Model experiments on barges in still water and in waves

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IN. STILL WATER AND IN WAVES:.

J.M.J. Journée

Report No. 814

December 1988

DoiftUnivorelty of TochnoIoy

Ship Hydromechanics Laboratory

Mekelweg 2 - -

-2628 CD DeIft The Netherlands

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by J.M.J. Journé.e

December 1988

Report No. 814

Delft University of Technology Ship Hydromechanics Laboratory

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Summary

Results are reported here of _{systematic series of experiments with}

two models on a different scale of a rectangular barge with a

length to breadth ratio of 3.00. _{For each model a range.of draughts} and speeds have been used.

Drag forces and moments. in still _{water, heave and pitch motions and} added resistances. in regular head waves and heave and roll motions

and drift forces in regular beam _{waves have been measured.}

The results are presented in _{a tabular form and in figures. Some}

preliminary analyses are given.

Content s

page Introduction

1

Model Definition and Testing Program .

. 2

Experimental Results

4

Analyses of Some Experimental Results

7 5.. Nomenclature 16 References 17 Figures 18

Appendix. I. _{Summary of Experiments on Drag Forces}

30

Appendix II. _{Summary of Experiments in Regular Head Waves} _..

. 39

Appendix III. Summary of Free Rolling _Experiments ₄₈

Appendix IV. _{Summary of Experiments in Regular Beam Waves}

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This report describes the results _{of experiments, carrie,d out with} two models on a different scale of _{a rectangular barge with several}

draughts. The length to breadth ratio of _{the models was 3.00.}

Still water experiments have been _{carried ou,t to measure the drag} forces in a horizontal plane and _{the moment around a vertical axis} due to water currents _{or a transport velocity of the barge'. The} forces and the moment have been _{measured at a range of velocities} a.nd drift angles. These experimental _{results have been translated} into simple empirical formulas, _{valid for rectangular barges with}

a

length to breadth ratio of 3.00.

In regular head' waves the heave _{and pitch motions and the mean}

added resistance due to _{waves have b:een measured at a range of}

forward 'speeds.. The measur'edheave _{and roll motions have been}

compared with some results of strip _{theory calculations. The}

measured added resistances h'avebeen, _{compared with .t'he"result.s of} two theories:, a radiated _{energy method and an .'lnte'gra'ted.pressure} method.

In regular beam waves the heaie _{and.roll-mot'jons and the mean drift} force.s due to waves have been measured at zero forward speed. The

measured heave and roll motions have been compared with results of

strip theory calculation's.

To investigate the effect of _{tankwall interference two models} _{on a}

different scale have been used. _{In particular the pitch motions} _are very much influenced by tankwall interference.

This report describes the models, _{the testin.g program and the}

experiments. All. experimental data have _{been tabled in an appendix.}

Most of the data have been plotted _{in figures too, together with}

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2. Model Definition and Testing Program

The experiments have been carried _{out in Towing Tank Number I of}

the Deift 'Shiphydromech;anj,c,s _Laboratory.

The dimensions of the _{cross section of the towing tank are:}

width: 4.2O meter

water depth:. 2.31 meter

Thes.e tank dimensions dictated _{the dimensions of the model. Tank}

wail interference should be _{as low as possible and the effects of}

blockage had to be within the _{accurac.y of the measurements.}

The following main dimensions of _{a model of a rectangular barge}

with a length to breadth ratio L/B _{- 3.00 were choosen}

Model A: _{L = 2.250 meter and B = 0.750 meter}

To investigate the effect of. tank wail _{interference on the motions} of the model in waves, _{a geometrical similar model with half the} size of model A have been tested too:

Model B: _{L = 1.125 meter and B - 0.375 meter}

A range of breadth to. draught ratios B/T was choose.n for the two

models.

The typ.e.s of experiments,, _{carried out wi.th model A and model B}

at

these differen,t B/T ratios, _{are tabled below.}

When carrying out the drag force _{and moment measurements} _{a range of} speeds have been used, varying from zero speed until even a speed corresponding to Froude number 0.15.

During the measurements o.f the heave _{and pitch motions and the}

added resistances in head _{waves four fixed speeds have been used:}

Fn = '0.00, 0.05, 0.1:0 and 0.15 _{respectively.}

T:he measurements of the 'heave.and _{roll motions and the drift forces}

in regular beam waves could be carried out at zero speed only.

B/T Trim . 2.50' ' 0.00 . 5.00 0,00 7.50 0.00 10.00 'H 0.00 13.33 0.00

Drag Forces a.nd Moments

in

Still Water

A A+B A+B A+B A

Heave and Pitch Motions and Added, Resistances

in. Regular H'e,a,d Waves

A+B

A-i-B A+B _A

H'eave and Roll Motions

an,d Drfft Forces

in Regular Beam Wave,s

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These Fou'de numbers are defined by:

V Fn

(g.L)½

in which g is the acceleration of gravity.

The experimental conditions of _{the two models are presented i.n the}

following table. B/T 2.50 5.00 7.5:0 10.0:0 13.33 Model A T (m) 0.300 0.150 0.100 0.075 0.056 Trim (ni) 0.000 _0.000 _0.000 _0.00:0 _0.000 KG (m) 0.151 0.099 0.074 0.056 GM (m) _0.237 _0.420 _0.588 _0.798 T (s) _1.461 _1.139 _1.021 KG/T (-) 1.003 0.990 0.993 1.005

k/L (-)

0.252 0.252 0.251 0.256

k,/B

(-) 0.473 _0.491 0.520 Model B T (m) _0.075 _0.050 _0.038 Trim (m) _0.000 _0.000 _0.000 KG (m) _0.075 _0.050 _0.046 GM (m) _0.119 _0.209 _0.285 Tq, _(s) _0.999 _0.826 0.710 KG/T (-) 1.000 1.0:00 1.2:27

k/L (-)

0.250 0.250 _0.250

k/B

(-) 0.458 0.502 0.504

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3. Experimental Results

During the experiments the _{average temperature of the fresh water}

in the towing tank was about 15 °C.

This means for the density and the kinematic _viscosity:

p = 999.1 kg/rn3

= 1.139 .10-6 rn2s

Drag Forces and Moments in Still Water

The definitions and the axis system, used during _{these still water}

measurements are shown in the following figure.

V

Figure 3.1. _{Definitions and Axes System,} _{as used during} Still Water Measurements

The drift forces are considered to be current forces. The drift

angle _{is defined here as the angle between the} _{vector of the}

relative water speed and the positive x-axis.

A range of drift angles has been _used: _{8 = 180, 150, 120 and 90}

degrees. In some cases a few intermediate _{angles have been included}

too.

The relative water velocity, _{so the opposite speed of the towing}

carriage, varied from Fn = 0.05 until Fn = 0.15.

The drag forces X and Y in the _{x- and y-direction and the moment N}

about the z-axis were measured by dynamometers, based on

strain-gauge measurement of bending resulting from shear forces. _The

electronic output has been integrated over a certain time, to get

an average value.

The still water resistance _{can be obtained from the drag forces at}

the experiments with _{a drift angle of 180 degrees.}

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Vertical Motions and Added Resistance

The definitions and the axis system, used during the heave, _pitch

and added resistance measurements are shown in the following figure.

Figure 3.2. Definitions and Axes system, as used during Heave, Pitch and Added Resistance Measurements These experiments in regular head waves were carried out at four

forward speeds, including zero speed.

A flap-type wave maker was used. To avoid refections _{of the waves}

at the end of the tank a conventional beach is used. _{The waves were}

measured by a two-wire conductance _{wave probe. The wave meter was}

mounted at a distance of about 2.50 meter in front of the model at

the half width of the tank.

The models were free to _{carry out heave and pitch motions only.}

The motions were measured by two low-friction potentiometers above

and at the center of gravity of the model. _{At the larger model B a}

vertically sliding rod forward was guided by the _{towing carriage,}

to keep the model on the right course.

The waves and motions were recorded on an U.V. recorder as a

function of time and the records _{were analysed for motion}

amplitudes and phase lags.

