The effect of wave grouping on slow drift oscillations of an offshore structure

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ARCHIEF

BY

SØREN SPANGENBERG

THE EFFECT OF WAVE GROUPING

ON SLOW DRIFT OSCILLATIONS

OF AN OFFSHORE STRUCTURE

Technische Hogeschool

ki

bstektab

t

lu m

Deift

Danish Ship Research Laboratory

I

i

ADDRESS: HJORTEKRSVEJ 99 DK-2800 LYNGBY DANMARK

TELEPHONE: (02) 87 93 25 TELEGRAMS: SHIPLABORATORY TELEX 37223 SHILAB DK

MEDDELELSE

BULLETIN NO. 46

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SKIBSTEKNISK

LABORATORIUM

Danish Ship Research Laboratory

THE EFFECT OF WAVE GROUPING

ON SLOW DRIFT OSCILLATIONS

OF AN OFFSHORE STRUCTURE

by

SØren Spangenberg

April 1980

Bulletin No. 46

esche Ho03

DOCUMENTATE

: k?3

_{- q i}

[L

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TABLE OF CONTENTS Page LIST OF APPENDICES ii NOMENCLATURE iii ABSTRACT INTRODUCTION 2

DISCUSSION OF SPECTRUM REPRESENTATION 3

Consequences of spectrum representation 4

Statistical theories on ocean waves 5

Spectrum simulation methods 5

Generation of wave groups 9

MODEL TESTS 12

Description of the model tests 12

The model waves 13

List of measurements and analyses . 14

Summary of results 15

CONCLUSION 17

REFERENCES 18

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LIST OF APPENDICES

Appendix No.

Different wave patterns.

2, 3 Time series composed of 2, 3, 4, lO and 50

equidistant spaced components.

The "beating" and the period of repetition

are demonstrated.

4 The effect of random shift of frequencies

on the time series.

5 The effect of random shift of frequencies

on the energy spectrum.

Three wave patterns with different wave

grouping.

Energy spectra of three wave patterns with different wave grouping.

Time series for waves, motions, forces

and moment. Beam sea.

Energy spectra of waves. Beam sea.

Energy spectra of motions, forces and

moment. Beam sea.

Mean, maximum and minimum amplitude values for

waves, motions, forces and moment. Beam sea.

Time series for waves, motions, forces

and moment. Bow-quartering sea.

Energy spectra of waves. Bow-quartering

sea.

Energy spectra of motions, forces and

moment. Bow-quartering sea.

Mean, maximum and minimum ampiitu.de values for

waves, motions, forces and moment.

Bow-quar-tering sea. 6 7 8 to 16 17 18 to 26 27 to 29 30 to 38 39 40 to 48 49 to 51

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a Amplitude of the i-th Fourier components

f. Frequency of the i-th Fourier component

h Wave height

n Number of frequency intervals

t Time

t Time of random shift of frequencies

r. (t) Random term

i

z Surface elevation

p (z) Probability distribution for

surface elevation

N Number of Fourier components

Tb Time interval between beats

Tg Period of wave group

T Period of repetition of the time series

T Length of the time series

S ()

Power spectral density

Variance of probability distribution

Cyclic frequency of the i-th Fourier component

Maximum of the cyclic frequency interval

max

min Minimum of the cyclic frequency interval

The i-th cyclic frequency after random

i

shift of frequencies

Wib The i-th cyclic frequency before random

Fixed cyclic frequencies defining

i

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a

ib

NOMENCLACURE - continued

Phase angle of the i-tb Fourier

component

The i-th phase angle after random

The i-th phase angle before random

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ABSTRACT

THE EFFECT OF WAVE GROUPING ON SLOW DRIFT OSCILLATIONS OF AN

OFFSHORE STRUCTURE

The effect of wave grouping on slow drift oscillations of an offshore structure is investigated experimentally by testing a semisubmersible

in three different wave patterns. The energy spectra are almost

iden-tical for the three irregular waves but the wave grouping is different.

Six motions, two forces and one moment have been measured and the

re-suits are presented in time and frequency domain. The results show

that the succession of the waves has a significant influence on the

low-frequency part of the motions, forces and moment. Representation

of a natural sea state solely by the energy spectrum is demonstrated to be insufficient when testing the performance of systems for mooring

or dynamic position control. A method to control the formation of wave

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1. INTRODUCTION

In this report is discussed whether model test in waves should be carried out in accordance with the probabilistic description in its present form where irregular waves are generated solely from an energy spectrum, or whether the probabilistic description should be extended by information about other relevant characteristics of a natural sea state, e.g. the

wave grouping.

A more comprehensive understanding of ocean waves has become of great practical importance in the last decade because of the expansion in

off-shore activities. These activities have resulted in completely new types

of ocean structures. The wave grouping has a great influence on the

dy-namical response of many of these new structures. This applies for instance

to dynamically positioned or moored offshore systems.

The resonance frequencies associated with the surge, sway and yaw motions

are normally low for moored offshore systems. The oscillations in the

horizontal plane therefore takes place within two distinct frequency

ranges. One part of the motion corresponds to each wave in the wave

pattern, while the other takes place in the low-frequency range

characte-rized by periods up to several minutes. The low-frequency motions are

denoted by slow drift oscillations. The excitation force for these slow

drift oscillations is the wave grouping. The largest response will occur

when the period of the wave groups is equal to or lies in the vicinity of

the natural periods of the offshore system.

Model tests have been carried out in order to investigate the effect of wave grouping on the slow drift oscillations of an offshore structure. A semisubmersible suspended in a linear, elastic spring system was tested

in three wave patterns with different wave grouping. All six motion

com-ponents and the surge force, the sway force and the yaw moment have been

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2.

DISCUSSION OF SPECTRUM REPRESENTATION

The accurate prediction of the dynamic response of ships and offshore structures by means of model tests depends on the ability to produce

realistic waves in the model basin.

The natural sea state is a random process. It is probabilistic by nature

-its characteristic properties are only known within certain lim-its of

probability.

The random nature of ocean waves is usually described as a stationary

Gaussian process. This means that Gaussian distribution of instantaneous

surface elevations and the equality of the ensembles with respect to space

and time are assumed. The surface elevation, z, follows the distribution:

2 2

-z

p(z)

=

JTi.a

. e (1)

where a2 denotes the variance of the surface elevation.

The assumption mentioned above means that waves can be resolved in an infinite number of regular waves with infinitesimal amplitudes and random

phases by virtue of the central limit theorem. Thus the surface elevation

at a fixed position can be expressed as:

z(t) = a. cos(. . t

+4.)

i=l

i

(2)

where a is the amplitude, c.. the frequency and ₄₎ the phase.

It appears that the amplitude spectrum entirely specifies the probability distribution of all the parameters of the wave pattern - heights, periods,

grouping etc. - if the assumption of the classical theory apply.

The Gaussian distribution of surface elevation of ocean waves is an

approxi-mation. The deviation from the classical linear theory is demonstrated

by the breaking of waves and by the tendency of crests being greater than

troughs. The non-linear effect is in particular important for ocean waves

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Consequences of Spectrum Representation

The assumption that the surface elevation of ocean waves follows the

Gaussian distribution is generally accepted and has been the basis for

the description of ocean waves until now. The consequences are:

The results of field records are often represented

solely by amplitude spectra. Phase information is

not described. _{This means that it is not possible}

to reproduce the wave samples in the time domain.

Many efforts have been made in order to determine the

influence of the shape of the spectrum on the

essen-tial properties of the wave pattern. Different

spec-trum parameters have been defined - significant height,

moments, peakedness, width etc. - in order to describe

the spectrum. _{The influence of the spectrum}

para-meters on the essentiel properties of the wave pattern has been investigated, both theoretically, /1/, and

numerically, /3/. Results have been obtained for

certain spectrum shapes - often narrow banded spectra,

/2/. But in general the relations between the

funda-mental properties of the wave pattern and the

parame-ters which determine the shape of the spectrum are

not clear.

There exists at present a considerable diversity in

spectrum simulation methods. it is shown in /4/ that

the chosen method of simulation has a significant

influence on the resulting wave pattern. This is

further demonstrated in the next section.

Iv) The knowledge of the statistics of certain properties

of ocean waves - such as grouping, waves with large

amplitudes, breaking of waves, slopes etc. - is little

because only few field records have been analysed in

order to study these properties. This makes it

diffi-cult for the laboratory engineer to give a realistic wave input to systems for which the response is mainly determined by the non-linear effects of the waves.

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Statistical Theories on Ocean Waves

In connection with II) the following important results can be mentioned. The wave heights are not uniform, but are statistically distributed. Longuet-Higgins has shown theoretically that when the wave spectrum is narrow banded the distribution of wave heights follows a Rayleigh

distri-bu t ion:

1h

h

p(h)dh = exp ( )dh (3)

C _8q2

In /1/ a theory is presented which describes the relation between a narrow

banded spectrum and the wave grouping. Statistícal parameters which

describe the probability of occurrence for the number and height of

conse-cutive waves in a group are derived.

Cartwright and Longuet-Higgins /2/ have presented a theory on the distri-bution of maxima of surface elevation for broad banded spectra, but a

consistent theory covering all important wave properties seems still to

remain.

Another way to gain experience on wave statistics is by numerical

expe-riments. In /3/ spectra of various shapes have been investigated. The

simulated wave profiles were examined for surface elevation, wave heights, correlation between wave height and period, and the grouping of waves.

These numerical experiments show that the method of simulation of the

energy spectrum is of decisive importance for the obtained results. This

problem is earlier mentioned under III) and will be discussed below.

