The Effect of Bowshape on the Seakeeping Performance of a Fast Monohull

The Effect of Bowshape on the

Sea-keeping Performance of a Fast

Mono-hull

By J . A . Keuning

Report 1291-P September 2001

Published in the 6th International Conference on Fast Sea Transportation, FAST2001, 4th - 6th September, Southampton,

ISBN: 0 903055 70 8, The Royal Inst, of of Naval Archtects, UK

TU Delft

Deifi Umvereity of Teclmology

Faculty of Mechanical Engineering and Marine Teclmology

The 6th Intemational Conference

on FAST SEA TRANSPORTATION

4th - 6th September 2001 S O U T H A M P T O N

PAPERS

Volume I

THE ROYAL INSTITUTION OF NAVAL ARCHITECTS

FAST200^

The 6 Intemational Conference on

FAST SEA TRANSPORTATION

4 - 6'" September 2001 S O U T H A M P T O N

© 2001: The Royal Institution of Naval Architects

The Institution is not, as a body, responsible for the opinions expressed by the mdividual authors or speakers

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FAST 2001: 4"' - ö** September 2001, Southampton, UK

VOLUME I

D E S I G N COMPARISON AND ASSESSMENT

A Decision Making Model for Alternative High-Speed Ferries I - 1 T. Karayannis, Ship Design Laboratory, National Technical University of Athens, Greece

A.F. Molland, School of Engineering Sciences, Ship Science, University of Southampton, UK

An Evaluation of the Effect of Hull Form Choice on the Operability of Fast Ferries I - 13 John Bonafoux, Edward Dudson, David Sherwood, Nigel Gee and Associates Ltd, UK

Monohull, Catamaran, Trimaran & SES High Speed Sealift Vessels I - 23 Chris Broadbem, DERA MOD UK

Colen Kennel NSWCCD, David Taylor Model Basin USA

Transport Economy-Based Evaluation and Assessment of the Use of Fast Ships in 1 - 3 5 Passenger-Car Ferry and Freighter Systems

Mitsue Morishita and Shinsuke Akagi, Osaka Sangyo University, Japan

Fast Cargo Vessel: Concept Assessment 1 - 5 1 Jesus Garrido Lindez and Fernando Maria Guarido Villa, IZAR Construcciones Navales,

S.A. Spain

D E S I G N METHODS AND A N A L Y S I S

Direct Calculation in the Design of HSC I - 63 Anders Rosén and Karl Garme, Division of Naval Architecture, KTH, Sweden

The Effect of Hull Form on Loss of Stability and Heel Yaw Coupling for High Speed 1 - 7 1 Monohulls.

Martin Renilson, Trevor Manwarring, Australian Maritime College, Tasmania Australia. Simon Kelly, Logistics Technology International, Melbourne Australia.

An Analysis of Planing Craft Vertical Dynamics in Calm Water and Waves I - 77 J.I.R.Blake and P. A. Wilson, University of Southampton, School of Engineering Sciences,

Ship Science, UK

W A K E W A S H I

Ships Wash Impact Management (SWIM) 1 - 9 1 Ronnie Allen, Maritime and Coastguard Agency, UK

Richard Clements, Marinetech south Limited, UK

Focussing the Wave-Wake System of a High-Speed Marine Ferry 1 - 9 7 Lawrence J. Doctors, The University of New South Wales, Australia

Stephen J. Phillips, Seaspeed Technology Limited, England Alexander H. Day, The University of Glasgow, Scotland

FAST 2001: 4'" - ö'" September 2001, Southampton, UK

A Study of Fast Ferry Wash in Shallow Water. I - 107 Rory Doyle, Trevor J.T. J^^ittaker and Bjönj ElsaJSer, Queen's Universit)' Belfast, UK

Concept Evaluation for High-Speed Low-Wash Vessels 1-121 Alexander H. Day, Universit}' of Glasgow, UK

Lawrence J. Doctors, The University of New South Wales, Australia

Fast Ferry Wash Measurement and Criteria 1-135 Ernst Bolt, Transport Research Centre, Ministry of Public Works and Water Management,

Netherlands

W A K E W A S H n

The prediction of the characteristics of ship generated near-field wash waves 1-149 A.F.Molland, P.A.Wilson, S.R. Turnock, D.J. Taunton andS. Chandraprabha, School of

Engineering Sciences, Ship Science, University of Southampton, UK

Experimental and Theoretical Investigation of Walce Wash 1-165 Kourosh Koushan, Per Werenskiold and Rong Zhao, MARINTEK, Norway

Jago Lawless FBMBabcock Marine, UK

Wash of Ships in Fmite Water Depth 1-181 Qinzlieng Yang and Odd M. Faltinsen, Department of Marine Hydrodynamics, NTNU,

Norway

Rong Zhao, MARINTEK, Norway

S E A K E E P I N G I

The Effect of Bowshape on the Seakeeping Performance of a Fast Monohull I - 197 Alexander (J.A.) Keuning and Jakob Pinkster, Delft Universit)' of Technology, The

Netherlands

Serge Toxopeus, MARIN, The Netherlands

Nonlinear Reliabihty Based Seakeeping Performance of Naval Vessels 1-213 Wouter Pastoor, Ship Hydromechanics Laboratory, Deifi University of Technology, The

Netherlands

Optimisation of the Seakeeping and Performance of a 40 Knot Pentamaran Container I - 225 Vessel

Edward Dudson and Nigel Gee, Nigel Gee and Associates Ltd, UK

Investigation on Optimization Strategies for the Hydrodynamic Design of Fast Ferries 1-235 Stefan Harries and Claus Abt, TUB - Technical University of Berlin, Institute of Land and

Sea Transportation, Germany Federica Valdenazzi, CETENA, Italy

Umberto Viviani, FINCANTIERI- Cantieri Navali Italiani S.p.A., Italy

Seakeeping Performance of High Speed Catamaran Vessels in Head and Oblique I - 247 Waves

Dominic Hudson. Anthony Molland, W. Geraint Price and Pandeli Temarel, University of Southampton, UK.

FAST 2001: 4"" - ó" September 2001, Southampton, UK

S E A K E E P I N G H

Rolling Dynamic in Planing and Semi-Planing Range 1-259 Flavio Balsatno, Stefano Milanesi and Claudio Pensa, Dipartimento di Ingegneria Navale,

Universita degli sudi di Napoli 'Federico II", Italy

Dynamic Stability and Roll Motion Modelling of MultlhuUs 1-263 Alberto Francescutto and Antonio Cardo, University of Trieste, Italy

Vertical Motion Control of Twin-Hull Vessels Using Neural Optimal Control 1-271 Farhad Kenevissi, MehmetAtlar and Ehsan Mesbahi, University of Newcastle upon Tyne,

VOLUME n

P R O P U L S I O N

Counter Rotating PropeUers Without Complex Shaftmg for a Fast MonohuU Ferry E - 1 Eckhard Prae/ke and John Richards, Hamburgische Schiffbau-Versuchsanstalt

Jürgen Engelskirchen, Blohm+Voss, Germany

Gaseous Fuels for Passenger Vessel Apphcations n - 13 Greg Cox, Kamira Holdings Pty Ltd, Australia.

