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 Infante Prof. João Carlos de Campos Henriques Examination Committee Chairperson: Prof. Luis Manuel Varejão de Oliveira Faria Supervisor: Prof. Virginia Isabel Monteiro Nabais Infante Member of the Committee: Prof. Luis Manuel de Carvalho Gato November 2014 ii iii The problem is not the problem; the problem is your attitude about the problem Capt. Jack Sparrow iv 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 vi Resumo Desde 2004 que a competic¸ao˜ international de catamarans de classe-C tem ganho adeptos e sus- citado o interesse dos engenheiros no desenvolvimento e optimizac¸ao˜ das embarcac¸oes.˜ 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 embarcac¸ao˜ quando esta comec¸a a ganhar velocidade. Neste trabalho, o perfil alar do patilhao˜ foi optimizado de forma a que este crie a sustentac¸ao˜ sufi- ciente para levantar a embarcac¸ao˜ 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 optimizac¸ao˜ Differential Evolution para os parametrosˆ das condic¸oes˜ estabelecidas. Procedeu-se a` analise´ estrutural do modelo tridimensional do patilhao˜ atraves´ da utilizac¸ao˜ do soft- ware Ansys. Foram comparados os resultados dos perfis NACA 2412 e NACA 5412 ja´ existentes, com o perfil optimizado gerado no ambitoˆ do programa de trabalhos da dissertac¸ao.˜ Inicialmente utilizou-se uma configurac¸ao˜ mais simples para o perfil, tendo sido verificado grande deformac¸ao˜ 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 deformac¸oes.˜ Por fim, foi realizado um estudo do material atraves´ do software CES Edupack. Foram definidos os constrangimentos para a utilizac¸ao˜ do patilhao˜ em competic¸ao˜ e selecionado dois materiais de forma a reduzir o custo total da contruc¸ao˜ da mesma. Palavras chave: Patilhao,˜ Perfil Alar, Class-Shape-Transformation Method, Differential Evolution, Analise´ Estrutural, Analise´ de Materiais. vii viii 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 - complementary5 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