave height : 27/Tv
T Visual average wave period
Regarding the spectrum of irregular waves, the
I.S.S.C. wave spectrum (1964, Delft) shown in Eq. (105) is usually used, while in this system designers can apply
wave spectrum other than I.S.S.C. wave spectrum, if
necessary.
For the non-linear response, the linear superposition method is not applicable in the strict sense of the theo-ry. As the approximate treatment for these cases, stati-stical calculation is performed using the equivalent re-sponse function which is calculated for a proper wave
height (usually 10 m for large ships).
If the standard deviation of ship responses R is ob-tained, the mean and the maximum expected values in
irregular waves can be predicted as follows:
Mean value 1.25R
1/3 highest mean value = 2.00R 1/10 highest mean value = 2.55R
1/100 expected maximum value = 3.22R 1/1000 expected maximum value = 3.87R 1/10000 expected maximum value = 4.43R
The probability that the maximum value of the ship responses exceeds a given value x1 can be predicted by
the following formula, assuming the Rayleigh
distribu-tion.
q(x > x1) = exp (x12/2R2)
where,
q(x > x1) : Ratio of the number of times when a
response x exceeds a given valuex1
to the total number of responses.
The minimum significant wave height H s(q 0), where
the probability exceeding a critical value f of ship
re-sponse exceeds a given value go, can be calculated by the following formula:
1
H s(q 0 )= (108)
N/21oge (1 1q0) RIH
(2) Long-term prediction
If the standard deviation of ship response in
short-term irregular waves is obtained as previously explained, and if there are sufficient data for long-term wave stati-stics in the ship service route, a long-term prediction of
ship response can be made.
Two aspects are considered for the long-term predic-(106)
(107)
'3.
4.
tion of ship. response.:
One is the case of prediction of extreme value which
is related to the safety of the ship directly, and the
security of sufficient safety is indispensable in the design process (for instance, wave bending moment). The ex-treme value of response over the life of ships is derivedin the, following formula.
pQ 1
7,
r-f-2n j
J exp.,[-x2 / 2R 2 P(H 7)idHdTd& 009), lo 20 30 40 -211f, 23INIFIAMMI-W
tra
lie
111 '11.7..,rii
WAN
,Iiik
itErit
AFMNIMMtigi
12it
itakyrisi
io 44 4511 -r 32 31 30Ezra
Ea.gEl=
,Japam -North America
39 41 29 50 80 60 40 20 0 80 60, 4+7 20 20 40 60 80 l'Arabian 10 It .-..Europe Europe North America
w
...--I 100 : According to Hogben & Lumb
According Ito Yamanouchi
apan Arabian Gulf
'I 1:II 4 II ii I P 0E
101 20- 40 60 80 100
120 140 .160
Fig. 6 Block names of sea area(35)
Table 3 Wave occurrence frequency in the route from Japan to Arabiani Gulf
I f2nr,
80 160
11 I 11 11 I ii
40 120
where, p(H ,T)r: long-term probability density function
of waves
The other is the case of prediction of probability of
occurrence (for example, deck wetness) which has a harmful effect on the navigation performance. The
probability of responses which exceeds. a certain limit is
derived in the following formula.
