Influence of wave climate modelling on the long term prediction of wave induced responses of ship structures

1. INTRODUCTION

In the context of a reliability approach to ship structural

design [1,2], it

is necessary to consider all the steps that lead

to the prediction of the design values of the load effects on the ship structure as well as the ones involved in the

quantification of the various strength criteria and in

the formulation of the design goals.

A particularly important aspect is the prediction of the

wave induced loads and motions in any type of marine vehicle or structure. The established approach starts from a

probabilistic description of the wave climate and from (lie

transfer function of the response of interest. The latter

is

generally obtained by methods based on the

linear strip

theory, although more sophisticated numerical methods or

experimental approaches are poasible alternatives. A

short-term analysis yields a response spectrum, from which (lie

probabilistic properties of the response are derived. A

long-term model is constructed by uiiconditioning the short.teriiì

response on all the parameters that it depends oil. The

long-term model is often the basis to extrapolate the reference

values adopted for the design.

Several sources of uncertainty in the above refered procedure have already been considered in previous studies. lii

the short-term situation, the effect of the uncertainty in the

shape of the sea atate spectrum has been considered in

[3]

while the effect of (lie uncertainty in the transfer function is

explored in [4].

When constructing the long-term model based on the

short-term results it is necessary to

use a probabilistic

description of the wave climate. On a worldwide scale, there are some compilations of wave data available [5-8]. However, although they refer to a long period of data collection, ranging

from 10 to 20 years, the various probabilistic descriptions of

the wave climate do not agree with each other.

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INFLUENCE OF WAVE CLIMATE MODELLING ON TilE LONG.TERM PREDICTION OF WAVE INDUCED

RESPONSES OF ShIP STRUCTURES

C. GUEDES SOARES and M. F. S. TROVÀO

Naval Architecture and Marine Engineering, Technical Uiiiversity of Lisbon (Instituto Superior Técnico), 1096 Lisboa,

Portugal

A discussion is provided about (lie different sources of wave data which are compared so as to assess (lie existing degree of

uncertainty. The long terni distribution of different types of ship responses is determined for different wave climate

descriptions and the differences of the results are used to quantify the sensitivity of the response predictions. New results based

on hindcast wave cliiiiate description are compared with exist ing oiies derived from visual observations of waves. The effect of

the transfer function uncertainty on the long term predictions is also quantified and it is compared with the one due to the

wave climate uncertainty, showing that the latter is significantly larger.

An analysis of the uncertainties involved iii the

probabilistic descriptions of references 5 and 6 have beemi

reported in

(9] and [10] for the significant wave height and

average period respectively and calibration equations were

proposed to correct (hein.

More recently Hogben, DaCunlia and 011iver [7] revised

and updated the data from

[6],

introducing a significant

correction on the wave period data. The influence of using the

description of references 5 to 7 in

the long-term reference

values was studied

in [11], for various

types of marine

structures and responses.

lt

was concluded that the

10-B

design value could differ by as much as 100% when using

different sources of wave climate description while for

the same source, the differences between different ocean areas was only about 50%. Another study that considered the wave data

from different ship routes that cross various ocean areas is

reported in [12], where it is shown that the differences ou the resulting design values are only about 15%.

Those studies use wave data based ou visual observations of different type with amid without corrections. The available

descriptions of wave climate, which are based on measured

data often concerns more localized coastal regions [13,14]. A different basis of obtaining wave climate description is used iii

[81, which compiles the results of hindcast simulations

concerning a 20 years period on the North Atlautic. This work compares the i0 response predictions based omm this hindcast

wave data with the ones from visual observations so as to

complete the range of uncertainty that are due to the wave

climate description.

The uncertainty that can be ascribed to the wave chinate

description

is compared with the long-term predictioum that

affects the uncertainty in the prediction of transfer functions, so as to assess their relative importance.