The resistance in waves was measured in the center of gravity by a dynamometer, based on strain-gauge measurement of bending resulting

from shear forces. The electronic _{output has been integrated over a}

full number of periods of encounter of the waves.

The experiments have been carried out for a range of wavelength -shiplength ratios: A/L = 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0 and some additional values. At a few wavelengths the wave amplitude has been

varied too, to investigate non-linearities in _{motions and forces.}

The experimental results are summarised in _{Appendix II.}

The amplitude characteristics of the heave and pitch motions have

been plotted in the figures 7.l.a-b-c-d and the _{transferfunctions}

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Free Rolling Tests

The meta.centric height GM _{was measured by means of an inclination}

test. As far as possible, it was tried to locate the center of gravity of the models at the waterline.

During the "free" rolling tests in still _{water the model could}

carry out heave and roll motions only.

The roll signal was registrated by _{an TJ.V. recorder as a function}

of the time.

The average roll period T _{and the metacentric height GM give}

information about the total moment of inertia _{for roll, defined by:}

in which: g½ -

2ir

with: GM½ . T V = volume of displacement

From the logarithmic decrement of the _{recorded roll angle}

amplitudes pa(t) follow the non-dimensional _{roll damping}

coefficient K as a function of the mean roll angle amplitude by:

1

2,r

loge[

q(t)

] IC Pa(t+T(p)

The results, derived from these _{experiments, are summarised in}

Appendix III.

The non-dimensional roll damping _coefficients _{have been plotted}

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Heave and Roll Motions and Drift Forces

The definitions and the axis system, used during the heave and roll

motion and drift force experiments _{are shown in the following}

figure.

Figure 3.3. Definitions and Axes System, as used during

Heave, Roll and Drift Force Measurements

The experiments in regular beam waves were carried out at zero speed.

The models were free to carry out heave and roll motions only.

The waves, the motions and the forces _{were measured in an analog}

way as done during the heave and pitch motions. _{The model, under}

the measuring equipment, _{was simply turned in a horizontal plane} over 90 degrees.

The experiments have been carried out for a range of wavelength

-shiplength ratios: A/L = 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 4.0 and some

additional values. At a few wavelengths _{the wave amplitude has been}

varied too, to investigate non-linearities _{in motions and forces.}

The experimental results are summarised in Appendix IV and in

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4. Analyses of Some Experimental Results

Blockage

According to Ractliffe, Fisher and Mitchell _{[1], blockage can be}

taken into account by using the _{following relation between the} corre.cted model speed Va and the speed V of the towing carriage:

VaaV

with: 1 a 1

kmm

km = 1 +exp(-lO.m)

model cross section area

m

tank cross section area

This results in speed correction _{factors a for the different}

loading conditions of the two. _{models as tabled below...}

The table shows low correction fact'ors. _{These co;r,r.ectjons are in}

a

similar order as, the _{accuracy of the measurements.}

This is a reason why the effect _{of blockage, which is still}

uncertain, is not taken into account _{here when analysing the}

experme.nts.

Speed Correction Factor a

B/T , 2;50 5.00

i50

10.00 13.33 Model A Model B 1.043

L022

1.006 1.015 1.004 1.011 1.00.3 1.009

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Drag Forces and Moments in Still Water

The flow of a current around _{a fixed model has been simulated by}

towing the model forward in still water with different drift angles at a range of speeds, even until _{a Froude number of 0.15.}

The longitudinal and lateral _{drag forces and the moments in} _a

horizontal plane _{on the barge are approximated in a usual way by}

the following expressions:

X C

½p.V2.V2/3

Y Cy

½pV2.V2/3

N ₌ _CN

_½p.V2.V

The coeffcients C, Cy and

_{CN have been derived for bothmodels}

from a large number of measured _{data at four angles of attack of} the current : 180, 150, 120 and 90 degrees. The smaller amount of data for _{is 135 and 105 degrees has been analysed} _too.

In a first analysis it _{appears that the :s.p;eed .dependency..of these}

coefficients is low, at least _{whencomparing this with the} influence of the breadth to draught _ratio.

As a first approximation, these _{coefficients are given here} _{as a}

second degree polynomial of B/T:

CX _{CXO + CX1.(B/T) + C2.(B/T)2}

Cy _{Cy0 + Cy1'(B/T) + Cy2.(B/T)2} = CNO + CNl.(B/T) .+

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The coefficients Cj,

Cyj

and CNj have been derived for each from

the measured data by using a least squares method.

The number of measurements and the _{resulting coefficients for each} 8 are tabled below.

P 180 p iso _P ₁₃₅ _p ₁₂₀ _{p = 105} _p ₀₉₀

Nra 52 49 12 47 12

-Cxo 4.058*10 _4.683*101 _3.586101 _2417*101 +9.1171O2 0.00D*1O

C +3.3451O2 +3713*102 +3.532*102 _+2.482fl102 _4557102 _0.000*10+0

-1.364*10 -1.278*103 -i.gii*103 +3.O27*1O 0.000*10+0

Nra _- 49 12 47 12 51

Cy 0.000*10+0 +1.020*10+0 +1.550*10+0 +1.841*10+0 +2.417*10+0 +2.055*10+0

C, 0.000*10+0 _1.485*101 _2.392*101 _2.509*101 ,_3.620*10'l _-2.913*10

Cy2 0.000*10 +6.752*jO +1.297*102 +1128*1O2 +1.943*102 +1.389*1O2

Nra _- 49 12 47 12

-0.000*10+0 +3.657*101 4073*101 +2.856*101 +2.851*101 0.000*10+0

0.000*10 -4.222*10 _4.840*102 _{_8.544*103} _2.623*102 _oo*io°

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Heave and Pitch Motions in Regular _{Head Waves}

The measured amplitude characteristics _{of the heave and pitch}

motions are presented in figures 7.l.a-b-c-d _{in a non-dimensional}

form. These figures show the very large influence of tan'kwall interference on the pitch motions, in _{particular for model A. On} the other hand, model B is _{a very small model wich requires small} wave lengths what can result into _{a lot of spreading in the}

measurements.

In the figures a comparison _{is given with the ordinary strip theory}

calculation.s of heave and pitch mo:tions, _{carried out as described}

in detail in [2].

In general these coupled heave and _{pitch equations of motions are}

given by:

(p.V+a33).z +b33vz +c33z + a35

9 +b35O+c35.9

Z

a53 .

+b53z +c53z +(Iyy+a55).9 +b55O +c556

=

Because of the symmetry of the barge with.respect _{to the midship}

section these equations reduce to:

(p/+a33).z-f-b33.z+c33.zZ

(Iyy+a55).9 +b55O +c55.O

-So there is no coupling present between _{the heave and the pitch}

motions.

A conformal mapping method, using _{a Lewis transformation of the}

cross section forms to the unit circle, has been _{used to calculate}

the hydrodynamic mass and damping _{coefficients au} _and _{by the}

Urs.eli-Tasaj method.

The calculated heave motions show _{a fair agreement with the}

experiments for the full range of. breadth, _{to draught ratios..and} forward speeds.

The measured pitch motions of _{model A are very .much -;influenced by}

the tankwall interference, _{Extreme high response amplitudes}

were

measured. This interference effect _{is no.t included in the}

calculations, reason. why for model A the agreement between t.heory

and experiments is very poor.

Model B, with a much smaller inflüence _{of tankwall interference,}

shows a better agreement.

The. figures can show a fair agreement when extrapolating the

measured pitch data on base of the model breadth _{to tank width}

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Added Resistances in Regular Head _Waves

The measured frequency characteristics _{of the added resist.anc.e due} to waves are presented in figures _{7.2.a-b-c-d in a non-dimensional}

form.

In the figure.s a comparison _{is given with two prediction methods,}

based on the strip theory, of which the algorithms are described in

detail in [2].

The first method is the radiated _{energy method of Cerritsma and}

Beukelmari [3] and the second method _{is the integrated pressure} method of Boese [4].

The figures show _{a fair agreement between theory and experiments}

at

very low speeds (Fn - 0.00-0.05). At higher _{speeds non-linearities}

play an important role and the _{agreement with strip theory} predictions is very poor.

