Some notes on the shipping of water on a model of a cargo ship in irregular waves

ARCH1EF

SOME NOTES ON THE SHIPPING OP WATER

ON A MODEL

OP A O.AIiGO SHIP IN IRREGULAR WAVES

BY

V.

PERDINANDE

Laboratory of Naval Architecture

University of Ghent, Belgium

- 1 9 6

8

-CEBERENA,

21, rue des Drapiers - Bruxefles

5

Lab.

_{v Scheepsbouwkijncje}

Technische Hogeschool

Delfi

Ref.: S III / 32

OF A CA}IGO SHIP IN IILILEGiJLAI1 WAVES

by

V. FERI)INANDE

Laboratory of Naval, Architecture

University of (ihent, lielgiuni

-SOME NOTES ON THE SHIPPING OF WATER ON A MODEL OF A

CARGO SH1P IN IItREGULALt WAVES

by _V. Ferdinanda

Summary

odel teats in irregular head waves were analyzed with poCial emphasis on the ehippin of water by a cargo ship.in the fullload condition.'lIistogrnms of mOaSured "double, ampli-tudes" of relative bow motion and of meaaured "ampliampli-tudes" of

relative bow emergence and relative bow imAuereion are compared

with the Rayleigh density function, and the validity of the distribution hypothesis isteated. The frequency of Occurrence of.observed.bowaubmergence is compared with the results of

the theOretiCal prediction, for which the bow freeboard iscOr-rected for the static swellup of the water surface, in

accor-dance with.TASAKI. The frequency of occurrence ofobservéd green water impactS is compared with the results of the theo-retical prediction, for which the actual bow freeboard is taken

into account. The OCcurrenCe of impact. by green water is found

tObe stE'onglyrelated to the time rate of bOw suWmergence. A criterion for allowable wetness severity is suggested.

Introduction

The shipping of water depends primarily On the relative bow motjon,

i.e., the motion of the bow

_with

respect to the Wave surface, and on the freeboard at the bow.

LSlative bow motions in regular and in irregular. waves can be

measu-reu on oodela1 and can be calculated theoretically. _{several authors} had to conclude that the measured values of relative bOw motion were j

excess of the calculated values. _{A plausible explanation car' be based}

on the existence of a swellup of water at the. bow, fIii

8e1lup is

due to the bow wave (including sinkage), the height of _{which is dependent}

on ship speed,, and to the vertical motion of the forebody with respect to the water surface.

Shipping of water at the bow can occur if the relative bow motion

exceeds the local freeboard. The frequency of occurrence can be calcu-lated by means of statistical methods, but the result will depend on the

introduction, or on the ignoration of the swell-up of water in the cal-culations. For instance, Ii. K. Ochi (ref. 1) considers the relative

bow motion merely with respect to the undisturbed'wave surface, while

'[asaki (ref. 2) preconize the introduction of the concept "effective

freeboard", i.e., the actual freeboard at the bow reduced by the

resul-tilnt height from "static swell-up" (bow wave + sinkage) and "dynamic swell-up". The probabilities of relative bow motions exceeding the

actual and "effective" bow freeboard can differ considerably, especially

at higher ship spee4. ,

It may be useful to exäine the practical importince Of paying atten-tion to, or neglecting the swell-up of water at the bow. In fact, rising

of the piled-up water surface. above the level of the forecastle deck (or the bulwark) is pot necessarily followed by a hnrmful' shipment of "green" water, At sea, some overcoming water may 'be transformed by the wind into

a spray, which can he spectacular, but not dangerous.

In order to gather some information, which might be helpful' to

throw more light on this problem, test results on .a model of a cargo ship in the full-load condition were examined. _{These tests were carried out}

some years ago at the Davidson Laboratory (Stevens Institute of

Techno-logy, UA) (ref. 3 and 4), but. they are. discussed here with _{a special}

emphasis on the shipping of wtOr.

odel tests in irregular waves

3

NLU_.hipw (of the "Compagnie MarItime Beige') in irregular head wavel. Fullscal, trials on this ship were made too and are described in ref. 5. Similar tests on this modelin the ballast cOndition., with apecial empha-sis on slamming, are described in ref. 6. The irrOu1ar wave pattern, simulating a sea state B 7-8 (according to the PiersonMoekowitz curve), ii substantially the same as the wave pattern, the energy spectrum of which I. given in ref. 6.

