Parametric Modelling of Hull Form for Ship Optimization
Filipa Marques Sanches
Thesis to obtain the Master of Science Degree in
Naval Architecture and Marine Engineering
Supervisor(s): Manuel Ventura
Examination Committee
Chairperson: C. Guedes SoaresSupervisor: Manuel VenturaMember of the Committee: José Miguel Varela
June 2016
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
I was taught that the way of progress was neither swift nor easy (Marie Curie)
iii
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Acknowledgments
This research project was conducted during my time as student in Instituto Superior Técnico. My deep-
est gratitude goes to my supervisor and teacher Manuel Ventura for giving me the opportunity to pursue
such an interesting topic and for always pushing me to do more and better. I also want to thank the
CENTEC and the University for giving me the opportunity to learn and work with the FRIENDSHIP-
Framework, a system completely different from what I have been working with so far, and such a powerful
tool with a great potential in the future.
I also have to thank to the members of the FRIENDSHIP forum for the help and all the answers to my
doubts, on the development of the model. I am truly grateful to Karsten Wenzked (Service and Support
Engineer for FRIENDSHIP-Systems) that help me understand the FSP language and create some of
the Features for the import and export of model data.
I have to thank all of my family, especially my parents, that help me getting through these last months,
supporting me and believing in me, ever since I was born. Thank you so much for giving me the oppor-
tunity to study and finding what i truly love to do.
Thank you also to Pedro Carrilho that since of the beginning of my thesis believed in my objectives and
in my capability to reach them. Thank you so much for supporting me during the rougher times and for
challenging me to overcome them and to go further, reaching the best work possible.
Last, but not least, thank you to all my colleagues that helped me during my studies, to my friends that
were always there to support me, and to Orquestra de Amadores de Música de Lisboa for helping me
release all the stress during these last months.
v
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Resumo
Este trabalho apresenta um método para a geração paramétrica de curvas e superfícies tridimension-
ais, de modelos de cascos de navios mercantes. Primeiro, uma breve análise de formas de cascos já
existentes é apresentada, com maior foco em navios graneleiros, de transporte de contentores, navios
tanques e ferries. Algumas curvas, como as tão conhecidas DWL, FOS, FOB, contorno do convés, SAC
e outras, são estudadas de acordo com o tipo de navio, assim como o conjunto de parâmetros adequa-
dos para a sua total caracterização. Segue-se a apresentação dos parâmetros e suas definições, usa-
dos para criar as várias curvas geométricas e de propriedades que caracterizam a forma do casco. Um
modelo paramétrico foi desenvolvido usando o software FRIENDSHIP-Framework, de forma a avaliar
a relevância dos parâmetros escolhidos e os intervalos de variação dos mesmos consoante o tipo de
navio. Alguns cálculos hidrostáticos foram feitos, bem como a aplicação do método de Lackenby de
modo a que o casco final tenha o coeficiente prismático e a posição longitudinal do centro de impulsão
desejados. Por fim, é apresentada uma discussão dos resultados obtidos através da reprodução de
cascos já existentes no modelo desenvolvido.
Palavras-chave: Otimização de Navios, Modelação Paramétrica, Forma do Casco.
vii
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Abstract
This thesis presents a method for the parametric generation of the three-dimensional surface model of
merchant ship hulls. First, a brief analysis of the hull shape of some existing merchant ships is carried
out, focusing on containerships, bulk carries, tankers and ferry ships. Some geometric and property
curves, as the well known FOS, FOB, DWL, deck contour, SAC, and others, were studied according to
the type of ship, as well as the smaller set of parameters suitable for each curve characterization. This
study is followed by a determination of a suitable variation range of each parameter in order to create
more realistic curves. A parametric model was developed using the FRIENDSHIP-Framework system in
order to evaluate the suitability of the parameters chosen and their variation ranges to correctly describe
the hull form. Some hydrostatic calculations were made and the Lackenby Transformation was used in
order to obtain the desired prismatic coefficient and the longitudinal position of the centre of buoyancy.
Finally, the developed model was applied on some existing hull shapes, and the results were presented
and discussed.
Keywords: Ship Optimization, Parametric Modelling, Hull Shape
ix
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Contents
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Resumo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
1 Introduction 1
2 Hull Form Design 3
2.1 Ship design process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Hull Geometric Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 Conventional design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Semi-parametric design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3 Fully-parametric design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.4 Comparison among the geometric modelling concepts . . . . . . . . . . . . . . . . 9
2.3 Curve fairness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Ship design optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 Holistic ship design optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.2 Pareto optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4.3 Design of Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.4 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4.5 Evolutionary Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Previous Research Work 17
4 Analysis of the existing hulls 23
4.1 Main Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Geometric Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.1 Main Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
xi
4.2.2 Longitudinal Contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.3 Flat of Bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.4 Flat of Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.5 Design Water Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2.6 Deck Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.7 Stem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.8 Bulbous Bow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.9 Stern Bulb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.10 Transom Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Property Distribution Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3.1 Sectional Area Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3.2 Flare at Bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.3 Flare at Design Water Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.4 Flare at Deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3.5 Stem Property curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 Development of the hull model 41
5.1 Main Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Geometric Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2.1 Main Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2.2 Flat of bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2.3 Flat of side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.2.4 Design Water Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2.5 Deck Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.2.6 Stem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2.7 Bulbous Bow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2.8 Stern Bulb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.9 Transom Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3 Property Distribution Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.3.1 Sectional Area Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.3.2 Flare At Bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3.3 Flare At Design Water Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.3.4 Flare At Deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.3.5 Stern Property curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.4 Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.5 Hydrostatic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.6 Lackenby Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.7 Control Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
xii
6 Validation of the parametric modelling of the hull form 67
6.1 Geometric Curves Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.1 Main Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1.2 Flat of Bottom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1.3 Flat of Side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.1.4 Design Water Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1.5 Deck Contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1.6 Bulbous Bow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.1.7 Transom Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2 Property Curves Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.3 Submerged Hull Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.4 Reproduction of existing hulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7 Conclusions 73
7.1 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Bibliography 77
A List of the Model Parameters - ASCII input file 81
xiii
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
List of Tables
3.1 Kracht Bulb Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Set of curves to define the hull form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.1 Beam vs Length Between Perpendiculars . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Draft vs Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3 Depth vs Length between perpendiculars . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.4 Parallel midbody length vs length between perpendiculars . . . . . . . . . . . . . . . . . . 25
4.5 Block Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.6 x-position of the beginning of the parallel midbody vs length between perpendiculars . . . 25