P(H , T) dHd (1).0) 27 0 T=0 H=Hs(40) 70 20 10 10 20 so Block name 1 2 3 4 5 6 7 Weight .111111 .111111 .111111 I .111111 ..333333
1111 1./11/11
Mean wave period Sum over
all periods 5 7 9 11 13 15 17' 1 ' _ 4,0
-, 4.) > c ,.I w M 176.08 68.21 I 5.38 I 1.40 0.39 0.15 0.05 7.63 1 259.29 0.75 194.47 190.96 71.95 17.35 4.95 1.45 0.53 2.31 484.47 1.75 2.75 15.80 I 62.10 61.13 25.61 7.19 1.99 0.47 0.15 174.44 I 3.75 1.95 11.06 18.50 13.84 6.21 2.46 I 0.57 0.10 54.69 0.52 2.32 4.73 5.63 3.67 1.55 0.45 0.10 I 18.97 4.75 0.14 . 0.18 0.68 0.78 1 0.49 0.17 0.11 0.04 1 2.59 5.75 0.061 0.37 0.72 0.85 0.62 I 0.37 1 0.14 0.11 I 3.24 6.75 0.00 0.13 0.16 0.36 0.17 0.03 I 0.02 0.01 0.88 7.75 8.75 0.05 0.06 1 0.15 0.20 0.16 0.13 0.03 0.03 0.81 0.00 0.09 1 0.06 0.05 0.05 0.,10 0.04 0.19 0.58 9.75 I 10.75 0.00 I0.00 0.00 0.00 0:00 01.00 0.01 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.02 0.01 I 0.03 11%75 12.75 0.00 1 0.00 0.00 .0.00 I 0.00 0.00 0.00 0.00 0.00 13.75 0.00 0.00 lI 0.00 0.00 0.00 0.00 0.00 0.00 0.00 14.75 0.00 0.00 I 0.00 0.00 0.00 0.00 0.00 0.00 0.00 15.75 0.00 0.00 0.00 0.00 I 0:00 I, 0.00 I 0.00, 0.00 0.00 i Sum overall heights 389.07 1 335.48 163A6 66.07
, 23.90 I 8.40 2.44 11.16 I 1000.00 50 -30 25 C.-.207 II I I 4 14 I. I 80 100 70 601 4 33 1 34 35 120 140 .160 180 If 11 11 I 1 II 1, III I, .1. 160 1140- -120 - 900iSO 10
-21 E I [1:11 W I --50 - 50 -40 -30 30 50 110
The Eqs. (1.09) and (1 1 0) represent the long-term prediction for all heading angles, assuming that the long-term probability density function of the heading angle of ship is uniform over the range; 0-27r.
For long-term prediction, Walden's wave statistics of
the North Atlantic Ocean(34) is usually used. But a
recent ,study(35) has suggested that the wave statistics of the actual navigation route should be applied, because the wave data of sea areas other than the actual one will
S.S. 5
Load water line
Weather side
Fn= 0.15
.0 - 30r
.60' 90'Course. angle
Fig. 7 Results of long term prediction of hydrodynamic
pressure(35)
/
LOG (Q) Europe- North America
Japan Arabian Gulf
Japan- North America Europe- Arabian Gulf
North Atlantic (Walden),
-8 0 0 -5 0.51 1.0, 15 L
.Fig..9 Surging amplitude in regular waVes(40
4
'
120- 1151C 180'
0.5
Fig. 11 Pitching amplitude in regular wayes(42) Fe = 0.15 ID 0 0.5 LO 1.5 210 A/L fe= 0.15 /". 1:3 --
0.9-
ye-IP --Q5 1.5 2.0 A/LFig. 12 Swaying amplitude in regular
waves(42)
cause a difference in the results of prediction.
Therefore, the system is prepared to be able to apPly not only Walden's North Atlantic data but also data of other sea areas in the world which are divided into small
blocks as, illustrated in Fig. 6, in accordance with Hogben & Lumb's and Yamanouchi's data(36)(37).
Table 3 shows an example of wave statistics data sum-,
med up along the route from Japan to Arabian Gulf.
The predicted values of hydrodynamic pressure in Japan-Arabian Gulf route are lower than the ones in the North
Atlantic Ocean, as shown in Fig. 7..
Under severe sea conditions, there may naturally
occur nominal speed loss and deliberate speed loss, but
the long-term prediction are usually made on the as-sumption of constant speed without paying any con-sideration to speed loss. However, as the speed losses
may often considerably influence the long-term predic-tion values, this system is able to involve nominal speed
loss as shown in Fig. 8(38). Response function of
wave loads and
I hydrodynamic pressures 1. Standard deviationm of I response in irregular waves, Short-term prediction Long-term prediction
Fig. 8 Flow chart of long-term prediction of wave loads and hydrodynamic pressures including speed loss(38)
_
Fn= 0.15
Shipspeed,in irregular waves
Interpolation of
response
to ship speed
0.5 1.0 15 2.0
Al L
Fit, )4 Rolling amplitude in retular
waves(42) Fn p Measured Calculatedll 150
0
-
----120 A 0.195 90,1 0 601 ----1 30". p Measured Calculated 180°1 0 II
---135' A '9C 0 ---# Measured Calculated 135° 9C A 0 p Measured Calculated 135' 90' A CI Measured Calculated 135° 90° A 0--- !
