Seakeeping of High Speed Craft

Delfi University of Technology

Seakeeping of High Speed

Craft

Dr.ir. J.A. Keuning

Report No. 1114-P

Oçtober 1997

25th WEGEMT School on Small Craft in

Athens, Greece.

"I'i.J Ie1ft

Faculty of Mechanical Engineering and Marine Technology Ship Hydromechanics Laboratory

EGEMT

National Technical University of Athens, GREECE Department of Naval Architecture & Marine Engineering 6th - 11th October 1997

FINAL PROGRAMME

(httpil/www.ntua.gr)

ABOUT WEGEMT

The Foundation WEGEMT is a European Association

_{of Universities in}

Manne Technology and related sciences. The aim of the Foundation is to

increase the knowledge base, and update and extend

_{the skills and}

competence of engineers and postgraduate students

_{working at an}

advanced level. in marine technology and related sciences. The Foundation

considers collaborative research, education and training at an advanced

level such, as graduate Courses, workshops and seminars, .and the

dissemination of information, as activities Which further

_{the aims of the}

Foundation. Since its foundation in 1975 by IFS Universities

_{from 1.0 West}

European

_{countries, the membership of WEGEMT has}

_considerably

increased and counts today more than 39 Universities

_{from 19 European}

countries and more than 22 Graduate Schools on a variety of subjects of

Manne Technology have been successfully organised

_{by its members.}

Teaching staff

at

'WEGEMT Schools have been drawn from member

Universities,

marine industry, research organisations,

classification

societies, or wherever the best expertise in Europe is

_{available. WEGEMT}

Schools 'are run on a non-profit basis. and they are essentially self-financed

through the fees of the participants and the support of external national

and European organisations.

ABOUT NTUA

The National

_{Technical University of' Athens (NTUA) Is the oldest}

_and

largest Technical University in Greece. lt is' divided In nine academic

departments, eight being for all traditional engineering sciences, including

naval architecture and marine engineering, and

one for general. sciences.

NTUA shows a most distinguished record of achlevements going back to

its foundation in 1836, thus engineering education, research and'

_ifldustrial

development in Greece has been always linked to NTUA. The

Department

of Naval Architecture and Marine Engineering (NAME) .of

_{NTUA is the}

youngest and by size the smallest department of NTUA. lt was formally

founded in 1969 as part of the then united School' of

Mechanical and

Electrical Engineering. Since 1982 :NAME is 'an independent department

with more than 450 undergraduate students, 35 Dr.-Eng. candidates

_and

permanent staff of abt 35' members, half of which

are Professors and

Lectures

representing all disciplines

of Naval

Architecture,

Marine

Engineering and related sciences, including Maritime Transportation

_and

Offshore EngineerIng. Today NAME is by size and

_{educationallresearch}

activity one of the 'largest Departments of Marine Technology in Europe.

ABOUT THE 25th SCHOOL

The School is aimed at a largely neglected but

_{very important sector of the}

maritime industry, namely the small craft/boat shipbuilding and _{operating, and}

intends to cover many currently Important aspects of the design, construction and operation of small ships in the light of new market trends and recent technological

25th

WEGEMT SCHOOL on SMALL CRAFT TECHNOLOGY, Athens, October 6-11, 1997

devàlopments in the shipbuilding industry. The school will address a variety of aspects for marine craft _{to approximately 40m In length and thus includes}

commercial 'and naval fast vessels, multi.hulls, ferries and pleasure craft, rescue boats and sailing craft,. small' naval and' patrol vesseIs. The_{school will review the} fundamentals of small' craft design and the 'methodologies and tools available to small shipbuildors, design offices and operators, m'the 'light of recent developments in small craft technology and modern, CAD systems. lt will_{«inClude typical design} examples and 'address the hydrodynamic performance of _{various hull forni. and} vessel typos In calm water and In waves, modern structural_{design, manufacturing} and quality assurance methods, main machinery auxiliaries and various outfitting issues and finally operational matters related to the technology _{of navigation 'and} the market economics. Practical examples, exerclàes and smaÍl case studies will

'be used to illustrate the theoretical aspects and discussion _{sessions will folloW}

each lecture to stimulate the participation of the

_{audience, and ensure an}

interchange of experience and VieWs. The course program is structured into four main modules, namely:

Design and Hydrodynamics Materials and Construction

Machinery and Outfitting

Navigation and Operation

COURSE PARTICIPANTS

The target group of participants will consist from postgradùate students of

naval

architecture,

ocean and

mechanical engineering,

practising

engineers from SMEs shipyards, designers of small craft and operators,

small boat suppliers and outfitters, navy 'and coast guard personnel. A part

of the postgraduate student participants, from the

_{WEGEMT university}

network, might qualify for support through a related Training and Mobility

of Researchers (TMR) Program of EU-DG XII. Information about

the TMR program funding' procedures is avai!able through the WEGEMT network. An application form Is attached.,

ABOUT THE LECTURERS

The School

lecturers are high-quality

experts 'from

the WEGEMT

universities network,, the' European marine industry and major

European

research institutions. They are all selected by the formed International

Steering 'Committee of the School in their capacity as internationally

respected authorities in the field of small craft technology. A

_{complete 'list}

of lecturers Is attached1

25th

WEGEMT SCHOOL on SMALL CRAFT TECHNOLOGY, Athens, October 6-11, 1997

OUTLINE OF PROGRAM

Ship Design and Hydrodynamics: Type of small craft. Design Methodology, CASD system applications. Design examples. Fast Ferries, Pleasure Craft,

Rescue Craft, Sailing Craft, Naval Ships and Patrol Vessels. Stability and

Safety Rules. Hydrodynamic Performance of

_{High Speed Small Craft,}

Resistance

and Seakeeping. Propulsion Systems

for

Small Craft. Hydrodynamic Performance of Sailing Craft, Aerodynamics of Sails. Model

Testing of Small Craft.

Materials

and _{Construction:}

_Alternative

_construction

_materials,

Composites, metals and wood. Structural

_{Design Methods and Design}

examples. Construction methods, CAM system

_{applications, Composites}

and aluminum constructions. Quality Assurance methods.

Machineuy and Outfitting: Marine Engineering, Main Machinery and

Auxiliaries. Electrical Installation, navigational equipment and electronics.

Speclalised electronic equipment for naval craft. Rigging of sailing craft

and outfittìng. Noise and vibration control.

Operation: Global navigation systems, GPS, VTS.

_{Economics of operation}

and market aspects Design of ports and marinas.

Technical Visits: NTUA Ship Model Testing Facility. Small craft shipyards ¡n Athens-Piraeus area.

The detailed program ¡s attached.