Some for this 8tudy important main.characteristics of the ship are

The teat conditions (fullscale dimensions) were

Draft (fore and alt),. metrea _9.00

Ulock coefficient _0.71

Longitudinal radiu. of gyration, metres 32.40

Still water natural pitching period, sac 6.94. Still water natural heaving period, sec 7.51

Freeboard at stem, metres _10.00

Lenght between perpendi.culars,L, metres 136.00

lireadth, metres' _18.70

Depth. to atrength. deck, metres 12.00

E - twice the variance of the wave record, m .7. 1

The model was run at different aped., corresponding to _{ship speeds}

of 0.21, .5J, 10.82 and 13.10 knots.

The recording of the relative bow motion was done by means of a

resietance wire gauge, fixed 1/2. .in.(1.L mful1scae) forward _{of the stem,}

Analysis of the model. teats

a) L)eck wetness

The "double amplitudes" (peak-to-trough values) on the records of relative bow motion were read off and their di8tribution was compared with the theoretical Rayleigh distribution

a

Esr

)

where sr ia the value of peak (trough) "amplitude" and Ear is twice the variance of the record. The value E was derived from the average of

- v sr

the "double amplitudes" by means of the Longuet-kliggins formula

Avg

(2 sr) "I'77V' (2)

The in this way derived value is merely an estimate of the actual E,

but previous exp,eriencà showed that generally there is a good"agreernent with the value as derived .froi the area under the spectrum curve. The

val'uea of' E, corresponding to thi' different èhip speeds, are given

in Table I. The fact of finding a lower value of

'

at the highest ship speed ii rather surprising.' '-rhe speed of ia.io knots"is'obviously

not super-critical in the considered 8ea state. Moreover,' t was seen that the pitch motions, which wire recorde4' a.imultaneously, followed a similar trend with speed, (ref. 4). There is little chance that the

cause is some defectiveness 'of thi apparatus. - Full bow' immersion,

fol-lowed by shipping of water, might he a factor, which causes an

additio-nal "damping" of the ship notiofla.' If thi8 would be" the case, 'one' might presume that the ship motions do not' follow the RaylOigh dis'tributiàfl law, though the wave heights have such' di8tribution. Therefore, 'the

dis-tribution'. of the' Wave he'ighti, .pi'tch angle. and 'relntive motions' at 'the bow, as r.corded, were represented in the form'

of

histàgráa'an 'àompa-' red with the theoretical Rayleigh diStribution curve at a corresponding

5

scale of density. The values of _E for the wave heights1 and B9 for

the pitch aulea are given in Table 1. rrhe goodness of fit of the actual

data to the theoretical Rayleigh distribution for the value of B as

given in Table I, Was determined by means of the -chl-s4uare teat. The

values of xt with the numbers of "degrees of freedom", are given in

Table 11. The wave heights paas- the test at a 8ignificance level.

0.100 for V =

8.53

knots and at o( 0.250 for the other speeds.

The pitch angles are failing at a significance level o( - 0.05 for the

ship speed 6.21 knots, but for V 8.53 knots they pass- the test at o(--= 0.10 and even at 0.260 for V 10.82 and 13.10 knot8. The relative bow motions: pass the test for the: ship speedR

62l

and 13.10

knote at a signifiCance level of 0.250, but they are failing for the two other ship speeds for low significance level8 0.050 and 0.010

respec-t.:iyely.

