AD-AI6i 961 CORRELATION OF WAVE LORDS PREDICTED BY THE EXTENDED i/iSIPHO COMPUTER PROGR (U) DEFENCE RESEARCHESTABLISHMENT ATLANTIC DARTMOUTH (NOVA SCOTI S ANDO

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TECHNICAL MEMORANDUM 85/218AUGUST 1985

U

(0

I CORRELATION OF WAVE LOADS

PREDICTED BY THE EXTENDED

SHIPMO COMPUTER PROGRAMWITH EXPERIMENTS

S. Ando

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ELECTE

Defence Centre deResearch Recherches pour laEstablishment Defense

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CORRELATION OF WAVE LOADSPREDICTED BY THE EXTENDEDSHIPMO COMPUTER PROGRAM

WITH EXPERIMENTS

S. Ando

AUGUST 1985

Approved by T. Garrett Director/Technology Division

DISTRIBUTION APPROVED BY

D/TO

TECHNICAL MEMORANDUM 85/218

Defence Centre deResearch Recherches pour laEstablishment D6fense

Atlantic Atlantique

Canadl

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* ,.- .- - ..-.... '. - .4-. . -: % :-..:.:-i ,. ,.-,.:-,r~, ,' - --.> --.: : . .--- '-.-- ..., . -.- .: .:-..

ABSTRACT

Wave loads predicted by the extended SHIPMO computer program were

compared with experimental data in an attempt to assess the range ofvalidity and to estimate the uncertainty of the predictions. In general,the agreement between theory and experiment was good for the verticalbending moment, but fair to poor for the horizontal bending moment. Thepredicted torsional moment was found to be in gross disagreement with themeasured values in terms of both magnitude and trend. It was not possibleto find any correlation of the pattern of the discrepancy between theoryand experiment with the principal design characteristics, such as hullform or weight distribution. The present comparison shows that theprediction of ship motions in oblique seas needs to be further improved.Also, systematic model tests covering a wide range of the variables arerequired to assess the uncertainty of the measurement, and hence, todetermine the range of confidence of the predicted loads more clearly.

RESUME

On a compare les charges exercfes par lea vagues, telles queprivues par le programme informatique augmentA SHIPMO, aux donniesexpfrimentales, dans un effort pour 4valuer la ganne de validit6 etestimer 1eincertitude des pr4visions. En gdn~ral, l'accord entre lath&orie et l'expfrience est bon pour le moment flfchissant vertical, maisde passable A m4diocre pour le moment horizontal. Le moment de torsionprfvu s'fcarte beaucoup des mesures, tant en amplitude qu'en direction.On n'a pu 4tablir de corr4lation, quant A la tendance des 6carts entre lathforie et l'expfrience, en ce qui a trait aux caract&ristiquesprincipales de conception comme la forme de la coque ou la repartition dupoids. La pr&sente comparaison rfv~le qu'une amelioration des pr~vis-onsdes mouvements d'un navire qui prend les vagues de c8tg s'impose. Il fautaussi procfder I des essais systfmatiques sur maquettes qui portent surune vaste gamme des variables pour ivaluer l'incertitude des mesures etdfterminer ainsi avec plus de pr&cision lintervalle de confiance descharges pr~vues.

7

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TABLE OF CONTENTS

-: ABSTRACT i

NOTATION iv

1. INTRODUCTION

2. METHOD OF ANALYSIS

3. DISCUSSION OF RESULTS 9

4. CONCLUDING REMARKS 11

TABLES 13

FIGURES 19

REFERENCES 32

APPENDIX

Comparison of Predicted and MeasuredMotions of Destroyer Models I and II.

, Accession For

NTIS GRA&IDTIC TABUnannounced ElJustification

ByDistribution/

AvaJlability Codes(-U--yAvail and/or

. P Dist Special

iii

N ,,- ¢ •, . - ' , . ' .- - . , " . ,2 , , • " - . - -. . :',',. . " . . ' ., - . . ' - " . ' . - "-.- . - .. ' . - " - . . -

..... --- , .,. ¢ ,,,.. , , ,,,,, . , , . , .; . . . . .. . , . . : .. . . . .: .

NOTATION

AP aft perpendicular

B beam

CB block coefficient, V/(LBT)

' CM bending moment coefficient ( VBM/pgBL2a, or HBM/pgBL2c)

'C shearing force coefficient ( shearing force/pgBta)

CT torsional moment coefficient (-torsional moment/pgBLc)

D. hydrodynamic force and moment on portion of hull due to body

motion

E. exciting force and moment on portion of hull

F. external force and moment on portion of hull

Fn Froude number

FP forward perpendicular

HBM horizontal bending moment

I. inertia force and moment on portion of hull

L length between perpendiculars

R. restoring force and moment on portion of hull

Re{'} real part of {'}

T draft

U speed

V. wave load component

Vjo complex amplitude of V

VjR real part of Vjo

,, Vji imaginary part of V.o

VBM vertical bending moment

X. complex variable for either of Vi. I., Ri, E., D.

Xjo complex amplitude of X

XjR real part of Xjo

Xjl imaginary part of Xo

a submerged sectional area

ajk two-dimensional sectional added mass coefficient

b sectional beam at waterplane

b two-dimentional sectional damping coefficientjkf- sectional Froude-Kriloff force

iv

:~~~~~~~~~~ ~~~~.[..- . ....... . .. --. ..... ,...... ..• . .. .. .... ... . . .. .. . .. . . . .. ... ... . .