4.7 Main Frame - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.8 Bilge width vs bilge height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.9 Flare range of values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.10 FOB - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.11 FOS - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.12 DWL - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.13 Deck - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.14 Deck - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.15 Bow Bulb - Kracht Parameters Study - Types of Bulb . . . . . . . . . . . . . . . . . . . . . 33
4.16 Bulb Length vs Length between perpendiculars . . . . . . . . . . . . . . . . . . . . . . . . 33
4.17 Bow Bulb - New Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.18 Stern Bulb - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.19 Stern Bulb - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.20 Sectional Area Curve - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.21 FAB - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.22 FADWL - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.23 FAD - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.24 Stem Property Distribution - Parameters Study . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1 Main Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Main Frame - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 Main Frame - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
xv
5.4 Main Frame - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.5 Flat of bottom - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.6 Flat of Bottom - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.7 Flat of Bottom - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.8 Flat of side - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.9 Flat of Side - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.10 Flat of Side - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.11 Design Water Line - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.12 Design Water Line - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.13 Design Water Line - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.14 Deck Line - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.15 Deck Line - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.16 Deck Line- Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.17 Stem - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.18 Stem - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.19 Stem- Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.20 Bow Bulb - Kracht Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.21 Bow Bulb - New Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.22 Bulb Longitudinal Contour - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.23 Bulb Longitudinal Contour - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.24 Bulb Halfbeam Elevation Distribution - Points . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.25 Bulb Halfbeam Distribution - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.26 Stern Bulb - Longitudinal Contour - Parameters . . . . . . . . . . . . . . . . . . . . . . . . 53
5.27 Stern Bulb - Boundary - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.28 Stern Bulb - Boundary - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.29 Stern Bulb - Boundary - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.30 Stern Bulb - Shaft - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.31 Transom Panel - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.32 Transom Panel - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.33 Transom Panel - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.34 Sectional Area Curve - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.35 Sectional Area Curve - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.36 Sectional Area Curve - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.37 Flare at Bottom - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.38 Flare at Bottom - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.39 Flare at Design Water Line - Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.40 Flare at Design Water Line - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.41 Flare at Design Water Line - Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.42 Flare at Deck - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
xvi
5.43 Stem - Radius Distribution - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.44 Stem - Angle Distribution - Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.1 Main Dimensions of reproduced hulls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.2 Differences of the hydrostatic calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
xvii
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
List of Figures
2.1 Product life-cycle [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Topology Levels [2] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Traditional design spiral (left) vs. integrated approach (right) . . . . . . . . . . . . . . . . . 5
2.4 Geometric modeling concepts [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.5 Hull design process steps [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.6 Comparison among the different geometric modelling techniques . . . . . . . . . . . . . . 9
2.7 Conventional modelling (clockwise) vs Form parametric modelling (counter-clockwise) [8] 10
2.8 Optimization system [15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.9 Pareto Frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.10 Past (top), present (middle) and future (bottom) drivers of design . . . . . . . . . . . . . . 15
3.1 Linear and non-linear bulbous bow measures [27] . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Bulb section type: ∇ type, O type and ∆ type (circles represent the section’s centre of
gravity) [28] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Definition of a generic curve - Example SAC for a container carrier [8] . . . . . . . . . . . 19
3.4 Set of generic form parameters for planar curve design [8] . . . . . . . . . . . . . . . . . . 20
3.5 InSAC [8] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.1 Bilge width vs bilge height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2 Ship Type vs Bulb Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.3 Position of the Flares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Stem Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.1 Input Parameter Order and Curve Generation Order . . . . . . . . . . . . . . . . . . . . . 42
5.2 Main Frame Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.3 Flat of Bottom curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.4 Flat of Side curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.5 Design Water Line curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
5.6 Deck Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.7 Stem contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.8 Bulb Longitudinal Contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.9 Stern Bulb - Longitudinal Contour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
xix
5.10 Stern Bulb - Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.11 Transom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.12 Sectional Area Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.13 Flare at Bottom curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.14 Flare at Design Water Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.15 Flare at Deck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.16 Stem - Radius distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.17 Stem - Angle distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.18 Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.19 Hull Surfaces - Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.20 Hull Surfaces - Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.21 Lackenby Transformations [34] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.1 Main Frame and FOB Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.2 FOS and DWL Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.3 Deck and Bulb Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.4 Transom Panel Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.5 Submerged Hull Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.6 Containership - Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.7 Containership - Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.8 RoPax - Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.9 RoPax - Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.10 Tanker - Original . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.11 Tanker - Modelo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
xx
Glossary
CAD Computer Aided Sesign
CAE Computer Aided Engineering
CFD Computational Fluid Dynamics
DWL Design Water Line
EEDI Energy Efficiency Design Index
FAB Flare At Bottom.
FADWL Flare At DWL.
FAD Flare At Deck.
FOB Flat of Bottom.
FOS Flat of Side.
IGES Initial Graphics Exchange Specification.
MCDM Multiple Criteria Decision Making.
NURBS Non-Uniform Rational B-Spline.
SAC Section Area Curve.
xxi
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Chapter 1
Introduction
The increase of international competitive pressures and emission regulations, are motivating the ship
owners to pursue more efficient and greener ships. There is also an increasing pressure on shipbuilders
to deliver ships in a shorter time-scale, with increasing complexity and modularity, and to comply with
environmental rules, while lowering initial build and operating costs. A considerable number of design
alternatives and their complete evaluation increases the competitiveness of a shipyard and speeds up
the selection of a suitable product for each ship owner.
Ship design is a complex activity that requires a successful coordination of many different fields. The
bulk of the costs is typically fixed very early while the knowledge about the product is still quite limited.
The freedom to make design decisions is high at the preliminary and conceptual design, but approaches
zero as the product evolves. This decision-taking at the early design stages fixes the major costs while
uncertainties about the upcoming one have to be reduced as much as possible, stimulating the engineers
to find efficient methods to deal with the multidisciplinary tasks, in order to achieve better performance
within available time and budget resources. The design of marine systems is commonly dominated by
a considerable number of objectives and constraints which are related to the many competitive aspects
pertinent to the ship’s life cycle. With this in mind, the optimization procedures appear as tools to help
engineers to solve problems in the early stages of the ship design, considering several different, and
usually conflicting, objectives.
