C-Class Catamaran Daggerboard: Analysis and Optimization · PDF fileC-Class Catamaran...

C-Class Catamaran Daggerboard:Analysis and Optimization

Sara Filipa Felizardo Santos Silva

Thesis to obtain the Master of Science Degree in

Mechanical Engineering

Supervisors: Prof. Virginia Isabel Monteiro Nabais InfanteProf. João Carlos de Campos Henriques

Examination Committee

Chairperson: Prof. Luis Manuel Varejão de Oliveira FariaSupervisor: Prof. Virginia Isabel Monteiro Nabais Infante

Member of the Committee: Prof. Luis Manuel de Carvalho Gato

November 2014

iii

The problem is not the problem; the problem is your attitude about the problem

Capt. Jack Sparrow

Acknowledgments

First and foremost, I would like to offer my special thanks to professor Joao Henriques for the patience

and for presenting me to the topic of hydrofoil improvement. I would like to express my appreciation to

professor Virginia Infante for the guidance and support through the work and for introducing me to

Optimal Structural Solutions company. Without them this dissertation would not exist.

Additionally, I would like to thank Engineers Antonio Reis and Andre Coelho from Optimal Structural

Solutions for giving me the opportunity to work with their daggerboards and for always being available

to answer my questions.

A special thanks to my family: my father, my mother, my sister, my grandmother and grandfather, for

all the support and inspiration which allowed me to overcome this journey. Another special thank you to

my friends and colleagues for their support along this journey.

Finally, I would like to thank my beloved Rui for all the support, patience and love that allowed me to

proceed and succeed in this project.

v

Resumo

Desde 2004 que a competicao international de catamarans de classe-C tem ganho adeptos e sus-

citado o interesse dos engenheiros no desenvolvimento e optimizacao das embarcacoes. Um dos

componentes que tem sido sujeito a mais estudos e o patilhao, o leme central que atravessa o casco, e

que permite o levantamento da embarcacao quando esta comeca a ganhar velocidade.

Neste trabalho, o perfil alar do patilhao foi optimizado de forma a que este crie a sustentacao sufi-

ciente para levantar a embarcacao a uma velocidade reduzida. Para isto, foi utilizado o software Xfoil

incorporado no programa principal onde foi desenvolvido o modelo Class-Shape-Transformation, de

modo a gerar a geometria do perfil. Utilizou-se tambem o modelo de optimizacao Differential Evolution

para os parametros das condicoes estabelecidas.

Procedeu-se a analise estrutural do modelo tridimensional do patilhao atraves da utilizacao do soft-

ware Ansys. Foram comparados os resultados dos perfis NACA 2412 e NACA 5412 ja existentes, com

o perfil optimizado gerado no ambito do programa de trabalhos da dissertacao. Inicialmente utilizou-se

uma configuracao mais simples para o perfil, tendo sido verificado grande deformacao da estrutura, o

que contribui para o aparecimento de fracturas devido a fadiga. Por esta razao, o perfil foi alterado de

modo a evitar estas grandes deformacoes.

Por fim, foi realizado um estudo do material atraves do software CES Edupack. Foram definidos os

constrangimentos para a utilizacao do patilhao em competicao e selecionado dois materiais de forma a

reduzir o custo total da contrucao da mesma.

Palavras chave: Patilhao, Perfil Alar, Class-Shape-Transformation Method, Differential Evolution, Analise

Estrutural, Analise de Materiais.

vii

Abstract

Since 2004, the international C-class catamaran championship has gained fans and the interest

of engineers for the development of these vessels to become faster and lighter. The daggerboard, a

hydrofoil that creates lift to take the boat out of water when the speed increases, is one of the catamaran

components that has been subject to greater development and studying.

In the present work, the hydrofoil profile was optimized in order to create enough lift to lift up the

boat at a low velocity. It was used an interface between Xfoil software and the main program. The main

program uses the Class-Shape-Transformation method to generate a profile geometry and an optimized

program known as Differential Evolution. The interface between the three components allows the user

to generate a profile for the desired conditions.

The structural analysis of the structure was made using the Ansys software. The three-dimensional

structures are modeled with three different profiles: NACA 2412, NACA 5412 and the new profile created

by the program developed under the dissertation’s scope. Initially, it was used a simple configuration

which was modified along the study in order to create a final structure with mechanical properties that

contributes to a non permanent deformation of the structure, thus avoiding fatigue related damage.

Finally, a study of materials was presented using the software CES Edupack. Constrains for the

daggerboard’s material utilization were defined to select two materials which can be applied to the

structure in order to reduce the daggerboard’s construction cost.

Keywords: Daggerboard, Hydrofoil, Class-Shape-Transformation Method, Differential Evolution, Struc-

tural Analysis, Material Analysis.

ix

Contents

1 Introduction 1

1.1 Motivation and objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 State of Art 5

2.1 C-Class catamaran racing boat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Daggerboard profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Hydrofoil design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.1 Eppler’s hydrofoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.2 Hydrofoil characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3.3 Cavitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Material evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Methodology 19

3.1 Project conditions and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Daggerboard design 23

4.1 Hydrofoil design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1.1 Class-Shape-Transformation Method . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1.2 Differential Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.3 Hydrofoil Shape Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.1.4 Case of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.5 CST shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.6 Control coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1.7 Objective Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

5 Structural Analysis 37

5.1 Pre-study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.1 Static analysis - blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1.2 Modal analysis - blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2 Daggerboard’s analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.2.1 Static analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

xi

xii CONTENTS

5.2.2 Modal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.3 CST daggerboard improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.1 Structural designing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.3.2 Static analysis - improved CST daggerboard . . . . . . . . . . . . . . . . . . . . . 47

5.3.3 Modal analysis - improved CST daggerboard . . . . . . . . . . . . . . . . . . . . . 47

6 Material analysis 53

7 Conclusions 59

8 Future work 61

Bibliography 63

A Xfoil software 1

B Structural analysis - complementary 5

B.1 Blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

B.2 Daggerboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

B.3 Original L daggerboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

C Material Complement 11

C.1 Daggerboard with different materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

C.2 Material data sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

List of Figures

2.1 Team Cascais Catamaran [9]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Catamaran Components. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Flyer - Team Hydros boat [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Daggerboard - degrees of freedom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 Daggerboard Overview [4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.6 Alpha’s first daggerboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.7 Forces Involved - V Profile [10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.8 Airfoil’ forces [24] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.9 Hydrofoil Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.10 Positive image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.11 Negative image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.12 NACA 0012 - cp distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.13 NACA 0012 - cp distribution - angle of attack = 3 . . . . . . . . . . . . . . . . . . . . . . 15

2.14 Cavitation - Three Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.15 Pressure Coefficient vs Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.1 Daggerboard dimensions nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 NACA 2412 - angle of attack = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 NACA 5412 - angle of attack = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1 Bernstein polynomial decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.2 Two-dimensional cost function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3 D = 7 parameters, crossover example [33] . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Hydrofoil shape - example. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.5 CL vs alpha - NACA and Eppler profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.6 CD vs alpha - NACA and Eppler profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.7 cp vs x/c - NACA and Eppler profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.8 NACA 2412 - Re = 2.5× 106 and Alpha = 3.5 . . . . . . . . . . . . . . . . . . . . . . . . 31

4.9 NACA 5412 - Re = 2.5× 106 and Alpha = 3.5 . . . . . . . . . . . . . . . . . . . . . . . . 31

4.10 Hydrofoil Eppler 836 (black line) and initial shape (red line) . . . . . . . . . . . . . . . . . 32

4.11 Eppler 836 and CST shape approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

xiii

xiv LIST OF FIGURES

4.12 CST shape with thickness in the trailing edge . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.13 L/D ratio evolution - E836 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.14 cp,min evolution - E836 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.15 CST final shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.16 CST final shape - pressure distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.17 E836 - pressure distribution for the same conditions of CST . . . . . . . . . . . . . . . . . 36

5.1 Mesh Refinement - Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 Mesh Refinement - Displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.3 Stress distribution - NACA 2412 blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.4 Paddle stress distribution - NACA 5412 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.5 Stress distribution - CST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.6 Mesh detail - CSTinitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.7 Total constrain - CSTinitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.8 Pressure distribution - CSTinitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.9 Deformation - CSTinitial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.10 Daggerboard stress distribution - NACA 2412 . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.11 Daggerboard stress distribution - NACA 5412 . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.12 Daggerboard stress distribution - CSTinitial . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.13 NACA 2412 x-direction displacement vs time [s . . . . . . . . . . . . . . . . . . . . . . . . 45

5.14 CSTinitial x-direction displacement vs time [s . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.15 NACA 2412 y-direction displacement vs time [s . . . . . . . . . . . . . . . . . . . . . . . . 45

5.16 CSTinitial y-direction displacement vs time [s . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.17 NACA 2412 z-direction displacement vs time [s . . . . . . . . . . . . . . . . . . . . . . . . 45

5.18 CSTinitial z-direction displacement vs time [s . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.19 CSTimproved - trapezoidal blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.20 Stress distribution - CST improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.21 Total displacement - CST improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.22 graphic x direction vs frequency [Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.23 graphic y-direction vs frequency [Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.24 graphic z-direction vs frequency [Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.25 Total displacement - CSTfinal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.26 Stress distribution - CSTfinal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.27 Graphic x-direction (CSTinitial and CSTfinal ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.28 Graphic y-direction (CSTinitial and CSTfinal ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.29 Graphic z-direction (CSTinitial and CSTfinal ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

6.1 Ashby map - Young’s modulus vs density . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6.2 Ashby map - Yield strength vs density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.3 Ashby map - Elongation vs Price. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

LIST OF FIGURES xv

A.1 Load of the geometry coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

A.2 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

A.3 Minimum pressure coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

A.4 Pressure distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

A.5 Output file example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

B.1 Displacement distribution - NACA 2412 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

B.2 Displacement distribution - NACA 5412 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

B.3 Daggerboard displacement distribution - NACA 2412 . . . . . . . . . . . . . . . . . . . . . 7

B.4 Daggerboard displacement distribution - NACA 5412 . . . . . . . . . . . . . . . . . . . . . 7

B.5 Daggerboard displacement distribution - CST . . . . . . . . . . . . . . . . . . . . . . . . . 8

B.6 NACA 5412 x-direction displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

B.7 NACA 5412 y-direction displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

B.8 NACA 5412 z-direction displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

B.9 Original L daggerboard dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

C.1 Daggerboard displacement- CFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

C.2 Daggerboard stress distribution- CFRP . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

C.3 Daggerboard displacement- Titanium alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

C.4 Daggerboard stress distribution- Titanium alloy . . . . . . . . . . . . . . . . . . . . . . . . 13

C.5 Composite T800 data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

C.6 Composite T800 data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

C.7 CFRP - data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

C.8 GFRP - data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

C.9 Titanium alloys - data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

C.10 Rigid Polymer Foam HD - data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

C.11 Rigid Polymer Foam MD - data sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

List of Tables

2.1 ICCCC 2013 - Teams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1 Scenario of study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 CST Final Geometry Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.1 Material Properties - T800 material (data sheet in appendix C) . . . . . . . . . . . . . . . 38

5.2 Stress and Maximum Displacement - Blades . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.3 Natural frequencies - blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.4 Maximum displacements and stress - rectangular blade . . . . . . . . . . . . . . . . . . . 42

5.5 Natural frequencies - rectangular blade . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.6 CST blade improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.7 Natural frequencies - CST profile improvement . . . . . . . . . . . . . . . . . . . . . . . . 47

5.8 Final daggerboard results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.9 Natural frequencies - NACA and CST profile evolution . . . . . . . . . . . . . . . . . . . . 51

6.1 Selected materials and properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6.2 T800, CFRP and Titanium Alloy results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

B.1 Mesh Refinement - NACA 2412 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

B.2 Mesh Refinement - NACA 5412 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

B.3 Mesh Refinement - CST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

xvii

Nomenclature

Symbol Units Description

L N Lift force

D N Drag force

CL − Lift coefficient

CD − Drag coefficient

ρ kg/m3 Fluid density

c m Chord length

v m/s Velocity

cp − Pressure coefficient

cp,min − Minimum pressure coefficient

cp,neg − Negative pressure coefficient

p∞ Pa Freestream static pressure

pv Pa Vapour pressure

U − Sum of negative pressure

α Angle of attack

σcavit − Cavitation number

d m Depth length os structure

A − Aspect ratio

g m/s2 Gravitational acceleration

A m2 Section area

b m Span length

m kg Mass

x m x coordinates

y m x coordinates

β − Panel distribution angle

n − Number of panels

ψ − x non-dimensional coordinates

ζ − y non-dimensional coordinates

C − Class function

S − Shape function

xix

xx LIST OF TABLES

N − Shape parameters

AU − Upper curvature coefficients

AL − Lower curvature coefficients

K − Binomial coefficient

Np − Number of parameters

D − Vector dimensions

G − Generation

xi ,G − Target vector

vi ,G+1 − Mutant vector

ui ,G+1 − Third vector

F − Amplification control

CR − Cut off parameter

Re − Reynolds Number

L/D − Lift-drag ratio

βOF − Weight value of objective function

λ − Constant

σmax MPa Maximum stress

Sy MPa Yield Strength

ν − Poisson coefficient

E GPa Young’s modulus

nSF − Safety factor

fn Hz Natural frequency

Cmaj m Major chord

cmin m Minor chord

P N Weight

Sty MPa Tensile Strength

KIC MPa√

m Fracture toughness

ε % Strain

Cm EUR Cost

Acronyms

Acronym Meaning

2D Two-dimensional

3D Three-dimensional

CFD Computational Fluid Dynamics

CFRP Carbon Fiber Reinforced Composite

CST Class-Shape-Transformation method

DE Differential Evolution method

DOF Degrees of freedom

GFRP Polyester Glass Reinforced Composite

ICCCC International C-Class catamaran championship

NACA National advisory commitee for aeronautics

LSE Least Squares Error method

RPF HD Rigid polymer foam HD

RPF MD Rigid polymer foam MD

xxi

xxii LIST OF TABLES

Chapter 1

Introduction

The main purpose of this study is to improve the lift velocity performance of a Portuguese C-Class

Catamaran by upgrading the design of the hydrofoil structure, known as daggerboard. The catamaran

championship has been the leader in this field allowing great developments of the catamaran’s main

components: wing, hulls, rudders and daggerboards.