Spectrum Simulation Methods

The simulation of the surface elevation can be carried out in two different

ways. One method uses modification of pseudo-random signals by means of

transformation functions selected for specific spectral characteristics.

The other method is based on eq. (2). The surface elevation z(t) is assumed

to follow the Gaussian distribution. Thus the surface elevation at a

fixed position can be expressed as:

N z(t) = 11m Z a.

cos (.

t + .) (4) i i N-3

i1

2 a. = 2

_S(.)Ew.

i

In the following some variants of the method given by _eq. _{(4) are}

de-scribed and also their different effects on the resulting wave pattern.

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One of the most easy and often used methods for reproducing a certain

energy spectrum is to divide the frequency interval w . to w into

min max

n equal subintervals. The amplitude a. of the i - th frequency

w

where

is the mid-point of the i - th interval is determined from the energy

spectrum S(w):

2

a. _{wmax - wmin}

i

- n

Even though the surface elevation follows a Gaussian distribution the wave grouping gets a special character which is not in accordance with a natural sea state. This is demonstrated in eq. (7) for a wave composed

of two components:

z(t) a sin w t + a sin w

2 =

2 a cos

_{- w2)}

t sin

(w1 +w2)

. t (7)

The resulting time series is oscillatory with angular frequency

+ and amplitude 2 a cos (w. -w2)t. The phenomenon is

known as "beating". The time interval between the beats is

T

2n

b

w1w2

In Appendix 2 and 3 the resulting time series are shown for N = 2, 3,

4, _{10, 50 equidistant components. The influence of this method on the}

succession of the waves is clearly demonstrated. A detailed discussion

of the method is given in /4/.

For methods based on eq. (4) applies that if the díscrete frequencies

are harmonically related then the time series will repeat itself. The

repetition period T is determined by the intervals between the

fre-quencies. With equidistant distributed frequencies the period is given

by

T 2Tr

r

_Lw

The repetition period is clearly seen from Appendix 2 and 3.

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The required number of components N can be determined when the length of

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NT

s

with properties normally used in model tests - T = 600 s, f = 1.2 Hz,

s max

f . = 0.2 Hz (model scale) - the minimum number of components becomes:

min

N 600.

A non-repetitive time series based on eq. (4) can be generated if the frequencies w. are not harmonically related. Independent of the number of frequencies the time series never repeats itself but the resultant spectrum has of course distintly recognizable peaks. A variant of the method is described in /3/ and will be briefly summarized below. The

frequencies f! dividing the frequency interval f . to f are defined by:

i _min _max f w

2rr

f -f max min f'1 = f . + min

N-1

f _1/N-2 max CN =(f! ) ft2 = 'i CN f'. = f'. . C i i-1 N N-2 f' = N-1 f'l CN

The secondary dividing frequencies f1", fi',

EN-1" are chosen at

random in the respective sub ranges (f!1 f." f'.). The frequency

f. and the band width f. are determined by

i i

= _{(f"1_1 + f.")}

f!!

-i i i-1

The phases are chosen at random.

It is concluded in /3/ that if more than 50 components are used for the generation of the wave, then the surface elevation will be distributed

in accordance with the Gaussian distribution with sufficient _accuracy

for practical laboratory applications.

max min

= T . (f -f . ) (10)

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In /5/ a method has been outlined, which overcomes the previously mentioned draw-backs and does not give any repetition of the time

series, no distinctly recognizable peaks in the energy spectrum and no fixed frequency differences. The method is based on a modification of

eq. (4): N z(t) = hm a. cos (L).(t) . t + . (t)) (11) i i N-' i=1 = + r. (t) ₍₁₂₎ L) '

- L)

i < 7

-

r (t) < -- 2 L) i i-1 r. (t) +

N-N-1

< _{rN (t)} <

N-N-1

2 2

The fixed frequencies L)t are chosen as equidistant, as non-harmonically

related or in any other feasible way. r. (t) follows a given probability

distribution in the i-th interval, e.g. uniformly distributed. The

intro-duction of the term r

.

(t) makes it possible to produce a certain

pro-bability distribution for the frequency difference L). - ., which

deter-mines the succession of the waves - the wave grouping. This is described below as the generation of the different wave groups for the model tests is based on this method. The frequency shift can be done regularly or random under the generation of the time series. The start values of the phases are chosen at random. The continuity of the time series during a

frequency shift is kept if:

L). . t

_++.

ia s ia

= Wib

t

+ 'ib

where L) . and L). are the i - th frequency before and after shift,

ib ia

ib and 4 ja are the i - th phase before and after frequency shift and

t is the time of frequency shift.

In Appendix 4 the effect of random frequency shift on the time series is demonstrated. The fixed frequencies L). are chosen as equidistant in this case. Fig. A shows the resulting time series without random shift of frequencies. The period of repetition is clearly seen. The time series in Fig. B and C are generated with frequency shift every 3Osec. and 10

sec. There are no longer any repetition in the signals.

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The energy spectra of the three time series are given in Appendix 5.

Distinctly recognizable peaks are seen in Fig. A (no frequency shift). Fig. B and C show that the introduction of random shift of frequency tends to smooth the energy spectrum. This effect is important for a correct determination of the response of narrow banded response

systems.

Generation of Wave Groups

The introduction of the term r.(t) in eq. (12) makes it possible to

produce a certain probability distribution for the frequency difference

-.. _{The relations between the random shift of frequencies determined}

i

J

by the probability distribution of r.(t) and the corresponding probability distribution for the frequency difference

.

- u. are described in the

following.

f1(x) is the probability density for x in (x1, x2) and f2(y) is the

probability density for y in (y1, y2). The probability density f3(z)

for z = x-y is determined by:

f3(z)

ff1(z+y)

f(y)dy

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When x and y are uniformly distributed f1(x) and f2(y) are given by:

f (x)

=a

1 x2-x1

-p

y2 - y1

and the probability density for z then becomes:

f3(z) = f1(z+y) . f2(y)dy y2 p (17) y1

x1 x<x2

y1 < y y2 (15) (16)

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If

21

x2-x1 the solutIon of eq. (17) is:

f3(z) = O for z<x1 -y2

= a

p(z+y2-x1)

for x2y2z>x1-y2

= a p (x2 - x1) for x1 - y1 z x2 - y2

= a p(x2-y1 -z)

for x2-y1z>x1

y1

= O for z>x2-y1

The mean value,

i

, of the probability distribution f3(z) is equal to

the difference between the mean values of the probability distributions

f1(x) and f2(y):

=

(x2+x1) -

(18)

When x2-x1 = y2-y1 =

Lix,

and x2 = y1 the mean value,

i

, and the

variance, 2, _{of the probability distribution f3(z) becomes:}

Il =

(x2+x1) -

y2+y1) = Lix (19)

co

a2-

(z-)2

f3(z) dz = (20)

-CX)

It appears from eq. (19) and eq. (20) that when the fixed frequencies

- see eq. (12) - are chosen equidistant with c..-.1 =Liw and

r.(t) is equally distributed in the i-th interval, the mean value of the probability distribution for the frequency difference

- is

Liw. The corresponding variance is The time series will contain

wave groups with periods Tg determined by:

2ii

T

g Li(i)

The small variance of the probability distribution for the frequency

difference causes an almost regular wave grouping.

In Appendix 6 three wave patterns are shown. The time series are

generated in accordance with the method described above. The wave

grouping is almost regular because of the small variance of the

proba-bility distribution for the frequency difference.

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of the resulting probability distribution f3(z) is larger than the

variance given by eq. (20). A wave pattern containing all wave group

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3. MODEL TESTS

To illustrate the importance of a more comprehensive knowledge about wave grouping, the Danish Ship Research Laboratory has made a series

of model tests where the effect of the grouping of the waves on the

slow drift oscillations of an offshore structure is investigated.

A semisubmersible _{is tested in three different wave patterns. The}

energy spectra of the waves are almost identical, but the succession of the waves is different, i.e. the lowfrequent excitation force is

different.

Description of the Model Tests

The test of the model (Fig. i ) was carried out in the Laboratory's

large towing tank which is 240 m long, 12 m wide and has a depth of

5.5 m. The model scale was 1 to 27.5.

The semisubmersjble was attached to the equilibrium position by _means

of a linear spring system. The spring constants which determines the

restoring forces in the horizontal plane were 7 . 7 x lO4 N/rn in surge

direction and 8 . 2 x lO4 N/rn in sway direction. The properties are

given in full scale values.

The natural frequencies for the system were determined by decay tests

and the results are listed in Table 1. It is seen that the natural

frequencies for all the modes are well below the frequency range of the waves. The response is then separated into two different frequency

ranges - one related to the wave and one related to the wave group-ing - and therefore the effect of wave groupgroup-ing is easily identified

in a frequency analysis.

All six motion components, surge, sway, heave, roll, pitch, yaw, two forces - the surge force and the sway force - and one moment - the

yaw moment - have been measured. The wave was measured opposite the

equili-brium position of the system. The coordinate system is shown in Fig. i

The sernisubmersible was tested in two headings: beam sea and

bow-quartering sea. Because of practical reasons it was not possible to perform wave grouping tests for head sea. The draught was approx. 25% greater in beam sea, but both draughts can be classified as operational.

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Heading

z

Y

X

Fig. 1. Coordinate system and headings.

Surge Sway Heave Roll Pitch Yaw

900 _{156 s} _{166 s} _{21.6 s} _{34.4 s} _{29.0 s} _{90 s}

135° 148 s 150 s 21.5 s 36.8 s 31.2 s 84 s

Table 1. Natural periods of the

semisubmersible (full scale values).

The Model Waves

90°

i co

______

i-J

The semisubmersible was tested in three different wave patterns with

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The generation of the time series was based on the method described by

eq. (11) to (13). The fixed frequencies c.'. were chosen as equidistant.