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Heave and Roil Motions in Regular Beam Waves

The measured amplitude characteristics _{of the heave and roll}

motions at zero- forward speed are presented in figure 7.4 in a non-dimensional form.

In the figures a comparison is given with _{the ordinary strip theory}

calculations of heave and rolimotions, carried _{out as described in}

detail in [2].

The uncoupled heave and roil equations _{of motions are given by:}

(pV+a33).z+b33.z+c33.z.Z

(Txx+a44) .rp +b44.q +c44'q

The radius -of, inertia _{forroll..kxx....of.;...the solid mass of the model}

can -be derived by subtracting the--cal.culat-ed---h-ydrodynam-ic-m-ass

moment of inertia from the measured-total _{moment of inertia.}

The -non-p.o:tenti.al part of -the- roil.damping _{.coeff..i.cient.s-:has been}

derived from the- measured -va-lu-es.--.in. _{figure 7.3 at a roll angle}

amplitude o.f 3 degrees..

The-se data are tabled below.

Figure 7.4 shows a fair _{a-g'reement-between..the predicted and-the}

measured heave and roll motions. i-Howeve-r--, _{.there.4-s-- some-- doubt about.}

the natural frequency- for roil _{-of-mo-del .B for the B/T-= 5.00} _case.

I.n figure 7. 5 a -compariso-n- i-s given _{of :the results of-;two-:-d-iffe-r-ent}

strip theory -calculations of r-ollrno-tion-s _{at-. -zero sp!eed for the}

-barge with a -breadth to draught r-at-io _{of 7.5.}

T-he Calculations- have be-en _{c-arrie-d.out.with.the..stri.p.theory}

algorithms as described in [2] and the _{SC.ORES-D:E.L-FT program [3],}

which is derived from work of Kaplan -and .Raff [6].

B/T. 5.00 7.50 10.00 Model A B A B - A B

k/B

0.405 0.049 -0.390 0.061 03t87 0.1.01 - 0.400 0.113 -0.3.85 0.14-0 -

0367

0.163

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In the strip theory algorithms in [2] _{the sway wave forces and the} roil wave moments are defined by:

and: and: D(Vw2*) = Dt M22 + M24' M22', N22' N44' M24', N24' M42', N42' D(Vw2*) Dt D(Vw4*) Dt D(Vw,4*) Dt + [ N2' 24 D(Vw2*) Dt +

[N42

In the SCORES-DELFT _{program [3,6] these forces and moments}

are defined by:

Y' -

Mfl'. D(vw2*) + I dM 44 - V. dXb 22 + [ N

dM2'

Vw2 ₊ _{+ OG.Y} dxb dM

-V.

2,2 * dXb dM4.,' - V. '7

*

w4 w2* + FK4' _{+ O.G.Y'}

The different terms in these _{expressions are explained by:}

- two-dimensional potential hydrodynamic _{mass and} damping coefficient of sway

= two-dimensional potential hydrodynamic inerti,a _and damping coefficient of roll

- two-dimensional potential .hydrodynamic _{mass and} damping coupling coefficient of roll into sway

- two-dimensional potential hydrodynamic inertia _and

damping coupling coefficien.t of sway into roll

V. V. dM22' * Vw2 Vw4* + FK2' dXb dM dXb

+ M24. k

D(vw2*) I -dXb ' k

V2

+ FK2

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the sway component of _{an equivalent orbital velocity of}

the waterparticles in the undisturb'e.d wave,

relative to the cross section

V4' - the roll

_{component of an equivalent orbital velocity of}

the waterpa'rt.icles in th.e undisturbed _wave,

relative to the cross section

FK2' _{the two-dimensional Froud'e-Krjlov lateral} _force;

this is. the lateral force _{on a ship's cross section,} caused by the undisturbed wave

FK4' _{the two-dimensional Fr'oud'e-Krjlov} _{roll moment;}

this is the roil moment on a ship's cross section, caused by the undisturbed wave

OC = distance. of the center o.f-gravt.y.ab'ove _{the still water level}

k = deep water wave number

V _{= forward speed of the model}

T'h,e better results in figure 7.5 of _{the first.:method .are.mai.nly}

caused by a difference in the hy:drodynamic _{corrections of.th'e} Froude-Krii.ov wave moments .n [2] and a difference in the algorithms to calculate the directional _{components of the}

equivalent orbital velocties of the _{wat.erparticles relative to the} cross section.

Besides this,, both the Lewis f:orm _{transformation and the Frank}

Close Fit method have been used _{to determine the two-dimensional}

hyd.rodyn'ami,c properties.. Fi.gir'e 7.5 shows _{somewhat better results}

for the Frank Close Fit method.

Drift Forces, in Regular Beam Waves

These forces have not been analysed _yet.

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5. Nomenclature

B _{breadth of the model}

CX longitudinal hydromechani.c force coefficient longitudinal hydromechanic force coefficient

Cy _{lateral hydromechanic force coefficient} Cyj _{lateral hydromechani,c force coefficient} CN _{horizontal hydromechanic moment coefficient}

CNj horizontal hydromechanic moment coefficient

Fn _{Froude number based on length}

Fnv _{Froude number based on displacement}

C _{center of gravity of the model} g _{acceleration of gravity}

K _{keel point of the model}

k wave number

km constant

including the hydrodynamic contribution

L length of the model

M _{metacentric point of the model}

m ratio of hull cross sectionto..tankcross _section.

N! _{. hydromechanjc moment in a horizontal plane} or a limit value

RAW added resistance due to waves

longitudinal drif force due to waves

Ry _{transverse drift force d:ue to waves} 1 constant

tj Constant

T _{draught of the model} T period of roll

V _{forward model spoed}

Va _{forward model speed, corrected for blockage}

X _{longitudinal hydromechanic force} Y _{lateral hydromechanic force}

Za heave amplitude

a _{forward speed correction factor}

drift angle, 1800 is a head current

czç heave phase lag

pitich phase lag roll phase lag

c°a roll amplitude

non-dimensional roll damping coefficient

A _{wave length}

V _{volume of displacement}

kinematic viscisity of water

p density of water

circular wave frequency

circular frequency of encounter

wave amplitude

9a pitch amplitude

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6. References

Ractliffe A.T., P.J. Fisher and CH.C. Mitchell.

An Experimental Study of the Parameters _{Affecting the Drag of}

Barge,s in Current and Waves.

13th Annual. Offshore Technology Conference, Houston, Texas, U.S.A., May 4-7, 1981.

Journée J.M.J.

Strip Theory Algorithms.

Delft Shiphydromechanics Laboratory, Deift University of Technology,

Report No. 815,, December 1988.

Gerritema J., and V. BeukeIman.

Analysis of the Resistance Increase _{in Waves of a} Fast Cargo Ship

International Shipbuilding Progress, Volume _{18, No 217, 1972.} Boêse P.

:Eine Einfa'che Methode zur Berechnung der _{Widerstan'dser.hhung} eines Schiffes in Seegang.

institii.t für Schiffbau _{der'Universitt Hamburg.,}

Berich.t Nr 258, 1970.

Journée J.M.J. and A. Versluis.

Scores-Deift on a Personal Computer. User Manual of Release 2.0.

Delft Shiphydromechanics Laboratory, Delft University of Technology,

Internal Report No. 805-M, October 1988. [6] Kaplan P. and A.I. Raff.

Evaluation and Verification of Computer _{Calculations of} Wave-Induced Ship Structural Response.

Ship Structural Committee _{Report.SSC-22:9,. 'July 1972.}

[5],

Acknowledgement.