COURSE LANGUAGE AND MATERIALS

Lectures and course materials will be

_{presented ¡n English. Lecture notes}

will be issued at course commencement.

SCHOOL ORGANISATION, VENUE,

FEES

The host of the School is the Department of Naval

_{Architecture and Marine}

Engineering of NTUA. The school organisation is supported _{by the Training and}

Mobility of Researchers Program. of the European Community, the National Technical University of Athens, the WEGEMT network, the _{Greek Chamber of}

Engineers and the Hellenic Institute of Marine Technology. Course fees are 750 ECU. This Includes registration, course notes,. lunches, coffees and. course dinner. A reduced rate of 250 ECU will be available for selected bona.flde students according to the TMR program and WEGEMT specifications. An _{application form for qualified} students is attached.

The fees will be increased by 100 ECU for registÈation after September 15, 1997. The course will be held at NTUA's new campus In AtheAs-Zografou area in the week from October 6th to October 11th, 1997. For non-local participants accommodation can be arranged on request through the School Secretariat at reasonably _prized 25 WEGEMI SCHOOL on SMALL CRAFT TECHNOLOGY, Athens, October 6-11, 1997

nearby hotels. There will be a cecial program for the evenings, _{including.the school} official dinner, and at least one industrial visit at the end of the_course.

25th

WEGEMT SCHOOL onSMALL CRAFT TECHNOLOGY, Athens, October 6-11,1997

fiNTERNATIONAL. STEERING COMMITTEE

Chalniian

Professor Apostolos Papanikolaou

National T.chnical University of Athens Laboratory of Ship Design

Department of Naval ArChitecture and Marine Engineering

GREECE

Members Ass Professor Jan Baatrup Danmarks Tekfliske Hojskole

Dep. of Ocean Engrg DENMARK

Professor Claus Kruppa Tech. Univ. 3erlln.

Inst. f. Sóhiffs- und Meerestechnik

GERMANY

Profóssor Theodore Loukakis

National Technical University of Athens LaboratoryofMärine Hydrodynamics

Department of NavalArchitecture and:.:Marine Engineering

GREECE

Professor Jo Pinkster Tech. Univ. Deift

Fac. of Mechanical Eng and Marine Technology

THE NETHERLANDS.

Dr. John Wellicome

Un$v. of Southampton

Dep. of Ship Science

UNITED KINGDOM

Secretary

Professor Vassillos Papazoglou

National Technical University of Athens Laboratory of Shlpbúlldlng Technology

Department of Naval Architecture and Marine Engineering

GREECE

Ass. secreta,y Dr. Gregory Grigoropoulos

National Technical University Of Athens Laboratory of Marine. Hydrodynamics

Department of Naval Architecture and Marine Engineering

GREECE

25thWEGEMT_{SCHOOLon SMALL CRAFT TECHNOLOGY, Athens, October 6-1 1, 1997}

REGISTRATION AND CONTACT

Registration forms are attached. If you would like to 'have

your name

placed In the mailing, list for further information please complete and return

the attached form or contact directly the Shool Secretariat

_{at the}

'following address:

25th WEGEMT SCHOOL SECRETARIAT on SMALL CRAFT TECHNOLOGY

.Att: ProfessorV. Papazoqlou

National Technical Univ. of Athens

:Dop. 'of Naval. Architecture and Marine Engineering Heroon Polytechniou 9

15 773 Zografou, Athens GREECE Teb (x) 772 '14 22, FAX: (z) 7721408

e-mail: papazog@deslab.ntua.gr

25th

WEGEMT SCHOOL on SMALL CRAFT TECHNOLOGY, Athens, October 6-11, 1997

25th

WEGEMT Graduate School

on

Small Craft technology

Athens, 6-1 I October 1997

List of Lecturers

Dr J. Baatrup', Danmarks Tekniske Hojskole Dep. of Ocean Engineering

Building 101 E

DK 2800 Lyngby, DENMARK

Tel: .0045 45 25 1380, FAX: 0045 45 88 4325 Dr. M. Caponnetto, Univ. of Genoa

DINAV - Univ. of Genova Via Montallegro

I 16. 145 Genova, ITALY

Tel: 003910 353 241 1/13/30, FAX: 0039 10353 2127 .3. Dr G. Grigoropoulos, Nat. Tech. Univ. ofAthens1 Greece.

Prof J. Ioannidis2, Nat. Tech. _Univ. ofAihens, Greece.

Dr. J. A. Keuning, Tech. Univ. Deift

Fac. ofMechanical Engineering & Marine. TechnolOgy Shiphydromechanics Laboratory

Mekelweg 2 2628 CD DeIft The Netherlands

Tel: 0031 15 278 18 36, FAX: 0031 15 278 6882 Prof. C. Kruppa, Tech Univ. of Berlin, Germany Tech. Univ. Berlin, Inst f. Schiffs- und. Meerestechnik

ISM Sekr SG6

Saizufer 17/19, D 10587Berlin, GERMANY Tel: 0049 30 3142 3411, FAX: 0049 30 3142 2885 Prof S. Mavrakos, Nat. Tech. _{Univ. ofAthens, Greece.}

Dr B. Müller - Graf,, VWS: Berlin.: Müller-Breslau Str. (Schlèuseninsel) D 10587 Berlin, GERMANY

Tel: 0049 30 311 84 224, FAX: 0049 30 31.1 84 200

9, Prof V. Papqzoglou, Nat. Tech. Uñiv. ofAthens, Greece.

'Finally replaced by Professor V. Papazoglou 2Finally replaced by Assoc. Prof. C. Frangopoulos

10. _{Professor A. Papanikolaou Nat. Tech. Univ. of Athens, Greece.}

11., Capt. J. Pfeiffer Dessauer Str. 15

D 28832 Achim, GERMANY

Tel: 0049 4202 3855, FAX: 0049 4202 882 462 12 Prof H. Psaraflis, Nat. Tech. Univ. ofAthens, Greece.