The Portuguese catamaran’s components were made by Optimal Structural Solutions, a Portuguese

company that develops projects on aeronautical and automotive fields. They are involved with the de-

sign work, composites manufacturing process selection, and testing. After the first participation on the

International C-Class Catamaran Championship (ICCCC), the team is now making new studies in order

to optimize parts of the structure and to improve the catamaran’s performance.

Daggerboards are hydrofoils placed on the middle of the hulls that allow the catamaran to reduce drag

and thus increase speed. Since there is less resistance in the air than underwater, the sooner the boat

rises in the water, the earlier it increases its velocity, making the daggerboards the main components

responsible for improving the catamaran’s performance on race.

The daggerboard has been developed along the years by changing its structural profile. The dif-

ferent configurations produce modifications on the catamaran’s behaviour by improving its stability and

velocity. Since the creation of the C-Class championship, there have been significant advances on both

the profiles and the materials. The lighter the boat, the bigger the increase in speed, leading to the

appearance of new materials and profiles.

This work illustrates the developments already achieved until the present date, and contributes to this

cause by making an investigation about the main daggerboard problems and by elaborating a method-

ology for the daggerboard’s improvement.

1

2 CHAPTER 1. INTRODUCTION

1.1 Motivation and objectives

The motivation was to find efficient solutions for the hydrofoil’s design, with the objective of increasing

the catamaran’s performance on the race. Taking this into account, a new hydrofoil geometry was

generated aiming to improve the lift and reduce the drag. A structural analysis was also performed in

order to improve the daggerboard’s mechanical behaviour.

The two-dimensional hydrofoil improvement was done using a computational program written in

Python. A three-dimensional daggerboard structure was then designed with the new hydrofoil section

and a structural analysis was performed in order to create a daggerboard capable of supporting the load

of the boat without permanent deformations. A study of material was also performed in this work. An

alternative material was explored to be applied on the daggerboard’s structure.

1.2 Structure of the thesis

This work is divided into three core parts: two-dimensional, three-dimensional design, and study

of material. There are 7 main chapters apart from the introduction: 2 State-of-Art, 3 Methodology, 4

Daggerboard design, 5 Structural analysis, 6 Material analysis, 7 Conclusions, and 8 Future work.

Chapter 1: Introduction

This first chapter carries out an overview of the work developed throughout this thesis as well as the

main objectives that were set. It also shows how the thesis is organized.

Chapter 2: State of Art

In this chapter, literature research regarding hydrofoils, daggerboards, and material is performed.

The daggerboards used in the last C-Class catamaran championship by the different teams were col-

lected as well as the main advantages and disadvantages of these profiles found by each team. The

history of hydrofoils and their materials are described as well as the main hydrofoils characteristics. Cav-

itation is presented as one of the responsibles for the drag force increase and as the starting point for

the new geometry generation.

Chapter 3: Methodology

The steps taken developing this work, and the project conditions for the new hydrofoil design, are

described in this chapter. The methodology is applied for the hydrofoil’s geometry generation and for the

1.2. STRUCTURE OF THE THESIS 3

daggerboard’s structural improvement. The project conditions are described and summarized in order

to collect the main goals for this work.

Chapter 4: Daggerboard design

The two-dimensional hydrofoil geometry is generated. The theory behind the design is described

and the main characteristics resulting from this new shape are presented. A hydrodynamic character-

istics comparison between the new and the used hydrofoil geometries is made in order to verify the

performance improvement of the generated geometry.

Chapter 5: Structural analysis

A three-dimensional model is designed. Static and modal analysis are performed on the structure.

First, it is made a pre-study only to the blade of the daggerboard. Then a structural analysis is performed

to the daggerboard with the new geometry section and then it is compared to the daggerboard section

used by the portuguese team in the last race. The daggerboard with the new section is then improved

until the displacement values avoid great deformations on the structure.

Chapter 6: Material analysis

A material analysis is performed in order to find different solutions for the structure, aiming for cost

reduction. The mechanical parameters, as well as the environment conditions, are set in order to select

the materials for the daggerboard’s structure.

Chapter 7: Conclusions

In this chapter, the main conclusions are summarized. The results obtained in each part of the work

are analyzed and the final structure’s characteristics are presented.

Chapter 8: Future work

Future work suggestions that are beyond the scope of this work are described in the final chapter

of this dissertation. A Computational Fluid Dynamics (CFD) analysis is the main suggestion for future

work. Adding this analysis to the methodology presented in this work, it is possible to design a dif-

ferent daggerboard configuration more alike the daggerboards that were used by other teams in the

championship.

4 CHAPTER 1. INTRODUCTION

Chapter 2

State of Art

In this chapter, it is described the C-Class Catamaran race and its rules as well as a literature

research about the different existing types of hydrofoil most used in race. A brief description of the

Eppler hydrofoils history and materials evolution is done in order to create a better understanding about

this theme. The hydrofoil nomenclature and cavitation effect’s description are essential due to their

importance for this work. Cavitation is one of the most problematic issues in the hydrodynamics field.

It can cause serious damage in submarine machines and there is still no efficient solution to extinguish

cavitation effects. This problem is used in this work to define a design limit to the hydrofoil geometry.

2.1 C-Class catamaran racing boat

The International C-Class Catamaran Championship (ICCCC) is a high speed boat race where com-

petitors can show their creativity and engineering skills. Since 2004, this race contributes to the devel-

opment of this catamaran class improving their performance year after year by constantly researching

for new designs, new materials, and new solutions. The few existing rules challenge every participant to

be creative with their designs and engineering.

As mentioned by the Canadian’s team designer, if you ask most designers what kind of project they

enjoy, they will tell you it is the project with technical uncertainties that sketch the imagination, and the C-

Class rules certainly leave ample room for imagination [16]. This challenge is composed by few teams

of different parts of the world. This very last year, 2013, 8 teams participated on the championship, from

Canada and USA to France, Switzerland, Great Britain, Spain, and Portugal (Tab. 2.1).

Team Cascais was born from a partnership between Tony Castro and Optimal Structural Solutions.

The main purpose of this project was the participation on ICCCC with the first Portuguese C-Class

catamaran totally built in Portugal, illustrated in Fig. 2.1. The rules for this competition are described

below [3].

5

6 CHAPTER 2. STATE OF ART

Table 2.1: ICCCC 2013 - Teams

Country Team

Canada Fred EatonUnited States of America Cogito ProjectFrance Challenge FranceFrance GroupamaGreat Britain Team InvictusPortugal Team CascaisSpain Sentient BlueSwitzerland Team Hydros

Figure 2.1: Team Cascais Catamaran [9].

1. A catamaran is defined as a two-hulled sailing boat with essentially duplicate or mirror image hulls,

fixed in parallel positions.

2. Sail area shall not be more than 27.868 m2.

3. The overall length of the catamaran shall not be more than 7.62 m. The length shall be measured

between perpendiculars to the extremities of the hulls with the catamaran in her normal trim.

The measurement shall be taken parallel to the center line of the craft and shall exclude rudder

hangings.

4. The extreme beam shall not be more than 4.267 m.

5. The crew shall be two people.

6. The C class emblem shall be carried on the mainsail and shall consist of the letter C over two

parallel horizontal lines over national letters and sail numbers.

As can be seen, these rules only cover the measures of the sail, hulls and extreme beam. No rules

for the design nor material types are available which means these are open fields to explore, aiming to

improve the boat’s performance on race.

2.2. DAGGERBOARD PROFILES 7

2.2 Daggerboard profiles

In C-Class, the daggerboard has been a constant subject of investigation, consisting in finding and

experimenting with different daggerboard profiles in order to get less drag at higher speeds. For better

understanding, a brief demonstration of the several parts from a catamaran is provided in Fig.2.2.

Figure 2.2: Catamaran Components.

Each team that participated over the last years in the ICCCC made their decisions choosing different

daggerboard profiles. All the teams had the same goal on daggerboard profile design: generate higher

lift so they could go faster.

L Foils - Team Hydros

In 2010, Switzerland’s team sailed the Patient Lady VI and it was the launchpad for Team Hydros

challenge in 2013. This time, the team made improvements on foils in order to get a faster boat. They

ended on the 2nd position last year with Flyer boat.

Thanks to interviews, it is possible to briefly explain the daggerboard mechanism, which is all manual

through a game of ropes. This team chose to use an L shape foil (Fig. 2.3). This decision is justified by

the good results on stabilization of the boat at low speeds and the faster creation of lift when the speed

increases [7].

This daggerboard has three degrees of freedom (DOF) through the hull illustrated in Fig. 2.4: vertical

and horizontal along the hull and perpendicular to the flow direction, represented by black and red row

colors, respectively.

When the boat starts to move, a big angle of attack is obtained in order to guarantee enough lift to

maintain the balance between the hydrodynamic and aerodynamic forces and to lift up the boat. The

sailor moves the foil by changing both angles (x and y directions). By changing the foil position, the

angle of attack also changes. By increasing speed, the produced lift also increases, making the boat fly


above the water. In order to keep this position, the angle of attack is then reduced, by the modification

of both angles again. Beyond that, on this position the foil is able to take the side force more efficiently

while the tip keeps doing the lift. This strategy allowed team Hydros to get the second place on the race.

Figure 2.3: Flyer - Team Hydros boat [1]

Figure 2.4: Daggerboard - degrees of freedom

S Foils - Team Groupama

Team Groupama decided to improve their foil profile to an S shape Fig. 2.5. This decision had as

consequence the conditioning of the daggerboard’s DOF [6]. In contrast with team Hydros, this profile

cannot change the horizontal position over the hull neither the horizontal position perpendicular to the

flow direction. There is no mechanism to do this. In order to achieve this position, team Groupama

has an S shape which only allows vertical movements. Beyond being the profile with better stability, it

also has the advantage to get a simpler mechanism for the sailors. The main disadvantage is that this

mechanism causes friction between the foil and the hull, which makes the vertical movement slower.

T foils - Team Canada

In 2007, Team Canada won ICCCC with the Alpha boat. The team made a previous study regarding

the design applied to the two boats, Alpha and Rocker [28]. Despite the fact that Rocker was a stable

boat, it could not match the 20 knot (10.3 m/s) plus speed of Alpha.

2.2. DAGGERBOARD PROFILES 9

Figure 2.5: Daggerboard Overview [4]

The team decided to construct a T foil for the Rocker boat. It seemed a good idea since it has good

performance on motor boats where the main goal was only to reduce the drag force in order to reduce

the fuel consumption. So they developed the T foil and achieved stable flying. At the end, the Rocker

was a stable and slow boat. They could not achieve competitive speeds around the course.

Figure 2.6: Alpha’s first daggerboard [28]

The team’s conclusion also states that ”After this fairly careful experiment in foiling, we are com-

fortable concluding that hydrofoils don’t perform in this configuration on a C-Class catamaran. There is

no doubt that fine-tuning our parameters could increase Rocker’s speed, but it will take more than fine

tuning to make the required leap in performance”, [28].

Alpha’s performance was different. The team developed a thinner foils section that outperformed the

others - less drag with slightly greater maximum lift. The thin profile had the added benefit of less weight.

Besides the straight foil profile, as shown in Fig. 2.6, this team was able to combine several factors to


produce success, which include lower overall weight, thinner foil section, and more time on the water to

experiment enabling the creation of race tactics.

V Foils - Team Emirates

Looking to a different class, the A-Class, whose main differences for C-Class are the boat dimen-

sions, there are some different solutions at the daggerboard’s field with the same purpose as the C-

Class. Using the Team Emirates example [10], they decided to use a curved daggerboard. When the

board is lowered, the daggerboard gets a V shape instead of an L shape.

On an interview given by Team Emirates [10], the catamaran sits on the V so that when the boat

speed increases, and the lift increases, the foil rises higher in the water with both legs of the V at

an inclined angle instead of nearly horizontal ( Fig. 2.7). As team leader Morrelli says, ”The advan-

tages/disadvantages are that this V is self-levelling. As it raises up to the surface at high-speed, it loses

lift, because it stalls a little bit, and it settles back down where a true L will go completely out of the water,

and you have to find another way of controlling the angle of attack and the amount of lift it creates” [10].

Because the foils extend to their tips at an upward angle instead of flat, as the foil reaches the surface,

the portion of the foil with water flowing over it, generating lift, is reduced incrementally, and the boat

comes down gradually to an equilibrium point. The idea is to balance the forces as speed changes,

avoiding the all-or-nothing conditions that a more horizontal lifting foil encounters.

Figure 2.7: Forces Involved - V Profile [10]

This is a foil shape example that could be used on C-Class but until now there are no records of this

profile being used on race.

2.3. HYDROFOIL DESIGN 11

Team Cascais

Team Cascais has less experience both in boat construction and racing performance. From last year,

the team decided to make some changes in order to create a better equilibrium between the boat and

team performance in race. For this, it was decided to change the way of controlling the angle of attack

of the daggerboard. Instead of changing the angle by modifying the movement of the daggerboard, it

is easier for the team, since there are only two persons sailing the boat, to control it only by the rudder.

Besides, the rudders are in a better position of the boat, and they are lighter and easier to control. The

daggerboard is maintained still while the rudders do the rest of the job.

Last year, Optimal company and Team Cascais chose a National Advisory Committee for Aeronautics

(NACA) 2412 profile for the hydrofoil shape and an S profile for the structure of the daggerboard. Beyond

this profile, Optimal has also developed an L daggerboard with NACA 5412 section.

In this work it was compared the NACA profiles used by Team Cascais to an Eppler profile and then

to a generated shape.

2.3 Hydrofoil design

Since the 1950’s, hydrofoils had great development both on design and performance. Engine boats

were always a matter of concern mostly because of the needed power to move the boats. Increasing

the velocity also increases the drag force and, therefore, the fuel consumption. In order to find a good

balance between speed and drag, new studies were performed and new hydrofoil profiles started to

emerge.

It was concluded, as mentioned in [16], that it was possible to achieve higher speeds on the water

by making the boats fly over it. It would reduce the drag force and consequently the fuel consumption.

This conclusion let engineers develop hydrofoils that created enough lift to get the boat up and maintain

balance between hydrodynamic and aerodynamic forces while it is over the surface [14].

A hydrofoil is similar to an airfoil. The main difference lies on the fact that when choosing the profile it

should be considered cavitation effects and the pressure distribution over the upper surface. There are

several airfoil profiles designed for several specifications. For example, for aircraft wings it is common

to use NACA profiles because of their good behavior in lift generation. For the vessels, it is prudent to

choose a geometry that avoids cavitation, like an Eppler hydrofoil.