This may suggest the following -judgment. The-wavi height may be re-garded a following, a Rayleigh distribution, and, though the amplitudes

seems to be influenced by another external factOr (probably the shipping

of water), -the pitch angles as -well. Liowaver, the relative bow notions may be suspected of -being not generally ila1eigh distributed. _{In order}

to illustrate the observed deviation from the theoretical Rayleigh distri-

-butiona, h8tograms are given in Fig. 1 and 2 for _{wave, heights and}

rela-tive bow notions respecrela-tively. _{'One can notice -a lack of lowest and}

highest "double amplitudes" on the histograms of relative bow motions,

(Fig. 2) '

-Apparent disagreement of the relative bow iotions with the

theore-tical Itayleigh distribution is possibly due to the existence Of the hydro-d-ynamic swell-up phenomena at the bow., _{As the resistance Wire gauge was}

fixed 1/2 iu. forward of the stem, it,can be aesumed that _{only a small} part of dynamic sWell-up has been recorded, beóause the height of

piling-up of the water surface around a surface-piercing body is only important

and increasing fast near. the -boundary. On the contrary, the bow wve iá

supposed to be entirely rec9rded. .. . "'

The zero-line of the record8 was seen to be.- unvarying. lience, the

"lImplitudeH" of relative bow immer8ons and eergence8 could be read off.

tine may expect to notice the influence of the bow wave on the distribution

of

these "amplitudes" of relative bow immersiona and bow emergencea

res-pectively. The. histograms are given in Fig.- 3 and 4.- The Rayleigh dis-tributions, for E . . and .E , i.e., twice the vitriance of- the doubled

ar,a

-amplitudes..of relative bow immeraions and relative bow emergence9 respec-tively, are shown too.- The values of E -

- and E.

are given in

- sr,i sr,e

Table I. The histograms of relative bow..imrnereions (Pig. 3) generally. show large deviations' from the curve of the- Rayleigh. distribution, ,ea-pecially at the high values. The, agreement with Rayleigh's distribution

law seema to be better for the histograms of relative bow emergence

(hg. 4), eapeciatlly for the values- higher than 10 m ,ampl:i.tud'e '.. (the bow

freeboard.). - ' ,, -

-The values of E are considerably larger than those of E

- sr,e

't any ship speed. This inuicatea an actual influence of the bow wave

and sinkage. , . .'

The "static swell-up", Ii hi where h0 and

hT is -the' bow

wave and the siiikage of .the bow- reapec,.tively, is given' by TAAKl _{' (ref..}

)

-where F is the Froude number, and kj is a constant, dependent on the entrance angle of the waterline (or on the length of the entrance

for the given breadth _s)..

k'=o.7g

LE

(4)

7

V

(knott)

t.2l

8.53

-

10.82

.

13.10'

are (metres) .0.49 0.92

1.48

2.1.6

if thee. values are regarded as remaining constant during the bow motion, the relativebowmotion record wil.1 be the dashed line in Fig. 5, while the fullydrawn line repreSents the relettiye bow motion with respect to the undisturbed surface of the oncoming waves. deuce, the two records coincide by shifting the heroline upwards by h, or one can introduce

the concept "effective freeboitrti", i.e., the actual freeboard reduced

y h, what is convenient for thö examination of water shipment.

One can assume that the. largest relative bow immersions are ihcrea-sed by h5, but it. is not reasonable to decrease the largest relative

bowemergencesby t) same amount. 'The height of the bow wave isnot as largest the forefoot when it emerges, or nearly emerges. The

rela-tive bow motion as recorded can better be represented by the dotted line

in the sketch of Fig.. 5. . . '

To calculate the prob'ability of the occurrence of deck letnéss,

with the meaning of the water surface rising beyond a fixed pOint'at the bow (here 10 m above thecalm.Water'eurface), one has to consider 'the

"effective" freeboard, ano the relative' bow-motions without the

distor-tions as indicated for example by the dotted line in Fig. 5. The

lar-gest relativebowmotion "double amplitudes", say 1/3 highest of the total number of oscillations, are aaaumedtO be:exempt of the' bOw wave

when

at the forefootjemerging.. One Oandetermine the average of the 1/3

highest of the measured "double' amplitudes" 'FrOm' thi'à average, the

value of b (corresponding to' the ship speed) has to be subtracted. A corrected E'-value of 'the relative bow motions without distortions,

caused by variable bow waves, shOuld be

Esrc=P

i sr)

according to the Longuet-Iliggins formula. The in that manner calculated

values Of E for the different ship speeds are given in Table 1. They are considerably lower than the corresponding values Of E8 for

the relative bow motona as measured on the record8.