Experimental Vahdation of the Calculated Flow in a Waterjet Steering and Reversing I I - 31 Unit

Gregory J. Seil, Rolls-Royce Hydrodynamic Research Centre - Rolls-Royce AB, Sweden

H I G H S P E E D F E R R Y D E S I G N

Preliminary Design of High-Speed Monohuh ferries I I - 41 PrabhatK. Pal and Dugald Peacock, The University of New South Wales, Australia

High Speed and Low Vibration Design for a Twin Screw Passenger Ferry U - 57 Giovanni Brescia, Gianpiero Lavini and Gennaro Avellino, Fincantieri, Italy

V u ^ a l RoPax - The Design of a Target Ship for R«&D Purposes on High Tensile Steel n - 65 Friedrich Schöttelndreyer, Berend Bohlmann and

Stefan Kriiger, Flensburger Schiffbau-Gesellschaft, Germany

H I G H S P E E D C A R G O V E S S E L D E S I G N

Prediction of Global Wave Induced Response for the A D X Express High-Speed U - 71 Pentamaran

Axel Köhlmoos, Germanischer Lloyd, Germany Ed Dudson, Nigel Gee and Associates Ltd., UK Hans Jorgen Rambech, MARINTEK, Norway

FAST 2001: 4" - ó"" September 2001, Southampton, UK

Conceptual Design Investigations of a Very High Speed TranspaclRc Container Vessel 11-81 Grant E. Hearn, University of Southampton, UK

Ivo J.S. Veldhuis, Ocean Fleets Ltd, UK Riaan van 7 Veer, MARIN, The Netherlands

Robert Jan Steenbergen, Volharding Group, The Netherlands.

Experimental and Numerical Study on Trimaran Configuration Efficiency for High- n - 109 Speed Very Large Ships

Amedeo Migali, Salvatore Miranda and Claudio Pensa, Universita degli Studi di Napoli "Federico II", Italy

R E G U L A T I O N AND S A F E T Y

Revised IMO Stabihty and Buoyancy Requirements for High-Speed Craft U - 115 Andrew G. Blyth, Blyth Bridges Marine Consultants Ltd, UK

Classification Requirements for High Speed Naval Craft n - 125 Robert Curr)>, ABS London

Derek S. Novak, ABS New Orleans

Safe Handling and Operational Limits of H S C 11-137 Egil Jullumstr0, Per Werenskiold and Svein P. Berge, MARINTEK, Norway

Interactive Multimedia Technology for Safety Training on Stena Line's HSS1500 n - 147 Chengi Kuo, Alison Smith, Simon Craufurd, University of Strathclyde, UK

Chris Cain, John Ferguson, Stena Line Ltd, UK

A Formal Method to Balance Safety Requirements and Regularity of Fast Ships I I - 157 Claudia Vivalda, European Commission, DG RTD, Belgium

Marc Lassagne, Ecole Normale Supérieure de Cachan and Bureau Veritas, France

S T R U C T U R A L R E S P O N S E I

Motions and Loads of a Trimaran Travelling in Regular Waves 11-167 Alexander E. Bingham and John K. Hampshire, DERA Rosyth, UK

Shi Hua Miao and Pandeli Temarel, University of Southampton, UK

Determination of Wave Bending Loads on a 40 knot, Long Slender Open Topped 11-177 Containership Through Model Tests and Hydrodynamic Calculations vdth Particular

Reference to the Effects of Hull Flexibility on Fatigue Life Edward Dudson, Nigel Gee and Associates Ltd, UK

HansJorgen Rambech andMingKang Wu, Marintek Sintef Gruppen, Norway

Global Wave Loads for a Trunaran Ship H - 191 Stefano Brizzolara & Enrico Rizzuto, DINAV-Dept of Naval Architecture & Marine

Technologies, University of Genoa, ITALY

Practical Calculation of Global Design Loads and Load Effects for Large High Speed H - 203 Catamarans

Svein Erling Heggelund and Jan Roger Hoff, MARINTEK, Norway

Torgeir Moan, The Norwegian University of Science and Technology (NTNU), Norway Stig Oma, Fjellstrand AS, Norway

FAST 2001: 4'" - 6'" September 2001, Southampton, UK

S E A K E E P I N G m

Motions of Mono- and Multi-HuUed Vessels in Regular Waves Using a Partly Non- 0 - 2 1 9 Linear Time Domain Metliod

Edward Ballard, Shuang Xing Du, Dominic Hudson and Pandeli Temarel, University of Southampton, UK.

Different Three Dhnensional Formulations for Evaluatmg Forward Speed Effects in H - 235 Seakeepmg Calculations of High Speed Hulls

Dario Bruzzone and Paola Gualeni, DINAV-University of Genoa, Italy Luca Sebastiani, CETENA, Italy

Comparison of Two Seakeepmg Prediction Methods for High Speed Multi-Hull Vessels, n - 243 Wen-Yang Duan and De-Bo Huang, Harbin Engineering University, China.

Dominic Hudson and W. Geraint Price, University of Southampton, U.K.

Hydrodynamics and Hydroelastic Analysis of Bodies in the Time Domain n - 251 Fuat Kara & Dracos Vassalos, University of Strathclyde, UK

O P E R A T I O N A L E C O N O M I C S

Natural Gas FueUed Fast Craft - Challenges and Development n - 271 Paulo Bemardes-Silva, Iguana Seacraft Ltd, UK

R E S I S T A N C E & F L U I D D Y N A M I C S I

High Speed Trimarans Vahdation of Numerical Results by Geosim Tests U - 285 Ermina Begovic, Carlo Bertorello and Pasquale Cassella, University of Naples Federico IL

Italy

Dario Bruzzone, University of Genoa, Italy IgorZotti, University of Trieste, Italy

Experimental and Numerical Investigations into Viscous Resistance n - 295 I.K.A.P. Utama, Institute of Technology Sepuluh Nopember (ITS), Indonesia.

A.F. Molland, School of Engineering Sciences, Ship Science, University of Southampton, UK

Advances in Stem Flap Design and Apphcation ü - 307 Dominic S. Cusanelli and Gabor Karafiath, David Taylor Model Basin, NSWCCD, W.

Bethesda, MD, USA

Free Surface C F D Simulations of the Flow Around a Planing Plate n - 321 Richard Pemberton and Stephen Turnock, University of Southampton, UK

Stephen Watson, Defence Evaluation and Research Agency Haslar, UK

FAST 2001: 4"' ~ 6** September 2001, Southampton, UK

VOLUME III

S P E C I A L C R A F T

Development of a New Wing-in-Surface-Effect Craft for Eight Passengers IH - 1 Hiromichi Akimoto and Syozo Kubo, Tottori University, Japan

Kunimitsu Fukushima and Nobumitsu Fukushima, Fukushima Shipbuilding Ltd., Japan

High-Reynolds-Number Flow Computations for Wings in Ground Effect IO - 7 Chun-Kai Wu and Kirill V. Rozhdestvensky, St Petersburg State Marine Technical

University, Russia

SES Performance Evaluation in Model and FuU Scale H I - 19 Sverre Steen, Norwegian Marine Technology Research Institute (MARINTEK), Norway

Gisle Strand, Royal Norwegian Navy, Norway

An Airlifted Catamaran - Hydrodynamica! Aspects IU - 29 Björn Aliens tröm and Hans Liljenberg, SSP A Sweden AB, Sweden

UlfTudem, SES Europe AS Norway,

H Y D R O F O I L S AND H Y D R O F O I L ASSISTANCE

Design and Efficiency of HydrofoU Assisted Catamarans I I I - 41 Günther Migeotte and Karl-Günter Hoppe, Dept of Mechanical Engineering, University of

Stellenbosch, South Africa.

Nikolai Kornev, Dept. of Hydromechanics, State Marine Technical University of St. Petersburg, Russia.