Geometric modelling and optimization concepts have evolved during the recent years, since favourable
geometries are significant in many optimization problems, especially in industries which deal with com-
plex shapes. To investigate and develop innovative solutions, the designer requires a tool that does not
push detailed definition allowing easy reconfiguration. In addition, many calculation exercises may be
automated allowing the designer to spend more time focusing on the solution. To allow the definition of
complex assemblies, detailed design tools introduced topological relationships allowing the definition of
components to be based on others. This is commonly known as parametric design, where the shape is
described in terms of curves developed by form parameters, greatly improving the design as changes
can propagate through the model, updating all the related parts.
The building of the hull shape, is the first and most important part of the ship design, where the main
1
decisions are taken, influencing all the tasks of the design. In the preliminary design several hull gener-
ations and variations are needed and analysed, in order to find the optimum hull shape.
The aim of this thesis is to develop a fully parametric model, that could be used in other tasks of ship
design, such as the hull dimensions and shape optimization, CFD studies and so on. The model should
be able to reproduce as much as possible, all existing geometric shapes of merchant ships, from scratch
without needing a parent hull, since there is a huge urge to create and improve this type of ships. This
model should also be capable to deal with hull shape variations without losing its coherence. For that to
be possible, a study of a set of parameters, and its boundaries and range of values have to be studied.
With the same input parameter values, the model should create exactly the same hull shape, speeding
up the creation of the final hull.
This thesis is organized as follows. In the second chapter, there is a brief description of the different ship
design tasks, how they are connected to each other and the different modelling procedures that can be
applied in the hull development process. The ship optimization is another topic focused on this chapter,
since the hull model developed could be used for this propose. Finally, there is a description of what is
simulation and integration, and their applications in ship design, especially on hull shape design.
A brief study of the previous works focused on the hull shape parametrization is presented on chapter
three.
The fourth chapter presents a study of some existing hulls, focusing on the main dimensions, geometric
curves and property curves. In this chapter, all relations between the curves are explained as well as
the parameters that should be created on the hull model.
The hull model development is explained in chapter five, describing all the curves used and the surface
generation procedure. All parameters and points created are explained, as well as the curves seg-
ments and their characteristics. The Lackenby Transformation is used, and the sections construction
mechanism for export to an ASCII file are also explained.
Finally, the results analysis resume is presented as well as a brief discussion with some conclusions
according to these results. Some guides about what could be done in future research works are also
suggested.
2
Chapter 2
Hull Form Design
In the past, hull form design was more an art than a science, with high dependency on the experience of
naval architects, with good background in various fundamental and specialized scientific and engineering
subjects. The hull form design used to be done using heuristic methods, namely methods derived from
knowledge gained through a process of trial and error.
Nowadays, ship design is a complex activity that requires a successful coordination between different
disciplines, of both technical and non-technical nature, with the objective of creating a valuable and
optimum design solution. The ship is a complex system, and in order to meet the market requirements,
its complexity will continue to increase. So, to cover all the requirements and constraints of the ship
design, the designer has to consider the complete life-cycle of the ship: concept/preliminary design,
contractual and detail design, ship construction/fabrication process ship operation and scrapping.
The figure 2.1 represents the generic phases of a product, in this case a ship, her life-cycle and all
repercussions on her design and planning [1].
The hull description for the modelling process depends on the topology level: Topology of Appearance,
Topology of Design or Topology of Representation [2]. In the figure 2.2 is presented an example of the
different types of information that can be found on the three topology levels.
The different information types applied in each level of topology, difficult the hull form development, mak-
ing the optimization a time-consuming and a highly interactive process. To solve this problem, a method
of hull modelling was developed in order to have a mathematical parametrized hull representation (see
subsection 2.2.3).
In order to facilitate the work between the design members and project team, a tighter integration of CAD
and CFD has to exist. With that in mind, the designers created a CAE environment to allow a better use
of CAD and CFD, called FRIENDSHIP-Framework and it is the software that was used to develop the
hull form in this thesis.
3
Figure 2.1: Product life-cycle [1]
.
Figure 2.2: Topology Levels [2]
2.1 Ship design process
Ship design, is usually considered as an interaction between many design issues, which must be con-
sidered in a sequential process, increasing the detail by each step, until a single design that satisfies all
constraints, balancing all considerations. It was earlier named by Evans the General Design Diagram
[3] and is now known as the Design Spiral (see left scheme on figure 2.3). Several refinements have
been made, such as economic aspects by Buxton [4] and time by Andrews [5]. It combines synthesis
4
and analysis in a sequential process. Despite representing an idealization, the traditional work flow is
to study one issue at a time, advancing the design step by step, undertaking modifications and estab-
lishing refinements iteratively, allowing an increase in complexity and precision across the design cycle.
Several improvements have been made to the design spiral, since it is an inefficient method for handling
complex and simultaneous design changes, especially when doing late changes on variables that affect
the ship’s performance characteristics. Although the spiral approach may result in satisfactory designs,
it doesn’t promote the identification of superior solutions [6].
However, the designers can adopt an integrated approach, which brings together key aspects of design
tasks at the same time (see scheme on the right of the figure 2.3). This method is called Holistic Design
Approach [7].
.
Figure 2.3: Traditional design spiral (left) vs. integrated approach (right) [7]
With evolution of computer hardware and software, more and more parts of the design process are done
on computers, particularly the heavy calculations and drafting elements of ship design.
2.2 Hull Geometric Modelling
With the increasing of fuel costs and the requirement to reduce the ship’s emissions, the ship optimiza-
tion became a big part of ship design. Since the hull form is like a platform that supports the entire
ship systems, making it the most important entity in ship’s hydrodynamics and structural behaviour. The
economic success of the entire system, from production to operation, will depend on the best lines for
the anticipated operational profile.
So, and efficient hull geometric modelling process is very important in ship design since, usually, it
requires a generation and variation of different shapes. The main objective on the hull definition is to
develop a geometric description in which all the relevant physical and geometric characteristics, as the
displacement, the waterplane area, are met with an acceptable shape quality, usually measured with a
fairness criteria.