2.3.1 Eppler’s hydrofoil

Airfoil design has been developed over the past century, beginning with copies of bird wings and

cut-and-try shapes, some of which were tested in low-Reynolds number wind tunnels. NACA system-


atized this approach by perturbing successful airfoil geometries to generate series of related airfoils.

This approach was not the most indicated if the main goal was to design an airfoil with specific charac-

teristics. At that time, the airfoil design was developed by the application of the next doctrine: the desired

boundary-layer characteristics result from the pressure distribution, which results from the airfoil shape.

The inversion of an airfoil analysis method provided the means of transforming the pressure distri-

bution into an airfoil shape [22]. The transformation of the desired boundary-layer characteristics into a

pressure distribution was left to Richard Eppler, who developed a computer code that provides a much

more direct connection between the boundary-layer development and the pressure distribution.

With this code, instead of intuitively or empirically transforming the desired boundary-layer character-

istics into a pressure distribution, the designer can determine directly the modifications to the pressure

distribution that will produce the desired boundary-layer development at any given angle of attack.

The hydrofoils presented in this work belong to a set of several airfoils and hydrofoils developed by

Eppler’s method. They have been tested over the years for different Reynold’s numbers and different

environment conditions.

Summarizing, Richard Eppler developed an experimentally-verified, theoretical method that allows

airfoils and hydrofoils to be designed for almost all subcritical applications. Since these hydrofoils and

data are available for common use, an Eppler hydrofoil was chosen to be the base for the development

of this work.

2.3.2 Hydrofoil characteristics

The hydrofoil creates a lift force, perpendicular to the flow direction, and a drag force, which has the

same direction of the flow (Fig. 2.8). Since the purpose of this work was to make the boat fly over the

water, the main goal was to increase the lift generated by the hydrofoil.

Figure 2.8: Airfoil’ forces [24]

The angle of attack is the angle between the flow direction and the hydrofoil chord. If the angle of

attack increases, the lift force also increases, while the drag force decreases. The main problem of


these daggerboards is the variation of the angle of attack, with the changes of the sea currents and the

occurrence of waves. It is very dangerous for the sailors and for the vessel if the waves impact directly.

At the beginning, with reduced velocities, it is necessary to have big angles of attack on the foils, in order

to increase speed and, consequently, lift.

Lift (L) and drag (D) forces can be calculated by Eq. (2.1), respectively. Both equations have similar

constants, like the flow velocity, represented by v, the fluid density, ρ, and the hydrofoil chord, c. Both lift

(CL) and drag (CD) coefficients are dependent of the hydrofoil shape.

CL =L

12ρcv2

(2.1a)

CD =D

12ρcv2

(2.1b)

The mean camber line defines the hydrofoil curvature, as shown in Fig. 2.9. Due to the changing of

the curvature, the lift and drag forces values change as well.

Figure 2.9: Hydrofoil nomenclature [24]

The upper surface is where the velocity reaches high speeds and the static pressure reaches low

values. The static pressure in the lower surface is higher than in the upper surface. The pressure

gradient between both surfaces generates the lift force.

In this work it was not considered the free surface effects in the hydrofoil pressure distribution. The

incorporation of this parameter could be done by considering two limiting cases: low Froude number and

high Froude number.

In the first case (Fig. 2.10), it can be simulated by calculating the flow about the body and its mirror

image in the z=0 plane, creating the positive image. Considering a low Froude number, the velocity is

equal to zero, making the pressure in the free surface not constant.

In the second case (Fig. 2.11), having a high Froude number, the signs of the image singularities

are reversed, creating a negative image. This simulation gives zero horizontal velocity on z=0, making

the velocity there equal to free stream. In this case, the pressure drops near the surface making the lift

coefficient increase.

For this work, the second case is the most indicated to be considered since the Froude number

obtained is a high number. However, this was not considered since this would require to change the


code of the software used to compute the hydrofoil pressure distribution which is beyond the scope of

the current work.

Figure 2.10: Positive image [19]

Figure 2.11: Negative image [19]

The distribution of pressure over a hydrofoil is usually expressed by the pressure coefficient,

cp =p − p∞

12ρv2

, (2.2)

where p is the local static pressure, p∞ is the freestream static pressure, ρ is the fluid density, and v is

the flow velocity. In Fig. 2.12, a NACA 0012 is represented such as the cp evolution with the increasing

of the angle of attack. This representation was obtained from the Xfoil software. This is a symmetric

profile and it is commonly used for the design of wings. Note that the leading edge peak becomes more

extreme as the angle increases. For equilibrium we must have a pressure gradient when the flow is

curved. In the case shown here, the pressure must increase as we move further from the surface. This

means that the surface pressure is lower than the pressures further away. This is why the cp is more

negative in regions with curvature in this direction. The curvature of the streamlines determines the

pressures and the net lift.

Fig. 2.13 represents the pressure coefficient distribution in both upper and lower surfaces, for an

angle of attack equal to 3 degrees. This airfoil is an example just to illustrate the dependence of the pa-

rameters from each other. NACA 0012 is an airfoil commonly used for flying purposes and experiments

due to the availability of many data sources for comparison.


Figure 2.12: NACA 0012 - cp distribution.

Figure 2.13: NACA 0012 - cp distribution - angle of attack = 3 .


2.3.3 Cavitation

Hydrofoils have an important issue to avoid: cavitation. Cavitation is the formation of vapor cavities

within a flowing liquid due to both the excessive decrease of local pressure and the moment when

the critical speed is reached or exceeded, [14]. It is common to verify the cavitation phenomenon on

hydraulic systems, like turbines or pumps. On the case of the hydrofoil, it also depends of the distance

between the surface, the localization of the daggerboard underwater, and the minimum pressure value.

In this study, the effect on the flow past hydrofoils was a matter of concern, since it was one of the

identified problems in last race. This can be characterized into three stages:

• The inception stage.

• A partial cavitation stage in which the vapor forms an attached cavity shorter than the chord.

• A fully cavitation or supercavitation stage where the vapor cavity is distinctly longer than the chord.

Fig. 2.14 illustrates those three stages. Using the description of cavitation by [23], If the pressure

above the liquid is reduced by any means, evaporation recommences until a new balance is reached. If

the pressure is sufficiently lowered, the liquid boils when bubbles of vapour are formed in the fluid and

rise to the surface, producing large volumes of vapour. In hydraulic engineering the vapour pressure

of a liquid is of importance, for there may be places of low local pressure, particularly, when the liquid

is flowing over a solid surface. If, in one of these places, the pressure is reduced until the liquid boils,

then bubbles suddenly collapse. There, very rapid collapsing motions cause high impact pressures if

they occur against portions of the solid surface, and may eventually cause a local mechanical failure by

fatigue of the solid surface.

Figure 2.14: Cavitation - Three Stages [15].

2.4. MATERIAL EVOLUTION 17

The cavitation number is commonly represented by σcavit and it is defined by Eq. (2.3).

σcavit =p∞ − pv

12ρv2

, (2.3)

The p and pv are the ambient and vapor pressure, ρ represents the fluid density, v is the velocity of

upstream flow which corresponds to the boat speed.

The static pressure has a minimum value somewhere at the surface of the foil. The corresponding

reduction of the static pressure is indicated by the pressure coefficient, Eq. (2.4).

cp,min =pmin − p∞

12ρv2

(2.4)

For the critical condition of pmin = pv , it is possible to conclude that the critical cavitation number is

represented by Eq. (2.5).

σcavit = −cpmin = |cpmin| (2.5)

This equation represents the beginning of cavitation. It can also be concluded by Eq. (2.14) that

when velocity increases, the cavitation number decreases, which reduces the range of the pressure

coefficient allowed to avoid cavitation.

In cambered sections, there is an optimum lift coefficient, at which the streamlines meet the section

nose smoothly [26]. If a thinner profile is chosen with a non-smooth nose it would have had a higher

pressure coefficient (cp) contributing to higher cavitation and, consequently, increasing the drag. In

Fig. 2.15 it is possible to see an example of cp evolution with velocity for different depths from free

surface.

The only way to avoid cavitation, although it will never be totally avoided, is to generate balance

between the angle of attack, the velocity of the boat and the profile pressure coefficient. In [32], several

studies were already made in order to create a ”formula” to avoid cavitation problems but there still isn’t

a reliable solution.

2.4 Material evolution

Since 1906 [5], the hydrofoil boats have been developed in order to create more velocity. The first

hydrofoil was built by Enrico Forlanini [11], an engineer and aircraft pioneer who contributed to the heli-

copters and hydrofoils development. Forlanini designed a classic ladder type construction with multiple

struts. The material used for this first hydrofoil was a metal, the same used in the boat construction. With


Figure 2.15: Pressure coefficient vs velocity.

the world war, the hydrofoil profiles had advances in their development in order to improve the military

ships’ velocity and decrease the fuel consumption, raising the chances to gain advantage over other

boats, both tactically and economically, whilst maintaining the type of material.

Only when the boat racing started to emerge, the materials of these boats started to change. Thanks

to racing rules, that provide limits for the components dimensions and boat total weight, the reduction

of the weight of the boat started to be matter of concern between the teams. Engineers have joined

the designing of the boats, improving it with new material solutions. Thanks to these modifications, the

composites started to arise among the race participants boats and a new era for the materials started,

in order to create better and faster boats.

Chapter 3

Methodology

The work is divided in three parts: hydrofoil design, structural design and material analysis. In the first

part it was generated an improved two-dimensional (2D) geometry. In the second part, it was designed

and analyzed a three-dimensional (3D) structure. Finally, a material analysis was performed.

Since one of the project requirements is to develop a new hydrofoil geometry, it was decided to

choose an Eppler’s profile with similar characteristics that benefits the non-appearance of cavitation

effect. Starting from this point, it was easier to provide a new profile with the necessary characteristics

for the imposed conditions. It was used a set of programs, such as Xfoil software, that provides profile

data such as lift, drag and pressure coefficients, and it was included an optimization method in the main

program in order to improve the parameters.

The design approach implemented on this work [19] was performed by setting the mass and speed

of the boat. Since the total mass is the sum of the boat mass and two regular persons, the equilibrium

of the boat is very sensitive to the position of both sailors. This speed-weight combination must provide

the maximum lift-drag ratio relation with minimum cavitation effects. Besides these fixed variables, there

were two global design variables defined for the current project:

• Depth of the structure, d - since there were already two models developed, an L and S profiles,

the depth of these structures was used as starting point of the new structure design.

• Aspect ratio,A - defined as a range of values and leading to the daggerboard’s dimensions.

The first daggerboard structure was designed considering the original L daggerboard provided by

Optimal company. The structural study started with a simpler geometry and then it was developed until

the structural results were acceptable. The principal dimensions that define a daggerboard’s geometry

are illustrated in Fig.3.1.

The design methodology can be described as follows:

1. By selecting a depth, the cavitation number can be calculated setting the minimum pressure coef-

19

20 CHAPTER 3. METHODOLOGY

ficient of the structure before the occurrence of cavitation effect Eq. (3.1).

σcavit =patm + ρgd − pv

12ρv2

= −cp,min (3.1)

2. With the minimum pressure coefficient defined, it was possible to generate a hydrofoil profile and

optimize the geometry until the maximum lift-drag ratio was achieved.

3. The correspondent CL, produced by the optimized geometry, can be used to calculate the section

area of the hydrofoil Eq. (3.2).

A =mg

12ρv2CL

(3.2)

4. By defining the aspect ratio, the span b of the hydrofoil was calculated Eq. (3.3).

A =b2

A(3.3)

5. Using the original dimensions and a simpler geometry for the blade, a daggerboard was designed

and a static and modal analysis were performed. The analysis results were compared to the

daggerboards with NACA 2412 and NACA 5412 profile sections.

6. A redesign of the structure was made in order to improve the displacement results maintaining a

safety factor above of the required by the Optimal company.

Since a fluid dynamics analysis was not included in this study, it was not possible to provide the

pressure distribution over the depth panel of the daggerboard. For this reason, only the L configuration

without any inclinations was studied in this work.

Figure 3.1: Daggerboard dimensions nomenclature.

3.1. PROJECT CONDITIONS AND ASSUMPTIONS 21

3.1 Project conditions and assumptions

As mentioned before, Team Cascais has two different hydrofoils, L and S profiles with two different

sections. The L profile is composed by a NACA 5412 section, Fig. (3.3), and the S profile by a NACA

2412, Fig. (3.2).

Figure 3.2: NACA 2412 - angle of attack = 0 .

Figure 3.3: NACA 5412 - angle of attack = 0 .

Since these two profiles are used more often as airfoils, they are not the most indicated for underwater

use because of the tendency for cavitation effects. In spite of this fact, the lift coefficient produced is

enough to lift the boat over the water.

For this configuration, the boat gets out of the water at a velocity of 18.5 m/s. One of the goals for

22 CHAPTER 3. METHODOLOGY

the present work was decreasing this velocity to 10 m/s. The first vessel constructed by Optimal had

a mechanism that allowed the movement of the daggerboard through the hull. Now this mechanism is

different, the daggerboard must be still, and always in the same position. Since rudders are lighter than

daggerboards, they are the ones who change the angle of attack, but they are also maintained on the

same position most of the time. This corresponds to an angle of attack equal to 3.5 .

This structure had to have enough thickness to avoid fatigue and undesirable permanent deforma-

tions. The safety factor of, at least, 5 is a company requirement. All these conditions were taken into

account in order to achieve a hydrofoil with better performance than the first ones. To summarize,

• A new hydrofoil geometry was required.

• The lift-velocity was 10 m/s.

• The lift angle of attack is equal to 3.5 .

• There are no constrains for the hydrofoil dimensions - depth, span and chord.

• The cavitation number has to be controlled in order to avoid cavitation effects.

• The safety factor of the structure must be above 5.

Chapter 4

Daggerboard design

In this chapter, it is specified how a two-dimensional hydrofoil shape optimization was made and

which tools were used to achieve the final shape desired. Since a hydrofoil is similar to an airfoil, there

are some methods in the literature that were already used to design a new shape and that can be applied

to this work. However, cavitation must be considered and avoided in order to get less drag force and

improve the boat’s lift velocity. It means that a special attention was given to the pressure drop on the

upper and lower surfaces of the hydrofoil: it had to be under control in the optimization process in order

to guarantee the best performance in race conditions.

It was used a hydrofoil shape already known to start the process. In order to get a smooth geometry,

a Class-Shape-Transformation (CST) method was applied. It defines a basic shape, with the class

function, and modifies the geometry with the shape function.

