Seakeeping performance prediction program SKP - Program Manual

VALTION TEKNILLINEN TUTKIMUSKESKUS TIEDOTTEITA STATENS TEKNISK FORSKNINGSCENTRL _MEDDELANDEN TECHNICAL RESEARCH CENTRE OF FINLAND,_{RESEARCH NOTES}

LAIVATEKNIIKAN LABORATORiO_{- SKEPPSTEKMS) LABORATORIET} -SHIP LABORATORY

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818 _{Riska, Kaj, Ship ramming multi-year i hoes. Model}

test results. 1988. 67 p. + app. 48_p.

837 _{Karppinen, Tuomo, Helasharju. Hejkki & Aitta, Timo, Seakeeping perforinane prediction}

program SKP. Program manual. 1988. 57 p. + app. 31 p.

¡S'a jI&oi,o r,,py

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VALTION TEKNILLINEN TUTKIMUSKESKUS TIEDOTTEITA STATENS TEKNISKA FORSKNINGSCENTRAL MEDDELANDEN TECHNICAL RESEARCH CENTRE OF FINLAN RESEARCH NOTES

ECHNISCHE

UNIVERJTFJT

Laboratorium

or

SCheepshydmecn

Arch let

Mekelweg 2,

_{2628 CD Deift}

Tel' 015-78

Thomo Karppinen, Heikki Helasharju

& 5Ï'imo

MfF015.le183e

r

Irr

Seakeeping performance prediction

program SKP

Program manual

ESPOO 1988

1

rrniwY.

J

.j A

tic3ci CD

tA

Valtion teknillinen tutkimuskeSkus, Tiedotteita

Statens tekniska

forskningscefltral, Meddelanden

Technical Research Centre

of Finland, Research Notes

Sakeepiflg performance

prediction

program

SKP

Program

ranua1

l'uomo Karppiflefl

Heikki Helasharju

Timo Aitta

Ship Laboratory

Espoo, February 1988

837

CONTENTS

F

APPENDICES Page

1. Method of curve fitting for frequency response

ABSTRACT and phase angle data

PREFACE 2. Wave spectral formulae

INTRODUCTION 8 _{3.. Default sea areas}

9 4. Input/output example

2 BACKGROUND .

s. weibull probability function 2.1 Seakeeping performance indices.

6. List f primary variables

2.2 Percentage operability ...,.1

7. Input data card description

3 METHOD OF COMPUTATIONS 15

3.1 Ship responses to regular and irregular waves 15

3.2 Operability 18 4 SEAXEEPING CRITERIA

. ...22

4.1 General 22 4.2 Vertical acceleration 26 4.3 Lateral acceleration 27 4.4 Roll 29 4.5 S1mining 29

46 Deck wetness

30

4.7 Operability limiting criteria - human factors 31

5 PROGRAM ORGANIZATION 35 6 INPUT DESCRIPTION 42 7 OUTPUT DESCRIPTION 44 8 PROGRAM VERIFICATION 46 9 CONCLUDING REMARKS 52 REFERENCES 54

i INTRODUCTION

In a seaway ship performance deteriorates as compared with the performance in calm water. This degradation of performance due to weather and wave induced motions may appear as an involuntary speed loss, -a voluntary speed reduction or as a lowered working effectiveness of ship

personnel. Violent motions may prevent essential work onboard thus causing lost working days.

The Nordic co-operative project '!SEAKEEPING PERFOR1(ANCE

OF SHIPS" dealt with various aspects of seakeeping

problems. The task of the

VTT Ship Laboratory in the

project was to find a general ranking system for

seakeeping performance of ships and to define limits to

acceptable wave induced motions. The operability limiting

criteria with regard to ship responses are used in the

procedure for predicting a numerical value for a seakeeping performance index. This index is in the

present work defined as the operability percentage and it

is used as an overall measure of merit or ranking for

seakeeping performance of ships.

The program manual consists of a description

of the

general background of seakeeping ranking systems and

especially the seakeeping performance index selected to be used in the project.

An outline of the

method of

computations

is given together with the

principles of selecting the operability limiting criteria of

the various responses.

The structure of the program and the input data fleeded

are explained. The manual also gives a complete run as an example.

Finally the verification of the program is discussed and remarks concerning the present status of the program and

further modifications are dealt with.

2 BACKGROUND

2.1 Seakeepina performance indices

The practical evaluation of-, ship

seakeeping performance

requires a numerical index by

which to measure

the

seakeeping performance. The index

should measure the

ability of the ship to fulfil its function in the environmental conditions the ship is

likely to encounter

in its lifetime or over a long-term

interval. Since the

effect

of the

seaway and weather

is- to degrade the

mission performance of the ship in

relation to the calm

sea performance, it seems natural

to formulate the

seakeeping performance index so that

it measures the performance degradation. 'The mission

performance in still

water is taken as a standard of reference.

It is important that a numerical

value for the index may

equally well be computed on the basis-of basic

seakeeping

model test data and theoretically

predicted ship responses. In seakeeping model

tests the number of speeds, headings and recorded responses

'is always limited

compared with, for example, theoretical

predictions-by a

computer. Thus the. measure of merit should

be such that a

numerical value -can 'be determined on the bas-is.of minimum

amount of data on the elemental motion components

of the

vessel. When more information

on the seakeepi-ng

characteristics of the vessel -accumalates, it should be

possible to update the value

of the seakeeping

performance index.

it has often been suggested that seakeeping

performance

of merchant ships cou-id

simply be measured

by their

ability to maintain speed in heavy weather.

If the

measure of

merit is based on

the ability

to maintain

speed, the operational

ability may be

defined as the

ratio of the maximum speed in the'

r

condition to the maximum calm water speed, V. The

seakeeping performance index then becomes the ratio ôf the long-term speed ma seaway - the sustained sea speed - to V. The sustained sea speed reflects the ability of a merchant ship to fulfil its function, i.e. to deliver cargo and passengers safely and precisely from port to

port, regardless of sea conditions.

Procedures for predicting the sustained sea speed have

been presented by Chryssostomjdjs (1972), St. Denis

(1976), Journee & Meijers (1980) and amamoto (1984).

Kitazawa et al. (1975) consider the speed loss due to

voluntary speed reductions and Naito et al. (1980)

present a simple method to estimate the required speed reduction to keep the ship motions within the maximum

acceptable limits.

10

-In predicting the sustained sea speed both the involuntary speed loss due to added resistance and loss of propulsive efficiency caused by wind, waves and ship

motions and the voluntary speed reduction due to

excessive ship motions at the discretion of the ship's master should be considered. However, it is not usual in seakeeping model tests to measure all

the basic data

required for a prediction of the sustained sea speed.