2. LONG-TERM MODELS OF WAVE INDUCED LOAD

EFFECTS

The long-term models are constructed by building upon the various short-terni situations expected to occur during the lifetime of tite structure and weighting them iii an appropriate manner. The short-term results are based on a mathematical formulation that allows the derivatioti of the probabilistic properties of the process under study. On the other hand the long-term variation of the various parameters that influence the load effects to be experienced is of an empirical nature and thus, different probability distributions must be tested before

the best one is chosen.

In the short-term situation one assumes that the sea surface elevation can be modelled as a stationary Gaussian stochastic process. This implies that tIte amplitudes of the wave elevation are described by a Rayleigh distribution, in which case the probability Q9 of exceeding the amplitude x iii a sea state of variance R is given by (15];

Qs(xIR)=exp

_2R (1)

The variance R of the sea surface elevation cali be

determined from the spectrum SH of the wave elevation. It is in fact its zeroth moment;

R

=

f

SH(w) dw (2)

The wave spectra are described by theoretical models that have become established, lit fully developed sea states one can

use the ISSC parameterisation

of the

Pierson-Moskowitz

spectrum 116], while for developing sea states the JONSWAP spectrum (17) is the appropriate one. In combined sea states a

double peaked spectrum can be used [18].

The effect of adopting the different spectral models was studied in [3] and it was concluded that, while the short term responses are sensitive to the type of spectral model used, the long term results could be well established using only the Pierson-Moskowitz model in tite calculations. TItus, only titis type of spectrum will be used in the long-terni calculations

reported here.

The linear response to tite wave spectrum can be

determined in the frequency domnaiti as the product of the square of the transfer function H by the wave spectrum. where the effects of the directional spreading D(9) of energy in tIte

sea State can also be accounted for.

The transfer function will depend on the direction of the wave system as well as on the wave frequency. Thus the variance of the response is obtained by integrating both in frequency and over the various relative headings;

R()

=

J

J

S(m') H2(w,

+9) I(9) dO dì

(3) O

where is the main wave direction relative

to the ship

heading, 9 is the relative direction of the wave system relative to the main direction, D is the directionality function and the

response variance R(8) concerns tIme niairi wave direction 9.

Different functions have been proposed for the spreading function but a common one is a cosine type:

ir

D(9) = k costi(o),

_{- i < 9 <}

(4a)

where k is a normalisiiig con8tattt:

=

(f12

cos9

do)

- ir/2

It is common to adopt a value of mt=2 to represent a sea state with significant spreading. A unidirectional wave system can be represented by adopting large values of t. The different

types of sea states can be modelled using intermmmediate values

of the exponent n.

Since the response is linear with respect to the wave

excitation, it has the saine probabilistic properties i.e.. it cati be modelled as a stationary stochastic process. Thus, the probability of exceedance

of an amplitude

cati also be

described by equation (1) where tite appropriate values of tite

variance R must now be used.

To extend this short-term formulation to the long-tenu case one must recognise that these results are conditional oit a sea state defined by a significant wave height 118 and by an average period, as is implied in tite value of the variance R iii

expression (1).

Considering the whole lifetime of the structure, tite value of the variance of the response at a random point itt time cati be described by a probability demisity fumtctioit fR(r). Titus tite probability QL of exceeding an antplitude x at a random poimtt. in time during the structure's iifetimne cait be obtained by

uncondttionmng the short-term probability of exceedance:

QL(x)

=

Jw(To)

. Q(x)R) fR(r) dr (5)

where w(T0) is a weighting factor that is a function of tite average period of the sea state T0, and accounts for the different number of antplitudes that occur iii sea states of

different periods.

The probability density function of the response variance can have different aspects, depending on the type of structure. The most complicated case is probably the case of a seagoing ship where one must account for different load conditions,

headings, speeds amid evemm the voluntary changes of speed and heading that are performed under heavy seas.