---p Measured Calculated 180 0 135° a 9C ,0.-
--5.0 4.0 ("" /0' \
A E .o7.3.0 ./ .
\
2.0 . /.../1
LO '...6...A...A.:./Ir: 9 A 1 1.51 Fn.=0115 015 10 1.5 201 A/ LFig. 10 Heaving amplitude in regular
waves(42) A -1;1-
---0 0.51 1.0 [5 2.0 LFig.. 1.3 Yawing amplitude in regular
waves(42)
Resistance .Added resistance
in still water in regular waves
Added resistance Powe in irregular waves estimation 1 5 10.5 -6.Q Fe=a15 10 0.5 0 20 0 0 1.0 0 10 0.5 -A 0 0 0.5
12 PV
TLZ2g
a12 : Damping force coeff. of sway
If
/
_S.,:
i2
0 4 0.6 0.8
to Bag
Fig. 15 Virtual mass and damping force coefficient of sway obtained by forced oscillation test(21)
002 es-F 001 _ o I At midship 05 1.0 1.5 2.0 A I L 0.01-
\
Fig. 17 Vertical bending
moment(40)
4. Confirmation by model experiments
The reliability of prediction method has been confirmed through the comparison with the model experiments.
4.1 Ship motions
Model experiments have been carried out for various
types of hull form (for instance, tanker, bulk carrier,
con-tainer ship, LNG carrier, etc.). Calculated amplitudes of ship motions were compared with the measured ones in
regular waves. The calculated values of surging amplitude
show favorable agreement with the measured ones as shown
in Fig. 9. The calculated values of heaving and pitching
show a good agreement with the measured ones as shown
in Figs. 10 and 11. For swaying, yawing and rolling, the
calculated values seem to give sufficient agreement with the
measured ones as shown in Figs. 12 to 14. To improve the calculation method, we have made forced oscillation tests in still water to examine the coefficients of motion equa-tions, and restrained model tests in waves to examine the wave exciting terms("). Examples are shown in Figs. 15
and 16.
From these comparisons, it can be said that the motion prediction method by O.S.M. has been confirmed to have
the applicability to practical design.
4.2 Waves loads
Comparative investigations between results of theoretical
calculation and experimental ones of vertical, horizontal wave bending moments and torsional moments were made in oblique waves(40). Typical examples are shown in Figs.
1.0 Fig. 16 Amplitude of wave exciting sway force(39)
At mids
\
o 0 0 0 5 1.0 1.5 2.0 A/LFig. 19 Torsional moment(40)
17 to 19. From these results, the calculation method of
wave loads seems to have sufficient applicability to design. However, it may be necessary to improve the accuracy of
prediction of wave exciting force in the range of short wave length.
4.3 Wave hydrodynamic pressure
As regards wave hydrodynamic pressures, many experi-mental studies have been carried out. Not only total hydro-dynamic pressure but also each component has been meas-ured and investigated in detail(39)(41). Typical examples are shown in Figs. 20 to 22. Generally speaking, the cal-culated values show fairly good agreement with the
meas-ured ones and may be said to be practically applicable,
althouth some room for improvements are left in the pres-sure estimation near water surface in the short-wave length
range.
4.4 Relative motions to wave surface
Calculated values of relative motions to wave surface are
compared with measured ones as shown in Fig. 23. From these results, a practically sufficient estimation seems to be achieved by the theory without paying particular attention
to dynamic swell up in the case of a fine ship.
4.5 Motion accelerations
Investigations of longitudinal distribution of ship accel-eration have been made by model test(42). One example is
shown in Figs. 24 and 25. These results have confirmed that
the calculated values show a good agreement with the
measured ones and are fully applicable to design.