Hosoda et al. (1983, 1984 and 1985) apply methods of

reliability engineering and define the operational

ability as the mission effectiveness. In rough seas the

mission effectiveness measures the rate at which the

mission of the ship can be accomplished in relation to

calm sea. In calm sea the mission effectiveness is

assumed equal to 100%. The mission.effectjveness concept is well suited for assessing the seakeeping performance when the efficiency of the personnel and equipment of the vessel are of primary importance in carrying out the task of the vessel. How to define the mission effectiveness of

a ship hull is not so clear.

ships. By naval

Hosoda et al. consider salvage missions by patrol boats and Lloyd & Hanson (1985) apply the misston effectiveness concept to the assessment of operational effectiveness of

shipborne naval helicopters.

2.2 Percentage onerability

in the present work the percentage of the time of

Operation has been taken as the measúrè of seakeeping performance. This meàsure of merit has often been applied to assessing Of the seakeeping performance of naval ships (e.g. Johnson et ai., (1979), Chilò & Sartori, (1979),

Bales, (1981.), McCreight & Stahl, (1:985), and Chilò et

al., (1986)), but as a comparative measure of seakeeping

performance it is equally well applicable to merchant ships this seakeeping performance index

expresses the percent of time the ship is capable

of

certain operations according to its mission on a given

sea area over a long-term interval. The operational

capability of the vessel

is defined in terms of ship

motion limits. When ship responses exceed the limiting criteria, the operations cease. Thus,the index value expresses the percent of time the ship motions are smaller than the operability-limiting criteria.

By ordinary merchant ships the value of the seakeeping performance index at a particular speed and heading may be defined as the percent of time the ship is capable of

maintaining the speed and heading on a specific sea area. If only voluntary speed. reductions due to excessive ship motions are considered, this operation index can be computed for all ships on the basis of frequency response

functions and the phases of the various responses. If the

frequency response functions are known at several speeds and headings, all speed and heading combinations can be weighted according to their importance and the index value

is obtained as

a weighted mean.. If the added resistance and the propulsion efficiency in waves are

12

-known, too, the effect of involuntary speed reduction -can be taken into account in the index value When the

percentage of operatIon is determined or several speeds up to the maximum calm water speed, it is possible to derive the average annual or seasonal speed, as shown by

Chilò- & Sartori (1979).

The basic steps in the procedure for predicting the

percentage of tine of operation at a particular speed and

heading are (Figure 2.1):

Transformation of -the experimental or

computed discrete frequency response data to continuous functions over the whoÏe relevant

frequency range.

computation of-the roôt mean square response amplitudes of the various responses in -wave

spectra with nodal wave periods over the

entire -period range.

Selection of limiting response criteria and computation of the limiting significant wave

heights in each wave period group.

Computation of operability time in each wave

period group and in the whole sea area.

The numerical value -of the seakeeping performance index,

or the percentage operability in the specified

environ-ment at a given speed and heading is determined by:

P0(v,,i)=rP(T1;V:p) Q(T1) (2.1)

where P is the probability of significant wave -height not exceeding the operabi-lity-limit-ing value and Q is the

percentage of wave observations in the period range with

central period T1.

A more detailed desription of the

procedure is- presented in the next chapters.

- The final result, the percentage Operability Po,

should -not be considered as a -deterministic figure defining

exactly the. number of operational days in a year. The sea

13

-onditionB the ship encounters on a specific sea area

vary statistically from year to

year. statistical

uncertainty of the prediction is - furthér

increased for

instance by the human differences in the

characters of

ship masters.

The seakeeping performance index is best

suited for evaluating the seakeeping performance of alternative designs on a comparative basis, and for

revealing

possible problems in the seakeeping qualities of the vessel in the design phase.

14

-WAVE FREQUENCY WAVE FREQUENCY RESPONSE SPECTRA. S,.RS RMSft(.)dw WAVE FREQUENCY RMS, XX X-X LX LX WAVE SPECTRA H,lm T, = 3 ... 30 s CRITERION KAXIItJK ALLOWABIO PIlS VAlLE CRITERION RMS, PERCENTAGE OF OPERABILITY MODAL WAVE PERIOD

Figure 2.1. Principles f the prediction of the

percentage of operability time at a particular speed and

heading.

SIGNIFICANT SEA AREAY OPERABILITY LIMITING

WAVE HEIGHT Il, DUE TO RESPONSE X.

I

-

15

-3 METHOD OF COMPDTATXON8

33. Ship responses to reqular and irreaular waves

in deriving the formulae for predicting the seakeeping performance index it has been assumed that the linear superposition principle and the Rayleigh distribution can

be used.

in spite of these, assumptions also the roll motïon was

included in the predictions.. 'Although the roll response

of most ships is non-linear,, at least at resonance, the operability limiting boundaries with regard to roll to be so low that the effeòt of

extrem ily important.

Applying the linear superposition principle and assuming the irregular waves to be unidirectional, the spectral

density of the ship response to waves can be found from:

'f

S,=IR(w)J. S(w)

(3.1)

where

w

is the wave or absolute frequency 5(w) is the wave spectral density and

R(w) is the frequency response function i.e the

amplitude of the ship response. X in regular

wave of unit amplitude.

Here the ship response can be any of the linear responses

of the

ship to waves

such as heave, pitch, relative

vertical motion, vertical velocity or acceleration.

When, the ship response is expressed as:

x=x0cos(w,+)

(3.2)'

the frequency response function is obtained by:

R,(w)=x0/A(w)

(3.3)

non-linearities is

RES. AMPI. TRANSFER FUNCTIOII R

WAVE AMPI. RESPONSE X SPEED V kn

HEING: p deg.

seem not

AP

16

- I O.g.o. Co..oponds Io Hood Waoo

p - 90 O.goos Co'oopond. Io

i. - O D.g,.ss Co..000.'dI to Fcltow4ng Wr.00

PP

17

-Different frequency respòflse functions are obtained for

different ship speeds and headings. This cañ be indicated by writing the frequency response function in the form

R. (w;V.p)

The mean square value of the response. in irregular seas

is obtained as the area under the response spectrum function:

o-m0,=

_f

S(w)dw

(3.5)

where

cia,

Is

the standard deviation, or root mean square

response.

The wave spectrum is here defined by an analytical

spectral density function such as the ISSC- or

JONSWAP-spectra:

S(w)=(A/w)eXp(-B/W)

(3.6)

where the significant wave height, Hs can be factored out.

and the spectrum may be written in the form:

S(w). H

f(ùi;T)

(3.7)

The significant wave height is defined by

H,=4J

(3.8)

When the expressions (3.7) and (3.1) are combined for

g is the acceleration of gravity

(3.5), the mean square response can be written in the

p is the ship heading to waves (Figüre 3.1) following form:

V is the forward speed of the ship. .

02112f(R(w))2/(w;T)dw

H(g(T;V.P)2)

(3.9.)

I, - SURGE - HEAVE - PITCH

- SWAY - OtL - YAW

Figure 3. l Definition of ship heading and notion components.

In 3.2 and 3.3

A is the àmplitude of the incident regular wave

w, is the frequency of encounter.