Dr. E. Rizzuto, Univ. of Genoa DINAV - Univ. of Genova Via Montallegro

116 .145 Genova, ITALY

Tel: 003910 353 2411/13/30, FAX: 0039 10 353 2127 Mr. N. Warren, FBM Marine

Cowes Shipyard, Cowes Isle .of Wight, P031 7DL United Kingdom

LIST OF PARTICIPANTS -25th WEGM T SCHOOL ON SMALL CRAFF TECHNOLOGY - ATHENS OCTOBER 6-11, 1997

'LFR: Less Favored Region: acç. to E.C. here: GREECE, PORTUGAL

D :\My Docuinents\WEGEMT-SCT-SCHOOL\LIST-OF-PART-TMR-2.1O-97.doc _i

02/10/97

Ñìví

Ma1&fetha1 Role Industiy/not LFR' Place of work

Afflhiàtion Room Funding Ticket Ongin Payment

1 Abatzoglou, A _{Male Student yes yes Greece Greek Coast Guard No}

No No Piraeus

2. Begovic, Ermina Female Student Not Yes

----CrOatia Zagreb Univ. Yes Yes,room

only

No Zàgréb

3 Bertorello, Carlo Male Student Not Yes - Italy Naples Umv Yes No No Naples 4. Boulougouris,

Evangelos

Male Studént Not Yes Greece Ship Disign Laboratory

-NTUA No FEES 250 ECU No Athens 5. De Ulzurrun, Diez, Ignazio

Male Student Not Yes Spain ETSIN Madrid Yes No i No Mádrid

Den Dikkeñ, Jan Male Student yes not United

Kiigdôm

Private Company Yes Yes Yes London

7. Dimou, Dimitris Male

-Student

-Not Yes Greece Shipbuildmg Technology Laboratory - NTUA

No FEES 250

ECU

No Athens

8 Drouva, Maria Female Student Not Yes Greece NTUA No FEES 250 ECU

No Athens

9. Dyson, K. Male Studení Yès Not Umted Kingdom

Private Company Yes No No London

10 Ehopoulou

Eleftheria

Female Student

-Not Yes Greece Ship Design Laboratory

-NTUA No FEES 250 ECU No Athens 11 Erinfolanu, Lateef

Female Student Not Yes Poland Gdansk Univ Yes Yes room

only

No Gdansk

12 Ferreira, Sergio Male Student Not Yes Portugal iST Lisbon Yes Yes Yes Lisbon

13. Figarri, Massimo

Male Student Not Not Italy 1)INAV Yes Yes Yes - Náples

14 Garofallidis, Dirnitris

Male Student Not Yes Greece Ship Hydrodynamics Laboratoiy,NTUA No FEES 250 ECU No Athens 15. Goumas, Dimitris

Male Student yes Yes Greece Greek Fire Déàthnent No No No Chalkis

16 Gualezu, Paola Female Student Not Not Italy DINAV Yes Yes Yes Genoa

17. Hadzikonstantis; George

Male Student Not Yes Greece Athens Higher Teéhnical

School

No No No Athens

LIST OF PARTICIPANTS - 25th WEGEMT SCHOOL ON SMALL CRAFT TECHNOLOGY - ATHENS

_{- OCTOBER 6-11, 1997}

02/10/97

Anastasios 19. Huang, Shaíi

-Male Student Not Not United Kingdom

Glasgow Univ. Yes Yes Yes Glasgow

20. Jonsson, Gunnar Màle Student Not Not Deñniark/ Iceland

DTU-Lyngby

-Yes Yei Yes Copertha

gen 21. Juergens, Dirk Male Student Yes Not Germany JAFO Company Yes Yes Yes Hamburg 22 Kahlen, Urs

-Male Student Not Not Germany Duisburg Univ Yes Yes Yes Hamburg 23. Karayannis,

Theo

Male Student Not Not United Kihgdom/

Greece

Southampton Univ. No Yes Yes Sòuiham pton 24. Kouzof,

Stefanos

MàIe Student Yes Yès Greece ALPHA Marine Ltd. No No No Piraeus

25. Leenders, Jan Male Student Not - Not The Netherlands

Deffi Univ. Yes Yes Yes Delfi

26. Matzafos, M. Male Studànt Yes Yes Greece Greek Coast Guard Ni No I - No Pìraeus

27 Monaderas,

Nektarios

Male Student

-not Yes Greece Manne Engineering

Laboratory NTUA

No FEES 250 ECU

No Athens

28. Odysseos, Zetta Female Student Not Yes Greece Athens Higher Technical

School

Nó No - No Athens

29. Papadimitriou, Haiilaos

Male Student Yes Yes Greece Greek Navy No No No

Athens-30. Papadòpöulos,

Christos

Male Student Not Yes Greece - Márire Engineering

Laboratory - NTUA No FEES 250 ECU No Athens 31. Papakyrillou, Abraham Male Student

-Not Not United

Kingdom

Suthampton Univ.

-No Yes Yes southam

pton

32 Peppa, Sofia Female Student Not Yes Greece Manne Hydrodynanucs

Laboratory- NTUA No FEES 250 ECU No Athens 33. Perissalds, Stelios

Male Student Not Yes Greece Marine Hydrodynamics Laboratory- NTIJA

NO FEES 250 ECU

No Athens

34 Politis Kostas Male Student Yes Yes Greece Hellemc Register No No No Piraeus 35. Pseftelis,

Giorgos

Male Student Yes Yes Greece Greek Coast Guard No No - - Ño Pimeus

36. Rodriquez-Garcia

Male Student Not Not Spain ETSIN Madrid Yes Yes Yes Madrid

37 Roeleveld, 4 Male Student Not Not

The j\v,f

DeIft Univ Yes Yes Yes _Amsterda

LIST OF PARTICIPANTS - 25th S EGEMI SCHOOL QN SMALL CRAFT TECHNOLOGY - ATHENS

- OCTOBER 6-11, 1997

Ruben _{Netherlands m}

38 Sakellans, D Male Student Yes Yes Greece Hellemc Register No No No

- Piraeus

39 Spanos, Dmutns Male Student Not Yes Greece Ship Design Laboratory

-NTUA No FEES 250 ECU No Athens 40 Voutiras, Vassilis

Male Student Yes Yes Greece Skarainanga Shipyard No No No Piraeus

41. Wadskaer, Pou! Erik

Male Student Not Not Denmark DTh Lyngby No No No Lyngby

42 Weijs Hennette Female Student Not

-Not The

Netherlands

Deffi Umv Yes Yes Yes London

43 Zafiratou, Niki Female Student NÓt Yes Greece Shipbuilding Technology Laboratory - NTUA No FEES 250 ECU No Athens D:\My Documents\WEGEMT-ScT-SCHOOL\LIST-OF-PART-TMR.2-10-97.doc ₃ 02/10/97

LIST OF PARTICIPANTS - 25th WEGEMI SCHOOL ON SMALL

CRAFT TECHNOLOGY - ATHENS - ÖCTOBER 6-Ï!, 1997

D:\My

4

02/10/97 44. Baatrup, Ján _{Male Lecturer Not}

Not Denmark _{DTU-Lyngby Cópènhágen}

45. Caponnetto, Mariò

46.