Design Slamming Pressures of a High-Speed HydrofoU-Assisted Catamaran 111-55 Xuekang Gu andJiajun Hu, CSSRC, China

Torgeir Moan, Norwegian University of Science and Technology, Norway

Study of hydrofoU assistance arrangement for catamaran with stern flap and I I I - 69 interceptor

Jing-Fa Tsai, Institute of Naval Architecture and Ocean Engineering, National Taiwan University, ROC

Jeng-Lih Hwang, Shiu-Wu Chau and Shean-Kwang Chou, United Ship Design and Development Center, ROC

How Many FoUs? A Study of Multiple HydrofoU Configurations I U - 79 Michael Andrewartha, Lawrence Doctors, The University of New South Wales, Australia

S T R U C T U R A L R E S P O N S E H

Coupled Fluid-Structural ModeUing to Predict Wave Impact Loads on High-Speed IU - 87 Planing Craft

Simon Rees and David Reed, Frazer-Nash Consultancy Limited Colin Cain and Bob Cripps, Royal National Lifeboat Institution

FAST 2001: 4"" - ó"" September 2001, Southampton, UK

Slamming Response of Large High Speed Catamarans I H - 97 Giles Thomas, Michael Davis, James Whelan, University of Tasmania, Australia

Tim Roberts, Incat Tasmania, Australia

A Theoretical / Experimental Investigation of the Slamming Pressures on Fast I I I - 109 MonohuU Vessels

Luca Sebastiani and Federica Valdenazzi, CETENA., Italy Luigi Grossi, Fincantieri Cantieri Navali Italiani S.p.A., Italy

Geert K. Kapsenberg, MARIN, The Netherlands

Hydrodynamic Impact Response, a Flexible View IU - I I 7 Alex W. Vredeveldt, Martijn Hoogeland, and Gerard Th. M. Janssen, TNO, The Netherlands

Catamaran Wetdeck Structural Response to Wave Impact i n - 125 FalkRothe, Pierre C. Sames and Thomas E. Schellin, Germanischer Lloyd, Germany

S T R U C T U R A L RESPONSE H I

Fatigue Strength of Aluminium Stmctural DetaUs of Special Service Craft U I - 135 Helena Polezhaeva and Warwick Malinowski, Lloyd's Register of Shipping, UK

Stmctural Design and Results From FuU Scale Stmctural Measurements on the RNON I I I - 143 High Speed S E S "KNM Skjold"

Alf Egil Jensen, Jon Taby, and Bjem H0yning, FiReCo AS, Norway

Stress Distribution at CoUapse for Fast MonohuU Vessels IH - 153 Dario Boote and Massimo Figari, Dipartimento di Ingegneria Navale e Tecnologie Marine,

Universita di Geneva, Italy

R E S I S T A N C E & F L U I D DYNAMICS H

Resistance Performance Investigation of High-Beam Draft Large Size Displacement I I I - 163 HuUs

Siu C. Fung, Liam O'Connell and Kenneth M. Forgach, Naval Surface Warfare Center, Carderock Division, USA

Resistance Characteristics of High-Speed Trimarans m ShaUow Water III -177 Branislav Gligorov and Milan Hofman, Department of Naval Architecture, Faculty of

Mechanical Eng. University of Belgrade, Yugoslavia

The Resistance and Trim of Semi-Displacement, Double-Chine, Transom-Stern HuU IU - 187 Series

D. Radojcic, T. Rodic and T. Kuvelic, University of Belgrade - Yugoslavia

G. J. Grigoropoulos andD. P. Damala, National Technical University of Athens - Greece

M A T E R I A L S

Optimum Design for Steel Sandwich Panels FiUed with Polymeric Foams m - 197 Jani Romanoff and Pentti Kujala, Helsinki University of Technology, Ship Laboratory,

Finland

FAST 2001: 4"" - 6"" September 2001, Southampton, UK

Non-Linear Core Behaviour in Sandwich Panels for High Speed Craft i n - 207 Brian Hayman, Peter Hoffmann, Dag McGeorge, Philippe Noury, Det Norske Veritas,

Norway

Transient Analysis of F R P Sandwich Panels Used in High Performance Craft I E - 215 M. Meunier and R.A. Shenoi, University of Southampton, UK

New Ahoy Development at Pechmey, a New Generation of 5383 I E - 223 Alexandre Duran, Pechine}' Marine, France.

Ronan Dif Pechiney Centre de Recherches de Voreppe (CRV), France.

Design Considerations for Lightweight High-Speed Ships Usmg Planked Constmction I E - 231 Stephen WBoyd, Alexander HDay and Ian E Winkle, University of Glasgow, UK

Nigel Warren, FBM Babcock Marine Ltd.

A U T H O R S C O N T A C T D E T A I L S

Principal Editors: Professor Philip Wilson, University of Southampton, U K Professor Grant Hearn, Uruversity of Southampton, U K

FAST 2001: 4"' - ó"" September 2001, Southampton, UK

T H E E F F E C T O F B O W S H A P E O N T H E S E A K E E P I N G P E R F O R M A N C E O F A F A S T M O N O H U L L

Alexander (J.A.)_Keuning, Delft University of Technology, The Netherlands Serge Toxopeus, Marin, The Netherlands

Jakob Pinkster, Delft University of Technology, The Netherlands SUMMARY

In the earlier publications on the Enlarged Ship Concept (ESC) attention has aheady been given to the possibilities of improving the seakeeping behaviour of a fast monohull significantly through a thorough change in the bowshape both below and above the stillwaterline. The aim of this bow modification was to reduce the nonlinear hydrodynamic forces in particular at the foreship. In the present study this has been taken one step ftirther and the effect of a rather radical change in shape of the bow over some 25% of the length is studied. The behaviour ( i.e. heave and pitch motions) in both head- and following irregular waves of three systematic bowshape variafions has been studied. Also the manoeuvring characteristics for these variations are investigated. Because one of the serious concerns about these proposed bow modifications lies with a possible increased sensitivity of the ships with the sharper and deeper bows to broaching in following waves, this aspect of the behaviour in waves has been studied also.

The results of the comparison between these three designs (with this increasing change in bowshape) will be presented in this paper and the pro's and con's of the proposed changes in bowshape will be discussed.

AUTHORS BIOGRAPHY

Alexander (J.A.) Keuning holds the current position of Associate Professor at the Ship Hydromechanics Department at the Delft University of Technology, The Netherlands. He specializes in hydrodynamics of advanced marine vessels including yachts.

Serge Toxopeus graduated in 1996 at Delft University of Technology, Faculty of Mechanical Engineering and Marine Technology with a MSc. in Naval Architecture. Since that time, he has been employed at MARIN as a consultant in the field of ship hydrodynamics, specialising in ship manoeuvring. His previous experience includes the development and application of the cross flow drag theory for high-speed surface ships. Jakob Pinkster holds the current position of Assistant Professor at the Ship Hydromechanics Department at the Delft University of Technology, The Netherlands. He is currentiy responsible for setting up new education curriculum for ship hydromechanics department, is active in teaching and research and carries out research projects for industry. His previous experience includes involvement with fast marine vehicles with regard to design, construction, testing and trouble shooting.