The hull form design, can be done in two different scenarios: redesigning an existing hull shape or
5
creating one from scratch. Usually, the shipyard utilizes its data based on previous projects to set
up an initial hull which then serves as the starting point for another vessel. Designing from scratch is
considered more often in the yacht design field in which the entire hull shape is established virtually from
scratch. Due to the simpler bare hull yachts geometry and appreciably higher influence of aesthetics,
many designers prefer this work method.
An advanced modelling approach will improve significantly both the design process and the final product.
So, the geometric modelling techniques can be classified in many different ways. In this thesis we will
consider three basic geometric modelling concepts: conventional design, partially-parametric design
and fully-parametric design [1] (see figure 2.4).
Figure 2.4: Geometric modeling concepts [1]
The modelling concepts can be characterized and compared, as done in the following subsections, in
terms of:
• Flexibility: the ability to cope with any possible shape;
• Efficiency: the swiftness with which information (here geometry) is generated;
• Effectiveness: the quality of the outcome (correctness, completness, comprehensiveness, fair-
ness).
6
2.2.1 Conventional design
The conventional design is built on low-level definition of geometry. The curves and surfaces are defined
by points, making the work predominantly interactive.
Using this method, the designer has two approaches to create the geometry. In the first one, he creates
the geometry starting with points, then curves and finally with surfaces created by patches and eventually
meshes. In the second approach, the designer manipulates the geometry, moving each point separately,
associating each surface with a polyhedron of vertices as in the Bézier and the B-spline concepts, in
order to achieve the desired geometry. After the geometry development, the designer evaluates the
hull form obtained in terms of various derived properties. This means that the designer analyses and
compares the desired form fairness by comparing, for example, form curvature plots. Then, the designer
has to modify the geometry several times until he achieves the desired form parameters and fairness.
With this geometric modelling concept, the designer has the absolute control over the hull shape, having
a greater flexibility into the geometry creation, therefore requiring experience and specific knowledge.
However, it is very difficult to achieve the desired hull form, especially if a specific fairness and/or con-
straints are requested, consuming a lot of time in the initial creation and with each manipulation.
2.2.2 Semi-parametric design
Some CAD tools allow the designers to build on existing shapes and to modify the given hull form by
controlling parameters, the descriptors of the geometry, that create variants. Each new hull will have
characteristics related with the parent form.
The new hull creation is based on mathematical transformations or distortions, which can be local or
global. The global transformations refers to methods that simply work on the basis of hull form coeffi-
cients and are therefore easier to use. Examples of partially parametric approaches are [1]:
• Merging/morphing: two ore more shapes are combined to produce a new shape;
• Box deformation: a parent shape is placed into a box and, instead of varying the parent shape
itself, the box is distorted, dragging and squeezing the original shape;
• Added patch perturbation: a patch is placed on top of a given shape, and is used to perturb the
original geometry which itself is left untouched;
• Swinging/shifting: the sectional area curve of a parent hull is systematically changed and new
hull is determined by moving the entire sections longitudinally to match the new sectional area
curve. It also utilizes positional modifiers to evoke shape variation. One example of this method is
the Lackenby method, used in many commercial CAD tools and in the present work.
This has some advantages such as the speed and simplicity for the designers, allowing them to execute
optimization and creating a vast number of variants, in a short period of time. The major disadvantages
are the inflexibility and the lack of shape control, which make variations in hull form types prohibitive.
7
2.2.3 Fully-parametric design
With this geometric modelling concept, the shape is created using fewer data, capturing the essence of
the intended shapes and their possible variations.
Unlike the conventional design, that has to move several points to obtain the desired hull form, this
method creates the geometry based on relationships created by form parameters. These parameters
are high level entities that reflect the functional characteristics of the geometry, expressing some of the
desired properties of the form/geometry:
• Positional: length, beam, draft, etc;
• Integral: area, volume, high order moments, etc;
• Differential: tangents, curvature information, slope, etc.
A ship’s geometry is described in terms of longitudinal curves, so-called basic curves as the sectional
area curve and the design waterline. The modelling of the basic curves is based on form parameter
input, ideally containing all information needed to produce a hull’s shape.
A fully-parametric curve and surface design requires values of form parameters to be known. In general a
naval architect may not be able to immediately specify all form parameters needed to model an entire hull
geometry from scratch. However, the introduced mathematical model allows that any form parameters
beyond a small set of necessary (mainly positional) parameters may be left to be determined from
the optimization if unknown at the beginning. They can then be modified and reintroduced into the
optimization, to gradually build up the final shape.
New hull forms are created by modifying the model parameters values, updating the relationships among
the parameters, and creating curves and surfaces with excellent fairness. The parameters values can
be changed manually or through formulas/equations, which could include other parameters, depending
on certain conditions, making the final hull close to perfection.
Considering bare hulls, the modelling process is subdivided into three consecutive steps [8] (see figure
2.5):
1. Parametric design of a suitable set of longitudinal basic curves (Deck Line, DWL, SAC)
2. Parametric modelling of a sufficient set of design sections derived from the basic curves
3. Generation of a small set of surfaces which interpolate the design sections
Maisonneuve et al. said [9]: Within the project the primary aim of parametric modelling has been to fa-
cilitate the modification of hull shapes to be improved and, eventually, to optimise a ship’s hydrodynamic
performance. In a parametric approach the diversity of possible hull forms is confined by the topology
and the design rules established in the parametric set-up. Nevertheless, once a suitable set- up is im-
plemented, variations can be accomplished in less time and with higher quality.
This method will be used in the present thesis to create the hull form model.
8
Figure 2.5: Hull design process steps [8]
2.2.4 Comparison among the geometric modelling concepts
In the figure 2.6 there is a comparison between the different modelling concepts, presented earlier in
this thesis. It is focused on the flexibility, required knowledge, effectiveness and cost, versus efficiency
[10].
Figure 2.6: Comparison between the different geometric modelling techniques [10]
It is clear that the fully-parametric modelling is more efficient, but lacks on flexibility, since only a few
modifications are required in order to achieve a new fair hull form, but always hulls of the same type.
Extreme changes will cause problems since a particular parametrization is, on itself, a specialization
rather than a generalization. So, it requires a good knowledge and almost all of the time is consumed
developing the whole geometry structure.