Differential Evolution (DE) is a population based optimization algorithm developed to optimize real

parameters and value functions. It is an easy method where it is possible to control the minimum

and maximum value for each parameter in order to get the best set of parameters which minimize the

objective function.

In order to perform the hydrofoil shape study in a viscous environment, Xfoil software was included

on the main program. Xfoil is a program for the design of airfoil shapes. The geometry’s coordinates and

the Reynolds number must be specified in order to get pressure distribution in upper and lower surfaces,

as have to be the lift and drag coefficients for a given angle of attack, or a set of them.

The final hydrofoil geometry is presented, as well as the main characteristics. The improvement

process and results are compared to NACA 2412, the daggerboard section used by team Cascais in

last race.

23

24 CHAPTER 4. DAGGERBOARD DESIGN

4.1 Hydrofoil design

The main goal of hydrofoil design proceeds from a knowledge of the boundary layer properties and

the relation between geometry and pressure distribution. On this work, the main goal was to create

a hydrofoil with a good lift-drag ratio, to get a maximum amount of lift while producing low drag, and

maintain a constant pressure distribution over the hydrofoil surface.

The design approach for this work consisted on choosing an existing hydrofoil, that was already

studied and analysed for similar projects, whose goals coincide with the present work goals. The main

advantage of this approach is that there is test data available making the prediction of the hydrofoil

behaviour easier in similar conditions. The approximation of the known geometry to a new one was

done by using the Least Squares Differences (LSD) method between them, generating the new hydrofoil

coordinates by the CST method. Then, an optimization method, differential evolution, was applied.

4.1.1 Class-Shape-Transformation Method

Before using the CST method, it was necessary to define the x coordinates of the hydrofoil. In most

of the cases involving airfoils, a denser panelling is used near the leading and trailing edges, where the

radius of curvature is smaller. A frequently used method for dividing the chord into panels with larger

density near edges is the Full Cosine method. With this method the x coordinate was obtained from

Eq. (4.1).

x =c2

(1− cosβ) (4.1)

The chord is represented by c and, for n chordwise panels needed, β is given by Eq. (4.2), where i

is from 1 to n+1.

β = (i − 1)π

n(4.2)

The CST method was developed for aerodynamic design optimization by [20], and it can be used

to generate two and three-dimensional shapes. For this work, it was only used for the two-dimensional

generation. Any geometry can be represented by this method. The class function defines which type

of geometry it will produce. Since it was defined to generate an airfoil or hydrofoil, the only thing that

differentiates one shape from another is a set of control coefficients that is built into the defining shape

equations. These control coefficients allow the local modification of the shape of the curvature until the

desired shape is achieved.

This method is based on Bezier curves with an added Class function. The non-dimensional coordi-

nates are defined in Eq. (4.3).


ψ =xc

(4.3a)

ζ =yc

(4.3b)

The upper and lower surface defining equations are represented as follows,

ζU (ψ) = CN1N2

(ψ) SU (ψ) + ψ∆ζU (4.4a)

ζL(ψ) = CN1N2

(ψ) SL(ψ) + ψ.4 ζL (4.4b)

Eq. (4.5) represents the class function where, for a round-nose hydrofoil, the parameters N1 and N2

must be equal to 0.5 and 1, respectively.

CN1N2

(ψ) = ψN1 (1− ψ)N2 (4.5)

As mentioned before, CST method allows to represent a hydrofoil only by defining the class function.

In order to achieve the desired shape, it is necessary to define the shape function,

SU (ψ) =NU∑i=0

AUi Si (ψ) (4.6a)

SL(ψ) =NL∑i=0

ALi Si (ψ) (4.6b)

where NU and NL are the order of Bernstein polynomial for upper and lower surface, respectively. In this

work NU = NL = N and they are equal to one less than the number of curvature coefficients (AU and AL)

used. S is the component shape function and it is represented by

Si (ψ) = K Ni ψi (1− ψ)N−1 (4.7)

where K Ni is the binomial coefficient, that is related to the order of the Bernstein polynomials used. It is

defined as follows

K Ni =

N!i !(N − i)!

(4.8)

In Fig. 4.1, it is represented a series of Bernstein polynomials in the form of Pascal’s triangle.

The complete equations, for upper and lower surfaces by CST method, are presented in Eq. (4.9a)


Figure 4.1: Bernstein polynomial decomposition [20].

and Eq. (4.9b), respectively. The last term, ψ.4 ζ, represents the tail thickness.

ζU (ψ) = ψ0.5(1− ψ)1.0K Ni ψ

i (1− ψ)NU−1] + ψ.4 ζU (4.9a)

ζL(ψ) = ψ0.5(1− ψ)1.0K Ni ψ

i (1− ψ)NL−1] + ψ.4 ζL (4.9b)

Given that the control coefficients AU and AL were the only unknown terms, it was used an approx-

imation method to a known geometry to obtain the respective control coefficients, creating a smooth

shape to begin the study.

4.1.2 Differential Evolution

Since the maximization of the lift-drag ratio was one of the goals to achieve, and it was granted by

finding the control coefficients of the shape, it was used a method that optimizes these control coeffi-

cients independently and in parallel, minimizing the time of these calculations.

Differential Evolution (DE) is an optimization method to minimize the function value, by the definition

of a range of values for every single variable of the function. DE uses a number of parameters in vectors

of dimension D to optimize a population of each generation, G, i.e. for each iteration of the minimization

process, [33]. The number of optimization parameters, Np, does not change during the minimization

process. The initial population is randomly chosen and it should cover the entire domain of research.

This space has inferior and superior limits, which should be defined, and it corresponds to the project

parameters. In the present work, it represented each control coefficient of the hydrofoil shape.

For each generation, a new population is born using three stages: mutation, crossing and selection.

DE generates new vectors with parameters by adding a weighted difference between the two previous

vectors to a third vector of the same population - mutation operation. The mutated vector’s parameters

are then mixed with the parameters of the target vector, to yield the third vector. This mixing stage is

called crossover. If the result of the objective function is reduced with this new vector, the vector remains

and it is used in the next generation (iteration). If the result of the objective function is superior than the

target vector, the vector is not replaced - selection operation.


Mutation

For each target vector xi ,G, a mutant vector is generated according to,

vi ,G+1 = xr1,G + F (xr2,G − xr3,G) with i = 1, ... , Np (4.10)

with random indexes r1, r2, ... ∈ 1, 2, ..., Np, which are chosen to be different from the running index

i , so that Np must be greater or equal to four to allow for this condition. F controls the amplification of

(xr2,G − xr3,G) and F > 0. An example is illustrated in Fig. 4.2.

Figure 4.2: Two-dimensional cost function showing its contour lines and the process for generating [33].

Crossover

The third vector is presented as,

ui ,G+1 = (u1i ,G+1, u2i ,G+1, ..., uDi ,G+1) (4.11)

The crossover operation crosses two vectors, xi ,G and vi ,G+1 and generates the third vector, ui ,G+1. For

each vector component, it generates a random number in range U[0, 1], randj . Cut off, CR, parameter

is introduced and it is between zero and one. If randj < CR,

ui ,G+1 = vi ,G+1 (4.12)

Otherwise,

ui ,G+1 = xi ,G (4.13)

In order to guarantee the existence of at least one crossover, a ui ,G+1 is randomly chosen to be part

of vector vi ,G+1. This operation is illustrated in Fig. 4.3.


Figure 4.3: D = 7 parameters, crossover example [33].

Selection

In order to decide whether or not it should become a member of generation G+1, the third vector

ui ,G+1 is compared to the target vector xi ,G using the greedy criterion. If vector ui ,G+1 yields a smaller

cost function value than xi ,G then xi ,G+1 is set to ui ,G+1. Otherwise, the old value is retained, xi ,G.

The study performed by [33], where different optimizing methods are compared to DE, concludes that

DE outperformed all the other minimization methods in terms of required number of function evaluations

necessary to locate a global minimum of the test functions. DE can be used in this type of problem as it

requires few robust control variables.

4.1.3 Hydrofoil Shape Generation

The CST method provides a smooth geometry by the definition of the control coefficients. Just to

illustrate the shape generation, it was introduced the following coefficients.

AU = [1, 1, 1, 1] (4.14a)

AL = [1, 1, 1, 1] (4.14b)

These coefficients generated a hydrofoil geometry (Fig. 4.4).

This was not the most indicated shape to begin the study, so a known hydrofoil was selected and all

the process started from this point.


Figure 4.4: Hydrofoil shape - example.

4.1.4 Case of Study

A hydrofoil with desirable characteristics, such as low pressure coefficient (in order to avoid cavita-

tion) in a viscous environment and a good lift-drag ratio, was chosen. Hydrofoil Eppler 818 (E818) was

a good hydrofoil to start our approximation, since it had a constant pressure value in both surfaces with

a small area between them. However, Eppler 836 (E836) was also a good starting geometry as it can

be seen by comparison between the already used profiles, NACA 2412 and NACA 5412, and E817 and

E836, in Fig. 4.7, Fig. 4.5 and Fig. 4.6.

In Fig. 4.7, it is possible to visualize the pressure distribution only on the upper surface where the

load of the vessel is distributed. The more constant the pressure distribution, the more constant the

load distribution. It means that the daggerboard will suffer less oscillation in race, while the vessel gets

out of water. In spite of this, the E818 generates more lift, and produces much more drag than E836

or even than NACA profiles. Even though both generate constant pressure distributions, the E836 has

an inferior value for the minimum cp value, which provides less cavitation effect appearance. For this

reason, the E836 profile was chosen to begin the shape generation and the optimization process.

4.1.5 CST shape

With the known geometry and the CST method, it was possible to generate a CST shape and ap-

proximate it to the E836 shape. The LSE method was used in order to minimize the error between both

curves. By finding the E836 control coefficients it was defined the first set of control coefficients to begin


Figure 4.5: CL vs alpha - NACA and Eppler profileswith Re = 2.5×106.

Figure 4.6: CD vs alpha - NACA and Eppler profileswith Re = 2.5×106.

Figure 4.7: cp vs x/c - NACA and Eppler profiles withRe = 2.5×106 and α = 3.5 .

the hydrofoil shape optimization. The used Differential Evolution code was taken from [25].


Xfoil software performs analysis to the airfoils in viscous conditions by introducing the Reynolds

number (Re). The Re was calculated with the formula represented in Eq. (A.1). The original chord has

0.23 m of length. For initial analysis it was used a chord of 0.25 m. The lift velocity was equal to 10 m/s

and a density of 1025 kg/m3 was considered.

The corresponding lift-drag ratio and cp,min values are 114 and -1.115 for NACA 2412, 169 and -

1.2467 for NACA 5412, respectively. The correspondent cp distribution for both profiles in Fig. 4.8 and

Fig. 4.9.

Figure 4.8: NACA 2412 - Re = 2.5× 106 and Alpha = 3.5 .

Figure 4.9: NACA 5412 - Re = 2.5× 106 and Alpha = 3.5 .

The new geometry, which from now on is called CST shape, had to achieve the lift-drag ratio and

had cp,min value as its highest reference, in order to avoid cavitation.


4.1.6 Control coefficients

First of all, it was used the LSD method to approximate both shapes. In Fig. 4.10, the E836 shape

(black line) and the initial geometry (red line) are presented. The main goal of this approximation was

to reduce the error between them until the initial geometry becomes equal to E836 shape and thereby

achieved the correspondent control coefficients.

Figure 4.10: Hydrofoil Eppler 836 (black line) and initial shape (red line).

The approximation of the CST shape and E836 was accomplished. The coefficients obtained for

E836 geometry are represented as follows.

AU = [0.10825, 0.15195, 0.15925, 0.14782, 0.31366] (4.15a)

AL = [0.14485, 0.14163, 0.14873, 0.15288, 0.31482] (4.15b)

In Fig. 4.11 both shapes are presented. As can be seen, there is a slight difference between both

shapes, 1.36% minimum error. Since the CST shape control coefficients were found, it was constructed

an objective function based on the main goals to be achieved. It was added some thickness, 0.5 mm, in

the trailing edge, as can be seen in Fig. (4.12) inside the red circle, in order to prepare the geometry to

perform structural analysis.


Figure 4.11: Eppler 836 and CST shape approximation.

Figure 4.12: CST shape with thickness in the trailing edge.

4.1.7 Objective Function

Before defining the objective function it was important to recall the main goals to be achieved.

• (Cp,min)CST ≥ (cp,min)NACA 2412;

• (L/D)CST ≥ (L/D)NACA 2412;

• The pressure distribution should be the most flat possible.

Since the daggerboard used in the last competition was the S profile with NACA 2412, the first set of

analysis were performed using only these geometry values as reference.

The objective function is defined in Eq. (4.18). It was used an initial βOF = 0.50 and then this value

was increased to βOF = 0.75 and βOF = 0.90.

The first attempt to define an objective function focused on the pressure distribution of the hydrofoil.

Since there was a minimum pressure value defined by the cavitation number, it was decided to design

the pretended pressure distribution using only the negative pressure values. For this, it was defined a

vector U which included the sum of negative pressure values, sum(cp,neg) and the pressure limit to be

achieved, -0.5. The result equation is presented in Eq. (4.16).

U = (cp,neg − 0.5)2 (4.16)

Eq. (4.16) is then added to lift-drag ratio, defining the objective function, Eq. (4.17).

ObjFuncpre = −[βOF U − (βOF − 1)

(LD

)λ

](4.17)


However, this combination was decreasing the minimum pressure but not the lift-drag ratio. For this

reason, it was decided to use the minimum pressure of the profile and maximize it, Eq. (4.18). This last

decision worked, and lead to an increase in the lift-drag ratio and the minimum pressure.

ObjFunc = −[βOF cp,min − (βOF − 1)

(LD

)λ

](4.18)

The optimization program minimizes the objective function. In this case, Eq. (4.18) is negative in

order to be maximized. The lift-drag ratio has to be multiplied by a constant λ to have the same order

magnitude of cp,min. It was used λ = 0.01.

As the boat starts to increase the velocity, it tends to lift up of the water, making the depth of the

hydrofoil decrease, until the weight of the vessel equalizes the lifting force provided by the daggerboards.

Considering that the cavitation effect is one of the responsible parameters for the drag increase, it was

established to give a biggest importance to the cp,min control by giving it a higher weight in the objective

function formula along the iteration process.