ThO probability of the wave surface rising higher than the point

the bow,eituated 10 m above the calrn water. line, or of th. relative bow

motion amplitudes exceeding the "effective" freeboard

jjt

1.

P[sr>HJ=e

''

. (6)

where 11' - Ii

-.

h.

The calculated probability expressed. in per cent, or the number of occurrences per 100 low cycle oscillation. is given for each ship spee4 in Table I, under thedenomination "predicted

num-ber of bow submergencesperl00 oscillations". _{These values can be}

com-pared with the numbers of observed. bow submergence. _{per 100 oscillations} in Table I, as counted on. the records of the several model _{runs. The}

agreemOnt is pretty good; it may be interesting, to nOtice that these

numbers, calculated by means of fOrmula (6), but after introducing _E8

instead of J , are .17.5, 22.1, 27.5 and 30.0 for the respective

speeds, and thus in poor agreement with the numbers of observed bow submergence.

These result. seem .to confirm the reliability of the _{prediction of}

deck wetneas, if assuming Itayleigh distribution of the relative bow otiona (with respect. to. the undisturbed _{surface of the 'onCOming waves),}

and considering an "effective freeboard",.to take account of the height of the bow ways (and ainkage) as given _byTASAKI.

b) Impacts by ,&róen water

The model was provided with an accelerometer, measuring the vertical acceleration at a station 0.17 L aft of the _{forward perpendicular. Acce-.}

leration and relative bow motion were reCorded simultaneously.

Bow sUbmergence, noticed at a given, moment on the relativebow-motion record, sometiea was followed by a discontinuous deviation of

the vertical bow acceleration, (k'ig. 6). This. obviously is an indica-tion of impact. It usually occurred, after serious forecastledeck

immersion. Slight bow submergence was not followed by any deflection in

the acceleration record. _{The lapse of time from the beginning of the}

bow submergence (near the.r.sistauce wire gauge) to the occurrence of

the impact varied from 1.0 sec to l.4.sec (ship scale) but it is

stri-king - nearly all measured lapses of time were about 1.3 sec. It may be assumed that the shipped' mass of water _{was fallen from the forecastle} deck upon the main deck, causing an, impact and inducing a sudden

deflec-2

tion of the acceleration at the considered station _{up to 2 rn/ sec} . This

deflection hasnot the classic appearanCe of a slam deceleration peak The length of the forecastle is 29 metres, and the _{wave, wire i.e} about 1 metre in front of the stem. _{The horizontal relativ.e velocity of}

the mass of green water, with respect to the ship _{thus would be .23 rn/eec,} and the actual velocity could be 'about 1,8 rn/sec at an average ship speed.

This velocity corresponds with the wave celerity of the long wave compo-nents in the spectrum of the tank wave pattern.... This _{suggests that a}

flooding wave crest seems to travel over the deck at a velocity, about

equal to that of, the undisturbed wave crest.

As not every noticed case of deck wetness is _{characterized by a}

trace of impact on the acceleration record, _{it is suggested here to test}

the hypothesis, that dOck immersion by the bow wave only is not folloled by tu impact, and that deck immrsion _{by the primary undisturbed}

wave crest is.

sometimes there is only a small trace in _{the accelerogram,}

some-times the deflection is considerable.. _{The number of deflection's,} or

the numbsr of observed impacts p.r 100 olcillations as counted on the record., is given for the different ship speed. in Table I. The

pre-dicted number of impacts per 100 oscillations, based on th. hypothesis as stated above, is derived from

P [r

H]=e

Esr,c

(7)

The results are given in Table I. The agreement with the number of ob-served impacts is not quite satisfying. Consideration of the

discrepan-cies might give some indicatione. For the lowest ship speeds, V - 6.21 and 6.53 knots, an immersion of the bow by the undisturbed wave crest,

if not in excess of say .1/ to 1 m, does not seem to cause impacts on

the deck. For the highest. speed of 13.10 knots however, it is possible

that impacts are to be expected in greater number than predicted in this

manner. In fact, the bow wave at this speed is big and might be

respon-sible for the occurrence of impacts as well.