The frequency of encounter is related to the wave frequency by:

w,w_(w2/g)vcosp

_(3.4)

where

g,(T;v,p) is the the root mean _{square response for unit} significant wave height _{as a fúnction of wave}

period: with ship speed and heading as

parameters

3.2 Operability

If the g _{functions have been determined,}

the operability limiting significant _{wave heights for different types of}

criteria with regard to linear _{ship responses can be}

asily found.

For a criterion defined _{as the, maximum allowable root} mean square valúe, as for instance _{for accelerations and} angular motions, _{the Iimiting significant}

wave height,

hx, is given by:

h,,(T;V,p.)= d,,,/g,,(T;V,p)

_(3.10)

An alternative way to express the limiting criterion with

regard to response x is to define _{a maximum allowable} probability for exceeding _{a critical value Xcr.}

B' the Rayleigh distribution the _{probability of exceeding is}

given by

P(x>

_{X,j= exp(-x,/2m0j<}

_{P (3.1 I.)}

where P _{is, the prespecified maximum allowab)e exceedance}

probability and inOx has been defined _{in (3.5). When (3.9)}

is _{substituted for}

Inox in (311), the limiting

significant wàve height _{can be' solved from the resulting}

expression., and is thus obtained by:

X,,

h,,(T: V ;p)

_(3.12)

g,,(T;V;p),J-2Inp,,

Equation (3.12) is equivalent to setting the maximum

permissible root mean square value to:

= x,,/j(-21npj

(3.13)

The criterion wjtI regard to deck wetness j5 _most

conveniently expressed' in' terms of the maximum

permissi-ble probability,

dw :'---

-P(deck welness)- exp(_F2/2m0,) <'ed.,,

(3.14)

where 'F is the effective freeboard' at the section

considered and mor is the mean square relative vertical

motion. By (3.12) the limiting significant wave height

with 'regard to deck wetness can be expressed in the form:

hd,,(T;'1' ji)

F

g(T: V ,p),[-2ln

Pd,,

(3.1i5)

where _gr is the root mean square value of' relative

vertical motion' for unit signIficant wave height as a function of wave period with ship speed and heading as

parameters.

The slammIng criterion 'is conveniently defined in the same form as' the criterion for deck wetness.

By the Rayleigh d'isri'bution the' probability of slamming becomes (Ochi 1964)

P(slam)= ex'p(-d2/2m0,

+ V,/2m,,,) <P,,

(3.16)

where d

is local draft, Vcr Is the' critical re-entry

velocity and mor and rn0 are the mean square relative

motion and' relátive vel'oôity, respectively. tt follows

from (3.16) for, the limiting significant wave height with 'regard to slamming

hs(T;1/.P).j

_2InP.{gg,)

(3.17)

where P5, is the maximum, permissible slamming probability

and g and g are the root mean square relative motion

and relative velocity for a unit significant wave' height, respectively.

f

fh(T)- H0\

P(T;V,M)P(He<h(T))

i

_{H,-H0 ¡}

where

, 20

-When limiting significant wave heights have been

determined with regard to all critical responses as a

function of wave period, the hx(T) curves at a particular speed and. heading can be plotted on a wave scatter

diagram (Figure 2.1) expressing the joint probabilities of occurenCe for H5 and T in the operation area of the

ship. The operational boundary of the ship on the Hs - T

plane is obtained by taking the lowest of the limiting

significant wave heights at each wave period. In mathematical terms

h(T ;V ,p) m.in{h,(T;V p)) (3.1.8)

The probability of the significant wave height not

exceeding the operability limiting value h in each wave

period class can either be determined by counting directly from the wave scatter diagram or from the

Weibuli distribution fitted to the wave data in. each wave period class. When the Weibuil distribution is used, the probability of the significant wave

height

not. exceeding

the. operational iiiniting

height

in a particU1r wave

period range is given by

(3.19)

H0 is the lower limit of observed, significant

wave height for a specific period range are parameters to be determined by the fit

The percentage operability in the specified enviroinent at and heading speed the particular determined by: P.0(V,p)=).' P(T1;V.p) Q(T1) (3.20) can finally . be

where Q is the percentage of wave

observations in the

period range with central period Tj..

The foregoing procedure can ba repeated for

several

headingS .at .each speed jf

only the

0espondthg

frequency response fuflctiOfl5 are known.

The

percent-age operabiÏltY becomes

the weighted mear1 over all

eadiflg5 and speed&

p0(Oceafl area)'

(ii) j(v1 v)

P.O(1'kP')

Here

is the conditional

frequency distribution of

hading at a given ship speed and'

j,, is the frequency

distribution of speed',

Both frequencY ,djstribution5

are to be defined' in

accordance with the mission

profile of the

ship. The

procedure can easilY be extended to

include several ocean

areas with different wave, climates.

4 _8EAKEEp

CRITE1IA

Criteria for _{acceptable levels of ship}

motions, Which are used _{in the}

procedure of predicting

the percentage of

operability, have been defined on the basis _{of full-scale} data _and

criteria proposed in the _{literature. The}

information available has been

supplemented with our own

.bservatjons during

full-scale tests with _{small naval}

vessels

In _generai,

speed is _reduced,

operations are _{discontinued if} personnel is in danger, the

personnel has remarkably

dropped

is

signifjcantiy reduced. The captaj _are:

a)

excessive. vertical and _lateral

b,) _slamming

deck wetness

rolling.

screw racing.

All ship _{responses are not}

equally important from the

point of view _{of different ship}

subsystems as shown in

Table 4.1.

For instance,

vertica'i velocity is _{important only from}

the point of

_{view of helicopter}

recovery and lifting operations while

vertical acceleration _{has an effect} on almost all _activities

onboard. In the _operability

predjctjo _procedure

criteria have been _{defined with}

regard to all

responses marked with _{# in Table 4.1.}

A

criterion with _{regard to pitch has}

not been considered necessary since _ofl

merchant ships large _{pitch angles as} such are

Usually not a problem.

The effects of pitch that course is _{changed, or}

the ship, _{cargo or}

effectivenéss of the or habitability onboard main concerns of the

accelerations

may be experienced

onboard. are accounted for by the

criteria with regard to slamming, deck wetness and vertical acceleration;

No limiting level has been

set for the frequency of

propeller emergence. There is little information

available on screw racing in full scale and lt is not

quite evident how propeller emergence or racing should be

defined in the prediction.

The basic set of criteria used in

theoperablity

prediction procedure are given in Table 4.2.

The slamming and deck wetness criteria have been defined in terms of critical probability (events per hundred wave encounters) while all other criteria are root mean square

values. The different points ôf view considered in

estimating the limiting magnitudes of ship motions given

in Table 4.2 are presented in Table 4.3.

Thus, in defining the critical level of vertical

acceleratioñ at the forward perpendicular (FI) safety of ship hull and cargo, in general, have been considered.

The acceptable level of vertical acceleration on the, bridge has been defined from the point of view of crew safety and performance. The roil and lateral acceleration criteria take into account the working conditions of the

ship personnel and the safety of the cargo.

From the

point of view of equipment operation the critical

magnitudes of notion could probably

in most cases be

somewhat higher than in Table 4.2.