To avoid the formation of regular wave groups random frequency shift has been introduced. See eq. (12). The time series for the model waves

were generated with _r (t) _{uniformly distributed in every frequency.}

interval. All the frequencies were randomly shifted at the same time.

By means of random frequency shift a variation of the wave groups in

a single time series is obtained.

The number of components N were determined from eq. (22)

umax - min

N = Tg (

2rr

so that the period Tg of the wave groups for the three wave patterns were approximately 20, 40, 50 seconds in model time corresponding to

105, 210 and 262 seconds full scale time. With - )/2Tr =

max min

1 Hz, N becomes 20, 40 and 50. The three wave patterns are denoted A,

B and C. See Table 2.

Wave Wave group period

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Table 2. Wave group period of wave pattern

A, B and C. (Full scale values).

In Appendix 6 the time series for the three resulting wave patterns are shown (model scale). It is clearly seen that each time series shows dif-ferent wave grouping. The frequency analyses in Appendix 7 show that the

energy spectra are approximately identical.

List of Measurements and Analyses

All the measured properties - motions, forces, moment and wave - were recorded simultaneously. The signals were transmitted through an ana-log low-pass filter to a 10 Hz AID data ana-logging system. The digitized

signals were then stored on discs for analysis.

A 105 s

B 210 s

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The measurements have been analyzed both in time and frequency domain

and are given in appendices as shown in Table 3. All the results are

in full scale values.

Heading Measurements Analysis Appendix

Beam sea waves, motions, forces, moment time series 8 to 16

Beam sea waves energy spectrum 17

Beam sea motions, forces, moment energy spectrum 18 to 26

Beam sea waves, motions, forces, moment mean, max, min 27 to 29

Bow- q uar t e r in g

sea waves, motions, forces, moment time series 30 to 38

Bow-quartering

sea waves energy spectrum 39

Bow-quartering

sea motions, forces, moment energy spectrum 40 to 48

Bow-quartering

sea waves, motions, forces, moment mean, max, min 49 to 51

Table 3. List of measurements and analyses.

Each appendix contains the three different wave patterns and the

corre-sponding responses. From Appendix 17 and 39 it appears that the energy

spectra of the three wave patterns are approximately the same.

Summary of Results

A summary of the results is given in the following. The discussion is

concentrated about the sway motion in beam sea, Appendix 9 and 19,

since the wave grouping effect is most pronounced for this motion

com-ponent. However, the same conclusions are also valid for the surge and yaw motions.

The time series show a significant difference in the slow drift oscil-lations dependent on the wave input. The largest response is obtained in wave B and C. The period of the slow drift oscillations correspond

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The frequency analyses show that the response is separated into two

frequency ranges. The high frequency part corresponds to the waves,

while the low frequency part lies in the vicinity of the natural fre-quency of the sway mode. The period of the sway mode is 166 seconds in beam sea, see Table 1. The periods of the wave groups are given in

Table 2.

None of the periods of the wave groups correspond to resonance but appendix 9 and 19 demonstrate that the response of the mooring

system is much greater at excitation periods corresponding to the wave group periods of wave B and C. This is also in agreement with the fact

that the response of a dynamic system will be small for excitation fre-quencies well above the natural frequency.

The mean, maximum and minimum amplitude values of the sway motion in beam

sea are:

Wave Mean Max Min

A -1.32 m 0.20 m -2.71 m

B -1.57 m 2.87 m -7.06 m

C -1.61 m 3.11 m -7.19 m

Table 4. Mean, maximum and minimum amplitude values

of the sway motion in beam sea.

The corresponding values of the sway drifting force are:

Wave Mean Max Min

A -8.87 x 104N 5.92 x 104N -2.17 x 105N

B -1.05 x 105N 2.35 x 105N -4.93 x 105N

C -1.03 x 105N 2.34 x 105N -5.51 x 105N

Table 5. Mean, maximum and minimum amplitude values

of the sway drifting force in beam sea.

Analyses of the remaining motion components of beam sea show that the

slow drift oscillations also are very important for the surge and yaw

motion. There has not been recognized any effect of the wave grouping

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The results for the corresponding measurements made in bow-quartering

sea are given in Appendix 30 to 51.

4. CONCLUSION

The effect of wave grouping on slow drift oscillations of an offshore structure has been investigated experimentally by testing a semisubmer-sible in wave patterns with almost identical energy spectra, but different

wave grouping.

The model tests showed that the wave grouping has a significant influence on the low-frequency part of the motions and forces in the horizontal plane

and is decisive for the obtained maximum values. The period of the slow

drift oscillations corresponded to the wave group period where the wave

grouping was pronounced. There has not been recognized any effect of the

wave grouping on the other motion components.

At present there exists a considerable diversity in spectrum simulation

methods. It is shown in the report that the spectrum simulation method

has a significant influence on the wave grouping of the generated wave

pattern.

A method to control the formation of wave groups in a time series has been

outlined. The generation of the wave patterns for the model tests was

based on this method.

The present report underlines the necessity of field records also being

analysed for wave grouping. At present the knowledge of ocean wave groups

is very limited. When testing the performance of systems for mooring or

dynamical position control it is therefore recommended to test the structure

in the most severe situation as regards wave grouping, i.e. in wave patterns

where the period of the wave groups lies in the vicinity of the natural

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REFERENCES

Nolte, K.G. and Hsu, F.H.: "Statistics of ocean wave groups". OTC paper number 1688, 1972.

Cartwright, O.E. and Longuet-Higgins, M.S.: "The statistical

distribution of the maxima of a random function". Proc. Royal Soc., A., Vol. 237, pp. 212 to 232, 1956.

Goda, Y.: "Numerical experiments on wave statistics with

spectral simulation".

Report of the Port and Harbour Research Institute, Vol. 9,

No. 3, 1970.

Ness, A.: "On experimental prediction of low-frequency

oscilla-tions of moored offshore structures". Norwegian Maritime Research, No. 3, 1978.

Spangenberg, S.: "Irregular waves". (In Danish).

Internal Report of the Danish Ship Research Laboratory, May 1978.

Hsu, F.H. and Blenkarn, K.A.: "Analysis of peak mooring force

caused by slow vessel drift oscillation in random seas". OTC paper number 1159, 1970.

Verhagen, J.H.G. and Sluijs, M.F.: "The low-frequency drifting

force on a floating body in waves". Publ. No. 320 of the N.S.M.B., 1970.

Remery, G.F.M. and Hermans, A.J.: "The slow drift oscillations of a moored object in random seas". OTC paper number 1500, 1971.

Newman, J.N.: "Second-order, slowly-varying forces on vessels in

irregular waves".

International symposium on the Dynamics of Marine Vehicles and

Structures in Waves, University College London, 1-5 April 1974.

Bucharth, H.F.: "The Effect of Wave Grouping on On-shore

Struc-tures".

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Rye, H.: "Wave group formation among storm waves".

Proc. 14th Coastal Engineering Conference, Denmark 1974.

Johnson, R.R. and Ploeg, J.: "The problem of defining design

wave conditions".

Port's '77, March 1977, ASCE specialty conference.

Johnson, R.R., Mansard, E.P.D. and Ploeg, J.: "Effects of wave

grouping on breakwater stability".

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A o I Y 0.0 -1 . Q0_

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-2.00...

TitlE 1Ft SEC. 2.00 SL.EEP 1 .00 0.00

i0

i

-1.00

-2.00

PLUN , 1, V V 2.00 IFLREGULPft 2.00

l.00

(29)

2.00... 0.00 Ö -2. 00... q.00_ 2.00... 0.00 -2. 00... 2.00

.J

0.00 (.0

li

TffiEE CI1NENTS $ t

r

s e f. e '4.00 FOUR CWI?ØNENTS s $ a I p I s s L)01h V Period of Repetition TitlE IN SEC. Period of Repetition

4----.

----p. I 4 5. a a I

j

I

i

p TitlE IN SEC.

f

I p. o I

4 V'

$

f

I s s

f

0.0

-2.00... I t s I

RUN 3

s I I

q.00

Period of Repetition RUN i _LLOO_ TitlE IN SEC.

SKIBSTEKNJSK

Time series composed of

LR8ORRTOR JUN

2, 3, 4 equidistant components

(30)

1.00 0.00 -1 .00 -2.00 6.0 TEN C11PNENTS 3.0 0.0 -3.0 2. 00 i alo i . oo__ 0.00 o -i. Q0_ FIFTY CMPNENTS

AUN 3

TillE IN MINUTE -6.0 TIME IN MINUTES Period of Repetition 4- --- --- -p Period of Repetition .00

SKJSTEFN1SP(

LP5OAPTOA JUM

LYNCBY DAN11ftK

Time series composed of

2, 10, 50 equidistant components

(31)

2.50... 0.00 2.50 0.00 -2. 50 o -2.50_ -5.00.. 5.00__A -5.00. UN: FIG. C TIM.E IN MINUTES -5.00 TJF1.E IN rIJNLJTES 1111E IN MiNUTES Period of Repetition J

5.00 FIG. B Random shift of frequencies every 30 sec.

Random shift of frequencies every 10 sec.

.00

LD

SKIBSTEKNISK

Effects of random shift of

LABOTOFUUM

frequencies on the time series

L'wGa't 0AÑFtFßK

b

g

(32)

a 2.00 (rl 1.00 0.00 0.00

No random shift of frequencies.