g acceleration of gravity

h. sectional diffraction force.3

|i Vrix sectional mass moment of inertia about x-axis

, j,k subscripts indicating modes (j,k = 1,2,...,6 refer to surge,

sway, heave, roll, pitch and yaw, respectively)

kw wave number - w2/gw

ix sectional mass per unit length

om sectional metacentric height

t time

x,y,z coordinate system as defined in Figure 1

z z-coordinate of sectional centre of gravity

CL wave amplitude

- principal sea direction relative to ship's heading, Figure 3

V displacement volume

-inj motion displacement

r~.(= dn./dt) velocity.3 .3

TI. ( d2 rj/dt2 ) acceleration

e. phase angle of wave loadX wavelength

variable of integration in x-direction

P mass density of water

W frequency of wave encounter

W absolute wave frequency.~w

V

S. . . - .".

1 . INTRODUCTION

One of DREA's ship dynamics research objectives is to provide the

warship designer with analytical "tools" which enable him to estimate the

motions and the associated wave loads on qhips at sea. Recently,additional subroutines i to calculate the wave loads have been developedand integrated into the ship motion computer program SHIPMO2. The newsubroutines calculate the root-mean-square values of wave loads in fivedegrees of freedom in irregular short-crested seas as well as the transferfunction for wave loads in regular seas.

The purpose of this Technical Memorandum is to report the resultsof a study which compared the wave loads predicted by the extended versionof SHIPMO1 with those measured in experiments.

The method of analyses of motions and wave loads adopted inSHIPMO is essentially based on the linear strip theory due to Salvesen eta13. However, the coefficients in the equations of lateralanti-symmetric motions, including roll, are modified by taking intoaccount the contribution from the lifting surfaces on the hull (stabilizerfins, bilge keels, rudders, propeller-shaft brackets, etc.), the detailsof which are found in Reference 4. The summary of the method of analysisof wave loads in regular waves is presented in Section 2.

In Section 3, the predicted wave loads are compared with fivesets of published experimental data.

2. METHOD OF ANALYSIS

Figure 1 shows the right-handed moving cartesian coordinatesystem used for the calculation of wave loads and motions. The origin islocated at the equilibrium position of the centre of gravity of the ship.The x-axis points to the bow and the y-axis extends to port, both beingparallel to the undisturbed free surface; z is measured verticallyupward. The coordinate system maintains a fixed orientation with respectto the undisturbed free surface while it translates with the mean velocityof the ship. The dynamic wave load components acting on a ship cross

section are defined in Figure 2.

The sea direction BS is defined in Figure 3 as the anglebetween the mean velocity vector of the ship and the principal directionof propagation of the wave train. Thus, 0s1; 00 for following seas,

s 90 ° for beam seas from port, and s = 180 for head seas.

~1

2.1 Wave Loads in Regular Waves

Consider a ship moving in a train of long-crested, or unidirectionalregular waves of a particular absolute frequency, w, on a straightcourse at a fixed orientation, 8s, to the direction of the wavesadvance.

Due to its forward motion, the ship encounters the waves with afrequency of encounter w which is related to the absolute wave frequencyw via:

W = Ww - kw Ucos~s (1)

where kw = wave number = w2/gw

U - ship speed

.s - sea direction

The resulting wave loads as well as motions will then be harmonicfunctions of time with the frequency given by Equation (1), and having asolution of the form:

Xj(t) - Xjoexp(iwt) - (XjR + iXjl)exp(iwt) (2)

where Xj = complex variable indicating formal solution for themotion or load in the jth mode

Yjo complex amplitude of Xj

XjR XjI = real and imaginary partq of Xj0 , respectively

w = frequency of wave encounter

t =time

In order to facilitate the algebraic work, the computation isperformed in the complex field.

In expressions involving complex numbers, only the real parts arephysically realizable; thus,

Re{xj (t)} = XjRcoswt - Xjjsirut

= IXjolcos(wt + ej) (3)

2

where Re{Xj (t)} real part of Xj2 2

IXjo I = (XjR + XjI )1/2 amplitudej = arctan (Xjl/XjR) = phase angle

The total force acting on a cross section of a ship's hull may bedivided into two components: inertial force and external force. Since

inertial fnrces, the magnitude of which are equal to the mass timesacceleration, act in the directions opposite to those of the externalforces, the net loading per unit length of a ship's hull is equal to thedifference between these two forces:

dVj/dE = dIj/dE - dFj,'dE (4)

where dVj/dE = net load in jth mode per unit length,

Slj/dE = local inertial force in jth mode per unit length,

dFj/dE = local external force in jth mode per unit length.