4.6 Added resistance and nominal speed loss in waves
Comparisons between measured values and calculated
ones of added resistance are shown in Figs. 26 and 27.
Fairly good agreements between them are recognized in-Calculated Measured -+-Fn =0 Swaying amplitude --0-- 0.15 7/.4/ B=0.0424 Fn p Measured Calculated 150° 0
----120° ,o, 0.195 90° 0 ---60° ----30° Fe p Measured Calculated 150" 0 120° LS - ---0.195 90° 0 60° 30 Fn p Measured Calculated 150' 0 --120 A 0.195 90° 0 ---30° 2 0 0 1.0: Virtual mass of sway
Pt': Mass of the ship
1 0 05 I 1 i 1 1 1 0 02 04 0.6 col Bag 0.8 10 0 0.2 1.0 . Fn =0 IC Fe =0.275 S. S. S. ....- ...
t
0.5 14./
-0.5-/ ,..... -,
.
,
--... ...,...-_ / -.,... 0 4,-k-1--.'" 1 , ___±_ 0 __---1- ---1-ris -',.. .., 4 -_____A . 05 10 1.5 210 21.5 05 1.0 1.5 20 2 5 PL. A L At midship 002"\\
\
\
Measured Calculated Ii 90° 60° 30° c.0 0.002 0 001 an PC Vf0
-'`A... -°\--.
-=---0 0.5 1.0 15 20 A 'LFig. 18 Horizontal bending moment(40)
0
- -
-
-z
ara°t, 0 1801-r 90 -go -180 Leewardtskle 0.5 80 1.5 =0.30L (S.S.8)' 'Longi. axis Fn= 0.15, 0 51/ 0.5 ti0 1.5 AIL ss.8 1/2 Fn=0. j p=45° 0.5 0:75 1.0 1.25 11.5 Fig: 22 -ee." 10 ,Pig- 25. Amplitudes of transverse accele-ration induced on the
longitudi-nal axis in regular waves(42)
,cluding the Added resistance dueto,reflection of wave for
full ship in shorter wave length range.
As for ship speed loss, model experiments were carried out for various ship forms and compared with theoretically
predicted values, as shown in Figs. 28 and 29'. The examples'
show an agreement between prediction and experiment, and the calculation method is confirmed to have the
suf-ficient applicability to design..
'This calculation can be applied to the evaluation of the
14'
'Weather side'
Al L
Fig_23, Relative motions taking account of
.nominaLspeed loss in regular waves
Distribution of hydrodynamic pressure amplitude and phase'
.due to wave(41)
Con ainer ship o
Cb= 0.5725 180.
k\?\
\ °\\\\
\se ss \\\ 01 . 10 5 110 1.5 20 AILFig. 26 Added reSistance coefficients of
a fine ship in regular head waves
10 180 90 ,-;-1 0 -90 k. fi=135% Long'. axis 20 ,1 .-- I -"'.N
N
s\ / V
-60, -30 0 30 90 II' (,deg) -as°Fig. 21 Girthwise distribution of hydro-dynamic pressure amplitude and phase due to motions(41
p= 180° Series 60, C-0.8
/
0 -- 0.5. 110
-
1.5 -20 AlLFig. 27 Added resistance coefficients of a full ship in regular head waves
AP7__$
FP2-2
I
2
Fig. 24 Longitudinal distribution of amplitude of vertical acceleration induced by ship
mo-tions in regular bow waves(42)
effect of waves, on the results of speed tria1(43).. 4.7 Responses in irregular waves
As for responses in irregular waves,, comparison between
theoretical values and experimental ones were made in the form of the standard deviation of vertical accerelation and
heave and pitch response in irregular waves as shown in Figs. 30 and 31. It has been confirmed that the linear
superposition method is effective to predict ship respOnse,s,
in irregular waves.