The partially-parametric methods proved to be an easy-handled approach for many tasks, but not rec-
ommended for global and multi-objective optimizations.
In other hand, conventional techniques provide highest flexibility, since the designer is completely free
9
to change any part of the geometry.
According to Harries [11], the great advantage of parametric modelling is the ability to find the optimal
balance between variability and simplicity, more precisely the balance between the freedom to be able
to do everything and the restriction to do only what you really need .
Figure 2.7: Conventional modelling (clockwise) vs Form parametric modelling (counter-clockwise) [8]
2.3 Curve fairness
Nowadays, there are numerous methods for the construction of different types of curves and surfaces.
Among the different mathematical representations, NURBS are outstanding due to their several advan-
tages [12].
Nowadays, B-Spline is the method that is mostly used by ship design software packages, due to its
advantageous characteristics, as local shape control, internal continuity and variability. In free-form
design the shape of a B-spline is usually controlled by manipulating the defining vertices, making the
achievement of the desired form not trivial, specially when a suitable fairness and/or specific constraints
are requested.
In the recent years, substantial research on fairing of curves and surfaces has been undertaken. The
method that is mostly applied, consists on improving an initial curve or surface, globally or locally, ac-
cording to a various fairness criteria, while keeping a deviation from the initial object below a certain
tolerance. Some fairness evaluating techniques have been presented by incorporating energy measure-
ment criteria, applying a mathematical formula, and making the fairness criteria one of the objective
functions in ship’s optimization.
For some design problems, the answer to obtain the desired shape with a certain fairness is the definition
of the geometry by a set of form-parameters, as explained in subsection 2.2.3.
10
2.4 Ship design optimization
The ship optimization is the selection of the best solution among a set of different and feasible alterna-
tives, considering one or more objective functions, for example, cargo area optimization, EEDI decrease,
etc. For that the designer must consider the ship has a complex system integrating a variety of subsys-
tems and their components.
Solving the requirements of the sub-systems alone will often not produce an ideal result, instead, the
interactions among all the sub-systems must be analysed, leading to a ship design that truly is a multiple-
criteria decision problem. So, inherent to ship optimization there are conflicts of requirements resulting
from the design constraints and optimization criteria, reflecting the interests of the various ship design
stakeholders: ship owners/operators, ship builders, classification society, port authorities, regulators,
insurers, cargo owners/forwarders, port operators, etc.
Before 1990, there was a significant amount of work conducted on ship design optimization, incorpo-
rating linear programming to solve ship design optimization that included structural problems. It was
documented by Lyon and Mistree [13] and Smith and Woodhead [14].
In the early 1990’s, the first studies on ship optimization combining analytical estimates, such as CFD,
and hull form geometry were made. This was motived by the advances on CFD.
The formulation of optimization problems is a conceptual modelling process that follows certain standard
procedures and result in a specific problem definition tailored for an application, e.g. in ship design. From
the viewpoint of information flow, the generic optimization problem and its basic elements can be defined
as follows (see figure 2.8):
• Input data, Ei: may include numerals quantities, and also more general data knowledge types, as
drawings and qualitative information that need to be properly translated for inclusion in a computer-
aided optimization procedure;
• Design variables, D: free variables of the optimization problem, for example, ship’s main dimen-
sions (controlled by the designer) ;
• Design parameters, P: vector or design variables, that characterized the design under optimiza-
tion (not controlled by the designer);
• Constraints, G: list of mathematically defined criteria, in the form of mathematical inequalities or
equalities, that are function of the design variables and parameters (G=f(D,P));
• Optimization criteria, M: list of mathematically defined performance/efficiency indicators (M=f(D,P));
• Output data, Eo: includes the entire set of design parameters (vector of design variables) for which
the specified optimization criteria/merit functions obtain mathematically extreme values (minima or
maxima).
So, an optimization problem can have only one objective (single objective optimization) or more than one
objective (multiple objective optimization). For each one of these two types of optimization problems,
there are several different methods to solve them and several ways to look at the same problem.
11
Figure 2.8: Optimization system [15]
In the classical approach, there is only a single optimization criterion and a set of constraints, leading
to an easier decision making process. So, the choice of the criterion leads directly to a solution that all
parties can agree on.
However, most of the optimization problems have more than one mission or must meet multiple objec-
tives simultaneously. In those cases, the decision makers can, and will in general, have different value
systems leading to different priority orderings of the multiple, potentially conflicting performance crite-
ria. Then the aim in multiple criteria decision making is to find the best compromise solution from the
so-called Pereto set of solutions, a collection of infinite solutions for the same optimization problem, on
which the optimum solution may be selected on the basis of trade-offs by the decision designer.
As said before, there are several methods to choose the optimum solution. Some of them, will be pre-
sented on the following subsections. Most of the methods presented are available on the FRIENDSHIP-
Framework, used to develop the hull model in the present thesis.
2.4.1 Holistic ship design optimization
According to Aristotle the Principle of Holism is: "The whole is more than the sum of the parts". So, in
this method the optimization process comprises product’s aspects over the many stages and across the
different disciplines [16].
2.4.2 Pareto optimization
The Pareto optimal solution is a set of possible solutions, a set of non-dominated solutions, in which no
single objective can be improved without degrading the achievement of at least one other objective [15].
In figure 2.9 is clear that if each criterion is maximized within the possible set of solutions, and those so-
lutions are represented by the points "A" and "B" respectively. The ideal, but nearly always unattainable,
solution will be point "I". So, considering "O" as the baseline design, the optimum solution may be found
in the feasible region, shown shaded in figure 2.9. This region is defined by the functional constrains,
and all solutions inside will be better than the baseline "O", at least regarding one criterion. With the
optimization process the baseline moves towards the boundary, until it is reached, where every solution
12
Figure 2.9: Pareto Frontier
are equally acceptable. This boundary is referred to as Pareto Frontier and contains all solutions of
interest because no point anywhere, except on this boundary, can be better than the others.
In the absence of any further information, one of these Pareto-optimal solutions cannot be said to be
better than the other, demanding the user to find as many Pareto-optimal solutions as possible.
With the Pareto Frontier the designer can select an optimal solution according to his preferences. This
can be done in a number of ways, such as [15]: using a utility function to rank the different designs, using
scatter 2D or 3D diagrams to visually identify the more attractive designs or using other visual tools.