- - indebted- to Mr. A _{. J. van} _{S:trien fo7r btfl}

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7. Figures

The following figures _{are included here.}

Figure 7.l.a. _{Measured and Calculated Heave and Pitch Motions} at Fn = 0.00

Figure 7.l.b. _{Measured and Calculated Heave and Pitch Motions}

at Fn= 0.05

Figure 7.1.c. _{Measured and Calculated Heave and Pitch} _Motions at Fn - 0.10

Figure 7.i.d. _{Measured and Calculated Heave and Pitch} _Motions at Fn 0.15

Figure 7.2.a. _{Measured and Calculated Added Resistances} at Fn 0.00

Figure 7.2.b. _{Measured and Calculated Added Resistances} at Fn = 0.05

Figure 7.2.c. _{Measured and Calculated Added Resistances} at Fn 0.10

Figure 7.2.d. _{Measured and Calculated Added Resistances} at Fn = 0.15

Figure 7.3. _{Measured Non'-dimensional Roll Damping.Coefficients}

atFn = 0.00

Figure 7.4. _{Measured and Calculated Heave and Roll} _Motions at Fn = 0.00

Figure 7.5. A Comparison of Some Calculation Methods for Roll Motions at Fn = 0.00 and B/T = 7.5

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(23)

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(24)

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(26)

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(28)

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(29)

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(30)

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(31)

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(32)

1

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Theory

Report 815

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(33)

Appendix I. _{Summary of Experiments on Drag Forces}

Table I-i-A. _{Current Forces on Model A} _with _BIT _2.5

Run no. L (m) B Cm) T (m) $ (deg) (rn/B) X (N) Y (N) N (Nm) 154 2.250 0.750 0.300 180.0 0.150 -2.38 0.04 -0.06 155 2.250 0.750 0.300 180.0 0.237, -5.67 -0.26 -003 156 2.2500.750 0.300 180.00.358 -13.14 -0.87 0.34 :157 2.250 0.750 0.300 180.00.47O -23.67 1.18 0.09 158 2.250 0.750 0.300 180.0 0.586 -36.90 -1.62 0.31, 1592.250 0.750 0.300 180.0 070i -55.12 -1.08, 0.36 1602.250 0.750 0.300 150.0 0.155 -2.66 5.29: 1..78i 161 2.250 0.750 0.300 150.0 0.238 -6.86 11.79, 3.66i 162 2.250 0.750 0.300 150.0 0.357 -15.85 26.65 7.89 1632.250 0.750 0.300 150.0 0.470 -27.51 50.41 15.29 1642.250 0.750 0.300 150.0 0.588 -45.64 79.17 21.42 1652.250 0.750 0.300 150.0 0.705 -65.18153.99 49.27 181 2.250 0.750 0.300i 135.0 0472 -19.80 72.15 17.55 1822.250 0.750 0.300: 135.0 0.592 -30.99 115.68. 27.32 183 2.250 0.750 0.300. 135.0 0.704 -46.23 168.07, 37.73 1662250 0.750 0.30O 120.0 0.153 -1.40 8.68 1.98: 167:2.250 0.750 0.300 120.0 0.240 -3.46 24.32. 3.70 1682.250 0.750 0.300 1200 0.359 -7.52 53.49 8.45: 1692.250 0.750 0.300: 120.0 0.471 14.47 98.42. 15.63 1702.250 0750 0.300 120.0 0.588 -21.33 162J8 23.70 1712250 0.750 0.300120.0 0.702 -33.25 233.65 32.97 1782.250 0.750 0.300 105.0 0.470 -3.07 108.91 11.65 179 2.250 0.750 0.300 1050 0.586 1.26 180.94 19.97 180 2.250 0.750 0.300 105.0 0.702. _{4.12 267.46 27.79} 172 2.250 0.750 0.300 90.0 0.152 028 8.95 0.11 173 2.250 0.750 0.300 90.0 0.238 0.36 25.09 0.54 174 2.2500.750 0.300 90.00..358 . 0.33 60.51 -0.07 175 2.250 0.750 0.300 90.0 0.472 _{-0.71 117.41 -0.34} 176 2250 0.750 0.300 90.0i0.586 -2.58 183.60 -2.24 177 2.250 0.750 0;300 90.0 0.703 4.49 271.13 5.21

(34)

Table I-2.A. _{Current Forces on Model A} _with _B/T _5.0 Rm' no. L. Cm) B Cm) T Cm) (dog) V (mis) X (N) Y (N) N (Nm) 122:2.250 0.750 0.150180.0 0.151 -1.17 -0.01 -0.02 123 2.250 0.750 0.150 180.0 0.239 -2.88 -0.04 -0.05, 124 2.250 0.750 0150 180.0 0.358 -6.36 -0.11 -0.05 125 2.250! 0.750 0.150 180.0 0.473 -11.87 -0.26 -0.11 127 2.25010.750 0.150 180.0 0.589 -1925 -0.40 -0.20 128 2.2500.750 0.150 180.00.704 _-2984 -0.671 0.13 129 2.2500.750 0.150 80.0I0.,704' -29.01 -0.76 -0.30 130 2.250 0.750 0.150 150.0 O.152 -1.29 1.75 0.52 131 2.250 0.750 0.150 150.0 0.237 -3.15 4.25 1.26 132 2.250 0.750 0.150 150.0 0.358 -7.42i 9.70 280 133 2250 0.750! 0.150 150.0 0.469' -13.601 173 _4.75 134 2.250 0.7500.150 150.0 0.588 -22.30 27.44 7.36 135 2.250 0.750!0.150 15000.704 -33.37 41.97 10.29 151 2.250 0.750!0.150 135.0 0.470 -9.33t 26.70' 6.16 152 2.250 0.75010.150 135.0 0.588 _{' -153i} _44.11 _9.74 153 2.250 0.750 0.150 135.0 0.703 _-23.56 68.95 15.02 136 2.250:0.750015o 1200 0.151 -0.60! 3.40 0.70 137 2.2500.7500.150120.0 0.238 -1.55 8.06 1.65 138 2.250 0.7500.150 120.0 0.359, -3.51 20.64 2.87 139 2.250 0.75010.150 120.0 0.472' -6.27' 39.03 5.08 140 2.2500.7500.150 120.0 0.589 -9.94 63.72 9.18 :1412.250 0.7500.150 120.0 0.704 -15.09101.59 13.65 148 2.250 0.750: 0.150 105.0 0.473 -3.40! ' 43.80 5.36 149 2.2500.7500.150 105.0 0.589 -4.20 74.40! 8.44 150 2.250 0.7500.150 105.00.704 _-6.26'114.32 12.56 142 2.2500;750 0.150 90.0 0.149 0.09 2.871 0.20 143 2.250 0.750 0.150 90.0 0.238 ' 0.09! 8.10! 0.11 '144 2.250 0.750 0.150 90.0 0.358 0.07: 23.52 0.72 14512.250 0.750 0.1501 90.0 0.472 -0.13 43.59' 0.66 1:462250 0.750 _9000588 _-0.13 _75.02 _1.52 1472.250 0.750 0.150! 90.0 0.705 -0.86 116.44 0.72

(35)

Run no. L (m) B Cm) T (m) (deg) V (rn/B) X (N) Y (N) N (Nm) 523 L125; 0.375 0.075 180.0 0.167 -0.35 0.02 0.01 524 1.1250.375 0.075 180.00.25O -0.81 0.02 0.01 5251.125 0.375 0.075 l8O.O.O.333 -1.50 0.02 0.01 526 1.125 0.375 0.075 180.0 0.415 -2.38 0.04 0.02 527 1.125 0.375 0.075 180.0 0.499 -3.58 0.06 0.02 528 1.125 0.375 0.075 150.0 0.167 -0.40 0.53 0.09 529 1.125 0.375i 0.075 150.0 0.250 -0.93 1.16 0.20 530 1.125 0.375 0.075 150.0 0.334 -1.74 2.15 0.35 531 1.125 0.3750.075 150.0 0.417 -2.85 3.52 0.55 532 1.1250.3750.075 150.0 0.499 -4.25 4.26 0.76 533 1.125 0.375 0.075 120.0 0.167 -0.17 0.84 0.11 534 1.125 0.375 0.075 120.0 0.249 -0.37 1.96 0.25 535 1.125 0.375 0.075 120.0 0.332 -0.67 3.76 0.44 536 1.125 0.375 0.0751 120.0 0.415 -1.11 6.30 0.75 537 1.125 0.375 0.075 120.0 0.499 -1.69 10.00 1.10 538 1.125 0.375 0.075 90.0 0.167 0.01 0.81 0.02 539 1.125 0.375 0.075 90.0 0.249 -0.02 1.83 0.03 540 1.125 0.375 0.075 90.0 0.334 -0.02 3.72 0.08 541 1.125 0.375 0.075 90.0 0.416 -0.02 7.17 0.11 542 1.125 0.375 0075 90.0 0.499 0.06 11.15 0.12