Different forms of titis function have been proposed in the literature but probably the most complete one cali be found itt

[11] as;

fR(r) = f(9, V, T0, Ils, c) = f(°l"s) 1'D(0i11S) t'M(9]S)'

1M("t'S) r0 H5(t, h) fc(c)

(6) where f9 is the probability density function of relative

headings between the ship and the waves, which is usually

assumed to be uniform, f0 reflects the directionality of the

wave climate, M models the effect of manouvering in heavy

weather [19] both on the ship heading and speed,

_{T H}

is the

joint probability density

function

of average peros and

significant wave heights and

is

the probability density

function of ship cargo condition. This latter one cati be ait

homogeneous distribution as in the case of coiitaiiierships or

an heterogeneous one for the bulk carriers in general which

tend to operate in ballast atid loaded condition [20].

The probability density futiction of the response variance simplifies very much for the case of fixed offshore structures, in which case only the wave climate needs to be itiodelled:

fR(r) = 9

_T

H59' t, li)

(7) which includes already the effect of wave climate directionality in the mean wave direction 6.

Mobile structures like seini-submersibles

and Jack-up

platforms act like ships during transitiiig periods and like

fixed platforms during operation. Titus, they would require

both type of descriptions.

The long term distribution (eqit. 5) is used as a basis for

design. In tIte design related with fatigue strength the whole

distribution is of interest since it is tIte basis for coutititig tite number of stress cycles at different stress levels [12].

To design structures against collapse or other extreme

load conditions otte is often interested in predicting a value

large enough, not to be met more titan once during tite

structure's lifetime. This is tite rational behind tIte use of a

return period between the occurrence of these extreme events.

A return

period larger

than a structure's

lifetime is required for an acceptable level of probability, as discussed for example in (21]. The periods commonly accepted for offshore

structures are

101) or 50 years but for ships it

lias been

common to consider the characteristic

value at tite 10-8

probability level, which corresponds to tite nutitber of wave

cycles to be expected in a period of 20 years of operation ofa

ship without stop. These values can be obtained from tite

empirical probability distribution of the wave climate (eqti.7)

or from a theoretical niodel that is fitted to the measured

date.

lt is worth mentioning that when one considers fitting tIte

measured data with theoretical distributions there is not one

that is completely suited. In fact several probabilistic methods will pass formal statistical tests of fit but they will yield quite different characteristic values, as was indicated in [22].

A Bayesian approach was adopted in [22] to coin bitte tite

information of various prediction methodsin a way that

minimizes the variance of the predictions.

lii the example considered the range of the predictions of extreme wave height using different methods went froto 22.5m to 349m, while for the Bayesian predictions it narrowed from 269m to 27.Snt.

1. WAVE CLIMATE MODELLING

Tite model of tite wave climate is made iii two hiffereiit

time scales as already indicated in tIte previous sectioit. 'lilie short-term descriptioti is summintariseci iii tite wave hemgitt

spectrum and tite bug term model indicates how tite spectrai

parameters vary in large tinte scale. TIte bug terni model is

empirical in

nature and

is built front measurements or observations in differeitt ocean areas, to which it concerns.

The first

type of ocean wave statistics

that becattte available was based on visual observatiotis of tue waves wlticlt were performed either iii statiottary ocean wave meteorological stations [5] or iii transiting ships that were reporting observations in a voluittary basis [ti]. This type of observatiotis

cover large ocean areas like tite North

Atlantic [5] or eveti

worldwide [6].

Another type of wave statistics result front utteasureinetits

made with buoys of tite waverider type. However they are

more bocalised in coastal waters [13, 14].

The visual observations of tIte wave properties itave a

larger variability than the measurements. ilowever because

there are very many observatiotis acumuhated it is possible to

obtain good estimates of tite nican values of tIte observed

conditions and tue dispersion tends to decrease. Titis lias weit studied iii [9] and [10] for the observations of tite wave height atid period respectively.

lii

addition to reviewing ail tite previous work oit

tite subject, those papers proposed calibration equations that are

based on regression studies atid which correct

tIte visually observed values to yield the spectral parameters that would be measured

by a waverider

buoy.

lt

was foutid that tite observations in Ocean Weather Stations had different

characteristics from tite ones of transiting ships. Titus two

differetit calibration expressions were proposed.