NOMENCLATURE

Ax(t) momentaneous submerged transverse area of cross section [m]

FpK Froude-Kiilov force [N/m] g Gravitational constant [m/s ]

Hl/3 signficant wave height [m]

k wave number (2i^%) [-] KG height of centre of gravity

(C.o.G) above above keel [m] KM height of metacentre above

keel [m] J-pp I r NpAïp 1^= N/(Yy-M') M'= M/(0.5pLpp'T) mvY Np= N„40.5pLpp^T) N^=N^(0.5pLpp^T) U V yw(t) Yp= Y^(0.5pLppT) Y,= Y^(0.5pLpp^T)

length between perpendiculars [m]

lever of application of lateral force due to drift, forward of CG [m]

lever of application of lateral force due to yawing, forward ofCG[m]

sSection added mass for Heave [kg/m] sectional added mass for sway [kg/m] non-dimensional Imear derivative of yaw moment in CG due to drift motion non-dimensional linear derivative of yaw moment in CG due to yaw motion mean zero crossing wave period [s]

longitudinal (ship-fixed) velocity [m/s]

ship speed [m/s]

water velocity component normal to the local planning surface [m/s]

momentaneous waterline half beam of cross section [m] transverse (ship-fixed) velocity in CG [m/s] local transverse (ship-fixed) velocity [m/s]

non-dimensional linear derivative of lateral force due to drift motion

non-dimensional linear derivative of lateral force due to yaw motion

FAST 2001: 4"' - 6" September 2001, Southampton, UK

p= arctan(v/u)

p

C(t)

drift angle [rad]

non-dimensional yaw rate [rad]

wave length [m] density of water [kg/m^] distance from the forward perpendicular, positive in aft direction [m]

momentaneous wave height [m]

1. INTRODUCTION

The seakeeping behaviour of fast monohulls has a very strong influence on the actual operability that can be obtained with those ships in particular in the more "exposed" working (sea) areas. Since the application of fast planing monohulls in the role as patrol-, coastguard-, survey- or naval vessels has increased considerably over the last two decades or so, the improvement of this behaviour of these fast monohulls in waves has been an intense research topic for a long time now. It has been shown by numerous authors in varies studies, both analytical and experimental and in particular also ftili scale measurements, that the level of vertical accelerations in those positions onboard the ship, where the crew has to perform its primary duties, is the most dominant limiting factor for the comfortable and safe operation of the ship. The voluntary speed reduction applied by the crew and caused by excessive levels (and more in particular extreme peaks) in the vertical accelerations is the prime reason for the loss of ftill operability of the ship in a seaway.

Many aspects of the hull design of the planing ship, which could lead to a possible improvement in their seakeeping behaviour, have been investigated. Among those parameters are the deadrise-angle of the planning bottom, the running trim of the ship at speed, the length to beam ratio of the hull.

In 1995 Keuning and Pmkster, [1], introduced the Enlarged Ship Concept (ESC) as a possible contribution to these improvements. In principle this concept was aimed at "bringing the length back into the design". The design practice over the precedmg decades had focused strongly on minimizmg the length of the ships because of its assumed direct relationship with the (building) cost of the ship. Enlarging the length introduced many possibilities for optimizing the design with respect to resistance and seakeeping.

In 1997, [2], Keuning and Pinkster demonstrated that the Enlarged Ship Concept gave even further opportunities because significant bow shape modifications became possible due to the large amomt of available "void space" m these designs. These applied bow modifications improved the operability of these craft even more. In the present study this is taken even one step ftirther. Based on the obtained insight in the dominant hydrodynamic forces acting on a planning hull m head waves, a radical bow shape modification is introduced

aimed at minimizmg the hydrodynamic (exciting) forces and by doing so aimed at reducmg the peaks in the vertical accelerations. This bow shape has been named "Axe bow" for obvious reasons and its shape and the philosophy behind it are explained in the following paragraphs. In the present study the seakeeping behaviour of the ESC with this new bow shape is compared with the results obtained with the previous ESC ships as reported earlier in [1] and [2].

In addition a first quick assessment is made of the influence of this Axe bow shape on the meanoeuverabUity of the ESC ship. This has been done to obtain some insight in the possible draw backs of this extreme bow shape that may arise when the ship is sailing in large and steep following waves, i.e. when there is a risk of broaching. Earlier fmdings with the ESC revealed a large increase in the course stability when compared to the shorter "base" ship. For some specific applications such as patrol boat or navy vessel this increase in course stability was considered even to be too large and hence reducing the manouevrability of the craft. The local deepening of the forward bow sections and the fineness of these sections were thought to be destabilizmg in that respect and therefore increasmg the manoeuvrability again.

2.1

TBDE ENLARGED SHIP CONCEPT INCREASING THE SHIP LENGTH

In the general quest for optimizing the seakeeping behaviour of fast planning monohulls commonly used as patrol- and naval-vessels, Keuniag and Pinkster mtroduced in 1995 the "Enlarged Ship Concept" (ESC) as a possible contribution to the process.

This ESC concept was auned at getting the "length back m the design" of the fast monohull. The general design trend at that time and applied over the last decennia for fast planing monohulls was to reduce the overall length of the ships as much as possible. Many ship owners stipulated the maximum allowable length of their new designs aheady at the beginning of the design process. This trend was based on the supposed direct relation between the building cost of the ship and its overall length. In their fu-st report, [1], Keurung and Pmkster took an existing and quite successful design from DAMEN SHIPYARDS, the Stan Patrol 2600, as their "base" design and lengthened this ship with 25% and 50% respectively, whilst keeping all other design parameters, such as speed, payload, functions, beam etc. constant. The advantages of the enlarged ship ESC when compared wdth the base boat were:

• Increasing the length and so reducing the Froude number for the same forward speed. • Increasing the Length to Beam ratio, beneficial

for the calm water resistance and reducmg the "hump" behaviour and beneficial for the ship motions in waves.

FAST 2001: 4'" - 5'' September 2001, Southampton, UK

• Increasmg the Length to Displacement ratio, beneficial for the calm water resistance and the ship motions in waves.

• Reducing the pitch gyradius of the ship.

• Optmiizing the longitudinal position of the prime working areas on board with respect to the vertical motions of the ship.

A picture of the general arrangements of these three designs is presented in Figiu-e 1.

The results obtained from this initial study, which were based on calculations as far as resistance and motions m waves were concerned and on data presented by DAMEN SHIPYARD as far as buildmg costs and weights were concerned, showed :

• A significant decrease (around 30%) in the required installed power to maintain the design speed of 25 knots.

• A significant reduction of the vertical accelerations in the wheelhouse and more m particular of the distributions of the peaks and their frequency of occurrence.

• A significant mcrease m the operability of the ship in the Southem North Sea and Dutch Coastal waters by some 50%.

• Only a small increase in the calculated building cost: for mstance only some 6 % for the longest ship.

A graphical representation of these results is presented in Figure 2. From these results it was concluded that the Enlarged Ship Concept looked very promising indeed.

2.2 OPTIMAL POSITIONING OF THE WORKING AREAS

A possibility introduced by increasing the length without increasing the number of "functions" on board the ship is that of optimizing the longitudinal position of the most important working areas aboard the ship with respect to the vertical motions. In the cases under consideration this has been the wheelhouse. From motion analyses it is known that, due to the phase lag between pitch and heave, the minimal vertical motions do occur at roughly 30% of the ship length from the stem. Positionmg the wheelhouse as close to that position as possible might easily reduce the vertical motions at that place by some 30% to 50%

Another aspect of this repositioning of the accommodation etc. is foxmd in a significant shift of the longimdinal position of the Center of Gravity of the ship to the stem also. This implicates for instance that the pitch restoring moment with respect to the CoG can be maintained when the bow is modified, because although the volume forward is reduced its leverage is increased. This aspect will be deaU with in the next paragraph.