S.S Position Measured [Calculated
8 1/2 LWL Bilge Keel 0 A 0
---..I---S.S Position Measured Calculated
,8 1/2 ' LWL Bilge Keel 0 A Measured Calculated Vertical motion Horizontal motion ,Rolling motion A l'
---hu,/L r.t Measured Calculated 1/50 180° 90° 0 A WA Measured Calculated 0.7 0 0.9 A 1.0 b
---1 1.1 o ----1.4, gr Measured Calculated 135° 90° A 0, Fn, Measured Calculated , 0.15-0-
----1'0.20 --A--1,0.30 ---0-'- Fe Measured Calculated 0.15 0.20 0 1 A.--
-,--
I A/1., AIL AIL (b) Fn 0.11 1./ =90.Fig. 20 Amplitude of hydrodynamic pressure(39)
A./L 4,,a) Fn==0.1 =45
S.S.5 Fe =0.0 A. L=1:091
,g(deg) Measured Calculated 20 50 80 I 20 1.5 10 0.5 30 20 1.0 Weather side 1.5 2.0 25 A/L 2 0 05 -A 10 2.0 10 Fn= 0.15 0 90
-0. 5 0 025 ---0----
--21.0 20 0 5 1.0 1.5 2.5 1.5 1.0 05 5 4 301 5 in still water Vm =1 465m s
0.5
0.3
- 0.2
1.0 Wave height hu, (cm)
(a) Effect of wave height °
N
Container ship u =180" Constant torque ti= 180°. Fn = 0.15 # =180°, Fri= 0.15 Longi.axisFig. 28 Nominal speed loss in regular waves(33)
-1.5 0.02-0.01 0 AP 21 7 FP 2 2
Fig. 31 Longitudinal distribution of standard deviation of vertical acceleration induced by ship motions in long-crested
irregular head waves(42)
4.8 Comparison with full scale measurements
As already mentioned, the applicability of the
calcula-tion methods in the Total System has been confirmed
through extensive model tests.
Full scale measurements need much expense, long period
and large amounts of data analysis, so that it is difficult
that one ship builder can afford all the test. In Japan, full
scale measurements were carried out as the cooperative
research of SR-108, SR-124 and SR-125 organized by Ship
Research Association of Japan. Mitsubishi Heavy Industries
participated in these committees and took partial charge of
the analysis of these data.
instill wa er Vm= 1.463 m s
05 10 15 2.0 0 0.5 1.0 15
T.(s) Tu, (s)
a) Heaving (b) Pitching
Fig. 30 Standard deviation in long-crested irregular head waves(42)
20 200 100 111 3 [mrn] 5 Hi .3 1mrti 6 6 7 8 9 10 Beaufort scale
Nominal speed loss in irregular waves(33)
Container ship, Pitching (doable amplitude)
(Model)
(Ship)
30 8 (deg)
Fig. 32 Short-term distribution of pitching
by on-board measurements(44)
In full scale measurements all phenomena are irregular,
so it
is necessary to treat these data through statistical analysis method. Many considerations were paid to thecollection and analysis of data in order to be able to con-firm the validity of various assumptions used in the estima-tion method. Examples of the results of full scale
measure-ments are shown in Figs. 32 to 34, cited from the
refer-ence(44).
It was confirmed that the frequency distribution of the total amplitude of ship responses is close to Rayleigh
dis-tribution as shown in Fig. 32. The measured significant
values are generally in good agreement with that of
estima-tion.
As for long-term prediction, there is few evidence of the
extreme values directly obtained by long-time observations,
and the estimation based on Fukuda's method is said to
give slightly higher values than the prediction of Gumbel's extreme value distribution obtained from short-term
meas-urements.
It can be conclusively said that the short-term and long-term prediction based on Fukuda's method are useful, and that a practical long-term prediction can be made by using
reliable data of the long-term wave statistics in each naviga-tion sea area.