Using the Eq. (2.3) described in the previous chapter, and defining a depth of 1.8 m, and a velocity

equal to 10 m/s, the real cavitation number is 2.285 (Tab.4.1). This value provides a limit for the pressure

coefficient, Eq. (4.19), and it allows a better control on the pressure coefficient obtained from each

iteration.

Table 4.1: Scenario of study

velocity [m/s] depth [m] σcavit

10 1.8 2.285

The pressure value allowed must respect Eq. (4.19).

σcavit ≥ |cp,min|CST (4.19)

Several iterations were made by changing the weight of the objective function. In the first iterations it

was used a βOF = 0.5 and then it was increased until βOF = 0.9. The iteration’s evolution is illustrated in

Fig. 4.13 and Fig. 4.14.

Eq. (4.20) clarifies the final control coefficients for the CST final shape.

AU = [0.109363, 0.271069, 0.028628, 0.543274, 0.015074] (4.20a)

AL = [0.060382, 0.018628, 0.007965, 0.000362, 0.012472] (4.20b)


Figure 4.13: L/D ratio evolution - E836. Figure 4.14: cp,min evolution - E836.

The lift-drag ratio values converged to 158 and the cp,min to -0.80157. These were acceptable values

since the modulus of the pressure coefficient stayed below the cavitation number defined as 2.2846.

The lift-drag ratio had an increase of 38 % and the minimum pressure coefficient had an increase of

39 % when compared to NACA 2412 lift-drag ratio and pressure coefficient values, respectively, which

fulfills one of the goals of this work.

The CST final shape and its pressure distribution are presented in Fig. 4.15 and Fig. 4.16, cor-

respondingly. The CST hydrofoil has a flat pressure distribution when compared to E836 (Fig. 4.17)

pressure distribution, considering the same conditions.

Figure 4.15: CST final shape.

For the scenario presented in Tab. (4.1) the final shape has the following hydrofoil characteristics,

Tab. (4.2).

Table 4.2: CST Final Geometry Characteristics

Angle [ ] Velocity [m/s] CL CD L/D ratio Cpmin

3.5 10 0.642 0.004 158 -0.802


Figure 4.16: CST final shape - pressure distribution.

Figure 4.17: E836 - pressure distribution for the same conditions of CST.

Chapter 5

Structural Analysis

In chapter 4 an improved two-dimensional hydrofoil was generated. In this chapter, this hydrofoil was

used to design a new three-dimensional model which was then improved using Ansys software until the

displacement distribution results were satisfactory.

First, it was done a pre-study to the blade of the daggerboard. With this study the main characteristics

of the different profiles (NACA 2412, NACA 5412 and CST) in three-dimensional structure are presented.

The natural frequency results from CST blade were compared to the results from an experimental study

by Marco and MacGillivray [29].

The first daggerboard structure has an initial rectangle blade geometry with similar dimensions to the

original. Static and modal analysis were performed to CSTinitial and NACA 2412 daggerboards and the

displacement results were compared.

The CSTinitial blade daggerboard was modified to a trapezoidal geometry, like the original one has

been. This daggerboard is named CSTimproved. The dimensions of this improved blade were calculated

following the methodology described in chapter 3. After the blade’s improvement, the depth panel also

suffered a thickness modification in order to decrease the maximum displacement of the daggerboard.

This last modification changes the daggerboard’s name to CSTfinal.

5.1 Pre-study

Without a fluid analysis to the structure it is not possible to get the right pressure distribution over

all the structure. Instead of making assumptions for the pressure distribution it was decided to perform

analysis with real values and get acceptable results. For this reason, a pre-study of the blade was

performed in order to start the daggerboard structural analysis.

The element chosen for the analysis was SOLID185 which is used for the modelling of solid structures

37

38 CHAPTER 5. STRUCTURAL ANALYSIS

and is defined by eight nodes having three DOF at each node. The material simulated was T800, a

composite used by Optimal company. The main mechanical characteristics of the T800 material are

presented in Tab. 5.1.

Table 5.1: Material Properties - T800 material (data sheet in appendix C)

Young Modulus Yield Strength Poisson coefficient DensityE [GPa] Sy [MPa] ν ρ [kg/m3]

170 2650 0.3 1810

The mesh refinement was elaborated for the three profiles (NACA 2412, NACA 5412 and CST)

in order to find a good compromise between the mesh length and computational time waste. The

convergence for stress and displacement is visible in Fig. 5.1 and Fig. 5.2, respectively.

Figure 5.1: Mesh Refinement - Stress. Figure 5.2: Mesh Refinement - Displacement.

The correspondent values of each graphic are presented in appendix B.

5.1.1 Static analysis - blade

The three profiles have the same dimensions: chord of 0.25 m and length equal to 0.5 m. The

pressure distribution was obtained by the Xfoil software and distributed over the blade surface. Since

the pre-study was only to understand the main differences between the three different profiles, they

are totally constrained on one side. A static analysis was performed and stress distribution results are

illustrated in Fig. 5.3, Fig. 5.4 and Fig. 5.5. Since the CST profile is thinner than the NACA profiles,

it was expected a higher displacement of the CST profile blade. The results from these analysis are

summarized in Tab. 5.2.

5.1. PRE-STUDY 39

Table 5.2: Stress and Maximum Displacement - Blades

Profile Refinement [m] σmax [MPa] Max. displacement [m]

NACA 2412 0.006 57 0.001341NACA 5412 0.006 87 0.001841CST 0.004 109 0.003125

The CST profile presents an increase in displacement of 133% and 69% when compared with NACA

2412 and 5412, respectively. It also developed a higher stress distribution over the blade with an increase

of 91% and 25% when compared with NACA 2412 and 5412, respectively. The maximum stress verified

in the CST profile provides a safety factor of 24, Eq. (5.1), which is higher than the project requirement.

nSF,CST blade =Sy

σmax⇔ nSF, CST blade =

2650109

= 24.3 (5.1)

Figure 5.3: Stress distribution - NACA 2412 blade. Figure 5.4: Stress distribution - NACA 5412 blade.

Figure 5.5: Stress distribution - CST.


5.1.2 Modal analysis - blade

In the modal analysis it was used the Block Lanczos [31] method to perform the analysis. Using an

experimental work elaborated by Marco and MacGillivray in [29], a blade vibrational study was done in

order to get a range of natural frequencies underwater and in vacuum. This experimental study aims

to compare the natural frequencies obtained for both situations. Since the experimental results are

significant for the present work, they are used and compared to CST blade results to conclude if the

behaviour is similar between computational and experimental environments. Taking into account the

results, a refinement was done and only the five modes were considered. The natural frequencies were

obtained and presented in Tab. 5.3. The experimental results are also presented in Tab. 5.3. The CST

frequencies are much higher than the experimental results. Only the first mode frequency is similar

or at least at the same magnitude of the experimental. This fact is due to the different material used

in the experimental, which is a metallic material, and CST blade. Therefore, since the CST blade has

higher natural frequencies for the same modes when compared to the metallic blade, it means that CST

has a better resonance resistance which prevents large structural oscillations and consequently, fatigue

fractures.

Table 5.3: Natural frequencies - blade

Profile f1 [Hz] f2 [Hz] f3 [Hz] f4 [Hz] f5 [Hz]

CST blade 6.3 29.9 36.8 79.2 80.8Experimental [29] 6.4 14.1 15.1 33.0 54.9

Since the material used by the article is not specified, a comparison study using the same material

was not performed.

5.2 Daggerboard’s analysis

The main goal of this study was to understand the behaviour of the L daggerboard with the CSTinitial

profile and compared it with NACA 2412 and NACA 5412. Since the CST thickness is lower than the

NACA’s profiles, the deformation should be higher. This fact had already been verified in the pre-study,

but since the applied constrains are different, it was necessary to perform a full structure static analysis.

The profiles dimensions are based on the original ones. The depth considered in chapter 4 is equal

to 1.8 m, the initial span is around 0.5 m and the chord equal to 0.25 m. The material and element type

were maintained, such as the mesh refinement. At this time, the constrains were applied on the top of

the daggerboard, simulating the hull fitting. The pressure distribution was applied only over the blade.

The static analysis was performed for the three profiles. In order to have more data about the CSTinitial

5.2. DAGGERBOARD’S ANALYSIS 41

daggerboard behaviour, a modal analysis was also performed.

The final mesh, the constrain, and the pressure applied are illustrated in Fig. 5.6,Fig. 5.7 and Fig. 5.8,

respectively.

Figure 5.6: Mesh detail- CSTinitial.

Figure 5.7: Total constrain - CSTinitial. Figure 5.8: Pressure distribution - CSTinitial.

5.2.1 Static analysis

After the pressure distribution and constrains applied in the structures, the CSTinitial daggerboard

deformation is illustrated in Fig. 5.9 and the stress distribution over the daggerboards are presented in

Fig. 5.10, Fig. 5.11 and Fig. 5.12. It is visible that the CSTinitial daggerboard has higher stress distribution

over all the surface. The NACA 5412 daggerboard has lower stress value distribution over the depth

panel due to its higher thickness which allows lower deformation in this zone. The critical stress point

is common in all structures. This is a curved zone where stress tends to concentrate and it can lead to

critical situations like fatigue. The daggerboard has a higher deformation in the y-direction. The CSTinitial

profile has a higher displacement due to its thickness. To prevent this fact, one of the possible solutions

is to increase the thickness in the depth panel since it is where the structure has the higher stresses.

The CSTinitial structure has a security factor of almost 17, Eq. (5.2). To summarize the results of this

analysis, the displacement, and stress values for each profile are presented in Tab. 5.4


Table 5.4: Maximum displacements and stress - rectangular blade

Profile Displacement [m] σmax [MPa]

NACA 2412 0.055 85.6NACA 5412 0.072 137CSTinitial 0.118 158

nSF, CSTinitial =Sy

σmax⇔ nSF, CSTinitial =

2650158

= 16.77 (5.2)

Figure 5.9: Deformation - CSTinitial.

5.2.2 Modal analysis

The static analysis was just a first step to perform a daggerboard behaviour study. A modal analysis

allowed to obtain the natural frequencies of the structure and respective modes of vibration. Initially

were chosen ten modes for the analysis but since the structure begins to deform in a non-sense way, the

number of modes was reduced to five. This range of frequencies deforms the daggerboard in different

directions. For a better understanding of the structure’s deformation, a node was picked in the critical

displacement zone which was coincident on the three profiles. It was presented the correspondent

graphics of this node displacement for the different profiles in order to verify if the deformation direction

is similar on each. The different natural frequencies, fn, for each mode and profile are presented in

Tab.5.5.

It is necessary to pay special attention to the graphic time lecture, since the range of the natural

frequencies in NACA 2412 profile was higher than in CSTinitial profile, the time considered was also

higher. For this reason, all the graphics were compared for a time range between 6 and 80 Hz.

Since the NACA profiles have a similar pressure distribution between them and the original L dag-

gerboard has a NACA 5412 profile, it is only presented the NACA 2412 graphic results. The NACA 5412

5.2. DAGGERBOARD’S ANALYSIS 43

Figure 5.10: Daggerboard stress distribution - NACA 2412.

Figure 5.11: Daggerboard stress distribution - NACA 5412.


Figure 5.12: Daggerboard stress distribution - CSTinitial.

Table 5.5: Natural frequencies - rectangular blade


NACA 2412 7.82 38.31 45.63 88.86 101.02NACA 5412 8.40 39.06 49.08 88.53 107.93CSTinitial 6.32 29.99 36.82 79.24 80.83

results can be consulted in appendix B.

Both profiles have different displacement movements in the same direction. While NACA 2412

(Fig.5.13) moves in the positive x-direction, CSTinitial profile moves into negative direction (Fig.5.14).

It is due to the profile geometry and how it distributes the pressure along its curve. The maximum dis-

placement over x-direction is around 0.9 m and 1.05 m for CSTinitial and NACA 2412 profiles, respectively.

Despite of both having similar displacement paths, in the vertical direction, (Fig. 5.15 and Fig. 5.16)

CSTinitial profile tends to have a smaller amplitude of movement. It contributes to prevent fatigue in the

structure. Finally, in z-direction the displacement of CSTinitial profile was flatter than NACA 2412 profile.

This profile is able to distribute the load uniformly over the surface (Fig. 5.18) in order to have a more

linear deformation of the structure when compared to NACA 2412 (Fig. 5.17).

5.3. CST DAGGERBOARD IMPROVEMENT 45

Figure 5.13: ]NACA 2412 x-direction displacement vs time [s].

Figure 5.14: ]CSTinitial x-direction displacement vs time [s].

Figure 5.15: ]NACA 2412 y-direction displacement vs time [s].

Figure 5.16: CSTinitial y-direction displacement vstime [s].

Figure 5.17: ]NACA 2412 z-direction displacement vs time [s].

Figure 5.18: ]CSTinitial z-direction displacement vs time [s].

5.3 CST daggerboard improvement

The static and modal analysis results demonstrated the CSTinitial behaviour when the pressure and

the natural frequencies were applied on the blade. In this section, the geometric dimensions were

modified in order to get a daggerboard structure similar to the one constructed by Optimal company, in

which the blade has a trapezoidal geometry instead of a rectangular one.


First of all, structural modifications were done in order to decrease the displacement of the blade

to avoid vibrations on it when the boat increases the velocity. So, in order to obtain an optimized dag-

gerboard it was designed a new blade structure and compared it to the CSTinitial daggerboard. The

methodology described in chapter 3 was applied on this section.

In chapter 4, it is found the final profile geometry by the definition of a cp,min limit regarding the

cavitation number from the correspondent velocity. Since the lift coefficient is defined as 0.6423, and

recalling the Eq. (5.3), it is possible to define a section area for the daggerboard. As mentioned in chapter

2, the mass considered for the boat is around 300 kg, where 150 kg corresponds to the vessel and two

sailors with 75 kg each. The boat is supported by two daggerboards and two rudders. It was considered

that the rudders supports around 400 N each, according to Optimal company calculations. From this

point, it was also considered a conservative approach. When the catamaran changes direction, it tends

to lift up one side of the boat, the weight is placed totally on one daggerboard. For this reason, the

weight considered was equal to the total weight of the boat, around 2543 N without counting on rudders.

5.3.1 Structural designing

With the weight and the section area defined, Eq. (5.3) the same aspect ratio (A) of original dagger-

boards is used, which is equal to 3. The Eq. (5.4) calculates the CSTimproved span.