A differemit approach was taketi by Baies et al [8], who adopted hiindcast modeis to predict the evolution of tite wave

spectra in the North

Atlantic, based on inforiuiatiout of tIte wind fields. Using the spectral paranseters titat were obtaitted at regular tinte intervals, a statistical coutipilatioti of tIte wase parameters was produced [8]

as an altermiative to existing

sources of information.

The authors are not aware of published

consparisomts

between the hong territ distributiout based on visual observations and on these Iiittdcast predictions. The comparisons indicated in figures

1 and 2 coticern the whole

North

Atlantic, which are obtained by combining the data

from ail ocean areas of the North Atlantic. Incidentally, this

was done by combimsing tite density functions so that tite fluaI results would not be biased by atiy particular area which could have more observations that others.

The probability density functiomt of significant wave height

that is obtained from the data sets of Hogben et ah

[7] aitd

Bales et al

[8] agree reasonably well.

Tite distribution of

Walden's data [5] has a larger percentage of waves of low

significant wave height, around 3m and a smaller frequency iii waves of 6m.

0.5 0.4 0.3 0.2 0.1 1.2 0.8 0.6 0.4 0.2 o o b.I*s.L SL -+- Hogb.n S -*- lICOSa 1. al, -a- W.Id.n 5 lO

Significant Wave Heigth

Figure lb. Probability distribution function of significant wave heights iii I.lre North Atlantic

given by different data sets.

A similar situation occurs for the average period data. The two most recent wave data sets [7, 8) agree relatively well but show a tendency to larger periods that the existing data sets. The long term average of tire mean wave periods differs

by about 2 seconds in these two sets of data.

The ISSC paranneterizatiorr of the Piersorr-Moskowitz

spectrum includes as a parameter ari average period given by the first (m1) and the zeroth moment (in0) of the spectrum (T0=m0/m1). This value can be directly related with the observed periods that are reported in the data of refs. 5 to 7.

However Bales et ai [8] reported tire long terrir wave

statistics in ternis of tire peak period of the spectrum or tire modal period as they call it. Therefore to use their long-term data with a spectral formulation based ori T0 ¡t rs required to transform the peak periods T in average periods, in the case of a Pierson-Moskowitz spectrum this is easely done by

observing that tire spectral peak occurs at tire maximumof the function i.e. when tire derivative rs zero. in this case

T0=l.296 T.

I5 0.3 0.25 0.2 0.15 0.1 0.08 -. Bai.. .r. SL -- Hogs.. ¡ LosS -*- rIoOl.n Ir. al. -a- W.id.n

- 6.4.. r. al

4 HOGSOS L Lomb Plesbin .t al -a- w.Id.n

Figure 2b. Probability distribution function of nnrearì wave periods irr tire North Atlantic given by different data sets.

When comparing tire four different data sets one nrrust

keep in mind that the data of Hogben et al

(6, 7] being

obtained from transiting ships has inbuilt tire effect of tire normal bad weather avoidance, and tends to have a surlaller percentage of high seas tiran one would expect in observations at fixed locations like in tire case of Walden [5).

The statistics of tire hiirdcast predictions of Baies et ai [8] are based only oir nrreteorologic data and thus should be compared directly with Walden's set.

4. UNCERTAINTY IN THE PREDICTION OF

TRANSFER FUNCTIONS

Presently most of the predictions of wave induced niiotionis and loads in ships are based on the-linear strip theory, despite the availability of some results based on difractiorr theories. For large offshore structures tire hydrodynarnic forces an-e

normally calculated from diffraction theories.

Figure la. Probability density function of Figure 2a. Probability density function of nirearr

significant wave heights irr the North Atlantic wave periods in tire North Atlantic given by given by different data sets. dïfferent data sets.

o 6 10 18 20 25

Mean Wave Period

o 6 lO 15 6 10 IS 20 25

From a mechai cs point of view. the theoretical

predictions of the linear strip theories have coiiipared satisfactorily with the results of experimental studies. It has been shown that iii general the agreement is better for siiip motions than for the wave induced load effects.