The modes j of the loading are defined as follows:

j = 1 axial forcej = 2 horizontal shearing force

* j = 3 vertical shearing forcej = 4 torsional momentj = 5 vertical bending momentj = 6 horizontal bending moment

The net wave loads*, Vj acting on an arbitrary cross sectionare obtained by integrating the load per unit length of Equation (4) fromone end of the hull to the specified cross section.

Thus Vj = (dVj/dE)dE = net wave load

-" Ij = P(dIj/d )dC = inertial forces and moments

Fj = f(dFj/d)dC = external forces and moments

Hence, from equation (1)

Vj - F (j = i,..,6) (5)

• When the motion of an entire ship is considered, the external forces are

exactly balanced by the inertia forces, so that the sum of all forcesacting on the ship is zero. However, the two kinds of forces acting onan elemental section of the hull are generally not balanced.

-e L 3lip-

It can therefore be seen that in order to determine the waveloads at a particular cross section, the forces and torsional momemtsacting over the portion of the hull lying on one side of the cross sectionin question must be known a priori, and that unlike the calculation ofmotions, in which a set of equations must be solved simultaneously, thecalculation of wave loads on a cross section consists simply of thesummation of the predetermined forces and torsional moments acting on oneside of the section. The choice of the side in any case is of coursearbitrary. In the subprograms, the summation is performed over the hullforward of the cross section under consideration.

The axial force (j 1), the force acting in the direction of thex-axis, is assumed negligible3 and is not considered herein.

The method of analysis adopted in the subprograms is thestripwise computational technique of Salvesen et a13 . The forces andmoments acting on cross sections are derived in terms of motions(displacement, velocities, and accelerations) and hydrodynamiccoefficients such as added-mass, added moment of inertia, and dampingcoefficients. The data that are extraneous to the calculation of motions,but required for the wave load calculatiin, are section masses, sectionalradii of gyration for roll, and positions of sectional centres of gravity.

Outlined below is the computational technique implemented in thesubprograms.

The hull is divided into a number of equally spaced ordinatestations, with No. 0 station at the forward perpendicular (FP). The totalnumber of stations may be up to 21. Each hull section, or "strip", spanstwo consecutive half-stations and is considered to be a cylinder with aconstant cross section identical to that of the it.tegral station at itslongitudinal midpoint. The extreme fore and aft strips, which span theintegral stations at the perpendiculars and the adjacent half-stations,have cross sections identical to those at the perpendiculars.

For the purpose of wave load calculation, the followingassumptions are made:

(i) that the ship is a rigid body;

(ii) that the external forces and moments acting on each strip aswell as the mass of the strip are concentrated in the plane ofthe integral station contained in the strip.

4

* .

The external forces and moments are caused by the water exertingforces on the hull, and consist of three components: hydrostatic restoringforces and moments due to the displacement of the rigid hull from the

- equilibrium position, exciting forces and moments due to the oncoming

waves, and the hydrodynamic forces and moments due to the ship's motion.. Henrce,

Fj= Rj + Ej + Dj (j = 2 ......,6) (6)

where Rj = hydrostatic restoring forces and moments

Ej= exciting forces and moments

Dj= hydrodynamic forces and moments due to ship motions

From Equations (5) and (6), the wave load in the jth mode on across section can be expressed as:

=Vj i j - Rj - Ej - Dj (j = 2 ..... ,6) (7)

The following expressions for the Ij, Rj, E* and Dj aregiven in Reference 3, to which the reader is referred for a detailedderivation. Note that all of the integrations indicated are over thelength of the hull forward of the specified cross section.

The inertial forces and moments are given by:

12 =fm(N 2 + E6- " 4 )dC (8)

13 =ff m( 3 - Cfi)d (9)

14 = f{ix i 4 - mE( 2 + Ei 6 )}dE (10)

15 - fm( - x)( 3 - 45 )d (11)

16= fm(& - x)(j 2 6 - z 4 )d (12)

where ix sectional moment of inertia about the x-axis

m sectional mass per unit length

x f x-coordinate of the cross section

7 z-coordinate of the sectional centre of gravity

. integration variable

"= acceleration

[.5

The hydrostatic restoring forces and moments are given by:

R3 = -pgfb(n 3 - n5 )d (13)

R4 = gn4f(Pa -- mi)d (14)

R5 = pgfb(& - x)(n 3 - n5 )d& (15)

with R2 - 0 and R6 - 0.

Here a - submerged sectional area

b = sectional beam at waterplane

- g = acceleration of gravity

o- = sectional metacentric height

nj = motion displacement

p = mass density of water

The exciting forces and moments due to the oncoming regular wavesare given by:

cEj = Df(fj + hj)dC + 7ZU hWj(x) e )t j-2,3,4 (16)

E5 = _ pc{f[( _ x)(f 3 + h3 ) + U h3 ld}eiwt (17)

E6 = pa{f[(C - x)(f 2 + h2 ) + -U h2 ]d}eiwt (18)

where U = mean speed of ship

fj =Froude-Kriloff force (see Equation (49) of Ref. 2)

hj= diffraction force (see Equation (50) of Ref. 2)

. wave amplitude

I.-

:.%- .