Shipping of water may be regarded as severe, if it is followed by

an impact on the deck. It may be useful to be able of predicting the occurrence of "green water" impacts. For the here investigated ship, the application of formula (7), where U is the actual bow freeboard,

seems to be justified for ship speeds of 9 - 11 knots.

The measured acceleration deflection. are plotted versus bow sub-mergence for the four ship speeds in Fig. 7. The large scatter of the

spot. has to be expected, because of speed influence. Besides, the

scatter of the lowest values can partially be explained by the diffi-culty of precise measurement of small, irregular deflection. on the

re-cord. Nevertheless, the general tred of the severity of impact with increasing bow submergence can roughly be evaluated.

c) Relationship number - duration of bow submergence

1.1

station (here t the stem) can be predicted by meafls of the formula,

(ref. '7)

v

e

a)

(8)

. v'1J0

ihe effective freeboard (taking account of the bow wave and sinkage, according to Tasaki) and the corrected value E are introduced in

this formula. The results of this prediction, expressed in per cent o total duration of sailing, and the observed total dur.tion of bow

sub-mergence in per cent of the total duration of the rnodel runs are, given in Table I. As Can be seen, the agreement is strIkingly good, except

for the lowest ship speed.

In order to make a comparison between the number per 100 oscilla-tions and the total duration of bow submergence for the observed, and for the theoretical predicted values, Fig. 8 was prepared. In the same figure, the observed number of impacts by greefl water is plotted versus

the total duration of bow submergence. The ratio of these last values s about the same at each ship speed. _{The total duration of bow} submer-gence seems to be a good basis for the prediction of green water impact.

It might be interesting to look at the relationship between the

depth of bow submergence and its duration as observed. As can be seen in Fig. 9, this relationship aeSms to be the same for all considered

ship speeds. _{The main purpose of this figure however is to indicate the}

cases of submergence which were followed by an impact (dark spots), and those which were not (clear spots) _{The static swell-up h8, according}

to Taaaki, is indicated too, in order to compare it with the actual depth of bow Submergence, which caused an impact. _{In a broad sense, the}

re-marks made formerly concerning the hypothesis _{for the prediction of the} number of impacts seem to be confirmed by the _{general configuration of}

the spots. _{No definit, conclusions can seemingly be}

drawn from the du

ration of bow submergences. _{However, plotting the acceleration}

lee-tions versus the products of bow-óubmergence depth and the correápon-ding duration (Fig. lo), which ought to be roughly proportional to the mass of the chipped water, reveals's positive trend, especially for higher values of the acâeleration deflections.

Concludin, remarks

No circumstances of water shipping were iaet with the Lu-ship at sea, but the full-loaded "Jorthtens", a similar, though 8ornewhat longer

cargoliner (L 146 m) encountered head seas, which are as high as the

wave pattern in the tank during the model teats of the. Lu-ship.

Deflec-tion. in the bow accelerometer record were noticed and indicated by the

symbol d111 in ref. 8. These deflections are similar to those recorded

during the here discussed model tests and both are Occurring., at about

the same time after the maximum upwards directed bow acceleration. These deflections were followed, by whipping stresses in the main deck of the "Jordaans". _{The salient weather and propulsion data are given in ref. 9} under the observation number 13. The ship speed was 8 knots. Experience

at

sea with this ship lets one suggest that a captain will ask to reduce the engine power, in order to reduce the ship speed, if green water

shipping occurs

5, 6

or 7 times in a lot) low cycle oscillations.. These numbers, related to the speed of. 8 knots of the Jordaens, sailing

hea4-on in the given sea state, corresphea4-ond with the numbers of observed im-pacts per 100 oscillations in Table 1. This correlation suggests a

cri-terion for allowable deck wetness : 5 to 7 green water

impacts

(thus

nut the number of all bow aubmergunces, which is about 14) in a 100

Os-cillations.