Froni the point of view of probabilisticalv based design, one is interested in quantifying the uncertainty involved i,,

that prediction process as well as any systematic deviation that the theory might be producing. This was the approach taken in [4]. where the theoretically calculated wave induced

bending niomeiits in ships [23] were compared with

Ineasurenielits and a model uncertainty function was derived.

The modelling error was defined as [4]:

(8)

where ÍI(i) was the ideally correct

value of the transfer

function, as determined for example from experiments, and H)ii) is the theoretically predicted value, If one considers that the experimental errors can be removed before Il is quantified,

will measure the errors of the theoretical model.

In principie, cali be a linear function of the frequency:

Ø = a + bw ('J)

but in [3] it was concluded that a constant would be accurate enough on the average along all frequencies iii any given transfer function.

This constant was determined from a regression analysis on many results and it was fouiid that the miiodehhiiig error,

would vary with the speed V and the block coefficient CB of

the ship as well as with the relative heading 6. A linear

regression model was postulated to represent this effect:

=A9+BV+CCB+D

([0) where A, B, C, and D are regression coefficients.

When applying this model to the results of the theory of

Salvasen, Tuck and Faltimisen [24], they calmie out as:

= .00631 0 -t. 1.22V + .657 CB + .064 O°<9<90°

(lia)

= .00495 0 + .422 V + .701 C6 + 1.28 900<0<1800 (lib)

where V is the Froude imumber, O is the heading iii degrees aiid

9=1800 represents head seas. Two regression equations liad to be derived for headings on the bow and aft sectors, due to the nature of . These regression equations were derived from comparisons with the results of tests iii five different models in a total of 70 transfer functions [4].

To assess the effect of this modelling error on the bug-term predictions is straightforward. It is only necessary to

substitute the H(,9) in equation (3) by

(0).11(w,O) where (9) is given by the above expressions. 'rIme variances obtained

in this niaminer are introduced iii equations (1) and (3) to yield the long-term values.

W 8, CB..63 F5.160 I'- 8. 60 CB-TO FN,1O '4' 6L7 CB-SS FN-lb -- W88 C8-.49 FN-SS

0 30 60 90 120 150 180

Heading (degrees)

Figure 3. Transfer function modelling error for

different ships as a functioim of heading. 5. NUMERICAL RESULTS

The influence of the wave climate model on the long terni predictions is assessed by comparing the i0 characteristic

values obtained with the differeiit sets of wave data. 'rie importance of this effect is compared with tIme nue due to (lie uncertainty in the transfer functions by assessing also (lie sensitivity of long terni predictions to transfer function uncertainty.

This work complements the one of ref.11, by using most of the transfer functions included jim that study, which are now used to recalculate the long-term distributions for tIme wave climate based on hindcast data [8]. Additional transfer

functions froni other ships at different speeds, that have beemm determined in [23], have also been used ill this study. TIme results obtained with time data sets of visual observations have

been normahised by these hatter ones from hindcast data.

5.1 Influence of Wave Climate Data Sources

Table I shows the 10-8 characteristic values of wave induced bending moments which have been norunahised by the value obtained on the basis of the data set of Bales et. al [8]. lui addition to time basic wave data of references 5 and 6, (lie modified data set that resulted frommt applying tIme calibration

equations of refs. 9 and 10 was also used.

Analysis of the results of the ships in Table 1 imudicate

that the relative value of the design predictions camm be larger or smaller than 1.0 depending basically on tIme length of tIme

ship. Furthermore time results show that time ship speed also influences the results. Both observations point out for tIme

great effect that the definition of mean wave period lias on time results. Changes in ship speed affects the encounter frequency and the ratio of wave length to slmip length, ami effect which

depends obviously on time length of the ship.