As can be seen in Table 4.2., a particular set of criteria has been defined for fast small craft.

24

-Table 4.1. Limiting criteria versus ship' subsystems.

Spècial' operations:

helicopter sonar

lifting

'1). 'For equipment on foredeck

2') For' deck .cargo

3)'For opératïons'on open lower decks

This has been done mainly to point out the different nature of the motions of small vessels at very high speeds. The linear methods used in determining the operabi1tY are not particularly well suited for seakeeping predictions of fast

small' craft.

-Table 4.2. Genera'l

operabilitY jmitiflg

criteria for ships.

Vert. aCC. riuS, FP

()

Vert. acC. riuS, bridge (g)

Lat. ac. rius,

bridge (g)

Roll rius (deg-)

5lammiug, cri.t. probab.

peck wetn., cnt. prob.

0.275 0.2 0.1 4,. 0. 0.03 0.05 0.65 0.27 5 o.. 3. 4.0 0.03 0.05

Table 4.3. points of view

considered in the criteria.

Criterion

Vert. acceler. , FP Vert. acc., bridge

Lateral acC., bnidt5 Roll aiumiflg Deck wetness Ilul I safetY Equip. operat. Cargo safetY perSOflfl-safety and efficiency slam deck wetn. 01 vert. accl. lat. acci. roIl

I

pitch o o o o vert. mot. vert. veic. rel. mot. 0 SHIP SUBSYSTEM Ship hull Propulsion machinery Ship equip-ment Cargo Personnel effect. Passenger comfort o o o o o o o

26

-In the case of fast _{craft also the numerical}

values of the operability _{limiting criteria}

are only directive. When a fast craft _{operates at a low speed the}

criteria set for naval vessels _{should be used.}

4.2 Vertical acceleratIon

Though ships do not

usually reduce speed or change course

as a result of high

vertical accelerations at the forward perpendicular _{criteria have been}

defined also with regard to this motion _parameter.

Criteria at _{the FP shoüld}

be considered rather as criteria for _comparing

seakeeping _{perforuance of'} alternative designs than as limitIng _{criteria for}

reducing speed or

changing course in actual' _{service., The}

Vertical acceleration _{criterion at the FP}

refïects the overall level of

vertical motion of the ship _{in weather} conditions where slamming _{or deck wetness,}

the primary reasons for a _{manoeuvre to reduce ship motions,}

may be

critical. _{On the basis of the}

published information it may be assumed that

the vertical acceleration _criteria are more _{reliable than the}

slamming and deck _wetness criteria. As shown in _{Figure 4..l}

for merchant ships _the

operability limiting

ras vertical acceleration at _{the 'FP} decreases with _{increasing ship length.}

The _critical acceleration boundary i's in close _{agreement with}

Aertssen's (1968) _{proposal and correlates well}

with later

full-scale observations _{as shown by Karppjnen}

'& Aitta

(1986)

A spedial criterion' _{of O.;17g ras vertical}

acceleration at

the FP has been

defined 'for vessels carrying ro/ro-cargo.

This limiting

magnitude of acceleration _{is based on the} full-scale 'data 'by _{FerdinandO & De}

Lembre '(1970) and Lindemann et ai. (1977).

27

-The criterion of 0.275g rus at the FP has c'

in comparisons of naval ship 'operabil4 (1981') and Walden & Grundsan (1985);

The high acceptable vertical acceìerationN small craft are due to the different frequency vertical accelerations on this type of vessels. 'o craft the acceleration spectrum is much wider and loca at higher frequencies than on displacement type vessejrk:

Hwnan bei'ngs tolerate high frequency vibrations much "better than low frequency motions as shown in Figure 4.3.

Usually also the mission of a fast, small craft is such that operations 'at high speed are only required for a short period of time making the high accelerations more

acceptable.

The criteria with regard to vertical acceleration on the bridge are intended only for basic work on the, bridge such as steering, observation and navigation. Criteria

for other types of work. onboard are proposed. later in

section 4.7.

4.3 Lateral acceieratior

The lateral acceleration criterion of 0;lg rus on the

bridge is equal to the U.S. Navy surface ship criterion estimated on the basis' of crew safety and' perforaance. This' motion limit, applies to such operations as transit and combat in general and underway replenishment. On the

basis of some

full-scale observations (Aertssen & van

Sluys, 1972, and 'Hoffman, 1976) it seems that masters on merchant ships permit slightly higher lateral

004 I--J 0,03 002 -J V) -J t_j 001 I-t_J

-

28 -loo 200 LEÑGTh BTW PP Im)

Figure 4.1; Criteria with regard to vertical acceleration

at the FP.

29

-The roll criterion for merchant ships

is mainly based on

full-scale data recorded on the same vessels as the data

used for estimating the limiting magnitude of vertical

acceleration at the FP. On the basis of safe footing, for

which the critical roll angle appears

to be about

14

degrees (St. 'Denis, 1976), and the fast

degradation of

human performance with increasing roll motion as summarized by Cox & Lloyd (1977), the operability

limiting ms roll angle could not be much higher than 6

degrees. Already at a degrees rms roll the probability

of

roll angle exceeding 14 degrees is more

than one

exceedanCe in five oscillations. A roll criterion around

4

degrees ms has often

been referred to as

an upper

limit to ensure maximum crew effectiveness onboard naval

vessels.

4.5 Slammiflq

The critical slamming probability, or the critical number

of slams per 100 wave encounters for merchant ships

is

shown in Figure 4.2 against length between

perpendicu-lars. The limit has been defined partly on the basis

of

published full-scale data and partly so that the

operability limiting wave heights obtained by applying the slamming criterion are sensible compared with the operational limits due to vertical acceleration at the

FP. In the operability predictions Ochi'S (1964)

definition of a slam is used. ccording to Ochi a bottom

impact is called a slam if the foreship

(approximately at

0.l5L abaft of the FP) emerges

from water

and the vertical velocity relative to water

surface at the station exceeds the critical valUe

V,,O.O93[7p

(4.1).

Figure 4.2. critical slamming probability for merchant

ships.

300

loo - 200

30

-where g is acceleration due. to gravity and L is the

length-between perpendiculars in metric unIts.

On the average Ochj's formula for the critical _re-entry

velocity is sound, _{but more precise definition} of, the critical _{re-entry velocity would take into account at} least the suspectibility

of the

forebody shape to slamming and the speed of the vessel. In fast _{small craft} the slamming criterion should be applied with care.

For passenger vessels the operability limiting wave height obtained by applying the bottom slamming _criterion

may be

too high. The- comfort of the passengers may

require a speed, reduction or a course alteration _already

on the

basis of whipping vibration induced by

_flare

slamming. Unfortunately the available data are too scarce for reliable defininjtjon of a criterion.wjth regard to

flare slamming.

4.6 Deck wetness

Like the slamming criterion also the deck wetness

criterion must be sed with deliberation for small craft.