(36)

Table 1-3-A. _{Current Forces on Model A} _with _{B/T = 7.5} Rtm no. L Cm) B Cm) 7 (m) (deg) V (rn/a) X (N) Y (N) N (Nm) 092 2.250 0.7500.100 180.0 0.149 -0.74 0.01 0.01 093 2.250 0.7500.100 180.0 0.238 -1..78 -0.03 0.00 094 2.250 0.750 0.100 180..00.356 -4.16. -0.08 -0.03 095 2.250 0.750 0.100 180.0! 0.471 -7.83 -0.06 -0.01 096 2.250 0.750 0.100 180.00588 -13.091 -0.23 -0.13 97 2.250 0.750 0.100 180.0 0.703 -20.56 -0.27 -0.14 099 0982.250 2.250 0.750 0.750 0.100 0.100! 150.0 150.0 0.149, 0.239 -0.76 -1.98 0.94, 2.37 0.24 0.65 100 2.250 0.750 0.100 150.0 0358 -4.65 5.7,7 1.53, 1012.250 0:750 0.100L 150.0 0.472 -8.74 10.41 281 1022250 0.750 0.100' 150.0 0.589 -14.31 16.80 4.33 103 2.250 0.750 0.1001 150.0 0.705 -21.87 25.52 5.91 119! 2.250: 0.750 0.100135.0 0.472 _-6.61 _16.53 _3.77 120 2.2501 0.750 0.100 135.0 0.589 -10.74 26.79 6.14 121 2.25010.750 0100 135.00.705. -16.99 42.21 9.55 104 2.250 p.750 0.100 120.0 0.1501 -0.39 1.80 0.42 105 2.250 0.750 0.100 120.00.239 -0.97 4.52 1.05 1082.250 0.750 0.100120.0 0.358 -2.31 11.52 2.01' 106 2.250 0.750 0.100 120.0 0.472, -4.02 22.30 3.26 107 2.250 0.750: 0.100 120.0 0.588 -6.87: 39.95 4.90 108 2.250 0.75010.100 120.00.703 _-9.84 _60.79 _7.77 109 2.2500.75010.100 120.0 0.703 ;iO.2O 6276 8.29 116 2.250 0.75010.100 105.0 0.472 -2.50. '25.10' 2.33 117 2.250 0.7500.100 105.00.588 -4.00 42.35 3.59 118 2.250 0.750 0.100 105.0 0.706 -5.68: 69.60 5.74. 110 2.250 0.750 0.100 90.0 0.152 0.01' 1.61 0.04 111 2.250 0.750 0.100 . 90.0 0.238 0.06; _4.99 0.17 1121 2.250 0.750 0.100' 90.0 0356 , 0.13 14.05 0.30 113' 2.250 0.750 0.100 90.0 0473 -0.20: 25.29,: 0.34 114:2.250 0.750 0.100' 90.0 0.591 0.08: 43.28'009 1'I52.25O 0.7500.1001 90.0 0.702 -0.54 69.93 0.061

(37)

TabLe 1-3-B. _{Current Forces on Model B} _with _{B/T = 7.5} Run no. L Cm) B Cm) T Cm) fi (deg) (rn/a) X (N) Y (N) N (Nth) 503 1.125 0.375 0.050 180.0 0.165 -0.21 0.01 -001 504 1.125 0.375 0.050 180.0 0.250 -0.50 0.00 -0.01 505 1.125 0.375 0.050 180.0 0.335 -0.97 -0.01 0.00 501 1.125 0.375 0.050 180.0 0.416 -1.56 -0.01 0.01 502 1.125 0.375 0.050 180.0 0.500 _-2.46 _{-0.02 -0.01} 506 1.125 0.375 0.050 150.0 0.166 H -0.28 0.25 0.04 507 1.125 0.375: 0.050 150:.0 0.250 -O.63 0.62 0.10 521 1.125 0.3750.05Ô 150.0 0.250 H_-0.58 _0.66 ₀₁₁ 508 1.125 0.375:0.050 150.0 0.333 -1.22 L16 0.19 522 1.125 0.375: 0.050 150.0 0.333 -1.07 1.20, 0.20 509 1.125 0.375 0.050 150.0 0.415 -2.00 1.91 0.31 Sb 1.125 0.375: 0.050 150.0 0.500 -3.05 2.96 0.45 511 1.125 0.375 0.050 120.0 0.167 -0.11 0.50 0.07 512 1.125 0.375 0.050 120.0 0.249 -0.25 1.16 0.16 513 1.125 0.375 0.050 120.0 0.333 -0.48: 2.24 0.31 514 1.125 0.375 0.050 120.00.416 0.79 3.74, 0.49 515i1.125 0.375 0.050 120.0 0.500 -1.21 5.97 0.75 516 1.125 b.375 0.050 90.0 0.167 0.01 0.48 0.01. 5171.125 0.375 0.050: 90.0 0.250 0.05 1.16 0.01 518 1.125 0.3750.050i 90O 0.334 0.06 2.37 0.03 519 1.125 0.3750.050 90.0 0.416 0.08 3.96 0.05 520 1.125 0.375 0.050 90.0 0.500 0.13 6.89 0.11

(38)

Table 1-4-A. _{Current Forces on Model A} _with _{B/T - 1O.00} Rim1 no. L Cm) B Cm) T Cm) $ (deg) V (mis) X (N) Y (N) N (Nm) 061 2250 0.750 0.075 180.0 0.151 -0.56 0.00 -0.01 0622.250 0.750 0.075 180.0 0.238 -1.34 -0.03 -0.02 0632.250 0.750 0.075 1800 0.358 -3.18 -0.07 -0.03 064 2.250 0.750 0.075 180.0 0.472' -6.17 -0.09 -0.04 0652.250 0.750 0.075 180.0 O.5gl-lO.82 -0.13: 0.00 066,2.250 0.750 0.075 180.0 0.7031 -16.36 -018 0.05 0672.250 0.750 0.075 150.0 _{°'50H -0.54} 0.65 0.18 0682.250 0.750 0.075150.0 -1.42 1.62 -0.48 069 2.250 0.750 0.075 150.0 0.3591 -3.40 3.83 1.09 0702.250 0.750 0.075 150.0 0.472 -6.29 7.00 1.98 0712.250 0.750 0.075150.00.58811-jO.31 11.43 3.09 072 2.250 0.750 0.0751 150.0 0.704' -16.49 18.01 4.18 091 2.250 0.750 0.075 150.0 0.705'-16.59 17.97 4.28 0882.250 0.7500.075 135.0 0.471, -5.15 11.49 2.74 0892.250 0.750 0.075 135.0 0.589' -8.47 18.84 4.45 090 2.250 0.750 0.075 135.0 0.705' -12.84 30.72 681 0732.250 0.750. 0.075 120.0 0.151 -0.30 1.31 0.36 074 2.2500.7500.075 120.0 0.237 -0.74 3.20 0.78 075 2.250 0.750 0.075 120.0 0.356 -1.68 7.99 1.46 076 2250 0.750' 0.075 120.0 0.471 -3.02 15.19 2.69 077 078 2.250 2.250 0.7500.075 0.750 0.075 120.0 120.0 0.588 0.703 -5.181 -7.93 27.38, 45.82 4.10 5.75 085 2.250 0.7501 O075 105.0 0.473 -1.52: 17.97' 1.64 086 2.250 0750 0.075 105.0 0.590 -2.83. 31.89 280 087 2.250 0750 0.0751 105.0 0.704 ' -4.30 51.82 423l 079f 2.250 0.750 0.075 90.0 0.151' 0.02 1.30 O.13 080 2.250 0.7500.075 90.0 0.238 -004 3.95 0.01 081 2.2501 0.750 0.075 90.0 0.358 , -0.13 10.31 -0.04 082 22500750,0.o75 90.0 0.471 -0.24 18.64 -0.14 083 2.2501 0.750 0.075 90.0 0.588 0.11 34.13 0.30 084 2.250 0.750 0.075 90.01 0.703 -0.26 55.33 -0.24

(39)

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(42)

Table

11-2-A-Appendix II. _{Summary of Experiments in Regular Head Waves}

Motions in Simple Regular Head Waves

of Mode]. A with B/T = 5.00

Note: In these tables some values _{are marked with *,}

This means that this partic:uiar measurement failed.