The relative values obtaimmed range from 1.45 to .78 indicating a large level of ummcertaimmty. 1mm geimeral time results

obtained with the new data set of Ilogben et ai [7) are very

close to the ones obtaimmed by mnodifyimig [9, 10] time data of Hogben and Lumb [6] but they have a small but systematic

difference from tite results based on tIme data of Bales et al [8]. 1.1

0.9

o

0.7 0.6

Using the data set of Walden (5] always leads to values

significantly different from the oites obtained from Hogben et al [6, 7]. Applying the modifications [9, 10] to Walden's data

always approaches the results to the ones of liogbeit et al,

which was an expected modification. however, it is surprising

to observe that for long ships tite results based on Walden's

data (0.9-10) are closer to tite olies of Hales et ai

[8] than

the ones based ori ilogben et al (.78-9).

Overall one can conclude that the results of Roghen et al

are consistently lower than the ones obtained front

Walden's

data, as one would expect because the first ones have the

effect of weather avoidance inbuilt.

The two data sets that describe only tite meteorological

conditions without any

modifying effect are tite

ones of

Walden and of Bales et al. 'lite relative values obtained with

this set change from .93 to 1.45 which isa relatively large

scatter band. However, these values are clearly dependent oit ship length.

with values on the range of 1.40 to 1.45 for

lengths of 100 to 150m and values of .9 to 1.02 for lengths of 268 to 300m.

Figures 4 and 5 show the long-term distributions obtained

for two ships of equal block coefficient and speed but of

different length. lt

is clear that tite predictions based our tite

hindcast data [8] uuiderpredict the characteristic valute for the shorter ship and overpredicts it for tite longer otte. Comparing these predictions with tite ortes based ott tite modified

Walden's data which

is tIte one directly couitparahle, the relative values are 1.29 and 0.95 respectively.

5.2 Influence of Transfer Functioii Uncertainty

Tite response predictions depend both out tite wave cliritate description as well as on tite transfer functions for tIte response considered. 'Ihus, it is of interest to compare tite effect of tite uttcertainty frotti each of these origiits.

Tite transfer functions used

iii

tite calculatiotis of tite

results in Table i have been modified according to eqn. O atid

tite corresponding long term characteristic value has been

calculated for different wave climate.

Ship

L(m) Cß

F Average Walden Modif. Waldeti Hogbert Luinb Modif. Hg & L Hogben Cunuta Bales et ai Bales et al Wolverine 151 .63 .214 1.13 1.40 1.18 1.10 1.04 1.05 1.00 1.36 State 151 .63 .160 1.11 1.32 1.19 1.10 1.03 1.04 LOO 1.33 151 .60 .214 1.20 1.50 1.29 1.18 1.12 1.13 1.00 1.22 151 .60 .160 1.16 1.36 1.26 1.14 1.08 1.09 1.00 1.22 Average 151 .62 .187 1.15 1.40 1.23 1.13 1.07 1.08 1.00 1.28 Coittainersh 270 .60 .215 0.95 1.02 0.95 0.92 0.86 0.93 1.00 4.95 Series 60 150 .70 .10 1.11 1.19 1.22 1.13 1.05 1.06 1.00 1.41 150 .70 .15 1.12 1.25 1.23 1.13 1.05 1.06 1.00 1.44 150 .70 .20 1.15 1.37 1.23 1.14 1.07 1.07 1.00 1.49 150 .70 .25 1.16 1.42 1.24 1.15 1.08 1.08 1.00 1.65 Average 150 .70 .18 1.14 1.31 1.23 1.14 1.06 1.07 1.00 1.50 Series 60 300 .70 .10 0.85 0.91 0.81 0.81 0.75 0.79 1.00 2.06 300 .70 .15 0.86 0.92 0.84 0.84 0.77 0.81 1.00 2.10 300 .70 .20 0.89 0.94 0.89 0.87 0.80 0.84 1.00 2.17 300 .70 .25 0.91 0.96 0.91 0.88 0.82 0.86 1.00 2.42 300 .80 .15 0.84 0.90 0.81 0.81 0.74 0.78 1.00 2.52 Average 300 .72 .17 0.87 0.93 0.85 0.84 0.78 0.82 1.00 2.26 SL7 268 .55 .251 0.98 1.06 1.03 0.96 0.89 0.92 1.00 1.81 268 .55 .301 0.86 0.92 0.81 0.83 0.76 0.81 1.00 1.84 Average 268 .55 .276 0.92 0.99 0.92 0.90 0.83 0.87 1.00 1.83 Warship 100 .48 .29 1.26 1.45 1.40 1.27 1.24 1.22 1.00 1.93 Average 196 .61 .20 1.02 1.17 1.08 0.96 1.02 0.97 1.00 1.94

Table I - Relative value of the 108 characteristic value of wave induced beudng momenta normalised by

the prediction based on the hindcast data. The last column indicate the absolute value of

the latter prediction.