On fast. vessels already thick spray may be an incentive

for a slow-down. In the _{operability predictions deck}

wetness is defined to take place when at a particular station the amplitude of vertical relative motion _exceeds

the freeboard. This definition does not distinguish

different degrees of deck wetness from _{spray to green}

water.

It is also worth considering the effects of static _and dynamic swell-up to the freeboard. Depending _{s-lightly on} speed and forebody section shape they may considerably

affect the freeboard. No empirical formulae for

31

-corrections have been included in the present program. A survey of. the available methods has, been presented by Karppinen & Aittà (1986). -

-4.7 Oerabilitv limitino criteria - human factors

Depending on the mission of the ship the ability of the personnel to carry out a particular job may be critical from the, point of view of the' operability of the ship. Limiting criteria from the point of view of safety and working efficiency of' ship personnel and comfort of the passengers have been defined with regard to vertical and lateral acceleration and roll. Wheñ ship motion exceeds the limiting magnitúde at the work site, it is assumed that work is discontinued. Respectively, when the same takes place in the passenger spaces, it is assumed that

the operational boundary of the ship has beân reached.

The criteria with regard to ms vertical acceleration and

a short description of the corresponding working and .living 'conditions are given in Table 4.4. Sorne references

on the basis of whiòh the limiting magnitudes have been estimated. are also given ïn the same table'. Additional references can be found in Karppinen & Aitta (1986).

Table 4.4. Limiting criteria with regard to vertical acceleration.

Table 4.5 repeats the vertical

acceleration criteria and

shows the 0orrespofldiflg criteria

with regard to roll and

lateral acceleration which may

not be as reliable as the

vertical acceleration criteria.

Vertical ac-celerat ion 0. 20g o.isg o. log o.. 05g 0. 02g Lateral ac-céleration Roll (deg) 6.0 4.0 3.0 2.5 2.0 Description

Light manual work Heavy manual work Intellectu work Transit passengers

cruise liner

(performance) In terms of human effectiveness

critical motion levels for light

correspond approximatelY to an effectiveness

the scales of Hosoda & Kunitake

(1985) and

(1977). According to Lloyd

k Hanson

(1985)

effectiveness may be related to

the time

complete a task in relation to the

time required

áondltiOns. Thus 50 % effectiveness

would imply that

task takes twice as long as in calm weather.

and heavy of 70 Cox '& the taken in human to calm the Vertical acc. rms Description

0.275g Simple light work. Most of the àttention must be devoted to keeping balance. Tolerable only for short periods on high speed craft.

Conolly (19.74),, Bakenhus(1980).

0.2g Light manual work to be carried out by people adapted to ship mottons. Not tolerable 'for longer periods. Causes quickly fatique. Mackay & Schmitke (1978), Applebee & Baitis

(1984)

0.15g 'Heavy manual work, for instance on fishing vessels and supply ships.

0.Ïg intellectual work by people not so well 'adapted to ship notions. For instance

scientific personnel on ocean research

vessels (Hutchison & Laibie, 1987). Work of a more demanding nature. Long-term tolerable for the crew according to Payne. (1976). The International Standard ISO 2631/3 (1985)' for half an hour exposure period for people unused to ship motions (Figure 4.3). 0.05g Passengers on a ferry. The International

Standard for two hours exposure period for people unused to ship motions. Causes symptoms of motion sickness (vomiting) in approximately 10 % of unacclimatized adults. Coto (1983), Lawther & Griffin (1986). 0.02g Passengers on a crüise liher. Older people.

Close to the lower treshold below which vomiting is unlikely to take place. Lawther & Griffin (1986)

32 - 33

-Criteria with regard to accelerations

and Table 4.5. roll. the work % on Lloyd

2,0 .! 1.6 1 . 1,25 1.0' 0,63 0.5 0,4 0,315 0,25 O,? 0.16 0,125 0.1 0,1 0,1a,16 4.3V

_{The sere}

dlscosfort boÛndary

_CCordi

to iflternati stndard ISO

2631/3985

With

_ega

to acce1eraton as _a functi0 _{of freq14}

for

POsUre times, of O minUto5 2 hOurs

and, tentativ

8

The figure 4sa

Got0,5

(1983) Prop05 for _a and _of Iaborato

expej

by

MccaUley

et al(976)

coresPondjflg to

lo

iCkfle incide/ce ratjo (VOThltiflg) among

Uad,t

health men. S PROGRAM

.OROARIZATION-The Seakeeping Performance Prediction Program - program SKP -, begins the calculations with the basic data source of ship motions, i.e. the frequency response functions of

the different responses The final result is the

percentage operability time in the specified sea area at

one forward speed and heading angle.

The program has .a rather straightforward structure.- The main program serves as a control for -the job processing

calling the various subroutiñes as required. At present one run of the program involves computations in only one

unique condition defined by ship's load condition, speed-, heading to-waves and so forth.

The f-low chart of the main program is shown in Figure

5.1. in the f-low-chart the five - key positioned

subroutines are found:- INPUT, PAO, RNS, CRIT and OPERA. Various subroutines with more limited tasks are ca-lied by

these. The mutual order of the- main program and a-l--1 of

the subroutines is shown in Figure 5.-2.

The input data file is

read and

a-iso printed by the

subroutine INPUT. The input data may be categorized to-:

basic data such as -ship dimensions, F-roUde

number etc

frequency responsés of the different

measured (-or computed) responses in

discrete form as a fUnction

of circular

frequency

optional criteria for accelerations and -roll in addition to default criteria

wave data (scatter diagrams) of additional

sea areas.

-Figure 5.1. Flow chart of the main program. subroutine names are given in parantheses

and names of the

external files inside circles.

36

-fit a curve through frequency response

and phase angle data

(P.Ao)

compute wave spectral

densities and stOre

results, (WAVES)

compute rius responses (BNS)

set. criteria and cotn

pute limiting signif

icant wave heights (,CRIT) INFILE ma

0aUs

2 o . 5. . .- -

--an8

Jo

-Table 5. 1,. Selection of

the responses included in the program.

Response

Heave

frequency response and phase angles Pitch

frequency _response and phase angles

Vertical accéièration stations i -RoIl Reltjve motion i 2 3 Vertical accl. FP Vertical acceleration bridge Lateral acceleration bridge Vertical acci. St 1. Lateral acci. St i. Vertical accl. St 5. Lateral accl. St 5. Default criteria input criteria + + + + Note

no. crïterj set;

used to compute

ver-tical accelerations

computed vertical ac-celerations

for slamming for deck wetness

accelerations with frequency response as input

39

-Table 5.1 shows the scope of responses from which the

user may select the responses to be used in the operability calculations according to ship type and

frequency résponse data available. Note that instead of pitch and heave phase angles it is sufficient to know the phase difference betwéen pitch and heave in order to

compute the vertical accelerations at arbitrary cross

sectIons of the hull.

Discrete frequency response data are smopthed and nade continuous by.a polynomial fitting procedure. Subroutine RAO controls the procedure and calls subroutines .RAOFIT and RAOCOM, in which the actual fitting and a comparison between polynomial transfer functions and the

correspond-ing; input data are carried out.