Male _{Lecturer Not Not}

Italy' _{DINAV, Gnoa Genoa}

Grigoropoutos, Gregoiy 47 Male Lecturer, Ass. Secrataiy

Nôt Yès Greece Marine

Hydrodynamics Laboratozy- NTUA Athens Frangopoulos, Christos 48. Male

-Lecturer Not Yes _{Greece Marine Engmeenng}

Labóratozy - NTUA Athens loannidis, bannis 49. Male Lecturer

-Not _{Yes Greece}

-Marinc Engineering

Laboratory NTUA Athens

Keunmg, J. A. 50

Male Lecturer Yes Not _Netherland

s

Dem Univ. _Amsterdam Kruppa, Klaus

51.

Male Lecturer Not Not Germany _{T U Berlin Berlin}

Mavrakos,

Spyros

Mak Lecturer Not -Not - Greece -Shiptiùildiìig Technology Laboratory - NTUA Atheus 52. Mue1ler.GraJ Burkard 53

Male Lecturer Yes Not _{Germany VWS Berlin}

Berlin Papanikolaou

Apostolos

Male Lecturer,

Chairthan

Not Yes Greece' _{Ship Design}

Laboratory - NTUA Athens 54. Papazoglóu, Vassilis Male Lecturer, Secretazy

Not _{Yes Greece Shipbuilding}

Technology Laboratory - NTIJA

Athens 55 Pfeiffer,

Joachim

Male Lecturer Yes _{Not Germany}

-STN Atlas Electronics Hamburg 56. Psatajujs, Harilaos Male

-Lécturer Not Yes Greece Ship Design Laboratory - NTUA

Athens

57 Rizzuto _{Male Lecturer Not}

Not Italy _{DINA V-Genoa Genoa}

58. Warren, Nigel

-Male

-Lecturer yes Not United Kingdom

FBM Màrüe

Paper to be presented at the workshop on Small Craft Design by

WEGEMT in October 1997 at Athens. (Greece).

SEAKEEPING OF HIGH SPEED CRAFT

by

Dr.ir J.A.Keuning

Deift University of Technology

The Netherlands.

ABSTRACT.

In this paper an overview will be presented of some of the specific design aspects

and the. pros and contras of the various high speed: design concepts with respect

to their hydrodynamic behavior and more in.particular theirbehavior in waves.

Special attention will be given to the nonlinear behavior of fast craft with respect

to the waves. This will be demonstrated using as an example the motions of a fast

planing monohull in waves. Various sources of the nonlinear behavior will be

discussed The imphcations of nonhnear behavior with respect to operabthty will

be discussed.

ThTTRODUCTION.

The combination of high forward seeds and acceptable motions and even moite important acceptable level of (vertical) accelerations in a seaway onboard a fast moving ship have uptill now been proven difficult to achieve.

In the contmumg search for this combmation all kinds of so called "advanced" concepts have been designed, evaluated, built and used. Each of them however with their own specific benefits and drawbacks. The philosophy behind most of these concepts is based on an attçmpt to reduce the resistance of the craft through the water by reducing the volume of displaced water or the wetted surface of the hull at speed or both. Only a limited number öf these

concepts has been "invented" with the aim of reducing the motions and accelerations at high speed in mind.

Many actual applications of fast ships consist of relatively small ships, i.e. fast ferries, service craft, patrol boats, rescue boats and pleasure craft, although in the ferry businessthere is a tendency to considerably larger craft. In general because seakeeping for a given condition improves with the size of the ship. However for most applications itmay be stated that related to the environmental conditionsthis usually means that the waves are relatively large with respect to the size of the vessel. In additionthe high..forward.speed.of the ships under consideration.implies that the waveswhich excite :the ship in or near its natural period for heave and pitch are generally longer (and higher) with respect to the shiplength than customary for ships sailing with "normal" speeds. This implies that in particular in those conditions which must be considered to be of special interest or even critical with respect to the operability of the ship, for instance high forward speeds and high wave heights, large (relative) motions may

occur. Significant bow submergence and occurrence of moments in which the ship is partly free of the water are nOt unrealistic for fast ships.

This implies that the small motion amplitude which underlies the linear theories may no longer be a valid assumption and that the behavior of the ship becomes strongly nonlinear with respect to the height of the incoming waves. In addition,a number of "lift" generating. devices used in the fast shipconcept, like planing lift; aircushions.with seals, foil etc. introduce nonlinearity in the system anyway. due to their veryphysics:

In the followingchapters a shortoversight-of the basic'advanced ship concepts-wili.be given

together with some short remarks on their dynamic behavior. . .

To show the importance of nonlinear behavior when it comes to the evaluation ofa design and possible operability analyses, the nonlinear behavior of a fast planing monohull in head waves will be considered in more detail. It will be demonstrated where this nonlinear behavior in this case originates from and how it affects the motions and accelerations of the ship when sailing in head waves.

An important aspect with these-operability, studies is ,theuse of .adequate.criteria withrespect. to the motions and accelerations which determine the limit of the "save" and/or "comfortable" operation of the ship in a seaway. It will be show that nonlinear behavior may strongly

influence the results of such studies.

2 TYPES OF ADVANCED VEHICLES.

In this chapter a very short and rather condensed oversight will be given of a number of advanced marine vehicle concepts and their main design characteristics as may be seen within the framework of this paper. Apart from the concept presented hereafter, a wide variety of "combined" or also "hybrid" concepts do exist, in which one is trying to combine the best of other concepts. These will not be presented here and the given oversight has certainlynot the pretention.of being comprehensive and/or complete The following concepts will be presented: fast Planing Monohull (PM), Small Waterplane Area Twin Hull (SWATH) ship, Air Cushion Vehicle (ACV) and Surface Effect Ship (SES) and the Hydrofoil

2.1 - PLANING MONOHULL.

Normally a division is being made between Semi-Planing and Planing craft although this distinction is rather arbitrary and more or less based on how much of the total weight of the

craft is considered to be supported by the hydrodynamic lift. Planing craft became increasingly popular during the period between World War I and H and even more during the World War II. They are considered to be relatively easy to build and to have a high speed potential. The lift generating capabilities are strongly influenced by the hard chine and the submerged transom edge. Flow separation at these points gave the possibility to generate adynamiç lift force on the planing bottom of the hull andweli to suchan extent that alarge portion of theship. weight (up to 75%) is carriedby the lift and so 'reducingdisplaced volumeof water and wetted area. A typical example of a planing hull from is presented in Figure 1 and a typical

hydrostatic- to hydrodynamic-lift ratio as function ofthe forward speed is given in Figure 2.. Important parameters influencing the resistance are the Length to Beam ratio, the Loading factor (i.e. the weight related to the planing area), the deadrise of the planing bottom and the longitudinal position of the Center of Gravity.