Bending Moment

-

W.ld.n mod) -*-i409b.fl &Lomb (mod) -b-- 00000nSt. SI.

-e- se..

.1 SL Bending Moment

L

- WSId.n (mod) t- 600b.n Lomb (mod) -#- 000b.n.t. s). -S-- Bai.. st. SI -7 -6 -5 -4 (agiO) o il

Table2 - Relative value of the l0 characteristic value of wave induced bending moments obtained with

the corrected transfer function and iiormalised by their respective value corresponding to the

uncorrected transfer function.

Ship

L(m) CB

F11 Average Walden ilodif. Walden Hogben Lutub Modif. Hg &. L Hogben Cunha Bales et al Wolverine 151 .63 .214 1.07 1.12 1.05 1.07 1.09 1.08 1.00 State 151 63 .160 0.99 1.06 0.91 U.98 0.99 0.98 0.94 151 .60 .214 0.99 1.08 0.94 0.99 1.02 1.01 0.87 151 .60 .160 0.89 1.00 0.85 0.88 0.91 0.89 0.80 Average 151 .62 .187 0.99 1.07 0.95 0.98 1.00 0.99 0.90 Containersh 270 .60 .245 1.23 1.23 1.23 1.23 1.23 1.23 1.23 Series 60 150 .70 .10 0.91 (1.93 0.90 0.90 0.90 0.91 0.91 150 .70 .15 0.94 1.01 0.94 0.94 0.95 0.96 0.95 150 .70 .20 1.03 1.08 1.02 1.02 1.04 1.04 1.00 150 .70 .25 1.09 1.14 1.08 1.09 1.11 1.10 1.03 Average 150 .70 .18 0.99 1.04 0.99 0.99 1.00 1.00 0.97 Series 60 300 .70 .10 0.91 0.90 0.91 0.91 0.91 0.91 0.90 300 .70 .15 0.99 0.97 1.00 0.98 0.98 0.99 0.95 300 .70 .20 1.05 1.05 1.07 1.06 1.06 1.07 1.01 300 .70 .25 1.09 1.12 1.14 1.12 1.13 1.14 1.06 300 .80 .15 1.08 1.08 1.08 1.08 1.08 1.08 1.08 Average 300 .72 .17 1.02 1.02 1.04 1.03 1.03 1.04 1.00 SL7 268 .55 .251 1.05 1.08 1.09 1.06 1.08 1.06 0.95 268 .55 .301 1.00 1.00 1.00 1.00 1.00 1.00 0.98 Average 268 .55 .276 1.03 1.04 1.05 1.03 1.04 1.03 0.97 Warship 100 .48 .29 1.09 1.26 1.02 1.18 1.22 1.00 0.85 Average 196 .61 .20 1.02 1.07 1.02 1.03 1.04 1.03 0.97

Figure 4.Long-term distributions of Wolverine Figure 5. Long-terni distributions of a State (L=151m, CB=O.60, F11=.21) for the four _{containership (L=270nì, CB=(J.60,} F11=.245)

wave data sets. for the four wave data Bets.

The results, which are indicated in Table 2, have been normalised by the corresponding value obtauted with the

original function. The inodificatioiis of tite transfer functions affect them in a different manner depending oit the relative heading to which they concern. The combination of the

relative headings and ship speeds result iii different average encounter frequencies. This implies that using the various wave data sets will induce different effects, as is indeed shown in Table 2.