This seems to correspond with a total dur,;tion of bow

.13

Acknowi edmenti

Tb. modal teats were carriidout _{tthóDavidsonLráboratory}

(St.-vens Inotitute of Technology) under the guidance of Prof. E. V. Lewis, and sponsored by the Society of Naval Archtecta and Marine Engineers

The cited full-scale tc.ts.w.re carried out by the Laboratory of Naval

Architecture of the State University of Ohent, undeF the directorship of Prof. 6. Aertsssfl and und.r th. auspices of the CeBaRNa (Centre

Beige 4. Recherches Naval..), with the financial assistance of .I.R.S.l.A. .(Jnstitut pour la Recherohe Scientifique _{dans l'Industrié et} 1'Agricul-ture).

References

1. M. K. 0cM : _{"Extreme Behavior of a Ship in Rough Seas", SNAME,}

Novem-her 1964.

L The Society Of Naval Architects of Japan : "Resoarcheø on Seakaeping

ua1itiee of Ship in Japan",Cbapter 8 :

"Model

Experiments in

Waves",

80 th Anniversary Series, _{VOluMe ,}

_{Tokyo 1963.}

V. Ferdinand. : "Analysis of Model Tets on the M.V. _{Lubumbashi in}

Regular and Irregular Waves", theaia (M.s.), _{Stevens Institute of}

Techflology, ipso.

V. Ferdinande : "Model Tests in Regular and IEreguiarWaves.at the

Pavidson Laboratory, Steviflo Institute _{of Technology, U.S.A",}

appen-dix of

ref. 5.

0. Aertisen : "Service Performance and Seakeeping Trials

on m.v Lu-kuga", Trans. R.1..N.A., 1963.

V. Ferdinand. _{:. "Analysis of Slamming Phenomena on a Model of a Cargo}

Ship in Irregular Waves", _{International Shipbuilding }rogress,}

Novem-ber, 1968.

J. Fukuda, J. Shibata, "The Effects of _{Ship Length, Srieed and Course} on Midship Bending Moment, Slamming and Bow _{Submergence in Rough Sea",} Memoirs of the Faculty of Engineering, _{Kyoshu LJrAiversty, Vol. XXV,}

V. Fsrdinande and R. De L.brs : "Impact Phenomenaind Wave Stresses on MV. ujordaenau in Mediu-Load and Full-load Conditions, appendix

of ref. 9.

G. A.rtss.n : "Service-Performance and Seakeepiu Trials on M.V.

Table I

ship apeed knots 6.21 8.53 10.82. 13.10

wave-heights., sq. mj 7.1. - .7.2. 6.8.. 7.4

pitch angles, (dog)2

4 .

relative bow motions, as measured, a

78

-5.() 8.2 5.l 10.], ..-5(1.5 .0 50.8 relative 'bow immersion .

8i.,,i

' 53.8 60.4 .65.0 65.3

relative bow emergence - .

sr e ' 51.3 50.8 48.3 38.1

J.

.,

arc

corrected relative bow motions, m ' 43.4 41.5 .41.3

Effective freeboard (TAAKl), metres _9.51 ' 9.08 8.ä2 7.84

Predicted number of bow aubmergencea . . .. '

per 100 osCillations .

'

. 12.3 13.4

.. 17.2 21.8

Number of observed bow iubmergenoea:

'per .100 oscillations

_1U2

_{14.2 17.7}

Observed number of impacts per 100

oscillations

. 4.2 6.3 8.2 11.6

Predicted nUmber of iEpacta per 100

oscillatione _9.8

9.0 8.9 8.3

Observed duration of bow submergence

(in per cent of total duration of run) 1.45 2.0 2.8

37

Predicted duration of bow submergence (in per cent of total duration of

cailiug) .