The hydrodynamic forces and moments due to ship motions are given

by:

D 2 f{a22 (2 + h"6 ) + b2 2( 2 + "6

+ a24 j4 + b24)4 + - b2 2 6 - Ua2j 6)dw 2

U_ [Ua 2 2(i2 + - b 2 2(fi2 +

+ U2( a2i46 + b 22) + U(a2 4f4 b 2"*b 4 2 ) (19)•i " 1 bii) ( 9

r 2~

3 f{a 3 3 3 -n ') + b - &i5)

U"+a -3a(fJ - n5)

2 b3 3 5 3 U3(5d 5

U U2 ..2 33 3 "5) - 3 3 5 b3 3 5 )] x

D -f{a 4+(b + b *)A + a nj+4 444 44 44 42 2

+ b 24 (fi2 + +6 6 b24ii6 - Ua24i16}d

U- [Ua 24 (f 2 + &h - b24(f2 +

+ U 2(a4n + b 24i 6) + U(a 441 "2.b 4Ji4 )] (21)

7

--

- - f5) + b3 3 ( 3 - )

+ f{Ua 33(A 3 _ x45) U 2 b33(+"3 _ xf'5 )

u2-U(a33"5 + b33y5 )1dC (22)

w2

D f - x){a (TI + 6) + b(r +6 22 2 6 22 2 6

+ a24 4 + b244}dC- f{Ua22(fi2 + x66

U b22, 2 + + (an + b2 22 2 x 6) 2 2& 22

+ Ua24 r14 - b24f 4}d (23)

where ajk - two-dimensional sectional added mass coefficient

bjk M two-dimensional sectional damping coefficient

b44" two dimensional sectional viscous damping coefficientfor roll

j = velocity

8

. -

.

3. DISCUSSION OF RESULTS

Table 1 summarizes the cases examined in the correlation study.In the following discussion, only the minimum proportion of the resultsnecessary to illustrate the overall correlation characteristics arepresented.

Principal particulars for the five model ships shown in Table 1are given in Table 2. In fact, some of the dimensions given are for shipscale, like the SHIPMO input, so that SHIPMO computed results wouldcorrespond to published experimental ones. The reason for the apparentinconsistency in the choice of the variables for the abscissas andordinates in Figures 4 through 8 is to preserve the original formats inwhich the experimental results are presented in the References, and henceto facilitate the correlation of the predicted and experimental results.

Firstly, the predicted moment and shearing force coefficients forDestroyer Model Is* are compared with the experimental results inFigure 4. Agreement between the predicted and measured vertical bendingmoments (VBM) at stations 5, 10 and 13 is good in head seas (Figure 4a),but poor in following seas (Figure 4b). The predicted VBM for this modeltended to overestimate the experimental results. Note in Figure 4a thatthe magnitudes of the experimental variations between the pairs ofmeasurements at X/L - 0.6 for stations 10 and 13, at X/L - 1.2 forstation 5, and at X/L = 1.5 for station 10, range from approximately 30to 100% of the lower values.

The predicted VBM at midships in oblique seas are compared withexperiments in Figure 4c. Correlation is somewhat better for quarteringseas than for bow seas.

Figures 4d and 4e show fair agreement between the predicted andmeasured horizontal bending moments (HBM). Though the maximum HBM are notclearly defined by the experiments, the theory tends to underestimate theexperimental results. This trend is opposite to that observed for theVBM. Incidently, it will be noted in Figure 4d that the predicted maximumHBM occurs in waves whose so-called effective wavelength - defined as thewavelength multiplied by the absolute value of secant of the wavedirection - is approximately equal to L.

* The numbering of ordinate stations in Reference 5 is slightly different from

that adopted in SHIPMO in that the station at the forward perpendicular (FP)is numbered 1 in the former, while it is to be numbered 0 in the latter.The numbering of ordinate stations in this memorandum conforms to that ofSHIPMO. Thus, station 5 is situated at L/4 from the FP, where L is thelength between perpendiculars, and station 10 at midship, etc. Incidently,Reference 5 contains the most comprehensive model test data for wave loadspresently available in the open literature.

9

- . - . --- - .- - .- W, - - -_ Vg~

The predicted and measured torsional moments show grossdiscrepancies in Figures 4f and 4g. Further work is clearly needed to

resolve these. (Note, the scale division of the ordinate in Figures 4fand 4g is 100 times smaller than in Figures 4a through 4e.)

The comparison of the predicted vertical shears with experimentsin head seas is shown in Figure 4h. The predicted and measured maximaappear to be of the same order of magnitude for station 5, where shear isexpected to be greatest. The scatter of the experimental data isparticularly evident in this figure.