One of the serious drawbacks of planing craft appeared to be their rather poor seakeeping behavior, in particular in head waves . Due to the generated hydrodynamic lift even in

moderate seastate unacceptable high levels of vertical accelerations may occur. The seakeeping behavior may be significantly improvedby increasing the deadriseof the planing bOttom, by

reasmg the length to beam ratio of the hull and by reducing the weight of the craft and

further .::

improvenents:in.ffie?seakeepingbehavioroftheplaning craft;:like.theEnlarged ShipConceptff: ESC) and the Veiy Slender Vessel

concept (VSV).

The behavior of the craft in waves is strongly nonlinear. This originates from a considerable change in the reference position of the craft with speed (.i.e. sinkage and trim), the very nature of the hydrodynamic lift on the hull, the considerable relative motions which the craft

performance and the associated large changes in submerged hull geometry of the craft and the influence of the high forward speed on the distribution of the hydrodynamic färces over the length of the ship.

2.2 - CATAMARAN,

The catamaran is in principal a twin hull vessel. The hulls are placed on a certain distance from h other therefôre making it possible to increase the transverse moment of inertia of the waterplane area which determines the transverse metacentrc height positively and so the transverse stability. The waterplane area of each hull itself may therefore be decreased thus leading to a very high Length to Beam ratio of each separate hull (upto 20) .This has a very positive effect on the wavemaking resistance of the concept. An additional advantage is that the two hulls are connected by a "bridge deck" at some height above the water, which gives the concept a considerable deck area.. A typical example is presented in Figure 3.

The concept is capable of attaining high speeds due to its low wavemaking resistance. The behavior in waves is generally not better than that of a monohull and high vertical accelerations and loads will occur when the bridge deck hits thewater. The height of the deck above the water (the clearance or airgap) 1s therefore an important design aspect with respect to

seakeeping The high speeds introduce nonlinearities in the motions in particular due to sinkage and trim, although less than with a planing hull. Interaction effects between the two hulls however may introduce strong speed dependencies into hydrodynamic forces on the hulls. In following waves there is a tendency to "bow diving" due to the decreased longitudinal stability originating from the very slender hulls, a highly nonlinear phenomena. The structural loads on the cross beams and girders in waves may become very high.

4

2.3 - SMALL WATERPLANE AREA TWIN HULL SHIP.

This SWATH concept was originally tried out in the 1930's but only fully investigated in the 1980's. In principal it is a fill displacement ship of which the biggest part (upto 90%) of the displacement is being carried by two filly submerged cylinders. These two cylinders are connected to a superstructure placed high above the water (the "Box") connecting the two widely separated hulls by means of two (or four) very slender struts. These struts have a very small longitudinal cross section and so waterplane area. Therefore the concept is sometimes referred to as Semi Submerged Catamaran, i.e. a catamaran with most of the displaced volume deeply submerged. A typical layout is depicted in Figure 4.

The principal aim of the concept is improving on the seakeeping behavior. Although the wavemaking resistance is generally small when compared to a monohull of similar

displacement, due to the highly submerged volume and the slenderness of the struts, the wetted area of the two cylinder and two struts is very high. The size of the waterplané area is largely determined by stability considerations. Due to the small waterplane area the wave exciting forces are small and the natural periods in heave, roll and pitch are long placing the resonance frequency far outside the frequency range of the seaspectrum.

The concept however is very sensitive to payload variations and the longitudinal stability decreases with increasing speed. Therefore the concepts needs considerable stabilizing fins fore and aft and preferably with active steering to control the stability as well as pitch motions in particular in following seas. This makes the concept rather complicated.

Viscous components in the hydrodynamic forces play an important role in the motions of these craft, in particular damping dúe to cross flow drag etc. This is in addition to the significant nonlinearities in the. considerable forces introduced by the large number and size of the (active) stabilizing fins.

2.4 - AIR CUSHION VEHICLE AND SURFACE EFFECT SHIP.

The ACV and the SES obtain their weight carrying capability by the introduction ofan air cushion. In the ACV concept this is "kept in place" inside a flexible rubber skirt surrounding the entire cushion and just skimming the water surface, see Figure 5. In the SES concept the air cushion is maintained between two very slender hulls and-two flexible seals : one fore and one aft. See Figure 6. The hulls ofa SES in "on cushion" mode are still in the water so sealing the cushion more rigorouslythan in the case ofthe ACV so reducing air losses and may be considered as an catamaran with extreme slender hulls and an air cushion underneath the bridge deck.. The ACV concept however is the only amphibious one. Typical ACV propulsion is therefore with air propellers by which she is 'also maneuvered, typical SES propulsion is by water propellers with normal rudders or steerable wateijets. This concept can attain very high speeds upto 90 knots.

For stability reasons the aircushion of the ACV has to be devided in several compartments and stability in 'all directions is troublesome. Also the air losses underneath the skirt are generally high necessitating larger power on the fans maintaining airflow and cushion pressure.

Maintenance costs of the skirts are very high. Seakeeping performance is moderate and maneuvering performance'is poor due to the way of steering and the lack of hydrodynamic sideforce generation, since there are no submerged parts.

Controllability of the SES is much better. The seakeeping behavior is moderate to poor. Nonlinearities in the motions are introduçed among others by the loss of air underneath the seals which are dependent on the size of'the gap which is introduced by the relative motions of

the seals with respect to. the waves, air cushion dynamics itself and the air fans dynamic characteristics etc. A major problem of the SES ships uptill now is the relatively very large added resistance they experience when sailing in waves.

2.5 HYDROFOILS..

In the hydrofoil concept the weight ofthe craft is fully supported by the hydrodynamic lift generated by a system ofhydrofoils The displaced volume ofthe hull therefore reduced to zero (and so the wave making resistance) as is the wetted surface of the hull. The resistance of the craft in this condition is composed ofthe viscous drag ofthe foils (friction and form drag)

and: the resistance due to lift generation (i.e induced drag including wave drag).

In principal two basic concept ofhydrofoil boats do exist, i.e. the one with the surface piercing foils forward combined with a fully submerged foil aft , seeFigure 7, and the one with only fully submerged foils fore and aft, see.Figure 8.

The: system with he surface piercing foilisinherent stable due to. the restoring moments. ;. , .

heave, .pitchorroll.motions'::Thi.type' hastherefore.no needL'fut

açtiver.controlon'tbe flnsThe

r

r rV V

accelerations' may occur andinfollowingwaves largerelativemotions...V

The fully submerged type is dependent on an active control of the wing flaps to maintain stability and control motions in a seaway. This enables the craft however to be fully controlled in waves with respect to the motions and this type of craft is therefore superior to all other in that respect. The deeply submerged foils are hardly troubled by the orbital velocities in the waves and the active control imposed by the automatic pilot "smoothes out" all resulting motions. This is called "platforming", i.e. no heave and pitch (or roll) motions of any

significance in waves. When the waves become.larger the ship motions are controlled is such.a way as that the craft moreor less "follows" the wave. profile, this is. called "contouring". V

The nonlinearities in the motions response for both types ofhydrofoll craft as well as in the wave- and motion-induced forces are considerable, both by the very nature of the physics of the lift generation itself, which is dependent on variations in submerged foil area, in angle of attack on the foils and in the relative speed over the foils due to the combined action of the forward speed, the orbital velocities in thewaves and craft motions or by. the introduction of active control.