2

- values

V (knots)

Ii .21

8.53

10.82

13.10

Wave height

8.35 (7)

10.64 (6)

7.62 (7)

8.50 (7)

Pitch angle

9.88 (4)

2.65 (s)

3.15 (s)

2.78 (5)

el. bow

motion

6.39 (6)

l.5l (5)

18.96 (7)

3.54

(7)

n;.;;ai) a

- observed frequency

in

group i

e - theoretical frequency in group i

- number of groups (with at least 5 occurrences) in brackets : number of "degrees of freedom"

1. Iii8tograms and Rayleigh 4tstributiona of, wave heights at different ship speeds

Luship,

fullload oondition - 11i8togras and Rayleigh distributions

of relative bow Otions itt different ship spoe4s

Luship, fullload condition - histograms and Rayleigh distributions of relative bow imórsion itt different ship speeds

Luship, fullload condition - ilistograme and Rayleigh distributions of relative bow emergence at different ship speeds

Sketch of relative-bowrnOtion time history

Recorded dflectiou of accelerogram at the momen.t of water shipping

Impact deflections of accelerfttion at 0.17 L aft of PP versus depth Of bow submergence

B. Relationship number..total duration of bow submergence 9. Relatioflship depth duration of bow submergence lu. Relationahip impact - masa of shipped water

20

15 10 5 10 5

/

/

/

I

.1

I.

\

EX P ERIM EN TA

WAVE HEIGHT

RUNS AT V:6.

THEORETIC

DIS 2

RUNS AT V=8.53 knots

FIG.1 a,b

I HISTOGRAM

8 10 12

WAVE HE GHT,(m)

1 knots

AL RAYLEIGH

TRIBUTION

10

.12 14

WAVE HEIGHT,(m)

I

15 10 5 15 10 5 0

/

.E X PERI ME

THE

4

U

-z

w

-C-)

0

-o

j

/

/

RUNS AT

I TR---,

8 10 12

WAVE HEIGHT(m)

ILl 2

FIG. 1 c,d

NTAL HISTOGRAM

ORETICAL RAYLEIGH

DISTRIBUTION

N

N

V=13.10 knots 14 8 10 12 14

WAVE HEIGHT,(m)

WAVE HE IGHT

RUNS AT V:10.82 knots

15

20

15 10

/

10 15

FIG. 2 a&b

EXPERIMENTAL HISTOGRAM

RELATIVE BOW MOTION

RUNS AT V=6.21 knots

THEORETICAL RAYLEIGH

DISTRIBUTION.

2O 25

DOUBLE A+4PLITUDE Cm)

/

/

/

-I

/

RELATIVE BOW MOTION

RUNS AT V:8,53 knots

10 15 20 25 ₃₀ 35

20

15 10 5 0

-I

H

5

7

10 15

\

FIG. 2 c.&d

EXPERIMENTAL HISTOGRAM

RELATIVE BOW MOTION

DI SIR BUT 10 N

RELATIVE BOW MOTION

10 15

20

25 30 35

DOUBLE AMPLITUDE (m)

\

RUNS AT V :13.10 knots

20 25 30 35

DOUBLE AMPLITUDE (m)

AT V:10.82 knots

RUNS

20

/

2.5 2.5

7

FIG. 3a&b

EXPERIMENTAL HISTOGRAM

RELATIVE BOW IMMERSION

RUNS AT V: 6.21 knots

THEORETICAL RAYLEIGH

DISTRIBUTION

75

10 12,5 15

AMPLITUDE (m)

RELATIVE BOW IMMERSION

RUNS AT V :8.53 knots

THEORETICAL RAYLEIGH

DISTRIBUTION

_N

.-7.5 10 12.5 15 17.5

AMPLITUbE Cm)

20

15 10 5 15 10 5 L&

o

N

\

EXPERIMENTAL HISTOGRAM

RELATIVE BOW IMMERSION

RUNS AT V1O.82 knots

THEORETICAL RAYLEIGH

01ST RI BUT 10 N

N

N.