It may be important tasks in future to carry out a long ,, 'kaiL h u. Measured Calculated
1/30 1/50 11.7cm 7.0 cm 0
----180 1/70 5.0cm 0 A ---1/100 3.5 cm 0 ---90° 1,50 7.0cm---A/L, Measured Calculated
0.5 0
-
--1.0 A 1.5 0 Measured Calculated 0 Using measured ) wave spectrumH13 Tu. Measured Calculated
570cm 0.93s 0 5.78 1.28 A
-5.52 1.46 0
--5.61 1.64 0 ---5.70 1.91 ----6.91 2.23 ---1.5 in still water V.=1. 465m, A A A Constant torque Measured Calculated 1.0 180" 90°
1.5 in still water Vm =1. 465mis
Constant revolution 0 0 1.0
\
0.5 15 E 1.0 in still water Vm =1.465m Constant revolution Fig. 29 0.5 11.0 11.5 210 AL(b) Effect of wave length
\
I,\
I Constant torque 1.0 ' A 0 --2.0(o=45-135) a a 116 8 12 Tv ( s)
Fig. 33 Comparison between predicted value and on-board
meas-urements on significant values of pitching and rolling(44)
period observations for various responses and toinvestigate
the correlation of long-term prediction through
accumula-tion of full scale data.
5. Concluding remarks
As mentioned above, the Total System for Prediction of Seakeeping Qualities of Ships, which provide a consistent
computation extending from the prediction of ship motion
to the determination of design value of wave load, was
20 Reference 20 0 EA '0, iv)pa7 Winteo
6 4
2 Logo Q (6) Amplitude of pitchingFig. 34 Comparison of long-term prediction between theoretical calculation and the expected value based on the measured data by an actual ship(44)
completed with experimental confirmation, and the system
has been widely used in our design department.
For the calculation items in which a little discrepancy
was found in the comparison with model experimental
results, improvements have been continued, for example,
the calculation method of bow relative motion of a full
ship in shorter wave length region.
In addition, many programs has been prepared for the
use of design calculation, such as prediction program of
bow flare impact pressure(45), sloshing force(46)(47) bot-tom slamming(48), coupled motion with free surface of liquid tank, stabilized motion by antirolling tank, etc.
Furthermore, many computer programs are being devel-oped for the purpose of research such as non-linear simula-tion program of ship mosimula-tion and wave load, and they will be incorporated in routine use in future.
Open Ship (1st Report) - Calculation of Total Hull Girder
Stress -, Jounal of the Society of Naval Architects of Japan, Vol. 142 (1977)
J. Fukuda, M. Konuma, et al., Estimating the Design Values
of Hydrodynamic Pressure Induced on the Ship Hull in Waves.
Trans. of West-Japan Society of Naval Architects, Vol. 49
(1975)
A. Shinkai, Estimating the Design Values of VerticalBending
Moment Induced on the Ship Hull in Waves, Jounal of the Society of Naval Architects of Japan, Vol. 138 (1975) J. Fukuda, R. Nagamoto, 0. Tsukarnoto, A. Shinkai, Estimat-ing the Design Value of Vertical ShearEstimat-ing Force Induced on the Ship Hull in Waves, Journal of the Society of Naval
Archi-tects of Japan, Vol. 136 (1974)
J. Fukuda, R. Nagamoto, 0. Tsukarnoto, A. Shinkai, etal.,
Estimating the Design Values of Horizontal Wave Shearing
Force Induced on the Ship Hull in Waves, Journal of the Society of Naval Architects of Japan. Vol. 139 (1975) A. Shinkai, Estimating the Design Values ofHorizontal
Bend-ing Moment Induced on the Ship Hull in Waves, Journal of
the Society of Naval Architects of Japan, Vol. 140 (1976) J. Fukuda, 0. Tsukamoto, A. Shinkai, S. Kamiiri, Estimating the Design Values of Wave Torsional Moment Induced on the Ship Hull in Waves, Trans. of West-Japan Society of Naval
Architects, Vol. 53 (1976)
J. Fukuda, R. Nagamoto, A. Shinkai, Estimating the Design
Values of Axial Force Induced on a Ship Hull in Waves, Trans.