Next, Figure 5 shows the comparison of the predicted and measuredVBM coefficients at midships (station 10) and L/10 abaft midships (station12), for Destroyer Model 116* in head seas. (Note the experimentalresults are presented by the solid lines from Reference 6 rather thanpoints.) The predicted maximum VBMs are seen to be consistently 30 to 40%greater than the measured maxima over the Froude number (Fn) range from0 to 0.40. The good agreement shown in Figure 5b for station 10 appearsto be fortuitous judging from the trends in the other figures fordifferent values of Fn,

Thirdly, the predicted VBM and HBM coefficients at midships of aT-2 tanker model7'1 0 are compared with experiments in Figure 6.Overall, the predicted VBM shows a good correlation with experiments,though the discrepancy seen in Figure 6c is appreciable. On the otherhand, predicted HBM correlates poorly with experiment; the theory tends tounderestimate the experimental results considerably, and the discrepancyincreases with increasing ship speed. A "weather" HBM causes the bow andstern to deflect toward the oncoming waves; a "leeward" HBM producesdeflections in the opposite direction. The analysis, of course, does notdifferentiate the two, because the ship is assumed to be executing thesimple harmonic oscillatory motions, Linear and angular, about thetranslating axes.

The fourth case in Figure 7 shows the comparison between thepredicted and measured VBM and HBM coefficients at midships of the Series60 (CB 0.80) hulle '10 . The agreement between the predicted andmeasured VBM appears to be good in nearly head seas, but poor in otherwave directions (Figure 7a). The tendency of theory to underestimateexperimental results in Figure 7a is more conspicuous in Figure 7b, inwhich the predicted HBM is shown to be consistently less than theexperimental results in all wave direction.

* In Reference 6, ordinate stations are numbered from the aft perpendic-ular, AP (station 0) to the forward perpendicular, FP (station 10) withhalf-stations between integral stations. The station numbers citedabove correspond to the numbering system of SHIPMO; so station 0 is theFP, and station 20 the AP.

10

.1----------------------', .

" - .. - / . . . -, - .' . . ' - . . . , . - - . - . - . . . ." o ' . . , . , .' . " . . '. " , , . " " . .; . . . . "

Finally, the predicted ratios of VBM and HBM to the waveamplitude at midships of a cargo ship, the WOLVERINE STATE9 .0, arecompared with experimental data in Figure 8. The agreement between thepredicted and measured VBM results is generally good in head seas, butbecomes poor in other wave directions (Figures 8a and 8b). As seen inFigures 8c and 8d, the predicted HBM results correlate poorly with theexperiments.

Because wave loads on ships are derived as a function of theship's motions (displacement, velocity and acceleration) and thehydrodynamic coefficients (added mass, added moment of inertia, anddamping), the predicted wave loads will at best be only as reliable asthese variables; but when compounded, even relatively minor inaccuraciesin hydrodynamic coefficients and motions tend to be amplified and resultin a significant inaccuracy in the predicted loads. Comparison of thetrends of the correlations of wave loads (Figures 4 and 5) and of motions*(Figures Al and A2 in the appendixt) pertaining to the two destroyermodels bears out this fact.

The results of the present comparison show varied degrees ofagreement between theory and experiment. Granted that, considering thecomplexity of the model tests, it will be prudent to make a due allowancefor the accuracy of the experimental data when assessing the reliabilityof the theoretical prediction; yet, in view of the wide margins betweenthe predicted wave loads and the experimental results shown in the presentcomparisons, the need for further improvement of the theory is evident.

4. CONCLUDING REMARKS

1. The purpose of the present study was to obtain information aboutthe accuracy of the predicted wave loads from the extended SHIPMO computerprogram, and hence to determine its usefulness as a working tool for shipstructural design. The wave loads for five ships in regular waves werecalculated by SHIPMO and compared with the experimental data. The mainresults were as follows:

(a) The agreement between the predicted and experimental results wasgenerally good for the vertical bending moment in head seas, butthe correlation became less satisfactory for oblique and followingseas.

* Even though phase angles of ship motions do not appear explicitly inthe equations for wave loads given in Section 2 owing to the fact thatmotions are expressed in terms of complex variables, their accuracy isequally important as that of the motion amplitudes in the wave-loadprediction.

t For a comprehensive correlation study of the predicted ship motion withexperimental results, see Reference 11.

11%

*.. . .ii%. .

(b) The predicted horizontal bending moments were at best in fair

agreement with experiment.

(c) The predicted and experimental results showed glaring discrep-ancies with respect to the torsional moment.

(d) There appeared to be no regularity in the pattern of discrepancybetween theory and experiment.

No definite assessment could be made about shears because of lack of therelevant experimental data.

2. It was encouraging that the predicted maximum vertical moment inhead seas was for the most part in satisfactory agreement withexperimental data. However, for the ultimate statistical prediction ofthe loads in realistic short-crested waves, the accurate predictions ofthe loads in other headings are equally essential. Thus, the correlationbetween theory and experiment for the loads in oblique waves would have tobe further improved, before the wave loads predicted by SHIPMO could beused with confidence for structural design purposes.

3. The present comparison illustrates the need for systematic modeltests with adequate descriptions of the uncertainties in the measurements.The published reports lacked this information. Consequently, it was notpossible to clearly define the range of confidence of the predicted waveloads.

12

% ....- . -. . .