:: L B 7

"

A ci-1L i

LJ

a Za -s:--- ezc 1a

Cm) Cm) Cm) _(deg)'(mfs), _C-) _C-) _(1/s) _Cm) _(-) _(deg) _(-) _(deg) _(-) _(deg)

(N) (-) 416 2.250 0.750 0.150 180.0 0.000 1.000 1.0001 5.240 0023 0.100 0 0.274 -111 0.89 0.69 378 2.250 0.750 0.150 180.0 0.000 1.170 0.926 4.856 0'.'020 0.222 * _0.534 * 0.53 0.55 379 2.250 0.750 0.150 180.0 0.000 1.330 0,866 4.540 0.017 0.337 -7 '0.562 -106 0.23 0.32 383 2.250 0.750, 0.150 180.0 0.000 1.500 0.816: 4.268 0.01:9 0.405 -8 :0.831 _-97 _0.10 _0.12 408 .250. 0.7501 0.150 180.0 0.000 2.000 0.707: 3.700 0.011 0.733 -11 1.036 -97 -0.01 0'00 387 2.250 0.750 0.150 180.0 0.000, 2.000 _{0.707 3.700 0016' 0.688} _-5 _i.000: _-98 * * 412 2.2500.75010.150 180.0 0.000 2.000. 0.707 3.700 0.0221 0.733 -10 .01.979' 95 0.02 0.02 395 2.250 0.750' 0.150 180.0 0.000 2.500 0.632 3.307 0.016 0.804 -3 1.150 -97 0.01 0.02 396 2.250 0.750 0.150 180.0 0.000: 3.000 0.577 3.038 0.012 1.042 -8 ' 1.446j -99' 0.06 0.18 403. 2'250 0.750 0.150 180.0' 0.000 3.500: 0.535: 2.796 0.018: _0'921 _-5 _1.335' _{100, H0.10} ₀₁₃ 404 2.250 0.750, 0.1501 180.0 0.000 4.000 0.500 2.620 0.0181 0.8861 -3 1.400' -991 0.04 0.05 417 225O 0.750 0.150' 180.0 0.235 1;000 1:000 5.900 0.023: 0.0701 -16 0.181 -1481 2.63' 2.07 3752.250 0.750 0.150 180.0 0.235 1.170 0.926 5.449 0.015 0.292 -33' 0.734 -132. 2.53 4.36 380 2'.2500.75a1 0.150 180.0 0;236 1.330 0.866 5.043 0.021' 0.327 ' -281 ₀₈₉₃ _-113 _2.13 _2.01 384 2.2501O.75OO.15O 1800 0.236 :1.500 0.816 4.707 0.019 0.527 '25 0.887 -118 1.36 1.61 409 2.250 0.750 0.150 '180.0 0.234 2.O00 0.707 '4.043 0.011 0.709 12 1.068 -100 0.24 0.81 389 2.2501 0.750 0.150 180.0 0.235 2.000 0.707 4.043 0.017 0.697 -8 1.061 -101 0.53 0.80 413 2.25010.7500.150 180.0 0.236:2.000, 0.707 4.028 0.022'. 0.736 -8'' 0909 -97 0.96 0.81 394 2.250(0.750 0.150 180.0 0.237 2.500 _{0.632 3.594 0.017} _0.848 _-13 ' 1.146 -106 0.35 0.53 397 402 2.250" 2.2501 0.750 0.750 0.150 0.150, 180.0. 180.0: 0.236 0.236' 30O0' 3.500' 0.577 3.244. 0.535 2.995 0.018 0.018 0.876 0.931 -7 -6. , 1.222 1.312 -99 -99' 0.32 0.40 0.41 0.53 405 2.250 0.750 0.150' 1800 0.236, 4.000 _{0.500 2.802 0.017 1:0.91.8} _-10' ' 1.365 -101 0.29 0.39 418 2.250 0750 0.150 180.0'0:.:469'1.000, 1.000 6.545 0.020 0.092 -75 ' 0.112 -172 4.47 4.80' 376 2.250 0.750 0.150 180.01 0.471 1.1701 0.926 6.007' 0.018 _0.217 _-46 ' ' 0.429 -178 5.85 7.53: 381: 2.250 0.750 0.150 180.01 0.4711 1.330' 0.866 5.5361_{0.O1T 0.4351} _-62, _0.760 . -127 4.90 6.92' 3852.250 0.750. 0.150 180.0' 0.472 1.5001 0.8161 5.197 0'.021 0.5071 -54: ' :0.942 'i50 4.74 4.27 410 2 250 0 750 0 isol180 0 0 47012 0001 0 707' 4 3791 0 011 _{0 794} _-27 I 1 168 -114 1 04 3 71 39022500750015018000 472,2 000 0 707'4375O 016 0785 -27 1150 -115 149: 229 41422500 7500 150 18000470i2000 0707'4366'0022 0814 -27 1131 -116 094 0791 393 2.250 0.750 0.150 180;0' 0.471 2.5001 0.6321 3.843 0.'018 0832 -8 1.087 -991 149 1.80 398 401 2.250 2.250 0.750 0.750' 0.150 0.150 180.0 180.0 0.470' 0.470 3.000' 3.500 0.5771 3.468, 0'.'535 3.181 0,017' : 0'017' 0.920 0.994 -13 -9 ' 1.315 1416 :-98 -100' 1.19' 0.45 1.61, 0.61 4062250075010150180004714000 0500129780017' 0965 -11

11.47-103048

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(43)

Table 11-2-A-b. _{Motions in Simple Regular Head Waves} of Model A with B/T = 5.0,0 L B T I V A 1L

::

(m) Cm) Cm) (deg) (mis) _(-)

[-j

C-) e (1/s) a (m) C-) (deg) _(-) 6ç (deg) C-) (deg) AR, (N) (-) 419 2.2500.750 0.150 180.0 0.704 1.000 1.000 7.181 0.019 0.000 0048 * * *' 377 2.250!0.75OO.150 180.0 0.701 1.170 0.926 6.531 0.017 0.135 * _0.269 * _0.62 _0.87' 382 2.2500.750 0.150 180.0 0.705 1.330 0.866 6.018 0.018 0383 -74 0.574 -156 4.31 5.43 386 2.2500.750 0.150 180.0 0.704 1.500 _{0.8165.5850.0180.413} _-61 _0.846 _{-168 435} _2.00! 411 2.25010.750 0.150 180.0 0.705 2.000 0.707 4.699 0;010 0.874 -26 1.347 -117 0.37 1.421 391 2.250! 0.750 0.150 180.0 0.705 2.000 0.707 4.707 0.015 0.857 -25 1.315 -117 0.79 1.361 415 2.25010.750 0.150 180.00.703 2.000 0.707 4.826 0.022 0.810 -24 1.302 -118 2.00 1.75 392 2250 0.750 0.150. 1800 0.705 2.5001 . 0.632 4.115 0.016 I 0.950 21 1.318 -104 1.30 2.07 399 2.250 0.750 0.150 180.0 0.708, 3.000 0.577 3.711 0.013 1.472 0 .980 -85 1.42 3.71 400 2.250 0.750 0.150 180.0! 0.706' 3'.5001 _{0.535 3.391r 0021 0.778} ₁₅ _1.853 ₁₀₃ _0.44 _0.40 405 2.250 0.750 0.150 180.0 0.703! 4.000 _{0.500: 3153j 0017} _1.000 _-16 _1.544 _-100 _0.27 _0.38,

(44)

Table 11-2-B. _{Motions in Simple Regular Head Waves} of Model B with BIT = 5.00

L B T V

A L

a 5zç

1RL

P82B2'