RUNS AT

N

13.10 knots

10 12.5 15 2.5 5

AMPLLTUDE(rn)

FIG. 3 c&d

17.5 2.5 7.5 10 125 15 17,5

AMPLITUDE (rn)

BOW IMMERSION

RELATIVE

15 -C-)

-o

-U--o

10,

C) UJ

-a

-U-.

o7'

20

25

5 7.5 10 12.5 15

AMPLITUDE (m)

RELATIVE BOW EMERGENCE

15--C-) C-)

0

U--o

10_>_

-Q

z

-w

-Ui

c

-I

10 12.5 15 0

2.0

7.5

AMPLITUDE (m)

FIG. 4 a&b

N

EXPERIMENTAL HISTOGRAM

RELATIVE BOW EMERGENCE

RUNS AT V:6.21 knots

THEORETICAL RAYLEIGH

DISTRIBUTION

RUNS AT V :8.53 knots.

I, 20 15 10 0 : LLi -C.,

-z

IaJ

--u

U

-o

-Li

/

of

2.5 5 7.5 10 2.5

EXPERIMENTAL HISTOGRAM

RELATI:VE BOW EMERGENCE.

RUNS AT V:10.82 knots

\;

75

10 12.5 15

AMPLITUDE (m)

FIG. 4 c&d

THEORETICAL RAYLEIGH

\,V

DISTRIBUTION

\

N

12.5 . 15 17.5

AMPLITUDE Cm)

RELATtVE BOW EMERGENCE

RUNS AT V:13.1O knots

-n

ACC

upwards

_-1c)

C)

_i-rn

rn

_{0> 'iO}

2.9 rn.sec

0

.4. 2.5 m

0

I

0

rn I- -1 rn BOW FREEBOARD BOW I

(10 m)

SUBMERGrNCE

ACTUAL BOW

FREEOAO

I

Lh1

..FFCJIVE J

N OW N . 1 FREEBOARD

-I'D

-1ó

I H I h I ______

r

AMPL REL

AMP

flBOW EMERr' BOW IMMERSION

L

2.0 1.5 1.0 .5 20 15 10 0 0

7

a o/

_j

/

1.

//V

/

₀ I--D: V

6.21 knots

8.53 i,

A: .ilO.82

0:

13.10 w FIG. 7

-tn

-z

₀

-I---4

-J

--a

C.)

-U)

0

r.w

-Ui

-z

TOTAL DURATION OF BOW SUBMERG.

- -Á - I

1 2

/. Of totat duratisfl Of run

4 6 8 m 10

DEPTH BOW SUBMERGENCE

FIG. 8

4

V

V

2.5 U U

-z

20 _w

-C., -LaJ

--m

CI)

-1.5_

4

U, Li..

0

DEPTH OF BOW SUBMERGENCE Cm)

2 3 4

V: 8.53 knots

V

DEPTH OF BOW SUBMERGENCE Cm)

II --.1 I I _- I 1 2 3 4 5 6

FIG, 9a&b

10z

.5

.Q

4

-0

V.., -p

2.0 1.5 1.0 2.5

-u

_I, U SI LU C-,

z

Lii

ow

z

0

4

C

4

4

*4

8

0 PTH OF :0W SUBMERGENCE Cm)

V:1.0.82 knots

.

8

V :13.10 knots

FIG 9 cId

A

£

DEPTH OF BOW SUBMERGENcE Cm)

I .- I I 3 4 5 6 n 1.5 1.0 -LU

Z

CD -Lii

-rn

--o

CD

-o

-z

0.

I-..

-D

0

4

U)

4

I

0

I.

2 3 4 5

1.5 1.0 .5

_V:..

v

6.21 knots

-8.53 : 10.82

0

- 13.10

(

_-I-

I I I I I i 10 15 20

DEPTH x DURATION BOW SUBMERGENCE (msec)