-The evaluation of polynomial results is performed in

subroutine RAOVAL.

Súbroutine RAO' consist of successive loops.. Each loop

deals with data of an identical type of responses.

Subroutine RAOFÌT calls two. subroutines LIMFIT and REGR.

LIMFIT performes a least squares polynomial fit of third

order... ThIs prodedure is adapted to the first and last

piece of the curve to be fitted. SubroutIne REGR performes a linear least multiple variable general

regression analysis, which is used for fitting a fifth order polynom in

the mid section of the curve to be

fitted. Subroutines MINV and GMPRD are called by REGR for

matrix multiplications and inversions, respectively

The method of curve fitting is in detail described in

Appendix 1.

After the polynomial fit and checking of the results the

run proceeds with computations of root mean square

response amplitudes. The computations are performed in subroutine RMS, which calls subroutine RAOVAI to compute.

the frequency responses at the appropriate circular

40

-RuS also calls subroutine WAVES which

computes the wave

spectral densities with both issc and JONSWAP wave

spectral formulae for 15 seaways with unit Bignificant

wave height. The modal wave periods range from 3 to

30

seconds. Each seaway is defined by 50 spectral density values which are computed at frequencies with a fixed

relation to the modal wave frequency.

Descriptions of the wave spectra formulae are given in

Appendix 2.

Since the wave spectral densities, are a constant data

source for 'rifle computations, it is necessary

to use

subroutine WAVES only once in a specific computer

enviroment. The wave spectral density values are stored in a data file (WAVSCP). The data file is then utilized

during subsequent runs of the program SKP.

The next subroutine, CRIT, computes the limiting

significant wave heights as a

function of modal wave

period. Criteria may partly be from data

sentences of the

program and partly determined by the user in the input data file. The structure of the subroutine CRIT is again

that of successIve loops organized according to the similarity of the character and units of the responses.

Finally the operability calculations are performed

by

subroutine OPERA. In the program there are wave data of

six sea 'areas as default data. The operability

calculations are automatically carried out at these six

locations. A suitable reference area for ships of various

size and type can be found from these six wave climâtes.

They also

form a rather continuous set from milder

(Almagrundat) to heavier (North Atlantic/winter.) Wave

conditions. Appendix 3 deals wïth the default sea areas

more thoroughly.

The modal wave periods used in the différent

wave climate

data vary and do not match the modal wave

periods used in

the calculation of limiting

significant wave heights.

Therefore, first in the operability

calculétions an

interpolation is made

to make these

two data sources

coincide. A simple parapolic type interpolation

procedure

is adapted to the limiting

significant' wave height data

in subroutine ThYRA. Subroutines

TTOO1, TTOD2 and TT003

are called by KAYRA in order to perform the job.

After the interpolation the

lowest limiting significant

wave height at each modal wave period

(mid period of each

period rénge) is searched in subroutine AALTOM.

Once the limiting 'significant

wave heights are' found the

operability percentage within

each period group is

calculated by using the Weibüll coefficients stored

in

the data sentences of the program.

Subroutine KERTYM

performs the calculations.

The final results of the operability

calculations are

printed in subroutine TULOS.

The operability calculations are

repeated for new

sea

areas if additional data in form of

scatter diagrams are

included in the input data file. The Weibull

fit is first

performed by subräutine WEIBULL.

A linear least squares

fit provided by subroutine

LINFIT (called by WEIBULL) is

used for the determination of the Weibul]. coefficients

of

each wave period group in each sea area.

Appendix 6 gives a list of the primary variables

used in

subroutines and also repeats a short

description of the

6 _{INPUT DESCRIPTION}

42

-The first five data

cards specify the tit]e _{and transfer} general information for running the program and' _selecting the appropriate _{set of limiting criteria}

with regard 'to

ship responses _{Most of the' rest} used for defining the _frequency

phase angles, which âre _given

non-dimensional frequency :,

UJWJL/g (6.!)

The fitting procedure

requires at least _{il data points to} work properly and up to 50 points can be _used.

In the i'nput the

frequency response functions _{are defined} in a non-dimensional

form according to table 6.1.

of the data cards _are response functions and

as a' _{function of a}

In the table

Z _{heave amplitude}

O _{pitch amplitude}

roll amplitude

p wave heading angle

-w _{circular frequency of encounter}

A _{wave amplitude}

4_3

-k wave number

r relative motion amplitude and

a acceleration, amplitude.

Asymptotic values of the responses for low and high frequencies are also shown i-n the table. Outside the frequency range covered by the input válues these asymptotic va-lues are used as òonstant frequency response

function valües in order to enable the computation of ras responses at all relevant frequencies. Asymptotic values

must be given in the input as the first and the last

value of the frequency response function. The X -' co-ordinates of the asymptotic valües must be selected by the user.

The phase angles of pitch and heave with respect to wave elevation must be given in degrees. Constant values at the beginning and end of the frequency range are used, and the va-lue of them is -to be selécted by the user. It

is a-iso possible- to leave the heave phases undefined and

instead give the phase difference of pitch with respect

to heave as an input.

All

frequency response and phase angle input must be

given in a rising order from l'ow to high frequencies. Note- alsO that thé fitting- procedure does not work if the

highest absolute value of Y input is found in the third

section 'of thé curve to 'be f itted 'In practice this may

take place only in case of phase angle -input. The data

should then be modified according to trigonometrical rules.

A detailed description of the input data file is given at

the end -of the manual in Appendix 7. Table 6.1 Input form definitions.

Response Form _Low

freq. High 'freq. Heave Pitch Roll Relative mot. Accelerations Z / A,

O/kA

r, A

a/(wA)

1.0 Jcos/i J Sin (L o 1.0 o o o 2 o

44

-7 OUTPUT DEBCRXPTXON

The output begins with the repeated input of general ship

datae frequency responses and phase angles.

After the polynomial fit a comparison is made

between

input and results computed with the polynomial expres-sions. A numerical goodness of fit is computed as the standard deviation:

2)1/2

_(7.1)

where .Yi is the input and Yci the calculated frequency response value at frequency xj and N is the number of

X

-y pairs.

Any negative values of frequency response results âfter the fit are shown in the comparative print-out. Later in the program, when computing the frequency response values for ms calculations, negative values are set equal to

zero.

The root mean square response amplitudes are printed out

as a function of modal wave period in the 15 wave spectra. Displacements are given in metres, angular

motions in degrees, and accelerations in fractions of the

acceleration of gravity, g.

The next sections of. output consist of limiting criteria and operability limiting significant wave heights for all responses, again as a functÌon of modal wave period.

The final rèsults give for each sea area the modal wave

periods (central periods of each period range), the

probäbility of occurrence of each period group Q(T), the ultimate limiting significant wave heights at each period

and the probabilitY of H9 > h in

period group Tj..