0.00 RUN I T-PERK S 2.85 T02 S 2.12 SIGN.VPL. = 6.32E+00 TEST TIME 5.00 0.00 RUN I 2.50 FFEQ. i . QQ

0.00

5.00 0.00 RPO/S RUN

i

T-PEK S 1.S'4 T02 S 2.13 SIGN.VL. 6.25E+00 TEST TillE 5.00 2.50 FFIEQ. 5.00 ffl0/S

Random shift of frequencies every 30 sec. Random shift of frequencies every 10 sec.

SKIBSTEKNJSK

LP5OIRTOH IUI'1

L'fNGB'r 0NrtRK

Effects of random shift of

frequencies on the energy spectrum

('J a I-' 2.00 5.30

111111 ¡TI iliI

2.50 FFEQ. RRO/S ct T-FERk S = 2.10 T02 S = 2.12 SIGN.VRL. 6.31E+00 TEST TIME 5.03

(33)

0.00 -1 . 00 -2. 00 2. 00 10 i . 00 -1.00 -2.00 .1 III i I i II II Ii t i I L i 'i I' l i..1tl.

III.,

I

'1

iÍiI

ti I:' iPiIiIilIiL!li! iIIIli IIPItl.'. I :1111 iItII_. HUN 205 WAVE (Cri) B TillE Ill MINUTES

Hi.

H

tHllL

2.00 WAVE (Cli) .10 C I IIIII i i i i I L. I!iIIlI li lIIiiI' r !'IFIIIIIII'

IIIl!I

T - 50s g HUN 201 TIME 1H MINUTES

H ill

I II'I' 'i 1 Ii! I

IIIfI

11(1(1 SKIBSTEKNISK LABORAl 0H J UM L)N8'1 OANMAIIK

Three wave patterns with different wave grouping (model scale).

i .00 T - 40s g 0. 00 11111

u H

liii.,

L Ii II .111.11

I,

Iii

ii

i,,

.1 1 .1 II i i' I,IlI, ti,). i I I . 00 HUN 207 -2. 00 TIME IN MINUTES 2 00 WAVE (CM) T g 20s .10 t . 00 _0.00 I Ii liii t

(34)

0.0 e 20.0 Q 10.0 L) 0.0 0.00 UF1 205 0.00

9UN 201

1PERK S 2.07 102 S = 1.76 SIGN.VRL. 1.8I+Ql TES TIME 6.00 SAD/s e I-20 TPEAIc S 2,13 Q oc F FIE Q 102 S 1.82 SIGN.VRL. 1.73E-01 u, 3.00 FPLE Q. 6.00 RADIS tu 0.0 0.00 J9UN 207 1PEAK 5 = 2.07 102 s 1.82 SIG.VRL. l.68E+0l TE5T TIME 1l.7 3.00 FAEQ. 6.00 RAD/S

SK1STEKNJSK

LR6OflPTO11UM

PRt'fl1RK

Energy spectra of three wave patternc with different wave grouping (model

(35)

5.00 0.00 -5.00 2.00 0 00 0.00 1111f IN lUNUlES AALA1AhI

rv'

,.

, FI ,. .' Frl) SFJMGE Ill) A HUN 209 -2.00 lIME IN MINUTES s.00_. w11v1 5113f (rl) 000

II

LAi . . .A&.

r'

'FVV t 0 15.0 HUN 207 -2.00 1111E IN MINUTES 5.00 UNVE 510f 1M) 0. 00 OU 206 TIME IN MINUTES SUACE IM)

Ai.iALA

ILi

ii k.. L..4a&

11.4 .LA.liaeA4.,kLAA.1&&á...

At,

Li

Aòii

.'

' '

7 l 'y F )

...I,!,

15.0 30.0 45.0 HUN 206 1111f IN MINUTES .AÎàL ,

AL,

.L&. 30.0 45.0

SKI BSTEKN J 5K LP500RTOH J UM LfNGB'F

£IPNFRAK

The surge motion in waves with different wave grouping. Beam sea. Fullscale values.

-S. 00. 2.00 TIBE IN MINUTES SUI1SE IM) B 2. 00 0 Dl .0 -2.00 15.0 30.0 NS. O

(36)

00

5.0

0. 00 8.0 - 110

9UN 209

-8,0 5. 0U_

WPVE slot IM)

B SUP'! (nl B 5.00_a URVE 510E MI C 0.00 00 -8.0

TIllE IN MINUTES TIME IN MINUTES _{TitlE IN IIINUTET}

4.

.

A

wy

!

y

rrvrw. 'w" "

207 5.0 St J5STEKNI SK QF14T OR J li tI L'!ND'! 0RMP1P!K

The sway motion in waves with different wave grouping. Beam sea. Full-scale values.

FUN 206

'rw

wyAyyr

'rr

'y

v'v"

30. -5.00 TillE IN luNUlES UPVE 510E IF1) A 8.0 -TitlE IN MINUTES -S. 00_ 8.0 TitlE IN MINUTES SUP'! (M) C

(37)

s.00. uPV 5I0 III) 0.00 -5.00 2.00 Q 00 -2.00 5 00 0.00 -5.00 2.00 UN 209 5.00 UV SIDE (n) B IIEPV( (rl) B

TillE IN MINUTES 1111E

IN MINUTES i i Li i I I I i ¡ I I I b L ¡ ill ii i. t I'' ti i

'i'i'ii

(,lii

i

t. L i

¡iiI

IL, i I i i i . .i

ii

i. iihiIJ I

''I

I'

''i

Appendix 10 wpvc SIDE (nl C

TIME IN MiNUTES 1111E

IN MINUTES

it.,,iu,i,iii,iiIti

ti i

Lii,Ii.I

Iii.aIIIL,ltiiA

tililiLi ti

ii' ''iiii rl i.i ' 5.0 HU 206 tlEí(Vt (M) fi JI

iIiJ

i I uAi)1\ ALA k!Iik i

iA

A1I1IL 1thM J1L1LiJ1dI!1lbI11/WJti

AAAh

1ryv V '4V TÇT'V'n ' V' IY ''Iy y1jy tY y y Y

pr'

Ii

I''

I o HUJ 206 TillE IN MINUTES

SKJBST[KNi 5K L RB OAR T OR lUll LINOBI

OANIIPRK

(38)

0.0 5 00 0. 00 -5.00 6.0 OD on A .1 II I i n i I t L L t .i i. i. I t L ¡ ;. i t I k . k I i I. t. ¡ t I I t. i u .. t. h I I I i I i t k I h I . I t i i i t L h r t ! r i r t i i ' r t , t -i I t i i i r l OD 5.0 AUN 209 TIME IN 1111401ES UVE 510E ((13 R ç. o WtV( 510E (Ii) C _{AU 206} MOLL )OEG1 C TIME 1)4 I1JNUTES I It J I li i, .3 A I L t t ¡ i L L i . t, h m L t L t t g

r'!)

'rji' rtn'r(Ii.(1i ?!!!P

.0

1111E IN ((INUItS TillE IN luNUlES

& U A i i ii Lt i. t i L L i

'1J

¡ I .L T'

t, irt:

t. ¡tilt

tjhitii,3i,i:ti t.

,Ittt.ihtiit

r ' t S J 5STEN JSK LABONATOfl I Uil -L'TNGB'V OAN0Rt(

The roll motion in waves with different wave grouping. Beam sea. Full-scale values.

-6.0 5. 00_t 0. 00 -5. 6.0 -. LPVí 510E ((1) A Appendix 11 0.00 AUN 209 -5. O0.. 2 A6LL (DEG) TIME IN IIINUTES AUN 206 -6.0 TitlE IN 1111401ES

(39)

0.00 0.00 -5.00 2.00... 0.00 -2. 00 5.00 0.00 -5.00 2.00 Q 00 -2.00 5.00 IIRVE SIDE MI A

itt,

It.tt

it .ii ..a.i

Aiiit,.iL1AI1

PItE

l!'1tJPIV

lIt'''Itr''!l

't!ItP V'PI

P11111 (DEOI A HUN 209 I4ÇVE SIDE (P)) B HU 207 FItr.)1 ICES) B HUN 207 PITCH (0ES) C RUN 206 5.0 TIME IN IIINUTES 30. TJI1[ IN MINUTES TitlE IN MINUTES .1 41.11 . 'V.tP ti ',-vT'

'ir -311.0

TIME IN MINUTES TIllE 1H MINUTES

Li ,Lii

t i

T'i?

t!

15 31.0 TillE IN MINUTES 1)5 0 npendix 12 . 44 L . L. k L L £ i ¡ ¡ L i

! r'' '1

t'!

! ¶ I

t.1 iii4IiiLi, tL

.'''''

lit

LLLL

la il.

Li

I!!r(li1[cT.1Iptd1Ju)t

SKIBSTEKNJSK L P80 H A TO H J Li M L1N083 DRNMRfI11

The pitch motion in waves with different wave grouping. Beam sea. Full-scale values.

0 00 .0 -2. 00. 5.00 n

gj

k L 14.1 -,

!vL'i1

(40)

0 00 0. 00 -5.00 0.00 _{-1 .00} HUN 209 'fAN BEG) A HUN 209 TIME IN MINUTES

'w y v'-w '-0-v

w

V- 1F't

TIME IN MINUTES

.A A

. mk&

. A .

vi vvv'''5."

HU' 207 'tRW bEG) B WAVE SIDE (M) B .0 TIME IN MINUTES

ARA.

.AAAAIAII,

L

ì&AA

.. V

'

,y.

VVY

T..

TitlE IN MINUTES TIbIE IN MINUTES TIME IN MINUTES

1.0CL.. TRW BEG) C 00' .