2.3 MODIFYING THE BOW

In 1997 Keuning and Pmkster, [2], extended theh research on the possibilities with the ESC by using the extra space, the "void" space, that is generated by applying the ESC, to optimize the hull geometry of the design with respect to the wave exiting forces and the resulting (vertical) motions in a seaway. This change in hull geometry was in particular applied in the forward sections of the ship.

From an extensive study analyzing measurements and observations made onboard real ships, such as Patrol boats, Search and Rescue vessels etc, it became evident that the limiting factor for the safe operation of the ship as applied by the crew aboard of these high speed vessels is the occurrence (once or maybe twice) of single high peaks in the vertical acceleration. Once these occur the crew vdll voluntary reduce the forward speed of the vessel to prevent it from happenhig again. This action of voluntary speed reduction was carried out almost irrespective of the value of the actual significant value of the vertical acceleration at that time. It is known from both full scale measurements and from model experiments and calculations that the relation (or factor) between the significant value and the extremes (high peaks) in the vertical accelerations is strongly dependent on the non-linearity of the system. The factor between these two, i.e. significant value with roughly 13.5% chance of exceedance and the maximum with circa 0.1% chance of exceedance, is not constant for non-linear systems and increases significantly with the non-linear behaviour of the system, [3].

So evaluatmg the operability of fast ships on the basis of significant values only is not sufficient or even misleading. The distribution of the peaks m the motions and in particular the vertical accelerations should be compared when comparing fast ships. The aim of any optimization of the operability of fast ships in a seaway should be the reduction of the value of the extremes in these distributions.

From the results obtained from extensive research on the nonlinear behaviour of fast planing monohulls in head waves, [3], [4] and [5], it became evident that the most important components of the exciting (wave) forces on a planmg hull, which contribute most to the nonlinear behaviour, are the non-linear Froude-Krilov force and the (non-linear) hydrodynamic lift. So minimizmg these forces therefore should lead to the desired reduction in the extreme peaks in the vertical accelerations.

The non-lmear Froude-Krilov force is found by integrating the (hydrodynamic) pressure, as found with potential theory, in the undisturbed wave over the actual momentaneous submerged volume of the hull, whilst this hull is performing non small relative motions with respect to the mcoming waves. In formula:

F'FK (t) = 2pgCy^ (t) + pgKGA^ (t)

FAST 2001: 4"' - 6"' September 2001, Southampton, UK

From these formulations its is obvious that m i n i m i z i n g

the change in time of this force should be achieved by reducing the change in the sectional y^,(t) and Ax(t) when the section is carrying out a vertical displacement with respect to the water surface. Translatmg this to the geometry of the shape of the ship sections this means that the flare of these sections, in particular Ln the fore ship, should be reduced over the "range" of the instantaneous waterline.

Since the paper of Von Karman, [4], the theory used for the calculation of the hydrodynamic loads on the hull of a planing boat has been based on the concept of the added mass. In concept this theory corresponds with the "slender body" theory as it is fi-equently used to calculate the hydrodynamic side force on, for instance, low aspect wings and on the underwater part of the hull of surface ships sailing under oblique flow. This slender body theory is therefore also applied in the section of this paper dealing with the manouevering characteristics of the hulls.

Usmg this theory of Von Karman for the determination of the normal force on a transverse section of a hull, this force is given by the rate of change of the momentum of the oncoming fluid expressed in the terms of added mass ofthe particular cross section under consideration:

D

The rate of change of momentum of the fluid at a particular section is then further elaborated to:

D , Dt

m . V +Vm„ d(m3V)d^ d^ dt

As may be noticed a time dependent added mass of the cross section is introduced which originates also from the not small relative motions of the sections with respect to the incoming waves.

From both the analytical and the experimental research as reported by Keuning in [3] it became apparent that this non-linear added mass is much more important for the time dependent magnitude change of these hydrodynamic forces (and so for the behaviour of a planing hull in head waves) than was the frequency dependency of this sectional added mass. Smce the change in the sectional added mass at these relatively high encounter frequencies (fast ship in head waves) may be considered to be proportional to the change in sectional beam yw(t), once again this change in y„(t) should be minimized.

2.3.1 The TUD 4100.

hi 1997 this lead to flie mtroduction of the TUD 4100 hull shape for the Enlarged Ship Concept, as reported by Keuning and Pmkster m [2] at the FAST 1997.

The change in hull shape when compared to the original hull ofthe Enlarged Ship is summarized by:

• Reducmg the flare of the bow sections • Narrowing the waterline

• Increasing the waterline length • Deepening the fore foot • Increasing the freeboard

A picture of the lines plan of the modified bow of the TUD 4100 according to these lines of thought is depicted m Figure 3. The change of the hull shape with the more traditional one of the ESC 4100 is immediately evident. 2.3.2 The Axe bow

A far more radical "elaboration" of this same design philosophy to minunize the nonlmear behaviour of the system "fast planmg monohull in head waves" is mtroduced by what has now been christened the "Axe bow".

The most striking features to the eye of this new shape are:

The flare m the bow sections is reduced to almost zero for minimizing the change in momentaneous added mass (hydrodynamic lift) and momentaneous submerged volume (Froude-Krilov) whilst the foreship is carrying out relatively large relative motions with respect to the waves.

The stem is placed almost vertical to increase the waterline length to the maximum and by doing so bringmg "back" volume of displacement m the forward part of the ship and ftirther forward with respect to the center of gravity of the ship.

The sheer forward is significantly increased, to minimize the risk of green water on deck and to guarantee sufficient reserve buoyancy.

The centerlme of the hull has been given a negative slope towards the bow (downwards or reversed sheer), to minimize the risk of hull emergence when sailing in waves. The change in momentaneous added mass of a section is obviously most abrupt when a section is re-entering the water (slamming).

Great care has been taken to mamtain a comparable pitch restoring moment and reserve buoyancy in the hull forward when compared to the other (parent) hull, i.e. tiie ESC 4100.

Also shown in Figure 3 are the Imes plan ofthe Axe bow hull form derived from tiie ESC 4100 and also tiie Imes plan of tiie TUD 4100. Figure 4 shows a number of 3-D renderings of tiie AXE 4100 hull form.

It should be clearly stated at tiiis point tiiat no serious attempt has been made in this study to generate a

FAST 2001: 4'" - 6" September 2001, Southampton, UK

complete and fiilly feasible design of this AXE 4100 from all points of view. The principal idea ofthe present study is to investigate the possible benefits of such a new design concept on a conceptual level of design only. So a "comparable" design with respect to the other two designs, i.e. the ESC 4100 and the TUD 4100, has been the main objective.

For the sake of clarity all main dimensions of the three designs used for the comparison are presented m Table 1. 3. THE COMPUTATIONAL RESULTS The computations on the three designs to evaluate their hydrodynamic performance have been carried out with two different programs: FASTSHIP of the Delft Shiphydromechanics Department has been used to calculate the calm water resistance, the trim and the smkage of the three designs as well as the motions in irregular head waves and SURSIM of MARIN in Wageningen has been used to assess the maneuvering characteristics of the designs.

FASTSHIP is extensively described m [3] and is purpose made for predicting the nonlinear behaviour of fast (planmg) monohulls m irregular head waves. SURSIM is a sunulation program developed at MARIN for the prediction of the maneuvering characteristics of surface ships. Both computer codes have been found to yield reliable results for the applications they have been designed for. The Axe bow design however is clearly not a common design and therefore the programs had to be adapted somewhat to accommodate this concept. That is also the reason for carrying out rather extensive model experiments wiüi scale models of these three designs m the Delft Tovraig Tank. The results of these tests however are not available on the time of writing of the present paper and will therefore be the subject of future reports.