3 NONLINEAR BEHAVIOUR.

As indicated in the description of the various advanced concepts in the previous paragraph most of these craft must be considered to be more or less nonlinéar system through various sources as far as their behavior in waves is concerned. So when dealing with the design and evaluation of these designs this must always be taken into consideration.

To' show the implications of this nonlinear behaviorthe nonlinear behavior of a fast planing craft iii head waves will be elaborated a little further. The effect this has on' operability analyses will 'be shown and much of the items discussed will he applicable to the cases of other of'these fast ships concepts as well.

First it is necessary to define nonlinear behavior. In the context of ship motions studies non linear behavior is considered to be the non linear dependency of the amplitudes of motions, of

velocities and of accelerations (and forces) on the amplitude of the incoming disturbingwave. If nonlinearities in this behavior prove to be of any significance then their sources of origination should be localized and possibly be introduced into the physical or computational models used to analyze the designs.

3.1

_{- EFFECTS OFNONLllARJTES.ONTHE:BEHkWOUR OFAPLANThTG BOAT}

3.1.1 - LARGE RELATIVE MOTIONS.

As explained earlier the fact that the fast ships commonly are relátively small with respect to the incoming wayes A typical range from shiplengths used to be from 1!O to 40 meters,

although much larger planing ships have been build recently. From both theory ad experience it is known that the longer waves with respect to the shiplength are capable of generating larger exciting forces. This may lead to large motions when the ship is being excited in or near its resonance frequency: In the case of a fast ship moving against the. waves; resonance occurs ,. at re1atively:longerwavesdue. to:the highforward .speed:'. :T.his.may introduce.relative:large. ::'

relative

techniques is:that.the.craftperfoims:infinitely:small motionswith. respect to thewaves::This.simp1ificationwillnotlonger:holdtrueunder these circumstances and considerable discrepancies between assumed linear and actual nonlinear behavior may be observed. Not taking into account the whole geornetty of the ship in the calculations may therefore lead to erroneous results.

To demonstrate this an experiment has been carried out with three models having thesame aft body shape body but different bow shapes and more in particular different deadrise angles in the fore body in particular above the waterline. The design waterline shape was kept the same

as much as possible.. .The.model.bodyplans.are.presented.in.Figure 10 together. with the results. of the maximum vertical'.accelerations:at the bow as measured in three different seastates, (Irregular waves!) The effect of the change in body shape is obvious. Visual observations of the. models during the tests revealed the models performed large relative motions in particular at the bow with frequent bow emergence and immergence. The re-entrance of thè bow in the water was much more severe with the low deadrise. models. This will account for the

nonlinearities and the differences between the designs.: the V-shaped sections will yield strong nonlinearities in the wave exciting forces and the hydrodynamic reaction forces when it is being "pushed" in and out of the water.

.1.2 - EFFECTOFTHEDEADRLSE

Since the studies of Fridsma and Van der Bosch the noticeable effect of the deadrise on the motions and accelerations of planing boats in a seaway is known This effect lies somewhere in line with the effects mentioned in 3.1.2 since the change in geometry of the craft in contact with the water plays an role. But also the lift generatedon the planing surface is strongly dependent on this deadrise angle : the smaller the deadrise the higher the lift. The

hydrodynamic lifthowever is a strong nonlinear force by the character of the physics involved. To demonstrate this some results of Van der Bosch will be given here. He tested two models: one with 12.5 degrees and the other with 25 degrees deadrise angle All other variables were kept constant as much as possible. Bodyplans are presented in Figure 12. To demonstrate the nonlinear behavior he tested the models in regular waves with two different waveheights.

During the tests recordings were made of the heave, pitch and vertical acceleration signals. Typical examples of such recordmgs of both modelsare presented in Figure 13 The nonlinear response of the models with respect to the regular (sinusoidal!!) incoming waves is obvious! The nonlinearity increases with decreasing deadrise angle, as predicted.

1.1.3 CHM GRIN REFERENCE POSITION

An important phenomenon introducing nonlinearities in the behavior of most fast sips but in particular planing boats and one that is not accounted for in linear computational models is the change of the reference positions of the craft. at speed. Although not strictly a nonlinear behavior in its self in' the way as defined in the previous paragraph it introduces considerable nonlinearities in the behavior. The reference position of the craft changes due to what is known as "sinkage" and "trim", introduced by the effects of he hydrodynamic lift generated by the high relative velocity between the planing bottom and the water. A typical examplè of this sinkage and .trim:as, functionoftheforward speedis presented in Figure9.for one particular... design The magnitude ofsinkage and trim and their dependency on forward speed is strongly

. . .. .

andtrim ontheheaveanthpitchmotions.

inregular

_{byFridsmaandVanderBosch:}

In Figure lithe influence of a change of only 2 degreesm the stationary runnmg trim of a schematic model on the.heave and pitch motiöns is shown. From this figure it may be conçluded that this influence is substantial. This conclusions holds also true for the vertical accelerations.

3.1.4 - THE. RYDRÓMECHANIC FORCES ON APLM4ING HULL

Various modeisdo exist to describe theforces on' and the motions offast'planing bóats: One' group is based on the formulations as given by Zarnick This is in pnncipal a 2-D strip theory approach and is based on the lift theory as described by Von Karman. His theory is based on the concept of change of momentumof the flow expressed in terms of the "added mass" of the section nderconsideration. .(See Figure 14.)

dF=(ma .v)

in which: dF the force per strip

ma = the added mass of the strip

The rate of change of momentum of the fluid at a particular section may be further elaborated into:

-P(m .v)=

Dt a

.V+V.rn---(m

a

d,

a dt

In contradictionto "ordinary'striptheoty" .there.is atime dependent term of the, added mass.. The last term in the expression is related to the distribution of the added mass over the length of the hull.

In the steady state planing condition, i.e. no waves no motions, then:

V=U0.sine

and ma may be approximated by

ma = 7C.PY2 Cm

in which: Uo = horizontalvelocity. of the:.hull. trim:angle of the' hull

density of water

half width of the section added mass coefficient

The formulations were found by Von Karman from tests with wedges which penetrated the water surface at a constant velocity.'