AAAIAAAaAAgAAAAAÌlAA

A. w ,

y

y y

y

e y

y

V w

' w V

'

Y

W V

I

-Y

0.0 5.0 .0 HUN 206

SKI STEKN1SK LHBOfflR 10H i Uil L'vlGe'f

DRNMAMK

The yaw motion in waves with different wave grouping. Beam sea. Full-scale values.

-t .00.. 5.00 0,00 -5,0 WAVE HUN C 207 520E MC WAVE SIDE CM) A Appendix 13

(41)

5.00 0.00 -5.00 5.00 _.10 0 00 -5.00 A 5.û0.... SU)GE F110E (N) 4 .10 B

LLJUI

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gii.i

gi

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PI1 15.0 0.0 95.0 HUN 207 TillE IN luNUlES SUOGE rasct (N) 1111E IN MINUTES SU11GE F010E (N) C

TIllE IN 11INUTES 1111E IN luNUlES

ÌA11LAiL.A ALL

tI

''i'

.0 HUN 206 15.

.itIL4i

t

,IAba.kIltII

LI .1 i.

,S,à1tihLtAAII.i

IhiLii flL

I '' l

t''

,,,I,l,i,)

45 50. 0 TIllE IN MINUTES S ic IBSTE FNJ S LRB 0H IR T 09 JUN LTNG BANMA11N

The surge force in waves with different wave grouping. Beam sea. Fullscale values.

LlIttIl1

Lt LL

Lk.iLLL

I

IT

','.,.'.l..!.

r''

t

'rti

.Ir,(Il,II I. 15.0 ao. HUN 209 -5. 1111E IN luNUlES 0 00 .0 -5. o0 -5.00 O 00 0 00

(42)

0. GO 0.00 -5,00 00 o. 00 0.0 6.3 .. SURS FORCE (N) 5 A

W". 'W"' "r""

'"W'"

'W""

'r '' W' 'Je" '!?,I,!Y,'

P

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"WT

HUN 209 TillE IN IIINUTES 5,0

URVE SIDE Uil

B MU' 207

V.,

!V.

-

yIS

W

'

r-r" 'W

;0 :'

RUN 207 S.00.. URVE 510E (ii) C HUN 206

TIME IN MINUTES 1111 IN MINUTES TIME IN MINUTES 1111E IN luNUlES

30.0 -6.3 TIfl IN MINUTES 5Ç J BSTEKN1SK L MB 019M T OFiJUM L'fNG'V OANIIAITh 50

The sway force in waves with different wave grouping. Beam sea. Fullscale values.

Appendix 15 5. D_ URVE 510E ((1) 6.0 SUPS FORCE INI C 6.3 .10

SURS F0CE IN)

(43)

0.00 2.00 0.00 0.00 0 00 1W I1..M.fNT (NM) 6 RUN 209 ç 2.00 tPIJ rtrtEN1' (NM) RUN 207

*

A -_ a

V

' W

.,.," ¶

TIME IN luNUlES 5.0 .10 A -u 15.0

-I

30.0 Y

95:! ! V !

" Y

TIME IN MiNUTES

£A.a

-I

V u-W 1' V '

'

!

' '

.0 PLUN 206 -2. 0Q TIM.E IN MINUTES

S K J B ST E KN J S K LABORPIORI Uil L5ftG6'E

DRNMPM

The Yaw Moment in Waves with Different Wave Grouping.

Beam Sea. Full-Scale Values. 5. 00 IflWE 510E In) \ppendix .5. Q0.. TIME IN rtJNUTES -S. 00_

TIME ¡U luNUlES

2.00 thI I1IiEN1' lUft) 6 -2.00 1111E IN MiNUTES 5.00 WRVE SIDE (Il) -.2.. 00 5._00 W)YE 510E (n)

(44)

N u s I-0.00 '4.00 Li D w 0.00 0.00

9Ur' 209

0.50rREQ. RAD/S 1.00

0.00 0.50

i.00

91JN 206 rREa. RRO/S s. Li L)

0.00

0.00 9UN 20?

0.50

PrEQ. RADIS

t.00

SKJ5STEKNJ5K

LPQRTOfl IUM

LNG0'Í ORNIIRrnÇ

Energy spectra of wave A, B and C. Beam sea.

s

c.oa

1-PERK

S =

11.06

T-PRP(

S -

l0.73

D

102 5

5.12

102 S

9.69 SI.VPL.

'*.7'4E.00 SIG4.VRL. '4.6iC.00

TrST TIME -

60.13

TEST TIME

8.00

T-PEAK S

10.50

102

S =

9.76 Lt SIGPI.VRL. =

'rcsî

g

_60.13

'LOO

(45)

(.4 a s

I-z

s

o

0.50

L

w

0.00 0.00

RUN 209

1-PERK S g 27.50 102 S = 26.90 SIGN.VRL. = 1.12E+00 TEST TIME = 60.13 0.50 FIiEQ. 1-PERK S = 102

S=

SIGN.VRL. = TEST TIME L) 1-PERK S 102

S=

SISN.VRL. = TEST TitlE 29.47 30.21 1. 11E+00 60.13

SKIBSTEKNJSK

LRBORATOF JUM

LING8I DRNIIRRK

Energy spectra for surge motion

in wave A, B and C. Beam sea.

32.51 t . 00 RRD/S 1.00 171.90 o l.23E+00 60. 13 1.00 0.50 mEO. 0.00

RUN 206

i . 00 RRD/S

050

FIiEQ. 0.QQ

RUN 207

(46)

ç.J s s

z

SKIBSTEKNISK

LABOI9RTO

I Uil LYNG8Y DANMAHK

Energy spectra for sway motion

C

z

u, 25.0 0.0 1-PERK S 102 5 SIGN.VRL. TEST TitlE = = 121.3'4 2:3.13 2.08E+00 60.13 0.00 0.50 1.00

ç'J

RUN 209

rREU. HAD/S

s s s

i

I-50.0

_z

50.0 s 1-PERK S = 181.53 1-PERK S 171.90 C C 102 S = '48.6q 102 S = 52.9'4 u, SICN.VAL. TEST TIME = 6.1Q(+00 60.13 SIGN.VRL. = 6.69Ei00 1(51 TIllE 60.13 25.0 25.0

z

£

u (n

0.0

0.00 0.50 1.00 0.00 0.50 1.00

(47)

0.00 LOO C

w

Li

r

0.00 0.00

UN 209

0.00 I9UN 207

0.50 FAEQ. 1-PERK S = T02

S=

SIGN.VRL. = TEST TINE = 0.50 FAEQ. i .00 RRO/S E LU > ct LU

z

2.00 1.00 L) 0.00 0.00 I9UN 206 T-PERK 5 = 102 SIGN.VRL. = TEST TIME = 0.50 FÍiEQ. 21.94 13.61 i . BOE*00 60.13 i . 00 ejRo/5

SKIBSTEKNISK

LAB OHRTOR J UM LYNG8'( 0RNMRFK

Energy spectra for heave motion

12.43 13.32 i. 9'4E.00 60.13 T-FEtK S = T02

6=

SIG .VPL. = TES

TillE =

13.78 i . 00 ARO/S

I-z

21.71 l.66E+OO 60.13

(48)

0.0 10.0 0.0 SIN.VAL. = 3.76E+00 TEST TIME 60.13 0.00 0.50 1.00

AUN 209

FREU. HAD/S

20.0

£

Q

0.00 0.50 1.00

FIUN 207 FBEQ. HAD/S

10.0 W Q o -J cc 0.0 I

i

0.00 0.50 1.00

AUN 206

FAEQ. HAD/S

1LJ

SKJBSTEFNISK

Energy spectra for roll motion

LIRBOARIOI9JUM

LYUGBI DANMARK 1-PERK S = 3'4.96 102 5 = 16.06 1-PEAK S = 36.19 102 S = 12.67 1-PEAK S = 3'1.96 102 S = 13.25 SIGN.VAL. = 5.q3E+00 SIGN.VAL. = q.27E+o0

(49)

C.,' s I-1.00

I

T-PERK S 27.50

Q

I 102 S 18.61 SIGN.VAL. = l.23E.00 TEST TII1 60.13 0.00 0.00 TEST TIME = 60.13

A

TEST TIME = 60.13

SKJBSTEKNJSK

LRBOARTOA IUM

L'YNGØY DANrIRflK

Energy spectra for pitch motion

in wave A, B and C. Beam sea. £

-. 1 00

1-PERK S = 29.90 1-PERK S = 29.41

102 s 20.06 T02 S = 19.11

SIGN.VAL. = l.11E+00ì SIGN.VAL. = 1.08E-i00

0.00 0.50 1.00

AUN 209

FHQ. flRO/S

u

0.00 0.50 i . 00 0.00 0.50 1.00

RUN 207

FFIEQ. HAD/S

AUN 206

FfiEQ. HAD/S

0.50 CD 'u Q L)

I

- Q-0.00

(50)

0.50 ID

=

0.00 C" s

I

I--.

1 ₀₀

z

a Q (n 0.50 CD

J

Q 0.00 0.00

RUN 209

0.00

AUN 207

-I

z

1-PERK S = 93.76 Q 102 S = 56.44 SIGN..VAL. l.01E+O0 ltST 1111E = 60.13

SKI6STEKNISK

L P6 019 P 109 lUll

LYNGBY ORN1IARK u a I-0.50 CD Q o 0.00 1-PERK S = 89.69 102 S 59.40 SIGN.VRL. = 9.30E-01 TEST TIIIC = 60.13

Energy spectra for yaw motion

in wave A, B and C. Beam sea. c s s

s-z

u 1-PERK S = 103.I'I Q 102 5 = 48.80 0.00

AUN 206

0.50 FREQ. i . 00 RADIS (n SIGN.VRL. = 6.66E-01 TEST TINE = 60.13 0.50 FREQ. 1.00 R RD/S 0.50 FREQ.

LOO

nRC/S

(51)

z

O. N u s

I

9 t0 u

0.