(m) Cm) (m) (deg) (mis) (-) (-) (lIe') (m)

', (-) (deg) C-) (deg) C-) (deg) (N) (-)

597 1.125 0.375 0.075180.0 0.000 1.000 _{1.000 7.392 O.012 0179} _* O.173 -114 0.11 0.58; 593 1.125 0.375 0.075 180.0 0.000 1.500 0.816 6.036 0.010 0.378 0 b.545 -93' 0.03 0.26' 589 1.1250.375 0.075 180.0,0.000 2.000 _{0.707 5.232 0.011 '0.702,} -13 0.877 -96 0.01 008 601 1.1250.375 0.075.18Ooo.:oOo 2.500 0.632 4.668 0.010 0.808: 0 0.969 -89 -0.01' -o.o8 605 1 125 0 375 0 075 180 0 0 000 3 000 0 577 4 292 0 010 0 939 -11 1 137 -108 -0 04 -0 31 609 1.12510.375 0.075 180.0 0.000 3.500 0.535 3.952 0.011 0.868 _-7 _0.991 _{-98 -0.01} _-0.04 613 1.125!0.375 0.075 180.00.000 4.000 .0.500 3.703 0.011 0.907, .0 0.993 -98 0.02 0.13: 598 1.125! 0.375 0.075 180.0 0.167' 1.000 _{1.000 8333 0.012 :0.164'} _-6 . 0.307' -112 0.37 2.03' 594 1.125! 0.375 0.075' 180.0! 0.166' 1.500 0.816 6.642 0.013 0.413 -10 . 0.744 -108 '0.18 0.91 590' 1.125 0.375 0.075 180.0; 0..166 2.000' 0..7Ô7 5.707' 0.011 0.762 -11 0.952 . -99 0.05 0.33, 602 1.125 0.375 0.075 180.01 0.166! 2.500' 0.632 5.047' 0.009 0.914 -10, . 1:050 '-95 -0.04 -0.42' 606 1.125! 0.375 0.075 180.0! 0.167 3.000! 0.577' :4.580 0.011 0.805 . -7, " _{:0.905-102 '0.03} _0.16 610 1.1250375 0.075 180.Oi0.167'3.500 _{0.535;4228;Q.O1OO.874'} ₀ _0:956'' 98 0.06 0.44 614, 1.125 0.375 0.075 180.0 0.165! 4.000! 0.500 3937_{0.011, 'p.924} -'10 ' 1.048 102 0.01: 0.07 599 1.125 0.375 0.075 180.0' 0332' 1.000' 1'.00Oi 9.281 0.'Ol"l, 0.076 *' 0.149 -125 0.53 3.92 618112503750075180003311500 081672640006' 0455 -41 0750 -133 003 068 59511 1250 37510 075180003341500 _{0816729810011 0564} _-33 ₀₈₇₄ _-130 ₀₆₇ 455 617 1.125 0.375: 0.075 180.0 0.332 1.500 '0.816' 7.264 O.01'7: 0.532 -31 0.854 -130 1.25 3.42' '591 1.125 0.37,5! 0.075 180.0 0.333. 2.000 0.707 6.154 0.011 0.857 -23 1.018; -97 0.27 2.01 03 1.125. 0.375! 0.075 180.0 0.332 2.500. 0.632 5.4121 0.009 0.989 0 1.092! -87 0.04 0.33 607 1.125, 0.375' 0.075180.0 0.332 3.000 0.577 4.878 0.011 01.898 10 0.981. -95 0.00 '0.00 611. 1.125 0.375 0.075 180.0,0.3333.500 _{0.535 4.494 0.011} _0.925' -9 0.971 -105' 0.09 0.61 615! 1.125 0.375 0.075 180.0 0.331' 4.000 _{0500 4.172 0.010} _0.980: ₀ 0.925 : -0.05 600 1.125' 0.375 0.075! 180.0 0.499. 1.000 _{1.000 10.20 0.011 '0.038!,} _*: 0.113 -17& 0.31' 2.32 596 1.125' 0.375 0'.075 180.0' 0.500 1.500' : 0.816 '7.893' 0012 0.522 -43! _0.897 _-117 _1.08 _' _6.67 592 1.125:0.3750.075 180.0 0.500 2.000 _{0.707 6.621 0.011} _0.815 '21, ... 1.099 -106 0.50 ' 3.48:' 604'1.125!0.375' 0;075.180.010..500:500,O 632 5.786o.'olo.::o.893 _-12 ' .1.138 98; 0'28 2.13! 608 1.125 0.375 0.075 180.0 0.499! 3..000 0.577 5.206, 0011 0.'972 -11 . 1.025 -100' '0.19 1.30! 612 1.125 0.375 0.075 180.01 0..500j 3.500! 0535! 4J601o.,oio::0.!951 -11 1 , 1.019 -93 _'0.24 _1.88 616 1.125, 0.375'. 0.075, 180.01 0.5001 4000 ' 0.500! 4:397! 0!010: 1I.'051' ..4' ' ' .. . 1122 ' 95 '0.06 0.51

(45)

Table 11-3-A. _{Motions in Simple Regular Head Waves} of Model A with BIT 7.50

Run no. L B T P V

-L

rLi

L-i

A We

---

_a ER.L kc PSca B2 2

Cm) Cm) Cm) (deg) (rn/a) _C-) (-) _(1/B)! _(rn) _C-) _(deg) _C-) _(deg) _(-) _(deg);

(N) _(-) 3252.2500.750 0.075 180.00.000 L000! 1.000 5.2230.021 0.117 -288 0.260 -70' 0.59 0.57 349 2.250 0.750 0.075 180.03 0000! 1.5001 0.816 4.2803 0.013 0.385 0 0.672 -941_-0.06 _-0.15. 324 2.250 0.750 0.075 180.0' 0.000 1.500' 0.816 4.277 0.018 0.406 9 0.720 -87 0.03 0.04 353 2.250 0.750 0075 180.0! 0.000' 1.500 _{0.816, 4.2801 0025 0.407} ₉ _0.706 _-86 _0.23 _0.53 3262.250 0.750 0.075180.030.00032.000, 0.701 3.71130.019 0.616 0 0.890 -95 0.07 0.08 330.: 2.250 0.750 0.075 180.0 0.0001 2500) 0.632' 3.298 0.018 0.743 -2 1.055 -97 -0.08 -0.11 334 2.250 0.750 0.075 180.0 0.000) 3.000' 0.577 3.031 0.018 0.780 -4 1.114 -94 -0.03 -0.09 338 2.250, 0.750 0.015 180.0! 0.000! 3.500) .0.'535 2.808 0.018. 0855 9 1.187 -99 -0.03' -0.04 34212.250 0.750 0.075 180.0'0.00034.00O _{0.500'2.63030.0j8} 0.914 -5 ' 1.216 '-97 -0.04 -0.05 317 2250 O:.750 0.075 180.01 0.2371 1.000! 1.000; 5.916! 0.029. 0.084 42 0.056-105 2.28 _1.15 350 2.250, 0.750 0.075 180.0 0.2363 1.500' 0.816 4.7073 0.015 0373 _-14 _{0:595 '-110} ₀₆₀ _1.09 321' 354 2.250 2.250 0750 0.750 0.075 0.075 18003 180.0 0.2353 0.237' 1.5001 1.3003 0.816, 0.8161 4.696 4.699 0'.:022. O.029 0.382 0388 0 -18 . ' 0'627 0.607 -110 -1021.18 [.73 1.02 1.17 327 2.250 0.7,50 0.075 180.0 0.2383 2.000' 0.707 4.035 0.021 _{. 0.610} ₀ _' _0.886 _-87 _0:54 _0.53 331 2.250 0.750 0.075 180.0.0.23632.5oo,o63233.5663o':,o1g; _0.728 _-5 _. ' '1.005 '-95 0.18 0.18 '3352250075000751600 023633 000 0 577'32491 0183 0769 -3 1053 -96 007 009 339 2.250 0.7500.075 180.0 0.235:3.500 _{0.5352.9950.0181 0.852} _-8 _1.144 _-98 _0.15 _0.19 343 2.250 0.750 0.075 180.0 b.2364.000 _{0.500,2.808.0.018' 0.867} _-10 _1.176 _-103 _0.09 _0.11 318 2.250 0.750 0.075 180.0 0.471 1.000 i.000; 6.531. 0.020' 0.160 -8 0.250 -114 4.58 4.68' 351 2.250 0.75010.075 180.0, 0.470 1.500 0.816 5.171,0.018 0.389 '0 0.595 128 1.74 2.19' 322 2.250, 0.750, 0.075 180.0. 0.472 1.500 _{'0.816 5.184. 0.026: 0.365} ₀ _{'1.123, -126} _3.11 _1.88 354.2.250075010075 180.0 0.469:1.500 '0.816;5.180 0.02930.448 0 0.729 -123' 4.36' 2'12 328 2.250 0.7500.075 '180.0 0.472 2.000 0.7074.366 0.024i0.570, -16 0.7863 -111. 1.52 1.11 3322.250 0.750 0.075 180.0 0.469 2.500 .0.6323.8410.020 'O750i _0', _{1.017 '} _-90i _0.72' _0.74 33632.250 0.750 0.075 180.0 0.471:3.000 _{0.5773.462 001Q} _0.7813 _-8 _1.055 -961 0.61, 0.71 34012.250 9750 0.0753 180.0 0.4703.500 0.5353198 0.018 b,.as23 :-1O . ' 1.144 -99' 0.763 0.94 349 2.250 0.750 0.0753 180.0 0.470 4.000 0.500 2.965 0.017 0.884 -63 ' ' 1.230 -102 ' 0:28) 0.38 3192250)0 7500075180007051000 _{100072140021,0073} _0, L 0095 -132 132 1283 352 2.250, 0.750 0.075. 180.0) 0.,706' 1.5003 _{' 0.816 5.590 0.013'} _0.466 _{, -29} , . 0.791 -138: 1.29 _1.633 323,2.2500.750 0075 180.03 0.:706' 1.5003 0.816 5:5950.019, 0.430' -241 _0:803 _{'-.1293 246} _2.70 355 2.250 0.750 0.075 180.0' 0.7063 1.5003 0816 5.5753_{0.025 " 0.448} _-24'