An additional term is brought into the dynamic lift formulation based on the so called "Cross Flow Drag" and. reads:

D,c

=4.p.(UO.sinB).b.CD

in which: CD, = cross flow drag coefficient

b = 2 * y (local beam of the section)

The cross flow drag coefficient may according to Shuffold be approximated by: CDC =1.15cosl3

Finally a buoyancy force stilt works on the section. This force is assumed to work inthe vertical plane and to be equal to the equivalent static buoyancy of the section corrected by a correction factor abf accounting for the hydrodynamic rather than hydrostatic pressure distribution around the submerged part of the section, i.e.

in which: A = submerged cross sectional area of the 'sectiôn.

The total hydromechanic force on the hull is obtained by integration of these forces on the segments over the entire (momentaneous) wetted length of the hull influenced by its actual

s

e

p = = y = Cm =

forward speed, the wave elevation along the length of the hull and the motions. This yields for the vertical force as an example:

;cosed -I-abf Ap.gd

and U and V are the velòcity components in an earth fixed coordinate frame along the length of the hullresulting from the combination of the forward velöcity of the hull and the heave and pitch motions and the wave orbital velocities. In the body fixed coordinate frame these become:

U =XCG cos6

-

sin O.

V =

xcG.sinO(z wi).

cose

Many of the variables listed in the formulations above are time dependent quantities just as the wetted length over which the integration is to be taken. This illustrates the nonlinear charaçter of the expressions and variables very well The momentaneous values taken mto consideration account for the total actual geometry of the. craft in contact with the water introducing the change in reference position whilst performingnon-small. amplitude motions relative to the incoming waves, an important nonlinear effect.

In the case of other fast craft sirmiar expressions and sources of nonlinear behavior do exist and it should be noted that this very short elaboration of the forces on a planing hull is, only presented here to highlight the origination ofthese in the case of high speed ships

4 - THE EFFECT OF NONLINEAR BHAVIOUR ON OPERABILITY ANALYSIS

In order to be able to asses the quality of various design variations the operability analysis plays an important role nowadays. First a description of the procedure followed in suchan analysis in the case of a "normal" linear system will be described.

The operability analysis is carried out given a known design which has to operate in a known sea area. From this area based on long-term statistical data a so-called "wave scatter diagram" may be obtained. This data is available from various sources and a typical example obtained from Hogben and Lumb (1967) is presented in Figure 15. In such a "wave scatter diagram" the wave data and: its frequency of occurrence is. presented in a matrix yielding for each significant wave heights (H113) and peak period (Tp) of the wave spectrum the percentage of occurrence of that particular combination. These wave scatter diagramsmay be obtained on a yearly basis, a seasonal basis or even a monthly basis depending on the kind of analysis one wants to make and is derived from long-term observations in the given area.

9

F(t) = Ncose =jf.cosed+5fBd

ma (,t).

'(,t) ±

a(,t) v(,t)

-=

To calculate the operability öfthe craft the relevant response ofthe ship to all those spectra under consideration must be obtained. So ifwe constrict ourselves to headsea_{conditions and} one service speed only, the heave and pitch response ofthe vessel under consideratión _{at the} given speed to all these spectra must be known. As is known from shiphydromechanic theory for a supposed linear system these relevant responses may be.obtained by combination of the Response Amplitude Operators (RAO) and thegiven spectrumto,obtain the wanted_{response :} spectrum and therewiththe significantvalües for heave;pitch or vertical accelerations. ata _.. s given point along the length ofthe ship. This must be done for each element inthe wave scatter diagram.

When a (hard) limiting criterion is known for the safe or comfortable operation ofthe ship it can be checked for each "cell" of the scatter diagram whether this criterion is being met or not and by adding the percentage of occurrence of each "cell" for which the ctherion is_{met the} "operability, i.e. the percentage oftime that the craft may be safely or comfortably operated in the given area at the given speed, may be obtained. If a more detailed analysis of the operability

is wanted also the "mission profile" ofthe ship_{may be taken into account, i.e. how much time} is spend at which. speed and with.which.heading with

respect. to,the, waves. In most cases....

however the worst. case; i e: 100% upwind is considered .asa.first,assessment, because bringing in the .mission.profilintothecaki.ilations sincreases:thenecessarywork.quiteconsiderably:.-.:It is :obv ouss.thatsthe.savailabilityofa: setoflimiting:criteriasfor.the: safe..operationof.the, ship.:is:.s'

essentialfor each:'operability-assessment...These criteriahoweverareratherdifficulrto'obtain.-. Quite often these criteria are based_{on the significant values of motions andíor accelerations} certainly for "normal" speed commercial craft and navy vessels. 'As far as the safe operation of ships is concerned many of these limiting criteria are based on the significant values of the vertical accelerations at important places of the ship, for instance the passenger areas or the wheelhouse or control room etc.

In the case of high speed craft however evidence does exist form tul scale experiments with patrol craft at. sea that the occurrence .of the high peaks:in the vertical accelerations as shown. for instance in Figure 13 are TFIE limiting phenomenon with respect .to the safe operation irrespective of the height of the associatedsignificant values. Once such_{a high peak occurs the} crew reduces speed or changes heading to "prevent it from happening again". From these experiments it became obvious that most professional crews reacted to peaks of the same magnitude in a similar way, i.e they all reduced speeds at peak values round and about 1.25 times g.

This implies that these peak values must be properly predicted in order to be able to asses the operability of different designs, which may vary considerably in theirresponse to the same waves in that respect as shown in Figure 13.

So nonlinear motion prediction methods must be used in the case of fast ships!

This complicates the operability calculations considerably. Assuming a proper calculation method for t.he fast ship concept under consideration is available, which is taking into account all the important nonlinear effects, than a simple RAO does no longer exist. -So for each spectrum of each of the "cells" of the scatter diagram a sufficiently lông simulation in the time domain of the motions of the ship at the given speed has to be made in order to be able to analyze the motions and vertical accelerations time traces with sufficient statisticalreliability. This implies in general the occurrence of at least 600 - 700 wave encounters in the simulation mn Then a distribution of for instance the vertical acceleration levels of the time signals (traces) has to be made in order to calculate the percentage of exceedance of

a given preset.

criterion limit.

Since the wave heights in a wave spectrum are normally considered to be Rayleigh distributed, its is cústomary to present these percentages of exceedance in a so-called "Rayleigh plot". A typical example is presented in Figure 16, in which for three different designs of a planing

monohull designed as a coast guard vessel for the Dutch Caribbean, the distribution of the vertical accelerations in the wheelhouse of the ships is presented The deviation from the Rayleigh distributiòn (givenas the straight line) duetothenon1iñearityof the system is

obvious, in particular for the design vanation which produces the most hydrodynamic kif and so the làrgest nonlinearities; Comparisons made between the various designs which are based on the exceedance of the significant values of the vertical acceleration (i. e. by definition the value with anexceedànce of 135 %M) reveal a much smaller differences between the three

designs than when based on the apparently more realistic occurrence of'the (peak) values of 1 25 times gU Even the trends between the different designs with respect to their operability may be completely different when based on these significant values, and so may lead to erroneous design decisions.