0.00

RUN 209

SIGN.VRL. = 3.75E-iO'i TEST TIME = 60.13 1.00 ARO/S 0.50 FIiEQ. z Q.

SKIBSTEKNISK

Energy spectra for surge force

LIIBORPTQFUUM

LYNGB'f 0RNI1RFK ...

lo

z

T-PRK 5 29.'f7 1PERK S = 29.'f7 102 S 20.66 102 5 = 20.25 1PERK S = 27.50 102 S = 21.86 51GN.VL.

3.4e.0'ì

TCST TIIIC 60.13 SIGN.VRL. 3,39(+Qq TEST TIME = 60.13 i . QQ 0.00 BUN 206 0.50 FAEQ. HRD/S 1.00

0.00 AUN 207

0.50

"ea.

(52)

z

"J C., u, 0. 0. 4 10 0.00 II ₂₀₉ 4. lo 1-PEAK S 121.aq 102 S z 17.68 SIGN.VAL. 1.oqE.o5 TEST TillE 60.13 0.00

RUN 207

0.50 FREQ. t.00 ARO/S SIGN.VAL. q.57Eo5 TEST TIME z 60.13 0.50 FIIEQ. 1.00 flAO/S

z

0. 4 10 0.00

RUN 206

T-PEAK S = 171.90 102 s 516N.VRL. 5.05E+05 TEST TIME 60.13 0.50 FAEQ. 1.00 RADIS

SKI BSTEKN ISK

LRB0fflRTO9IUrI

LYNGB'r DANtIARK

Energy spectra for sway force

T-PERK S = 187.53 T02 S =

35qQ

(53)

0. 0. 12 4 lo 0.00 RU

207

T-FEP S = 103.14 TQ2 S 46.03 SIGN.VPL. 1..29E+Q6 TEST TIM.E = 60.13 2. T-FEAK S 93.L6 T02 5 54.46 SIG.\RL. = 1.98E+06 TEST TII1.E 60.13 0. 12 4. 10 T-PEK S = 89.69 T02 5 59.13 SIGN.VPL. = l.BGE+06 TEST TINE = 60.1-3

SKJ6STEFNJSK

Energy Spectra for Yaw Moment in Wave

LPBOPRTOFtJUM

A, B and C. Beam Sea. LYNGBI DPÑtIPftK 0.00

12 209

4 10 0.50 FAf Q. 0.50 FftEQ. 0.00 FtUNJ 206 i . 00 ftp / S 0.50 E FOE Q. i .00 ftP OIS

(54)

¿8u

LYNGUV

OENMAIK

VARIANCE

Mean, Maximum and Minimum Values for

Motions, Forces and Moment in Wave A. Beam Sea.

kijN

(HMN'i.L

g Q9

NO

M.AN

VARIiJC

OATA MMX VAL.

MIN VAL.

<AV

(M)>

-1.96E-0e

1.41+O0

6881

3,70E400 -3.24E+00

(SUkGt (M)) 21. 1.341-01

7,69E-02 bØ1

9,93L-OJ. -5,50E-01

cSuy

(p4)> 22

-1.32E+00

2.65c.-01 681

1.98E-01 -2,TAE+O0

(r4Avt. (Nl)> 23

9,bQ-0d

2.35e-01 6881

1,'1E+00 -1,05E+00

(NlOLL (Ei,)>

24 1.O1E-01 d.91E.-01 bdäl

2,52E+00 -2,30E+00

<PITCri tOG)>

-2.34t.-O

9,611-02 6881

7,91E-01 -8.511-01

(Y#v tO.G)> 26 -7,2i1-0c

2.5S02 6881.

3,7S101

4,94101.

(SL).. FO<Cc. (N)) 34

3.55E+03

8,91+0T 6881

2,961+04 -2,22E+04

(swAY F)RCE

(N)>

..8.87+0'+

2,091+09 b881

.921+04 -2,A7Es'05

<YM

MOMLNT (NM))

36 -.1.071+05

9,60+10 6861

7,48105 -1,01.+06

C US TO <

iMV.

GROW' TESTS

>

LATL.

9 APk i90

SÇALE

1.

(55)

ÇRR NU.

COSTCTIE :

CAlL

SOALE

CALj RUN

_LHANNEL

(1AVE SILTh.

(M)>

'(SURGc, EM)> '(SWAY

(M)>

(HAVt

(M)>

(ROLL (UL)>

(PITci-1 (QE3) (YA

(UG))

'(SURGe. FOCL (N)>

(SWuY FORCE (N)>

<Y

QMENT (NM)>

< VE. GROUP TESTS >

29 IPN 1980

1 ;27,so

SHIP100

NO MEAN

VAkIANC

øOATA MAX VAL.

MIN VAL.

Mean, Maximum and Minimum Values for Motions, Forces and Moment in Wave B.

Beam Sea.

15

1.i1E-0

i,37E+00 6881

4,80E+00 3,88E+O0

21 1.31E-01

9.76E-02 6881

1,43E+0O 8,29E-01

22

1.57E+0O

2.76E+00 Ö881

2,i7E+O0 7,O6E+O0

23 8,33E-0c

1.78E-01 6881

1.48E+Q0 1,loE+00

24 1.25E-01

1.87E+00 6881

5,49E+00 3,63+Q0

25

-2,53E-02

7,71E-02 6881

9.O1E-01 1,05E+OO

26

1,29E-02

6,12E02 6881

7,84E-01 6,43E-01

34

3.19E+03

7,58E+07 bd1

3,74Es04 2.54E+04

35

1,OSE+O5

1,53E+10 6881

2,35E+Q5 4,93E+05

36

9.92E+04

2.33d+11 6881

1,85E+06 1.17E+06

MNI5H SHIP RESEARCH LAtSONTORY

(56)

CRLR N.

C US TO

ÇATE

5CAL ¡

CALIb

<HAVE S1D

(M)>

(SUFG. (M)>

<5qY

(t'i)>

(MEAVt (M)>

<RULL (UE()>

(YM. cLtG>

<SL)rGL rOCL

(N)>

<r FURC. (N)>

<YAw MOMEIT (NM))

<

_{WAVE GROUP TSTS}

>

¿S APR ).90

i SHIP loo 15

1.66E-02

1.45E+0u b8bl

¿1 1,41E-01

7,81'O2 6881

¿2

i.Ö1E+o0

3.12E+00 8881

¿3

9.02E-02

2,05E-01 0881

¿4 1,09E-01 i.1SE+O0 688). 25

-3.32E-02

7,35E-'02 8881 26

_2.19E-02

5,27E-02 6881

34

_3.40E+Oi

7,16E+07 a1

35

_l.03E05

i.77E+10 6881

36

9.63E+04

1,99E+11 6881

Motions, Forces and Moment in Wave C. Beam Sea.

4,.jOE+00 3,88E+OO

1.23E+00 7,85E.-01

3.11E+O0 7,19E+00

l,73E+00 ..l,39E+00

3.69E+OQ '3.À4E+Q0

8.61E-01 8,74E.0i

6.79E-01 6,71E»Oi

3.11E+04 2..9E+04

¿.34E+O5

).3E+06 1,28E+06

2600

LYNGY

OENMARK

VARIANCE

(57)

0.0 0.0 0 00 0.0 _-6.0

sutIct (n)

C

0 00

q

Tint IN MINUTES TIME IN NINUTES

HUN 201

S I1b S T E 1N ISK LA0HRT0H1 UM L'!NGB't

OANMRBI(

The surge motion in waves with different wave grouping. Bow- quartering sea. Full-scale values.

i 4h ..

¡A.

'vyvrv T'7T

!

IVy!Y'YT!'

'J!T1

wrYP!rY

r7'

TIllE IN MINUTES o oo q .0 !r.wryv!.vnuyI!!y,PTv'Y wr!rPr r

'r',wr'r

HUN 205 TIllE IN MINUTES 6.0 . WVC SIDE (1) A Appendix 30 HUN 205 SUA6t (M) A -6.0 5.00 -5.00_ 6.0 URVE SIDE (ti) C TIllE IN MINUTES WAVE SIIJE (Il) B 6.0 HUN 203 SUBOt (II) B -6.0 5. 00 TInE IN MINUTES

(58)

0.0 OU RUN 205 -8.0 TillE IN MINUTES 8.0 .... SUA) (M) _B 00 -8.0 6.0 0.0 RUN 201 -6.0 TIME IN MINUTES 0.0 '

rvw'

'-RUN 203

WAVE SIDE UI)

C . -r i 'w" RUN 201 I TIME IN MINUTES . ______

SKIBS1EFNJ5K LRROFiATORJ UM L')NOBY

UANMAMK

The sway motion in waves with different wave grouping. Bow- quartering sea. Full-scale values.

6.0 IJPVE SIDE (M) A Appendix 31 RUN 205 SUA') (M) A -6.0 6.0 TIME IN MINUTES 6.0 SUA') (Il) C 6.0 -TIME (N MINUTES -8.0 TIME IN MINUTES

(59)

0,3 0. 00 Q. C -4. UC. 6.0 0.0 -6. 0 q 00 -6. 0 0,00 RUNS 20 -6.0 T1tI..E IN tUlUTES 4.00...' III6VE (rl) A

iii)

Ii,,ilI,,,i(IJi,iIi,,,,LILI.11t.Ijl,,.,t iti,tI.I

1i1 .111,1,,

III ,IIlIIIIt,,I,t,It,t,t,I_III.I,lII,t,,l,l,,l,i,,.IIIlI,iIIIIJI,,,i,i,,,Ili.iI,I

IiI.I,,ljII,l,,,,.i.lII

I,

'II

II

I'

Il I' '7 t 'I ' ' I

I'')II)''tI'It It

''

''t'tpt

U4 205 0 00 RUI2Û3 -4. 00.. 6.0 j URVE SIDE (Il) I II,

't

t'

t It,

' lIih.,iuii

i It.