TABLE 1: SUMMARY OF CASES EXAMINED IN PRESENT STUDY

Range of WaveModel Reference Froude Number Heading Characteristics

Destroyer I (5) 0.21,0.29 0, 30 0.2 < X/L60, 90 2.2

120,150180

Destroyer II (6) 0, 0.075 180 1.0 < A, T90.15,0.20 <4.00.30,0.40

T-2 Tanker (7,10) 0 - 0.20 45,120 X/L 1135,150180

Series 60 (8,10) 0.15 10, 40 0 < oVV-jCB 0.80 60, 90 <4.5

120,150170

WOLVERINE (9,10) 0.160,0.214 0, 30 0 < X/LSTATE 60, 90 <1.8

120,150180

13

~. - - -

TABLE 2: PRINCIPAL PARTICULARS OF MODELS

Series 60 WolverineModel Destroyer I Destroyer II T-2 Tanker Cr.80 State

Reference 5 6 7, 10 8, 10 9, 10

Scale model model model ship ship

L, m 5.16 4.88 4.80 193.0 151.0

B, m 0.654 0.573 0.648 27.57 21.79

T, m 0.204 0.185 0.286 11.03 9.14

L/B 7.89 8.52 7.41 7.00 6.93

BIT 3.21 3.10 2.27 2.50 2.38

CB 0.572 0.490 0.740 0.800 0.655

14

11-SURGE q3 HEAVE 115 PITCH

a SWAY =ROLL 16=YAW

Figure 1 Definition of maotions

V, -COMPRESSION FORCE V4 aTORSIONAL MOMENT*z HORIZONTAL SHEAR V5 a VERTICAL SENDING

FORCE MOMENTV3 - VERTICAL SHEAR Vg - HORIZONTAL BENDING

FORCE MOMENT

Figure 2 Definition of positive loads

L

15

Figure 3 Definition of Sea Direction

16

.03

.0 0. . .2 16 0 24

.033

aSTATIO

.02 a. 1U~~-- / 1--,I**0

Us -180*

.01 -* **-,~ -- 10

a -'- 13

0 0.4 0.8 1.2 1.6 2.0 2.4X/L

(b) Vertical Bending Moment Coefficient in FollowingSeas 0* -Q)

.03

SHIPMO As

300 +

.02 .00 50

1500'

.. S . . ... _ 1

0 0.4 0.8 1.2 1.6 2.0 2.4

(c) Vertical Bending Moment Coefficient in Midships(Station 10)

Figure 4 Wave Loads on Destroyer Model I (Fn 0.21)

17

.20

STATION

.15-5

13

"10

SHIPMO

,05-

54

0 0.5 1.0 1.5 2.0 2.5VdL

(d) Horizontal Bending Moment Coefficient in Bow Seas(s = 1200)

.20

30 +.15 60° a

150* 4

.10 6M

I ++ SHIPMO>C&\ +

.05 /13. .,. ,, ...00

0 0.5 1.0 1.5 2.0 2.5X/L

(e) Horizontal Bending Moment Coefficient in Midships(Station 10)

Figure 4 cont'd

18

.20 -

STATIONSHIPMO",

.15 - 10

0.10 r

ad~ 5 5

05 - 1i *

010

0 0.5 1.0 1.5 2.0 2.5X/ L

(f) Torsional Moment Coefficient in Quartering Seas(a 600)

.20

306 +0 90

1200'SHIPMO

+ +4

1. I .I5% + +. J 120

0 0.5 1.0 1.5 2.0 2.5

(g) Torsional Moment Coefficient at Midships(Station 10)

.119

STA 120.04

EXP

0.03 SHIPMO-- .

0.02 0204

*-.. 0.4.01 0.03 STA 12

0 0.02

S-AI-0.01 S~

II

1.0 2.0 3.0 4.0

(a) Vertical Bending Moment Coefficient inHead Seas Fn - 0

STA120.04

EXPSHIPMO--.

0.03

STA,-0.02 0.04 / \

0.01 0.03- SAI

0 0.02 "STA io

0.011%."-

1.0 2.0 3.0 4.0

(b) Vertical Bending Moment Coefficient inHead Seas Fn = 0.15

Figure 5 Wave Loads on Destroyer Model II

20

. :. '. ;; . " -. .- . . .. . . ...-- . . ~~~- , . .- ... . ., .. . . , . . . , . . ,

-~~- -j F %. VW ' . 71

%T.1

0.04

EXP-0.03 SHIPMO--

,/-%STA.I2STA.1O

0.02 / I

'0.01 0.03/

0 0.02-/STA.I10

0.01

01I

1.0 2.0 3.0 4.0

(p) Vertical Bending Moment Coefficient inHead Seas Fn -0.30

0.04 X

SHIPMO--0.03 /'STA. 12

0.02 0.04

00.01 0.03 -

0 0.02 A/SA.10

0.01 /0/

1.0 2.0 3.0 4.0W. g

(d) Vertical Bending Moment Coefficient inHead Seas Fn =0.40

Figure 5 cont'd

21

LO

00 ~

0 0r

4w

0 w L

0 (,

-H 00 0 i

10 00)

-. 44

04 0CD0t (SB -NI) WH0 0

In H -W 01 0)

o C3 i. 0w zw w~~0

4 0- a. a 0 r

-n 0 -4 go w 0

x (D0 w O 4(

cn >~ E0-4

0 00 0 -H 0a

u0 P4404

-Co 4.

d) U)-1 4

pa w

(SI31-NI) W9A -w~

CL 11 0 4

0 0x 0

to w0>

*14

In 0 InO 0 0

00

(SSB1-NI) W13A

22

cu 0 .0

.0

0 0 If~ In!