A =mg

12ρv2CL

⇔ A =P

12ρv2CL

with g = 9.81 m/s2 (5.3)

A =b2

AwithA = 3 (5.4)

Since the sectional area of the original structures is a trapezium, it was defined that the major chord

was twice the minor chord, i.e cmin = 0.5Cmaj , which leads to Eq. (5.5).

A =Cmaj + cmin

2b ⇔ A =

Cmaj + 0.5Cmaj

2b ⇔ Cmaj =

2A1.5b

(5.5)

Using the equations above, the dimensions for the final blade using both conservative methods are

presented in Tab. 5.6.

Table 5.6: CST blade improvement

Weight Section Area Span Major chord Minor chordP [N] A [m2] b [m] Cmaj [m] cmin [m]

2543 0.077 0.48 0.21 0.11


The final CSTimproved blade dimensions described in Tab. 5.6 are illustrated in Fig. 5.19. With this new

configuration a static and a modal analysis were performed.

Figure 5.19: CSTimproved - trapezoidal blade.

5.3.2 Static analysis - improved CST daggerboard

The stress distribution and total displacement of the structure are illustrated in Fig. 5.20 and Fig. 5.21,

respectively. The maximum displacement decreased to 0.115 m from 0.118m which was not a significant

modification. However, the curved zone of the daggerboard was not a critical zone anymore, which

prevents fracture. The safety factor of the improved daggerboard remained at 17.

5.3.3 Modal analysis - improved CST daggerboard

By performing a modal analysis of this structure, the range of natural frequencies increases when

compared to the CSTinitial daggerboard which means that this configuration has a higher capability to

avoid oscillations and, consequently, to prevent fractures due to fatigue. The modal analysis results of

the structures are shown in Tab. 5.7.

Table 5.7: Natural frequencies - CST profile improvement


CSTinitial 6.32 29.99 36.82 79.24 80.83CSTimproved 6.07 37.12 38.39 71.33 84.62

In Fig.5.22, Fig.5.23 and Fig.5.24 the movements of the same point on both structures are compared,

CSTinitial, and CSTimproved daggerboard. It is notorious that there are almost no modifications in the

amplitude of movements. In fact, in the three directions the amplitude of movements higher.


Figure 5.20: Stress distribution - CSTimproved.

Figure 5.21: Total displacement - CSTimproved.


Figure 5.22: -CSTinitial and CSTimproved]graphic x direction vs time [s] - CSTinitial and CSTimproved.

Figure 5.23: -CSTinitial and CSTimproved]graphic y-direction vs time [s] - CSTinitial and CSTimproved.

Figure 5.24: -CSTinitial and CSTimproved]graphic z-direction vs time [s] - CSTinitial and CSTimproved.

Since the displacement values were not satisfied, it was decided to improve the depth panel by

increasing the thickness, this new configuration is named as CSTfinal. The maximum displacement

decreased drastically from 11 cm to 3 cm, Fig.5.25. The maximum stress verified was around 116 MPa,

Fig.5.26, which leads to the increase of the safety factor to 23.

The natural frequencies range also increased, meaning a structure more resistant to vibrations. The


Figure 5.25: Total displacement - CSTfinal.

Figure 5.26: Stress distribution - CSTfinal.


movements of the node were once again compared to CSTinitial. The amplitude of movements, consid-

ering the same time of analysis, decreased, which was the main goal of this structural improvement.

The final results of the CSTfinal daggerboard can be consulted in Tab.5.8. The modal results for the

NACA’s profiles, CSTinitial and CSTfinal are summarized and presented in Tab. 5.9.

Table 5.8: Final daggerboard results

Profile Displacement [m] Stress [MPa] Safety factor

CSTinitial 0.118 158 17CSTfinal 0.030 116 23

Table 5.9: Natural frequencies - NACA and CST profile evolution


NACA 2412 7.82 38.31 45.63 88.86 101.02NACA 5412 8.40 39.06 49.08 88.53 107.93CSTinitial 6.32 29.99 36.82 79.24 80.83CSTfinal 15.58 57.37 73.38 104.8 168.1

Figure 5.27: Graphic x-direction vs time [s] - CSTinitial and CSTfinal.


Figure 5.28: Graphic y-direction vs time [s] - CSTinitial and CSTfinal.

Figure 5.29: Graphic z-direction vs time [s] - CSTinitial and CSTfinal.

Chapter 6

Material analysis

Engineering designs must have a part where a material study is performed in order to choose the

material which better fits the loading conditions. A material selection is a necessary process that must

be done carefully, in order to enable the structure to be able to support the project’s requirements.

In this work, the material requirements were defined by the environment and loading conditions

applied on the structure. The daggerboard is underwater most of the time, appearing in the surface only

when the boat is changing direction. It has to support the sum of weight of the vessel and sailors, and

maintain the boat in a stable position, contradicting the moment force generated by the movements of

the boat. It must avoid deformations and fractures due to fatigue.

The mechanical properties required for the design were:

• High Young’s modulus, E.

• High yield and tensile strength, Sy and SUTS, respectively.

• High fracture toughness, KIC.

• High strain, ε.

• Low density, ρ.

• Low relative cost, Cm.

• High resistance to salt and fresh water.

CES Edupack is a software that creates maps of Ashby using the mechanical or material properties

defined. It provides a material and processes database which can be achieved by the input of the desired

material properties[17].

• E1/3/ρ, for the stiffness-limited design at minimum mass.

• S1/2y /ρ, maximizing the strength limit and minimizing mass.

• ε/Cm, with a limit for elongation of 10% and a price between 10 and 100 EUR/kg.

53

54 CHAPTER 6. MATERIAL ANALYSIS

To illustrate the input constrains, the maps of Ashby are presented in Fig. 6.1, Fig. 6.2 and Fig. 6.3.

The ceramic and electrical components categories were removed from the study.

The actual material considered for this study is a composite usually used in sport fields. Composites

are made by embedding fibers in a continuous matrix of a polymer, a metal, or a ceramic. The devel-

opment of high-performance composites is one of the great material developments of the last decades

[18]. The daggerboard is constructed layer by layer of T800 material fiber.

By crossing the information of each property requirement, the selected materials are presented in

Tab. 6.1. The data sheets of the materials can be consulted in appendix C.

The Carbon Fiber Reinforced composite (CFRP) offers more stiffness and strength and is also lighter

than Polyester-Glass Reinforced composite (GFRP), but the cost is higher. Titanium alloy has mechani-

cal properties similar to CFRP. Although it is a heavy material, it can be introduced in a composite matrix

of CFRP creating a final material ideal for the daggerboard. The Rigid Polymer Foam HD (RPF HD)

and Rigid Polymer Foam MD (RPF MD) are materials with a yield strength very low which develops a

safety factor below the imposed limit of 5. For these reasons, only the CFRP and titanium alloy were

considered.

Table 6.1: Selected materials and properties

Material E [GPa] Sy [MPa] SUTS [MPa] ε [%] KIC [MPa√

m] ρ [kg/m3] Cost [EUR/kg]

T800 170 2650 2650 1.6 - 1810 66.3CFRP 150 1050 1050 0.35 20 1600 33.1GFRP 28 192 241 0.95 23 1900 27.4Titanium alloys 120 1200 1450 10 70 4800 21.9RPF HD 0.5 12 12.4 10 0.09 470 19.8RPF MD 0.2 3.5 5.1 5 0.05 165 19.8

In order to check the daggerboard’s behaviour with these materials, a static analysis was performed

for both, the CFRP and titanium alloy, Tab.6.2.

Table 6.2: T800, CFRP and Titanium Alloy results

Material Displacement [m] Stress [MPa] Safety Factor Total Mass [kg] Cost [EUR]

T800 0.0300 116 23 21.19 1405CFRP 0.0346 116 9 17.55 523Titanium alloys 0.0431 115 11 51.50 1025

The composite T800 had a better mechanical behaviour, allowing a maximum displacement of

30 mm. However, the composite CFRP and titanium alloy had a displacement of 34.6 mm and 43.1 mm,

respectively, which were not a significant increase. The main difference between these materials were

the total daggerboard weight and the material cost. For a better performance on race, a lightweight

55

material like T800 material should be chosen. If the cost was the project priority, CFRP should be the

selected material instead. The titanium alloy remains as a suggestion for the composite matrix [30].


De

nsit

y (

kg

/m

^3

)100

1000

10000

Young's modulus (GPa) 0.0

01

0.0

1

0.11

10

100

1000

Rig

id P

oly

mer

Foam

(LD

)

Rig

id P

oly

mer

Foam

(M

D)

Rig

id P

oly

mer

Foam

(H

D)

GFRP,

epoxy m

atr

ix (

isotr

opic

)

Titaniu

m a

lloys

CFRP,

epoxy m

atr

ix (

isotr

opic

)

Figure 6.1: Ashby map - Young’s modulus vs density.

57

De

nsit

y (

kg

/m

^3

)100

1000

10000

Yield strength (elastic limit) (MPa) 0.0

1

0.11

10

100

1000

Titaniu

m a

lloys

Rig

id P

oly

mer

Foam

(LD

)

Rig

id P

oly

mer

Foam

(M

D)

Rig

id P

oly

mer

Foam

(H

D)

GFRP,

epoxy m

atr

ix (

isotr

opic

)

CFRP,

epoxy m

atr

ix (

isotr

opic

)

Figure 6.2: Ashby map - Yield strength vs density.


Pri

ce

(E

UR

/k

g)

0.1

110

100

1000

10000

Elongation (% strain)

0.11

10

100

1000

Rig

id P

oly

mer

Foam

(M

D)

Rig

id P

oly

mer

Foam

(H

D)

GFRP,

epoxy m

atr

ix (

isotr

opic

)

CFRP,

epoxy m

atr

ix (

isotr

opic

)

Titaniu

m a

lloys

Figure 6.3: Ashby map - Elongation vs Price.

Chapter 7

Conclusions

The main goal for this project consisted in creating a new hydrofoil shape that could increase the lift

velocity of a C-Class Catamaran. The new CST hydrofoil shape is able to lift the catamaran at a velocity

of 10 m/s without cavitation effects. The lift-drag ratio increased in 39% and the minimum pressure

decreased in 72%, when compared to NACA 2412 values for the same conditions which fulfills the

project conditions defined. For a depth defined as 1.8 m the cavitation appears at a pressure coefficient

equal to 2.285. Since the CST hydrofoil has a minimum pressure coefficient of 0.8016 it means that

the boat is able to increase the velocity up to 16 m/s without crossing the cavitation limit. The final CST

hydrofoil geometry characteristics is presented in Tab. 4.2. Despite of the fact that the main goals were

achieved, the pressure distribution at the trailing edge generates a negative lift which must be improved.

A pre-study of the blade was performed for the three sections: NACA 2412, NACA 5412 and CST.

Structural analysis demonstrated a higher displacement for the CST blade when compared to the other

two profiles(Tab. 5.2). In order to verify the modulation results given by Ansys, the CST blade natural

frequencies range was compared to an experimental work developed by Marco and MacGillivray [29].

The results were of the same order of magnitude but the CST profile demonstrated a better resonance

resistance (Tab. 5.3).

The three-dimensional daggerboard was designed with the CST section. The improving of the dag-

gerboard structure was developed until the maximum displacement verified became lower than the dag-

gerboard’s configurations with NACA’s sections. The final CST daggerboard has an L configuration, a

trapezoidal blade and a depth panel with variation of thickness. The safety factor of the final daggerboard

configuration increased from 17 to 23, which fulfills the safety factor requirement (Tab. 5.8). Beyond the

displacement improvement, the natural frequency range is also higher than the NACA’s daggerboard,

meaning a better fatigue damage tolerance due to a better resonance resistance.

After the three dimensional profile was developed, the two dimensional hydrofoil was again analyzed

in order to conclude if the changes on the chord due to the geometry modification changed the hydro-

foil’s characteristics. It was concluded that the lift-drag ratio had a decrease of 4.5% and the minimum

59

60 CHAPTER 7. CONCLUSIONS

pressure coefficient remains at -0.8016 that keeps this profile able for the purpose.

The study of material was elaborated by defining the main mechanical properties to be maximized,

minimizing the density and cost of the material. With these constrains, two materials were selected:

CFRP and titanium alloy. By performing a structural analysis to the final daggerboard with these new

materials, it was concluded that the maximum displacement verified had no significant change. The

main modification over the structure involved the total weight and the total cost of daggerboard for each

material (Tab. 6.2). The main conclusion is that the T800 material should be selected if the main goal

was to increase the total weight. On the other hand, if the cost was the main concern, then the composite

matrix of CFRP and titanium alloy should be considered for the daggerboard construction.

Chapter 8

Future work

Despite of all the work presented in this study, there is still room for improvements and research

in the hydrofoil study field. In this chapter, some future work is suggested aiming for the continuous

optimization of daggerboards.

A sensibility study should be done to the profile in order to verify the new hydrofoil geometry’s be-

haviour when the angle of attack is changed. By adding an angle of attack parameter to the objective

function, it is guaranteed that the hydrofoil is prepared for the changes in the angle without losing its

main characteristics.

Future studies and researches can be made considering the free surface effects. While doing this,

the constant pressure line, simulating the atmosphere pressure between the underwater daggerboard

and the hull, can be considered. This case can be simulated using computational fluid dynamics (CFD)

study in order to understand the real forces generated by the flow over the structure. For this, a refined

structural mesh must be carefully done as well as the choice of the turbulence modal. From the research

done for the present work, the K-ε turbulence model is the most common use for hydrofoil’s study [27].

This model uses two equations, which relate the energy of turbulence (K) with the turbulent dissipation (

ε). The method used for the hydrofoil generation creates a smooth geometry which allows us to modify

the hydrofoil shape locally. In order to achieve a better design in future research the thickness parameter

improvement should be included in the objective function.

The skin friction is also a matter of concern in the hydrofoil study and it was not included in this work

because it is out of its scope. The drag force has a skin friction component. Future work will include skin

friction in the drag study of the structure.

The geometry for the daggerboard structure adopted has the simplest configuration, an L structure

without any inclination. With the CFD study performed over the structure, the main forces can be calcu-

lated for any daggerboard configuration. The next step for this study is to design an S profile, perform

the CFD study and follow the methodology described in this work for the static and modal studies.