Figure 6. Long-tenu distributions of a Series 60

ship of C80.70 and L=l5Om based oli

Lite

calculated transfer function and on the one corrected (cor) with eqn. 11.

toglOCot)

Figure 7. Long-terni distributions of a Series 60 ship of CB=O.70 and L=300m based on the

calculated transfer function and ou the one corrected (cor) with equ. 11.

The dependence of this ratio on ship speed us very clearly

seen, with the values increasing with Froude number.

Furthermore, there are also differences between the averages obtained in the various data sets and the lower values are obtained consistently for the data of Bales et al [8].

Figures 6 auid 7 show that the difference between the longterm distributions based on the calculated value of the transfer functions and the corrected otues is larger for the lower speed. however, while at the lower speed the corrected values are smaller than the calculated, the contrary occurs at the

high speed.

- LSOOFH-w

b L300 esa

-4- L-300 CH-20 -a- L-300 CH-20 eo)

This observation shows that the effect of correcting the transfer function cannot be said to induce any delinite trend it

the results in general. This is well described by ait uncertain factor valid for auiy random situation occuriuug during tite ship's lifetime.

- CB-SO PH-.2t4

CB-SO Fbb.2 too,)

CB-_so FH-.1S0

-G- CB'SO F5.160 bon

Figure 8. Long-teno distributions for the

Wolverine State at the light load condition with the calculated transfer functions and the

corrected ones (cor).

pending Moment 06-65 F5.214 +- CB-SS F5.214 Coo,) -4-- CB..63 PH-100 -a- CB-SS CH-160 00,) IofQ(ofl

Figure 9. Long-terni distributions for the

Wolverine State at the full load condition with

the calculated transfer functions and the corrected ones (cor).

For example, the effect of changes iii speed and in block

coefficient caut be observed iii Lite long term distributions

shown in figures 8 and 9. For the Wolverine State, changing speed did not change the distribution whieuu CB=.60 but for tite loaded condition, (C=.63) there is a decrease in that value with increasing speed. However the differences are much larger between the characteristic values for the different block

coefficients than between the different speeds as can be observed in Fig. 10.

The range of values obtained iiiTable 2 goes from .85 to

1.23, which is significantly smaller than the oites due to wave climate which was from .78 to 1.45. Thus it can be concluded that tite influence of the uncertainty in the wave climate

description lias a larger effect on the predictions of

-5 -4 -3 -2 -1 loçlO(o)l -a -a -7 -e -5 -4 IoglO(x)l -3 -2 -4 -5

characteristic values than the uncertainty in cakuiating lite transfer functions.

- Cb-.

FN-.O 4 CS-es FN-leO (colt -4 CN-SO FN-SSO

-a- FN-SSO colt

Figure 10. Comparison of the effect of

correcting tite transfer function itt the high load (CB=O.6O) and full load (CB=O.63) condition.

6. CONCLUSIONS

This work itas shown that tite characteristic values

obtained front tite long-terni distributions, which are aimed at being incorporated in design codes, can have differences up to

50% when different wave climate descriptions are Used.

The larger differences are obtained between tite results

from tite hindcast data 18] and tite data of Walden which are tite two that represent the existing conditions itt the ocean. The results obtained from the two data sets of Hogbett et al are expected to show values lower titan the real otmes because

they have inbuilt tite effect that, all transiting ships that

perform the observatmoits always avoid certain ocean areas when the weather is too bad.

The design values based on hindcast data tend to he unconservative in relatiott to tite otiters for ships witlt lengtits of loo to 150m but they are conservative for sltips of length arouitd 300m.

There is at present no basis to say that Otte data set is

more correct titan tite otiter, which meatts that tite

discrepancies to witicit they lead must be considered as tite

range of uncertainty due to tltat lack of knowledge.

This rattge of uncertainty itas beett compared with tite oite that results from tite uncertainty in transfer function and it

was shown to be sigmtifìcantly larger.

ACKNOWLEDGEM ENTS

This work has beett imnancially supported by JNICT, Junta

Naciottal de itivestigaçad Cieittifica e Tecnológica under

resea.rcit comttract 87/55 MAR, "Bases for tite Development of Codes for Marine Structures".

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