2.4.3 Design of Experiment
Design of Experiment (DoE) is a method by which the designer studies multiple design parameters and
quantitatively understands their effect on the whole design.
This method uses tables to detect trends of the optimization variables with regard to the objectives of the
problem, being very effective on information gathering. Alternatively, the DoE may serve as database
for response surface fitting or for checking the response sensitivity of a design candidate. It can also be
used to search a suitable starting point of the optimization.
The DoE is used to identify the factors that are significant to the overall design, helping to find the
relevant changes, maxima and minima, and to better understand the design itself [15].
2.4.4 Genetic Algorithms
Genetic Algorithms (GA) are stochastic, non-linear optimization methods that apply the principals of
evolution [17]. They apply the selection, reproduction and mutation methods, retaining only the best
available solution, making them unlikely to adapt to multi-objective problems, as finding the Pareto fron-
tiers (see subsection 2.4.2).
According to Andre and Koza [18], "the genetic algorithm is a highly parallel mathematical algorithm that
transforms a set (population) of individual mathematical objects (typically fixed-length character strings
13
patterned after chromosome strings), each with an associated fitness value, into a new population (i.e.
the next generation) using operations patterned after the Darwinian principle of reproduction and survival
of the fittest and after naturally occurring genetic operations (notably sexually recombinations)”
The components of a GA are: representation for potential solutions, a way to create a initial population
of potential solutions, an evaluation function, some generic operators and values for various parameters.
There are some basic terminology related with GA:
• Fitness is the value that reflects the performance of one solution;
• Search space is a H-dimensional space where all the solutions of the problem are located;
• Exploitation is the process of using information from previous solutions in the search space, to
determine which places might be profitable to find the next solution with increased fitness. This
process is good to find local maxima and minima;
• Exploration is the process to study entirely new search space regions and to analyse if any-
thing promising may be found there. Unlike exploitation, exploration requires jumps into unknown
regions;
• Elitism is a mechanism which ensures that the characteristics of the highly fit solutions are passed
on the next set of solutions without being changed.
2.4.5 Evolutionary Algorithms
During 1993-1995, a number of different evolutionary algorithms (EAs) were suggested to solve multi-
objective optimization problems. Of them, Fonseca and Fleming’s MOGA [19], Srinivas and Deb’s NSGA
[20], and Horn et al. NPGA [21] got the most attention. These algorithms demonstrated the necessary
additional operators for converting a simple EA to a multi-objective evolutionary algorithms (MOEAs).
Two common features on all three operators were the assigned fitness to population members based on
non-dominated sorting and the preserving diversity among solutions of the same non-dominated front.
The Non-dominated Sorting Genetic Algorithm (NSGA), was developed by Prof. K. Deb in 1995, and it
was one of the first successful EAs. Over the years, this method had some criticisms [22]: high com-
putational complexity of non-dominated sorting, lack of elitism and the need for specifying the sharing
parameters. So, in 2002, Prof K. Deb presented a better algorithm, with the following features: fast
non-dominated sorting procedure, implementation of elitism for multi-objective search, using an elitism-
preserving approach, use of a parameter-less diversity preservation mechanism and the allowance of
both continuous ("real-coded") and discrete ("binary-coded") design variables.
2.5 Simulation
Simulation is the attempt to predict aspects of the behaviour of a system by creating an approximate
(mathematical) model of it while omitting certain (less important) characteristics.
14
The increase in computer speed and storage capacity over the years, has a direct impact on simulation
[1]:
• Higher number of variants: more designs can be analysed in the same time period;
• Faster response time: the same number of variants can be studied in less time;
• Better accuracy: denser grids can be used for higher resolution of phenomenons;
• Improved modelling: more sophisticated models can be utilized to better capture the real world.
In ship design context, the simulations are made mostly by computer, since physical models request
more time to build being quite expensive, and is very time-consuming to make changes.
In general, all aspects of the ship life-cycle are of interest and potentially subject to simulation. The hull
form models itself are used to simulate the ship behaviour, and the most commonly done simulations
are the ship hydrostatic characteristics, hydrodynamic performance and structural behaviour.
2.6 Integration
Typically, the creation of a new ship is done by several team members that are part of a system con-
nected via files. The geometry itself is given as simple offsets, IGES files or files in legacy formats. It
is then exported and converted before being pre-processed for CFD or other calculations/simulations.
Finally, the numerical simulations are run and the results are analysed. Most of the time, for any change
in the hull form, the previous process needs to be repeated partially or totally, consuming a lot of time
and work.
The answer to this problem is the integration of systems, bringing the steps, explained before, closer
together. So, some functionality is provided, some tools are replaced, several systems are plugged-in
while others are just launched. This is often referred as CAE. CAE is a key factor in speeding-up the
design process and in improving the product resulting from it.
Figure 2.10: Past (top), present (middle) and future (bottom) drivers of design
In the past, modelling was very much the driver of the process, while simulation is beginning to take over
(figure 2.10). This means that simulation is increasingly utilized in order to produce shapes rather than
just to evaluate a handful of interactively created alternatives. In order to have higher performances, the
15
success in product development will depend on the utilization of simulation and integration, as mentioned
by Harris [23].
An example on the systems integration is the software FRIENDSHIP-Framework that was used to de-
velop the hull model as explained in chapter 4.
16
Chapter 3
Previous Research Work
In ship design, the form-parameter design method was first used by Nowacki in [24], who started to
model curves for the ship form definition by means of cubic B-Splines with seven vertices on the basis of
14 form parameters. A few years later, Nowacki published the fully determined solution [25], a method
based on Bézier-curves, that are approached as an approximation problem with constrains. Since the
order of the curve increases with the number of form-parameters to guarantee under-determination the
method was restricted to not have so many form requirements. The fairness criterion was based on the
square of the second derivative norm. Further improvement was achieved by Nowacki and Lü in [26],
who developed a method for constructing planar composite polynomial curves to approximate given
points with an area constraint, considering, this time, the fairness criterion as a linear combination of
the second and the third derivatives. This method showed to be more suitable for practical use then the
previously presented method.
In 1978 Kracht presented a study of bulbous bows [27]. He presented a set of coefficients that according
to him, were enough to define any bulb (see figure 3.1 table 3.1).