61

62 CHAPTER 8. FUTURE WORK

In addition to this daggerboard work, a hydrodynamic and aerodynamic study of the catamaran could

be performed, including the daggerboard’s material modification to understand if this change influences,

for the best or for the worst, the boat’s performance. In this work, it was concluded that the main

advantage by using the two new materials, composite CFRP and Titanium alloy, is delimited by the

final price of the daggerboard. T800 material allows the construction of a lighter daggerboard with

less deformation. However, if the new mechanical system is applied to the new catamaran, where the

daggerboard position remains still, the sailors won’t have to move it during the race, making no difference

if the daggerboard is heavy. Due to this modification, the total weight of the boat increases. Since there

is not a weight limit in the rules for the boat, a study of all of the boat will be done in order to quantify

how does the weight difference influences the catamaran’s performance.

Finally, the daggerboard and rudder interaction must also be analyzed to understand their influence

on each other. This study is important to comprehend how much the rudder configuration influences the

daggerboard’s performance and vice-versa.

Bibliography

[1] Bob odge. http://www.catsailingnews.com. Accessed 28 February 2014.

[2] Cavitation and bubbles flows. http://cav.safl.umn.edu/. Accessed 4 March 2014.

[3] Championship rules. http://www.restronguetsc.org. Accessed 24 February 2014.

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launched.html. Accessed 28 February 2014.

[5] Hydrofoil history. http://www.hydrofoil.org/history.html. Accessed 24 February 2014.

[6] International c class catamaran championship -groupama walkthrough with designer martin fischer.

http://vimeo.com/76473008. Accessed 28 February 2014.

[7] International c class catamaran championship -hydros walkthrough with mischa and bastiaan.

http://vimeo.com/76441159. Accessed 28 February 2014.

[8] Material properties. http://www.tpub.com/doematerialsci/materialscience22.htm. Accessed 15

September 2014.

[9] A new challenger coming from portugal. http://theflyingboats.com. Accessed 24 February 2014.

[10] Shaping the foils that re-shaped the america’s cup: Part 2 - etnz designer gino morrelli (and pete

melvin). http://www.cupinfo.com/en/americas-cup-gino-morrelli-foils-multihulls-13144.php. Accessed

28 February 2014.

[11] Storia di milano - enrico forlanini. http://www.storiadimilano.it/Personaggi/Milanesi Accessed 24

February 2014.

[12] Swiss c-class catamarans prepare for little america’s cup.

http://www.sailweb.co.uk/multihull/2237/swiss-c-class-catamarans-prepare-for-little-americas-cup.

Accessed 18 March 2014.

[13] (1998). New advances in sailing hydrofoils. Saint-Cloud Cedex .

[14] (2010). L’hydroptere: How multidisciplinary scientific research may help break the sailing speed

record. Royal Institution of Naval Architects.

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64 BIBLIOGRAPHY

[15] (2013). Cavitation and its effects - a case study. MIT .

[16] Acosta, A. (1973). Hydrofoils and hydrofoil craft. California Institute of Technology .

[17] Ashby, M. (2010). Materials selection in mechanical design.

[18] Ashby, M., H. Shercliff, and D. Cebon (2007). Materials, engineering, science, processing and

design. Elsevier Ltd.

[19] Besnard, J., A. Schimtz, G. Tzong, K. Laups, H. Hefazi, J. Hess, H. Chen, and T. Cebeci (1998).

Hydrofoil design and optimization for fast ships. CSULB Foundation.

[20] Brenda, M. and Kulfan (2008). Universal parametric geometry representation method. Journal of

Aircraft, Vol.45, No.1.

[21] Drela, M. (2001). MIT Aero and Astro Harold Youngren, Aerocraft, Inc. User Primer.

[22] Eppler, R. (1990). Airfoil design and data.

[23] Francis, J. (1971). A textbook of fluid mechanics. Edward Arnold.

[24] Henriques, J. (2013). Fluid Mechanics slides. Instituto Supeior Tecnico.

[25] Henriques, J. C. C., M. F. P. Lopes, R. P. F. Gomes, L. M. C. Gato, and A. F. O. F. ao (2012). On the

annual wave energy absorption by two-body heaving wecs with latching control. Renewable Energy .

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[27] Ingvarsdottir, H., C. Ollivier-Gooch, and S. Green. Cfd modeling of the flow around a ducted tip

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[28] Killingi, S. (2009). Alpha and rocker - two design approaches that led to the successful challenge

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matrix composites: fabrication, structure and mechanical properties. Composites Science and Tech-

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optimization over continuous spaces. Journal of Global Optimization, vol.11, 341 - 359.

Appendix A

Xfoil software

Xfoil is used as flow solver in the present work. It was developed in MIT by Mark Drela in 1980s. It

is a free software commonly used for aircraft wing section design. This software is based on high order

panel methods with the fully-coupled viscous/inviscid interaction method used in the code developed by

Drela. In this work, a viscous analysis is performed with a Reynolds number equal to 2.5 × 106 and a

fixed angle of attack of 3.5 . The boundary layers (BL) and wake are described with a two-equation

lagged dissipation integral BL formulation and an envelope en transition criterion.

According to [21], the entire viscous solution (boundary layers and wake) is strongly interacted with

the incompressible potential flow via the surface transpiration model (the alternative displacement body

model is used in ISES code). This permits calculation of limited separation regions.

The drag is determined from the wake momentum thickness far downstream. The total velocity at

each point on the airfoil surface and wake, with contributions from the freestream, the airfoil surface

vorticity, and the equivalent viscous source distribution, is obtained from the panel solution with the

Karman-Tsien correction added.

If lift is specified, then the wake trajectory for a viscous calculation is taken from an inviscid solution

at the specified lift. In the other hand, if alpha is specified, then the wake trajectory is taken from an

inviscid solution at that alpha.

First of all, the file with the geometry coordinates is load at the software Fig. (A.1). For a specific

Reynolds number(Eq. (A.1)) and alpha, Fig. (A.2), Xfoil provides the pressure distribution,cp, the lift and

drag coefficients. It is able to give a minimum pressure coefficient, too Fig. (A.3). Summarizing, Xfoil

finds the flow around the hydrofoil for the given angle of attack and a window pops up showing the

pressure distribution, the section lift coefficient, the section moment coefficient and the angle of attack.

The drag coefficient and the lift-drag ratio are also presented. Both viscous and inviscid flow distribution

are shown on the pop up window. The dashed lines represent the inviscid flow distribution, Fig. (A.4).

This provides an easy way to compare viscous and inviscid flow. In addition, numerous boundary layer

1

2 APPENDIX A. XFOIL SOFTWARE

parameters are calculated. Transition was modeled by the en method with n=9.

Re =ρcvµ

(A.1)

Figure A.1: Load of the geometry coordinates.

Figure A.2: Input parameters.

All the results of each iteration are saved in an output file. The polar, with the angle of attack, lift and

drag coefficients and additional information is presented in Fig. (A.5).

In case of no convergence, no value is written in the output file. In most of the cases, convergence

can not be achieved due to boundary layer separation and stall regions. Moreover, specific points can

lead to numerical error (no convergence). In this case, preliminary computations have to be performed

to force the convergence (if it is possible). Indeed when performing viscous analysis calculations, it is

3

Figure A.3: Minimum pressure coefficient.

always a good idea to sequence runs so that alpha (the angle of attack) does not change too drastically

from one case to another.

For this work, it is specified the hydrofoil coordinates, introduced in Xfoil software that performed

a viscous analysis with a specific alpha. By the interaction between Xfoil and the optimized program,

several iterations are performed until the lift-drag ratio, given by the xfoil, reaches the maximum value al-

lowed by the geometry. It is possible to get information over the pressure distribution by graphic interface

and by coordinates. This information is implemented in Ansys software to create a pressure distribution

over the daggerboard in order to study the load effects over the structure. As can be concluded, this

software is very useful to perform this type of studies, by allowing the calculation of the main hydrofoil

characteristics in a fast and trustfully way.

4 APPENDIX A. XFOIL SOFTWARE

Figure A.4: Pressure distribution.

Figure A.5: Output file example.

Appendix B

Structural analysis - complementary

In this chapter, the information that is not presented in the work is illustrated and better explained

in this appendix. First, the mesh refinement information that is presented by graphics in section 5.1,

is presented in tables in this section. The displacement distribution and the displacement in the three

directions over the NACA 5412 daggerboard is also illustrated. The relations between the chords and

the aspect ratio used in the methodology adopted in subsection 5.3.1 are also explained.

B.1 Blade

In section 5.1 of chapter 5, a mesh refinement is made in order to have the best mesh and perform

the analysis with minimum computer time waste. In Tab.B.1, Tab.B.2 and Tab.B.3 are presented the

mesh refinement and respective stress and displacement values in each iteration for the three profiles.

The displacement distributions over the blades are illustrated in Fig.B.1 and Fig.B.2. The maximum

displacement values are collected and placed in tables in section 5.1.

Table B.1: Mesh Refinement - NACA 2412

Mesh Refinement [m] σ [MPa] Displacement [m]

1 0.05 31 0.00052 0.025 42 0.00103 0.0125 53 0.00124 0.006 57 0.00135 0.005 57 0.00136 0.004 57 0.0013

5

6 APPENDIX B. STRUCTURAL ANALYSIS - COMPLEMENTARY

Table B.2: Mesh Refinement - NACA 5412


1 0.05 46.5 0.00082 0.025 63 0.00133 0.0125 79.1 0.00174 0.006 85.1 0.00185 0.005 85.6 0.00186 0.004 85.8 0.0018

Table B.3: Mesh Refinement - CST


1 0.05 50 0.00102 0.025 74 0.00203 0.0125 94 0.00284 0.006 109 0.00305 0.005 109 0.00316 0.004 109 0.0031

Figure B.1: Displacement distribution - NACA 2412.Figure B.2: Displacement distribution - NACA 5412.

B.2 Daggerboard

For the first daggerboard configuration, it is performed a static and a modal analysis. The displace-

ment distributions over the three profiles are illustrated in Fig.B.3, Fig.B.4 and Fig.B.5. Since the original

daggerboard uses a NACA 2412 profile, only the modal results from this daggerboard are presented

and compared to CST daggerboard results. However, since the NACA 5412 has been analyzed in this

work, its results are presented in Fig.B.6, Fig.B.7 and Fig.B.8.

B.2. DAGGERBOARD 7

Figure B.3: Daggerboard displacement distribution - NACA 2412.

Figure B.4: Daggerboard displacement distribution - NACA 5412.


Figure B.5: Daggerboard displacement distribution - CSTinic.

Figure B.6: NACA 5412 x-direction displacement vsfrequency [Hz].

Figure B.7: NACA 5412 y-direction displacement vsfrequency [Hz].

Figure B.8: NACA 5412 z-direction displacement vsfrequency [Hz].

B.3. ORIGINAL L DAGGERBOARD 9

B.3 Original L daggerboard

The aspect ratio and major and minor chord’s relation presented in subsection 5.3.1, are obtained

from the original structure illustrated in Fig.B.9. The major chord from the original daggerboard is equal

to 0.225 m and the minor chord to 0.112 m. The relation between both is presented in Eq. (B.1) and it is

used to calculate the new chord length for the new CST daggerboard.

r =coriginal

Coriginal⇔ r =

0.1120.225

⇔ r = 0.5 (B.1)

The section area is obtained using the original chord lengths and the original span. The aspect ratio

is then calculated in Eq. (B.2). This value is also used for the CST blade geometry calculation.

[h!]Aoriginal =b2

original

Atrapezium⇔Aoriginal =

0.52

0.225+0.1122 × 0.5

⇔Aoriginal = 3 (B.2)

Figure B.9: Original L daggerboard dimensions.

Appendix C

Material Complement

In this appendix, the displacement and stress distributions of the materials selected in chapter 6 are

illustrated. The information about materials selected are also presented as data sheets provided by

software CES Edupack.

C.1 Daggerboard with different materials

In this section, the displacement and stress distributions of the daggerboard with the two selected

materials, CFRP and titanium alloy, are illustrated in Fig. C.1, Fig. C.2, Fig. C.3, Fig. C.4.

Figure C.1: Daggerboard displacement- CFRP

11

12 APPENDIX C. MATERIAL COMPLEMENT

Figure C.2: Daggerboard stress distribution- CFRP

Figure C.3: Daggerboard displacement- Titanium alloy

C.2. MATERIAL DATA SHEETS 13

Figure C.4: Daggerboard stress distribution- Titanium alloy

C.2 Material data sheets


I n te rmed ia te modu lus , h igh tens i l e s t reng th f i be r, w i th exce l l en t ba lanced compos i tep rope r t i es . Des igned and deve loped to mee t the we igh t sa v ing demand o f a i r c ra f t . Hasbeen used in p r imar y s t ruc tu re o f a i rc ra f t , i nclud ing ve r t i ca l f i n and hor i zon ta l s tab i l i ze r.

F I B E R P R O P E R T I E S

English Metric Test Method

Tensile Strength 796 ksi 5,490 MPa TY-030B-01Tensile Modulus 42.7 Msi 294 GPa TY-030B-01Strain 1.9 % 1.9 % TY-030B-01Density 0.065 lbs/in3 1.81 g/cm3 TY-030B-02Filament Diameter 2.0E-04 in. 5 µm

Yield 6K 6,679 ft/lbs 223 g/1000m TY-030B-0312K 3,347 ft/lbs 445 g/1000m TY-030B-03

Sizing Type 40A, 40B 1.0 % TY-030B-05& Amount 50B 1.0 % TY-030B-05

Twist Twisted, Untwisted

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

CTE -0.56 α⋅10-6/˚CSpecific Heat 0.18 Cal/g⋅˚CThermal Conductivity 0.0839 Cal/cm⋅s⋅˚CElectric Resistivity 1.4 x 10-3 Ω⋅cmChemical Composition: Carbon 96 %

Na + K <50 ppm

C O M P O S I T E P R O P E R T I E S *

Tensile Strength 380 ksi 2,650 MPa ASTM D-3039Tensile Modulus 25.0 Msi 170 GPa ASTM D-3039Tensile Strain 1.5 % 1.5 % ASTM D-3039

Compressive Strength 230 ksi 1,570 MPa ASTM D-695Flexural Strength 235 ksi 1,620 MPa ASTM D-790Flexural Modulus 22.0 Msi 150 GPa ASTM D-790

ILSS 14.0 ksi 10 kgf/mm2 ASTM D-234490˚ Tensile Strength 9.0 ksi 63 MPa ASTM D-3039

* To r a y 2 5 0 ˚ F E p o x y R e s i n . N o r m a l i z e d t o 6 0 % f i b e r v o l u m e .

T O R A Y C A R B O N F I B E R S A M E R I C A , I N C .