.4,it,,ituLi

.LIiI1L,, i.,ILtLLI,th,,,.

tut iIl,ttj4IIjtit,i

,Iu[L,4I,I.tijI

a..

iIL,i,hIi

t, .,

'''

. t, 'u I rtLpVt Ill) B RUN 201 30.

lUit IN IIINIJTES TillE 1M ttUiUTES TIME IN MINUTES

I .

.i

.Id. II I.,I.,tLIiI,...

Lt

LI Ia,JLt.,,iI,t Ji&I

ti Ikl

li

(f t ' t '' I'

''J,'

I, .11 tt. 1 t,,. l.a TitlE 1H FtII'iIJTES

SFUBSTEINJSK LP8ORPTORJUM L1NG'I

OANITRIIK

D

The heave motion in waves with different wave grouping. Bow- quartering sea. Full-scale values.

4.00 HEAVE (M) C IJAV 510E UI) A 6.0 Appendix 32 (5.0 30.0 45.0

(60)

0,0 00 O. T OD

RUN 20

-6.0

TillE IN MINUTES TIME IN 1JNUTUS

RUN 203

6.0 j

WAVE SIDE Ill) C '-6.0 - 6.0 MOLL IDEO) C RUN 201 TIME IN MINUTES

SKI 5STEKNJ 5K LRBORRTDRJ Un L'ONG8'Y

QANMNfIK

The roll motion in waves with different wave grouping. Bow- quartering sea. Full-scale values.

6.0 WAVE 010E CM) A Appendix 33 )1LL IDEO) A 6.0 OD RUN 205 -6.0 TIMI IN MINUTES 6.0 -MOLL IDEO) B

-TillE IN MINUTES TIllE IN MINUTES

(61)

-0.0 0.00 0 00 0.0 RUN 205 -6.0 TiME IN MINUTES FUN 205 i I .t I h t ¡ . L i

i i

i I t I i

I3'.I,,fIr!!',

i "r!'I

r!(l

)I'T

o FIUN 203 -4. 6.0 URVO GIME (Il) 4.00_ FITCh (MEG) C 0. 00 8UN 201 TiriO IN IIINUTES

IL

ii.

eli

''

!!Ij!hl

i1!Çh1'

SKI BSTEKN 15K LABOFiRTBFI J UM L'1N0614

ORNMRMH

L

I

i

T

'1 _{The pitch motion in waves with} _{different wave grouping. Bow-} _{quartering sea. Full-scale values.}

URVO 0J0 (ti) A 6.0 Appendix 34 PITCH (DOG) A 4.00 -9.00 6.0 0.0 -6.0 TillE IN MINUTES 4.00.... PITCH (0CC) B -6.0 TIMO IN MINUTES -4. 00..: 1111E 114 1INUTOS

(62)

6.0 WPVE 5110E III) A 0.0 -6. 0 6.0

UIVE 010E (MI

B 0.0 0 00 0.0

...

AA A ..Jk.

A A k

. .

Às.. Ms. À& ...

g. i*..j.M. 15.0 30. 0 RUN 205 TIME iN MINUTES -2. 9UN 20 RUN 203 TOIIC IN MINUTES

£AAk £Ai

kLi1.LA.A

y 150V VT

W V

'

ir"

r'

-W

!

'« TIllE IN MINUTES

SKI 5STEKN 15K LRBO9HTOR I UM L'INOal

DPNMRMM

The yaw motion in waves with different wave grouping. Bow- quartering sea. Full-scale values.

Appendix 35 0 00

.iAAAA,AâAALlI.Ag,AA.

uAgLAA_AA

q.0 W

!

V

'i

!

300 r

-"v

HUN 201 2. OIL. 'MMII IDEO) B -2. OIL. TillE IN MINUTES 6.0 MInNE 510 IM) C -6.0 TIllE IN MINUTES 2.00... 'MMII IDEO) C -6.0 T1FIC IN MINUTES

(63)

6.0 WF1VE 510E 0) A 0.0 _-6.0 6.0 0.0 0 00 0.0 0 00 -5. 00...

'r -:

RUN 20

SUOGE EaRCE (NI

B SUOGE FORCE INI C

'r '

-I1T!W RUN 201

TIME IN MINUTES TIME IN MINUTES

A

'T '

'r

-.

''7','

-..

'w

TillE (N MINUTES Appendix 36 y TIME IN MINUTES p,'p'vr -'"w-'

T

SKI BSTEKN 15K LABOt9RTOR I UM L'TNG6Y

OPNIIAMK

The surge force in waves willi different wave grouping. Bow- quartering sea. Full-scale values.

O .10 0 -5. 00 00 SUMOE ESIICE A IN) .0 RUN 205 Q0..

y VI'T

iwv' -T'

15.0 'r U. 11 TitlE IN luNUlES

'T!

V'IV' !y' "

v'rww'

vw- 'y -w" ,'v"

q 0

"

RUN 203 WAVE SIDE (M) C 1111E 111 MINUTES -5.00.: 6.0

(64)

6.0 o. o -6.0 5.00 0.00 -5.00 6.0 O. Q -6.0 5.00 _.10 0 00 -5.00 6.0 0.0 -6.0 5.00 _.13 0 00 -5.00 o a .0 wRV SIDE (M) A SWAY FMCE (N) A OUN 205

WAVE SIDE IM)

B

SWAT FOMCE IN)

B TIME IN MINUTES

w

w' w

'

w'

'

-w'

'

TitlE IN MINUTES TitlE IN MINUTES

WAVE 510E (M)

C

SWAY FORCE

(N)

C

TIME IN hINWIES TIME IN MINUTES TIME IN (1INUTES

SKI BST[KN ISK L IB O

OR J UM

LINGOT

DANMAMK

(65)

0.0 0.0 0 00 0.0 -6.0 4.00 YAW MOttENT IN(I) 10 000 âI

A

kA

àL

L

g LL.

V t'IO

Ç ''

V RUN 201 -4.00 TIME IN MINUTES 30. 0 TIME IN MINUTES

AA.

&AaM

r

!

j''

IT

45.0

SKIBSTEKNISK LPBORPTOR I UM LYNSO'!

EANMARK

Appendix 38.

6.0

WAVE 510E

((II

The Yaw Moment in Waves with Different Wave Grouping.

Bow-Quartering Sea. Full-Scale Values. RUN 205 -6.0 TIME IN MINUTES 9.003 YAW M0MENT (NM) 6 0 00

g, A

J

.&. A

bk.. *t ..*u. i. .

...ú .i

k.

.L ,M

it

L

gil

RUN 205 -q ou TIME IN MINUTES 6.0 WAVE 310E (M) RUN 203 -6.0 TIME IN MINUTES 4.003 YAW MOMENT (NM) 6 .10

£

.

£

AA A

L

4A1.M.

....âLLá4I,LAÀ

.Aí

T

V T T W

e')" ''

V V! 1 15.0 .0 45.0 RUN 203 TIME IN MINUTES

(66)

N 8.00 0.00 ('J 6.00 s Q 'z N C,-, t.., Q 's II.) L) 'z 0.00 0.00

AUN 205

T-PEPK S 10.90 102 S gqj SIGN.VPL. '1.92E#QQ TEST C = 60.13 T-P(PI S Q 102 S 9.?0 'z SIGN.VPL. 'i.72E+00(., TEST TIME = 60.13 L) Q -s L) 'z L) 0.00

SKJ8S1KNJS

LP5OHPT0 JUM

L'ÍNG'r DRN7IRFIP(

Energy spectra of wave A, B and C. Bow-quartering sea. 6.00 T-FRK 5 = 10.90 T02 S 5IGN.VRL. g TEST TillE L 60.l q. ou 0. 00 0.50 I 00

9UN 203

FrICO. FIPC/S

0.50 '1 00 IR0JS _N I-0.50 rMCQ. 0.00

9UN 201

i . 00 R140/S

(67)

5.00

r

LU C.D u-I 0.00 0.00 0.00

RUN 205

0.00

RUN 203

1-PERK 5 = 36.19 102 5 27.19 SIGN.VAL. = 2.qeE+oa TEST TIME = 60.13 0.50 FREQ. i. 00 BAD/S 0.00 T-PEF S 206.28 T02 S = 30.91

5IN.VRL.

3.25E400 TEST TINE = 60.13

SKIBSTEKNJSK

LP6ORTOR I UM

LYNGß ORPIMARK

Energy spectra for surge motion in wave A, B and C. Bow-quartering sea.

0.50 FAEQ. i . 00 BAD/S 10.0 T-'ERPÇ 5 = 171.90 102 5 33.09 SIGN.VRL. = 3.99E+00 TEST TUlE = 60.13 5.00 0.00 0.50

i

00 RUN 201 F FIE Q

(68)

L cc (n 15.0 0.0 15.0 0.0 T-FER S 121.3 T02 S 33.37 51GN.VIL. = 3.28E+00 TEST TIME 60.13 30.0 T FERN S 158.68 s cc _T02 ₅ L.j355 cc cc (n SJGN.VA . 5.50E+00 TEST TJME 60.13 30.0 15.0 0.0 T-PEPK S

t8L53

T02 S 30.65 SIGN.VPL. '1.'19E+00 TEST TIME 60.13

SKIBSTEKNISK

LP6OhPTOR JUM

L'NG8'r ORNMRRK

Energy spectra for sway motion in

wave A, B and C. Bow-quartering sea. 0.50 FIEQ. 0.00

RUN 205

RPO/S 1 .00 0.00

RUN 203

i . 00 RD/S 0.00 RUN 201 i .00 FiR 0/S 0.50 FIEQ. 0.50 FFiEQ.