3.1 CALM WATER RESISTANCE

FASTSHIP predicts the calm water resistance, the nmning trim and the sinkage under speed of a planing monohull based on the results obtained with the Delft Systematic Deadrise Series (DSDS). This DSDS is an extensive series of model experiments set up as an extension of the original Clement and Blount Series and carried out at the Delft Shiphydromechanics Laboratory with some 25 different models each of them towed in some 16 different conditions. The typical speed range is between Froude nmnber based on volimie of displacement from 0.75 to 3.2. For higher speeds the method of Savitsky is being used.

The results of these calculations are presented in Figure 5. depicting bare hull calm water resistance versus forward speed.

From these results it may be noted that at the design speed of 25 knots the TUD 4100 has the lowest resistance and the ESC 4100 the highest. The AXE 4100 is close to the TUD 4100 but will probably have a

somewhat higher resistance because the total mcrease in its wetted surface when compared to the other two cannot be fully accounted for. At higher speeds the resistance of the modified hulls of the Enlarged Concepts, i.e. TUD 4100 and AXE 4100, is significantly higher than the original ESC 4100, which may be explained from the modifications applied to reduce hydrodynamic lift in the forebody.

3.2 MOTIONS IN IRREGULAR HEAD WAVES The vertical motions of the fast planing monohull in hregular waves are calculated by a solution in the time domain of the three equations containing the important forces (X and Z) and moments (My) working on the hull. The running trim and the sinkage of the planing hull at the particular forward speed under consideration are determined using the procedure mentioned before. The hregular wave realization, yieldmg at each tune step the wave profile over the length of the ship, is generated using 50 different wave components to describe the given sea spectrum.

The two seastates used for the present calculations are the average conditions of Seastate 4 (1^= 6 s and H|/3=

2.25 m) and Seastate 5 (Tp= 7.5 s and Hi/3= 3.5 m)

respectively. The spectrum formulation used is the Bretschneider formulation for the energy distribution over the frequency range. Furthermore, for these conditions, a vessel speed was taken as being 25 knots for all different design concepts.

The results are presented as distributions of the peaks of the amplitudes of the heave and pitch motion of the ships in those conditions in Figure 6 and 7 respectively and as the distribution of the peaks in the vertical accelerations at the bow and the wheelhouse in the same conditions in Figure 8 and 9 respectively. For the sake of clarity only the negative peaks of the vertical accelerations (i.e. upwards) are presented. The positive peaks remam below the value of 10 m/s^ (i.e. the acceleration, g, due to gravity).

From these figures it becomes immediately evident that the reduction in the vertical accelerations both at the "bow" (i.e. 10%L aft ofthe forward perpendicular) and at the wheelhouse are aheady significantly reduced with the application of the TUD 4100 bow shape and dramatically reduced with the application of the AXE 4100 bow shape when compared with the original (traditional) bow of the ESC 4100. These computational findings correspond wdth the real life observations and experience obtamed so far with the Dutch Coast Guard vessels of the "Jaquar" type (25 knots 42 meter Loa Patrol boats) built along the Imes ofthe TUD 4100. hi the earher study on the TUD 4100, [2], these computational results were also validated with model experiments in the towing tank. The results obtained for the AXE 4100 indicate that an ever further and very significant unprovement is to be gained m these sea conditions, because both the significant values of tiie vertical accelerations and, in particular, tiie exheme peak

FAST 2001: 4'" - September 2001, Southampton, UK

values are very much reduced with the application of the Axe bow shape.

There is only a small increase in the heave and pitch motion of the AXE 4100 when compared with the other ones, which was to be expected.

3.3 DIRECTIONAL STABrLFTY

During the project, it was questioned whether the Axe bow concept would be more sensitive to broaching than the original TUD4100. Calculations were conducted at MARIN in order to determine the linear horizontal plane manoeuvring coefficients. The aun is to determine the hydrodynamic forces and stability levers for both drift and yaw motions in order to compare the risks of broaching for the two ships. Although the horizontal plane stability is only one of many factors determining broachmg risks, it is thought to be one of the major differences between the two hull forms.

Because of the unconventional hull form and the lack of data published m literature regarding sunilar hull forms, conventional methods to determine the hydrodynamic coefficients in the horizontal plane can not be applied successfully. Therefore, a method recently developed at MARIN was applied during the calculations. This method is based on the slender body strip theory method. 3.3.1 Slender body method

Already in 1966, Jacobs [7] proposed a ship theory alike approxunation for manoeuvring calculations. This strip theory is based on calculations related to the sectional added mass. By proper integration of the change of sectional added mass, the required hydrodynamic derivatives can be obtamed. A publication ofBeukelman, see [8], clearly illustrates the application of this method. Basically, the ship theory technique says that the lateral force per slice of the ship is the rate of change of fluid momentum per slice of the ship. This is expressed as:

D(myyV^) ~ Dt

m which myy is the lateral inertia coefficient or the two-dimensional added mass in lateral direction and v^ the local transverse velocity. This formula is used to calculate the non-dunensional linear manoeuvring coefficients Yp, Np, Yy and N^.

Just as with the other potential flow techniques, the calculation will faü to come up with lateral forces on the ship, while the turning moment wül come close to the Munk moment. When lookmg at the lateral force on the ship due to a drift angle, the theory states that the force is

equal to the change m sectional added mass between the most forward submerged section and the aftmost submerged section. Unless the aft section abruptly ends in a submerged transom, the sectional added masses at the forward and aft sections are calculated to be zero and therefore, the lateral force is zero.

Therefore, some modification has to be done to the added mass distribution in order to arrive at the actual force distribution along the length of the ship. Several proposed modifications are published in literature. For example, Beukelman [8] assumes a constant added mass distribution in the aft ship region up to the section with the maximum breadth. This actually means that for example the sway coefficient for drift motion Yp is only related to the sectional added mass of the section with maximum breadth. With that in mmd, the assumption clearly involves sunplifications that result in the same coefficients for ships v/ith the same section at the maximum breadth position, but different foreships. Therefore, other corrections to the theory are required in order to arrive at the realistic hydrodynamic coefficients. A comparison published m literature between the results of segmented model tests and the slender body theory is made by Clarke, see [9]. The objective of segmented model tests is to obtain insight into the distribution of the lateral forces and yawing moments along the length of the ship, hi this comparison, it is found that especially in the aft ship, deviations occur between the actual results and the theoretical estimation.

At MARIN, extensive data sets exist concemmg segmented model tests. These test results were used to verify and "tune" the slender body theory to arrive at the requhed values of the Imear manoeuvring coefficients. Based on this, a viscous correction formula was obtained, incorporatmg the fiill hull form.

3.3.2 Application to the TUD4100 and AXE BOW concepts

The MARIN slender body method has been applied to the two hull forms in order to determine the manoeuvring derivatives. By comparison of the results for the two ships, an indication of the relative differences m the coefficients is obtained. These differences might give an mdication about the sensitivity to broaching.

As a fhst step, the method was applied for the design loadmg condition, i.e. the ship on even keel. Figure 10 (a) mcludes a graph and a table wdiich shows the added mass distributions along the length of the ships as well as the derived linear manoeuvring coefficients,

hi this figure, the peak in the disttibution for the Axe bow is noteworthy. According to MARIN experience, the Imear manoeuvring coefficients are mostly mfluenced by the added mass m the forward part ofthe ship. Therefore, this peak wül have a large influence on the results of the calculations.

FAST 2001: 4'" - «5"' September 2001. Southampton. UK

It is seen that the differences in coefficients are considerable. It is found that the coefficients for the Axe bow are in some cases three tunes larger than the TUD4100 coefficients. The reason for this lies mainly m the shape of the bow: due to the very slender sections with high height to breadth ratio and large draught, the added mass distribution is considerably higher m the foreship of the Axe bow than for the TUD4100.

These results show that during a drift motion, the yaw moment on the Axe bow will be three times as high as for the TUD4100. The lever of application ofthe side force due to drift Ip indicates that the lateral force acts forward of the forward perpendicular. However, it is found that for the TUD4100, the force also acts very close to the forward perpendicular. From this, it can be concluded that the de-stabilising moments due to drift are large for both designs.

During yaw motion, the yaw moment on the Axe bow is also three tunes as high as for the TUD4100. The lateral force lever 1.^ indicates a distance of 34%Lpp forward of the centre of gravity. Due to the bow shape of the TUD4100, the lever for this ship is relatively small. To determine the amount of (in)stability, the difference

(ly - Ip) of the stability levers should be examined. The

above calculation results show that both the TUD4100 and the Axe bow will be directionally unstable, with the TUD4100 more unstable than the Axe bow. Because of the comparative nature of this study, the influence of the rudders on the directional stability of the hulls is not taken mto account.

More calculations have been conducted to detennine the linear manoeuvring coefficients for a more realistic attimde of the ships at fiill speed. Based on tests with sunilar ships, the runnmg trims of both hull forms have been estunated to be between 1.5° and 2° trim by the stem, combined with almost no smkage or heave. The distribution of the sectional added mass for 2° stem trim and the calculated manoeuvring derivatives are shown in Figure 10 (b).

The change in the stability lever (1^ - Ip) due to the stem him is remarkable. It is seen that both the TUD4I00 and the Axe bow are still unstable, but now the TUD4100 is less unstable than the Axe bow. The value for the Axe bow hardly changed due to the stem him. Remarkable is the fact that the "hump" in the distribution of the added mass for the TUD4100 disappears due to the stem trim, while for the Axe bow, this hump is still existing.

A third condition was investigated, to obtain an impression of the change in dhectional stability due to bow trim. This condition can occur when the ship runs into a wave crest in following seas. The distribution of sectional added mass and the derived manoeuvring coefficients are shown in Figure 10 (c).

In bow trimmed condition, it is found that the Axe bow now is aknost stable. This is mainly caused by the relatively large forward shift of the cenhe of gravity.

This results in a large reduction of the lever for drift, in combination with a relatively small change of yaw lever. The TUD4100 is found to be unstable, but slightly less than in the even keel condition.

3.3.3 Discussion of the risk of broachmg

The physics of broachmg have often been published m literature. A recent summary of broaching and capsizing was described by McTaggart and De Kat [10].

Lf loss of stability is the reason for broaching m following seas, a comparison of the K M values of both ships is of mterest. For these hull forms, it is found that in stem him or even keel condition, the KM values are almost the same, but m bow trim condition, the KM value for the Axe bow is about 0.6 m smaller than for the TUD4100. This means that when the ship runs mto a wave crest, the fransverse stability of the Axe bow is reduced considerably, possibly resulting m capsizing or broachmg.

Although the yaw damping moments for the Axe bow are calculated to be considerably higher than for the TUD4100, the yaw moment due to drift, de-stabilismg the straight ahead motion of the ship, is thought to be of major unportance m the determination of the risk of broachmg. If only a slight drift motion is present, the build up of the lateral forces in the foreship of the Axe bow is considerable, inducing a yaw motion. Combined with the inherent shaight-lme instability of the ship, it is expected that a risk of broachmg is present.

Another aspect of the relatively large yaw moments that act on the Axe bow lies in the compensating moments that are to be generated by the rudders. When the moments on the Axe bow are about three tunes higher than on the TUD4100, it means that to compensate this moment by the rudders, a rudder-mduced moment of also about tiiree tunes as high should be generated. Either the mdder deflection should be about three times higher than for the TUD4100, or the radder efficiency should be three tunes higher. This means that the conhollability of the Axe bow is expected to be less than the conhollabtiity of the TUD4100.

Finally, broaching can occur due to an excessive roll motion due to yaw-roll coupling. Because of the deep bow of the Axe bow hull form, and the large hansverse forces m the bow area of the Axe bow, it is expected that considerable yaw-roll coupling will exist for tiiis hull. With hansverse forces about three to four tunes larger than for the TUD4100, combined with probably a larger vertical lever of application with respect to the centre of gravity, the heelmg moment due to drift or yaw might be more than three tunes larger than for the TUD4100.

FAST 2001: 4'" - 6'" September 2001, Southampton, UK

3.3.4 Considerations

The original slender body theory does not incorporate any viscous or forward speed effects. The modified slender body method developed at MARIN to detennine the manoeuvring derivatives based on the added mass distribution was based on segmented model tests results with conventional and naval surface ships. The design of the hull of the Axe bow differs significantly from the ships on which the modified theory was based and therefore, the acmal values of the coefficients are likely different from the ones that might be obtained during model tests. Unfortunately, no comparable data was available at the time of vmting of this paper. However, because of the lack of mformation, the method was applied to determine the sensitivity for broaching m a qualitative way.

In order to obtam a more reliable prediction of the risk of broaching model tests with the Axe bow hull form should be conducted.

4. CONCLUSIONS

Smce the introduction of the ESC, the available "space" to modify the bow has been successflilly applied to the TUD 4100. The extension mto the AXE 4100 leads to further improvements in seakeeping capabilities. The results obtamed for the AXE 4100 mdicate that a significant reduction has been obtained for the vertical accelerations in the wheelhouse. This is excellent for workability and safe operation of the vessel. This holds true for both significant as exheme acceleration values. Pronounced reductions (50%) have also been found m the extreme peak values at the bow. The leads to less slamming and therefore lower slam forces which is beneficial to the constraction of the ship as well as the perception of the crew when sailing her.

There is only a small increase m the heave and pitch motion of the AXE 4100 when compared wdth the other ones, which was to be expected.

The actual difference m vessel resistance between the three concepts has yet to be fully examined (i.e. via model tests).

In extreme weather conditions (non-applicable for nimierous designs) the following may be stated regarding broaching: Based on the calculations of the hydrodynamic horizontal plane derivatives and additional determination of the metacenhe heights in several attitudes of the hull forms, it is concluded that the Axe bow may probably be more sensitive to broaching than the TUD4100 design. Also, it is expected that yaw-roll couplmg will be more pronounced for the Axe bow design, mcreasmg the risk of broaching.

The amount of sensitivity and hence the risk of broaching is still subject to further model test mvestigations.

Broachmg tendancy of the axe bow may be considerably reduced by the application of a center skeg in the stem region.

5. RECOMMENDATIONS

More calculations and model tests should be undertaken to gain a better imderstanding and qimntification of the aspects involved in the determination of the effect of bow shapes on the seakeeping performance of a fast monohull.

7. REFERENCES

[1] Keuning, J.A., Pmkster, Jakob, "Optunisation of the seakeepmg behaviour of a fast monohull". Fast'95 conference, October 1995.

[2] Keuning, J.A., Pinkster, Jakob, "Fmther design and seakeepmg investigations into the "Enlarged Ship Concept". Fast'97 conference, July 1997.

[3] Keunmg, J.A., "The Non linear behaviour of fast monohulls in head waves". Doctor's thesis TU Delfl, 1994.

[4] Von Karman, W., "A shidy on Motions of High Speed Planmg Boats with Conttollable Flaps", Int Shipbuildmg Progress, No 365, January 1985. [5] Wagner, H. von, "Uber Stoss imd Gleitvorgange an

der Oberflache von Flüssigkeiten", Zeitschrifft fiir Angewandete Matematik und Mechanik, Band 12, Heft 4, 1932

[6] Velde, J. van der, Pinkster, Jakob, Keunmg, J.A., "Enlarged Ship Concept applied to a fully planmg SAR Rigid Inflatable Lifeboat", Fast'99 conference, August-September 1999.

[7] Jacobs, W.R., "The Estunation Of Stability Derivatives And Indices Of Various Ship Forms And Comparison Experimental Results", Joumal of Ship Research, 1966, Vol. 10, No. 3.

[8] Beukehnan, W., "Manoeuvring Derivatives For A Low Aspect-Ratio Surface Piercmg Wing-Model In Deep And Shallow Water", Delft University of Technology Ship Hydromechanics Laboratory, Report No. 998, MEMT 35, March 1995. ISBN 90¬ 370-0127-0.

[9] Clarke. D., "A Two-Dhnensional Ship Metiiod For Surface Ship Hull Derivatives: Comparison Of Theory Witii Experiments On A Segmented Model", Joumal Mechanical Engmeering Science, Vol. 14, No. 7, 1972.

[10] McTaggart, K. and De Kat, J.O.; "Capsize Risk of Intact Frigates m Inegular Seas", Transactions SNAME Annual Meeting, Paper No. 8, Vancouver 2001.

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J

Figure 1. General arrangements of the 26 m. "Base" boat (1.0 L) and

Enlarged Ship Concepts (1.25 L and 1.50 L respectively), (taken from [1])

Final design results Overall performance Indexes

2600 3300 4000 Design concepts • Length • Building costs • Operational costs • Transport efficiency • Operability

Figure 2. Overall performance mdexes for the different design concepts (taken from [2])

FAST 2001: 4'" - 6"' September 2001, Southampton, UK

FAST 2001: 4'" - September 2001. Southampton. UK 140 120 g 100 0) O 80 c « 60 in O) 40 20 0 0.0 5.0 10.0 15.0 20.0 25.0 V (kn.) 'ESC 4100 'ESC 4100 ^ ^ ^ ~ T U D 4 1 0 0 - AXE4100 ^ ^ ^ ~ T U D 4 1 0 0 - AXE4100 / a / a 1 1 30.0 35.0 40.0

Figure 5. The resistance curves for respectively ESC 4100, TUD 4100 and AXE 4100

E S C 4100 TUD 4100 AXE 4100 Dimensions W.L. Length [m] 36.307 38.448 41 Length [m] 41 41 41 W.L.Beam [m] 5.628 5.662 5.608 Draft [m] 1425 1.463 2.713 Displacement Volume [m'] 11128 111.16 111.57 Displ. _[kg] 111285 111164 111570 LCB [%w.l.] 55.4 59.2 54.9 Waterplane W. P. Area [m^] 168.24 157.76 162.11 LCF [%w.l.] 57.6 61.9 62.5 Ctr.Flotn.X [m] 25.619 26.357 25.631 Wetted Surface Wetted S.Area 193.87 199.3 222.3 Initial Stability Trans. GM [m] 3.062 2.709 2.543 Long.GM [m] 124.352 112.347 134.113 Coefficients Waterplane _[-] 0.823 0.725 0.705 Prismatic _[-] 0.699 0.638 0.699 Block _[-] 0.382 _{0.349 0.179} Midsection _[-] 0.547 _{0.547 0.256} Lwl/(Displ'^0.3331 _[-] 7.56 _{8.01 8.53}

Table 1. Main dunensions and other relevant data for the ESC 4100, TUD 4100 and AXE 4100.

FAST 2001: 4'" - September 2001, Southampton, UK — neg. A X E 4 1 0 0 neg. T U D 4 1 0 0 neg.ESC 4100 pos. A X E 4 1 0 0 _ : pos. T U D 4 1 0 0 " " pos.ESC 4 1 0 0 Pe(X) (%)

FAST2001: 4'" - ó"" September 2001, Southampton, UK pos. TUD4100 pos. ESC 4100 / / ^ |pos.AXE4100 neg.ESC4100 Jieg. TUD4100 P9(X) (%) Pitch seastate 5 AXE4100/: - pos. ( ,-jr neg.ESC4100 . ^ n e g . TUD41(X) pos. TUD4100 neg. AXE4100 20 10 5 2 Pe(X) (%) dow\figpit-1

Figure 7. The distribution of the peaks of the pitch amplitude for respectively ESC 4100, TUD 4100 and AXE 4100.

FAST 2001: 4"" - 6"' September 2001. Southampton, UK

Negative vertical acceleration Bow Seastate 4 ESC 4100 1 0,5 ,2 Pe(X) (%)

i

Negative vertical acceleration Bow Seastate 5

r

/

/ .

//

Figure 8. The dishibution of the peaks of the negative vertical acceleration at the bow amplitude for respectively ESC 4100, TUD 4100 and AXE 4100.

FAST2001: 4'" - September 2001, Southampton, UK

Pe(X) (%)

Negative vertical acceleration Wlieelhouse Seastate 5 1 ESC410C TUD4100

1

Figure 9. The dishibution of the peaks of the negative vertical acceleration m the wheelhouse amplitude for respectively ESC 4100, TUD 4100 and AXE 4100.

©2001: The Royal Institution of Naval Architects

Design loading condition, 0° trim 20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

Even keel condition

1 * i • \ -5 10 1-5 aft « X [m] » front 20 25 30 35 40 -TUD4100 Axebow

Hull TUD4100 Axebow Yp -0.120 -0.329 Np -0.053 -0.178 Y, 0.003 -0.029 Ny -0.013 -0.042 Ip 0.446 0.540 1. 0.124 0.339 Vip -0.322 -0.201

Figure 10 (a). Added mass distribution and derived linear manoeuvring coefficients (design loading condition, 0° trim).

Full speed condition, 2° trim by the stem

20000 18000 16000 14000 12000 10000 8000 6000 4000 2000 0

Stem trimmed condition

i

. . . . . A

5 10 15

aft « X [m] » front

20 25 30 35 40

-TUD4100 - Axetxjw

Figure 10 (b). Added mass distribution and derived linear manoeuvring coefficients (trimmed condition, 2° trim by stem).

Hull TUD4100 Axebow Yp -0.169 -0.261 Np -0.040 -0.115 Y, 0.028 0.006 N , -0.007 -0.027 Ip 0.237 0.438 0.066 0.238 ly-lp -0.171 -0.200

I

Nose dive condition, 2° trim by the bow Bow trimmed condition

5 10 15

aft « X [m] » front -TUD4100 ' Axebow

Hull TUD4100 Axebow Yp -0.162 -0.480 -0.082 -0.219 Yy -0.013 -0.058 N , -0.020 -0.056 Ip 0.505 0.457 0.223 0.411 Vip -0.282 -0.046

Figure 10 (c). Added mass distribution and derived linear manoeuvring coefficients (bow trimmed condition, 2° trim by bow).