of West-Japan Society of Naval Architects, Vol. 54 (1977) J. Fukuda, R. Nagamoto, M. Konuma, M. Takahashi, Theo-retical Calculations on the Motions, Hull Surface Pressures and Transverse Strength of a Ship in Waves, Journal of the Society of Naval Architects of Japan, Vol. 129 (1971)
Container ship, Pitching (Head sea) 2 L7L-.) Fn=025Calculated 135'180) o A ° \Measured 6'180. GE ,° 0 4 12 116 20 Tv (s)
6 Container ship, Rolling (Beam sea)
F. Tasai, M. Takagi, Theory of Ship Responses in Regular Waves, Text Book of the Symposium on Seakeeping Qualities of Ships, the Society of Naval Architects of Japan (1969) J. Fukuda, Strip Theory and Its Application, Bulletin of the Society of Naval Architects of Japan, Vol. 485 (1969)
Y. Takaishi, Y. Kuroi, Practical Calculation Method of Ship Motion in Waves, Text Book of the 2nd Symposium on Sea-keeping Qualities of Ships, the Society of Naval Architects of Japan (1977)
F. Tasai. On the Sway, Yaw and Roll Motions of a Ship in Short Crested Waves, Trans. of West-Japan Society of Naval Architects, Vol. 42 (1971)
N. Salvensen, E.O. Tuck, 0. Faltinsen, Ship Motions and Sea Loads, Trans. of the Society of Naval Architects and Marine Engineers (1970)
F. Tasai, On the Damping Force and Added Mass of Ships Heaving and Pitching, Report of Research Institute for
Ap-plied Mechanics, Kyushu University (1960)
F. Tasai, Hydrodynamic Force and Moment Produced by
Swaying Oscillation of Cylinders in the Surface of a Fluid, Journal of the Society of Naval Architects of Japan, Vol. 110 (1961)
J. Fukuda, Statistical Prediction of Ship Responses, Text
Book of Symposium of Seakeeping Qualities of Ships, The Society of Naval Architects of Japan (1969)
R. Nagamoto, et al., Study on the Longitudinal Hull Girder
Strength in Waves (for Oil Tanker), Trans. of West-Japan
Society of Naval Architects, Vol. 51 (1976)
R. Nagamoto, et al., On the Transverse Strength of OilTanker
in Irregular Seas, Journal of the Society of Naval Architects of Japan, Vol. 140 (1976)
K. Umezaki, et at, Evalution of Hull Girder Stress on the
2
4 Logic, Q
(a) Amplitude of vertical acceleration at FP ( 8 0 1 I I
8
(1) (2) (3) (12) (13) (14) (5) (15) (16) (8) (18) (10) (19) (11)H. Walden, Die Eigen Shaften der Meereswellen in Nordatan-tischen Ozeean, Deutscher Watterdienst Seewetteramt Publi-cation No. 41 Humburg (1964)
a Tsukamoto, and T. Mori, Predicting Method of Wave Loads
for Ship's Routes, Trans. of West-Japan Society of Naval
Architects, Vol. 47 (1974)
N. Hogben, F.E.. Limb, Ocean Wave Statistics, NPL, London (1967)
Y. Yamanouchi, A. Ogawa, Statistical Diagrams on the Winds and Waves on the North Pacific Ocean, Papers of Ship Re-search Institute (1970)
R. Nagamoto, 0.. Tsukamoto, T. Mori, On the Calculation of
the Ship Speed Drop and Wave Induced Forces, Trans. of
West-Japan Society of Naval Architects, Vol. 47 (1974) H. Fujii, T. Takahashi, Experimental Study on the Ship MO-tion and Hydrodynamic Pressure in Regular Oblique Waves, Trans. of West-Japan ,Society of Naval Architects, Vol. 49'
(1975)
K. Ikegami, Measurement of Torsional and Bending Moments Acting on Ship Hull in Oblique Regular Waves, Journal of the Society of Naval Architects of Japan, Vol. 136 (1974) M. Matsuyama, Model Tests on Hydrodynamic Pressures
act-ing on the Hull Surface, Journal of the Society of Naval
Architects of Japan, Vol. 137 (1975)
K. Ikegami A. Shinkai, Properties of Ship Accelerations in Regular and Irregular Waves, Trans. of West-Japan Society of Naval Architects, Vol. 52 (1976)