5 CONCLUSION

From the results. presente&'aboveitmay be concludedthat mostadvance&marinevehiòles exhibit a nonlinear behavior in waves. This may originate from various sources dépending on the type of craft under consideration. A common source is the change in reference position (smkage and trim) the high forward speed and the relatively large relative motions These nonlinearities become important when assessing the behavior and operability in waves of he various design concepts and variations with respect to each other.

12

6 REFERENCES

Blok, J.J. and W. Beukelman, The high speed displacement ship systematic series hull forms, SNAME Trans., Vol. 92, 1984.

Beukelman., W,. Prediction of operability of fast..semi planing.v.essels.in a seaway, Report 700, ShiphydromechanicsLaboratoiyTUDeIft, 1986.

[311 Bosch, J.J. van den, Tests with two planing boat models in waves, Report 266, Shiphydrómechanics Laboratory TU Delft, 1985.

[4] Clement, E.P. and L.D. Blount,, Resistance tests of a systematic series of planing hull forms, SNAME, 1963.

[511 Keuning, J.A. and J. Gerritsma,, Resistance tests with a series of planing hull forms with 25 degrees. deadrise,. International Shipbuilding'Progress,. Vol. .198.

. . ..Keuning;:'JA.,Distribution.:of'added :massand dathping':along-the-lengthof aship

model moving at high forward speed, International Shipbutldmg Progress, Vol 410 Savitsky, D., Hydromechanic design of planing hulls, Manne Technology, October 1964.

Zarnick, E.E., Anon linear mathematical model of motions of planing boats in waves, AIAÁ, 1979.

Journée, J.M.J'., 'SEAWAYDeift' User manuaiofrelease 4.00, Report 9.1.0,. Shiphydromechanics Laboratory TU DeIft; 1992:.

1.2

o,..

0.4

MOD.85

M OD. 84

M 00. 85

cm

(both

I

P MO D. 8.4

i I -i -- i f Figure 1

CENTER OF AD

O.6L.

O:.4L

O.2L

modeLs)

6O

d e g r.

13

\1

"'20

o

13

o

0.8 L

14

i

Li ft

+

a

Waterverp.

0.50

02

AFT BOD PLAN Figure 3 =

Y/Vg V'b'3

Figure 2 FO RWARD

k im

vri

_rvr1j

Waterv.

I y

i

2 5

STRUT YIATER LINE REAR CONES HULL STABILITY BAGS REAR BAGS Figure 5 Figure 4 a' CROSSSTRUCTIJRE FINS OUTER SKIRT LANDING PADS

t

15 1(EEL _FINGERS

16 SIDEWALL CUSHION B EAM STERN SEAL RUDDER OR iENTRALFIN Figure 6 CUIIION LEtIGTH LIFT FAN Figure 7 BOW SEAL

deg.

-i:

-

0.2

-

0.1 ZG V1/3

o4

0.1.1 2 3 - Fn Figure 9 17

18

LO

25 degrees parent rne1

8 ord.18 = 45 deg. 8 ord.18 = 35 deq. g ord.18 = 55 deg. 1/ ! 3 I

11

I 30° 40° 500 60° 3 ord.Lt Figure 10 it) 20 F1113 I- 0.59 16.7 2 0.59 27 . 8 3 1.72 16.7 4 1.72 27.8

LO O . he3 ve 1= S 0 0 _{0.6 0.5 1.0 1.25} 1.5 ¡T7

-200 0.6 0.3 1.0 - pLtca f

;.Oflf

0.5_i

_Im

o i O 0.6 0.3 1.0 Figure 11 60

i

J

19. 0.8 t 40 0.4 T a 1.2

t40

0.8 0.4 L'5 1.0

0

Pjn

o H . o 20

t

model 84

Fn7 =2.9

x/L..= 2

-7i 2i + o

-.

Pth + o + 01. o -leave o MO08L Fn7 2.9

J

1L /

0L

i

t

Figure 13

/

ir

:C.d

/ -':

L

L____

:.

-!

L/2ç30

LMOD.85

L/

=Z0

-I.-

.

X/=2

'2Ç-/

L fl

--f\ -

'T

-Vg L V _i! t .

iII

L/231.S

+ L/2Ç]O

w

L/2Çi8.8

/7

model 85

Fn. = 2.9

À/L= 2.

M OD. 84 M OD.85 Figure 12 Figure. 14 Figure 15 21 Uo. T I freq-1 opera-(metres) uency bility 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 sec. of H113 L 3.2 2.4 2.4 24 - - - -. - - -2 4.8 3.5 3.5 1.8 1.7 - - - -3 6.3 11.0 10.8 P7.4 0.2 - - - -4 7.5 14.3 10.8 4.2 6.6 :3.6 - . - - - -5 8.8 13.3 6.8 3.2 3.6 5.6 0.9 - - - . - - -6'. 9.,7 17.6 7.1 3.7 3.4 5.3 4.6 0.5 - - -. -7 10.9 10.1 4.3 2.1 2.2, 1.6 1.8 2.0 0.4 - - - -8 12.4 9.8 4.3 2.1 2.2 U.. 0.9 1.2 1.6 06 0.1 - -9 13.8 5.2 J.) L.)

U3 O1

0.5' 0.3 0.1 0i. 0.3 Ô.! -LO 15.0 8.7 6.7 3.4 2.1 1.2 O..8 0.3 0.2 0.2 0.2 0.2 0.1 11 16.4 3.7 2.8 0.9 0.8 0.7 0.5 6.3 0.2 O1 0.1 0.05 0.1 Total 99.6 628

22 71 20 15 E 10 0Q 0 100 A----.A2600 (meas.) 2600 (Ray')) o o 3500 (meas) 3500 (Ray') TUO4100 (meaal TUO4100 (Rayl)

Ccndition 2. posÚve peaks

Percentage of exceeianca. Figure 16 A

-

o:

d.

:0

A,'

o...

:;.:

-50 20 10. 5 2 1 0.5 0.2 01 Percentageofexcedance (%) Condon4 A 2600'(meaz) 2600(Ray1) 0----0 3500(mea) A 25O0(Ra.) TUD4 100 (meas) _A TIJD4 100 (RaI)

/

.0 A .0 .A ..0.4. .-. 4. 0

---0 T 50 20 0 5 2 I 0.5 0.2 01. 20-15