A limit for physiCallY

unrealistic wave height - period

combinations is used in the form

H9 = 0.1

Finally the weight of each group

considering the total

time and the total operabilitY

in the

sea area

are

computed:

p(T,)*Q(T,) - p(V.) (7.2)

The results from Weibull fit for

additional sea areas are

printed also as part of the output. First the computed

cumulative probabilities P(x <

I1) in each period group

are compared with the source

distribution and then the

Weibull coefficients and the

correlation coefficient of

the least square fit (see

Appendix 5) are printed.

A complete example of output

After the approved to "Seakeeping program was laboratories difficulties ships and with' p heading 46 -8 _{PROGRp.j VERIFICATION}

initial testing phase the

_{program SKP was}

be used in the _{Nordjc co-operative}

project

performance of ships". In _{the project the} extensively used In

_{the four Nordic ship}

which participated _{in the project. No} major appeared during _{computations of}

several raètica].iy taken all possible response, speed combinations.

The fitting of

_{frequency response data}

is of primary importance when _{considering the quality of}

the final results, _{it was found that}

the procedure developed _for program SKP is quite

sufficient, for accuracy _{requirethents}

in the rus _{response computations.}

However, _{it should be}

pointed out that the _{procedure is not very efficient}

in

smoothing if the original _{data poInts have}

considerable scatter. _{The user should}

therefore drop out _obviously

anomalous data Points.

At least 11 data points are _{needed for the}

fitting

procedure to work, _{but usually 15 to}

20 data points is

required for _reasonab;e

representation of a complete frequency response curve.

Figure 8.,i shows _{a typical result of}

a basic type of

curve to be fitted. The awkward changes, which are

typical to phase

angle curves, are not always _{very well}

reproduced, but if the resulting _{computed vertical} accelerations are compared with the ones directly measured the _{accuracy proves, to be quite}

satisfying, Figure. 8.2 shows

representative results of this.

47

-Program SKP is able to produce rina response results quite

comparable with those measured directly in irregular

waves as illustrated in figures 8.2 - 8.4.

For obvioús reasons the f thai results can not be verified in the same way as the intermediate results above. None of the participating laboratories were able to represent any comparative data as far as operability results were. concerneth The results of the project are thus a first attemp to gather a data base of this type especially for

merchant ships.

The results of the NordiC co-operative project are

published by NORDFORSK in 1988. Some results of the

project were also featured in NSTM -87 A few examples of the information the latter part of the calculations give.

-

48 -1.0 2.0 3.0 NON-DIMENSIOÑAL FRED. 2 o 4

Figure 8.1. An example of fitted results for relative

motion frequency response function. Original data

points s results of the polynomiai fit -o.

.15 O Io IO

-

49 -- COIPUIED BY 5KP FR04 FREQUENCY RESPONSE OVIA

- - - CQUPUIED BY SOP FRQUPIICH

AND HEAVE DATA

5 MODEL TEST RESULT IN

IRREGULAR WAVES

IO 20

PEDAL WAVE PERIOD (S)

Figure 8.3. RMS response of relative motion.

-20 PDA). WAVE PERIOD (S)

Figure 8.4. RMS response of pitch..

.15

.10

.05

I 0.00

0.00 20 30

° _{DAL WAVE PERIOD (S)}

FigUre 8.2. P14S response of vertical

acceleration!

-cc.IpUTED9V SOP FR04

FREQUENCY RESPONSE DATA

W MODEL TEST RESULT IN

IRREGULAR WAVES

0.0

30

- - - CCPIPUIED BY SOP FR04

FREQUENCY RESPONSE DATA

W MODEL TESI RESULTS IN

IRREGULAR WAVES .20 .10 0.00

j

e m,

'D

3

w

lì

3 ('T

z

o

0. u)

j

e

w

_e

\

Io 20 30 1.0 2.0 _3.0 4 a

>-o

z

o

w

LI.

/

/

50

-I

DECK WETNESS SLAMMING -- VERTICAL ACCL. AT FP ARTIFICIAL LIMIT FROMBREAKING WAVES 10 20

MODAL WAVE PERIOD

_(S)

Figure 8.5.

Operability limiting. signifjca wave heights

as a fUflctj _{of modal wave period}

30

Froide m O.18 - O.t7

ioo.oc

80.00.

80

C

vwt ecc #'ite 0.1 gras et 0.0e.

-

.flcI - - -SWTHEA

II ATU0

I1H ATUIITIC Iø!flI AT MaW

on.m a

00

-. 80.00 -- 70 00 80.00 80 00 100.00 110.00 - LENGI4 (1

Figure 8.6. Percentage of operability vs. ship length.

o ₁₀ 20 30 I, 1'O 70.00. 80 B0.00. 4000 80 00., 2000 10.00

9 CONCLUDING REHARK8

52

-The seakeeping performance prediction program - SKP - and the results gained in the project "Seakeeping performance of ships" form a good base for studying the quality of the seakeeping behaviour of new desings. The work should be carried on for even wider data base for ships of all

types.

The program was originally intended to perform

operabili-ty calculations of ordinary merchant ships,. There is also

a special branch of ships - such as dredgers, pipe

layers, crane ships, diving support vessels and so fourth - for which the operability limiting criteria are, often

defined differently. However, the structure of. the program SKP is such that the modification of the program in order to include new responses or to exchange oid to

new ones Is not a tedious work,

The program can thus

easily be adapted to even wider handling of operability

calculations of ships as well as other floating structures.

The program could further be developed by defining more specific operability limiting criteria to certain groups of special vessels such as passenger vessels, research

vessels,, supply ships, fishing vessels, patrol vessels

etc. To simplify the comparison of seakeeping performance of alternative ship designs even the stations where the criteria are applied could be, prespecified. This would also promote the formation of a data base against which

the seakeeping performanôe of new designs could be judged.

A deficiency of the program is that an operability limiting criterion with regard to fleur slamming is

missing. This should be added to the selection of the

criteria in the program as soon as

the level of flowiedge

of the phenomenon is sufficient.

The definition of a

conventi0n- bottom slamming should be

refined, to take

into account the

suspectthitY of the

forebOdY section

shape to 5amming. prediCtiofl9

of crew effectiveness in a

seaway, as defined by

beoda,

could easily be incorporated in the program.

intereSti aspect not considered

in, the akeepiflg

performance prediction procedure

is the probabil15t

nature of the seakeeping criteria

in reality. The

decision to slow down or

change course in rough

enviromental conditiOflS always depends

on the subjective

judgetnent of the captain, and

there always

are many

onflictiflg factors affecting

this decision. Further

study is required before the

5akeeping criteria may be

REFERENCES

Aertssen, G. 1968.

LaborIng of Ships in

Rough Seas.

Proc. SNAME 1968 DIamond Jubilee tnt. Meeting,

New York, SNAME. 21 p.

Aertssen _{G. & van Sluys, ti.}

F. 1972. Service

Performance and Seakeeping Trials on a Large

Container Ship.

Transactions RINA, Vol. _{114. Pp. 429} - 447.

Applebee, T. R. &

Baitis, A. E. 1984.