T. Takahashi, 0. Tsukamoto, Effect of Waves on the Results
of Speed Trial of Large Full Ships, Trans. of West-Japan
Society of Naval Architects, Vol. 54 (1977)
S. Takezawa, E. Kajita, Results of Full-scale Measurements and Correlations to the Response Prediction, the Text Book
of 2nd Symposium on Seakeeping Qualities of Ships, the
Society of Naval Architects of Japan (1977)
R. Nagamoto, '0. Tsukamoto, On the Estimation of the Im-pact Pressure on the Ship's Bow, Trans. of West-Japan Society of Naval Architects, Vol. 49 (1975)
R. Nagamoto, et al., On Sloshing Force of Rectangular Tank
Type LNG Carrier (Results of Model Test), Journal of the
Society of Naval Architects of Japan, Vol. 145 (1979) K. Hagiwara, et al., On Sloshing Force of Rectangular Tank Type LNG Carrier (Some Problems on Evaluation of Design Load), Journal of the Society of Naval Architects of Japan, Vol. 146 (1979)
M. Usijima, et al., On the Strength of Bottom Forward Struc-ture against Slamming, Trans. of West-Japan Society of Naval Architects, Vol. 59 (1980)
H. Fujii, Y. Ogawara, Calculation on the Heaving and Pitching of Ships by the Strip Method, Journal of the Society of Naval Architects of Japan, Vol. 118 (1965)
H. Fujii, T. Takahashi, Measurement of the Derivatives of
Sway, Yaw and Roll Motions by the Forced Oscillation Tech-nique, Journal of the Society of Naval Architects of Japan, Vol. 130 (1971)
H. Fujii, T. Takahashi, Study on Lateral Motion of a Ship in
Waves by Forced Oscillation Tests, Mitsubishi Technical Bulletin No. 87 (1973)
Y. Watanabe, S. Inoue, T. Murahashi, The Modification of Rolling Resistance for Full Ships, Trans. of West-Japan Socie-ty of Naval Architects, Vol. 27 (1964)
R. Nagamoto, M. Konuma, M. lizuka et al., Theoretical Cal-culation of Lateral Shear Force, Lateral Bending Moment and Torsional Moment Acting on the Ship Hull among Waves, Journal of the Society of Naval Architects of Japan. Vol. 132 (1972)
H. Shimada, G. Ogata,, M. Konuma, Longitudinal Distribution of Wave Bending Moments and Shearing Forces of a Giantic Tanker in Regular and Irregular Head Waves, Journal of the
Society of Naval Architects of Japan,, VoL 121 (1967)
F. Tasai, Pressure Fluctuation on the Ship Hull Oscillating in Beam Seas, Trans. of West-Japan Society of Naval Architects, Vol. 35 (1968)
J. Fukuda, M. lizuka, M. Konuma, Investigation of Freeboard
based upon the Long-term Predictions of Deck Wetness,
Journal of the Society of Naval Architects of Japan, Vol. 128 (1970)
J.. Fukuda, K. Ikegami, T. Mori, Predicting the Long-term Trends of Loads on Deck due to Shipping Water, Trans. of
West-Japan Society of Naval Architects, Vol. 45 (1973),
(2) H. Fujii, T. Takahashi, Experimental Study on the Resistance'
Increase of a Large Full Ship in Regular Oblique Waves,
Journal of the Society of Naval Architects of Japan, Vol. 137 (1975)
Maruo, Resistance in Waves, Research on Seakeeping
Qualities of Ship in Japan, the Society of Naval Architects of Japan, 60th Anniversary Series Vol. 8, Chap. 5 (1963) H. Fujii, T. Takahashi, On the Increase in the Resistance of a Ship in Regular Head Sea, Mitsubishi Juko Giho Vol. 4 No. 6 (1967)
B. Wagner, Windkrafte am Uberwasserschiffen, Jahrbuch der Schiffbau-technischen Gesellshaft, Band 61 (1967)
K. Ikegami, Y. Imaizumi, Prediction and Model Experiments on Nominal Speed Loss of a Ship in Waves, MitSubishi Juko Giho Vol. 15. No. 3 (1978),