Figure 3.1: Linear and non-linear bulbous bow measures [27]
He concluded that the bulb section will directly influence the hydrodynamic properties, and will affect the
vertical volume distribution and the amplitude of the bulb waves. So, he classified the bulb section into
17
three types, according to its position of the weight of the centre of gravity (see figure 3.2).
Table 3.1: Kracht Bulb Parameters
Linear Bulb Parameter Non Linear Bulb ParameterName Parameter Expression Name Parameter Expression
breadth parameter CBBBB
BMS
cross sectionparameter CABT
AABTAMS
length parameter CLPRLPRLPP
lateral parameter CABLAABLAMS
depth parameter CZBZBTMS
volumetric parameter CV PRVPRVWL
Figure 3.2: Bulb section type: ∇ type, O type and ∆ type (circles represent the section’s centre ofgravity) [28]
He also concluded that the volumetric parameter is the one that has the greatest influence on the wave-
making resistance and on the phase lag of the bulb-generated waves, which is also a function of the
longitudinal volume distribution of the bulb area.
In 1992 Jacobsen and Kracht presented a new model-series, called D-Series, originating from a twin-
screw round-bilge hull form [29]. This model is a parametric model that uses some parameters defined
by Kracht in 1966 and some other new parameters. These parameters are ratios between lengths,
areas and volumes, some of them are set to have a specific value, others can change freely. They also
presented a list of the twelve longitudinal curves that, according to them, could fully represent the hull
form.
Table 3.2: Set of curves to define the hull form
Primary Basic Curves Secondary Basic CurvesSectional Area Curve Curve of tangent angles at beginningDesign Water Line Curve Curve of tangents angles at endFlat of Side Curve Curve of curvatures at beginningFlat of Body Curve Curve of curvatures at endCentre Plane Curve Curve of vertical moments of sectional areaDeck Contour Curve Curve of lateral moments of sectional area
Most of the primary basic curves are created with three segments: two curved segments representing
the run and the entrance body, and a linear segment representing the parallel midbody. When the length
of the parallel midbody is zero, this last linear segment disappears.
A full scale ship power prediction method was also developed based on the experimental results of the
propulsion and resistance tank tests in calm waters, done on seven of the eleven models created varying
the parameters considered on the D-series. The hulls were transformed by linear distortion of y and z
coordinates proportionally to given scales, and/or by alteration of the sectional area curve.
18
In 1997 Harries and Abt presented a modelling technique that is based on a parametric curve generation,
and in 1998, they successfully utilized it for the generation of bare hulls, and proposed a set of form-
parameters for general planar curves (see figures 3.3 and 3.4).
Figure 3.3: Definition of a generic curve - Example SAC for a container carrier [8]
A set of up to 24 parameters were used to define the SAC, containing important data as the displace-
ment, position of maximum section, centres of buoyancy, and slopes at the aft and forward perpendic-
ulars. Each primary basic curve, presented previous, are defined with a set of up to 13 parameters,
representing positional, integral and differential shape requirements. With this set of form-parameters,
the planar curve is more flexible and able to adopt almost any shape requested by the designer on the
basis of the geometric properties.
Despite all the advantages of this method, some shapes can be very difficult to model, so the form-
parameter method must be sufficiently flexible to incorporate new form-parameters as they appear, and
to be able to handle a subset (or any possible combination) of form-parameters by using default values,
or finding a natural and good values, for the unspecific form-parameters.
In 1999 Nowacki and Harries, presented a new approach for to the geometric modelling of hull forms, for
the preliminary phase of ship design [8]. The approach is based on form parameters and use B-Splines
and surfaces to mathematically describe the hull geometry. The B-Splines presented an outstanding
behaviour due to the possibility of local shape control, convex hull property and invariance under coor-
dinate system transformation. The modelling process was viewed as an optimization problem, where
fairness measures are considered as the quality criterion. The form parameters are treated as equality
19
Figure 3.4: Set of generic form parameters for planar curve design [8]
constraints and the B-Splines as free variables. This new parametric approach provided means for a
faster an accurate form generation and variation with better fairness.
Abt et al., presented in 2003 [30] a parametric approach for the modelling and hydrodynamic multi-
optimization, focus on complex hull shapes with bulbous bow, in particular the FantaRoRo, a Ro-Pax
ferry elaborated within the European project FANTASTIC, using the FRIENDSHIP-Modeler. The main
goal was to obtain a minimum wave resistance in calm water, varying some parameters of the DWL, the
SAC and the bulbous bow, and considering some constraints as the displacement and the longitudinal
centre of buoyancy.
Bole presented in 2005 [31] a comparison study between several different hull form generation tech-
niques, available in Paramarine, a software based on an object-orientated framework which allows the
parametric connection of all aspects of both the product model and analysis together, and considered
the building block methodology.
Also in 2005, Mancuso [32] presented an algorithm that automatically generates the submerged part
of the hull shape of sailing yachts, using parametric modelling. The algorithm has two steps. The first
one is the design of the keel line and the DWL, according to a set of parameters such as the length
of the water line, draft and some others, and using B-Spline curves. Then it was made the fairing of
the hull surface, considering a different set of parameters as the displacement and the waterplane area.
He used B-Spline surfaces to define the hull, the gradient method the determine a reliable solution and
the weighted sum approach. The design variables vary depending on the optimization type. He also
presents a set of different form coefficients and their acceptable range of values for yachts.
In 2006, Bole and Lee presented another two different hull generation techniques [33]. The first is a
single cubic B-Spline surface yacht hull generator, based on 19 geometric parameters and performing a
20
longitudinal fit to the control polygons of each section. The second one produces a B-Spline surface of
a single-screw cargo ship hull form with and without bulb, based on 25 geometric parameters, but this
time presented not so satisfactory results due to not being possible to control the hydrostatic properties
independently of the other input parameters.
Abt and Harries, presented in 2007 a study of the application of the Lackenby Method available on the
FRIENDSHIP-Framework [34]. They made two different examples. On the first they shift all the sections
until they could get the wanted hydrostatic properties. On the second they shift slightly forward the
maximum section and the centre of buoyancy, increasing the displacement.
Pérez et al., presented in 2007 a geometric modelling of the bulbous bow using a set of parameters [28].