_{..'. 0:783 132 '616}

_3.96 329 2.250 0.750. 0.075 180.0 0.1051 2.000 0.707! 4.6993 0.018! 0.867 0 1.231 -111 0.85 1.17 333 2.250 0L7501 0.075 180.0 0.704 2.500 _{0.632' f..104 0.019;, 0.795} _-13 _1.054 _-98 1.11 1.32 356 2.250 0.750'O.075 180.0 0.7063.000 0.577 3.698:0.018 1.097' -8 1.308' -102 116 1.97 337 2.250 0.750 0.075 180.0 0.705 3.000 0.57.7 3.698 0.018 1.061

7

' 1.1933 -103 1.26 1.72 341, 2.250' 0.750 0.075 180.0 0.705 3.5003 0.535. 3.369. 0.021, 0.714' _-25 _1.116 _-115 _0.34 0.32 345! 2.250 0.750 0075' 180.0 0.704 4.000 0.500 3.18130.019 0.840' -15 1.085, -99 0.96 1.12

(46)

Table 11-3-B. _{Motions in Simple Regular Head Waves} of Model B with B/T = 7.50 L Cm) B Cm) T (rn) (dog) V (rn/s) ) C-) L [;:-] C-) We (1/s) a Cm) (-) e (dog) e (deg) (dog) (N) (-) C-') pg2B2 C-) 554 1.125 0.375 0.050 180.0 _0.000:_1.000 _{1.000. 7418! 0.009: 0.148} 35 O.337 -114 0.10 1.10 5501 12503750050180000001500 081660590009 0468 0 0719 -97 003 031 546 1125 0.375 0.050 180.0 0.000 2.000 _{0.707 5.236' 0.010' 0.657} ₀ 0.797 91 0.01 0.07 558112503750050180000002500 063246890010 0789 -7' 0987 -94 002 015 562 1.125 0.375 0.050 180.0 0.000 3000 0.577 4.27.1 0.0101 0.898 0 1.052 -93 o.oi 0.11: 566 1.125 0.375 0.050 180.0 0.000 3.500 0.535: 3.957 0.010. 0.908 -3 1.094 -98 0.00 0.00 570 1.125 0.3750.050 _{180.0 0.000 4.000 0.5003.70010.010i 0.908} ₀ _1.059 -95 0.01 0.09 555 1.125 0.37510.050 1:80.0 0.166 1.000: 1.000: 8.322 0.009; 0.380 32 0.380 -133 0.29 2.84 551 1.125 0.3751 0.050 180.0 0.168 i.500; 0.816 8.468. 0.010: 0.490 0 0:.7421 -104 0.18 1.49 547 1.125 0.375 0.050 1800 0.187 2.000 0.707' 5.707 0.011 0.667 -3 0.868 -100 :0.09 0.63 559 1.125 0.375 0050 180.0' 0.165 2.500 0.632 5.047 0.010 0.777 0 . ' 0.9481 '-92' 0:05 0.37 563 1 125' 0 3751 0 050 180 0 0 165 3 000 0 577 4 580 0 010 0 847 -3 1 0331 -96 0 04 0 32 567 1.125:0.3751 0.050 180.0 0.165 3.500 '0.535 4.2231 0010 _{: 0899} ₀ .. 1.050 90 0.02 '0.16 571 1.12510.37510.050 180.0 0.1654000 0.500 _{3.932 0.009} _0.915 ₀ 1.104 -91 0203 030 556 1.125J 0.375 1.12510.375, 0,'050 180.0 0.333 1.000 1.000: 9.281 0.010 0.154 14 0.189; -158 0.72 5.44 575 _{0.050 180.0 0.334 1.500} 0.816 7.281 0.005 0.612 -7 0.7181 -125 0.20 6.87: 552; 1.125' 0.375 0.050 180.0 0.334 1.500 _{0.816 7.281 0.010} 10.650 4 0.731 -117 064 522 574 548' 560 564 1 125,0 1.125 1425 1.125 375:0 0375 0.375 0.375: 050 0.050, 0.050. 0.050 180 0 180.0 180.0, 180.0 0 334 0.334 0.334 0.333' 1 500 2.000 2.500 3O00 0 816 0.707 0.632 .0.577 7 281 6.166 5.435 4.893: 0 014 0.0101 0.012 0.010 0 559 ; 0.680 :0.802 0.875' 9 -10 0 .0 0 761, 1.0631 0.9431 1.055: -125 -98 -96 -88 1 02 0.24 0.17 0.32 4 08 2.10 1.03' 2.44 568 5721 1.125 1.125 0.375, 0.375 0.050 0.050 180.0 180.01 0.333 0.333 3.500 4.000 0.535 0.500 4.485 4.167. o.oio: 0.010 0949 0.909 . -5 ' 0 , 1.094' 1.180: -99 -90 0.04 0.27 0.31 2.26 557' 553 1.125 1.125' 0.375' 0.375 0.050 0.050 180.0 180.0 0.498 0.500: 1.000 1.500 1.000 0;816 10.18 7.884 0.010; 0.011. 0.0961 0.593: 18 -21 ' 0.165 0:809 -161. -131: 0.52, 0.97' 391 '6.17 549,1.125' 0.375 0.050' 180.0 Ô.499 2.000 _{'0.707 6.628 0.011} _0.790 _-14 . . "' 1.042 -114 04i 3.02 561 1.125;à.375 0.050' 180.0 b..499 2.500 0.632 5.796 0.010 0.847. '-4' _{''1236' -107} _0.33: _2.79 565, 1.1251 0.375 0050 180.0 0.499 3.000 .0.577 5201 0.010 10.942. 01 _1:028 . -95: 01251 1.94 5691125103750050180004gg3500 053547460011 0843 -8: ₁₀₁₃ -95 017 117 573 1.125, 0:375 0.050. 180.01 0.498 4.000 _{.0.500 4.397 01011} O.84l, _0: .' '" ₀₁₉₅₇ _'-91''₀₁₁₂ _0.82: