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High Performance Skiff Marine Design Project 2017

Naval Architecture and Ocean Engineering International Master Programme

Department of Mechanics and Maritime Sciences CHALMERS UNIVERSITYOF TECHNOLOGY Gothenburg, Sweden 2017

Chalmers Formula Sailing High Performance Skiﬀ Marine Design Project 2017

Acerbi, Tommaso Andersson, Rasmus Eriksson, Eric Granli, Simon Jacobs, Eike Rita, Francisco Sahlberg, Robert Werner, Emanuel Chalmers Formula Sailing High Performance Skiﬀ Marine Design Project 2017

Department of Mechanics and Maritime Sciences Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone +46(0)31-772 1000 Printed by Chalmers Reproservice Gothenburg, Sweden, 2017

ii Abstract

The 1001VELAcup is a sail race between European universities that takes place annually in Italy. The current report addresses the design and construction of a high performance sailing skiff to allow Chalmers University of Technology to participate in the race. The design is regulated by the Class Rule R3 and the current skiff is mainly inspired by the Olympic class 49er©. According to the class rules, the hull shall have a content of natural material of at least 70%. This is achieved by using a sandwich material with a balsa core and a composite from flax (linen) fibres, and an epoxy resin based on the shell of cashew nuts. Since there are no restrictions in draft or height of mast, this skiff has a relatively high mast and deep centreboard. All parts of the design are based on analyses of the race area in Mondello, outside of Palermo, in Sicily. Thus, the team chose to not use hydrofoils on the centreboard and rudder. The sail area is maximised according to the class rules. The work is carried out by eight students on the master program Naval Architecture and Ocean Engineering with supervision from teachers and experts from the industry.

Keywords: skiﬀ, dinghy, sailing, 1001VELAcup, Chalmers University of Technology, CDIO

iii

Preface and Acknowledgement

The Marine Design Project, MMA 151, is a mandatory 15 credits course within the master program Naval Architecture and Ocean Engineering at Chalmers University of Technology. The course is organised by the Department of M2, Mechanics and Maritime Sciences at Chalmers. The objective of this project is to design and build a high performance racing skiﬀ in order to compete in the upcoming 1001VELAcup 2018. Furthermore the participants have to manage the public relation work in addition to the whole process.

The project members would like thank and acknowledge the help, funding, expertise and support of the following:

To Lars Larsson, Adam Persson, John Mcveagh, Per Wretlind, Henrik Ottoson, Per Hogström and Rolf Eliasson, thank you for the guidance, knowledge and expertise throughout the duration of the project.

To Per Hogström and Lars Larsson, thank you for providing us the opportunity to work with such a unique project and for providing us with Ritsalen. This project would have been signiﬁcantly more diﬃcult without it.

To our sponsors and partners in the project: Seldén Mast, North Sails, SSPA, the ITH project supported by the EU regional fund, Chalmers Foundation "Fond för högskolans bästa" and Area of Advanced Materials at Chalmers.

To Professor Kai Graf for supplying his VPP.

To SSPA, for general support and SNIC (Swedish National Infrastructure for Computing) for computing resources

To our classmates, working alongside us and providing the good atmosphere and com- panionship.

To Chalmers University of Technology. Project Members

CAD Simon Granli Francisco Rita

CFD Tommaso Acerbi Robert Sahlberg

FEM Eric Eriksson Emanuel Werner

VPP Rasmus Andersson Eike Jacobs

v Executive Summary

The following section is a brief outline of the work accomplished in the project. The mission profile, main particulars for the skiff and a general overview of its rig and sail set up are presented in this section. Mission Profile

The mission of this project is to design and build a high performance racing skiﬀ in order to participate in the 1001VELAcup. The regatta will take place in the bay of Mondello, Italy, at the end of September 2018. Main Particulars

The dimensions of the skiff are set by the competition regulations as well as performance and structural optimisation. Since the goal is to finish in 1st place in the competition the focus has been on performance and hence the looks of the skiff are purely a result of that.

Type High Performance Racing Skiﬀ Flag Sweden Class R3 Hull Dimensions Length over all 4.60 m Beam of canoe body 1.22 m Beam 2.10 m Draft of canoe body 0.17 m Total draft 1.70 m Displacement 250 kg Moment of Inertia of the water-plane area 1.664 · 10−1 m4 Rig Dimensions Mast height 9.50 m Mainsail 16.0 m2 Jib 6.0 m2 Gennaker/Jib 0 11.00 m2

vi vii List of Abbreviations

Abbrevation - Description

CDIO - Conceive, Design, Implement and Operate FLAT – The ﬂattening of the main sail to empower it GA - General arrangement ISPRA - Istituto Superiore Per la Protezione e la Ricerca Ambientale kn - Knots MDF - Medium Density Fibreboard NACA – National Advisory Committee for Aeronautics ORC - Oﬀshore Racing Congress PDF - Probability Density Function PLA - Polylactic acid Pre-preg - Pre-impregnated RANS - Reynolds-averaged-Navier-Stokes RANS - Reynolds-Avergaed-Navier-Stokes RSM - Reynolds Stress Method RSM - Reynolds Stress Model SF - Scale factor s.f. - Safety factor SST - Shear Stress Transport VMG – Velocity Made Good VOF - Volume of Fluid VOF - Volume of Fluid VPP – Velocity Prediction Program

viii List of Varables

Variable Unit Description

A [m2] Planform area a [m] Distance between forces AR [−] Aspect ratio AW A [◦] Apparent wind angle AW S [m/s] Apparent wind speed b [m] Distance between forces B [m] Beam Bmax, canoe body [m] Maximum beam of canoe body BS [m/s] Boat speed C¯ [m] Mean chord length C1 [m] Upper chord length C2 [m] Lower chord length CB [−] Block Coefficient CD [−] Drag coefficient CD,2D [−] Profile drag coefficient CDI [−] Induced drag coefficient Cf [−] Skin friction coefficient CL [−] Lift coefficient ◦ CL,2D,1◦ [−] 2D lift coefficient at 1 angle of attack CL,3D [−] 3D lift coefficient CE [m] Centre of effort CLR [m] Centre of effort of the appendages CoG [m] Centre of gravity ELT [MP a] Elastic modulus in the longitudinal-transverse plane ETV [MP a] Elastic modulus in the transverse-vertical plane EVL [MP a] Elastic modulus in the vertical-longitudinal plane EL [MP a] Longitudinal elastic modulus ET [MP a] Transverse elastic modulus EV [MP a] Vertical elastic modulus FDI [N] Induced drag force Fx,aero [N] Aerodynamic force in x-direction Fx,hydro [N] Hydrodynamic force in x-direction Fy,aero [N] Aerodynamic force in y-direction Fy,hydro [N] Hydrodynamic force in y-direction Fz,maststep [N] Force in z-direction at the mast step FD [N] Drag force FL [N] Lift force Fx [N] Force in x-direction Fy [N] Force in y-direction Fz [N] Force in z-direction F n [−] Froude Number g [m3/(kg · s)] Gravitational constant GM [m] Metacentric height 4 Ix [m ] Moment of inertia of the cross section

ix 4 IxBS [m ] Moment of inertia of the cross section of the bowsprit 4 I49er [m ] Moment of inertia of the water-plane of the 49er© 4 IWP [m ] Moment of inertia of the water-plane area kDYN [−] Dynamic factor L [m] Length l [m] Distance on racks LBS [m] Length of the bowsprit that is unsupported LCF [m] Longitudinal Center Flotation LCG [m] Longitudinal Center of Gravity LOA [m] Length over all LW L [m] Length of Water Line mcrew [kg] Mass of the crew mtot [kg] Total mass Mx [Nm] Moment in x-direction My [Nm] Moment in y-direction Mz [Nm] Moment in z-direction P [N] Point load applied at the racks PBS [N] Point load applied at the tip of the bowsprit 2 pDYN [N/m ] Dynamic pressure 2 pfw [N/m ] Flat water pressure 2 p0 [N/m ] Uniform pressure ρBS [m] Density of the material composing the bowsprit R1 [N] Reaction force on the centreline R2 [N] Reaction force at the gunwale rBS [m] radius of the bowsprit’s cross section Re [−] Reynolds number Rex [−] Reynolds number at distance x from the stagnation point RM [Nm] Righting moment RM˜ [Nm] Righting moment approximation RMR [Nm] Righting moment from the crew on the racks RM˜ R [Nm] Righting moment approximation from the crew on the racks RMT [Nm] Righting moment from the crew in the trapeze RM˜ T [Nm] Righting moment approximation from the crew in trapeze σBS [P a] Stress at a bowsprit section σu [P a] Ultimate stress S12,max [MP a] Maximum shear stress in the XY-/LT-plane S12,min [MP a] Minimum shear stress in the XY-/LT-plane SL,max [MP a] Maximum stress in the longitudinal direction SL,min [MP a] Minimum stress in the longitudinal direction SL [MP a] Stress in the longitudinal direction SLT,max [MP a] Maximum stress in the longitudinal-transverse plane SLT [MP a] Stress in the longitudinal-transverse plane ST,max [MP a] Maximum stress in the transverse direction ST,min [MP a] Minimum stress in the transverse direction ST [MP a] Stress in the transverse direction STV [MP a] Stress in the transverse-vertical plane SV [MP a] Stress in the vertical direction SVL [MP a] Stress in the vertical-longitudinal plane SF [−] Safety factor T [m] Draft t [m] Thickness of the boundary layer x tBS [m] Thickness of the bowsprit Tmax, canoe body [m] Maximum draft of canoe body Tmax [m] Maximum draft TK [−] Draft of the centreboard TCG [m] Transverse centre of gravity TCGcrew [m] Transverse centre of gravity of crew TR [−] Taper ratio TWA [◦] True wind angle TWS [m/s] True wind speed U∗ [m/s] Friction velocity U∞ [m/s] Freestream velocity U2,max [mm] Maximum deflection in the transverse direction U2,no17 [mm] Deflection in the transverse direction of layup No. 17 U2,no18 [mm] Deflection in the transverse direction of layup No. 18 U3,i [mm] Deflection of node i in the vertical direction U3,max [mm] Maximum deflection in the vertical direction U3,no17 [mm] Deflection in the vertical direction of layup No. 17 U3,no18 [mm] Deflection in the vertical direction of layup No. 18 U1 [mm] Maximum deflection of 1st model U2 [mm] Maximum deflection of 2nd model U3 [mm] Maximum deflection of 3rd model V [m/s] Speed VCG [m] Vertical Centre of Gravity xLOA [m] X-position of the maximum beam y [mm] Distance to the nearest wall y+ [−] Non-dimensional distance from the wall zB [m] Z-position of centre of buoyancy zG [m] Z-position of centre of gravity zCE [m] Vertical centre of effort of the sails zCLR [m] Vertical centre of effort of the appendages α [◦] Leeway angle ∆ [kg] Displacement ∆S [m] Cell spacing µ [kg/(m · s)] Dynamic viscosity of the fluid ν [m2/s] Kinematic viscosity of the fluid νLT [MP a] Poisson’s ratio in the longitudinal-transverse plane νTV [MP a] Poisson’s ratio in the transverse-vertical plane νVL [MP a] Poisson’s ratio in the vertical-longitudinal plane ρ [kg/m3] Density τwall [MP a] Wall shear stresses

xi Contents

Abstract ...... iii Preface and Acknowledgement ...... v Executive Summary ...... vi Mission Proﬁle ...... vi Main Particulars ...... vi List of Abbreviations ...... viii List of Variables ...... ix List of Figures ...... xv List of Tables ...... xvii

1 Introduction 1

2 1001VELAcup 3 2.1 Class Rules ...... 3 2.2 The Race ...... 4

3 Design basis 7 3.1 Wind Statistics ...... 7 3.2 References for Design ...... 9 3.2.1 Hull ...... 9 3.2.2 Rig and Sails ...... 11 3.2.3 Appendages ...... 12 3.2.4 Racks ...... 14 3.3 Overall Design Features ...... 14

4 Theory 17 4.1 Computer-Aided Design (CAD) ...... 17 4.1.1 Hull Fairing ...... 17 4.2 Computional Fluid Dynamics (CFD) ...... 19 4.2.1 Resistance ...... 19 4.2.2 Governing Equations Solved ...... 20 4.2.3 Turbulence Model ...... 20 4.2.4 Numerical Solution ...... 21 4.2.5 Grid Description ...... 24 4.2.6 Aerodynamic Resistance ...... 25 4.2.7 CFD Analysis Setup ...... 25 4.3 Finite Element Method (FEM) ...... 29 4.3.1 Prestudy ...... 29 4.3.2 Hull Components ...... 29 4.3.3 Centreboard and Rudder ...... 30 4.3.4 The Sandwich Structure ...... 30 4.3.5 FEM Analysis Set Up ...... 33 4.4 Velocity Prediction Program (VPP) ...... 38 4.4.1 Input and output ...... 39 4.4.2 Solved equations ...... 39 4.4.3 Centreboard and Rudder ...... 41 4.4.4 Sail Set Up ...... 45 xii Contents

5 Design process 47 5.1 Hull ...... 47 5.1.1 Hull Analysis ...... 47 5.1.2 Hull Concepts ...... 48 5.1.3 Hull Design Optimisation ...... 51 5.1.4 Final Hull Geometry and Hydrodynamics ...... 58 5.1.5 Deck ...... 60 5.1.6 Structural Hull Design ...... 60 5.2 Sail and Rig ...... 75 5.2.1 Sail Set Up ...... 75 5.2.2 Rig ...... 83 5.3 Appendages and Racks ...... 89 5.3.1 Centreboard and rudder ...... 89 5.3.2 Racks ...... 91

6 Balancing of Final Design 97

7 Building process 99 7.1 Templates ...... 99 7.2 Planking ...... 100 7.2.1 Planking the hull and deck ...... 100 7.2.2 Planking the internal structure ...... 101 7.3 Lamination ...... 102 7.3.1 Laminating the hull and deck ...... 102 7.3.2 Laminating the internal structure ...... 103 7.4 Further Building ...... 103 7.4.1 Rudder and Centreboard ...... 103 7.4.2 Racks ...... 104 7.4.3 Bowsprit ...... 104

8 Future Work 105 8.1 Remaining Work ...... 105 8.1.1 Sails ...... 105 8.1.2 Local Reinforcements ...... 105 8.1.3 Structure of Centreboard and Rudder ...... 106 8.1.4 FE-Analysis of Racks ...... 106 8.1.5 Structure of Bowsprit ...... 107 8.1.6 Deck Layout ...... 107 8.2 Future Investigations ...... 107 8.2.1 Hull Fluid Dynamics ...... 107 8.2.2 Wing Sails ...... 108 8.2.3 Foiling ...... 108 8.2.4 Rotating Racks ...... 108 8.2.5 Rotating Bowsprit ...... 109

References 111

Appendix A - Drawings I

Appendix B - Plots VII

Appendix C - Rules IX

xiii Contents

xiv List of Figures

2.1 Map of Mondello, Sicily ...... 5 2.2 2017 Regatta track, wind from left side of ﬁgure ...... 5

3.1 Weibull probability distributions ...... 8 3.2 Weibull probability density functions ...... 8 3.3 Weibull probability density functions for diﬀerent time steps ...... 9 3.4 Model of a 49er©, (Wikipedia, 2010) ...... 10 3.5 Reference hull concepts ...... 11 3.6 Bowsprit reference concepts ...... 12 3.7 Racks reference concepts ...... 14

4.1 Keel line curvature graph for final hull model ...... 18 4.2 Water line curvature graph for final hull model ...... 18 4.3 Chine line curvature graph for final hull model ...... 19 4.4 Computational domain setup ...... 22 4.5 Numerical ventilation error ...... 24 4.6 Volume mesh growth ...... 25 4.7 Mesh detail for the bow in the CFD-simulations ...... 27 4.8 Mesh detail for the aft in the CFD-simulations ...... 28 4.9 Sandwich constituents ...... 31 4.10 The meshing of the hull surface ...... 34 4.11 Shear stresses in core ...... 35 4.12 Simplification of forces acting on the skiff considered in the VPP ...... 40 4.13 Description of planform ...... 42 4.14 Profile drag for different profiles ...... 43 4.15 Profile drag for different thicknesses ...... 44 4.16 Lift for different profiles ...... 44 4.17 Forces acting on a sail ...... 45 4.18 Lift and Drag coefficients as a function of the angle of attack α ...... 46

5.1 Transonic hull© ...... 50 5.2 Scaled 49er© hull...... 51 5.3 Straight vs flared freeboard sprays differences ...... 52 5.4 Max Beam position vs resistance. Red stars mark measured data; Blue line is the fitted resistance curve ...... 53 5.5 Max Draft position vs resistance. Red stars mark measured data; Blue line is the fitted resistance curve...... 57 5.6 Resistance curve for final canoe-body ...... 58 5.7 Wave pattern generation at 6 kn speed ...... 59 5.8 Location of hull nodes investigated ...... 62 5.9 Location of deck nodes investigated ...... 64 5.10 Overview of internal stiffening structure ...... 68 5.11 Comparison of stiffener design ...... 69 5.12 Schematic flange layup design of stiffener ...... 69 5.13 Comparison of model designs ...... 70 5.14 Comparison of model deflection ...... 70

xv List of Figures

5.15 Deformations magnified 50:1 for hull-with-trapeze load case ...... 71 5.16 Deformation of hull magnified 50:1 for hull-with-trapeze load case. Hull plating and deck are hidden ...... 72 5.17 Distortion of elements at forestay magnified 50:1 for hull-with-trapeze load case . 72 5.18 Bulkhead element for which stress is plotted in Figure (5.19) ...... 73 5.19 State of stress in bulkhead element shown in Figure (5.18) ...... 73 5.20 Strain plotted for bulkhead element in Figure 5.18 ...... 74 5.21 Hull element for which stress is plotted in Figure (5.22) ...... 74 5.22 State of stress in hull element shown in Figure (5.21) ...... 75 5.23 Final sail area and mast height dimensions ...... 80 5.24 Final sail area and mast height dimensions using the Jib 0 ...... 81 5.25 Final sail plan ...... 82 5.26 Highlighted are the Jib 0 (red) and Jib (green) ...... 85 5.27 Schematics of the attachment of the bowsprit to the hull ...... 85 5.28 Different levels of extension of the bowsprit, with the fixed conical section highlighted in red ...... 86 5.29 Rotating bowsprit concept model ...... 88 5.30 Final rig design, with the diamond rig ...... 89 5.31 Planforms comparison ...... 90 5.32 Analysed load case for the aft support of the rack ...... 93 5.33 Planforms comparison ...... 95 5.34 Analysed load case for the aft support of the rack ...... 96

6.1 General arrangement drawings of the skiﬀ ...... 97

7.1 Dog bones in one of the deck’s template ...... 99 7.2 Templates models in Rhino 3D ...... 100 7.3 Template assemblies used for planking ...... 100 7.4 Planking with divinycell blocks ...... 101 7.5 Faired hull ...... 101 7.6 Bulkhead template completely covered with balsa for the core ...... 101 7.7 Finished half-bulkhead core ...... 102 7.8 Layup procedure of stiﬀener component...... 103

B.1 Max beam position vs resistance. Red stars mark measured data; Blue line is the ﬁtted resistance curve ...... VII B.2 Max draft position vs resistance. Red stars mark measured data; Blue line is the ﬁtted resistance curve ...... VII

xvi List of Tables

3.1 Mean values and Weibull distribution fit for inspected wind statistics data . . . . 7 3.2 Mean values and Weibull distribution fit for different time steps ...... 8 3.3 Important dimensions of the 49er© ...... 12 3.4 Important dimensions of Federica (DeSantis, 2016) ...... 13 3.5 Comparison of rudder areas and lead for different skiff classes ...... 13

4.1 Computational domain boundaries ...... 22 4.2 Mesh properties vs ship speed ...... 26 4.3 Balsa wood properties ...... 32 4.4 Flax/epoxy laminate properties ...... 33 4.5 Load case crew on racks ...... 36 4.6 Load case crew in trapeze ...... 37

5.1 The simulated speeds for each hull in the CFD-simulations converted from knots to metres per second...... 48 5.2 Location of the centre of gravity (CoG) for each speed scaled from the 49er©. . . 48 5.3 Beam fom moment of inertia ...... 50 5.4 Resistance Comparison Between Transonic Hull© and Scaled 49er© Hull . . . . . 51 5.5 Positions for the maximum beam variation ...... 52 5.6 Resistance vs beam position comparison ...... 54 5.7 Scale factors to compare which hull to choose for maximum beam position variation 54 5.8 Ranked and scaled comparison between the beam position to evaluate where to place the maximum beam ...... 55 5.9 Positions for the maximum draft position variation ...... 55 5.10 Resistance vs draft position comparison ...... 56 5.11 Scale factors to compare which hull to choose for draft variation ...... 56 5.12 Ranked and scaled comparison between the beam position to evaluate where to place the maximum draft ...... 56 5.13 Final hull dimensions for the skiff ...... 58 5.14 Final drag along x-axis for the canoe body ...... 58 5.15 Drag along x-axis for hull LED3 ...... 60 5.16 Maximum stress for varying core thickness ...... 61 5.17 Variation of the sandwich skin laminates ...... 63 5.18 Deck layup analysis with 8 mm core thickness ...... 65 5.19 Deck layup analysis with 10 mm core thickness ...... 66 5.20 Deck layup analysis with 12 mm core thickness ...... 67 5.21 Comparison between models with and without flange...... 70 5.22 Different concepts ...... 77 5.23 Systematic variations within different Sail Concepts ...... 78 5.24 Systematic variations with an centreboard AR = 7.69 ...... 79 5.25 Constants assumed for subsequent computations ...... 86 5.26 Variables used for subsequent computations ...... 86 5.27 Results from the Matlab computations ...... 87 5.28 Leeway angle for different TWS at VMG ...... 91 5.29 Forces to dimension against ...... 92

xvii List of Tables

5.30 Material data for Aluminium EN-AW 6082 T6 taken from Alutrade (2017b) ans Alutrade (2017a) ...... 92 5.31 Dimensions for the aft support...... 93 5.32 Dimensions for the bow support ...... 94 5.33 Dimensions for the beam rack between the support...... 95 5.34 Dimensions of all the parts of the rack ...... 96

xviii 1 Introduction

This project aims at designing and building a high performance racing skiff, the report starts by explaining the competition context of the project and presenting the class rules that serve as a starting point for the design. The respective design basis follows, being further developed in the design method section. Fundamental theory is also presented in order to explain the main theoretical topics and assumptions that guide all the different sub-groups and their work. Finally the design process can be described without any additional restrictions. In that section, as well as the rest of the report, the process is described in terms of the different components of the boat, namely the hull, sail and rig, and appendages. The subsequent sections deal with the resulting design and its layout, and the last one with the building process. The project is inserted in three main contexts. Firstly, it is a mandatory 15 credits course for the Masters Program of Naval Architecture and Ocean Engineering at Chalmers. The course is organized by the department M2, Mechanics and Maritime Sciences. Secondly, it is inserted in the context of Chalmers Sports and Technology, which is where advanced sport-related research takes place involving engineers, researchers and students with the athletes and coaches, as well as the enterprise and governing bodies. In this context, one important objective is to improve the performance alongside safety for the athletes, which are, in this case, sailors. Finally, the last context this project is included in is the 1001VELAcup 2018, in which the built boat will be raced against competitors from other universities. This competition is the element linking all these contexts, being what justifies the building of the boat rather than just its design, as well as the need for connection with athletes to sail it in the future. These athletes are to whom the authors turn to for practical advice about several practical usages that are fundamental in the design process and yet are very difficult to realize if based only on a theoretical analysis. Naturally with several different contexts come several different goals. First it is intended to gain valuable knowledge and experience in designing yachts, and all it comprises in all the different areas of the utmost relevance to Naval Architecture. Furthermore, in the context of Chalmers Sports and Technology and the 1001VELAcup, the authors gain additional knowledge in the operation and practical matters of sailing, its equipment, and in boat building.

1 1 Introduction

2 2 1001VELAcup

Born in 2005 from the minds of the Italian yacht designers Massimo Paperini and Paolo Processi, the 1001VELAcup was brought to the university departments of Naval Architecture, Architec- ture and Engineering of all Europe, the concept of a Conceive, Design, Implement and Operate (CDIO),(CDIO, 2017), project similar to the world famous Formula Student, (Imeche, 2017). It is therefore a project aiming towards the unification and stimulation of academic, as well as research and innovation purposes. Further aim of the project is the formation of new professional profiles in the naval architecture world, through the concept design and further building process of a high performance racing skiff. The foundation of the project is the Class Rule R3 (A. 1001VELAcup, 2017), kept simple in its interpretation and minimalistic in order to leave wide margins to the design process. Such rules are mainly aimed to limit the dimensions of the hulls and the total sail area. The strength of the class rule lays however in the limitations that concern the materials used for the building process. It is indeed required that a large portion of the materials used for the hull are of sustainable, either animal or vegetable, derivation, while the mast, or at least its matrix, is expected to be realized in extruded aluminum. The mobilisation of students and universities toward the applied research of new composite materials applicable to nautical purposes has been without a doubt one of the main results achieved by the competition. Other relevant factor achieved has been the direct implication of realities outside the university walls. Collaboration between students, professors and other experts from the industry made it possible over the years to carry out focused researches in different branches of the yacht design and develop bilateral partnerships that benefit both the academic and the professional worlds. The most important achievement of the competition is however to be identified in the empowerment of students in relation to a real problem, aiming far beyond obtaining a grade or passing an exam and closing that gap between concept design and final product that defines unfortunately too often academic projects. The competition has seen over the years the rise of innovative concepts and the constant growing interest among Italian and other European universities, a signal perhaps that it is ready to expand.

2.1 Class Rules

As a proper sport competition, the 1001VELAcup is subjected to a regulation class specifically created for it, class R3, that allows room for innovation yet limits the differences among the teams taking part to the race. Such rules affect both the crew, which during the race will be expected to follow the Racing Rules of Sailing, and the skiff. A full rule book can be examined in Appendix 8.2.5. In the following section only the main limitations are listed. As far as the crew is regarded, the regulation states it to be composed of two students currently registered at the university they race for. A second rule aims toward a fair level of skills among the sailors, so that crew members that hold a Group 3 Classification (WorldSailing, 2017) are not allowed to participate. The class R3 is thought of as a box-rule in which limitations are minimal and principally affect the main dimensions and properties of the skiff in order to allow different design solutions. Beam and Length overall are limited respectively to 2.1 and 4.6 m with a tolerance of 15 mm.

3 2 1001VELAcup

No limits are put on draft, displacement nor the freeboard. A further geometrical limitation affects the shape of the hull, which has to be of mono-hull type, symmetric along the centreline and is not allowed to present transverse concavities below the waterline. As mentioned earlier, the class rules mainly focus their attention on the materials used for the hull, setting a 70% minimum limit in terms of weight for the amount of natural material used for the hull construction. Therefore all titanium, aramid, carbon fibres or other high-modulus fibres are banned for this component. The most recent update of the regulations introduced in the 2018 edition of the 1001VELAcup, put different restrictions to the design of the appendages. In fact, the latest update of the regulations allow the design of the appendages in carbon fibre, spectra, kevlar or other high-modulus fibres. Finally, the bowsprit, whether needed, can be realized in carbon fibre. Similar limitations in terms of materials are applied to the sail plan, so that aramid, carbon or other high-modulus fibres are prohibited. The total sail area carried onboard is furthermore limited to not exceed 33 m2. Finally, unlike most of the box-rules, no geometric limitations are set on the rig plan, it is although required for it to be realised out of extruded aluminium.

2.2 The Race

The trophy 1001VELAcup is held every year in Italy during the last week of September. The 2018 edition will be held for the second time in the bay of Mondello in Palermo. A map of the bay can be appreciated in Figure 2.1. Historically, the trophy consisted of an open sea regatta distributed in nine races, each consisting of four legs, over three days of total competition. A sketch of the regatta field, as published in the Istruzioni di Regata (1001VELAcup, 2017) is shown in Figure 2.2. Since the 2017 edition, a Midwinter Indoor Race has been introduced with the aim of evaluating the hulls only on their technical features. The skiff named LED, realised by the students of the Universita’ degli Studi di Palermo, graduated as champion of the first edition of the Midwinter Indoor Race. Hosted by the Universita’ di Napoli Federico II, the indoor competition sees the participant hulls towed at the speeds of 2, 4 and 6 kn and judged based on the total resistance, with and without appendages, wave generation pattern in calm water, and the seakeeping properties in head waves.

4 2 1001VELAcup

Figure 2.1: Map of Mondello, Sicily

Figure 2.2: 2017 Regatta track, wind from left side of ﬁgure

5 2 1001VELAcup

6 3 Design basis

In this chapter, a prestudy is presented. In this prestudy, all of the skiff’s parts that are designed are covered, alongside with an investigation of the wind statistics at the race site. Investigation of similar skiffs, both commercial and those participating in the 1001VELAcup in previous years are also presented. The limitations and the overall design features of the project are also identified and stated in the last part of this chapter.

3.1 Wind Statistics

When designing a hull for a competition, it is good practise to optimise it for the racing conditions, therefore, considering where the race will take place, in this case Mondello, Italy. The design can then be optimised for the expected wind speed. The data needed is thus primarily the mean wind speed together with its statistical distribution. The data is collected from two different sources, Windguru (Windguru, 2017) and Istituto Superiore per la Protezione e la Ricerca Ambientale (ISPRA) (R.M.N., 2017), focusing on those data corresponding to the second half of September. Time period and time frequency of the data extrapolated are different for the different sources. Windguru provides data since 2004 to present day with 3 hours time spans, while ISPRA provides acceptable data from 2009 to 2014 with a time frequency of 10 minutes. Both data sheets are consequently resumed in order to focus only at the hours during which the race takes place, therefore only data between 11 am and 5 pm are taken into consideration.

Analysis of the data provides a mean wind speed at the location of 3.84 m/s from Windguru and 3.37 m/s from ISPRA. A histogram is thus created to see how the data is distributed. Figure 3.1a and 3.1b show that trends for the data available well ﬁt a Weibull probability distribution. Hence, the expected value and variance are ﬁnally evaluated, and both probability density function (PDF) plots are presented in Figure 3.2a and 3.2b. In Table 3.1 below the expected value and variance are presented.

Table 3.1: Mean values and Weibull distribution ﬁt for inspected wind statistics data

Windguru [m/s] ISPRA [m/s]

Mean Value 3.8438 3.3716 Expected value 3.8616 3.3639 Standard deviation 1.1991 0.4740 Variance 1.4379 1.4379

Further and more detailed investigations focusing on three different consecutive time steps within which each single race will take place. Such division is needed in order to get a more detailed analyse of the wind conditions during the different races per day as well as to furthermore decide on the final sail set up. Results obtained from these latter inspections are presented in Table 3.2 highlighting mean value, standard variation and variance of the data. For each time step, probability density functions are plotted in Figure 3.3a to 3.3c.

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(a) ISPRA data (b) Windguru data

Figure 3.1: Weibull probability distributions

(a) ISPRA data (b) Windguru data

Figure 3.2: Weibull probability density functions

Table 3.2: Mean values and Weibull distribution ﬁt for diﬀerent time steps

Time step 8-11 [m/s] 11-14 [m/s] 14-17 [m/s]

Mean Value 3.5011 3.7382 4.0253 Standard deviation 1.5952 1.4041 0.8439 Variance 2.5446 1.9715 0.7122

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(a) 8-11 am time step data (b) 11-14 am time step data

Figure 3.3: Weibull probability density functions for diﬀerent time steps

3.2 References for Design

To avoid starting from a clean sheet, it is decided to start the design process with some references. The overall reference skiﬀ used in this project is the 49er©. The 49er© is a high performance sailing dinghy which was designed in the 1990’s (Bethwaite, 2010). However, some other references are used as well for the hull shape and the appendages.

3.2.1 Hull

When starting the design process for the hull shape, it was decided to start from a couple of reference hulls. This section presents the two hull shapes that are used as references and explains why they were chosen.

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3.2.1.1 49er© Hull A new hull, based on the 49er© (see Figure 3.4), is scaled down to 4.60 m LOA according to the regulations of the competition. The main design properties of interest from the 49er© are: • Maximum beam far aft • Flat bottom in the aft • Sharp bilge above the waterline • Slender and v-shaped bow The design objective of the 49er© was to make a dinghy of less than 5 m that performs well with no "hump" in the drag/speed curve. This means that there should not be a peak in the resistance during the transition between the displacement mode and the planing mode. Since a planing hull was desired, the focus for inspiration was on ’light dinghies’ only. The main inspiration for the 49er© was the 18-footer which at that point of time was a modern recently developed dinghy (Bethwaite, 2010). The 49er© is still today one of the highest performing skiﬀs in its class and is consequently chosen as the main reference hull.

Figure 3.4: Model of a 49er©, (Wikipedia, 2010)

3.2.1.2 Transonic Hull © The second reference hull that is used is the so-called ’transonic hull’©, see Figure 3.5b (Calderon & Maskew, 2015). The hull has a double wedge shape with a vertical stem, entirely ﬂat bottom from the deepest point at the stem to the widest point at the stern, which has zero submergence and the sides are vertical. The submerged part of the hull, thus, forms a tetrahedron). The basic idea of a transonic hull© is that it has a low wave generation when compared to the more regularly shaped hulls. Since the bow is very sharp, the bow wave will in principle be very small, and with no curvature along the hull there will be no pressure peaks and therefore no waves generated along the hull. However, at the stern there is a very small pressure rise due to

10 3 Design basis the water that is leaving the flat and rather horizontal bottom. Thus there will be very small waves generated, but they will practically not cause any negative interference between the bow and the stern waves. Most hulls have a wave resistance hump at a Froude number of 0.4-0.5, this is caused by a wave crest in the bow and a wave trough at the stern. Since the stern wave of a transonic hull© is very small, this effect will be very small. Because of this a transonic hull© will not have a specific "hull speed" for which the created wave system that is most favourable.

Furthermore, since in principle this shape allows the hull to pierce the waves, it translates in sailing with very small pitch, and is therefore almost free from slamming problems in the structure.

(a) Scaled 49er©-based hull (b) Transonic hull©

Figure 3.5: Reference hull concepts

3.2.2 Rig and Sails

The rig and sails are one of the most important parts of a racing skiﬀ. Both can be adjusted iterative over and over again. However, to start designing, a basis needs to be deﬁned. This is done by using well known references, among other things. The following sections contain descriptions of references used for the rig and sail design process.

3.2.2.1 Rig The rig reference is the traditional 49er© rig, see Figure 3.4. It contains a 8.3 m high mast made out of carbon ﬁbre as its boom. The rig has two spreaders for the lower and upper shrouds each. These shrouds are attached at the hull shortly behind the mast used for pretensioning the rig. The forestay goes on top of the bowsprit system attachment. Two trapezes are mounted on top of the upper shrouds pulled back to the racks. They are used for provision of the righting moment via hiking.

3.2.2.2 Bowsprit Using a third additional sail requires a bowsprit separating the sails that are set. The 49er© serves as inspiration not only for the sail and rig design, but also for the bowsprit. Furthermore, some opponent’s dinghies are also taken as a reference for the design of this component. Both systems can be seen in the following Figures 3.6a and 3.6b.

As shown in the figures, both bowsprits are retractable, meaning that they can be pulled inside the skiff when not in use. Therefore both references have installed a system connected to the sail setting. A reinforcement at the bow prevents the bowsprit of falling out as well as taking the bending force of the sail and serving as an attachment for the forestay. The material of the bowsprits is usually carbon fibre. Apart from a small piece sticking out in the bow, the length of the bowsprit is smaller than the distance between forestay and mast attachment.

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(b) Previous competitor in 1001VELAcup, picture taken by Adam Persson (2017) (a) 49er©, picture taken by Eike Jacobs (2017)

Figure 3.6: Bowsprit reference concepts

3.2.2.3 Sails For the sails, the 49er© is used as the main reference as well. The current 49er©model, Section 3.4, has a total upwind sail area of 21.2 m2. This area is divided into a main sail area of 16.1 m2 and a jib sail area of 5.1 m2. For the downwind course, the 49er©has an additional 38 m2 gennaker to hoist giving it a total of 59.2 m2.

Table 3.3: Important dimensions of the 49er©

Dimension

Main Sail 16.1 m2 Jib 5.1 m2 Upwind sail area 21.2 m2 Jib to upwind sail area ratio 24% Mainsail to upwind sail area ratio 76% Mast height 8.3 m Mast height to length Ratio 1.69

The main sail is shaped rectangular providing as much sail area up in the top part as possible using the uninterrupted wind. Furthermore, managing the twist of the main sail is easier. The sails itself are made out of Mylar and fully battened. Opponent skiﬀs from the previous years of 1001VELAcup are also used as references, where it is common to use 55 % for the main sail and 45 % for the gennaker, and trying to have the CE (center of eﬀort) as high as possible (DeSantis, 2016). One of the opponents sail plan is presented in Table 3.4.

3.2.3 Appendages

The design of the appendages, the centreboard and rudder, is based on comparisons between the appendages of other fast sailing dinghies and skiﬀs. The recommendations in Larsson, Eliasson, and Orych (2014) are also evaluated. A comparison between diﬀerent common wing sections is also implemented.

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Table 3.4: Important dimensions of Federica (DeSantis, 2016)

Dimension

Main Sail 13.794 m2 Jib 4.356 m2 Gennaker 14.85 m2 Upwind sail area 18.15 m2 Jib to upwind sail area ratio 24% Mainsail to upwind sail area ratio 76% Mast height 7.74 m Mast height to length Ratio 1.68

3.2.3.1 Rudder and Centreboard

For the design of the appendages, the most relevant comparison between diﬀerent skiﬀs is the planform area of the centreboard in relation to the upwind sail area. According to Larsson et al. (2014), the centreboard planform area should be between 3 % and 3.5 % of the upwind sail area. For the 49er©, this area ratio was found to be

centreboard area 0.3 m2 = = 1.42%, (3.1) upwind sail area 21.2 m2

where the centreboard area is measured in a CAD ﬁle of a 49er©, (Creative, 2012). Furthermore, this ﬁle is used to measure the 49ers© centreboard draft of 1.1 m as well as the 49er’s© rudder area of 0.2 m2. Since the recommendations in Larsson et al. (2014) are mainly for keel boats and not for high performance sailing dinghies, it is more reasonable to use the same centreboard to upwind sail area ratio as the 49er© rather than the one in Larsson et al. (2014).

The lead, the distance between the sail centre of effort and the centreboard centre of effort as a percentage of the length of water line (LWL), is investigated. For the design of the of the rudder the recommendations in Larsson et al. (2014) are disregarded for the same reason as above. Instead, the properties of several high performance skiffs are investigated and a decision based on this is made. The results from the study are presented in Table 3.5.

Table 3.5: Comparison of rudder areas and lead for diﬀerent skiﬀ classes

Boat class Rudder Area [% of centreboard area] Lead [%]

49er© 67 13 29er© 43 8 470© 43 4 505© 45 2 International 14© 60 7 Musto skiﬀ© 68 9

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3.2.4 Racks

To maximise the righting moment created by the sailors, in order to carry as much sail as possible during the races, it is preferred to have the centre of gravity (CoG) as far out from the centre line as possible. Since it is preferable to have a slender hull, it will most likely not be the maximum allowed width, so the racks will be used to move the sailors centre of gravity as far out as possible. To have some background of how the racks should look like inspiration is taken from the 49er©, since it is the main reference skiff. The racks on the 49er© are built like wings, which means that the space between the hull and the outer part of the racks is covered with material, see Figure 3.7a. Another dinghy that is used as inspiration is the International 14 footer. It has racks made out of tubes of carbon fibre which makes them light and moves the centre of gravity far out from the centre line. Finally inspiration is taken from the already existing boats in the 1001VELAcup. These racks are more similar to the International 14 footer, they are made out of aluminium profiles that give the racks, see Figure 3.7b.

(a) 49er©, picture taken by Kaupp (2007) (b) Previous competitor in 1001VELAcup, picture taken by Persson (2017)

Figure 3.7: Racks reference concepts

3.3 Overall Design Features

The authors of the project have decided to not go for hydrofoil nor wing sail. It would have been a great advantage to use hydrofoil since the resistance drops to a minimum due to uplifting of the hull out of the water. Had this been the group’s choice, the hull would have been shaped based on different criteria, such as lifting up as fast as possible. Nevertheless, the hydrofoiling option was disregarded based on the ruling concerning the sailors, as it is very unusual to have two sailors on a hydrofoiling skiff. It would have been difficult to find sailors who would do it properly and even then it would have required a disproportionate amount of practice. Consequently, this would add too much uncertainty to the results of the race, due to factors that are external to the design team. Similarly, it would have been a great advantage to use a wing sail since the efficiency of such is much better compared to a normal sail. Yet this option was also disregarded since the students would have had to construct the wing sail by themselves without having the possibility to purchase it from an external company. The handling of a wing sail requires a lot of training. Therefore, more uncertainty would have been introduced due to alien factors to the design team.

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Besides the uncertainties added and the eventual absence of backup hulls during the competition, there are also severe time constraints that limit the group’s focus, not allowing for proper design of more complicated concepts. Most of all, since this is the ﬁrst design for Chalmers University of Technology, the aim is to achieve a good position in the race as a way to assure the continuity of this project in the future years.

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16 4 Theory

In this chapter, the basic theory for the methods that are used is explained in deeper detail. The sections focus on the different softwares used and the assumptions made while using them. The softwares are, Rhinoceros 3D for CAD, STAR-CCM+ for CFD, Abaqus for FEM, and a VPP-program modified specifically for this project, used for velocity prediction.

4.1 Computer-Aided Design (CAD)

The CAD-software used throughout the whole project is Rhinoceros 3D (McNeel, 2017). It is a software based on NURBS mathematical model, which is suitable for designing a boat hull since it can create complex curves and surfaces. The following sections will explain the theory behind the designing procedure.

4.1.1 Hull Fairing

Fairing of the hull surfaces is a very important aspect of the modelling process that has to be regarded throughout the whole process. This is of particular importance at the bottom and freeboard. The fairing process constitutes a good practice of surface modelling, being a requirement for having high quality surfaces (Henry P. Moreton, 1992). It consists in smoothing the mesh through a proportional grid of control points that do not cross paths between each other, except if strictly demanded by an irregular or unusual shape. The global trend of the control points’ coordinates should also match the trend of the desired surface, except when demanded by extreme shapes, that, for example, need trimming. The goal with this is to obtain surfaces that are as smooth as possible in order to improve the results of subsequent computations, i.e. to have computational results that are as smooth as possible.

There are no objective criteria to measure smoothness or fairness, and furthermore, it is highly dependent on the application. Yet, a principle that should be followed in this particular application of yacht design is that the surfaces should result as simple as possible without any unnecessary details or oscillations. This means they should have the minimum number of control points that are not so restrictive as to inhibit the desired hull shape, but are just enough to achieve it. They should allow for a similarly smooth and relatively easy further manipulation. Adding to all of this, the aesthetics of the hull will also be greatly improved as a result. During the design of the hull, fairness of several key lines and surfaces has always to be made. These are explained in the following sections.

4.1.1.1 Keel line

The keel line extends over the length of the hull, and should assume a curvature close to that depicted by the blue line in Figure 4.1.

As seen in the Figure 4.1, the curvature decreases to very small values near the stern. This is important since a more convex curvature induces a low pressure that sucks the stern down, therefore it increases resistance as the Froude number is increased.

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Figure 4.1: Keel line curvature graph for ﬁnal hull model

4.1.1.2 Waterline

The waterline extends for almost the full length of the boat. It should also be smooth all the way along its length, to ensure there are no bumps on the hull surface and in order to minimise the disturbance of the ﬂow around the boat. The curvature graph of such line shall assume a clear trend as well as absence of sign changes. Furthermore, the curvature will naturally increase very signiﬁcantly near the aft due to the geometry of the hull. This is evidenced in Figure 4.2.

Figure 4.2: Water line curvature graph for ﬁnal hull model

4.1.1.3 Chine line

The same reasoning and principles mentioned for the keel and waterline apply for the chine line as well. In this case, the line shall have no curvature along a certain percentage of the length, this is from where the beam becomes constant. The chine line is presented in Figure 4.3.

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Figure 4.3: Chine line curvature graph for ﬁnal hull model

4.2 Computional Fluid Dynamics (CFD)

Practical CFD computations are carried out with the aim of predicting hull resistance with an acceptable accuracy. Such accuracy is only achievable if turbulence models, wall functions, mesh and evaluation times are appropriately considered. The tool used to carry out such evaluations is STAR-CCM+ (CD-Adapco, 2017) and in the following sections theoretical support to the solver set up will be presented.

4.2.1 Resistance

According to the theory of ship resistance initially developed by William Froude, the total resistance of a hull proceeding at the water surface can be defined as the sum of a viscous and a wave component. The former derives from the combined effect of the wetted surface, the surface smoothness, the length and the speed, expressed in terms of tangential stresses and viscous pressure resistance. The latter is instead caused by the distribution of pressure developing around the hull when in motion and weighs on the total resistance, for a planing boat with Froude number of 1.4, at most 44 %. For a containership with Froude number of 0.22 the wave components insists instead on at most 17.5 % of the total resistance (Larsson & Raven, 2010). Such values for the distribution of the total resistance can be taken as maximum and minimum references for the skiff under inspection in the project, which is computed for boat speeds ranging between 3 and 15 kn. As water flows along the hull, friction slows the water molecules and creates a layer that is carried along with the hull itself. This initially thin layer, called the boundary layer, gradually increases in thickness evolving from a laminar condition to a turbulent one and eventually breaks into eddies near the stern. As the hull furrows through the water, the flow has to travel around it. The local velocity of the water differs from the one characterising the undisturbed flow and will be slowed at the bow and at the stern, but increased along the main part of the hull causing an increase in friction. Moving along the water surface, a hull will force fluid particles to move from their equilibrium positions thus creating waves that radiate in two different patterns. The first, and most relevant,

19 4 Theory is the transverse pattern. The second pattern is the divergent waves that fans out from the hull. The resistance component generated by the energy removed from the wave system, which can be found in the wake, is thus called wave breaking resistance. The remaining portion of wave energy is instead radiated away from the hull and responsible for the so called wave pattern resistance.

4.2.2 Governing Equations Solved

Practical CFD computations can almost always be considered satisfactory when details about the time-averaged properties of the flow are obtained. At the heart of most these CFD ap- proaches is the modelling of informations and effects of the turbulent fluctuations. The treatment of such events can be carried out with procedures based on the Reynolds-Averaged-Navier- Stokes (RANS) equations, which represents time-averaged equations of motion for fluid flow. Assuming that a fluid behaves as a continuum, the Navier-Stokes equations allow to describe fluid flows. However, these equations are inherently unsteady and nearly impossible to solve unless multiple average solutions, solved numerically through discretization in space and possibly time, at a series of time steps are used. As stated in Versteeg and Malalasekera (2007), the decomposition of the Navier-Stokes equations, bringing to the definition of the RANS, is based on the assumption that, introducing a set of unknowns called Reynolds Stresses, the time- dependent turbulent velocity fluctuations can be separated from the mean flow velocity. Such unknowns are then functions of the velocity fluctuations and require the implementation of a turbulence model to solve them. Unsteady RANS for transient flow is a straightforward variant of the RANS in which, while still solving for the mean velocity separately from the turbulent velocity, a transient term is present in the momentum equation and retained during computation. This means that turbulence time scales are removed from the Navier-Stokes equations through the averaging procedure, while larger time scales are resolved. The development of unsteady RANS methods within the ship hydrodynamics evaluations unlocks extensions to applications for seakeeping and manoeuvring, as presented in (Wilson, Carrica, & Stern, 2006) in addition to the already covered resistance and propulsion evaluations. Nevertheless, the effects of turbulence on the mean flow have to be described, since the time-averaging operation on the momentum equations discard all the detail connected to the state of the flow in the instantaneous fluctuations. CFD breaks a fluid domain into discrete cells to then solve in each one of them the conservation laws. The accuracy of these simulations are strictly bonded to the grid generated.

4.2.3 Turbulence Model

Throughout the project both a normal k − ω turbulence model and the Shear Stress Transport SST-Menter expansion are considered in place of the more commonly used k − because of the high interest in the evaluation of close to wall features. There are multiple reasons supporting such choice. According to (Versteeg & Malalasekera, 2007) the most important however can be found in the improved behaviour of k−ω when dealing with wall effects, unconfined flows and curved boundary layers. The further implementation of SST-Menter model allows to take into account properly the behaviour of the free-stream, quality of the k − model, without falling into errors dictated by sensitivity as it would happen to a normal k − ω. Therefore, the turbulence model chosen for the calculations is capable of predicting, in a numerically stable way, both the near-wall and the far field behaviours of the flow. Another reason that guides the choice of the model is the under-prediction of separation provided

20 4 Theory by k − , leading towards an overly optimistic, and therefore, non-conservative performance prediction. On the other hand, SST-Menter results should provide higher accuracy when dealing with onset and amount of flow separation under adverse pressure gradients and thus more accurate in such prediction. It should also be noted the fact that such turbulence model fails to take into account more subtle interactions between mean flow and turbulent stresses when compared to the Reynolds Stress Model (RSM) model. Versteeg and Malalasekera (2007) state in fact that two-equation turbulence models are incapable of capturing the more subtle contributions introduced by anisotropy of the normal stresses, as well as correctly predicting the effects on turbulence caused by body forces and extra strains. The RSM is able to exactly incorporate such features, but the requirement for several unknown turbulence processes to be modelled, together with a significant increase in computational time and storage need, discourage its implementation.

4.2.4 Numerical Solution

The first step to process a CFD problem is the definition of the region of interest. Evaluation of encountered resistance of a skiff has to deal with both air and water, therefore the modelling of an eulerian multiphase computational domain is needed. Furthermore, as there is a change in physical properties, problems may derive along the interface between the two fluids considered. Subsequent mesh refinements are therefore needed in such region.

4.2.4.1 Computational Domain The problem requires the definition of a multiphase computational domain where air and water are considered as the fluids interfacing. Specific dimensions and boundary conditions of the domain are needed in order to capture with satisfying accuracy the computations results. Only half of the domain is modelled since symmetry properties of the problem allow to do so and the computational time will decrease considerably. It has to be noted that all the results obtained will refer to half of the hull, hence half of the total resistance if not otherwise stated. The computational domain, presented in Figure 4.4, can then be defined as a rectangular box and boundary conditions defined according to Table 4.1. The symmetry surface ABCD reflects the symmetry of the problem, as water and air are considered to flow parallel to this boundary, with no particle crossing through it. The two opposite surfaces ADHE and BCGF are respectively given inlet and outlet boundary conditions; the outflow surface has to be placed sufficiently downstream such that vortices are not yet present in the stream. The three remaining surfaces are instead given wall boundary conditions. The hull boundary is modelled by a wall law. To implement such condition, the skiff is positioned in the domain with the centreline on the mirror plane with the bow facing the inflow boundary. At least one ship-length L = 4.6 m has to be left clear between the bow and the inflow boundary. The hull body is then subtracted from the domain itself and wall boundaries are defined at the portion left empty as there is no velocity passing through these sides. The flow encountering a wall will then have to travel around it, generating pressure distribution and a boundary layer development that are the heart of the numerical computations. Finally, no boundary conditions are applied to the free surface.

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Figure 4.4: Computational domain setup

Table 4.1: Computational domain boundaries

Surface Corners Boundary

Top CDHG Wall Bottom ABFE Wall Side EFGH Wall Symmetry ABCD Mirror Inﬂow ADHE Inlet Outﬂow BCGF Outlet

4.2.4.2 Turbulent Boundary Layer According to Larsson and Raven (2010), a validated assumption is that the velocity proﬁle in the inner part of a boundary layer must be independent of the thickness of the layer and dependent only on the shear stress at the wall, and the ﬂuid density and dynamic viscosity. Reasoning in terms of dimensions, such non-dimensional distance from the wall may be written according to Equation (4.1).

U y y+ = ∗ (4.1) ν where y represents the distance to the nearest wall, ν the local kinematic viscosity of the fluid and U∗, defined according to Equation (4.2), and being τwall the wall shear stresses and ρ the density of the fluid, represents the friction velocity at the nearest wall

rτ U = wall (4.2) ∗ ρ y+ is thus used to define the proper size of a mesh for a specific flow pattern. The importance of this element concerns wall functions and the definition of the velocity profile, divided in four

22 4 Theory different regions according to the value of y+: viscous sublayer, buffer layer, logarithmic region and wake region. The first cell spacing, ∆S, on a flat-plate boundary is evaluated via the resolution of the following algebraic system:

ρU x Re = ∞ (4.3) x µ 0.026 C = (4.4) f 1/7 Rex C ρU 2 τ = f ∞ (4.5) wall 2 rτ U = wall (4.6) ∗ ρ y+µ ∆S = (4.7) U∗ρ where Rex represents the Reynolds number at distance x from the stagnation point, U∞ the freestream velocity and Cf skin friction coeﬃcient. Finally, knowing the Reynolds number, it is then possible to evaluate half of the total thickness of the boundary layer, of the total thickness of the prism layer for the entire length of the hull, according to the Equation (4.8). Such choice can be considered on the safe side an provide results accurate enough since the velocity gradient in the outer part of the boundary layer is very small.

0.185L t = (4.8) Re1/5

4.2.4.3 Volume of Fluid (VOF) Method The Volume of Fluid (VOF) method belongs to the class of eulerian modelling techniques characterised by the mesh, either stationary or moving in a prescribed manner, in order to accomodate the evolving shape of the small contact area between two fluids. It is a simple solver that allows for tracking the free surface using a volume fraction function for each fluid to describe the location of the interface. Such fraction function is tracked for each cell of the domain grid and assumes value 1 when the considered cell is full of water, zero when filled with air. However, with this method the free surface is not sharply defined and a distribution over the height of several cells is instead generated. Hence, in order to achieve accurate enough results, local mesh refinements are needed.

4.2.4.4 Numerical Ventilation An error that can occur in the cases where the flow is not properly resolved is numerical ventilation. Such a computational error is encountered when two fluids are considered interfacing in the domain and particles of one of them are considered trapped into the boundary layer and transported into the domain of the second fluid. Hence, the net physical transition between the two fluids is erroneously approximated as a gradual diffusion. An example of numerical ventilation error can be appreciated in Figure 4.5. The hull presented was tested at a speed of 15 kn and it can be seen how a wide portion of the submerged hull is covered by air (blue portion) instead of water and only after a gradual transition does it reach the wet condition. If not corrected, such error will affect the computations and provide a wrongly estimated lower resistance.

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Figure 4.5: Numerical ventilation error

4.2.5 Grid Description

Fundamentally, a mesh is defined valid if it respects the main concepts of classification and topological compatibility. Further features defining a valid mesh must be the geometric trian- gulation, the property of unique mappability, parametric intersection and geometrical similarity. Once a valid mesh is generated, the attention has to move toward its quality, as a still valid mesh can guide to entirely wrong results if the quality is too low or the physics models in use are not properly assumed. Definition of an accurate mesh is then crucial to obtain valid results. From such point of view, the given problem requires mesh refinements perpendicular to the wall boundaries in order to properly capture the boundary layer and predict the frictional resistance.

4.2.5.1 Mesh Refinement For fluid flow calculations, grid quality has to be optimised in order to best evaluate calculations regarding convective and diffusive fluxes. To achieve such optimised grid, CD-Adapco (2017) suggests to model the cells in a way that the line connecting the centroids of two neighbouring cells would pass as orthogonal as possible to the face separating the cells and as closely as possible to its centroid. Critical items to be considered are the first cell height, the total prism layer height, and the number of layers. It is good manner to initially generate an automatic valid volume mesh and later refine it. An initial guess on the dimensions of the cells characterising the grid can be made referring to the main dimension (length) of the geometry analysed and successively remesh the initial dimensions of the cells and surfaces to improve the overall quality of the model. Directly connected to the first cell height is the choice of a value for the element y+. Such choice is arbitrary, however, specifications are needed on the first cell spacing and total number of layers in order to generate a mesh that is accurate enough, with special regards toward the near-wall regions. Once the first cell heights and the number of layers have been decided, the growth rate must also be checked and adjusted in order to eventually modify the concentration of cells in the direction orthogonal to the analysed geometry. The mesh generated will result the same all over the geometry, final refinements are therefore needed in order to consider the z-direction of the domain close to the waterline, in order to resolve wave heights, and along the deck, hull and transom surfaces.

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Unfortunately no universal rule exists when it comes to determining whether the total number of cells forming a mesh is good enough. As mentioned earlier in this section, rule of thumbs can be followed considering the characteristic dimension of the geometry analysed and derive from it the dimensions for the ﬁrst cell’s height. An other validation can be found when comparing the generated mesh with one created for similar purposes and geometries

4.2.6 Aerodynamic Resistance

The computational domain in which the skiff is analyzed presents two different phases. It is therefore necessary for completeness of investigation to evaluate the influence of different deck shapes on the total resistance encountered by the skiff when sailing. In these evaluations, the height of the freeboard and the geometry of the transom play major roles. Due to time limitations such properties have not been properly analyzed with iterative investigations. Bethwaite (2008) Higher Performance Sailing is instead taken as reference when shaping the transom. According to Bethwaite, "when wind flows away from a surface such as a vertical transom, the effect is like a filter pump; the core of dead air behind the transom is dragged downwind by the viscous drag of the surrounding moving air, the pressure decreases, and the pressure difference between the undiminished pressure on the windward face and the reduced pressure on the leeward face shows up as drag" (Bethwaite, 2008). An inward sloped transom would therefore allow air to smoothly reach the water level without generating sudden pressure differences. Additionally, the hull is shaped as a solid brick, hence with no open top, such that the wind will only hit the windward end and sides of the brick and gently tug the leeward faces backwards.

4.2.7 CFD Analysis Setup

Figure 4.4 shows a representation of the defined computational domain. The turbulence model is chosen to be a k − ω model with SST implementation in order to better capture the flow behaviour both near-wall both in free-stream. It has been chosen to initially consider an automatically generated mesh and later refine it. In order to accurately capture the viscous boundary layer a Prismatic Cell Mesher has been chosen together with a Trimmed Mesher, which provides a robust method of producing a high- quality grid, with a Medium Growth Rate, shown in Figure 4.6. All the size types have been set to the value absolute in order to be able to iteratively modify each one independently of the characteristic dimension of the geometry. Starting cell sizes have however been chosen to be equal to 500 times smaller compared to the length of the hull. An initial value of 10 was chosen for the Number of Layers. The first iterations however, showed that increasing such value to 14 provided a better quality of the grid without compromising the computational time.

Figure 4.6: Volume mesh growth

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The interface between the two fluids is the most sensitive portion of the domain and easiest to lead to numerical errors if not properly defined. A mesh refinement in such region is therefore needed and defined between 15 cm above and 10 cm below the waterline During the process, a value of y+ = 30 is assumed. This value expresses the transition between the buffer layer, where neither the linear law nor the log law are valid, and the logarithmic region. The choice for a high y+ wall treatment determines a logarithmic law for the near-wall boundary layer and therefore a more accurate prediction of the behaviour of the flow in such region. As a direct consequence, the chosen value eliminates numerical ventilation errors up to speeds of 12 kn, while for higher speed the errors are considerably reduced but not completely erased. The first cell height, together with the total thickness of the boundary layer and therefore the total number of cells generated, result different for each simulation. It is intuitive to under- stand that, since cell height and total thickness of the prism layer depend on the flow velocity and Reynolds number, their values will result different each time the ship speed is modified. Reference values for these elements are presented in Table 4.2 while details of the grids at the front and aft section can be appreciated in Figures 4.7a to 4.8b.

Table 4.2: Mesh properties vs ship speed

Speed [kn] First cell height [m] Total thickness prism layer [m] Number of cells

3 0.0006 0.038 4701421 5 0.00038 0.033 4704362 6 0.0003 0.033 4707762 7 0.00028 0.031 4734721 9 0.00022 0.031 4714780 12 0.00015 0.028 4670987 15 0.0001 0.027 4572475

Finally, an implicit unsteady solver is chosen with a time step of 0.01 seconds over a total time span of 10 seconds. The solver is needed in order to assure the convergence of the computations. It has been noticed that for the chosen time span the solutions can be assumed stable, oscillating around a constant mean value with relatively small range. Therefore a longer evaluation time, as was initially set, resulted not needed; moreover the computational time deriving from that would drastically increase.

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(a) Mesh detail at bow for 6 kn

(b) Mesh detail at bow for 12 kn

Figure 4.7: Mesh detail for the bow in the CFD-simulations

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(a) Mesh detail at aft for 6 kn

(b) Mesh detail at aft for 12 kn

Figure 4.8: Mesh detail for the aft in the CFD-simulations

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4.3 Finite Element Method (FEM)

The structural work within the project has a wide scope. It concerns the choice of construction materials, finite element analysis, structural stiffening, construction method and more. The process of reaching a final result is tedious, and depends on many variables. The following sections describe the process of the structural work from the beginning to the current state.

4.3.1 Prestudy

Initially, a prestudy was performed. The study was divided into three parts where every part was needed to produce a final hull. Firstly, material options for the hull structure was studied with the aim of finding suitable materials for the hull plating, hull stiffening structure and deck. Secondly, studies were performed with the intent of finding a suitable methodology to assess the loads acting on the hull structure. These loads include the loads from the rig as well as hydrodynamic loads acting on the hull. Lastly, studies on methodologies to assess the material and load interaction in the hull structure using FEM-software were conducted.

4.3.2 Hull Components

In the prestudy, the hull structure was divided into three components: hull plating, internal stiffening structure and deck plating. The reason for the division is to identify specific characteristics for each component and thereby be able to adapt the material choice and design for each component according to their characteristics, while still considering how the components will interact with each other and how the material will affect this interaction. The material choice and the design of all hull components is significantly limited in the 1001VELAcup regulations that states: "the hull and racks should be made of wood or materials of vegetable and/or animal origin, expressed in weight, not lower than 70 %". This rule and its effects on the design and construction process will be covered in more detail further on in the report.

4.3.2.1 Hull Plating The hull plating is the main structural component of the skiff. It makes up the closed volume that provides buoyancy, as well as the main contribution of stiffness to the hull girder. This is true especially in locations where the curvature of the hull is high such as the bow. The stiffness of the hull girder is further increased by adding an internal stiffening structure. Common practice when designing a lightweight hull structure for small sailing craft is to construct the hull plating using sandwich laminates.

4.3.2.2 Internal Stiffening Structure The internal structures of the hull, consisting of transverse bulkheads and longitudinal stringers, contributes to the overall hull stiffness. The bulkheads and stringers are also the components that transfer the local loads from rigging and mast through the chain plates and mast foot to the hull. Using a sandwich structure similar to the one used in the hull plating is possible, though another option to consider is to make use of ordinary marine plywood for the stiffening structures. A complete FE-analysis comparing weight and strength of both options must be performed to make a conclusive decision, although this is not part of the project scope.

4.3.2.3 Deck The deck serves as the closing surface of the top part of the hull as well as contributing to overall hull stiﬀness. It is also the part of the boat where components such as deck hardware, mast, forestay, shrouds and mainsheet are attached to the hull. The material in the deck will therefore

29 4 Theory have to be able to withstand large local point loads at the attachment points of rigging elements, as well as the weight of the sailors during operation and the global bending moment. Making use of the sandwich structure in the deck to achieve low weight and high bending stiﬀness is desired. However to deal with the local point loads from the rigging, a sandwich structure in the deck would possibly require reinforcement of the core in these areas, to be able to handle the out of plane loading. FE-analysis is required to determine the design and location of these reinforcements.

4.3.3 Centreboard and Rudder

The appendages, centreboard and rudder, are structurally designed with the same design philosophy as the hull, which is to create a strong but light structure. The difference is that there are no restrictions in construction materials for the centreboard and rudder, as opposed to the hull’s limit of 70 % organic origin. This rule opens up new alternatives regarding the choice of material. Since the structures of the appendages are supposed to be light and strong, a sandwich structure may be favourable in this case as well. A material stronger than flax, such as a composite laminate made from carbon or glass fibre, will most likely be used to achieve a low weight and withstand the relatively high local loads. The rudder is mainly affected by the hydrodynamic forces when travelling through the water, whereas the centreboard needs to be dimensioned for the worst load case which is when the crew is standing on the centreboard tip in order to tilt the skiff upright after it has capsized. This load case will naturally cause a large bending moment at the base of the centreboard.

4.3.4 The Sandwich Structure

Early in the project, it was apparent that the final choice of construction material would stand between marine plywood in a cold moulded configuration, and a sandwich structure using organic constituents. Using plywood has the benefit of low cost and relatively easy building process with a rigid cross-section suitable for attaching hardware relatively easy. It will however make the hull heavier than necessary. A sandwich laminate using a lightweight core on the other hand has the benefit of low total weight together with high flexibility regarding the hull shape. The main reason for using a sandwich laminate is the ability to adapt the laminate layup according to the stresses in a specific load case, as opposed to using an isotropic material for example. Based on these arguments, as well as the information found in the prestudy, it is concluded that a sandwich structure would be the most beneficial, and also the most interesting to build. In this section the procedure of choosing material for the core and the skins of the sandwich will be described. The sandwich material consists of a weaker core covered by stiffer outer skins on both sides of the core. The skins act as the load carrying element for global bending and axial loads while the core is supposed to carry the major part of shearing loads as well as keeping the two skins separated. The distance between the skins is a key element of a sandwich structure since the distance increases the moment of inertia and strength of the sandwich section. The principle is similar to that of a common I-beam. The benefit of the sandwich structure is, as mentioned previously, its low weight to stiffness ratio in the bending load configuration. The main drawback of the sandwich structure is its limited ability to carry out of plane loads, especially compressive out of plane loads. Since the sandwich structure consists of different materials in the skins and core, alternatives for both of these had to be investigated.

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Figure 4.9: Sandwich constituents

The R3 class rules limits the use of classical sandwich materials such as glass and carbon ﬁbre for the skins and divinycell foam or (most) honeycombs, as the material for the hull and deck. This made it necessary to look for organic materials that are also readily available for purchase.

4.3.4.1 Sandwich Core After researching alternatives for an organic material to be used in the core of the sandwich structure three feasible options were found. The options were the following: • Balsa wood, • Cork, and • Bio-based PLA (Polylactic acid) honeycomb. The organic honeycomb made from bio-based PLA, could be discarded after researching the possibility of finding a supplier of this kind of material. Only one company, Econcore, that produces the PLA based honeycomb could be found. However upon contacting the company, it was found that they had temporarily stopped their production but that the material could be produced on demand. The cost of ordering this material produced on demand was considered too high for this project. There would also be a risk that the sheets of honeycomb would be so stiff that they would affect the design of the hull shape. Still the PLA based honeycomb is a material with interesting properties that could be a viable alternative for future projects if the material becomes more available. Comparing the two remaining alternatives, the balsa wood has slightly better mechanical properties than the cork, especially in compression. Another important property of the core material is its ability to absorb the epoxy used when laminating the skins of the sandwich onto the core. To keep the weight of the material as low as possible, it is desired to keep epoxy absorption in the core to a minimum. According to (Castegnaro et al., 2017) epoxy absorption is higher for balsa wood than for cork. However this is only true if the balsa wood is placed with the grains perpendicular to the laminates, so called end-grain. By placing the balsa grains parallel to the laminates of the sandwich, it is assumed that epoxy absorption can be reduced drastically, since the epoxy will not be applied to the end-grain surface in this configuration. Thus both lower epoxy absorption and better mechanical performance of the balsa wood in the longitudinal direction can be utilised.

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The main drawback of placing the grains parallel to the skins of the sandwich is the loss of ability of the sandwich to carry concentrated out of plane loads, e.g. concentrated rig loads or crew stepping on the deck. This however mainly concerns the deck structure. It was reasoned that, if necessary, the grains could be placed perpendicular on the deck or in certain areas of the deck and keep the grains parallel to the longship direction in the rest of the hull. This idea was later discarded because no supplier of end grain balsa could be found in Europe. To determine whether the grains should be placed parallel or perpendicular on the deck, further analysis of loads and strength would be required through FE-simulations. Through this reasoning it was decided that the core material of the sandwich would be balsa wood. The properties of the balsa wood used in calculations are presented in Table 4.3 (Newaz, Mayeed, & Rasul, 2016)

Table 4.3: Balsa wood properties

Elastic [MPa] EL ET EV GLT GTV GVL νLT νTV νVL 688 32.6 32.6 72.8 12.5 72.8 0.007 0.4797 0.007

Strength [MPa] SL ST SV SLT STV SVL Tension 10.12 0.82 0.82 1.35 0.35 1.35 Compression 0.71 0.71 0.71 - - -

Density [kg/m3] 150

Where L denotes the property of the material in the fibre direction, T denotes the property of the material across the fibres in the transverse direction and V the property of the material across the fibres in the vertical direction. Combining these notations (LT, TV and VL) will give the properties of the material in all three planes. These notations will be applied to describe the properties of all non-isotropic materials in this project i.e flax epoxy laminate and balsa wood. For compatibility with FE-software used in this project stress is denoted by S in this project.

4.3.4.2 Sandwich Skin When studying previous boats built with sandwich structures in the 1001VELAcup it was found that a common choice of material for the skins was a laminate made of flax fibre weave and epoxy. This material seemed interesting, and some time was spent finding literature with data and material characteristics. It was found that three main organic fibres were the flax, jute and hemp fibres, where the flax fibres seemed to have the best mechanical properties for the current application (Castegnaro et al., 2017). In order to limit the work spent on finding alternative fibres, it was quickly decided that flax would be the fibre component of the sandwich laminate. One major contribution to this decision was the fact that material testing of the skin laminate would have to be made, a practical exercise that would be of interest for the whole project group. However, shortly after choosing material another paper written in connection to the 1001VELAcup containing all the material data needed for FEM simulations was found (Pitarresi, Tumino, & Mancuso, 2015). This data was also given for different construction methods, one of which was intended to be used for the construction of the boat covered in this report. Therefore, the need to do material testing disappeared and the FEM simulations could commence immediately. In Table 4.4 the properties of a flax epoxy laminate, manufactured in a vacuum bagging process, are presented. The properties are obtained by contacting Bcomp Ltd., the manufacturer of the flax fibre used in this project.

4.3.4.3 Sandwich Epoxy The epoxy chosen to be used for the lamination is the FormuLITE 2501A resin, combined with FormuLITE 2002B hardener. According to the manufacturer, these are high-performance

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Table 4.4: Flax/epoxy laminate properties

Elastic [MPa] EL ET EV GLT GTV GVL νLT νTV νVL 31981 3239 3239 2552 - 2552 0.35 - 0.35

Strength [MPa] SL ST SV SLT STV SVL Tension 383 22 22 29 - 29 Compression ------

Density [kg/m3] 710 Area density [g/m2] 150 Thickness [mm] 0.21 Fibre ratio 0.51 bio-based products made from high amounts of renewable resources including Cashew Nutshell Liquid (Cardolite, 2017). This speciﬁc property of the epoxy is of special interest to the project due to the 1001VELAcup rules that demand a high level of bio-based construction components.

4.3.5 FEM Analysis Set Up

The finite element analysis (FEA) was carried out in the FE-software Abaqus CAE. The geometry to be analysed, i.e. the hull surfaces and stiffener geometry, was imported into the software as a 2D shell structure. Since the hull structure can be considered to consist of thin plates, plane stress can be assumed which allows for the FE-analysis to be performed on 2D-shells. After importing the geometry, it was assigned material properties, based on the conclusions drawn in Section 4.3.4. These properties, specifically the composite layup and balsa fibre directions, were varied systematically to evaluate the most efficient construction in terms of strength versus weight, with the goal of reaching the lightest possible structure while still being able to handle the applied loads. A mesh is then generated, shown in Figure 4.10, for the structure, where the goal is to minimise the number of distorted elements, with sufficient resolution to obtain reasonable results. The mesh element geometry is of the quad-dominated type with a nominal element size of 30 millimetres. This size was chosen based on the shape of the internal structure, in order to cover smaller details such as stiffener beams.

4.3.5.1 Element Type A question raised before FE-simulations were performed was what type of element that should be used in the simulations. The simulations can be performed with either shell or solid elements, where the latter requires significantly more computation time and is significantly more complex to model since it requires the skins and the core to be modelled separately and then assembled. This also makes varying the number of plies in the layup very tedious. However the concern was that the less complex shell elements would not capture shear stresses in the sandwich structure in a sufficient way. To determine the type of element to be used in the FE-simulation of the hull structure, tests on simple plate geometries were performed. The shear stresses in the core of the sandwich were compared for S4R shell elements and SC8R solid elements. According to (ABAQUS/Explicit, 2017) both of these are viable choices when modelling a sandwich structure. In a sandwich structure, the core is supposed to carry the major part of the shearing load which is why the core is chosen for comparison between shear stresses for the different element types in this case. In this procedure, a plate with dimensions 1000×1000 mm is modelled once with shell elements

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Figure 4.10: The meshing of the hull surface and once with solid elements. The same composite layup, a sandwich structure with skins made of ﬂax/epoxy laminate and a core made of balsa wood, is assigned to both plates.

Laminate plate layup :[−45 0 0 90 c010]s

In this layup, c010 denotes the balsa core of thickness 10 mm with the ﬁbres aligned to the 0-direction. The boundary condition simply supported along two edges and a uniform pressure of p0 = 0.001 MPa, are applied in both models. Finally, the models are meshed with quadratic elements with a size of approximately 30 × 30 mm. In the solid model, 3 elements are stacked through the thickness. One element each for the skins and one element for the core. Below, the results of the computations can be seen in Figure 4.11a for the S4R shell elements and Figure 4.11b for the S8CR solid elements. Comparing the plots of the shear stresses in the ﬁgures, it can be seen that similar stress distributions are achieved. A minor modelling mistake caused the coordinate system in one of the models to be reversed, why one the plots is shown upside down. As for the magnitudes of the shear stress, the following results are obtained for the shell elements and the solid elements respectively.

S4R: SLT,max = 0.028 MPa SLT,min = −0.028 MPa

S8CR: SLT,max = 0.020 MPa SLT,min = −0.022 MPa

According to these results, using the shell elements will give larger shear stresses in the core whilst the stress distribution will be roughly the same. It was therefore decided that S4R elements are to be applied in the FE-simulations of the hull structure. The S4R elements will give somewhat conservative results whilst signiﬁcantly reducing modelling complexity and computation time, therefore it is considered to be an economic and reliable option.

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(a) Core with S4R (b) Core with SC8R

Figure 4.11: Shear stresses in core

4.3.5.2 Load Cases To evaluate the strength of the hull structure, one needs to know the loads acting upon it. In this project the loads are divided into two main groups: hydrostatic and hydrodynamic pressure acting on the hull, and forces from the rig and its attachments to the deck. The total hydrostatic and hydrodynamic pressure load acting on the hull below the waterline is determined from the pressure distribution obtained from the flat water CFD simulation of the hull at its maximum speed as predicted by VPP simulations Section 4.4. Since the pressure distribution from the CFD simulations does not take any dynamic effects such as slamming into account, the pressure calculated in the CFD simulations is multiplied with a dynamic factor calculated from the ISO-standards for small craft design (ISO, 2015). In this case the dynamic factor for multihull sailing craft was selected since the multihull is sailed on even keel in a similar manner as the skiff. The dynamic factor is calculated using Equation (4.9).

3.086L2 k = WL where 1.2 ≤ k ≤ 2.4 (4.9) DYN ∆0.66 DYN

With numerical values, length of waterline LWL = 4.6 m and estimated displacement of ∆ = 250 kg in Equation (4.9) the dynamic factor is calculated to kDYN = 1.7. The pressure obtained from ﬂat water CFD simulations is pfw = 0.0015 MPa, which is a representative mean value of the pressure distribution on the hull. Equation (4.10) is used to calculate the dynamic pressure acting on the hull.

pDYN = kDYN · pfw (4.10)

The final hull pressure, including dynamic factors, is calculated to be pDYN = 0.00255 MPa. This should be interpreted as the sum of the hydrostatic and hydrodynamic pressures given in the CFD simulations, multiplied with the dynamic coefficient kDYN . This means that the final result includes the hydrostatic pressure and the hydrodynamic pressure, with the dynamic coefficient also taken into account. This pressure is applied to the entire wetted surface of the hull in the FE simulations. This can be considered as a conservative assumption since it can be reasoned that hydrodynamic pressure from slamming and waves will not be acting on the entire wetted surface at a given instance. On the other hand, from slamming, the craft could take air at a wave crest, completely leaving the water surface, and thereafter land flat on the water surface again. In that case, the hydrodynamic pressure would in fact act on the entire wetted surface. Without further investigations, it is impossible to evaluate if such an event may or may not occur. It was therefore decided to let the hydrodynamic pressure act on the entire wetted surface and thereby, at least to some extent, design against such an event. When performing FE-simulations, two load cases were considered. The first being the case

35 4 Theory when the crew is hiking in the trapeze as in Figure 4.12b, and the second when the crew is positioned on the rack without trapeze. The two load cases will hereafter be referred to as "crew in trapeze" and "crew on racks" respectively. In both cases, the same hydrodynamic pressure, as calculated in Equation (4.10), is acting on the hull bottom. All forces from the sails, the rig and crew need to be transferred to the hull structure. The internal stiffening structure and hull plating need to be designed with this in mind. Rigging loads are calculated by assuming that the rigging forces and moments are in internal equilibrium at all times with one exception: the righting moment from the crew, that is countered by heeling moment that derives from the wind force in the sails. To determine the loads acting on the hull from the rig, expertise from external resources is utilised. The mast manufacturer and supplier of rigging in this project, Seldén Mast, provided estimated loads from the rig designs that were sent to them. The results from Seldén Mast rig load calculations were then balanced to fulfil the above assumption concerning force equilibrium, still with the above mentioned exception. To accomplish this equilibrium, further simplifications are made. The first being that all forces engage at the same z-coordinate, that is all forces engage on a flat deck. In reality, the deck will have a slight camber giving slightly different vertical coordinates (z-coordinate) to the rigging loads. In the load case crew on racks, reaction forces at the rack supports are assumed to be evenly distributed between all four supports. To properly evaluate the reaction forces at the racks, the position of the crew on the racks and more detailed specification on the rack design need to be known, see Section 5.3.2. It was decided that evenly distributed reaction forces would be a sufficient approximation at the moment and that a more careful evaluation of the hull and rack interaction at the supports would take place when more was known about the racks. The two load cases are tabulated in Tables 4.5 and 4.6. Table 4.5: Load case crew on racks

Crew on racks Coordinate [m] Force [N] Moment [Nm] Component Point x y z Fx Fy Fz Mx My Mz Forestay 1.70 0 0 416 -183 -1491 0 -2534 -311 Shrouds -0.60 -1.05 0 -205 -457 -2577 2705 1546 397 Rigging Mast step 0 0 0 -211 608 4441 0 0 0 Main sheet -2.65 0 0 0 32 -373 0 989 -86 Fore 0 0 0 0 0 -1288 0 0 0 Rack inner supports Aft -2.65 0 0 0 0 -1288 0 3414 0 Fore 0 -0.60 0 0 0 1288 -773 0 0 Rack outer supports Aft -2.65 -0.60 0 0 0 1288 -773 -3414 0 P 0 0 0 1159 1 0

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Table 4.6: Load case crew in trapeze

Crew in trapeze Coordinate [m] Force [N] Moment [Nm] Component Point x y z Fx Fy Fz Mx My Mz Forestay 1.70 0 0 819 -229 -2794 0 -4750 -389 Shrouds -0.60 -1.05 0 -10 -19 -91 96 55 22 Rigging Mast step 0 0 0 -146 455 5511 0 0 0 Main sheet -2.65 0 0 -467 193 -1065 0 2823 -511 Trapeze -1.20 -2.05 0 -197 -400 -1560 3198 1872 883 P -1 0 1 3294 0 5

One should note that in the trapeze load case, see Table 4.6, the weight of the sailors is carried by the trapeze itself which allows for the racks and the shrouds to be unloaded. This is the ideal case. In reality, the racks will carry some of the crew’s weight since the crew needs to transfer some of their body weight to the racks to be able to keep their balance in the trapeze. In these calculations, this is neglected and the racks are assumed to be unloaded in the trapeze load case. As for the crew on racks load case, see Table 4.5, the opposite is true. The trapeze is unloaded because the crew is disengaged from it and the racks and shrouds will have to carry the weight of the crew. Another point to note is that, in FE-simulations and other calculations, force components of the trapeze load in Table 4.6 is to be added to the mast step force components, since the trapeze is attached directly to the mast the load from the trapeze has to be countered by the mast step. As an example the z-component of the mast step should be: Fz,mast step = 5511 + 1560 = 7071 N, in the FE-simulations. P The sum of moments around the x-axis, Mx makes up the total righting moment, RM. From Table 4.5 and 4.6 this is found as:

For the crew on racks load case: RMR = 1159 Nm

And for the crew in trapeze loadcase : RMT = 3294 Nm

Because the righting moment from the hull is negligible compared to the righting moment from the crew due to the low water plane area moment of inertia and the small heeling angles the craft operates with, it can be approximated with Equation (4.11).

RMg = mcy cos θ (4.11)

In Equation (4.11), mc is the mass of the crew, y is lever arm from the centre line to the centre of mass of the crew and θ is the angle from the water surface which the crew is hiking with. ◦ Setting these to mc = 150 kg, θ = 0 and yR = 1.05 m and yT = 2.05 m for the racks and trapeze loadcase respectively the following is obtained with Equation (4.11).

For the crew in racks load case: RMg R = 1562 Nm

For the crew in trapeze load case: RMg T = 3050 Nm

It can be seen that this approximation fairs quite well with the righting moments calculated

37 4 Theory in Table 4.5 and 4.6. This indicates that the loads in the load cases are a suﬃciently accurate estimation of reality. It was decided to proceed with loads the crew in rack and crew in trapeze load cases in the FE-simulations.

4.3.5.3 Boundary Conditions If a boundary condition is introduced at a point in an FE-model subjected to external loading, a reaction force is also introduced at that same point to fulfil Newtons 3rd law. In the case of the skiff in this project, introducing a boundary condition on any point, edge or surface means that a reaction force is also introduced at that location. This due to the fact that the load cases calculated in Table 4.5 and 4.6 are not in equilibrium since the righting moment is not countered by any heeling moment and the hydrostatic pressure is not countered by any reaction force. If for example the transom was to be fixed and the trapeze load case to be applied on the model, a reaction force and reaction moment would engage at the transom surface to counter the righting moment and hydrostatic pressure. In reality, no reaction force or reaction moment engages at the transom surface during operation therefore such a model would be a poor approximation. Similarly, if any other geometry in the model is fixed or simply supported the same argument can be reasoned. To get around this, inertia relief is introduced. Inertia relief is used to balance external loading into equilibrium by applying rigid body accelerations to the model (ABAQUS/Explicit, 2017). This means that righting moment and hydrostatic pressure will be countered by rigid body accelerations instead of reaction forces and reaction moments. Inertia relief gives a better approximation than introducing ordinary boundary conditions, thus it was decided that inertia relief would be applied in the model.

4.3.5.4 Post Processing Due to the numerous design options available, a systematic way of evaluating each option is needed. A well designed hull structure requires sufficient strength to withstand both load cases, sufficient stiffness to keep deflections low during operation and a low mass. Therefore key parameters to be evaluated for each design iteration are stress magnitude and direction, deflections and the mass of the model. In the performed FE-simulations, perfect bonding between skin/core interface and between the interfaces in the skin laminate is assumed. The deflection is thereby constant through the thickness of the sandwich structure. In contrast to the stress, that varies with the fibre directions through the thickness of the layers (Agarwal, Broutman, & Chandrashekhara, n.d.). Because of the previous decision to model with shell elements, out-of-plane stress cannot be captured by the solution. This means that no method exists to evaluate failure modes such as delamination. A way of circumventing this problem is to create local solid models in areas of the global model where large out of plane shearing is expected and from these local models evaluate the risk of delamination. However, even though the ambition to create such models existed from the beginning of the project, the time required to finalise the global model proved this ambition to fall short.

4.4 Velocity Prediction Program (VPP)

A Velocity Prediction Program (VPP) is used to determine the performance of sailing boats by using the properties of hull, rig, sails, and appendages. It calculates the boat speed for different wind speeds and heading angles by solving force and momentum equations. The VPP used in this project, originally created by Professor Kai Graf at the University of Applied Sciences in Kiel, is modified to model the skiff’s properties.

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4.4.1 Input and output

The input to the VPP is specified in an input file and defines the main properties of the skiff. The input is divided into three different parts, the aerodynamic properties, the hydrodynamic properties, and the geometric properties. The aerodynamic properties are defined as sail coefficients, used to determine the forces from the sails. The hydrodynamic properties are the resistance curve of the hull for different speeds and the lift and drag curves for the centreboard and rudder. The geometric properties are the main particulars of the hull, sails, and appendages. The input file also specifies which wind speeds and which wind angles that should be considered by the VPP.

The VPP calculates the boat speed, leeway angle, the lever arm of the crew (TCGcrew), and necessary depowering of the sails. The results are presented in a polar plot with the radius as speed and the angle as the true wind angle. One curve per considered wind speed is plotted. The calculated leeway angles, TCGcrew, and depowering of sails are presented in a table for all considered wind speed and wind angles.

4.4.2 Solved equations

There are three equations considered in the VPP, a force equilibrium in the x-direction, which is defined as the direction of motion. A force equilibrium in the y- direction, which is defined as the horizontal direction perpendicular to the x- axis, the z-axis is defined upwards. The third equation is a moment equilibrium around the x-axis. The equations are shown in Equation (4.12). The forces are assumed to be in equilibrium which means that there are no accelerations of the hull in the considered directions. It is assumed that the heeling angle can be set to zero, which will result in the best performance of the skiff.

Fx = Fx,aero − Fx,hydro = 0

Fy = Fy,aero − Fy,hydro = 0 (4.12)

Mx = Fy,aero · (zCE + zCLR) − mcrew · g · TCGcrew = 0

In Equation (4.12), Fx,aero and Fy,aero are the resultant forces from the sails in the x and y direction respectively. These forces depends on the apparent wind speed (AWS), apparent wind angle (AWA), the leeway angle (α), and the lift and drag coeﬃcients of the sails. The lift and drag coeﬃcients depends on the type of sails and the AWA. The methods used to calculate the forces from the sails are are explained further in Section 4.4.4.

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퐹푥,푎푒푟표 퐹푦,푎푒푟표

푧퐶퐸

퐹푥,ℎ푦푑푟표 푧퐶퐿푅 푇퐶퐺푐푟푒푤 퐹푦,ℎ푦푑푟표

푚푐푟푒푤 · 푔 (a) Driving and resistance forces (b) Heeling and righting forces

Figure 4.12: Simpliﬁcation of forces acting on the skiﬀ considered in the VPP

Figure 4.12a and 4.12b are simpliﬁed as the leeway angle is not taken into account, all lateral forces in both Figure 4.12a and 4.12b therefore have a force component perpendicular to the plane of the paper.

The forces Fx,hydro and Fy,hydro are the hydrodynamic fores on the skiff. Fx,hydro consists of three parts, the resistance of the hull, the resistance of the centreboard and the resistance of the rudder. The resistance of the hull depends on the speed and the shape of the hull, how this force is obtained is explained in Section 4.2. The resistance of the centreboard and rudder depends on the speed of the hull, the leeway angle, the area and aspect ratio, and the lift and drag coefficients of the centreboard and rudder respectively. Since there is no speed or acceleration in the y-direction, the forces in this direction will be caused by the speed of the skiff and the leeway angle. Fy,hydro will have three components, caused by the hull, the centreboard, and the rudder. The force due to the hull will be small compared to the other two. The forces on the centreboard and rudder are explained more thoroughly in Section 4.4.3.

The moment equation in Equation (4.12) is calculated in the vertical centre of effort of the appendages, (zCLR). Since there is no force from the hull in the transverse direction, the heeling moment will only be caused by the side force from the sails, and the righting moment will be created by the crew hiking in the trapezes. zCE, is the vertical centre of effort of the sails, zCLR is the vertical centre of effort of the appendages, mcrew is the mass of the crew, g is the earth gravitational constant and TCGcrew is the transverse centre of gravity of the crew. If the heeling moment is larger than the maximum righting moment created by the crew, the VPP will start to depower the sails. Depowering of the sails can be done in two ways, by twisting the sails and by flattening the sails. The VPP will start depowering by twisting the

40 4 Theory sails. Twisting of the sails is implemented in the VPP as a factor that decreases the lift and lowers the centre of effort. The twisting factor can lower the centre of effort by maximum 25%. If the sails need to be depowered more, the VPP will start flattening the sails. Flattening of the sails is implemented as a factor that effects the lift coefficients of the sails. It can vary between 1, where there is no influence on the lift, and 0, where there is no lift at all, This also decreases the induced drag according to Equation (4.17).

4.4.3 Centreboard and Rudder

The purpose of the centreboard is to create a counter force to the side force generated by the sails. This side force is created by the speed of the hull, creating an angle of attack for the ﬂow over the centreboard. The rudder’s main purpose is to create a moment that is used to turn the boat when steering. The rudder also supports some of the side force and is thereby unloading the centreboard. The forces on a foil, like a rudder or centreboard, are governed by Equations (4.13).

1 2 FL = V ρACL,3D 2 (4.13) 1 F = V 2ρA(C + C ) D 2 D,2D DI

The lift, FL and drag, FD, depend on the speed of the foil, V , the planform area, A, density of the water, ρ, and the coeﬃcients CL,3D, CD,2D, and CDI . These coeﬃcients depend on several factors, such as Reynolds number, wing section, and angle of attack.

4.4.3.1 Planform When designing the planform for a centreboard and a rudder, the aspect ratio (AR), is one of the most important parameters. The lift coefficient, CL,3D, and the induced drag coefficient, CDI , are both affected by the aspect ratio according to Equation (4.16) and (4.17). The aspect ratio is the ratio between the draft, TK , and the mean chord, C¯, and can be written as

T T 2 AR = K = K (4.14) C¯ A

Where TK is the draft of the centreboard or rudder and C¯ is the mean chord.

C + C C¯ = 1 2 (4.15) 2

When AR is increased the lift coeﬃcient, CL,3D, is increased according to Equation (4.16), where CL,2D,1◦ is the two dimensional lift coeﬃcient for the wing section for a angle of attack of one degree, and α is the leeway angle, approximately 2◦ to 3◦ in this case.

C ◦ C = L,2D,1 · α (4.16) L,3D 2 1 + AR

The drag coeﬃcient, CDI , is decreased with higher AR, as shown in Equation (4.17), but also increased with higher lift coeﬃcient.

C 2 C = L,3D (4.17) DI π · AR

41 4 Theory

Figure 4.13: Description of planform

To maximise the performance, the CL,3D should be as large as possible and the CDI should be as low as possible. In practice, this means that the draft of the centreboard should be as high as possible, but as mentioned in Section 4.3.3, it is restricted due to structural reasons. The tip shape of the centreboard and the rudder is not as important as the aspect ratio, but it is still something that is investigated. A v-shaped tip is the best shape overall, in comparison with a round, square and bulb tip (Larsson et al., 2014). By having a v-shaped tip, the AR will be lowered by 19 %. Although the v-shaped tip has an AR that is 19% lower, the beneﬁts of the shape are bigger than the disadvantages (Larsson et al., 2014).

4.4.3.2 Wing Profiles It is important to have as low profile drag as possible. One way to accomplish this, is to keep the flow laminar around the profile for as long as possible. This means that the transition from laminar to turbulent flow must be as far back as possible. By having the pressure minimum far aft, the flow can be accelerated over a longer distance and the transition from laminar to turbulent flow can be delayed. The location of the pressure minimum is governed by the location of the maximum thickness, because of this, a wing section with the location of maximum thickness far aft would be beneficial. The main difference between the NACA four series which have a quite simple geometry, and the six series which has a more complex geometry is that the six series profiles are designed to have laminar flow along the wing section. Larsson et al. (2014) states that the NACA six series is a good choice as the wing profile for a centreboard. It is typical for the NACA 6 series to have low profile drag and more or less constant drag for low angles of attack, but at a certain angle of attack, the drag increases quickly to a higher level, from which it increases more moderate with the angle of attack. Such a profile are said to have a drag bucket. This due to the shape of the graph created when plotting drag as a function of angle of attack, see Figure 4.14. Comparing the NACA 4 digit series profile with

42 4 Theory the 6 series proﬁles, both the 6 series proﬁles have a bucket shape while the 4 digit series have a does not have that.

V · L Re = (4.18) ν The Reynolds number effects the lift and drag coefficients of a foil. The Reynolds number is calculated according to Equation (4.18) and for a foil like a centreboard or rudder on a skiff designed for speeds around 3.5m/s the Reynolds number will be between 5 · 105 and 106. In this range, the changes in properties can be considered small. The graphs presented in Figure 4.14, 4.15, and 4.16 are calculated for a Reynolds number of 8 · 105 using XFOIL 6.99.

10-3 Profile Drag vs angle of attack 10 NACA 63012 9.5 NACA 65012 NACA 0012 9

8.5 D

7.5

Drag coefficient C 6.5

5.5

5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Angle of attack [°]

Figure 4.14: Profile drag for different profiles

In Figure 4.14, all three profiles have a maximum thickness of 12 % of the cord length. The effect of location of maximum thickness is important, and is visualised in Figure 4.14. Studying the blue and red line, where the the red line has the location of maximum thickness more aft, the resistance at small angles of attack is lower but the drag bucket is slightly more narrow and steep than for the blue line. The location of maximum thickness has effect on the shape of the drag bucket, although the effect of changes in thickness are more significant than the effect of location. A large thickness will cause a wider but but more shallow bucket than a thinner profile, which will have a more narrow but deeper drag bucket, see Figure 4.15. A location of maximum thickness more aft will cause a slight decrease in resistance for small angles of attack, although the bucket shape will be more extreme so the drag at large angles of attack will be larger than for a section with maximum thickness located more forward.

43 4 Theory

10-3 Profile Drag vs angle of attack 10 NACA 65018 9.5 NACA 65012 NACA 65010 9

8.5 D

7.5

Drag coefficient C 6.5

5.5

5 0 1 2 3 4 5 6 Angle of attack [°]

Figure 4.15: Proﬁle drag for diﬀerent thicknesses

The purpose of the centreboard and rudder is to generate lift. The lift coefficients of symmetric NACA profiles do not differ much from each other and the connection between lift and angle of attack is highly linear for small angles of attack. The proportionality coefficient, CL,2D,1◦ , can therefore be approximated as the two dimensional lift coefficient for one degree, and can approximately be stated as 0.1 for symmetric NACA profiles. Figure 4.16 shows that CL,2D,1◦ should be between 0.08 and 0.1 for all five wing sections, and that the relationship between lift coefficient and angle of attack is linear. This means that for the design of the centreboard and rudder, the lift will be approximately equal independent of the wing section while the drag of the appendages to a large extent can be optimised by choosing the right wing section.

Lift vs angle of attack 0.6 NACA 63009 NACA 65010 0.5 NACA 63012 NACA 65012 NACA 0012

L 0.4

0.3

Lift coefficient C 0.2

0.1

0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Angle of attack [°]

Figure 4.16: Lift for diﬀerent proﬁles

44 4 Theory

4.4.4 Sail Set Up

(Larsson et al., 2014), the sails can be considered wings in the same way as as the appendages, but with very low thickness. The presence of a jib in front of the main sail eﬀects the ﬂow over the main sail and thus also the force on the sails. With the presence of a jib, the main sail will be unloaded, compared to a case with no jib. The opposite is true for the jib. With the presence of a mainsail, the jib will be more loaded than without a main sail. Overall, the force from the sails are much larger with the presence of a jib.

4.4.4.1 Sail coeﬃcients The lift, drag, and induced drag of the sails are governed by Equation (4.13), the same equations as the centreboard and the rudder. Using the coeﬃcients governed by Equations (4.16) and (4.17). However, the speed term V, should be the wind speed that the sails encounter, the apparent wind speed (AWS). The AWS is calculated according to Equation (4.19).

q AW S = (TWS · cos (TWA) + V · cos (α))2 + (TWS · sin (TWA) − V · sin (α))2 TWS · sin TWA − V · sin (α) (4.19) AW A = arctan TWS · cos (TWA)V · cos (α)

The forces from a sail can, as mentioned earlier, be calculated using classical wing theory, according to Equation (4.13). The obtained forces, FL and FD, are orthogonal where FL is perpendicular and FD is parallel to the wind acting on the sail, this is shown in Figure 4.17 where the x axis is the longitudinal direction of the skiﬀ and the y axis is the transverse direction.

퐹푦,퐿 퐴푊퐴 + 훼

퐹퐿 푥 푦 퐴푊퐴 + 훼 퐹푥,퐿

퐹퐷 퐴푊퐴 + 훼 퐹푥,퐷 퐹푦,퐷

Figure 4.17: Forces acting on a sail

The resulting forces of FL and FD, in the x and y direction, will give Fx,aero and Fyaero, for each sail in Equation (4.12), are obtained using the calculated FL, FD, and using the apparent wind angle (AWA), calculated in Equation (4.19), and leeway angle α, according to Equation (4.20).

Fx,aero = Fx,L − Fx,D = FL · sin (AW A + α) − FD · cos (AW A + α) (4.20) Fy,aero = Fy,L − Fy,D = FL · cos (AW A + α) − FD · sin (AW A + α)

45 4 Theory

The coefficients used for force calculations of the sails in this project are the coefficients used by the Offshore Racing Congress (2016) (ORC). These sail coefficients are used in the ORC VPP software to calculate handicaps for racing yachts. The ORC uses different sets of coefficients depending on the type of sail. The sail coefficients depend only on the angle of attack of the sails. The sail coefficient used in this project are displayed in Figure 4.18a and 4.18b.

C vs C vs L D 1.6 1.4 Main sail Main sail 1.4 Jib 1.2 Jib

1.2 1 D0

L 1

0.8 0.8

0.6 0.6

Lift coefficient C 0.4 Drag coefficient C 0.4 0.2

0.2 0

-0.2 0 0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 120 140 160 180 Angle of attack [°] Angle of attack [°]

(a) Lift coeﬃcients (b) Drag coeﬃcient

Figure 4.18: Lift and Drag coeﬃcients as a function of the angle of attack α

4.4.4.2 Aspect Ratio To reduce the induced drag in the sail, it is desirable, as for the rudder and centreboard, to have as high aspect ratio as possible. Larsson et al. (2014), discuss the importance of the height of the attachment point of the jib. Having the attachment point at the full mast length increases the driving force compared to having it further down, while it does not have any effect on the side force of the sail. A limitation to an extremely high aspect ratio sail is that it will have very low cord length. This means that the size of the mast section will be large compared to the sail section, which also means that the influence from the mast on the flow around the sail will be large. A high mast will also need a thicker profile for structural reasons which means that the influence off the mast will be even more significant. The mast disturbance is introduced in the VPP as a function, depending on the ratio between mast diameter and mean cord, effecting both the lift and drag coefficients of the main sail. A higher mast also means that the centre of effort in the sails will be moved upwards, this will cause a larger heeling moment than a shorter mast.

46 5 Design process

In this chapter, the design process of all the components of the skiﬀ are covered. The knowledge and theory behind this chapter is based on the previous Chapters 3 and 4.

5.1 Hull

In the design process of the hull, modelling of the geometry and CFD simulations are done simultaneously in order to get updates for improvements and obtain an optimised hull for desired speeds. When the design of the outer hull shape is decided, the internal structures are designed. This process is presented in the following sections.

5.1.1 Hull Analysis

To obtain the best hull design, meaning a hull with a low resistance, all design changes have to be compared. This is done using CFD-software. To obtain good results, the simulations need to run in the same way. Therefore the same range of speeds for the hulls need to be evaluated while maintaining same displacement. The trim of the hull needs to be set for each iteration. All the simulations are run for just half of the hull, to save computational time. See Section 4.2 for further information and how to set up the simulations. Having just half of the hull analysed makes it needed to correct the results for the total geometry.

5.1.1.1 Simulations Speeds The speeds of the hull have to be the same in each simulation so they can be compared. To decide what speeds will be run, inputs from the VPP are used. Here the resistance for the 49er© is used with the same sail area as is allowed in this competition, 33 square metres(A. 1001VELAcup, 2017). This gave speeds according to Table 5.1, which will be considered in the simulations. The speeds are chosen in knots but has to be implemented in metres per second. From the VPP, the maximum speed the boat is most likely to reach is approximately 5-7 knots, in approximately equal values for wind speeds. This wind speed is chosen according to the wind statistics, see Section 3.1 for more information. The reason a wider range of speeds is analysed, instead of considering just the one expected for boat speed is for the estimation of resistance. To implement the resistance values into the VPP calculations for speeds that are not evaluated through CFD simulations, an extrapolation method would be required. Analysis of speeds not directly interesting for CFD evaluations make it instead possible for the VPP to obtain results through interpolation of a known range of values (Wahab, 2017). This interpolation method results more accurate than the extrapolation, and will therefore produce more accurate VPP predictions.

5.1.1.2 Hull Trim One peculiarity of the 49er© is that it can easily change the waterline just by relocating the centre of gravity. This makes it possible to have a waterline good both for low speeds, when trimming the hull forward, and for high speeds, when moving the centre of gravity toward the aft. This feature is transferred to the hull designed since it is based on the 49er© hull. Therefore the simulations will be run at diﬀerent trims for diﬀerent speeds. To have an idea of how to trim the hull, the longitudinal position of the centre of gravity is scaled from a 49er© for each speed.

47 5 Design process

Table 5.1: The simulated speeds for each hull in the CFD-simulations converted from knots to metres per second.

Speed [kn] Speed [m/s]

3 1.5433 6 3.087 9 4.630 12 6.173 15 7.7167

This data is derived from resistance tests carried out on a full scale 49er© in a towingtank test (Persson, n.d.). The positions of the centre of gravity for the simulations are set according to Table 5.2.

Table 5.2: Location of the centre of gravity (CoG) for each speed scaled from the 49er©.

Speed [kn] CoG from FP [mm]

1 1386.1 2 1718.2 3 1976.2 4 2172.7 5 2320.0 6 2428.9 7 2509.8 8 2572.0 9 2623.9 10 2673.2 11 2726.5 12 2789.7 13 2867.7 14 2964.6 15 3083.5 16 3226.8 17 3395.9 18 3591.3 19 3812.8 20 4059.1

The values in Table 5.2 are used in the ﬁrst evaluation to ﬁnd the optimal hull with the lowest resistance.

5.1.2 Hull Concepts

To obtain a starting point for designing the hull, some concepts have to be analysed. Here the two concepts that have been analysed are presented, the transonic hull© and the scaled 49er©

48 5 Design process hull, respectively. When creating the models of the two concepts, some properties need to kept constant. These are so that the hull is not changed too much making comparisons through the CFD-simulations invalid. These properties are, • General hull shape • Moment of inertia of the water-plane around the symmetry axis • The displacement of 250 kg The moment of inertia of the water-plane and the displacement are both taken from a 49er© Rhino 3D model. Furthermore, a weight of 150 kg was assumed to simulate the weight of the crew, and a weight of 25 kg for the estimated weight of the rig. These values are also the references stated in the rules as they are the weights to be added in the real test in the tank to simulate both the crew and the rig. Therefore, by assuming 250 kg of total weight, the estimated weight of just the hull is left to be 75 kg.

5.1.2.1 Transonic Hull© The first hull considered is the transonic hull©, whose main characteristics are limited by three fundamental constraints. Firstly, all the hull curves below the waterline are of degree one (i.e. straight lines) therefore the geometry is defined by the maximum draft and beam values. Secondly, the stability is dominated by the moment of inertia of the water-plane area, IWP , since the difference of height between the centre of buoyancy and centre of gravity is similar to the 49er©, leading to zB − zG ≈ (zB − zG)49er . Also, the displacement, ∆, considered is very similar to the design displacement of the 49er© (between 250 − 260 kg), therefore the displaced volume ∇ is also similar. Hence, the reason for which only considering the water-plane moment of inertia can be a valid approximation to the one from the 49er© is evident by inspecting the hydrostatic equation for the metacentric height, GM, Equation 5.1.

I GM = WP + z − z (5.1) ∇ B G Therefore, the maximum beam is deﬁned by making use of the ﬁrst constraint, along with a reference value for the water-plane moment of inertia. The used reference value is the moment of inertia of the water-plane of the 49er© hull, assumed to have a satisfactory stability and manoeuvrability. With this, the following equation arises by equalling the water-plane moment of inertia of a triangular section with respect to the longitudinal axis (solved for the beam) to the desired moment of inertia (from the 49er©), see Equation (5.2). From Equation (5.2) the beam can be solved for, see Equation (5.3). The values that are used in these equations can be seen in Table 5.3

L · B3 = I (5.2) 48 49er

1 48 · I 3 B = 49er (5.3) L

Thirdly, the total displacement of the skiff assumes a first value decided based on previously built skiffs, average weight of appendages, rig and assumed weight of the sailors (∆ = 250 kg). Therefore, given the value for both the length, beam and the desired displacement, and considering the first constraint again, the draft is already fully determined through an iterative process until the desired displacement is met. The final obtained value is then Tmax = 0.266 m.

49 5 Design process

Table 5.3: Beam fom moment of inertia

4 L [m] I49er [m ] B [m] 4.6 1.664 · 10−1 1.202

After computing these values, the obtained transonic hull© is depicted in Figure 5.1.

Figure 5.1: Transonic hull©

5.1.2.2 Scaled 49er© Hull The other evaluated concept is the scaled 49er©, see Figure 5.2. As implied in the name, the created model for the scaled 49er© has proportional dimensions to the 49er© skiﬀ and is scaled down to 4.60 m LOA according to the regulations of the competition. The main design properties tried to be kept from the 49er© in the new scaled-down version, along with the reasons for doing so are: • Maximum beam far aft, to reduce resistance • Flat bottom in the aft, to reduce resistance at higher speeds • Concavity above the waterline, to reduce spray along the hull sides • Slender and v-shaped bow, to reduce slamming and pierce waves with less interference Similarly to the transonic hull©, the design displacement and the moment of inertia of the water plane are also kept constant. By having these conditions satisﬁed, the obtained hull is depicted in Figure 5.2.

50 5 Design process

Figure 5.2: Scaled 49er© hull

5.1.3 Hull Design Optimisation

First, a decision on which of the two concepts, among the transonic hull© and the scaled 49er© hull, should be further investigated and optimised has to be taken. Hydrodynamic computations provide as a result that the transonic hull© should be disregarded. This is because of its higher resistances for all speeds when compared to the scaled 49er©, see Table 5.4 for the diﬀerence. It must be noted the fact that the high resistance achieved by the transonic hull© is probably due to its sharp edges that cause a large separation. Smoother edges between sides and bottom would have probably determined a drop in terms of resistance. Such aspect has not however been considered and the scaled 49er© hull was chosen for further optimisation.

Table 5.4: Resistance Comparison Between Transonic Hull© and Scaled 49er© Hull

Speed [kn] Transonic Hull© [N] Scaled 49er© [N]

3 15.32 8.29 6 79.81 60.71 10 261.79 140.60 15 688.697 337.80

The scaled 49er© hull is optimised adjusting its hull lines until an overall satisfactory shape is obtained. This means that the overall dimensions and main curvature are set. When the major hull lines are decided, the work continues optimising the hull with smaller changes. This means that the hull is faired to get a smooth hull shape. When the first model of the scaled 49er© is created, a flared freeboard characterises the hull. This is a feature that is later removed to minimise the weight. Making the freeboard vertical creates a clear transition between the bottom and the freeboard. This makes the water non- slipping along the hull. As can be seen in Figures 5.3a and 5.3b the straight freeboard gives a spray out from the chine, creating lift and decreasing the resistance. This feature is brought within the following optimisation of the hull. Unlike a displacement vessel, a racing skiff has to adapt and is affected by the conditions surrounding it. Design optimisation for a single speed is therefore limiting in the performance possibilities of the hull and a compromise between not-so-optimal solutions must be achieved. It is verified for the present skiff, through its sailing conditions, that the most likely speeds to be

51 5 Design process

(a) Dry straight freeboard (b) Wet ﬂared freeboard

Figure 5.3: Straight vs flared freeboard sprays differences reached range between 3 and 12 kn, corresponding to Froude numbers between 0.23 and 0.91. Wind statistics report guides toward a most probable ship speed around 6/7 kn and results for such event are therefore be considered as more relevant in the decision process. Main rule to be followed when positioning the maximum beam and draft is that both the buttocks and the waterlines should be as straight as possible. Very straight aftbody is most desired higher the speed is. This configuration helps reducing the low pressure caused by convex lines that will otherwise lead to undesired trimming conditions by the stern and an increased resistance. Similar higher resistance is experienced in case low pressure acts on the side of the hull, causing wave troughs that also increase the resistance. Geometrically, a hull for high speeds has to be designed positioning the maximum beam at the stern and the maximum draft as far forward as possible. An optimum design for low speeds would instead call for more curved lines such that the hull would taper off gradually towards the aft. A compromise between the position of maximum beam and maximum draft has therefore to be found.

5.1.3.1 Position of maximum beam Through systematic variation, the maximum beam is placed at locations ranging between 70 % and 97 % of LOA, see Table 5.5 for the variation scheme. Aft of the maximum beam the hull will be parallel so the beam does not change after the maximum beam position. This is a feature that does not come from the scaled 49er©, it is implemented to make the systematic changes easier. The result of such changes is that the further forward the maximum beam position is placed, the more bluff but less wide the skiff hull will be. The initial hull has its maximum beam at a position of 93 % of LOA, and does not have a parallel aft body. This has to be changed before the systematic variation. After some simulations are run, a resistance curve can be plotted against the position of the maximum beam, see Figure 5.4a to 5.4c. The resistance curve is created from the computed data, marked with red stars, and there after a two-degree polynomial curve, blue line, is fitted to better highlight the path of the analysed data. This might not capture the path perfectly, but the resistance data has some scatter in it, since it is solved by a numerical method, see Section 4.2 for theory behind the simulations.

Table 5.5: Positions for the maximum beam variation

% of LOA

xLOA 70 75 80 82 87 89 93 97

52 5 Design process

(a) Results for 3 kn

(b) Results for 6 kn

Figure 5.4: Max Beam position vs resistance. Red stars mark measured data; Blue line is the ﬁtted resistance curve

53 5 Design process

Aim of the computations is to determine a geometry that presents as low resistance as possible and their results are plotted in Figures 5.4a to 5.4c. Main focus in the post-processing of the results obtained is put on the range of speeds between 3 and 9 kn, while the higher speeds, 12 and 15 kn, are computed almost excusively in order to provide suﬃcient data to the VPP. At speeds of 3 kn the optimal position of maximum beam is suggested to be placed between 80 and 90 % of LOA. Higher speeds suggest instead to move the position of maximum beam toward the stern, reaching values in the range 85 − 95 % for speeds of 6 kn and even further for 9 kn. Furthermore, considering the fact that 6 kn of speed is the one most probably achieved by the skiﬀ, computations for speeds of 5 and 7 kn are also carried out. Choice for these two speeds also gives the opportunity to carry out a validation comparison with other data. Such comparison is presented in Section 5.1.4.1. The results of the computations for the full range of speeds are presented in Table 5.6.

Table 5.6: Resistance vs beam position comparison

Speed [kn] 3 5 6 7 9 12 15

Position in % of LOA for Resistance [N] max beam 80 19.12 67.84 115.04 149.98 231.78 345.98 431.68 87 19.04 67.42 114.76 149.62 237.54 348.38 434.7 93 18.94 68.14 115.68 150.28 236.18 348.1 433.4

From Table 5.6 it is hard to evaluate which beam position to choose. Therefore all the values have to be compared in some way. This is done by ranking all of the position based on resistance for each speeds. There after the rankings are scaled by a factor depending on how probable each boat speed is. The scale factor is chosen according to Table 5.7.

Table 5.7: Scale factors to compare which hull to choose for maximum beam position variation

Speed [kn] Scale Factor

3 0.16 5 0.23 6 0.23 7 0.23 9 0.15 12 0.00 15 0.00

The scale factors in Table 5.7 are set so they mostly privilege speeds around 7 kn, since this is the design speed according to the VPP. Then 5 kn and 6 kn are speeds that also need to be designed for. Therefore 5, 6 and 7 kn have the main influences on the final decision. Then the rest is spread out equally between 3 and 9 kn since these speeds are equally probable for the skiff to reach. For the higher speeds, 12 and 15 kn, it is not seen reasonable to take these into consideration since the skiff is designed for speeds around 7 kn. To see the result for the scaled ranking, see Table 5.8. As can be seen in Table 5.8 the maximum beam position should be placed at 87 % of LOA from the bow. After this position it should have a parallel aft body. This gives that aft of 4002 mm

54 5 Design process the deck beam should be constant. Table 5.8: Ranked and scaled comparison between the beam position to evaluate where to place the maximum beam

Speed [kn] 3 5 6 7 9 12 15

Position in % Scale of LOA for Factor 0.16 0.23 0.23 0.23 0.15 0 0 P SF · rank max beam (SF) 80 3 2 2 2 1 1 1 2.01 87 2 1 1 1 3 3 3 1.46 93 1 3 3 3 2 2 2 2.53

5.1.3.2 Position of maximum draft After the variation of the beam is made, the same systematic variation is done to obtain the position of the maximum draft. The starting position was placed of 22 % of the LOA from the bow. Then the variation is made between 12 % and 32 % of the LOA. see Table 5.9 for variation scheme. A similar plot for the resistance curve is made for this case but position of the maximum draft instead of beam, see Figures 5.5a to 5.5c. The resistance curve is created in the same way as for the analysis of the position of the maximum beam, see Section 5.1.3.1. Which means by approximating the curve to a polynomial of degree two. In the plots the red stars is the measured data and the blue line is the approximated resistance curve. Table 5.9: Positions for the maximum draft position variation

% of LOA

xLOA 12 17 22 27 32

By analysing Figures 5.5a to 5.5c, which are for speeds of 3, 6 and 9 kn, an interval for which position that should be chosen is derived. For speeds of 12 kn and 15 kn see Appendix 8.2.5. For 6 kn the preferred position of maximum draft is somewhere between 16 − 20 % of LOA, according to the curve. For low speeds of 3 kn it is around 28 − 32 % and for 9 kn it is almost the same as for 6 kn, around 18 − 22 %. One thing to take in mind when doing this analysis is that this is for the curve which is interpolated between the measured data. Therefore Table 5.10 is created to compare all the measured data whit each other. However, this table is just for the normal simulated speeds, without 5 and 7 kn. Since Table 5.10 just shows the resistance values, a new table is created to compare the ranking between the hulls with a scale factor. The scales factors can be seen in Table 5.11. The factors is chosen according to that the 6 kn is the one that is closest to the design speed of 7 kn why it has a quite big scale factor. For 3 kn and 9 kn there are still speeds that should be taken into account, why they have smaller values. Again the scale factors for higher speeds are set to zero, since such will not be reached. According to Table 5.11 the scale factors are added to the ranking of comparison of the resistance for draft position. Table 5.12 is created to give the results. According to Table 5.12 the maximum draft should be positioned at 27% of the LOA from the bow. This means that the maximum draft should be placed 1242 mm aft of the bow.

55 5 Design process

Table 5.10: Resistance vs draft position comparison

Speed [kn] 3 6 9 12 15

Position in % of LOA for Resistance [N] max draft 12 20.3 114.42 238.1 350.76 429.96 17 19.66 113.74 242.88 363.1 428.02 22 19.04 114.76 237.54 348.38 434.7 37 18.74 114.52 237.72 347.36 440.08 32 18.8 116.12 243.58 292.66 404.24

Table 5.11: Scale factors to compare which hull to choose for draft variation

Speed [kn] Scale Factor

3 0.25 6 0.50 9 0.25 12 0.00 15 0.00

Table 5.12: Ranked and scaled comparison between the beam position to evaluate where to place the maximum draft

Speed [kn] 3 6 9 12 15

Position in % Scale of LOA for Factor 0.25 0.50 0.25 0 0 P SF · rank max beam (SF) 12 5 2 3 3 2 3.0 17 4 1 4 5 5 2.5 22 3 5 2 2 3 3.75 27 1 3 1 1 4 2.0 32 2 4 5 4 1 3.75

56 5 Design process

(a) Results for 3 kn

(b) Results for 6 kn

Figure 5.5: Max Draft position vs resistance. Red stars mark measured data; Blue line is the ﬁtted resistance curve.

57 5 Design process

5.1.4 Final Hull Geometry and Hydrodynamics

From the optimisation of the hull design, the shape of the canoe body is determined. By this its main dimensions are set from an optimal point of view. All the main dimensions are presented in Table 5.13. Drawings for the ﬁnal design of the hull shape are detailed in Appendix 8.2.5.

Table 5.13: Final hull dimensions for the skiﬀ

B Position of max beam T Position of max draft LOA [m] max max canoe-body [m] [%LOA] canoe-body [m] [%LOA] 4.6 1.202 87 0.17 27

For the ﬁnal canoe body the resistance is presented in Table 5.14. Also a resistance curve is created, see Figure 5.6.

Table 5.14: Final drag along x-axis for the canoe body

Speed [kn] Resistance [N]

3 19.52 5 69.62 6 114.22 7 151.32 9 233.80 12 348.65 15 431.56

Figure 5.6: Resistance curve for ﬁnal canoe-body

58 5 Design process

The resistance curve will further on be used in the VPP to get how the hull will perform in diﬀerent conditions, see Section 5.2.1.1 for performance according to the VPP.

From the CFD-simulations the wave pattern of the canoes body is simulated. This is not taken into account when doing the optimisation since only the total resistance is taken into consideration. However, the generated waves are one component in the resistance, so it will in someway be taken into account but not speciﬁcally be optimised for. The ﬁnal wave pattern for 6 kn can be seen in Figure 5.7.

Figure 5.7: Wave pattern generation at 6 kn speed

5.1.4.1 Validation of Results

Being the first year that Chalmers University of Technology is taking part in a project of this kind, no direct reference hulls nor computational results were available. Validation of the results obtained comes from the comparison with the results presented by Mancuso, Pitarresi, and Tumino (2017). In this paper, results for the CFD evaluations carried out on LED3 are presented. The skiff chosen as reference was built with the same purpose of the one treated in this text. Another fact in favour of this choice is that the reference skiff graduated champion of the first Midwinter Indoor Race in February 2017. Table 5.15 presents a comparison between the obtained computational results for resistance, for three different speeds and no appendages attached, by LED3 and the ongoing project, CTH1. This comparison is not carried out on the final design, it is made for when the position of the maximum beam is decided to see that the results is reasonable.

Most importantly the comparison validates the modelled setup for the solver. Furthermore, the results obtained can be considered quite satisfying. With exception made for the speed of 5knots, the hull here under discussion is shown to perform better than last year’s best skiﬀ.

59 5 Design process

Table 5.15: Drag along x-axis for hull LED3

Speed [kn] Resistance LED3 [N] Resistance CTH1 [N]

5 67.9 69.62 6 115.1 114.22 7 168.2 151.32

5.1.5 Deck

When designing the deck, several parameters have to be considered. Such parameters are ease of movement for sailors on the deck, aerodynamics, water on deck and stiffness given by deck shape. Three different designs are discussed, one with a v-shaped deck downwards, a straight deck and one with a slightly upwards cambered deck. For the v-shaped deck the main feature with this design is that is make the movement for the sailors easily. The angle should follow the racks in this case to make get this easy movement. The disadvantage for this design is that there are risk for collecting water in the middle of the V, as well as the structure will be weaker by this solution. By this reason, it will not be chosen. Next design concept is the straight deck. This is some mix between the two other options and does not give any specific advantage or disadvantage. This is why this is not chosen since both of the other concept has bigger advantages that can be used. The last design is the slightly upwards cambered deck. This has it advantages in giving stiffness to the structural performance, see Section 5.1.6.2 for more information about it. Also the feature that the water not will be collected on the hull is something that is preferred as well as there are no big problems with the movement. One problem that can occur further on in the project when designing the deck layout is that there is no place under the freeboard to collect thing in. Like the gennaker sock. This does not seem as a big problem and with all advantages for this design this is chosen.

5.1.6 Structural Hull Design

The structural design of the hull can be divided into three steps. Design of the hull plating sandwich, design of the deck sandwich and design of the internal stiﬀening structure. In this section the design of each of these components will be explained. Structural analysis is performed in the FEM-software Abaqus. Details on the set up of the FE-model, elements used, boundary conditions applied and load cases considered are found in Section 4.3.5.

5.1.6.1 Design of Hull Plating Sandwich In this section, the process of designing the sandwich for the hull plating is described. Design of the sandwich include determining core thickness and design of the skin laminates. To begin, the core thickness is determined. This is done by choosing an arbitrary layup sequence for the skin laminates. It is not of great importance which layup is chosen at this stage, only that it is a reasonable layup and that it is held constant while the core thickness is varied. In this case, the following layup sequence for the sandwich was chosen, where x is the core thickness to be varied. See Section 4.3.5.1 for details on layup notation.

[−60 60 c0x]S

60 5 Design process

By varying the core thickness in the FE-model while applying the trapeze load case described in Section 4.3.5, the inﬂuence of core thickness on deﬂection and stress levels in the model could be evaluated. The evaluation is presented in Table 5.16.

Table 5.16: Maximum stress for varying core thickness

Stress [MPa] Deﬂection [mm] Core thickness [mm] SLT,max SL,max SL,min ST,max ST,min U3,max 12 0.244 39.5 -87.1 5.6 -11.0 4.04 10 0.245 41.7 -89.2 6.0 -11.2 4.54 8 0.245 41.7 -89.2 6.0 -11.2 5.21 5 0.260 43.1 -87.2 7.2 -12.0 6.71

In Table 5.16, the stress global maximum is shown for each stress component where index L denotes the fibre direction and T is the transverse direction relative to the fibres. Index LT denotes the shear stress. Maximum deflection for the third (vertical) direction recorded at the mast step, is presented as well. From these values it can be concluded that core thickness will not have a significant influence on stress levels in the sandwich structure. It is seen that the core thickness will be the governing factor for the deflection of the structure. Thus it is concluded that increasing core thickness will primarily add stiffness to the structure. It should be mentioned that when these values were recorded the design of stiffening structures and deck laminate layup were still at the conceptual level meaning the numbers are not representative for the stress levels or deflection of the final design. The design of the internal stiffening structure is covered in detail in Section 5.1.6.3. A previous FE-analysis conducted on a similar boat participating in the 1001VELAcup showed a deflection of 10 mm, recorded at the mast step (Mancuso et al., 2017). The boat in question utilises cork as the core material, a flax/epoxy laminate in the skins and marine plywood as the material of the internal stiffening structure. The core thickness is not mentioned. Another boat that previously participated in the 1001VELAcup was built with an end-grain balsa core thickness of 6.5 mm covered with flax/epoxy laminate (Castegnaro et al., 2017). In both these cases, the structural design, performance of material and load cases considered in design may vary from this project. However, the numbers mentioned in these reference studies are considered to be appropriate to serve as guidelines when choosing core thickness in this project. The core thickness chosen in this project is 8 mm. Increasing the thickness to 10 mm will result in an increase of 20 % of the core weight while only reducing the maximum defection with roughly 13 %. Since the deflections seen in Table 5.16 are already low compared to the reference studies it was reasoned that, if necessary, reducing the deflection could be done in a more weight efficient manner further on in the design work. Core thicknesses below 8 mm are deemed to fragile to handle in the building process intended for this project, where long thin strips of balsa is cut and attached to a male template. More details on the building process are found in Section 7. It should be pointed out that the method intended in this project is different than the one described in (Castegnaro et al., 2017) where the authors employed vacuum bag moulding in a female mould with 6.5 mm end grain balsa in the core of the sandwich. To decide which layup to use in the laminate of the skins, a total of 20 layup options are investigated. The results of this investigation are presented in Table 5.17. In the investigation, 5 nodes of interest are chosen in the FE-model. The locations of these are shown in Figure 5.8. For each layup tested the deflection of these nodes is measured. Stress levels are overall low for each layup. The effects of varying layups on the stress distribution and stress magnitudes in the hull were not analysed. The philosophy behind this is similar to when the thickness of the core was decided. A thorough analysis of stress is instead performed in Section 5.1.6.4.

61 5 Design process

Figure 5.8: Location of hull nodes investigated

The trapeze load case is considered the worst case scenario for the hull plating, since it induces the largest deflection and stress magnitudes, which is also why it is the only load case analysed in this section. A core thickness of 8 mm was already decided earlier in this section. The thickness of each ply is 0.21 mm according to flax/epoxy laminate properties in Table 4.4. The nodes that are investigated are chosen based on if they are located at a critical location or if the magnitude of deflection in a certain area is large. Deflection at the location of the fore stay and the mast step (nodes #1236 & #1182) in the vertical direction are two of the largest deflections on the hull. It is important that the hull layup is stiff enough to keep these deflections under control. Furthermore, node #7896 belongs to the hull plate where bulkheads are located furthest apart from each other in the conceptual design of the stiffening structure. Lastly, node #3216 belongs to the aft most hull plate. In the keel, this plate has the largest lateral deflection. At node #498 the largest deflection in the transverse direction occurs. The hull plating collapses inwards at this location. This node is chosen to be examined to evaluate the effect of hull layup on the transverse stiffness of the hull. In Table 5.17 the layup chosen for the hull plating in this project is layup no. 17. The deck plating is designed to give as large stiffness as possible to the keel plates while adding as little weight as possible. In Table 5.17 the two most promising layups are layup no. 17 and 18.

Observing the difference in deflection of node #7896 for layup no. 17 (U3,no17 = −0.25mm)& layup no. 18 (U3,no18 = −0.49mm), the choice of layup no. 17 over layup no. 18 is motivated by the philosophy that hull plating should contribute more to stiffness in the vertical direction at the keel than in the transverse direction at the side plating. The transverse deflection of node #498 is U2,no17 = 1.91mm for layup no. 17 and U2,no18 = 1.27mm for layup no. 18. Side plating stiffness will to a large extent be given later in design by the deck and bulkheads. Further, it should be mentioned that the possibility to add a bulkhead at the location of node #498 to reduce the transverse deflection at this point is possible, see design of stiffening structure sec 5.1.6.3. Other differences in deflection between layup no. 17 & 18 are considered to be so small that they are negligible. Adding more plies improves the stiffness of the hull plating while at the same time adding on to the total weight. In layup no. 17 four plies are stacked on the outside laminate. Four plies is assumed to be the maximum number of plies that can be handled during construction. In the inside laminate, three plies are stacked. There is also a possibility to add an extra 90 degree ply on the inside of the hull to improve the hulls transverse stiffness if found necessary in later analysis.

62 5 Design process [kg] 10.30 10.30 10.30 11.25 11.25 10.30 10.30 12.21 10.30 10.30 11.25 11.25 12.21 12.21 10.30 11.25 11.25 11.25 11.25 11.25 the plates Mass Of [mm] 1.40 2.11 1.71 1.35 1.95 1.50 1.37 1.29 1.33 1.33 2.13 1.92 1.24 1.79 2.08 1.92 1.91 1.27 1.52 1.57 #498 2 ,max U [mm] 3 ,i U -2.56-2.79 -0.53-2.68 -0.22-2.54 2.33 -0.40-2.70 2.38 -0.48-2.78 2.34 -0.24-2.72 2.14 -0.38-2.45 2.21 -0.53-2.63 2.38 -0.45-2.63 2.35 -0.54-2.53 1.99 -0.54-2.70 2.32 -0.49-2.44 2.32 -0.25-2.61 2.13 -0.45-2.79 2.21 -0.26-2.70 1.98 -0.23-2.69 2.07 -0.25-2.52 2.37 -0.25-2.68 2.21 -0.49-2.69 2.21 -0.54 2.13 -0.53 2.24 2.25 #1182 #7896 #3216 4.75 4.71 4.69 4.27 4.32 4.83 4.78 3.91 4.73 4.73 4.25 4.31 3.89 3.98 4.70 4.31 4.30 4.25 4.50 4.52 #1236 ply no. 5 6 7 0 0 - 6030 045 0 - 60 0 - 30 0 - 0 - - 60 0 0 30 060 - -60 - 60 30 - -60-60 60-30 60 - -60 30 - -30 60 - -30 30 0 -30 30 0 -30 30 - -60 30 - -60 60 - 60 - - Inside 4 0 0 0 0 0 0 0 0 0 0 0 0 90 90 -60 -30 -45 -60 -30 -60 able 5.17: Variation of the sandwich skin laminates 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 T mm Core 8 plate step ply no. plate in keel bow plate orestay F 1 2 3 00 60 30 -60 -30 0 60 -60 0 30 60 00 600 30 -60 45 -30 -45 00 0 30 90 90 Mast 6030 -6060 -30 0 30 -60 0 -30 0 30 0 -30 0 60 0 0 60 -60 0 30 -30 0 -30-60 0 0 0 0 -60 60 0 Description Aftmost Side Outside ------0 0 0 0 0 0 0 0 0 0 30 60 30 Largest 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 de no. #498 #1236 #1182 #7896 #3216 No Layup no.

63 5 Design process

5.1.6.2 Design of Deck Sandwich Design of the deck sandwich is performed in a similar manner as the design of the hull plating sandwich, only in this process the core thickness is varied together with with skin laminates, why the procedure for the deck is different from the procedure for the hull is explained in Section 5.1.6.5. In Tables 5.18 to 5.20, the variation of the core thickness and laminate layups can be seen. In Figure 5.9, the locations of deck nodes investigated are shown. Again, nodes at the location of the mast step (#6309) and forestay (#1236) are chosen since these are two critical locations with large deflections. Node #13108 is located at the midpoint of the largest plate in the deck, enough stiffness in the vertical direction (3rd direction) is required here to allow for crew members to operate on the deck without structural failure. The main sheet is predicted in this design stage to be located somewhere around node #15769. The large load from the main sheet will require high stiffness in this area. Node #2341 where the shroud placement is predicted, belongs to the largest deflection in the transverse direction (2nd direction). This node is chosen to evaluate the decks transverse stiffness.

Figure 5.9: Location of deck nodes investigated

In this project layup no. 3 in Table 5.18 is chosen. This means that a core thickness of 8 mm in the core of the deck is used. The gain in stiffness with core thicknesses above 8 mm is considered too small in relation to the weight added to viable. Decreasing the core thickness from 8 mm is not considered, since 8 mm is the minimum thickness assumed to be manageable during construction. A maximum of four plies in each laminate is considered, for the same reason. The deck is subjected to the largest risk for concentrated chock loads, such as tools being dropped on the deck, during rigging. Four plies are placed in the outside laminate to provide as much protection against concentrated shock loads as possible. On the inside laminate three plies are stacked (layer 5,6 and 7) and the eighth layer is reserved if it is found in later design work that additional plies are needed. Also a fifth layer on the outside is reserved for this reason. It should be noted that if a fifth layer on the outside is added it could reduce the possibility to laminate the deck properly, since as already stated four layers are assumed to be the maximum manageable amount of layers during lamination.

64 5 Design process [kg] deck 6.10 6.10 6.66 6.66 6.10 6.10 6.10 6.10 6.10 6.10 6.10 6.10 Of Mass mm -0.38 -0.31 -0.31 -0.31 -0.32 -0.34 -0.39 -0.36 -0.31 -0.31 -0.34 -0.36 #2341 2 ,max U mm 3 ,i U -2.71-2.68 -1.88-2.61 -1.91-2.62 -1.83 2.08 -2.70 -1.87 2.00 -2.71 -1.93 1.92 -2.73 -1.93 1.94 -2.75 -1.84 2.05 -2.71 -1.94 2.08 -2.77 -1.97 2.05 -2.78 -2.02 2.15 -2.72 -2.03 2.07 -1.87 2.17 2.21 2.06 #6309 #13108 #15769 4.55 4.34 4.17 4.30 4.60 4.67 4.34 4.78 4.53 4.91 5.00 4.46 #1236 Inside 6 7 8 00 900 - 90 - 90 - 0 90 - -45 45 - -45 90-60 - 60-30 - 30-45 - 45 - -45 90-60 - 60-30 - 30 - 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 mm 90 90 90 90 90 Core 8 able 5.18: Deck layup analysis with 8 mm core thickness T step sheet step area orestay Shroud Outside F Mast Main -- 45 -45 90 0 0- 0 - 90- 60 45- -60 30 0 0 - -30 45 0 - -45 90 0 - 90 0- 60 45 0 -60 30 0 0 -30 0 Description 1 2 3 4 9090 0 90 0 0 0 0 Crew ------0 2 3 4 5 6 7 8 9 1 10 11 12 No de no. #1236 #6309 #2341 #13108 #15769 No

65 5 Design process [kg] deck 6.77 6.77 7.34 7.34 6.77 6.77 6.77 6.77 6.77 6.77 6.77 6.77 Of Mass mm -0.37 -0.30 -0.30 -0.30 -0.31 -0.33 -0.38 -0.35 -0.30 -0.30 -0.32 -0.35 #2341 2 ,max U mm 3 ,i U -2.66-2.63 -1.84-2.56 -1.87-2.57 -1.79 2.04 -2.65 -1.83 1.97 -2.65 -1.89 1.89 -2.68 -1.89 1.91 -2.70 -1.80 2.01 -2.66 -1.92 2.04 -2.72 -1.94 2.02 -2.72 -2.00 2.12 -2.72 -2.01 2.04 -1.84 2.15 2.18 2.03 #6309 #13108 #15769 4.50 4.30 4.14 4.27 4.56 4.61 4.30 4.78 4.54 4.92 5.01 4.46 #1236 Inside 6 7 8 00 900 - 90 - 90 - 0 90 - -45 45 - -45 90-60 - 60-30 - 30-45 - 45 - -45 90-60 - 60-30 - 30 - 5 0 0 0 0 0 0 0 0 0 0 0 0 mm 0 0 0 0 0 0 0 90 90 90 90 90 Core 10 able 5.19: Deck layup analysis with 10 mm core thickness T step sheet step area orestay Shroud Outside F Mast Main -- 45 -45 90 0 0- 0 - 90- 60 45- -60 30 0 0 - -30 45 0 - -45 90 0 - 90 0- 60 45 0 -60 30 0 0 -30 0 Description 1 2 3 4 9090 0 90 0 0 0 0 Crew ------0 13 14 15 16 17 18 19 20 21 22 23 24 No de no. #1236 #6309 #2341 #13108 #15769 No

66 5 Design process [kg] deck 7.45 7.45 8.02 8.02 7.45 7.45 7.45 7.45 7.45 7.45 7.45 7.45 Of Mass mm -0.36 -0.30 -0.29 -0.29 -0.30 -0.32 -0.37 -0.34 -0.29 -0.29 -0.31 -0.34 #2341 2 ,max U mm 3 ,i U -2.61-2.57 -1.80-2.51 -1.82-2.52 -1.75 2.01 -2.60 -1.78 1.94 -2.60 -1.85 1.87 -2.63 -1.85 1.88 -2.65 -1.77 1.98 -2.61 -1.90 2.01 -2.67 -1.91 2.00 -2.67 -1.98 2.09 -2.61 -1.99 2.02 -1.82 2.13 2.16 2.00 #6309 #13108 #15769 4.45 4.27 4.12 4.23 4.51 4.56 4.27 4.78 4.54 4.93 5.02 4.46 #1236 Inside 6 7 8 00 900 - 90 - 90 - 0 90 - -45 45 - -45 90-60 - 60-30 - 30-45 - 45 - -45 90-60 - 60-30 - 30 - 5 0 0 0 0 0 0 0 0 0 0 0 0 mm 0 0 0 0 0 0 0 90 90 90 90 90 Core 12 able 5.20: Deck layup analysis with 12 mm core thickness T step sheet step area orestay Shroud Outside F Mast Main -- 45 -45 90 0 0- 0 - 90- 60 45- -60 30 0 0 - -30 45 0 - -45 90 0 - 90 0- 60 45 0 -60 30 0 0 -30 0 Description 1 2 3 4 9090 0 90 0 0 0 0 Crew ------0 25 26 27 28 29 30 31 32 33 34 35 36 No de no. #1236 #6309 #2341 #13108 #15769 No

67 5 Design process

5.1.6.3 Design of Internal Stiffening Structure The main purpose of the internal stiffening structure, from now on referred to as the stiffeners, is to provide structural support for the hull plating, ensuring that the global deflections are minimised. This task demands a well thought through design to render a good result. The design process of the stiffeners has been iterative, and is based partly on engineering guesses but also the results obtained from the finite element simulations. The stiffeners consist of two main component groups. One is the longitudinal supports that include one large stringer running along the length of the boat, and the centreboard casing. The transverse supports consist of several bulkheads. The geometry of the stiffening components have gone through several changes during the duration of the design process. The changes concern both the number of stiffening elements as well as their geometry. The goal was always to achieve a structure that is as light as possible while still keeping the global structure adequately stiff enough. The overall goal demanded the stiffeners to be efficient, in the sense that they are placed and designed where they are needed the most. The final result of the stiffener design is shown in Figure 5.10. The general design philosophy, as already mentioned, is to keep the stiffening structure light. This is achieved by cutting holes in the stiffening components, only keeping material where it is needed. The longitudinal stringer is reinforced with diagonal elements in the forward part in order to counteract the bending moment from the mast and forestay. The transverse bulkhead underneath the mast step is made solid since this is the point where the concentrated loads are the largest. Also note the diagonal bulkheads in the same position. These bulkheads are angled to account for the loads originating from the racks mounted on the deck. The intersection of the stringer, the diagonal bulkheads and the solid transverse bulkhead in this one point will create a very concentrated structure that will be sufficient to counteract the compressive forces from the mast step. The four other bulkheads will provide transverse stiffness to the hull as well as compressive forces acting on the deck from crew in operation. All internal corners of the stiffening structures have been modelled with a radius in order to decrease the stress concentrations. The radius was varied until an acceptable stress distribution was reached in the FE-analysis. The outer upper corners of stringer and bulkheads have been cut diagonally to facilitate attachment of deck.

Figure 5.10: Overview of internal stiﬀening structure

A possibility that is also implemented in the final design is to add flanges on the edge of the holes, as shown in Figure 5.11a where a bulkhead with a flange around the edge of the hole is shown to compare with Figure 5.11b where a bulkhead without flange is shown. This flange is mainly a result of the building process, but has been shown to contribute to the overall hull stiffness in FE-simulations.

68 5 Design process

(a) Bulkhead with ﬂange (b) Bulkhead without ﬂange

Figure 5.11: Comparison of stiﬀener design

The flange would be achieved by wrapping the laminates on the outside and inside of the core around the edge of the stiffener core template. Between the two laminate skins fibres will be placed along the edge of the hole for additional reinforcement. This is visualised in Figure 5.12, where the green lines symbolise the laminate on the inside and outside of the core, that is shown in grey. The fibres running along the edge of the hole are shown as orange cross-hairs.

Figure 5.12: Schematic ﬂange layup design of stiﬀener

To evaluate the flange contribution to stiffness versus its contribution to weight, two simple models are compared in Abaqus. The models are shown in Figure 5.13a and 5.13b. Both consist of a plate with dimensions 600 × 600 mm which is the approximate space between bulkheads. In both cases the plates are modelled with a web of height 60 mm. Both models have identical laminate layup, load, boundary conditions and mesh applied. The load is the hydrodynamic pressure in Equation (4.10) acting on the entire plate surface. Both plates are simply supported along two edges and clamped along the other two. S4R shell elements with a approximate size of 10 × 10 mm is applied in both models. The only difference is that the model in Figure 5.13b is modelled with a flange of width 15 mm on the web.

69 5 Design process

(a) Without ﬂange (b) With ﬂange

Figure 5.13: Comparison of model designs

The layup of the plates is layup no. 17 in Table 5.17. The web is modelled with the following layup, where 0◦ corresponds to the long edge of the web.

[45 − 45 90 c908]S c908 indicates that the ﬁbres of the core are parallel to the short edge of the web and that it has the thickness 8 mm. In Figure 5.13b, again with the long edge of the web as a reference. The ﬂange is modelled with the following laminate layup.

[45 − 45 90 0]S

The first three plies are extensions of the web laminates and the fourth is the fibres that are supposed to give the flange its stiffness. The deflection plots in Figures 5.14a and 5.14b are achieved with FE-simulation.

(a) Without ﬂange (b) With ﬂange

Figure 5.14: Comparison of model deﬂection

In Table 5.21 below, deﬂection and mass data are compared between the two models.

Table 5.21: Comparison between models with and without ﬂange.

Maximum deﬂection [mm] Mass [kg] U1 U2 U3 mtot Flange ∼ 0 0.122 0.491 0.71 No ﬂange ∼ 0 0.204 0.728 0.70 ∆ ∼ 0% 40% 33% -1%

It can be seen that vertical deflection increases with 40 % when the flange is removed and that transverse deflection is increased with 33 % while the weight only reduces with roughly 1 %. The flange adds some complexity to the structure and requires extra work in the building process.

70 5 Design process

Still the benefits of adding this laminate flange is considered large enough for the additional construction time to be invested in them. It was decided that the bulkheads and stringers will be built with a flange along the edges of the holes with a width of around 25 mm. The width may vary on some stiffening components since 25 mm of flange width will not fit at all locations inside the hull. As for the final layup of the stiffeners, only one was tested at first. The following layup was the one that was analysed.

[45 − 45 0]S

This layup was chosen based on the wish to keep the fibres of at least one ply more or less perpendicular to the hull surface around the whole circumference of the stiffeners in order to make use of the fibres’ strength along their length. The layup turned out to give good results already in the first FE-analysis. Since the building process was about to start, no further investigations were made.

5.1.6.4 Evaluation of Hull Structure Design When a draft design of hull, deck and internal stiffening structure is established, a final evaluation of deflection and stress is performed to verify the design. If intolerable levels of stress or deflections are found the design of the internal stiffening structure is changed. This stage mainly concerns increasing radii of corners, slightly modifying the positions of the bulkheads and other minor geometrical modifications of the internal stiffening structure. The intention of this process is to systematically improve the design towards lower stress levels and deflection. This stage can be seen as the fine tuning of the design towards its final form. Since these changes are many and minor presenting them in a structured way is hard and could cause confusion. Therefore, this section will focus on how the evaluation of stress and deflection is performed, rather than the many and minor modifications done to the stiffening structure. In Figure 5.15, the deflection of the hull subjected to the trapeze load case is shown. The largest deflections occur at the bow due to the force from the forestay, pulling the bow upwards causing a global bending of the hull. The force from the mast compression at the mast step causes large deflections in this area. This is visualised more clearly in Figure 5.16.

Figure 5.15: Deformations magniﬁed 50:1 for hull-with-trapeze load case

Figure 5.16 shows how the internal stiﬀening structure deforms under the trapeze load case. The ﬁgure clearly shows how the mast step causes the stringer and how (from the bow) 2nd,

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3rd and 4th bulkheads below it to deform a lot more than the other bulkheads. Except for the transom which is deformed by the main sheet force.

Figure 5.16: Deformation of hull magniﬁed 50:1 for hull-with-trapeze load case. Hull plating and deck are hidden

Figure 5.17 shows how the elements around the node associated to the forestay force are distorted. The distortion is possibly caused by a local buckling mode in this area, due to the forestay force being associated to a single node. When evaluating the deflection at this point this large distortion has to be taken into mind. Choosing a node belonging to an element just aft of the elements heavily distorted by the forestay force, will yield a more realistic deflection. The same reasoning can be applied when evaluating deflection at other points where a large force is associated to a single node, such as the locations of the mast step and the main sheet.

Figure 5.17: Distortion of elements at forestay magniﬁed 50:1 for hull-with-trapeze load case

Considering the stress levels, they are analysed by plotting: stress along ﬁbre direction SL, stress across ﬁbre direction ST and the shear stress SLT , through the thickness of the sandwich. An example of how this is performed is shown in Figures 5.18 to 5.22. In Figure 5.18 the element of interest is marked with a red arrow. The element is situated in close proximity to the mast step force. An element not directly associated with the single node in which the mast step force is applied is chosen, with the same reasoning as above. The

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Figure 5.18: Bulkhead element for which stress is plotted in Figure (5.19) element in question is positioned in a critical area. Since the stress is high at the 2nd (from the bow) bulkhead due to the mast step it is an example of an element where special attention is required. Figure 5.19 shows stress through the thickness of the sandwich. The stress varies in the sandwich skin through the plies of the laminate as the ﬁbre direction changes, giving the characteristic stress-thickness graph of a laminate. Stress appears to stay more or less constant through the thickness of the core and the plies, which was not expected.

Figure 5.19: State of stress in bulkhead element shown in Figure (5.18)

When comparing the results to already solved examples in (ABAQUS/Explicit, 2017), where analysis of sandwich structure in a sail yacht is performed, it is shown that strain varies through the core and that the strain stays constant through the thickness of the plies, but varies between plies as the ﬁbre direction changes. To verify that the same behaviour is achieved in this project a plot of the strain through the thickness of the sandwich is produced, shown in Figure 5.20 below. The ﬁgure shows that the strain varies through the thickness of the core. This complies with the example analysis found in (ABAQUS/Explicit, 2017). In Figure 5.21 another element considered critical is marked with a red arrow. This element belongs to the hull and is located directly below the area of the mast step.

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Figure 5.20: Strain plotted for bulkhead element in Figure 5.18

Figure 5.21: Hull element for which stress is plotted in Figure (5.22)

Figure 5.22 shows the stress plotted through the thickness of the sandwich for the element in Figure 5.21. It can be concluded that the behaviour noted previously in Figure 5.19 is repeated for the core. As for the plies the stress varies through the thickness of each ply. An explanation could be that the element in question is subjected to more pronounced bending in contrast to the bulkhead element that is subjected to compression from the mast step.

Similar analysis are performed on several elements throughout the model where considered necessary, making sure that stress levels are at an acceptable level. One has to take into consideration that certain areas, such as the mast step and the forestay, will be reinforced to be able to handle the loads in these areas. The stress and deflections presented here are calculated without these extra reinforcements, and therefore, may not represent the final structure exactly. How- ever, the bulkheads and stringers have to be defined before the extra reinforcement is designed. After analysing several elements in a similar manner as previously shown, and modifying the internal stiffening structure, the final design of the internal stiffening structure is decided. 2D drawings of the structural hull design is produced and the building process can be initiated, even though the design work of extra reinforcements still remains.

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Figure 5.22: State of stress in hull element shown in Figure (5.21)

5.1.6.5 Conclusions on Hull structure Design In this project the design of the hull plating sandwich is performed first, followed by the design of the deck sandwich and lastly the design of the internal stiffening structure was performed. In hindsight, a potentially better methodology could be to perform the design of the stiffening structure before performing the design of the sandwich structures for hull plating and deck. That way the procedure of working with conceptual design of the stiffening structure when designing hull and deck structures could be avoided. This is assumed to be a better methodology since stiffening structure influences hull and deck in a larger extent than the hull and deck influences the stiffening structure from a structural point of view. The reason this project did not employ this order has to do with time frame and planning. By the time the load cases had been established and a working FE-model was created, templates used in the building process had to be ordered for fabrication. To be able to order these templates the core thickness of the sandwich had to be decided to get the correct offset on the templates. The hull structural design process in this project starts at the core thickness of the hull plating sandwich. This also explains why core thickness in the hull is not varied together with laminate layups as was done with the deck in Section 5.1.6.2

5.2 Sail and Rig

When designing the sail and rig, there are many diﬀerent aspects that must be considered. According to the class rules (A. 1001VELAcup, 2017), there are no limitations of either mast height or draft, although the total sail area cannot be larger than 33 m2 and the mast and boom must be made of aluminium. Both parts, the sails and the rig, are design with professional help from the companies Seldén and North Sail. As a basis to start from, the 49er© distributions concerning both sections are used and customised. The adjustments made are stated in the following sections.

5.2.1 Sail Set Up

There are several diﬀerent factors that eﬀect the performance of the sails. The most important of these are described by section 4.4.4. Several of these interfere with each other in a complex way and the design process of the sail setup, therefore, consists of systematic variations where

75 5 Design process one parameter is altered at a time in order to find a value for this parameter that results in the best performance. The performance for a change in parameter value is evaluated with the VPP. To design a high performance sail setup it is important to consider in which weather condition it will operate. The wind statistics in Table 3.1 are therefore crucial for the design of the rig. It will be designed to perform optimally at the most likely average wind speed. The expected wind speed differs slightly between Windguru (3.86 m/s) and ISPRA (3.36 m/s). The design wind speed will therefore be chosen to 3.5 m/s as an intermediate value. There are also several types of sail setups that can be considered. In this project, four different concepts have been considered and evaluated. To choose the main particulars of the sail setup, as well as the best sail concept, the performance of different setups are evaluated with the VPP. Furthermore, the sail shape is adapted from the 49er©, see Figure 3.4. It provides more sail area in the upper part, gaining more lift (wind is stronger) and managing the twist of the sail is easier. These advantages apply on a rectangular sail shape but on a triangular. Another point of having the 49ers© shape of the main sail is the fitting of the area into the rig dimensions. A triangular sail needs a higher mast to fit in the same main sail area while keeping the same boom length.

5.2.1.1 Sail Concepts Regarding the racing time, more than two thirds of it is spend on the upwind course and one third going downwind. This observation sets the focus of sail set up optimisation on the upwind sail area. The aim of the VPP investigations is finding the sail concept providing the highest mean VMG, with focus on the upwind VMG, in design wind speed without the appearance of twist or flattening the sail. These boundaries make it possible to be able to sail in higher wind speed which might occur in gusts or even in several hours over the day. Therefore, the different ratios and dimensions of the 49er©, see Table (3.2.2), are used to get a design basis within the limited dimensions of the A. 1001VELAcup (2017). Different ratios, especially different main sail to jib ratios (50/50, 60/40 and 80/20) are investigated. The conclusion is an adjusted 49er© total upwind sail area ratio (70/30) is chosen, since unrealistic rig dimensions and worse mean VMG values are the results from above stated upwind sail ratios. Thus, the connections of upwind sail area and centreboard area, centreboard area and centreboard draft, rudder area and centreboard area as well as rudder draft and rudder area of the 49er© are set fix in the VPP input. Hence the sail area change in the input file of the VPP goes along with all ratios resulting in a simple smart optimisation process. Furthermore, a second focus lies on the mast height which is adjustable in the input of the VPP as well. The mast height opens the opportunity of applying higher ARs. Nevertheless, the limitation of it is done by using common sense. The higher the mast, the more weight, the more difficult to handle the skiff. However, the sail area has to fit into the rig dimensions as well, which limits the mast height regarding a lower bound. The Table 5.22 shows the different sail concepts, its upwind sail area and reasonable mast height range, which are investigated within the designing process. The Classic Concept implies a main sail, a jib and a gennaker, which is hoisted downwind. The reason to investigate upwind sail areas from 18 m2 to 24 m2 is to evaluate the opponents sail setup, see Table (3.4). For the VPP calculations the ORC aerodynamic coefficients are used for the main sail, jib as well as the gennaker and the hydrodynamic coefficients are imported from the CFD results, see Section (4.4.1). Investigating different total upwind sail areas combined with different mast heights show that the mean VMG increases with the mast height and the upwind sail area as stated in Table 5.23.

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Table 5.22: Diﬀerent concepts

Concept Upwind sail area [m2] mast height [m]

Classic 18-24 8-10 Two Sails 33 8-10 Three Sails 33 8-10 Jib 0 18-24 (33) 9,5

The larger the sail area, the higher the lift force resulting in a high driving force which is connected to a high VMG. Furthermore, the greater the aspect ratio (see Section 4.4.4.2) of the sail, the higher the lift force, which ends in an increase of the driving force as well. These connections lead to the investigation of the Two sails Concept with different mast heights. An upwind sail area of 33 m2 (23 m2 main sail area, 10 m2 jib) is analysed. The results, described in Table 5.23, in design wind speed show that the produced lift force is too high to be handled by the righting moment of two sailors. Twist and flattening of the sails occur. Also, changing the main sail shape to a triangular by lowering the luff height of the main sail for 25 % in the input file to reduce the CE or adjusting the mast height for the same reason does not result in a competitive VMG without twist or flattening. Reshaping the main sail also involves an extension of the boom length to still ensure the fitting of the main sail into the rig. Digging deeper into using the total sail area upwind, investigation of so called ’stay sails’ are performed. Stay sails are additional small sails between the jib and the main sail. They can enhance the performance of a skiff significantly. The driving force is increased by up to 12, 5 % depending on the AWA (D.J. Le Pelly, 2008). The idea is to use this advantage downwind and take down the stay sail when going up wind, still keeping a comparably large upwind sail area to handle. For the first VPP analysis of this concept a reasonable small mast height of 8 m is connected to a 14 m2 main sail, 13 m2 jib and 6 m2 stay sail. The calculations of the stay sail and the jib use the ORC jib aerodynamic lift and drag coefficient, see Section 4.4.4.1. The result, described in the Table 5.23, in design wind speed show a small mean VMG of 2.27 m/s as well as the occurrence of twist and flattening. Besides these facts, taking down the stay sail for the upwind course turns out to be difficult regarding forestay handling, rig tensions, taking down system and storage of the sail. The results, see Table 5.23, show that for the design wind speed the Classic Sail Concept is the best suitable. In almost all investigated setups neither twist nor flattening occur. The maximum VMG of the Classic Sail Concept is 2.38 m/s at a mast height of 10 m. This value is considered as competitive compared to the two other concepts. Regarding the twist and flattening of the sail the values are not acceptable. Lowering the mast height to reduce the heeling moment, though results in a non competitive VMG. Analysing the results of the Three Sails Concept neither the VMG nor the flattening and twist turn out to be competitive values, even with a low mast height of 8 m. Therefore, the Classic Concept is investigated further. To narrow the sail setup selection down, the mast height of 8 m is crossed out because of the high difference in the VMG values. Furthermore, two factors are taken into account: Firstly, the weight of the mast section, and secondly, the highest possible draft of the appendages. The adjustment of the centreboard draft is done by choosing a higher AR.

(1.4m)2 AR = = 7.69. 0.255m2

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Table 5.23: Systematic variations within diﬀerent Sail Concepts

Upwind sail area [m2] Mast height [m] mean VMG [m/s] at 3.5 m/s TWS TWIST / FLAT

Two Sails Concept 33 8 2,29 0 / 0,83 33 triangular 10 2,38 0,095 / 0,77 33 10 2,32 0,121 / 0,71 Three Sails Concept 27 8 2,27 0,031 / 0,95 Classic Concept 18 8 2,20 0 / 0 18 9 2,26 0 / 0 18 10 2,30 0 / 0 20 8 2.24 0 / 0 20 9 2.30 0 / 0 20 10 2.35 0 / 0 22 8 2.26 0 / 0 22 9 2.34 0 / 0 22 10 2.39 0,031 / 0 24 8 2.28 0 / 0 24 9 2.35 0,033 / 0 24 10 2.39 0,116 / 0,98

The centreboard area of 0.255 m2 is calculated by using the 49er© centreboard area to upwind sail area ratio, see Equation 3.1, with an upwind area of 18 m2. The centreboard draft 1.4 m results from reasonable hand calculations. Elaborating a smaller mast height variation step of 0.5 m within the investigation process leads to a preferable selection of the sail setup. The results of the Classic Concept with the higher AR is shown in the Table 5.24. The highest mean VMG is achieved with 22 m2 upwind sail area and a mast height of 10 m while 35.6% (0.089) twist occur. Taking into account the first factor, Per Wretlind from Seldén Mast states that the cross section has to be change though the weight per meter of mast increases by 0.05 kg/m when using a higher mast then 9.5 m. This increase has to be compensated by a higher mean VMG. The difference between the highest mean VMG in total and the maximum mean VMG regarding a mast height of 9.5 m is 0.02 m/s. Additionally, the occurring twist is lowered by the half to 16.4% (0.041). The higher weight as well as the higher twist results in huge disadvantage regarding the mean VMG compared to the increase of it by 0.02 m/s. The final sail set up is set to a 9.5 m mast height combined to a 22 m2 upwind sail area. This is split into a 16 m2 main sail and a 6 m2 jib. For finalising the setups performance result, the rudder area is adapted as derived in Section 5.3.1.1. The following polar plot show the performance of the chosen setup in different wind speeds. The last concept refers to the usage of the remaining sail area of the final sail setup. The classic downwind sail is called gennaker which is usually a light huge sail, which is hoisted sailing downwind. A new invention is called Code 0, which is a huge reaching sail designed for offshore racing. The third alternative is a way of combination of both sails. Called Jib 0, it is a sail which can be hoisted and taken down like the gennaker, but has the advantage of being able to be used upwind as well. The following polar plot shows the performance of the Jib 0.

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Table 5.24: Systematic variations with an centreboard AR = 7.69

Upwind sail area [m2] Mast height [m] mean VMG at 3.5 m/s TWS TWIST / FLAT

Classic Concept 18 9 2.29 0 / 0 18 9.5 2.31 0 / 0 18 10 2.33 0 / 0 20 9 2.30 0 / 0 20 9.5 2.36 0 / 0 20 10 2.38 0 / 0 22 9 2.36 0 / 0 22 9.5 2.39 0.041 / 0 22 10 2.41 0.089 / 0 24 9 2.36 0.077 / 0.978 24 9.5 2.38 0.103 / 0.956 24 10 2.39 0 / 0

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Formula Sailing VPP V17 22m2 cb adapted 9,50m AR,69 Polar Plot 7 TWA (deg) 0 10 7 20 TWS / Sailset 2 30 2.5 6 3 3.5 40 4 4.5 5 5 50 SS1 SS2 4 60 3.1418 3.0066 2.8558 BS (m/s) 3 2.6665

2.2843 70 1.9434 2 1.6442

80 1

0 90

100 -1.3508 -1.5504 -1.8085

-2.1104 110 -2.5106

-3.0484 120 -3.5814

130

140

150

160 170 180 27-Oct-2017 13:26:39

Figure 5.23: Final sail area and mast height dimensions

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Formula Sailing VPP V17 22 m2 cb adapted 9,50m AR 7,69 Jib0 Polar Plot TWA (deg) 0 10 7 20 TWS / Sailset 2 30 2.5 6 3 3.5 40 4 4.5 5 5 50 SS1 SS2 4 60 2.964 2.867 2.8725 BS (m/s) 3 2.7003 2.4844 2.1485 70 2 1.7734

80 1

0 90

100 -1.3502 -1.5497 -1.8085

-2.1086 110 -2.5069

-3.0437 120 -3.5768

130

140

150

160 170 180 03-Dec-2017 16:10:47

Figure 5.24: Final sail area and mast height dimensions using the Jib 0

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The polar plot shows, that the Jib 0 can not be used in wind speeds higher than 4.0 m/s without loosing mean VMG. However, up to 4.0 m/s wind speed the mean VMG increases compared to the mean VMG in Figure 5.23. Until a wind speed of 3 m/s the increase of mean VMG is 0.2 m/s. The detailed wind statistics (3.2) show an increase of the mean wind speed over the racing hours (11h to 17h), starting at ∼ 3.7 m/s, ending at ∼ 4.0 m/s.

5.2.1.2 Final Sail Concept After the investigation of different sail setup concepts combined different mast heights and its possibility of implementation, the final decision is a 22 m2 upwind sail area connected to a 9.5 m high mast, see Figure 5.25.

Figure 5.25: Final sail plan

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The sail area is divided into a 16 m2 main sail, a 6 m2 jib and a 11 m2 Jib 0. Regarding the sheeting, the main sail is sheeted on a rail in the aft of the hull, the jib is sheeted on a rail shortly in front of the mast and the Jib 0 is sheeted out on the racks extension. The sail shape is determined by the rig dimensions disregarding the main sail. It is shaped in a rectangular way having as much sail area as possible in the upper part. Furthermore, this shape makes it easier to twist the main sail.

5.2.2 Rig

The rig of a sailing dinghy is a complex part to design and optimise. This is the reason the R3 class rules allow outsourcing the rig design to an external company (A. 1001VELAcup, 2017). For the rig concept of this skiff, the expertise comes from Per Wretlind at Seldén Mast who takes care of the design. There are two rig solutions that could be an option for this skiff. One is the traditional rig, similar to the 49er© rig, and the second one is a diamond rig, used mainly on catamarans. These two concepts are based on different ways to handle the loads that the rig will be exposed to. The traditional rig is well used and a lot of the already existing skiffs, which are underlying these class rules, have something similar. This also shows that this type of rig works in reality. The diamond rig is not been used for mono hulls as first chose of design. By implementing this, some new ideas are brought into the design of the skiffs for 1001VELAcup. One feature of the mast, which will be unique, is the mast height. A mast height of 9.5 m is chosen based on the calculations from the VPP, see more information about this decision in Section 5.2.1.1. Since the mast is relatively high and needs to be built in aluminium, there is a risk of a heavy rig construction, as well as a high centre of gravity. The rig has to take care of the loads that are created from the sails, where mainly the side forces are important. For this, shrouds and stays are attached between the mast and the hull to make sure that the rig do not break or fall down. Because of this, the shrouds have a force pulling upwards. This force has its origin in the attachment point of the shrouds, the chain plates. Since the force is pulling upwards and the rig downwards, compression loads will occur.

5.2.2.1 Traditional 49er© rig The current rig that is used in the 49er© class is a conventional single spreader setup with top mast supporting jumper spreaders, which carries a large main sail on a fixed mast with a boom along the foot of the main sail. It also carries a smaller head sail, a jib, attached to the forestay. The standing rig is comprised of the mast and boom, which are stabilised in all directions by two or four shrouds, a forestay and a backstay. The fore- and backstay serves the purpose of providing the mast with the necessary longitudinal stability, while the shrouds stabilise the mast in the transverse direction. The shrouds are usually deflected backwards from the mast using a set of one or more spreaders in order to provide more longitudinal stability to the mast as well. By applying this rig design on the skiff the hull needs to be stiffened up due to the compressing loads that is transferred from the rig into the hull. Since these forces will occur and the hull needs to be stiffened up due to this, some extra weight will be added to the hull. In the case, where this design is applied on the skiff, the mast will both be heavier and higher than the 49er’s© mast. The rig will have a weight of about 25 kg, which is approximated from the weight of the 49er© rig of carbon fibre, that has a weight of 15 kg. By having both a higher and a heavier mast the skiff will be more unstable. This is something the sailor has to adapt when sailing.

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In this design there is a need to have a kicker that holds the sail down and maintain the correct shape of the sail. With this solution, the mainsheet just needs to change the attacking angle for the sail. To be able to hold down the boom, a kick is needed. This kicker is placed on top of the boom, why it is called gnav (vang, American word for kick, spelled backwards). When having this gnav, it needs an extra pair of shrouds that will be placed closed to the height of the boom, attached to the mast. This is because the gnav will contribute with bending moment at the mast and there will be a risk of buckling at this point. The possibility for movement in front of the mast will be limited by having the regular top shrouds to the deck together with the lower shroud. This makes it harder for the sailors to move in front of the mast, which can be needed in low wind speeds to change the CoG. This kind of rig is a proven and common solution, being used for the majority of small sailing dinghies. Therefore this is an alternative that is investigated.

5.2.2.2 Diamond Rig The design of the diamond rig looks as it sounds, the shrouds create a diamond shape around the mast. This rig is also able to carry the main sail as well as a jib and a Jib 0. For the mainsail it will have a boom that holds the sail out to get its shape. To stabilise everything, shrouds arranged in a diamond shape around the mast together with at least one pair of shroud out to the deck, will be used. These will make sure that the rig is stable in the transverse direction. For the longitudinal direction it will be stabilised with the help of the forestay, and some solution to be sure it do not fall forward, like an backstay. The diamond shaped shrouds around the mast are only attached to the mast and not to the deck. With this solution, the diamond shrouds will take care of the compression loads that occurs from the sail and by that, the hull does not need to be extra stiffened. To achieve the diamond shape, the spreaders will keep the shrouds out. The spreaders will at the same time be swept backwards, which will make the diamond shrouds to contribute to longitudinal stiffness as well. The outer shrouds to the deck will partly serve to achieve the longitudinal stiffness, but when the sailors are in the trapezes they will instead act as the shrouds that hold the mast straight. In the case the sailors are not in the trapezes the outer shrouds will be the ones that take the load and make sure that the mast will not fall. To solve the problem with the support in the longitudinal direction, the mainsheet together with the backwards swept shrouds or the trapezes will make sure that the rig does not fall forward. To make sure that the rig will have some kind of longitudinal support, the mainsheet can not be released too much in the case it needs to change sheeting angle of the sail. To solve this, the point touching at the hull needs a rail where the sheeting point can be transported on, to be able to change the sheeting angle. This solution with a rail in the aft makes it possible to sail without having a kick, since the sheet holds the boom down because it is connected to the most outer part of the sail. By this, the mainsheet acts as an backstay, main sheet, and a kicker. Since the rig is of the type free standing, it allows it to rotate around its own axis. This is a feature that is brought into the design. By doing this the interference between the mast and the sails is reduced since there is a smoother transition from the mast to the sail. As well as that the mast section will be in an attack angle against the wind and will contribute with lift force. By having the diamond rig, the mast can be seen as an individual truss structure with the mast and shrouds. This setup can therefore deliver a mast which can be both lighter and more

84 5 Design process slender than the traditional 49er© rig. The weight will approximately be around 15 kg for this concept. One problem that can occur by having this less robust mast is that there are risks for large deflections in the top of the mast, mainly from the Jib 0 but also from the main sail in upwind sailing. This will then affect the sail shape both for the downwind sail as well as for the main sail. This design is mainly used on multihulls where it is beneficial to have a free standing rig as this type. The reason for this is that the hull take less compression loads, therefore this solution is good for a multihull since then the hulls will not be pushed upwards due to the vertical component from the compression force. By applying this mast design on the skiff there will be less forces into the hull, why this is an alternative.

5.2.2.3 Bowsprit For the design of the bowsprit, the main factors that have to be considered are those that inﬂuence its dimensions. Mainly, it should be long enough so that there is at least 1 m distance between the jib and the jib 0. This condition is depicted below, in Figure 5.26:

Figure 5.26: Highlighted are the Jib 0 (red) and Jib (green)

As seen in Figure 5.26, the design of the bowsprit is not independent, being directly connected with racks. Its length is ﬁxed to a total of 1.6 m in total, and 1.1 m outside from the bow. Worth noting is that the bowsprit is also highly dependent on the sail plan and position of the mast, thus meaning that the design has also to be adapted to both of these elements. The attachment of the bowsprit to the hull is done by a tube through which it passes, which is then tapered with ﬁbers to the hull, as illustrated in Figure 5.27.

Figure 5.27: Schematics of the attachment of the bowsprit to the hull

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In order to obtain a preliminary design of the bowsprit, several assumptions have to be made regarding both it’s shape and structure, as well as theoretical assumptions in order to simplify hand calculations. Firstly, regarding its shape, it should be a conical section. This is motivated by the fact that this solution ensures that the bowsprit doesn’t progress forward of a certain point (in this case set to be when 1.1 m of the bowsprit structure is hanging forward of the forward-most point of the bow). This assumption is illustrated in Figure 5.28 below:

(a) Retracted bowsprit (b) Fully extended bowsprit

Figure 5.28: Diﬀerent levels of extension of the bowsprit, with the ﬁxed conical section highlighted in red

As observable, by increasing the diameter of the bowsprit aftwards and making the opening through which it passes (highlighted by the red lines) having the same dimensions than those of the thicker part of it, it cannot physically pass. In order to obtain a first estimate of the bowsprit’s diameters at both ends, as well as it’s thickness, basic beam theory calculations are performed. The assumptions needed to compute are: • The material properties considered are those of carbon-fiber • Even though it is not, the material is considered isotropic for the sake of simplicity on the calculations • The diameter variation is linear between both ends of the bowsprit • A stayed option is considered, where the bowsprit is stayed with a dyneema rope at half its length • Elementary case to be considered to represent the situation is a beam fixed at one end with a point load applied at the other (free) end • The load to which the bowsprit is subjected to is represented by a local load (of magnitude P) at its tip and inclined of an angle α = 73.58◦ on the x-direction. This represents the force that the jib 0 exerts locally The values used for the computations are summarized in Tables 5.25 and 5.26,

Table 5.25: Constants assumed for subsequent computations

3 LBS [m] PBS [N] ρ [kg/m ] σu [MP a] s.f. [−] 1.1 600 · sin(73.58) 1600 570 1.5

Table 5.26: Variables used for subsequent computations

4 rBS [cm] tBS [mm] IxBS [m ] 3 ∈ [2, 3] ∈ [2, 4] (π · rBS · tBS)

where LBS is the length of the bowsprit sticking out of the forward-most point of the bow,

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PBS is the point load a the tip of the bowsprit, ρ is the density of the material composing the bowsprit and σu is the ultimate stress of the material. The safety factor is represented by s.f.. Regarding the variables, rBS represents the radius of the bowsprit, tBS represents the thickness and IxBS the moment of inertia of the cross section. These factors are then inserted in Equation (5.4) in order to compute the resulting compressing stress at all points of the bowsprit, in an iterative process.

PBS · LBS σBS = · s.f. (5.4) 2rBS · IxBS

Finally, these values are compared with the ultimate stress considered in Table 5.25. The failure criterion chosen is a very simplistic one, it being that there’s failure if the computed stress is larger than the ultimate stress for the material (criterion formulated by Equation 5.5).

σBS > σu (5.5)

The results from computations applying this procedure for both the non-stayed and stayed (at 0.5 · LBS) cases is summarized in Table 5.27, for a bowsprit with a diameter going from 60 mm at the base to 40 mm at the tip, and with a thickness of 2 mm.

Table 5.27: Results from the Matlab computations

σBS [MP a] σu [MP a] Failure non-stayed 191 570 No stayed 96 570 No

So as easily verified by reading Table 5.27, the stress values on the component are well below the tolerated ultimate values, therefore meaning that the bowsprit could be in principle thinner. Yet, a thinner bowsprit isn’t considered for three reasons. First, these values for its diameter are already among the smallest manufactured by some companies. Second, it should have enough inner space for the attachments to slide through. Third, as this is a coarse approach, since in reality a composite is not isotropic, being constituted by several plies of fibers oriented in different directions, the results are not completely trustworthy, requiring further detailed analysis. This future analysis is further discussed in chapter 8. Another concept considered for the bowsprit was the rotating bowsprit. This concept consists on a pivoted bowsprit, that enables the Jib 0 to be at the desired shape for different angles of attack, by rotating the desired amount. The concept is depicted in Figures 5.29a and 5.29b. The bowsprit is pivoted around an axis, and the hull has to have a cut at the bow in order to allow the rotation. Through it, the attachments of the Jib 0 pass just like in the regular bowsprit. It can be seen that the staying of such a bowsprit can’t just be a dyneema rope due to the fact that it rotates. Also, two levers can be seen, whose function is to serve as attachments points for the ropes that would pull them. Due to the distance they would have had to be pulled, two horns would have to stick out of the deck, on top of which two wheels would be mounted in order to direct the rope. Such horns were never modelled given the fact that this concept was abandoned at a fairly early stage. This concept ended up being discarded. The main reason driving this decision is the fact that the sail plan consists on three sails. Therefore with the rotating bowsprit the distance between the Jib 0 and the jib would become small enough for it to be rendered inefficient.

87 5 Design process

(a) Rotating bowsprit-hull interaction (b) Pivot detail on top of the stiﬀeners

Figure 5.29: Rotating bowsprit concept model

5.2.2.4 Final rig design For the final rig design a diamond rig will be used. This is because with this solution the rig will absorb some of the compression forces by itself. This will make the hull lighter since it not needs to be stiffened up for these loads. Also by this solution, the rig itself could be lighter. Since the rig is made in aluminium the weight will be higher, saving weight is one important part when choosing the rig design. Since this concept allows the rig to be a rotating rig, this has to be investigated as well. To solve this, the boom will be locked in rotation around the z-axis, z-direction upwards parallel to the mast. By locking this when the boom is released with the sail, it will rotate the mast. This will be possible since it uses the generated force in the sails to rotate the mast. To stop the rotation of the mast, the rail for the mainsheet will be used. Since the rotation of the mast depends on the sheeting angle, the sheeting point will be moved onto the rail, and the maximum possible rotation will thereby be determined by the end of the rail. The height of the mast will be 9.5 m, this is calculated using the VPP, see Section 5.2.1.2. The boom will be between the mast and the transom of the deck. Compared to the sail, this means that the boom will go more aftwards than the sail. This to be able to have the the sheeting point on the the rail without a to big angle between the sheeting point on the deck and the boom. Trapezes is as well added to the rig to help the sailors to create more righting moment. These is also contributing with stability to the rig when they are in use. When they are in use they will remove the forces in the shroud and the compression forces comes from the sailors. To achieve more transverse stability to the rig, the shrouds will be attached out at the racks. This puts them further away from the centre line and gives therefore more stability. They will also be placed 1000 mm aft of the mast to also contribute with longitudinal stability to the mast. For the final rig design, see Figure 5.30. For drawings over the rig, see Appendix 8.2.5. To complement the mast and the boom, a bowsprit is stacked out from the bow. This will push the Jib 0 forward and extend the gap between the jib and Jib 0. In this way the sail performance is improved. The bowsprit will be one long piece made out of carbon fibre and will be retractable to be able to not have the whole bowsprit out when it is not in use. In the pulled out mode 1.1 m will be stacked out in front of the bow. With a total length of 1.6 m it will leave 0.5 m inside the hull when it is pulled out and nothing when it is retracted. The diameter is 40 mm at the tip and 60 mm at the base. See Figure 5.28 for the design of the bowsprit. The dimensions of the bowsprit is just made by simple beam theory and therefore it needs to be analysed by some FEM-software to make sure it does not break. This will tho be a future work. Also, the attachment to the hull needs to be decided later on.

88 Rig data no. M2211: FORMULA SAILING 2018 9.5M II

Customer: CHALMERS UNIVERSITY Sales manager: Per Wretlind Date created: 17-11-27 Latest revision: 17-11-30 Not approved 5 Design process For quotation only. Specifications may be changed in actual production

Figure 5.30: Final rig design, with the diamond rig

As mentioned earlier there are no limitations on the appendages designs according to the rules. As stated in Section 4.4.3, the induced drag of a wing, like a centreboard or rudder, decreases with increased aspect ratio, which means that a high aspect ratio is desirable for the design of both centreboard and rudder.

5.3.1 Centreboard and rudder

The design process of the centreboard and the rudder started by deciding the draft of the centreboard in the VPP. The choice centreboard draft has to be well balanced together with the mast height and sail area providing enough side force and keeping high aspect ratio without the need of depower the sails.

5.3.1.1 Planform When the draft is decided, the planform of the appendages is designed. Two diﬀerent planforms are designed, where both of the designs are based on theory for keelboat designs (Larsson et al., 2014) together with expertise from experienced skiﬀ designers. One of the planforms is designed with a straight chord line at 25 % of the total chord length from the front, keeping the same ratio at all points of the chord. With a straight chord line, the leading edge and the trailing edge need to have elliptical shapes in order to have a elliptical

89 5 Design process side force distribution over the centreboard and rudder. An elliptical side force distribution is desirable since the CD will in other case be higher and CL will be lower (Larsson et al., 2014). The other design is a trapezoidal form, based on the taper ratio, that is decided dependent on the sweeping angle that is being used. With a sweeping of 0◦ the taper ratio is recommended to be 0.4 (Larsson et al., 2014). The taper ratio is the ratio between the upper and the lower chord length of the wing.

C Taper ratio ≡ TR = 2 (5.6) C1

The approximate design of the two planforms is showed in Figure 5.31a and 5.31b.

(a) Straight quarter chord line (b) trapezoidal shape

Figure 5.31: Planforms comparison

The same planform design is used for the rudder as the centreboard. As stated earlier the rudder planform area is scaled to 50 % of the centreboard planform area.

5.3.1.2 Wing Profiles The selection of wing sections will largely be based on the leeway angle of the skiff, as shown in Figure 4.16. The lift of the foils are not dependent on the profile, but the drag of the profiles are, see Figure 4.14. This means that a suitable profile would be one that has low drag in the range of angles of attack where the foil is acting. If a profile can be selected so that the angles of attack are within the drag bucket, and that the drag bucket is as narrow as possible this would mean minimal drag, which is visualised in Figure 4.15. The leeway angle is an output from the VPP. The leeway angles at optimum VMG for different true wind speeds are visualised in table 5.28. Sailing upwind, the leeway angle will vary between around 2.9◦ and 3.2◦ and sailing downwind the leeway angle will be smaller than that. Since the largest leeway angle is approximately 3.2◦, the centreboard profile must have low drag up to this angle. In Figure 4.15, the NACA 65010 drag bucket is too narrow, the NACA 65018

90 5 Design process

Table 5.28: Leeway angle for diﬀerent TWS at VMG

TWS [m/s] TWA [◦] Leeway angle [◦] TWA [◦] Leeway angle [◦]

2 40 2.94 130 0.72 2.5 40 3.14 130 0.72 3 45 2.92 170 0.19 3.5 40 3.21 125 0.89 4 40 3.09 120 1.07 4.5 40 2.91 120 1.07 drag bucket is wide enough but has more drag than the NACA 65012 profile, which also has a wide enough drag bucket. Compared to other 12% thickness profiles, see Figure 4.14, the four digit series profile has lower drag at small angles but not at angles close to 3◦. The NACA 63012 and NACA 65012 have similar properties but the NACA 65012 seems to have slightly better properties than the NACA 65012 series profile. According to Larsson et al. (2014) the NACA 6 series is a good option in general for centreboards and rudders, since the NACA 65012 series seems to have the best properties in this case, it is selected for usage for the centreboard. Larsson et al. (2014) The leeway angle can not be used as the angle of attack for the rudder, the influence of the centreboard redirects the flow and the angle of attack will be smaller than for the centreboard. However, the rudder are not fixed to the hull but are used to steer the skiff. This means that the angle of attack for the rudder will vary more than for the centreboard, to account for this, the NACA 63012 profile is used rather than the NACA 65012 due to the wider drag bucket.

5.3.2 Racks

The design of the racks is based on the reference hulls in Section 3.2.4. Since most of the skiff is based on the 49er©, but slightly modified the racks will be so too. This is justified because it is shown that the 49er’s© design works, and that the crew will possibly be 49er© sailors so they will be familiar with the design. One feature brought from the 49er© is the height over the still water surface, since it works well according to 49er© sailors. One aspect to take into account is that the forward part should be high enough to not hit the water in case of either trim or heel. Since the racks are wider on the 49er© than allowed for the skiff, the height of the racks will be at the same height as the 49er’s© at the same corresponding width. One feature of the 49er© that is not brought to these racks is the solidness of the racks. This because it gives unnecessary increase in weight to the boat. From the rig design, see Section 5.2.2.4, the attachment points for the shrouds are designed on the racks. This configuration adds an extra force component to the racks. This force is pulling both forward and upward, reason why the racks need to be designed such loading condition. For the planform of the racks, inspiration is taken from the 14 Footer and existing skiffs com- peting in 1001VELAcup. This means that they are be built with tubes, so that it is possible to place them as far out as possible. The maximum distance from the centreline is be 1050 mm since this is half of the allowed beam(A. 1001VELAcup, 2017). For the length, the racks needs to be inside the LOA. A request from the 49er© sailors was to place the racks as far back as possible, why the end of the racks are at the same distance as the transom of the hull. The length of the racks is decided based on both sail performance and structural performance.

91 5 Design process

The position of where to attach the racks to the hull needs to be decided to design the concept. For this there are several options, on the deck, through the deck or freeboard and, at the side of a bulkhead e.g. If they in some way will go through the hull there will be a hole that has to be water tightened. Another problem is that the racks will be ﬁtted there permanent. By this it will be hard to replace them. Therefor the supports is attached on the deck where there is a bulkhead underneath. This to be sure that the forces acting on the racks will be taken cared of and transferred to the hull. For the dimensioning of the racks all the forces will be calculated with values according to Table 5.29. Where the sailors estimated gravity force is set to S ≈ 2000 N. The shroud force,PY , is set according to values in Section 4.3.5.2.

Table 5.29: Forces to dimension against

Force Value [N]

S 2000

PY 2600

The material that is used is aluminium EN-AW 6082 T6, with material data according to Table 5.30.

Table 5.30: Material data for Aluminium EN-AW 6082 T6 taken from Alutrade (2017b) ans Alutrade (2017a)

Material data Value

Young’s modulus, E 70 GP a

Yield stress, σu 290 MP a Density, ρ 2.71 g/cm3

5.3.2.1 Aft Support The desired location of the attachment point of the support is on a bulkhead to make it easier to attach and also to be able to take the forces that will be applied on the rack. Therefore, the attachment point was set to the most aft bulkhead since it is desired to have the racks as far aft as possible. It will be attached at the centreline on the longitudinal stiﬀener. There will also be an attachment point at the gunwale. Between these to attachment point the support will be horizontal to do not have curvature in to directions. The design of the attachments point will be done after this project ends. In an early stage one idea of having rotating racks was investigated. This idea build on having one attachment point at the centre line where it is able to rotate around. The two support arms for the racks are then attached to each other with a stay and a low angle between them. When the crew is moving from one side to another, the racks will be pushed down by the crew at the windward side and the leeward racks will be lifted up. This concept will not be implemented, but could deﬁnitely be investigated in the future. The reason for not implementing it is because it will be outside the maximum beam, but one option to solve this is presented in Section 8.2.4. For dimensioning the racks simple beam theory is applied to get both the reaction forces onto the hull and the stresses and forces in the support. In this case, load case is chosen as seen in Figure 5.32. Where R1 is the reaction force acting on the centreline, and R2 is the reaction force at the gunwale. The overhanging part a is the one from the gunwale to the rack. P is

92 5 Design process the load applied, in this case the sailor standing out at the end. This case is not totally perfect since it just is the support that is analysed and not the whole structure, as well as that the reaction force at the centre line should be a ﬁxed. This case was not found in elementary cases why the most similar was used to get some initial guess.

Figure 5.32: Analysed load case for the aft support of the rack

The reaction forces R1 and R2 according to Equations (5.7) and (5.8). These are decided to get the moment, Equation 5.9), in the support so the stress could be analysed. From this the diameter and thickness could be set.

P a R = (5.7) 1 l P R = (l + a) (5.8) 2 l Mmax = P a(at R2) (5.9) Mmaxr σmax = (5.10) Ix 3 Ix = πr t (5.11)

This is done by iterating over a diﬀerent diameters,D, and thicknesses,t, by making sure that they will pass the yield stress of the material, see Table 5.30. By using the maximum moment occurred in the rack, Mmax, the maximum stress could be calculated by help of the moment of inertia, Equation (5.10) respectively Equation (5.11). With forces according to Table 5.29 and a safety factor, SF = 1.5, the dimensions for the rack will be according to Table 5.31. These dimensions is corrected from calculations so there will be a manufacturer that can provide the proﬁle.

Table 5.31: Dimensions for the aft support.

Variable Value [mm]

D 55 t 2 L 1100

For the attachment to the hull there will be need of reinforcement due to the reaction forces. For this support the reaction forces will be R1 = 1.33 kN and R2 = 3.33 kN

93 5 Design process

5.3.2.2 Bow Support Since the rig design is constructed so the lower shrouds is attached out on the racks this will give forces pulling the rack upward and inward to the hull. To be able to handle this forces the racks supports has to be designed to be able to take the loads. The forces will contribute with both bending and compression. For the location of where the loads is acting, see Section 5.2.2.4 for the rig design. The load will act 1000 mm aft of the mast out on the racks. To be able to handle the compressing loads the support will be placed from the mast and 800 mm aft of the mast. It would have been preferred to have it to 1000 mm but then material would have been needed to be added. Underneath the support there will be a bulkhead to stiﬀ up the hull. This is done to be able the take care of the compressing loads from the racks, for more information see Section 5.1.6.3. This give the bow support an angle backwards from the mast. To get the racks in the correct height they have to have some kind of angle and the options is similar to the one for the aft support. This will be taken care of when designing the bow support. What also needs to take into consideration is that there will be a lot of ropes that will come from the forward part of the hull. This need in some way pass the support. Also the sailors need to be able to move smoothly in front of the support if that is needed in low wind. To be able tho get the sheets passing the support, the support will be one straight piece with angle increasing height. This is the geometry that will be dimensioned. This will be of a circular cross-section. For the bow support the dimensioning is using the same load case as for the aft support, see Figure 5.32. Therefore the equations for solving this will be the same. The force from the sailors is applied at the tip of the support out on the rack. Quite close to this point, 200 mm aft of the point the shrouds will be attached. This is discarded and will act as a safety instead, why the safety factor is set to SF = 1.0 in this case. This will give the dimensions according to Table 5.32. Table 5.32: Dimensions for the bow support

Variable Value [mm]

D 65 t 2 L 1250

For this support the reaction forces that the reinforcement need to handle will be R1 = 2.15 kN and R2 = 4.14 kN.

5.3.2.3 Rack beam The last part of the racks is the rack beam that runs between the two supports. The length of the beam should go as long aftwards as possible, according to 49er© sailor. This gives that the racks should go all way back to the aft, behind the aft support and create a overhang of 250 mm. The length in front of the forward support will mainly be decided by where the sheeting point for the Jib 0 will be attached onto the rack. This will for sure be in front of the mast, for more information about the reasoning about where to place it see Section 5.2.1.2. The rack beam will be analysed in two diﬀerent parts to see which one that is the most critical. The analysed cases are sailors between the supports, see Figure 5.33a, and sailors in front of

94 5 Design process the forward support, see Figure 5.33b.

(a) Loadcase for (b) loadcae 14

Figure 5.33: Planforms comparison

First analysed case is the sailors between the supports. The forces that is taken into account is the sailors weight downward and the shroud pulling upward. This gives reaction forces is calculated by Equation (5.12) and (5.13).

P (l − a) + P b R = 1 2 (5.12) 1 l P a + P (l − b) R = 1 2 (5.13) 2 l ( R1a if R1 < P1 Mmax = (5.14) Rb if R2 < P2

The reaction forces is calculated to get the maximum moment, Equation (5.14), and get the stress, Equation (5.10). By varying the diameter, D, and thickness, t, a design could be set that both passes the yield stress as well as having lowest weight as possible. This gives dimensions between the supports according to Table 5.33

Table 5.33: Dimensions for the beam rack between the support.

Variable Value [mm]

D 55 t 2 L 1110

To see which case that is the dimensioning the other load case is evaluated. For this the sailor will be placed att to most forward point which from a start point will be 1700 mm in front of the bow support. This to achieve the best possible sheeting angle for the Jib 0. The load case analysed in this case can be seen in Figure 5.33b. Where l = 1700 mm and a = 0 mm. This since the sailors will be places at the tip. The equations that is solved for the dimensioning are presented as Equations (5.15) and (5.16).

R = P (5.15)

Mmax = P b (at fixed end) (5.16)

From the maximum moment, Mmax, the maximum occurring stress σu, is calculated for diﬀerent diameters, D, as well for the thickness, t. This gives dimensions that is not possible to have since they are so much bigger than the part between the supports needs. This is calculated with a safety factor of SF = 1.5

95 5 Design process

Therefor the beam dimensions between the supports is used for this section as well. Therefor it had to be decided at wich position both of the sailors could be placed on. For this load case according to Figure 5.32 is used. In this the reaction forces is comes from the supports, why this not is conservative. By moving the sailors forward the will be allowed to move 500 mm in front of the forward support. But since the racks needs the extra part for achieving good sheeting angle they will in total be 1200 mm.

5.3.2.4 Final Rack Design The ﬁnal rack design is presented in Figure 5.34 with dimensions according to Table 5.34. There can though be some problem when the will be built. There can be some problem with mounting diﬀerent diameters together. One solution is to change the beam to the biggest diameter that is needed for the supports. Though, the bow support has some safety factor that has not been taken into account when designing, it is the shroud force that is pulling upwards. Furthermore, since the racks are up to date designed as a singular piece, a FEM-analysis is needed to be carried out to analyse the whole structure. More about this is Section 8.1.4.

Table 5.34: Dimensions of all the parts of the rack

Part Dimension Value [mm]

L 1100 Aft support D 55 t 2

L 1250 Bow support D 65 t 2

L 2300 Rack Beam D 55 t 2

Figure 5.34: Analysed load case for the aft support of the rack

96 6 Balancing of Final Design

After designing the single parts related to the hull, Section 5.1, sail and rig, Section 5.2 and the appendages, Section 5.3, a few details have to be considered while setting up a general arrangement, see Appendix 8.2.5, of the skiﬀ. Figure 6.1 shows the ﬁnal GA which is used as a basis for the building preparation.

Figure 6.1: General arrangement drawings of the skiﬀ

97 6 Balancing of Final Design

The stiffeners skeleton, as displayed in Section 5.1.6.3, is the result of the balancing of the different elements dimensioned during the project. The second transverse bulkhead from the bow is in fact placed right below the mast foot at a distance of 1.70 m aft from the bow. Such distance is scaled, for the current skiff, from considerations made on the mast positioning on a 49er©. Therefore, knowing the stability and good handling properties of the 49er©, the current skiff is expected to present similar properties. Right in front of the mast is placed the rail for the self-tacking jib. Hence, this second bulkhead is directly asked to provide support to the forces transferred from the rail to the hull. Moving toward the stern, bulkheads are strategically distributed and designed to not only structurally support the hull itself, but also provide additional support to the racks, the appendages and the sheeting points. In order to provide the best support to the forces transmitted to the hull by the racks, bulkheads are therefore positioned right below their attachment portions. Hence, the diagonal bulkheads spread from the mast foot and follow exactly the direction of the front attachment of the racks. One innovative feature of this skiff is that the front part of the racks is used to place the shroud attachment. With this solution, the shrouds are placed further out and will decrease the compression load of the rig and stabilise it, since the side forces will be greater. To provide additional stability in longitudinal direction, upper dyneema shrouds, starting at the top area of the mast and reaching the lower shroud attachment on the racks, are added. The most aft bulkhead provides instead support to the back attachment of the racks. This bulkhead is also given the task of supporting the main sheet, which is positioned in order to provide the crew with as much clear space as possible. Right beyond the last bulkhead the rudder is positioned. Opposed to more common solutions, the rudder is located under the hull. The reason for such solution is given by the consequent elimination of interference with the water surface. This provides a better inflow on the rudder blade resulting in more lift and less resistance. Once the mast and the rudder are set into position, considerations can be made on the placement of the centreboard. Such is critical in order to not compromise the capability of steering manoeuvres, as the higher the distance between rudder and centreboard the higher the lever. Hence, higher lever produces a higher steering moment. Furthermore, the lever is constrained by the lead, which describes the distance between the centreboard and the CoE of the sail area. Analysing reference skiffs and dinghies the lead is set to 8 %, see Table 3.5. Finally, local additional reinforcements are placed in correspondence of all the high load attachment points.

98 7 Building process

In this chapter the building process is explained in detail. The parts that are covered are the designing and assembling of the templates, followed by the planking of hull and deck, as well as their lamination and of the stiﬀening structure.

7.1 Templates

The first step in the building process is to design the templates from the final hull shape. One set of templates is designed for the bottom and freeboard while another is designed for the deck. The templates are designed in Rhino 3D using the final hull design as a reference. Each of the bulkhead templates is placed within a distance of 230 mm from the the neighbouring template(s). The smaller the distance between them, the more accurate will the shape of the hull be, therefore if a bigger distance would have been used, the precision when it comes to shape of the hull would be lost when planking. To obtain the desired shape of the aft part of the hull, one more template is placed in the aft, making the template model 230 mm longer than the actual hull. When designing the templates, all joints have a gap of 0.15 mm as a tolerance in order to make the assembly easier. Furthermore, all the inner corners have to be made with so called ’dog bones’, which have a diameter of 6.2 mm. This is due to the cutting process, where sharp inner corners can not be made due to the milling bit being circular, see Figure 7.1.

Figure 7.1: Dog bones in one of the deck’s template

When the design of the templates is done, they are ordered in Medium Density Fibre boards (MDF) that are 16 mm thick. The MDF boards are later assembled into the full scale template plug using epoxy to glue them together. A model of the ﬁnal design of the templates and a picture of the assembly can be seen in Figures 7.2a, 7.2b, 7.3a and 7.3b. Furthermore, templates for the bulkheads and stringers need to be ordered. These components are to be mounted and cut over these templates. This process is described in the following section dealing with planking.

99 7 Building process

(a) Model of hull templates (b) Model of deck templates

Figure 7.2: Templates models in Rhino 3D

(a) Templates for the hull (b) Templates for the deck

Figure 7.3: Template assemblies used for planking

7.2 Planking

The entire hull structure of the skiﬀ will be built in a composite sandwich. The core will be built using balsa wood. The following sections will describe the process of building the balsa core for the diﬀerent parts of the hull.

7.2.1 Planking the hull and deck

The planking process starts once the templates are assembled. Balsa-planks with 8.8 mm thickness to leave a margin for sanding, 45 mm width and 2.5 m in length are used. The planks are placed on top of the templates and bent along their curvature in order to achieve the desired shape. At the joints and sides of the planks, ﬁsh glue is used to glue the planks together. During the curing process of the ﬁsh glue, the planks are held in place by screwing them to the templates. To prevent the screws from damaging the planks and also to distribute an even pressure around the screw, small blocks of divinycell are placed between the planks and the screws. This can be seen in Figure 7.4.

100 7 Building process

Figure 7.4: Planking with divinycell blocks

When the planking is done and the ﬁsh glue is cured all the screws and divinycell blocks are removed and the hull is faired using sandpaper and a planer. This process is important in order to get the surface as smooth as possible when starting the laminating process. The faired hull core can be seen in Figure 7.5.

Figure 7.5: Faired hull

7.2.2 Planking the internal structure

In order to build the bulkheads and stringers diﬀerent pieces of the balsa core are cut and arranged so they cover the entire bulkhead template. See Figure 7.6 for an example where the largest stringer template is covered with balsa pieces that will constitute its core.

Figure 7.6: Bulkhead template completely covered with balsa for the core

101 7 Building process

The pieces of balsa that are then glued together and ﬁxed with blocks of divinycell like the hull. Once the glue sets and the divinycell blocks can be removed, the balsa is aligned with the template underneath and clamped together being ready for trimming. The contour is then cut into the balsa by making use of a router machine. An example of half a bulkhead core after cutting is presented in Figure 7.7, where the shape was followed and the edges were ﬁlleted by the router.

Figure 7.7: Finished half-bulkhead core

The need for ﬁlleting the edges arises from the concern of having a smooth ﬁbre transition through those edges when laminating later. The lamination process is covered in the following section.

7.3 Lamination

The general process of laminating the components of the skiff is hand layup of the fibre and epoxy, followed by vacuum bagging of the laminate during curing. Specific details in the process are described in the following sections.

7.3.1 Laminating the hull and deck

The lamination of the hull uses the finished planked and faired core as the starting point. The two skins of the hull will be laminated in two turns, starting with the outer skin. When the outside of the hull is sanded and faired, it is detached and removed from the templates. A sheet of plastic is then spread out over the templates, and the hull core is put back into place again. This sheet of plastic will create an air-tight seal on the inside of the hull, which allows for the usage of the vacuum bagging method. This method uses vacuum to create a well saturated fibre layup with evenly spread out epoxy resin. It also allows for some extraction of excess resin. With the inside of the hull sealed by plastic, it is ready for the outer skin to be laid up. The likely method laying up will be to prepare all plies and saturating them with epoxy resin on a flat surface in advance. The wetted layup is placed between two sheets of plastic to make handling easier. The layup is then carried and placed on top of the hull, making sure it lies in contact with the hull in all places. Naturally, the two sheets of plastic used during the layup are removed after this step. A new sheet of plastic is then used to cover the hull. An air tight seal is created between the two sheets that now surrounds the hull, only leaving a hole where a vacuum pump is connected. When the pump is turned on it will force the two sheets to press down on the wet laminate, spreading the epoxy resin evenly across the hull and through the thickness of the fibres. This

102 7 Building process setup is then left to cure in a heated atmosphere. The heat is needed for the epoxy to reach its maximum strength properties. After the epoxy has set, the vacuum bag is removed and the inside of the hull is ready to be sanded, faired and laminated in the same fashion. The deck is laminated on a fabricated female mould using the same method as the internal structure, of which the method is described in Section 7.3.2.

7.3.2 Laminating the internal structure

The components of the internal stiffening structure, the stiffeners, are laminated in a slightly less cumbersome way than the larger hull and deck. The stiffeners are also laminated using the vacuum bagging method, but their size allows for the whole component to be laminated in one step. A set of templates that have the same contours as the stiffeners are milled in an MDF-based board which has very smooth surfaces in another material to help in releasing the hardened epoxy. These templates are placed on a table. The epoxy resin is then applied on the template and covered with the correct layup of fibres. The balsa core, that has been cut to correct dimensions prior to the lamination, is placed on top of the fibres on the template. The other skin is then placed on top of the core. All edges of the core are covered with fibres which are shaped as a flange, mentioned in Section 5.1.6.3, around the edge of the template underneath. The component and laminate is then covered with a sheet of plastic, taped air tight to the table, and then connected to a vacuum pump. The setup is finally left under vacuum until the epoxy cures. The concept is visualised in Figure 7.8.

Figure 7.8: Layup procedure of stiﬀener component.

7.4 Further Building

At the time of writing, several construction details are left to build. The building process of these parts diﬀer from the techniques described in previous sections. These new building processes will be described brieﬂy in the following sections.

7.4.1 Rudder and Centreboard

The rudder and centreboard will be manufactured using a different kind of building technique compared to the hull structure. This is because of the higher demands on the appendage surfaces due to the desired properties of the water flow during operation. One of the best methods to obtain a smooth surface is to manufacture the appendages in halves, using CNC- milled aluminium female moulds. The halves are then joined around a honeycomb or foam core to make the finished part. The material used for the appendages will most likely be carbon fibre due to its high strength to weight ratio. As mentioned before, the updated R3 class rules

103 7 Building process allow this choice of material since there are no restrictions regarding material content for the appendages.

7.4.2 Racks

Since the racks can be built in aluminium as long as they comply with the rule of 70 % of natural material they are designed to be build in aluminium tubes(A. 1001VELAcup, 2017). Since the racks contain three parts of different shape they have to be fitted together. The method of joining the aluminium parts is still to be determined. The most likely solution will be a mix of welding and blind riveting. The finished racks will be attached to the hull using epoxy and flax fibres and possibly rope where applicable. To get the shape of the aft support, see Section 5.3.2.1, the tube will be bent.

7.4.3 Bowsprit

The bowsprit is allowed to be made out of carbon ﬁbre, and since it assumes a conical shape, as mentioned in Section 5.2.2.3, the method for building shall be roll wrapping. It consists on wrapping sheet of pre-impregnated ﬁbres (pre-preg) onto a mandrel, according to desired layers and angles. Then it is pressurised and heat cured to solidify. After solidifying the shape is extracted from the mandrel. This process is generally used for small to medium diameter tubes, that is from around 6 mm to 30 mm diameter, up to 2.5 m length, (west composites, n.d.).

104 8 Future Work

Due to the limited time available for the project, some work and investigations will inevitably have to take place further on in time. The following chapter will cover both work that needs to be done within the current project, as well as investigations that lie outside of the project scope but may be interesting to look at in future projects.

8.1 Remaining Work

Although the main part of the project is ﬁnished, there is still some design work left to be done in order to be able to produce a complete skiﬀ. This work has to be done parallel to the remaining building work, mentioned in Section 7.4. The remaining design work is covered in the following sections.

8.1.1 Sails

The plan form of the sail is set from the VPP program, see Section 5.2.1.2. Since the design for the sails are not done yet, some concept for handling of them is not decided. Therefore, some of the future work is presented at this section.

8.1.1.1 Jib 0 and jib handling The choice of using Jib 0 as a down wind sail that possibly can be used upwind sail as well is preferred. In the case the wind is too strong, the Jib 0 is just used on the down wind legs. For this, the Jib 0 has to be stored on the deck when going upwind. The system for this has to be decided. One idea for this is to furl it around the stay and then take it down onto the deck. The same problem will occur if the Jib 0 is used in upwind. In this case the jib and the Jib 0 will come to close to each other why the jib has to be taken down. Furling is one option to store the jib for the upwind leg. For making the handling of the jib easy it will be kept on a self tacking rail. By this the position will be close to the mast, and out to the freeboard. Another investigation is done on the shape of the jib which might be adjusted to a fat head jib, making it easier to trim. Both the systems, for the jib and Jib 0, are decided before the skiff will go out on sailing. To be able to use the Jib 0 both upwind and downwind the sheeting point has to be able to be moved around. The solution for this is not decided and has to be designed. Two options that should be investigated are the extend of the rail for the self-tacking jib so the sheeting point for the Jib 0 also will be attached on this and a flying sheeting point which will be fixed by sailing upwind

8.1.2 Local Reinforcements

Structural calculations that remain are those regarding local reinforcements of the hull where the basic construction may not be suﬃcient. One such point on the hull is the mast step where the mast rests on the deck. This is one of the highest loaded parts of the hull and needs to be reinforced accordingly. As mentioned in Section 5.1.6.4 the internal structure of the hull will most likely be able to support this load. However, the balsa core of the deck in this point will most likely be compressed beyond acceptable levels, which is why it will have to be replaced by

105 8 Future Work a stiﬀer material. The current options are to either use a stiﬀer wood core, or simply making a small area just underneath the mast step out of solid laminate. The decision is still to be made. Another high load point of the hull is the one where the rudder is attached to the hull. This point is positioned slightly aft of the transom, which means that some sort of supporting structure has to be designed in that position. There are still some uncertainties concerning the attachment of the standing rigging as well as the attachment of the racks to the hull. These attachment points are also yet to be designed and dimensioned. The design process of these attachment points will take inspiration from existing solutions on high-end sail racing boats and adapting these to the material options that are available, as well as the geometry of the hull.

8.1.3 Structure of Centreboard and Rudder

The centreboard and rudder need to be dimensioned and analysed using the FE-software Abaqus CAE just like the rest of the structures. A big difference is the separate rules regarding the material content. A late change in the R3 class rules now allows appendages to be fully made from carbon fibre composites, in addition to the bowsprit which already allowed the usage of carbon fibre. This change in the rules will allow for these parts to be designed at a lower weight than what would have been possible otherwise. Naturally, this will affect the structural calculations that have been carried out up to this point, as well as coming calculations.

8.1.4 FE-Analysis of Racks

Regarding the racks, some further structural work needs to be done. This work concerns the attachment of the racks to the hull, as well as FE-analysing the racks themselves. For the FE- analysis the whole rack structure should be investigated since the preliminary design looks at each member separately, and only using basic beam theory in hand calculations. The analysed load cases should be the following. 1. Sailors not on the racks • Pulling force from the down wind sail and, • Shroud force pulling upwards and inwards 2. Sailors as far forward as allowed, in trapeze • Sailors at a point 500 mm in front of the forward support, • Pulling force from the down wind sail and, • Shroud force pulling upwards and inwards 3. Sailors as far backward as allowed, in trapeze • Sailors at a point 250 mm back of the aft support, • Pulling force from the down wind sail and, • Shroud force pulling upwards and inwards 4. Sailor at the mid of the racks, • Sailors placed at 600 mm aft of the forward support, • Pulling force from the down wind sail and, • Shroud force pulling upwards and inwards

106 8 Future Work

8.1.5 Structure of Bowsprit

Given that the bowsprit’s structural characteristics do not affect any of the other different components of the skiff, only its main dimensions are needed during the design process. For this reason, a FEM analysis needs to be conducted as future work, in order to access the desired characteristics, such as the fibres orientation, number of plies and their respective thicknesses.

8.1.6 Deck Layout

Designing and building a skiff implements the point to make it run as well. After designing, building and joining all the individual parts an operating system on the deck is installed. The main sail is sheeted with a block on a rail at the stem connected to a block on the end of the boom. This sheeting replaces the kicker and can be adjusted via the main sheet. A rope which goes out to both sides of the racks is used to move the block on the rail veering the main sail. The trapezes are fixed with stretching ropes on the racks. Next to the mast and still reachable from the racks, the sheet of the selftacking jib is mounted and spread to both sides. The jib is sheeted over a block sliding on a rail, which is installed closely in front of the mast. Next to jib sheet, the system to hoist and take down the Jib 0 is installed. This system is connected to the retractable bowsprit and the Jib 0 storage making sure that the bowsprit is retracted when the Jib 0 is stored in the hose and extended when the Jib 0 is set. The Jib 0 is sheeted on the top part of the racks extension to enable the best wind attacking angle possible. Furthermore, the Jib 0 sheet is connected to a floating sheeting point between racks and hull for being able to use the Jib 0 upwind with a perfect sheeting angle as well. To make sure that all these system is working together, all the system has to be implemented in the GA. This to make sure that the ropes do not cross each other as well as the do not interfere with each other in a bad way. Therefore it has to be more investigated in the future.

8.2 Future Investigations

Many concepts have been mentioned during the project, but not all have been investigated. There are several reasons for this. Some concepts did not seem plausible, and many would take too much time from designing a proper hull. The fact that these concepts have not been investigated does not mean they are not interesting in the project context, which is why they are mentioned in this section for future reference.

8.2.1 Hull Fluid Dynamics

During the process, a proper CFD analysis has not been carried out as far as it regards the shaping of deck, freeboard height, and transom. Bethwaite (2008) has been used as a reference when alteration of the transom have been computed. Moreover, given the satisfying results obtained with the ﬁrst sloped transom, no further analyses has been implemented. The alter- ations that saw a lowered freeboard have been on the same track. Finalised the optimisation of the hull in terms of submerged portion, the freeboard has been cut lower. The interaction between the lowered freeboard and the sloped transom determined a further improvement in the performances of the skiﬀ, however no systematic variation of these two geometries and their interaction has been carried out. It might therefore be worthwhile investigate such combination of solutions in order to achieve an optimal ratio between the two components. The introduction of the cambered shape for the deck has been considered in terms of ergonomics advantages for the sailors, in order to avoid in total the presence of water on board and to

107 8 Future Work improve structural properties of the complete geometry. The contribution to total dynamic resistance has however not been computed, therefore such shape is probably not optimal and a further step in terms of CFD computations has definitely to investigate such solution. Furthermore a study on boat-tailing the skiff should also be conducted, as it might prove beneficial from a resistance point of view. Moreover a global resistance prediction, considering the hull complete with appendages, should be carried out. Time limitations and set up complexity have however prevent the implementation of such computations and therefore hydrodynamic optimisation under such point of view. Different CoG, therefore different trim angles, have been assigned to specific speeds. It has not been evaluated however a variation of the trimming conditions within a fixed speed. Future investigations can focus on such aspect and optimise the configuration of the skiff while sailing.

8.2.2 Wing Sails

The usage of wing sails on the skiff instead of a traditional rig and sails is allowed in the R3 class rules. A wing sail can be made as a hard wing consisting of two or more hinged vertical elements, or as a soft wing where the wing surfaces are made from regular sail cloth. The common trait for the two alternatives is the lack of standing rigging, and the variable camber of the wing. A wing sail is more efficient than a traditional rig and sail and is affected by induced drag to a much lower extent due to the more efficient square or elliptical planform, as opposed to the triangular planform of an ordinary sail (Nielsen, 2014). The main obstacle when using a wing sail in the design however, is that the R3 class rules state that this kind of sail must be designed and built by the project group. Aside from the high difficulty of building an advantage bringing wind sail, a considerable amount of workload is added. Furthermore, a certain amount of water hours are needed to perfect the handling of this sail. This may not be a problem if an existing hull is retrofitted with a wing sail.

8.2.3 Foiling

It has been proven and shown in practice that making a boat sail with its hull completely emerged (to foil), only resting on a set of hydrofoils attached to the lower end of the appendages, is entirely possible. Recently, even an optimist dinghy could be made to foil with some modification (Andersson et al., 2017). This opens up the future possibility of designing a foiling skiff, since the design of the appendages is completely unregulated in the R3 class rules. If such a design could be made successful, it would give a great advantage to the team. The idea of designing a foiling skiff in this project was dropped very soon in the initial stages since it would add a considerable amount of work to an already work intensive project. It was decided instead to design a more traditional skiff in order to focus fully on the hull design. Adding foils would most likely need the hull to be altered in order to provide optimal hydrodynamic performance. The possibility to use foils could however be interesting in future projects where more time can be spent on evaluating new alternatives to the design. There is already a bachelor thesis available at Chalmers University of Technology where the option of adding foils to the current skiff will be evaluated (Larsson, 2017).

8.2.4 Rotating Racks

As mentioned in Section 5.3.2.1 one opportunity is to implement a rotating system if the racks. This is crossed out due to the fact that it was not possible at that stage in the project to have

108 8 Future Work rotating forward support as well. Cause in the case it was just the aft section that was rotated it gave a to wide beam. If it is possible to get the forward support rotating this should be one thing to investigate, cause then it is possible to earn some lever arm for the sailors. This will help to create a higher righting moment which gives the possibility to have more sail area. At the same time the system can be built in to rotate the mast to the windward as well. This will give even better sail performance since then the projected sail area will be larger than it would have been in the case if the rig has some heeling angle.

8.2.5 Rotating Bowsprit

Furthermore, the rotating bowsprit concept mentioned in Section 5.2.2.3 is of great interest, as having the sails at their desired shape increases their eﬃciency. Therefore a study on the combination of such a bowsprit with a two sails plan is of potential interest to be carried out in the future.

109 8 Future Work

110 References

1001VELAcup. (2017). Istruzioni di regata. Retrieved 2017-12-03, from http://www .1001velacup.eu/images/documenti/EVENTO-2017/IDR%201001%20VELA%202017.pdf 1001VELAcup, A. (2017). Norme speciali di classe r3. Retrieved 2017-12-6, from http:// www.1001velacup.eu/regolamento/regolamento-di-classe.html ABAQUS/Explicit. (2017). Abaqus documentation [Computer software manual]. Vélizy Villa- coublay, France.. Adam Persson. (2017). bowspritcompetitor. ([Picture; September 29, 2017]) Agarwal, D., Bhagwan, Broutman, J., Lawrence, & Chandrashekhara, K. (n.d.). Analysis and performance of fiber composites. Wiley. Alutrade. (2017a). Fysikaliska värden. Retrieved from https://www.alutrade.se/ fysikaliska-varden/ ([Online; accessed November 29, 2017]) Alutrade. (2017b). Hållfasthetsvärden, extruderat. Retrieved from https://www.alutrade.se/ hallfasthetsvarden-extruderat/ ([Online; accessed November 29, 2017]) Andersson, A., Barreng, A., Bohnsack, E., Lundin, L., Sahlberg, R., Werner, E., . . . McVeagh, J. (2017). The foiling optimist. In The proceedings of the 4th international conference on innovation in high performance sailing yachts, lorient, france, 28-30 june 2017. (p. 19-30). Bethwaite, F. (2008). Higher performance sailing: Faster handling techniques. Bloomsbury USA. Bethwaite, F. (2010). High performance sailing: Faster racing techniques. Bloomsbury USA. Calderon, A. A., & Maskew, B. (2015). Transonic Hull: Theory, Validation, Breakthroughs and Applications to Ships. Cardolite. (2017, December). Formulite. Retrieved from https://www.cardolite.com/ formulite Castegnaro, S., Gomiero, C., Battisti, C., Poli, M., Basile, M., Barucco, P., . . . Lazzaretto, A. (2017). A bio-composite racing sailboat: Materials selection, design, manufacturing and sailing. Ocean Engineering, 133 (February), 142–150. CD-Adapco. (2017). Star-ccm+ (12.04.11 ed.) [Computer software manual]. CDIO. (2017). Cdio. Retrieved 2017-12-06, from http://www.cdio.org/ Creative, F. L. (2012). 49er full realistic model - january 2012. Retrieved from http:// www.9eronline.com/library/ ([Online; accessed October 12, 2017]) DeSantis, M. (2016). Progetto di una imbarcazione classe r3 per la regata 1001velacup. D.J. Le Pelly, R. F., L. Kjellberg. (2008, dec). The effects of staysails on yacht performance. In 3rd high performance yacht design conference (p. 247-256). Eike Jacobs. (2017). 49erbowsprit. ([Picture;, November 6, 2017]) Henry P. Moreton, C. H. S. (1992, July). Functional optimization for fair surface design. Computer Graphics. Imeche. (2017). Formula student. Retrieved 2017-12-07, from http://www.imeche.org/ events/formula-student ISO. (2015). NWIP, Small craft - Scantlings - Part 7: Multihulls (Tech. Rep.). Author. Kaupp, R. (2007). A 49er, fast sailboat. Retrieved from https://commons.wikimedia.org/ wiki/File:49er_sailboat.jpg ([Online; accessed December 6, 2017]) Larsson, L. (2017). Formula sailing – en flygande kappseglingsjolle? Re- trieved from http://www.chalmers.se/sv/institutioner/m2/utbildning/ kandidatutbildningar/PublishingImages/FORMULA%20SAILING%20%e2%80%93%20En% 20flygande%20kappseglingsjolle.pdf ([Online; accessed December 7th, 2017])

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Larsson, L., Eliasson, R., & Orych, M. (2014). Principles of yacht design. Bloomsbury Pub- lishing Plc. Larsson, L., & Raven, H. (2010). Ship resistance and flow. Society of Naval Architects and Marine Engineers. Mancuso, A., Pitarresi, G., & Tumino, D. (2017). Using FEM simulation to predict structural performances of a sailing dinghy. International Journal on Interactive Design and Manufacturing, 1–12. doi: 10.1007/s12008-017-0427-7 McNeel, R. (2017). Rhino 5 features. Retrieved 2017-12-02, from https://www.rhino3d.com/ features Newaz, G., Mayeed, M., & Rasul, A. (2016). Characterization of balsa wood mechanical properties required for continuum damage mechanics analysis. Proceedings of the Institution of Mechanical Engineers Part L: Journal of Materials: Design and Applications, 230 (1), 206-218. Nielsen, P. (2014). Have wingsails gone mainstream? Retrieved 2017-12-03, from https:// www.sailmagazine.com/diy/have-wingsails-gone-mainstream Offshore Racing Congress, . (2016). Orc vpp documentation. Persson, A. (n.d.). Resistance from towingtank test for a 49er. Persson, A. (2017). 1001 VELA Cup existing skiff rack. Pitarresi, G., Tumino, D., & Mancuso, A. (2015). Thermo-mechanical behaviour of flax-fibre reinforced epoxy laminates for industrial applications. Materials, 8 (11), 7371–7388. R.M.N. (2017). Velocita’ e direzione del vento. Retrieved 2017-10-03, from http://www.mareografico.it/?session=0S1584794367D886587866680P&syslng= ita&sysmen=-1&sysind=-1&syssub=-1&sysfnt=0&code=STAZ&idst=12 Versteeg, H., & Malalasekera, W. (2007). An introduction to computational fluid dynamics: The finite volume method. Pearson Education Limited. Wahab, M. A. (2017). Interpolation and extrapolation. west composites, R. (n.d.). Roll wrapping. Retrieved from https://www.rockwestcomposites .com/custom/processes/roll-wrapping ([Online, accessed December 07, 2017]) Wikipedia. (2010). 49er. Retrieved from https://commons.wikimedia.org/wiki/File:49er _skiff.svg ([Online; accessed December 2, 2017]) Wilson, R., Carrica, P., & Stern, F. (2006, June). Unsteady rans method for ship motions with application to roll for a surface combatant. Computers Fluids, 35 (5), 501-524. Windguru. (2017). Archive wind statistic. Retrieved 2017-10-03, from https://www.windguru .cz/archive.php?id_spot=11912&id_model=3 WorldSailing. (2017). World sailing classification. Retrieved 2017-12-07, from http://members .sailing.org/classification/

112 Appendix A - Drawings

1. CFS 2017/2018 - 0 - General Arrangement 2. CFS 2017/2018 - 001 - Hull Drawing 3. CFS 2017/2018 - 102 - Deck Drawing 4. Seldén Mast - Rig Drawing

Rig data no. M2211: FORMULA SAILING 2018 9.5M II

Customer: CHALMERS UNIVERSITY Sales manager: Per Wretlind Date created: 17-11-27 Latest revision: 17-11-30 Not approved 1000 For quotation only. CAP Specifications may be changed in actual production 8720 General rig description D3 8410 Double diamonds with lower shrouds FS Conventional Untapered ø3 11,2° Rig dimensions 1/4" Forestay height FH: 8 550 mm D3 mm Main sail luff length P: 8 700 ø3 Boom height above deck BH: 800 mm CAP 15,8° Main sail foot length E: 2 340 mm ø3 6,5° 2850 mm Main boom sheet pos S: 2 595 1/4" Chainplates dist. from cl mast Lateral Long Cap shrouds: 1050 1000 mm (43,6°) Lower shrouds: 1050 1000 mm (43,6°) Forestay: 1700 mm 800 Deck above chainplates: 0 mm P35 Linked Deck above waterline: 246 mm Craft data and righting moment CATAMARAN Length: 4 600 mm Beam: 2 100 mm RD2 10,7° C-C Hulls: 2 100 mm M24 Displacement: 310 Kg

LWR 2850 Equipped boat ø3 Dimensioning RM: 3,2 kNm 10,0° 1/4" Spar sections Mast: C069 Boom: B087 No kicker Square mainsail roach 2:1 purchase for main halyard 800 P35 Masthead gennaker and code zero OK 2:1 purchase system for code zero halyard Furlex Forestay: X Notes (17 lines) Rig setup for Chalmers University Formula sailing RD1/V2 competition 2018. 2850 ø3 17,3° 1/4" Total sail area with gennaker app. 33m2

Monohull with max length 4600mm, max beam 2100mm RD1 400 2x75kg crew in trapeze at cap shroud fitting 8720 Total length: 9550 (800+8700+50)

Rotating mast, main boom to be fixed to the mast in Diamond angle: 17° rotating direction.

Main boom Spin poole S038 main sheet fitting on mast S1=2500 Sheet lead block position on boom to be set. (section requirement may be changed) Panel 1 = 3250, Panel 2 = 2900

VI Appendix B - Plots

B.1 Max beam position vs Resistance

(a) Max beam position vs Resistance at 12 kn (b) Max beam position vs Resistance at 15 kn

Figure B.1: Max beam position vs resistance. Red stars mark measured data; Blue line is the ﬁtted resistance curve

B.2 Max draft position vs Resistance

(a) Max draft position vs Resistance at 12 kn (b) Max draft position vs Resistance at 15 kn

Figure B.2: Max draft position vs resistance. Red stars mark measured data; Blue line is the ﬁtted resistance curve

VII B.2 Max draft position vs Resistance

VIII Appendix C - Rules

IX 1001VELACUP CHALLENGE R3 Special Rules Class R3 2017-2020

!!! This is a translation of the original text : If there is a conflict between languages the Italian text will take precedence. !!!

Premise This Rules aims to promote a regatta’s program for sailboats designed and manifactured inside universities, under a common teaching program and in accordance with a Class Rule R3 which sets out the features. Premessa Con il presente regolamento si intende promuovere un programma di regate tra barche a vela progettate e realizzate all’interno di strutture universitarie, nel quadro di un programma didattico comune e nel rispetto di un Regolamento di classe R3 che ne stabilisce le caratteristiche.

Aims Aims of the universities participating in the initiative is to organize within their internal structures (in thesis courses, workshops, laboratory activities, extracurricular activityes, etc.) annual teaching activity aimed at the design and implementation of sailboats 15 feet long in accordance with the specifications and requirements of the Class Rule R3. Obiettivi Obiettivo degli Atenei che aderiscono all’iniziativa è quello di organizzare all’interno delle loro strutture (nell’ambito di corsi o tesi di laurea, workshop, attività di laboratorio, extracurriculari ecc.) un’attività didattica annuale finalizzata alla progettazione e realizzazione di una deriva da 15’ che risponda alle caratteristiche e ai requisiti previsti dal Regolamento di classe R3.

Purpose The purpose of the initiative is to promote an annual or bi-annual, meeting between the universityes that agree the 1001VELAcup aims. The calendar and the program of events will be defined by the Technical Committee provided for in Regulation R3 class, after hearing the proposals of the University who won the previous edition and the other participating universities. Finalità Scopo dell’iniziativa è quello di promuovere, con cadenza annuale o biennale, un incontro tra le Università che aderiscono all’iniziativa “Mille e una vela cup”. Il calendario e il programma delle manifestazioni verranno definiti dalla Commissione Tecnica prevista dal Regolamento di classe R3, sentite le proposte dell’Ateneo che si è aggiudicato la precedente edizione e degli altri Atenei partecipanti.

Generalities The boats partecipating to the program 1001VELAcup must comply with these "Special Rules, be designed and constructed, in accordance with the Rules of Class R3, and be governed by teams composed of Universities students. Generalità Le imbarcazioni che partecipano al programma “Mille e una vela cup” devono rispettare le presenti “Norme speciali di Classe R3”, essere progettate e realizzate, secondo quanto stabilito dal Regolamento di Classe R3, ed essere governate da equipaggi formati da studenti iscritti presso qualsiasi Ateneo.

1) Elegibility for the “1001VELAcup's Throphy Crew: a) The crews must be composed by students enrolled in participating Universities b) All crew shall not hold a Group 3 Classification (World Sailing Sailor Code) (Annex “D”). c) In regattas with multiple consecutive trials, the crew (min. 2 persons) is fixed for the duration of the event d) Students older than 30 are not admitted. Ammissione alla regata per il "Trofeo 1001VELAcup" Equipaggi a) Gli equipaggi che partecipano al programma “Mille e una vela cup” devono essere costituiti da studenti iscritti ad un ateneo partecipante (cfr. Allegato D). b) Tutto l'equipaggio non deve essere in possesso di una Classificazione di Gruppo 3 (World Sailing Sailor Code) (cfr. Allegato D). c) In una manifestazione a più prove consecutive la composizione dell’equipaggio (min. 2 persone) è fissa per tutta la durata della manifestazione. d) non sono ammessi studenti di età superiore a 30 anni.

Boats: e) Are allowed in the " Mille e una vela Cup " program, only boats that have been designed and built by students enrolled in degree courses of participant university. f) The boats will be identified by a sail number issued by 1001VelaCup. g) hulls and keel must to be built by students in a university's laboratory, also under teachers guide. If a university will use an external structure, the boatyard must release a declaration that attests that the personnel has not directly been involved in the construction or has furnished consultations. h) equipment, rigging and sails, except for wing sails structures, can came from external supplies of the university Imbarcazioni e) Sono ammesse al programma “Mille e una vela Cup” unicamente imbarcazioni che siano state progettate e costruite dagli studenti iscritti a corsi di laurea di un ateneo partecipante. f) Le barche saranno identificate da un numero velico rilasciato da 1001VelaCup. g) Lo scafo e le appendici devono essere realizzati, presso un laboratorio di ateneo,dagli studenti, sotto la guida di docenti scelti dall’Ateneo. Qualora l'ateneo decidesse di utilizzare una struttura esterna, il titolare del cantiere dovrà rilasciare una dichiarazione che attesti che il personale non sia stato direttamente coinvolto nella costruzione o abbia fornito consulenze. h) L’attrezzatura, l’armo e le vele, ad esclusione delle strutture delle wing sails, possono provenire da forniture esterne all’Ateneo partecipante.

Participants i) Each university participating in the race can bring up to 3 boats. l) For each boat must be associated univocally a crew, each crew member can be associated only to a single boat m) If more universities will participate as consortium, there must be designate the representing university Partecipanti i) Ogni ateneo partecipante può portare in gara un massimo di 3 imbarcazioni. l) Ad ogni imbarcazione deve essere associato univocamente un equipaggio, ogni membro di equipaggio può essere associato ad una sola imbarcazione. m) Nel caso più atenei decidano di partecipare in consorzio, deve essere nominato l'ateneo rappresentante.

2) Regatta rules The regattas will be run in real time under the following rules: a) The World Sailing Racing Rules of Sailing 2017 – 2020 using the “Low Point System”; b) The notice of Race and the Regatta's Instructions released for the Event ; c) The Special Rules R3 Class; d) the regattas will be run inside the following wind speed limits: min. 3 m/sec – Max 10 m/sec. The regatta Committee is free to evaluate the conditions of security even in that range. 2) Regole di regata Le regate si correranno in tempo reale applicando: a) Il “Regolamento di Regata World Sailing” in vigore con le norme integrative emanate dalla F.I.V. Sarà applicato il “punteggio minimo”; b) Il Bando emanato per la manifestazione e le Istruzioni di Regata conseguenti; c) Le “Norme speciali di Classe R3” d) Le regate saranno disputate all’interno dei seguenti limiti di vento: min 3 m/sec - Max 10 m/sec. A discrezione del comitato di regata resta in ogni caso la valutazione delle condizioni di sicurezza della manifestazione anche nel range di vento definito.

3) "Paolo Padova" Trophy Premise: The Trophy has been created in 2013 and is dedicated to Paolo Padova, a meaning figure in sharing, with his students, the 1001VELAcup's principles and philosophy. Boats a) will be applied the same rules of the 1001VELAcup trophy Crews b) The crews must be composed by a teacher and a students enrolled in participating Universities.

3) Trofeo "Paolo Padova" Premessa: Il trofeo, istituito nel 2013, è dedicato a Paolo Padova che con il suo agire e per il ruolo che ricopriva è stato una figura emblematica dei principi condivisi da 1001VELAcup. Imbarcazioni e Partecipanti a) Valgono le stesse regole del Trofeo 1001VELAcup Equipaggi b) Gli equipaggi che partecipano al Trofeo “Paolo Padova” devono essere costituiti da un docente strutturato nell'ateneo di rappresentanza ed uno studente iscritto ad un ateneo partecipante.

R3 class rules Introduction These class rules was compiled with the intent of making the universities designing and building sailing boats limited in dimensions and materials, with easy technologies and limited costs as well as be easily transportable on land and manoeuvrable at sea, putting universities on the same level even with different available skills and equipment.

Objectives The following rules aims to make regattas with boats, realized inside the Athenaeum, having similar characteristics and letting a great range of design possibilities

Regolamento di classe R3 Premessa Il presente regolamento è stato redatto con l’intento di far realizzare delle imbarcazioni a vela di limitate dimensioni, con tecnologie accessibili e costi contenuti, facilmente trasportabili via terra e manovrabili in acqua, mettendo sullo stesso piano laboratori didattici universitari con capacità e attrezzature differenti, anche attraverso l’introduzione di limitazioni sulla scelta dei materiali.

Obiettivi Il presente regolamento si propone di far regatare insieme barche con le stesse caratteristiche, realizzate all’interno degli Atenei, lasciando ampio margine per la loro progettazione.

1- Dimensions a) Maximum length overall: 4.60 meters. b) Maximum beam overall: 2.10 meters. c) For the measurements of the dimensions given at point a) and b) a maximum tolerance admitted is 15mm. d) The ruder and its mounting system are excluded in the overall length measurements. e) Bowsprits are allowed, only if used for flying sails off, and are excluded from the overall length measurement.

1- Dimensioni a) Lunghezza massima fuori tutto: 4,60 m.; b) Larghezza massima fuori tutto: 2,10 m; c) Per la misurazione delle dimensioni definite ai punti a) e b) è prevista una tolleranza max di 15 mm. d) Il timone e il suo sistema di aggancio all’imbarcazione sono esclusi dalla misura della lunghezza massima fuori tutto. e) E’ ammesso l’uso di un bompresso o di un tangone, escluso dalle dimensioni massime, solo se necessario alla manovra delle vele.

2- Materials and construction a) For the purposes of educational training in these rules, the hull and racks should be made of wood or materials of vegetable and/or animal origin (also called “natural”) , expressed in weight, not lower that 70%. The glue within natural materials can be calculated as part of natural composite only if it's not used as structural material. b) The use of hiking wings (or racks) is allowed if i's in accordance with the dimensional and material composition limits. c) The following materials are banned: aramid fibres, carbon fibres, titanium. d) Carbon fibre can only be used for the bowsprit and the appendices. e) Spectra (polyethylene) can be used for rigging. f) The sails cannot be made from Kevlar, spectra, carbon or other high modulus fibres and they must have a statement from the sail maker. g) The mast and boom must be made from extruded aluminium or, in exclusion of the matrix material, in natural fibers.

2- Materiali e costruzione a) Per gli scopi didattico formativi che si pone il presente regolamento, l’insieme scafo-coperta-terrazze dovrà prevedere un contenuto in legno o materiali di origine vegetale e/o animale (in seguito detti anche “naturali”), espresso in peso, non inferiore al 70%. Il collante può rientrare nel calcolo dei materiali naturali solo se necessario all' incollaggio tra questi e non sia utilizzato come materiale strutturale. b ) E’ ammesso l’uso di terrazze nel rispetto dei limiti dimensionali e costruttivi definiti. c ) Ad eccezione di quanto specificatamente consentito, nella realizzazione di scafo, coperta, terrazze appendici, albero e boma non sono ammessi i seguenti materiali: fibre aramidiche, fibre di carbonio, titanio. d) E' ammesso l'utilizzo di fibre ad alto modulo per la realizzazione del solo bompresso e delle appendici. e) E' ammesso l'uso di polietilene per il sartiame. f) Le vele non possono essere realizzate in fibre aramidiche, carbonio o altre fibre ad alto modulo e dovranno essere accompagnate da una dichiarazione del velaio riportante le misure di stazza come descritte negli allegati C e C1. g) L’albero e il boma devono essere realizzati con estruso in alluminio o, ad esclusione della matrice, in fibre di origine vegetale e/o animale.

3- Appendices a) The number of daggerboards and foils is free, the shapes are not restricted in design. b) It is allowed the use of Kevlar, spectra, carbon or other high modulus fibres for daggerboards and foils.

3- Appendici a) Il numero delle appendici è libero, le sagome e superfici sono libere. b) Per le appendici sono ammessi i seguenti materiali : fibre aramidiche, fibre di carbonio, titanio o altra fibra ad alto modulo.

4- Rig a) The height of the mast is not restricted. b) Trapezes are allowed.

4- Armo a) L’altezza dell’albero è libera. b) Sono ammessi trapezi.

5- Sail plan a) The sail plan will have a maximum total surface area of thirty-three square meters.The calculation of the areas will be carried out in accordance with Annex C for laminate sails and according to what is indicated in annex C1 for wing sail type; by wingsail is meant any sail which, when used, has a distance between windward surface and leeward surface is bigger that the thickness of the sheet. b) No kites are allowed. c) In a regatta with more manches, only one set of sails are allowed. d) Each university can present a measured sail set signed by an official measurer of the sail federation from the university's country, the measures will be taken as description in annex C and C1

5- Piano velico a) Il piano velico avrà una superficie massima complessiva pari a trentatre mq. Il calcolo delle superfici sarà effettuato secondo quanto riportato nell’allegato C per le vele in laminato ed in base a quanto riportato nell’allegato C1 per le vele di tipo alare (wing sail); si intende per wing sail o vela alare qualunque vela che, in esercizio, presenti una distanza tra superficie al vento e superficie sottovento superiore allo spessore proprio della lamina. b) Non sono ammessi armi tipo kite o aquilone c) In una manifestazione a più prove consecutive è ammesso un solo gioco di vele d) Qualunque ateneo può presentare le vele già stazzate da uno stazzatore, autorizzato della federazione velica dello satato di appartenenza, seguendo le indicazioni dgli allegati C e C1. 6- Hull a) The hull must not have concavities in cross sections below the waterline. b) It must be a monohull; multihulls are not allowed. c) The hull must not have asymmetrical cross-sections. d) The hull must be able to provide sufficient buoyancy to the safety of the vessel and its crew, of at least 80 litres; in the form of foam, expanded material, air bags and/or inspectable watertight compartments. The caps of the inspection holes will be minimum 2 an have a diameter of 12 cm min. They must be located in the anterior and posterior part of the boat to provide a complete inspection. e) The dagger-board and rudder must be securely fixed to the hull; the use of a quick release shackle with elastic is allowed for each appendix.

6- Scafo a) Lo scafo non deve presentare concavità nelle sezioni trasversali al di sotto della linea di galleggiamento. b) Lo scafo deve essere unico; non sono ammessi multiscafi. c) Lo scafo non deve presentare sezioni trasversali asimmetriche. d) Lo scafo deve poter garantire una riserva di galleggiamento sufficiente alla sicurezza dell’imbarcazione e del suo equipaggio, pari ad almeno 80 lt., sotto forma di schiuma, espanso, sacchi d’aria, compartimenti stagni ispezionabili. I tappi di ispezione dovranno essere minimo 2, avere diametro minimo di 12 cm ed essere posizionati uno nella zona posteriore e uno nella zona anteriore della coperta e comunque secondo logica in modo da permettere una adeguata ispezione. e) E’ obbligatorio assicurare la deriva e il timone allo scafo; l’uso di un grillo a sgancio rapido con elastici è permesso per ogni appendice.

7- Conformity and book of rules a) The boats must be in possession of a self-certification of the University represented showing compliance with this Regulation in accordance with the models in Annexes A and B. b) The boats could be subject to compliance testing. c) If a boat is damaged, repair or replacement of parts is permitted, as long as it complies with the class rules. d)If it is not possible to correct any discrepancies, they will be remedied with the installation of an on board corrector weights from 5 kg, in number established by T.C., placed at a distance less than 50 cm from the transom. e) Protests regarding measurement will be accepted until two hour before the start signal of the first race, except for infraction happened during the race/s f) 15 days before the start of the regatta/s each entry must present (also in numeric format) the following documents: f1) Annex A “Self Certification of Compliance” f2) Annex B “Weight Calculations” f3) Draws of the forms, waterlines and construction plan f4) Detailed technical description about the construction f5) Technical sheets of the used materials f6) photos and/or clips about the construction process to support the points: f1,f2,f3 and f4. f7)the annex D “Crew Sheet”

7- Conformità al regolamento a) Le barche dovranno essere in possesso di una autocertificazione dell’Ateneo rappresentato attestante la conformità al presente regolamento secondo i modelli allegati A e B. b) Le imbarcazioni potranno essere sottoposte a verifiche di conformità. c) Qualora una barca venga danneggiata è ammessa la riparazione o la sostituzione delle parti a seguito della quale si verificherà nuovamente il rispetto delle regole di stazza. d) Qualora non sia possibile correggere eventuali difformità, queste saranno sanate con l’istallazione a bordo di pesi correttori da Kg 5, in numero stabilito dalla C.T., posti a distanza inferiore a 50 cm dallo specchio di poppa. e) Le proteste di stazza saranno ammesse entro le 2 ore dall'inizio delle regate o serie di regate, salvo infrazioni commesse nel corso dell'evento. f) Entro 15 giorni dall'inizio delle regate dovranno essere presentati i seguenti documenti: f 1) Scheda di adesione all’evento “1001VELAcup” f 2) Allegato A “Dichiarazione di conformità” con allegata dichiarazione del velaio; f 3) Allegato B “Calcolo dell’esponente del peso”; f 4) Disegni delle linee d’acqua e del piano di costruzione; f 5) Descrizione dettagliata della tecnica di costruzione adottata; f 6) Schede tecniche dei materiali usati; f 7) Foto e/o filmati di tutte le fasi della costruzione sufficienti a supportare quanto riportato nelle voci 2, 3, 4 ed 5 f 8) Allegato D “Scheda equipaggi” che comprende : categoria di appartenenza degli atleti (sono esclusi gli atleti facenti parte del gruppo A – World Sailing), certificato di iscrizione all’ateneo per l’anno in corso (allegato alla scheda), tessera della federazione velica del paese di appartenenza valida per l’anno in corso.

8- Technical committee a) The technical committee is composed by four members named by 1001VelaCup and by the representatives appointed, time to time, from the first three universities classified in the regatta for the “Trofeo 1001VELAcup”.

8- Commissione Tecnica a) La Commissione Tecnica è costituita da quattro membri nominati da 1001VelaCup e dai rappresentanti nominati di volta in volta dai primi tre Atenei classificatisi nella Regata per l’assegnazione del “Trofeo 1001VELAcup”.

Emendments a) This Regulation will be valid until October 2016. b) This regulation could be supplemented and / or modified by the Technical Committee as a result of any proposals by the universities concerned. c) Proposed amendments must be submitted to the Technical Committee within 7 days of being awarded the "Trofeo 1001VELAcup." d) The Technical Committee will review the proposed amendments within 30 days from the date of award of the "Trophy 1001VELAcup."

Emendamenti a) Il presente regolamento è valido fino a November 2020. b) Il presente regolamento potrà essere integrato e/o modificato, dalla Commissione Tecnica a seguito di eventuali proposte da parte degli Atenei interessati. c) Le proposte di emendamento dovranno essere sottoposte alla Commissione Tecnica entro 7 giorni dall’assegnazione del “Trofeo 1001VELAcup”. d) La Commissione Tecnica provvederà a esaminare le proposte di emendamento entro 30 giorni dal termine della assegnazione del “Trofeo 1001VELAcup”.

Interpretation If a university requires clarification on the interpretation of some of these rules only the interpretation expressed by the Technical Committee will apply.

The official language of these class rules is Italian, all interpretations will refer to the Italian language meanings

Interpretazione Qualora un Ateneo richiedesse chiarimenti sull’interpretazione di alcune delle presenti regole sarà valida solo l’interpretazione espressa dalla Commissione Tecnica.

Roma, 16 Novembre 2017 Signed the president of the Technical Committee Massimo Paperini ANNEXES TO R3 CLASS RULES ALLEGATI AL REGOLAMENTO DI CLASSE R3 ANNEX A

CLASS RULES R3 SELF CERTIFICATION OF COMPLIANCE (pt. 7A)

Boat's name : ……………………………………………………………………………... Sail Number: (3 letters for the nationality) …...... - (sail number)…………………….. Construction year : ……………………….

University: …………………………… Faculty : ………………………………. Address : ……………………………………………………………………………… Telephone : +…… ………….…………….... Fax: +...... ……………………… E-mail:……………………

HULL: Rule. R3

LH (Leinght overall max) 1a (max mt. 4.60) : mt.………………………… B (beam overall max) 1b (max mt. 2.10) : mt.…………………………

PIANO VELICO Rule. R3

SA (total sail surface) 5a (max mq. 33,00) : mq…………………… In attachment the certification of the sailmaker.

Norme Speciali Wing Sail 1d) □NO □YES.

I declare to have read the Special Rules of R3 Class, I certificate the exactness of the information released in this declaration. I accept to make the boat available for verifications.

Date : ………………… stamp of the athenaeum and signature of the person responsible :

………………………………...

______

Pb (corrector weights) rule 7d □NO □YES → : kg. ……………………….. . notes:

...... at ...... date: ..../..../...... the measurer the president of T.C.

...... Annex B – WEIGHTS CALCULATIONS

Brief technical description about the construction ……………………………………………………………………. ……………………………………………………………………………...... Note: for “Natural Material” is intended Wood or vegetal/animal materials HULL Hull is considered being the the ensemble of surfaces for planking, topside, underside, stern surface.

Natural Materials Specific Weight (kg/m3) Surface (m2) Weight (kg) 1 2 3 4 5 Total Others Materials Specific Weight (kg/m2 o kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Total

STRUCTURES Structures are the ensemble of parts such as frames, keelson, stingers, and reinforcements. The reinforcements for rigging settings must be calculated in the “Rigging” section. Natural Materials Specific Weight (kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Total Others Materials Specific Weight (kg/m2 o kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Total SOVRASTRUCTURES (only in natural fibres builded) For sovrastructures is intended l' ensamble of the planking surfaces. Structural elements must be cocalculated in the “Structure” section. Natural Materials Specific Weight (kg/m3) Surface (m2) Weight (kg) 1 2 3 4 5 Total Others Materials Specific Weight (kg/m2 o kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Total

RACKS (only if maiden in “non-natural” fibers) This section must be filled only in case the racks (or “wings”) are maiden in materials different than “natural fibers” . It's necessary to calculate also the local renforcements and fastenings. Material Specific Weight (kg/m2 o kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Total Others Materials Specific Weight (kg/m2 o kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Total RIGGING To calculate only the elements that are directly attached to the hull. In this sections iare to be calculated also the reinforcements for the rigging . Fixed rigging Quantity Weight (kg) 1 2 3 4 5 Totale Others Materials Specific Weight (kg/m2 o kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 4 5 Totale Natural Materials Specific Weight (kg/m3) Quantity (m2 o m3) Weight (kg) 1 2 3 Totale

Total Weight Natural Materials Weight Other Materials Weight Percentage of Natural Material

Date : …………………

stamp of the athenaeum and signature of the person responsible :

………………………………...

Student's Responsable (must be a student) : ………………………………. ANNEX C

DRAWINGS AND INSTRUCTIONS Measurement of sails

The fabric must be dry, the tension applied for measurements must be sufficient to eliminate all the folds of the fabric. Measurements must be effectuated spreading the sails to the ground.

Il tessuto deve essere asciutto e la tensione esercitata su di esso durante le misurazioni deve essere tale da eliminare tutte le pieghe. La misurazione va effettuata con le vele stese a terra.

Randa/Mainsail

MSA = (LI/2 x (E5+E4)/2) + (LI/4 x (E4+E3)/2) + (LI/8 x (E3+ E2)/2) + (LI/8 x (E2+ E1)/2) + FTA

In cui :

a) E5 > E4 > E3 > E2 > E1 ; b) LI is the distance, in straight line, between head point and tack; both identified as descripted below è la distanza in linea retta tra il punto di drizza e il punto di mura, ambedue rilevati secondo il sistema di identificazione sotto riportato;

c) FTA = E5 x CO / 2 ; d) FTA is to be considered only if the case that the clew is not coincident with the endpoint of E5; CO is the distance between the measurement point E5 and the clew point. FTA si calcola solo nel caso in cui il conto di scotta non coincida con l'estremo della misura E5 sulla balumina. CO

è pari alla distanza dalla linea di misura di E5 al punto di scotta. e) The rounded excess of fabric under the line between tack point and clew point must not exceed 8% of the mainsail's base. La rotondità della base al di sotto della linea che unisce il punto di mura al punto di scotta non deve eccedere l’ 8% della base della randa ;

f) E1 is coincident with the width of the head measured perpendiculary to the luff by the head point coincide con la larghezza della penna presa perpendicolare all’inferitura, passando per il punto di drizza ;

g) E2 is coincident with the width of the mainsail taken at 1/8 of the luff perpendicularment to the line between between the head point and the tack point coincide con la larghezza della randa in corrispondenza a 1/8 della lunghezza dell’inferitura.

h) E3 is coincident with the width of the mainsail measured on the perpendicular to the line between the head point and the tack point at 1 / 4 of the line itself ¼ oincide con la larghezza della randa in corrispondenza a 1/4 della retta che congiunge il punto di drizza al punto di mura, in direzione perpendicolare a questa retta ;

i) E4 is coincident with the width of the mainsail measured perpendicularment to the line between the head point and the tack point at 1 / 2 of the line itself coincide con la larghezza della randa in corrispondenza di 1/2 della retta che congiunge il punto di drizza al punto di mura, in direzione perpendicolare a questa retta ;

j) E5 is coincident with the width of the mainsail measured perpendicularment to the line between the head point and the tack point at the level of the tack point coincide con la larghezza della randa all’altezza del punto di mura, rilevata lungo la direzione che si trova seguendo le istruzioni riportate di seguito, e comunque perpendicolarmente alla LI. k) For the identification of the points on the leach refer to the following instructions ( the same procedure is for the gennaker) Per quanto riguarda l’identificazione dei punti di misura alle estremità delle vele far riferimento alle figure di seguito riportate ( valide anche per le misurazioni di fiocco e gennaker ) . l) On the mast will be installed tree measurement stripes , two on the mast and one on the boom. These will be black colored and be 25 mm. high. The higher edge of the lower stripe on he mast will be at the same high of the top face of the boom. The sail will never be tacked beyond that line high Sull’albero e sul boma dovranno essere installate tre strisce di misurazione, due sull’albero e una sul boma, di colore nero e di altezza pari a 25mm oltre le quali la vela non potrà essere bordata. Il filo superiore della banda inferiore di P dovrà essere posizionato in corrispondenza della faccia superiore del boma.

Measurement method / Metodo di misurazione : 1) Overlap the head point on the tack point and pull the luff . Sovrapporre il punto di drizza sul punto mi mura e tendere bene l’inferitura. 2) The crease identifies two points, the first on the luff and one on the leech. Mark these points La piega ottenuta identifica due punti, uno sulla balumina e uno sull’inferitura. Segnare questi due punti.

3) Measure the distance (E4) between these points and mark the trace of this line nearby the luff. Misurare la distanza (E4) tra questi due punti e segnare la traccia della fettuccia in prossimità dell’inferitura. 4) Unfold the sail and pull the luff, trace the line between tack and head. The line will intercepts the taken trace of the measure E4 in the point O1. Stendere nuovamente la vela, tesare l’inferitura e congiungere con la fettuccia anch’essa ben tesata il punto di drizza al punto di mura. La fettuccia intersecherà la traccia della misura di E4 precedentemente

presa in un punto O1.

5) Overlap the head point on the O1 point and pull the luff . Sovrapporre il punto di drizza al punto O1 e tendere bene l’inferitura. 6) The crease identifies two points, the first on the luff and one on the leech. Mark these points .La piega ottenuta identifica due punti uno sulla balumina e uno sull’inferitura. Segnare questi due punti.

7) Measure the distance (E3) between these points and mark the trace of this line nearby the luff. Misurare la distanza (E3) tra questi due punti e segnare la traccia della fettuccia in prossimità dell’inferitura. 8) Unfold the sail and pull the luff, trace the line between tack and head. The line will intercepts the taken trace of the measure E3 in the point O2, mark this point. Stendere nuovamente la vela, tesare l’inferitura e congiungere con la fettuccia anch’essa ben tesata il punto di drizza al punto di mura. La fettuccia intersecherà la traccia della misura di E3 precedentemente presa in un punto O2.

9) Overlap the head point on the O2 point and pull the luff . Sovrapporre il punto di drizza al punto O2 e tendere bene l’inferitura. 10) The crease identifies two points, the first on the luff and one on the leech. Mark these points. La piega ottenuta identifica due punti uno sulla balumina e uno sull’inferitura. Segnare questi due punti.

11) Measure the distance (E2) between these points. Misurare la distanza (E2) tra questi due punti.

12) Overlap the tack point on the O1 and mark the position of the E4 leech point on the overlapped fabric. Sovrapporre infine il punto di mura sul punto O1 e riportare la posizione dell’estremo di E4 dalla balumina al lembo sovrapposto.

13) Spread the sail, the extention, on the leech, of the line between the last point ant the tack point gives the position of the point where to measure the E5 distance. Ristesa la vela, congiungendo il punto identificato con il punto di mura e proseguendo fino alla balumina si ottiene la posizione del punto per la misura di E5.

______

Fiocco

F = 0.125 ×JL×(2×LP+3×JGM+2×JGU)

a) JL is the leinght of the luff. Unfold the sail and pull the luff, measure the distance between head and tack. JL coincide con la lunghezza dell’inferitura. Si stende la vela in modo da evitare la formazione di pieghe e si misura la distanza tra il punto di drizza e il punto di mura; b) LP is the width of the sail, on the perpendicular of the luff, trough the clew coincide con la larghezza sulla perpendicolare all’inferitura passante per il punto di scotta. Si misura rilevando la minima distanza tra il punto di scotta e l’inferitura; c) JGM : overlap the head to the clew. The crease identifies the midpoint of the leech. Mark this point and measure the minimum distance between this and the luff. sovrapporre il punto di drizza sul punto di scotta. La piega che si viene a formare identifica la metà della balumina. Segnare questo punto e ristendere la vela in modo da poter misurare la minima distanza che intercorre tra tale punto e l’inferitura della vela. d) JGU : overlap the head to the point of JGM on the leech and mark the point on the leech in correspondence of the crease. Unfold the sail and measure the minimum distance between the point and the luff. piegare la vela fino a sovrapporre il punto di drizza al punto precedentemente trovato e segnare il punto sulla balumina in corrispondenza della piega. Stesa di nuovo la vela misurare la minima distanza tra questo punto e l’inferitura.

Gennaker

S = (SLU+SLE)/2×((SF+(4×SHW))/5)×0.83

a) SLU : il the leinght of the luff. Pull the luff and measure the distance between head and tack. coincide con la lunghezza dell’inferitura. Tendere l’inferitura e misurare la distanza tra il punto di drizza e il punto di mura. b) SLE : is the leinght of the leech. Pull the luff and measure the distance between head and clew. coincide con la lunghezza della balumina. Tendere la balumina e misurare la distanza tra il punto di drizza e il punto di scotta. c) SF : pull the the lower edge of the gennaker and tmeasure the distance between tack and clew. SF : tendere il bordo inferiore del gennaker e misurare la distanza tra il punto di scotta e il punto di mura. d) SHW : overlap the head on the tack and measure, on the luff, the point in correspondence of the crease that identify the half of the luff. Overlap the head point on the clew point and measure as above the midpoint of the leech. Unfold the sail and measure the minimum distance, on the sail, between the midpoint of the luff and the midpoint on the leech. portare il punto di drizza sul punto di mura e rilevare, sull’inferitura, il punto in corrispondenza della piega che coincide con la metà dell’inferitura stessa. Sovrapporre il punto di drizza al punto di scotta e rilevare, in maniera analoga alla precedente, la metà della balumina in corrispondenza della piega. Stendere la vela in corrispondenza di questi due punti e misurare la minima distanza che intercorre tra il punto di mezzo della balumina e il punto di mezzo dell’inferitura. ANNEX C1

DRAWINGS AND INSTRUCTIONS Measurements on wing sails

Definition For “Wing Sails” is intended sails where the distance between the upper-wind surface and the lower-wind surface is higher than the own thickness of the fabric or lamination even for a limitate portion of the chord line

Measurements The measurement of the wing sail will consider the larger of the surfaces of the wing eventually adding the half of the lateral surface of the wing-mast but if this is inserted inside the wing sail

Definizione Per vele alari si intendono vele la cui distanza tra la faccia sopravvento e quella sottovento sia superiore, in esercizio, anche se limitatamente, ad una porzione della corda, allo spessore proprio della lamina che le compone.

Misurazione Per la misura della superficie di vele alari si considererà la maggiore delle due facce della vela, compresa la semisuperficie laterale dell’albero, ad esclusione dei casi in cui l'albero sia inserito all'interno della vela.

The Wing Sails will be measured in working configuration with the devices, such as flaps or slats, if present, in extended position.

Le vele di tipo alare verranno stazzate nella configurazione di esercizio, con eventuali ipersostentatori di bordo di attacco (slat), ipersostentatori di bordo d’uscita (flap) e alettoni in posizione di massima apertura. individuation of the side to be measured for simple and multi sectioned profile

the measurement points will be indicated by the measurer or by the T.C. The calculation of the surface will be developed by decomposition of the surface in trapezes or triangles where possible

In case it's present at last one curved edge on the leading edge and/or the trailing edge, will be adopted the Cavalieri-Simpson method on min. 5 partitions

I punti di misura verranno definiti a discrezione dello stazzatore o della C.T. Il calcolo della superficie sarà effettuato per scomposizione in trapezi e/o triangoli dove possibile.

Nel caso sia presente anche un solo bordo curvo si adotterà la formula di Cavalieri-Simpson su un minimo di 5 partizioni

Some examples: Si riportano a seguito alcuni esempi:

Annex D – CREW SHEET

MILLE E UNA VELA CUP

Place ______date ______

NOME IMBARCAZIONE – BOAT NAME ______

Numero velico / Sail number ______

EQUIPAGGIO – CREW Group (World Federation's Nome / Name Cognome / Surname Ruolo / Role Sail) inscription N° 1 2

Trofeo “Paolo PADOVA” / “Paolo PADOVA” TROPHY EQUIPAGGIO – CREW (Regata docente-studente / student-teacher Regatta) Nome / Name Cognome / Surname Ruolo / Role Docente/ Teacher Studente/ Student

Data / Date FIRMA / SIGNATURE

______

Gommone Accreditato/ Assistance Boat

______TEL. ______

Annexed, at this sheet, the registration of the students for the current Academic Year

Certificate of conformity

Place ...... date …./..../20......

Sailmaker : Address : Tel.: Mail. Web:

Certification of conformity for the sail set in accordance of the R3 class rules

I declare that the material used for the realisation of the sail set for the boat: …...... sail number: …...... DO NOT includes Kevlar, spectra, carbon or other high modulus fibres.

I declare that the sail set has been measured in accordance with the “Annex C and C1” of the R3 Class Rules

Sheet sails MAIN SAIL JIB LI JL E1 LP E2 JGL E3 JGU E4 GENNAKER E5 SLU C0 SLE SF SHW

Wing sails H1 X1 H2 X2 H3 X3 H4 X4 H5 X5

Mr/Ms

…...... …...... (stamp and signature)