- 00L

w w

0o 0 a

C-4t

co "

Ic0 0 0ca

4.1X

.0 _____Do

In C i o 0 n 0in

0 >4

4 00cu 9 )0 u 9 0"444" 44

0(3 0 004* (D pa

in U __ _ __ n W

40 0 CL 00 0 44

_j 14.

zg~W 0 4 0

000

C))

o 0--

0 00

23

ae"- % *~..: :: .* . ..' . *%

.25 I

__. i..20- 70

130+170

.15 /:-

SHIPMO-,J% .

•/,, II ,.3,0• "" . .+,L"

.10. • . o"10

0 1 2 3 4 5AL -7g

(a) Vertical Bending Moment Coefficient atMidships

.25 .

.20 70 9 +++II0 ° 0 + 700.ri1300 + ,,"

+ ! ,...

SHIPMO A /.10-

%130'

.05 0'

0 1 2 3 4 5W"J g'i

(b) Horizontal Bending Moment Coefficient atMidships

Figure 7 Wave Loads on the Series 60 (CB 80) Hull(Fn = 0.15)

24

--;~~~~~~~~~................. -.-........ ..............-.....-.".-..-..............-......- . • ... ,.... .

'' " -' " . . ." -. . " . ' " " - -" .<.' . "- -, .. - ' -*". - . , +.' ' - x -. " . - .- ", . . .. " " ", . . .

FT-T/ FT

1 0000

6000 -0

6 000 +

2000 -+(

0 0.4 0.8 1.2 1.6X/L

*(a) Vertical Bending Moment at Midships in Head and

Following Seas

FT-T/FT10000 I

AsS8000 +60

12006000 O

> A

3C 2000 ta- SHIPMO

0 0.4 0.8 1.2 1.6

(b) Vertical Bending Moment at Midships in Bow and Quarteringseas

Figure 8 Wave Loads on the Cargo Ship "WOLVERINE STATE"(Fn -0.214)

25

"2 "FT-T/FT14000 ...

12000 - 0-..C 300+

• 10000 - 60 °"6iooo *N •08000 (mx60-

< 6000 + SHIPMO

> 4000 ....*

2000 + ..... +5-' + ............

0 0.4 0.8 1.2 1.6

(c) Horizontal Bending Moment at Midships in Bow Seas

FT-T/FT14000

" 12000 -.-- s

01200 +

_10000 1500e

8000 +

-< 60001200/ f-SHIPMO

> 4000 .

2000 ,50.'jI5I I I I I

0 0.4 0.8 1.2 1.6

(d) Horizontal Bending Moment at Midships in QuarteringSeas

**" Figure 8 cont'd

26

APPENDIX

COMPARISON OF THE PREDICTED AND MEASURED MOTIONS OFDESTROYER MODELS I AND II

The non-dimensionalized motions of destroyer model I predicted bythe SHIPMO computer program are compared with experimental results in FigureAl for Fn - 0.21. The results for Fn - 0.29 were similar in terms of bothmagnitude and trend. In Figure Ala, the predicted pitch shows a goodcorrelation with experiments in all headings, though theory tends tounderestimate the measured responses. The correlation of the predicted heavemotion with experimental results is reasonable for head seas, but somewhatpoor in oblique waves; particularly in beam waves, the discrepancy betweencomputation and experiment is significant (Figure Alb). The correlationbetween predicted roll and yaw with experimental data are reasonably good inall headings with the exception at 600 as seen in Figures Alc and d. Ingeneral, the correlation between the predicted and experimental results ispoor at long wavelengths.

Figure A2 shows the comparison of the predicted non-dimensionalizedheave and pitch motions of destroyer model II in head seas with experiment.The results are indicated by solid lines as done in Reference 6. Except forlow and high frequency tails, the correlation between the predicted andexperimental results is reasonably good over the Fn range 0 to 0.40.

27

................................................ ,.....,.." .. *,.."..• :.,

1.6

0 01.2 600*wIL. 1200 9

0

0. B 0.

0.4 ~6000.4

0 0.4 0.8 1.2 1.6 2.0 2.4X/ L

(a) Pitch

1.6

SHIPMOw- Y

90

CL 18 0 _

W 3C 0.4-

0 0.4 0.8 1.2 1.6 2.0 2.4

-P X/ L

(b) Heave

Figure A.1. Motions of Destroyer Model I in Regular Waves(Fn =0.21)

28

4.0Os

300 +,, 3.0 - :00-- 1200 -L 150 & - 900

a LO2.0 / -", + + . - -

.I . 6 300

0 0.4 0.8 1.2 1.6 2.0 2.4

X/ L

(c) Roll

1SHIPMO++

0.8

+--*" . + + +

.- 6.0

W.n 0.4 *

x/ 300 +

0. 2-' d600 0".0.