®

T800H DATA SHEETTECHNICALDATA SHEET

No. CFA-007

Figure C.5: Composite T800 data sheet


Composite T800/3900-2 Unidirectional Prepreg(Fv=60%)Toray Composites (America), Inc. - Carbon/Epoxy

segunda-feira, 1 de Dezembrode 2014

Copyright © 2014 IDES Inc. (www.ides.com), and Firehole Technologies Inc. (www.fireholetech.com)Information for this material was last updated: 12-12-2013The information presented on this datasheet was acquired by Firehole Technologies Inc., www.fireholetech.com, from various sources. IDES and Firehole make substantialefforts to assure the accuracy of this data. However, IDES and Firehole assume no responsibility for the data values and strongly encourages that upon final material selection,data points are validated.

Page: 1 of 1

Please Note: This symbol denotes data that is available when you purchase this datasheet , orsubscribe to Prospector:Composites.

General InformationProduct DescriptionT800/3900-2 is a carbon/epoxy unidirectional prepreg with high-strain fibers and a high-toughness matrix.

General

Generic Name • Carbon/EpoxyFiber • T800Matrix • 3900-2Fiber Supplier • Toray Composites (America), Inc.Matrix Supplier • Toray Composites (America), Inc.Fiber Volume Fraction • 60 %Form(s) • Unidirectional PrepregMaterial Status • Commercial: Active

Availability • Asia Pacific• Europe

• Latin America• North America

Cured Thickness

• 0,00586 in(• 0,149 mm)

Data Source • Journal Article 1

Data Rating • **

Technical Properties 2Mechanical Nominal Value (English) Nominal Value (SI)Compressive Modulus E11 - Longitudinal 22,6 msi 156 GPa E22 - Transverse 1,29 msi 8,89 GPa

Shear Modulus (G12 - In-Plane) 0,745 msi 5,14 GPa Poisson's Ratio (ν12 - In-Plane) 0,300 0,300

Additional InformationMechanical data was normalized to a fiber volume of 60%. This number was found on the product data sheet titled "Torayca T800H," TorayComposites (America) Inc., Santa Ana, CA.

Notes1 2 Properties are not to be construed as design specifications.

Figure C.6: Composite T800 data sheet


CFRP, epoxy matrix (isotropic) Description The material Carbon fiber reinforced composites (CFRPs) offer greater stiffness and strength than any other type, but they are considerably more expensive than GFRP (see record). Continuous fibers in a polyester or epoxy matrix give the highest performance. The fibers carry the mechanical loads, while the matrix material transmits loads to the fibers and provides ductility and toughness as well as protecting the fibers from damage caused by handling or the environment. It is the matrix material that limits the service temperature and processing conditions. Composition (summary) Epoxy + continuous HS carbon fiber reinforcement (0, +-45, 90), quasi-isotropic layup.

General properties Density 1.5e3 - 1.6e3 kg/m^3 Price * 29.8 - 33.1 EUR/kg Date first used 1963

Mechanical properties Young's modulus 69 - 150 GPa Shear modulus 28 - 60 GPa Bulk modulus 43 - 80 GPa Poisson's ratio * 0.305 - 0.307 Yield strength (elastic limit) 550 - 1.05e3 MPa Tensile strength 550 - 1.05e3 MPa Compressive strength 440 - 840 MPa Elongation * 0.32 - 0.35 % strain Hardness - Vickers * 10.8 - 21.5 HV Fatigue strength at 10^7 cycles * 150 - 300 MPa Fracture toughness * 6.12 - 20 MPa.m^0.5 Mechanical loss coefficient (tan delta) * 0.0014 - 0.0033

Thermal properties Glass temperature 99.9 - 180 °C Maximum service temperature * 140 - 220 °C Minimum service temperature * -123 - -73.2 °C Thermal conductor or insulator? Poor insulator Thermal conductivity * 1.28 - 2.6 W/m.°C Specific heat capacity * 902 - 1.04e3 J/kg.°C Thermal expansion coefficient * 1 - 4 µstrain/°C

Electrical properties Electrical conductor or insulator? Poor conductor Electrical resistivity * 1.65e5 - 9.46e5 µohm.cm

Optical properties Transparency Opaque

Processability Moldability 4 - 5 Machinability 1 - 3

Eco properties Embodied energy, primary production * 453 - 500 MJ/kg CO2 footprint, primary production * 32.9 - 36.4 kg/kg Recycle False

Figure C.7: CFRP - data sheet


GFRP, epoxy matrix (isotropic) Composites are one of the great material developments of the 20th century. Those with the highest stiffness and strength are made of continuous fibers (glass, carbon or Kevlar, an aramid) embedded in a thermosetting resin (polyester or epoxy). The fibers carry the mechanical loads, while the matrix material transmits loads to the fibers and provides ductility and toughness as well as protecting the fibers from damage caused by handling or the environment. It is the matrix material that limits the service temperature and processing conditions. Polyester-glass composites (GFRPs) are the cheapest and by far the most widely used. A recent innovation is the use of thermoplastics at the matrix material, either in the form of a co-weave of cheap polypropylene and glass fibers that is thermoformed, melting the PP, or as expensive high-temperature thermoplastic resins such as PEEK that allow composites with higher temperature and impact resistance. High performance GFRP uses continuous fibers. Those with chopped glass fibers are cheaper and are used in far larger quantities. GFRP products range from tiny electronic circuit boards to large boat hulls, body and interior panels of cars, household appliances, furniture and fittings.


Mechanical properties Young's modulus * 15 - 28 GPa Shear modulus * 6 - 11 GPa Bulk modulus 18 - 20 GPa Poisson's ratio * 0.314 - 0.315 Yield strength (elastic limit) * 110 - 192 MPa Tensile strength * 138 - 241 MPa Compressive strength * 138 - 207 MPa Elongation * 0.85 - 0.95 % strain Hardness - Vickers * 10.8 - 21.5 HV Fatigue strength at 10^7 cycles * 55 - 96 MPa Fracture toughness * 7 - 23 MPa.m^0.5 Mechanical loss coefficient (tan delta) * 0.0028 - 0.005

Thermal properties Glass temperature 147 - 197 °C Maximum service temperature * 140 - 220 °C Minimum service temperature * -123 - -73.2 °C Thermal conductor or insulator? Poor insulator Thermal conductivity * 0.4 - 0.55 W/m.°C Specific heat capacity * 1e3 - 1.2e3 J/kg.°C Thermal expansion coefficient * 8.64 - 33 µstrain/°C

Electrical properties Electrical conductor or insulator? Good insulator Electrical resistivity * 2.4e21 - 1.91e22 µohm.cm Dielectric constant (relative permittivity) * 4.86 - 5.17 Dissipation factor (dielectric loss tangent) 0.004 - 0.009 Dielectric strength (dielectric breakdown) * 11.8 - 19.7 1000000 V/m

Optical properties Transparency Translucent

Processability Moldability 4 - 5 Machinability 2 - 3

Eco properties Embodied energy, primary production * 150 - 170 MJ/kg CO2 footprint, primary production * 9.5 - 10.5 kg/kg Recycle False

Figure C.8: GFRP - data sheet


alloys.pdf

Titanium alloys Description The material Titan was a Greek god, remarkable for his size and strength. His name has been appropriated many times, not always aptly (think of the Titanic). But the alloys of titanium merit the association: the strongest of them have the highest strength-to-weight ratio of any structural metal, about 25% greater than the best alloys of aluminum or steel. Titanium alloys can be used at temperatures up to 500 C - compressor blades of aircraft turbines are made of them. They have unusually poor thermal and electrical conductivity, and low expansion coefficients. The alloy Ti 6%Al 4% V is used in quantities that exceed those of all other titanium alloys combined. The data in this record describes it and similar alloys. Composition (summary) Ti + alloying elements, e.g. Al, Zr, Cr, Mo, Si, Sn, Ni, Fe, V


Mechanical properties Young's modulus 110 - 120 GPa Shear modulus 40 - 45 GPa Bulk modulus 96 - 102 GPa Poisson's ratio 0.35 - 0.37 Yield strength (elastic limit) 750 - 1.2e3 MPa Tensile strength 800 - 1.45e3 MPa Compressive strength 750 - 1.2e3 MPa Elongation 5 - 10 % strain Hardness - Vickers 267 - 380 HV Fatigue strength at 10^7 cycles * 589 - 617 MPa Fracture toughness 55 - 70 MPa.m^0.5 Mechanical loss coefficient (tan delta) 5e-4 - 0.002

Thermal properties Melting point 1.48e3 - 1.68e3 °C Maximum service temperature 450 - 500 °C Minimum service temperature -273 °C Thermal conductor or insulator? Poor conductor Thermal conductivity 7 - 14 W/m.°C Specific heat capacity 645 - 655 J/kg.°C Thermal expansion coefficient 8.9 - 9.6 µstrain/°C

Electrical properties Electrical conductor or insulator? Good conductor Electrical resistivity 100 - 170 µohm.cm


Processability Castability 3 Formability 2 - 4 Machinability 1 - 3 Weldability 4 - 5 Solder/brazability 1 - 2

Eco properties Embodied energy, primary production * 651 - 720 MJ/kg CO2 footprint, primary production * 44.1 - 48.7 kg/kg Recycle True

Figure C.9: Titanium alloys - data sheet


Polymer Foam.pdf

Rigid Polymer Foam (HD) Description The material Polymer foams are made by the controlled expansion and solidification of a liquid or melt through a blowing agent; physical, chemical or mechanical blowing agents are possible. The resulting cellular material has a lower density, stiffness and strength than the parent material, by an amount that depends on its relative density - the volume-fraction of solid in the foam. Rigid foams are made from polystyrene, phenolic, polyethylene, polypropylene or derivatives of polymethylmethacrylate. They are light and stiff, and have mechanical properties the make them attractive for energy management and packaging, and for lightweight structural use. Open-cell foams can be used as filters, closed cell foams as flotation. Self-skinning foams, called 'structural' or 'syntactic', have a dense surface skin made by foaming in a cold mold. Rigid polymer foams are widely used as cores of sandwich panels.

General properties Density 170 - 470 kg/m^3 Price * 9.9 - 19.8 EUR/kg Date first used 1931

Mechanical properties Young's modulus 0.2 - 0.48 GPa Shear modulus 0.055 - 0.195 GPa Bulk modulus 0.2 - 0.48 GPa Poisson's ratio 0.27 - 0.33 Yield strength (elastic limit) 0.8 - 12 MPa Tensile strength 1.2 - 12.4 MPa Compressive strength 2.8 - 12 MPa Elongation 2 - 10 % strain Hardness - Vickers 0.28 - 1.2 HV Fatigue strength at 10^7 cycles * 0.84 - 9.6 MPa Fracture toughness 0.0236 - 0.0905 MPa.m^0.5 Mechanical loss coefficient (tan delta) * 0.005 - 0.15

Thermal properties Glass temperature 66.9 - 171 °C Maximum service temperature 66.9 - 167 °C Minimum service temperature -113 - -73.2 °C Thermal conductor or insulator? Good insulator Thermal conductivity 0.034 - 0.063 W/m.°C Specific heat capacity 1e3 - 1.91e3 J/kg.°C Thermal expansion coefficient 22 - 70 µstrain/°C

Electrical properties Electrical conductor or insulator? Good insulator Electrical resistivity 1e16 - 1e20 µohm.cm Dielectric constant (relative permittivity) 1.21 - 1.45 Dissipation factor (dielectric loss tangent) 8e-4 - 0.008 Dielectric strength (dielectric breakdown) 6.02 - 11 1000000 V/m


Processability Castability 1 - 3 Moldability 3 - 4 Machinability 3 - 4 Weldability 1 - 2

Eco properties Embodied energy, primary production * 96.6 - 107 MJ/kg CO2 footprint, primary production * 3.68 - 4.07 kg/kg

Figure C.10: Rigid Polymer Foam HD - data sheet


Polymer FoamMD.pdf

Rigid Polymer Foam (MD) Description The material Polymer foams are made by the controlled expansion and solidification of a liquid or melt through a blowing agent; physical, chemical or mechanical blowing agents are possible. The resulting cellular material has a lower density, stiffness and strength than the parent material, by an amount that depends on its relative density - the volume-fraction of solid in the foam. Rigid foams are made from polystyrene, phenolic, polyethylene, polypropylene or derivatives of polymethylmethacrylate. They are light and stiff, and have mechanical properties the make them attractive for energy management and packaging, and for lightweight structural use. Open-cell foams can be used as filters, closed cell foams as flotation. Self-skinning foams, called 'structural' or 'syntactic', have a dense surface skin made by foaming in a cold mold. Rigid polymer foams are widely used as cores of sandwich panels.

General properties Density 78 - 165 kg/m^3 Price * 9.9 - 19.8 EUR/kg Date first used 1931

Mechanical properties Young's modulus 0.08 - 0.2 GPa Shear modulus 0.0236 - 0.069 GPa Bulk modulus 0.08 - 0.2 GPa Poisson's ratio 0.27 - 0.33 Yield strength (elastic limit) 0.4 - 3.5 MPa Tensile strength 0.65 - 5.1 MPa Compressive strength 0.95 - 3.5 MPa Elongation 2 - 5 % strain Hardness - Vickers 0.095 - 0.35 HV Fatigue strength at 10^7 cycles * 0.455 - 2.8 MPa Fracture toughness 0.0066 - 0.0486 MPa.m^0.5 Mechanical loss coefficient (tan delta) * 0.005 - 0.15

Thermal properties Glass temperature 66.9 - 157 °C Maximum service temperature 66.9 - 157 °C Minimum service temperature -113 - -93.2 °C Thermal conductor or insulator? Good insulator Thermal conductivity 0.027 - 0.038 W/m.°C Specific heat capacity 1.12e3 - 1.91e3 J/kg.°C Thermal expansion coefficient 20 - 70 µstrain/°C

Electrical properties Electrical conductor or insulator? Good insulator Electrical resistivity 1e17 - 1e21 µohm.cm Dielectric constant (relative permittivity) 1.1 - 1.19 Dissipation factor (dielectric loss tangent) 8e-4 - 0.008 Dielectric strength (dielectric breakdown) 5.61 - 6.76 1000000 V/m


Processability Castability 1 - 3 Moldability 3 - 4 Machinability 3 - 4 Weldability 1 - 2

Eco properties Embodied energy, primary production * 96.6 - 107 MJ/kg CO2 footprint, primary production * 3.68 - 4.07 kg/kg

Figure C.11: Rigid Polymer Foam MD - data sheet

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