(69)

0.00 0.00 O 00

RUN 205

T-PEÇ1K S = 12.43 102 5 = 13.'P4 SIG VPL. = 2.52E400 TES 1111E = 60.13 T-FAK 5 = 2l.9 102 S l3)15 SIGN.VAL. 2.30E*00 TEST TJt'tE 60.13

liii 1I,I1JI

tu

>0

cE tu 1 .50 0.00 T-PEAK S Il.'L2 102 S 13.13 SIGN.VRL. 2.ISE+00 TEST TIME 60.13

SI'UBSTEKNJSK

LIRBOHPTOI9 J UM L'TNSB'. 0PNMRK

Energy spectra for heave motion in wave A, B and C. Bow-quartering sea.

0.00 0.50 1.00 0.00 0.50 i .00

ftUN 203 FAEQ. ftRD/S RUN 201 FREQS fipo/s

I . 00

açH3/ S 0.50

(70)

0.00 0.00

RUN 205

T-PEAK S 36.19 102 5 l'1.63 SIGN.VAL. = 3.51E400 TEST TIME = 60.13 0.50 FAEQ. MAO/S i .00 (N 8.00_t LIDO 1-PEAK S 36.19 -Q T-PERK S = 37.51 102 S = 11L'-P4 102 5 = 15.61 SIGNI.VRL. = 3.8SE+00i SIGN.VRL. '4.1IE+00 TEST TIME 60.13 T[5T TIME = 60.13

1 Jc) -j D D a: a: 0.00 0.00 0.00 0.50 i . 00 0.00 0.50 1.00

RUN

203

FMEQ. MAO/S RUN

201

FAEQ. MAD/S

SKJBSTEKNJSK

Energy spectra for roll motion in

r)ft

LR5ORPTORIUM

wave A, B and C. Bow-quartering sea.

(71)

s-(D D

z

Ci

I

a-0.00 3.00 0.00 I-PEAK S = 27.50 102 5 19.02 5IGN.VAL. 3.25E+00 TEST TIME = 60.13 I s-

-z

T-PEAK S 32.23 D 102 S = 19.96 SJGN.VAL. = 3.60E+0Q TEST TIME = 60.13 CD lai D 3.00 0.00 T-PEAK S 32.23 102 S 19.63 SIGN.VAL. = 3.55E+00 TEST TIME = 60.13

SKJBSTEKNIJSK

LRBO9RTOF9 I UM LYNGBY OANMRRK

-Energy spectra for pitch motion in

I . 00 RAD/S 0.50 FREU. 0.00

RUN 205

0.50 F REQ. 0.00

RUN 201

1.00 RADIS 1.00 RAD/S 0.50 FAEQ. 0.00 RUN 203

(72)

(D

w

C

4:

0.00 0.50 1.00

AUN 205

rBEQ. BAD/S

s-

-2.0

z

0.00 1-PEAK S 89.69 C 102 S =

SI6NVAL. 1.&7E+UDì SIGH.VAL. = 1.66Ei00

TEST TIME = 60.13 TEST TIME = 60.1

I . 00

CD

J

e0

O 00

SKISTEKN1SK

Energy spectra for yaw motion in

LING8'I' OANMRRK

LAB0FAT0H JUM

('J s s s-z 00 1-PEAK S l03.i' C 102 S = 32.'l SISN.VAL. = LO'4E+0O TEST TIME = 60.13 I . 00 1-PEAK S = 69.69 102 S = qQ55 0.00 0.50 1 .00 0.00 0.50 1.00

AUN 203

FREQ. BAD/S

AUN 201

FBEQ. RADIS

s-2.00 a C U) 1.00 CD w C 0.00

(73)

w

C-)

u-w

C.D U) a. 0. 5 10

c1

l0 0.00 205

510

1-PEAK S 121.3q 102 5 23.59 SIGN.VAL. = l.qoE+05 TEST TIME 60.13 Q 102 s = 31.68 SJGN.VAL. 2.29E+055 TEST 1111E = 60.13

z

0. I0 5 10 1-PEAK S = 206.28 102 S = 26.qi SIGN.VPL. 1.93E+05 TEST 1111E = 60.13 0.00 AUN 201 0.50 FREU.

SKIBSTEKN.ISK

Energy spectra for surge force in

LRBORRTOR TUFI wave A, B and C. Bow-quartering sea.

LYNGBY DANMARK 0.50 FREQ. i S00 RAD/S 0.00

AUN 203

0.50 FREU. i . 00 RAD/S C.,J

z

1-PERK S 158.68 .

(74)

O. 0.

lo

o.oci 11RUN 205 o 0.00

RUN 203

1-PEAK S =

12l.3q

102 S = 19.37 SIGN.VRL. = l.78E+05 TEST 1111E = 60.13 0.50 FIiEG. 0.50 FREQ. 1.00 8110/s 1.00 BAD/S SIGN.VRL. = 3.0qE+05 TEST TIME = 60.13

z

0.

lo

0.00 RUN 201 0.50 FREQ. SIGP4.VRL. = 2.'49E+05 TEST TIME = 60.13 1.00 RADIS

SKJBSTEKNJSK

Energy spectra for sway force in

LRBOFATOI9JUM

LYNgB'V DANIIARK

-4

z

1-PERK S = 156.68 _D T-PERIc S = 206.28

(75)

0. O.

10

13

SIGN.VRL. = 2.05E406 TEST TIME 60.13

S1GtLVL. =

2.93E*06 TEST TitlE = 60.13

r

z

E E 0.

lo

13

T-PERK S 89.69 T02 S = 40.57 5JGN.VRL. = 3.25E+06 TEST TitlE = 60.13

SKJBSTEKNISK

LRBOftRTOPL.I UM L'9G5? ORNMRFIK

Energy Spectra for Yaw Moment in Wave

A, B and C. Bow-Quartering Sea.

lo

0.00

13

205

0.50 I EFLEQ. RRO/S T-FERPÇ S 89.69 T02 S = 35.26 .00 ç'J

I-z

T-PEAK S = 103.14 T02 S = 27.43 i . 00 FIR 0 / S 0.50 E RE Q. 0.00 PLLJN 203 1.. 00 PLR O / S 0.50 EFtEQ.

0.00 NUN 201

(76)

NI5r$ SHIP NESERCH

LAQPTORY

2Q0

LYNGY

OEMIARK

VARIANCE

CtR NO,

¡

COSTQER

¡ OMIL SL ALE

CALW

UN CHANNEL

(iAVE 510E (M)

(SUkG. (M)>

(M)>

(HEAVE EM)>

(ROLL (OE(.)>

(euCH (UEG)>

(YA _(CEO)>

(SUrE

0RCE (N))

(SAY FORLE (N))

(YAw rlOîENT (NM))

( wV

GROUP

TESTS

>

29 APk 2980

1 127,0 SHIP 100

MEAN

VARIANCE

sCATA MAX VAL,

MuN VAL,

Motions, Forces and Moment in Wave A.

Bow-Quartering Sea.

15

-1,36E-02

1,60E+O0 6881

4.37E+00 -'4,20E+0O

¿1 6.70E-01

3,80E-01 6881

7,94E-01 -2,68E+00

22

_-9,50E-01

6,51.-0I

881

1,32E+00 -3,49E+00

23 1,70E-01

3.96E-01 681

1,91E+00 -1.31E+00

24

1,34E-0e

7,68E01 6881

2.$4E+00 -2.47E+00

25 .73E-02

5,bSE-01 6681

2,20E#0Q -d,21E+00

26 1.80E-01

6.27E-02 6861

1.12E+00 -4,37E-01

34

_-4,31E04

],20E+09 6881

4.56E+04 -1,62E+05

35

_-S,S1E+04

1,94E+09 6881

9,25E+04 -1,82.05

(77)

CR.)ER NO, ¡ cus roMER LAIE SCMt_E RLJ

OMuNNEL

O3

( NAVE GROP TESTS >

29 APR 1980

1 ¡27,50

SHIP1QO

NO MEAN

VARIANCE

ATA MAX VAL.

MIN VAL.

Motions, Forces and Moment in Wave B. Bow-Quartering Sea.

(WAvE SIDE (M)>

15

-1.63E-02

l,52E+QQ b33

5.13E+O0 -3,79E+00

(SUíGE (M)>

21

-8,43E-01

8.11E-01 b881

1.64E+Q0 '-4,09E+OO

(SW.Y CM)>

22

w1.32+0Q

d.OÔE+0Q 6883.

2,bOE+OO -7.42E+00

(HEAve. (M)> 2.3 1,58E-01

3.31E'Oi

al

2..9E+00 -1,98E+00

(ROLL (LE()>

24

7.71E-0d

9.29E-01 6883.

4,07E+0O -2,64+QO

<P11CM

DEG)> 25 S.64E..03 8,51F-03. 6881

3,37E+OO

-3.09E+O0

(VAn (CLG)>

26

1,7E-01

1,35E-01 6881

1,31E+00 -9.91E-01

(SUk

FORCE (N)>

34

-5.65+0'.

3.SbE+09

6a81

1,Q2E+05 -2,74E+05

<5AY FuRCE (N))

35

-?.26E+04

6,21E+09 6881

1,15E+05 -3.'.3E+Q5

(YAw MOMENT (NM)>

36 .3.58E+OS