Seakeeping Investigation of the U.S. Coast Guard 270-ft

Medium Endurance Class

Cutters: Sea Trials _{Aboard the USGC} BEAR (WMEC 901). DTNSRDC Report No. SPD-1120.01. 67 _p. Bakenhus, J. 1980. Ergebnisse von See-Erprobungen mit konventionellen und unkonventionel'len Schiffen.

Jahrbuch der SIG, 74'. _{Band. Pp. 23}

-, 49.

Bales, N. K. 1981.

Optimum Freeboard:

A Critical Reassessment _{of the} 'Balanced_Ship Concept.

Marine Technology 18, 3, _{pp. 264 - 275.}

Chilò, B. & Sartorj,

G. 1979. Seakeeping

Merit Rating

Criteria Applied to Ship Design. _{mt. Shipbuilding.}

Progress 26, 302,

pp. 29g - 313. Chilò, B.,, Sartori,

G. & Santos,, R.

1986. A New Methodolo9 _{Developed by} CETENA to Assess the

Seakeeping Behaviour of Marine Vessels. _Ocean Engineering 13, 3,

pp. 291 - 318.

Chryssostomidis, C. 1972..

Seakeeping Considerations

in a Total Ship Design Methodology. _{9th Symp. on Naval}

Hydrodynarnf5 _{Paris, Aug., Office of Naval} Research. Pp.. 1589 _{- 1627.}

Conolly, J. E. 1974.

Standards of Good

Seakeeping for Destroyers

and Frigates in Head Seas.

tnt. Symp. on the _{Dynamics of Marine}

Vehicles and Structured _fri Waves, London, April,

Inst. of Mech. 'Eng. _{Pp. 59 - 67.}

Cox, G. G.,, & Lloyd, _{A. R. 1977.}

Hydrodynamfc Design Basis

for Navy Ship Roll Motion Stabfl1zat1on

SNAME Transactions,

Vol. 85. Pp. 51 _{- 93.}

55

-Ferdinande, V. & De Lembre R. 1970. Service-Performance aid Seakeeping Trials on a Car-Ferry. 'international Shipbuilding Progress 17, 196, pp 361 - 394..

Fortnum, B. C. H. 1978. Waves Recorded by m.v. FAMITA in' the Northern North

Sea'. Inst. of Oceanographic Sciénces, Rep. No. 59, Somerset, England. 21 p.

Goto, D. 1983. CharacterIstics and Evaluation of-Motion Sickness Incidence on-bóard Ships. PRADS 83, 2nd tnt. Symp., Tokyo & Seoul, Soc. of Naval Architects of Japan and Soc. of Naval Architects of Korea. Pp 657 - 662.

Hoffman, D. 1976. The Impact of Seakeeping ori Ship Operations. Marine Technology 13, 2, pp. 241 - 262.

Hogben, N., Dacunha, 'N. M. C. & 011iver, G F. 1986. Glòbal Wave Statistics. British Maritime Technology Limited, Feitham. 661 p.

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À1

-Àppendix 1

Method of. curve fitting for frequency response and phase

angÏe data

Fitting a continuous curve through the discrete input values of frequency response or phase angle is performed

in three parts.

The first. part is a third oder least squares polynomial

fit with

a

value of the

first, input value and zero

derivative at the starting. point.

The number of data

points in the first fit is chosen as n1

2/3 * _ïnax

rounded to the closest integer less than or equal to n1, where 1max is the index of the maximum y - value of the

data points. However, at least the first f iye data points are included in the first fit. In practice it is advisable .that especially in case of prominent resonance peaks in the frequency response data points should be

selected so that 1max is more than five.

The second pa.rt is a fifth order least squares polynomial

fit. The range is from' n1 -

1 to i3 + 2, where i3 is

selected so that 'at least 40 per cent of data points are between _max and N, where N is the total number of data points'.

The last part is again a third order polynomial fit wi'th a terminal value equal to the last input value and zero

derivative 'at the terminal point.

The computation of frequency response function values in order: to further compute the rms values is performed in

AÏ2

-Each of the three polynoms cover the appropriate non-dimensional frequency ranges, but in addition a

simpte matching procedure between them is adapted. The

width of matching

regions is taken as 20 % between

X(imax) añd X1 and X(N) and X(inax) for joining the

first and second or second and third polynomial results,

respectively. The distance between two successive

original x data points is set as default values for the

minimüm of the width of the matching regions. The matching is performed with simple Ïinear interpolation

between Y values gained with the two successive polynomsl.

Figure Al.l illustrates the method of curve fitting.

-Wave spectra formulae

The computation of root mean square response amplitudes is performed iñ altogether l5 seaways using both the ISSC

and JOÑSWAP wave spectral density formulae:

1SSC:.

S(w)=(A/w)exp(-BIw4)

(A 2.1

where

A= 173H/T

B 691 /T

JONSWAP:

S(w)' 1554

5exp{

TW4}

(í42.2)

where y = exp A21 -[o.19.iwT-

l\2

JG

f

and

a=O.O7forw <5.24/T1,

='O.09/orw>.5.24/T1.

(A 2.3)

Appendix 2.

in the formulae N5 is significant wave height and

T

2,rm0/m

where rna, is the n'th moment of the spectrum.

Each wave spectrum is defined with 50 ordinate values at the following frequencies with respect to modal cirçular

16, 18, 20, 25 and

A31

-AppendiX 3

Default sea areas

The program has six wave

where the operability

autoltiatiCal1Y. Table A3. i

climates as default sea areas

gives a summary of these sea

calculations are performed

areas.

The scatter diagrams of these sIx wave climates

are given

in the following tables. The

scatter diagrams represent

the joint probability of occurrence

for significant wave

heights and either modal wave periods,

Tm, or mean zero

up_crossing wave periods, Tz. The data are given in parts per thousand.

The Weibull coefficients of the

default sea areas are fed

into the program in data sentences

in subroutine OPERA.

Table A3.l. Default wave climates.

mv FN4ITA, winters 69-76 Lloyd &HansOn (1985) hindcasted - A2- -w/w,=. 0.6, 0.84, l.O0, 1.20, 1.50, 1.80, 2.10, 2.45, 3 00 0.65, 0.87,, 1.03, 1.25, 1.55, 1.85., 2.15, 2.50, 0.70, 0.90, 1.06, 1.30, 1.60,, 1.90, 2.20, 2.60, 0.75 e 0.80, 0.92, 0.94, I. OB,. 1.10, 1.35, 1. 40, 1.65, 1.70, 1.95, 2.00, 2.25, 2.30., 2.70, 2.80., 0.82, 0.97, 1.15, 1.45, 1.75, 2.05, 2.35, 2.90,

The me response amplitudes and limiting significant wave heights are presented as a function of modal wave periods

for the following 15 periods:

T5 = 3, 4, 5, 6, 7, 8, 9, 10, 12, 14,,

30 seconds

The well-known relations between nodal wave period T5 and

characteristic wave peiod T1 are used

T = 0.834 T5 JONS WAP