,II I I

0 0.4 0.8 1.2 1.6 2.0 2.4,/ L

(d) Yaw

Figure A.1 cont'd

29

*:- : , : -: . : , .. : .- . ' . . : : - . ., ' -'. . " . . .... .. ..-. -... --,

j773 773

1.2 I 1.2

1.0 (a) 1.0 (b)0.8 Fn - 0 0.8 Fn = 0.15

0.6 0.60.4 1.2 0.4 1.2

0.2 1.0 - \ -f , 0.2 1.0

0 0.8 0 0.8

0.6 0.6

0.4 0.4

0.2 0.2

1.0 2.0 3.0 4.0 1.0 2.0 3.0 4.0

773 '1731.2 , 1.2 I

o. ( c ) - o. ( di

0.8 . Fn 0.3 0.8 Fn - 0.4

0.6 0.6 77

0.4 1.2 -0.4 1.2

0.2 1.0 . 0.2 1.0"-

0 0.8 0 0.8-

0.6- 0.6

0.4 0.4

0.2 0.2

1.0 2.0 3.0 4.0 1.0 2.0 3.0 4.0Srug w ru

LEGEND: 713 - HEAVE AMPLITUDE / WAVE AMPLITUDE

'77. = PITCH ANGLE / WAVE SLOPE

EXPERIMENT

SHIPMO

Fig. A2. Motions of Destroyer Model II in Regular Waves.

30

...................... .7

-17

REFPERENCES

1. Ando. S.: "Wave Load Prediction for the SHIPMO Computer Program", DREATechnical Memorandum 82/L, October 1982.

2. Schmitke, R.T. and Whitten, B.: "SHIPMO - A FORTRAN Program toPredict Ship Motions in Waves", DREA Technical Memorandum 81/C,September 1981.

3. Salvesen, N., Tuck, E.O., and Faltinsen, 0: "Ship Motions and SeaLoads", Trans. SNAME, Vol. 78, 1978.

* 4. Schmitke, R.T.: "ROLLRFT, A FORTRAN Program to Predict Ship Roll, Swayand Yaw Motions in Oblique Waves, Including the Effect of Rudder, Finand Tank Roll Stablizers", DREA Technical Memorandum 78/G, December1978.

5. Lloyd, A.R.J.M., Brown, J.C., and Anslow, J.F.W.: "Motions and Loadson Ship Models in Regular Oblique Waves", RINA Occasional PublicationNo. 3, 1980; Trans. RINA, Vol. 122; and the Naval Architect, No. 1,January 1980.

6. Nethercote, W.C.E.: "Motions and Bending Moments of a Warship Design",The Naval Architect, No. 4, July 1981.

7. Numata, E.: "Longitude Bending and Torsional Moments Acting on a ShipModel of Oblique Headings to Waves", Journal of Ship Research, Vol. 4,No. 1, p. 35, 1960.

8. Wahab, R.: "Amidships Forces and Moments on a CB - 0.80Series 60' Model in Waves from Various Directions", Netherlands ShipResearch Centre TNO, Report No. 100S, November 1967.

9. Chiocco, M.J. and Numata, E.: "Midship Wave Bending Moments in a Modelof the Cargo Ship 'Wolverine State' Running at Oblique Headings inRegular Waves", NAVSEA Ship Structure Committee Report SSC-201(AD-695123), November 1969.

10. Kaplan, P.: "Evaluation and Verification of Computer Calculations ofWave-Induced Ship Structural Loads", NAVSEA Ship Structure CommitteeReport SSC-229 (AD-753220), July 1972.

11. Graham, R.: "Ship Motion Program SHIPMO - Model Test Correlations andSuggestion for Use", DREA Technical Memorandum in print.

31

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Correlation of Wave Loads Predicted by the Extended SHIPMO ComputerProgram with Experiments

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ANDO, S.6. DOCUMENT DATE AUGUST 1985 7a. TOTAL NO. OF PAGES I ft NO. OF REFS

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Wave loads predicted by the extended SHIPMO computer program were

compared with experimental data in an attempt to assess the range ofvalidity and to estimate the uncertainty of the predictions. In general,

the agreement between theory and experiment was good for the verticalbending moment, but fair to poor for the horizontal bending moment. The

predicted torsional moment was found to be in gross disagreement with the

measured values in terms of both magnitude and trend. It was not possible

to find any correlation of the pattern of the discrepancy between theory

and experiment with the principal design characteristics, such as hullCorm or weight distribution. The present comparison shows that the

prediction of ship motions in oblique seas needs to be further improved.

Also, systematic model tests covering a wide range of the variables are

required to assess the uncertainty of the measurement, and hence, to

determine the range of confidence of the predicted loads more clearly.

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