They used a wire model, constructed with cubic B-Spline curves, and NURBS surfaces to create the
bulbous bow model. They also studied how to obtain certain bulbous bow parameters and their influence
on the hydrodynamic properties of the ship. Controlling the location of the waterline that crosses the point
of maximum bulb protuberance and the SAC, they were able to manipulate the longitudinal distribution
of the bulb volume and to control the phase lag between the bulb and the hull wave trains. An example
was presented, based on the modification of a bulbous bow of a fishing vessel considering some CFD
optimization calculations.
In the same year, Pérez et al. presented a simple parametric method for the hull generation of simple
hull shapes without bulbous bow, as sailing boats and round bilge hulls [35] considering some hydrody-
namic coefficients imposed by the designer on the definition of the SAC and the DWL. The definition of
those curves were mathematically made, and they presented all the equations of the curves and their
parameters. The method begins with the development of a wire model of spline curves and ends with
the automatic generation of the B-Spline surfaces of the hull and the analysis of the surfaces fairness.
They also presented some examples for the use of this method.
During the same year Harries et al. [36] presented some fully-parametric methods, experimental results
and potential economic aspects, related with the optimization of a new family of container ships by Nord-
seewerke (TKMS), comprising versions with 3100, 3400 and 3700 TEU. In addition, using FRIENDSHIP-
Framework, they presented a study for a potential new form Feature located in the hull’s forebody, that
displays addition inflection points in the sectional area curve and in several waterlines, the InSAC (figure
3.5). To validate this method, they did some model tests that confirmed a improved transport efficiency.
The K-Spline curves and its equations, were presented by Cudby in 2009, formulated considering a base
of 4 parameters including the area parameter [37]. This type of curve presented a inherently smoothness
and convex behaviour, reducing the need for heuristic computing. He also presented a family of light
displacement sailing boats with K-Spline sections, K-Spline centrer-plane curve and meta surfaces,
developed and analysed on FRIENDSHIP-Framework. These variants were created by manipulating
parameters and longitudinal curves. All variants present the same area coefficients, displacements, LCB
and LCF. The K-Spline showed that it was a very useful tool, since it allows to determine in advance
a set of parameters that will lead to a valid curve, being even more useful if the modelling software
automatically generates a family of variant hulls.
In the same year, Hochkirch and Bertram studied the formal optimization of an existing container ship
21
Figure 3.5: InSAC [8]
that considers slow steaming due to high fuel prices [38]. They considered two potential cases: the refit
of the bulbous bow and the modification of the ship’s forebody, achieving significant improvements in
both cases.
22
Chapter 4
Analysis of the existing hulls
Before the definition of the modelling procedure, a study on the existing hulls was made. This study has
the objective to know how, especially the geometric curves shape types and what parameters should
be considered to cover as many hull types as possible. This study is also very helpful to know the
boundaries and the most common parameter values that each type of hull presents, and to validate the
hull modelling procedure presented on chapter 5. For this to be possible, a database was built with all
the needed parameters.
With the urge to optimize merchant ships, the sample used on this database considered some tankers,
container ships, bulk carriers and ferry ships. It is important to refer that the sample dimension isn’t
big enough to ensure that all shapes, especially for some geometric curves, are covered. In the future,
it would be very useful to study more hull shapes of these types of ships. The database includes an
exhaustive study of almost every parameter of some hull models available on DelftShip [39], samples of
FRIENDSHIP-Framework and some lines plans from different shipyards.
The building of the database allowed to have a starting point on the hull form characteristics, and to
determine the boundaries acceptable for each parameter. These boundaries can be also very helpful
to the designer when creating a hull from scratch, especially for the parameters related to very specific
characteristics of the hull as the tangent angles of the FOB or the FOS, and some property distribution
curves. This database is also important for the creation of the ASCII input files, used in the hull model
validation and application.
To build the previously mentioned database, two types of curve were considered: the geometric curves,
that represent real contours of the hull, and the property distribution curves, that represent functions
of hull surfaces properties along one direction of the hull shape. To characterize these curves several
parameters were created. Some represent distance measures, angle measures and others, as the area
coefficients, integral measures.
It is important to mention that the definition for all parameters studied in this chapter are presented on
the chapter 5 where the hull model development itself is explained in detail.
23
4.1 Main Dimensions
The first step on the study of the existing hulls, was the analysis of the relations between the main
dimensions. As any naval architect knows, some relations are very important for the hull shape char-
acterization. This relations were studied considering coefficients with values between 0 and 1, in order
to facilitate the analysis of the trends and the detection of possible mistaken calculus. The considered
relations are the following:
• Beam (B) vs Length between perpendiculars (Lpp) (table 4.1);
• Draft (D) vs Depth (H) (table 4.2);
• Depth (H) vs Length between perpendiculars (Lpp) (table 4.3);
• Length of the parallel midbody (Lc) vs Length between perpendicular (Lpp) (table 4.4).
The relation of the beam with the length between perpendiculars almost doesn’t change among the
different ship types (table 4.1). The ferry ships, are the only type that showed values a slightly bigger
than the other ship types since the cargo cannot be stored vertically but only horizontally in different
decks, needing larger beam values.
Table 4.1: Beam vs Length Between Perpendiculars
B/Lpp bulker container ferry tankerMIN 0.14 0.13 0.13 0.14MAX 0.18 0.18 0.21 0.18
Ferry ships also presented the smallest values for the relation between the draft and the depth, while
the container and the bulker ships exhibited the biggest values (table 4.2).
Table 4.2: Draft vs Depth
D/H bulker container ferry tankerMIN 0.44 0.46 0.33 0.50MAX 0.63 0.70 0.68 0.59
As expected, the ferry ships presented the biggest relation between the depth and the Lpp, since they
need a larger enclosed cargo volume than the other types of the ship (table 4.3).
Table 4.3: Depth vs Length between perpendiculars
H/Lpp bulker container ferry tankerMIN 0.09 0.09 0.09 0.08MAX 0.14 0.13 0.18 0.13
It was also expected that the container and the ferry ships would present the biggest values for the
Lc/Lpp ratio, due to the necessity of having a larger and parallelepiped cargo space, but those weren’t
the obtained results (table 4.4).
Two other parameters were also analysed, the block coefficient and the start position of the parallel
midbody (table 4.5 and 4.6).
24
Table 4.4: Parallel midbody length vs length between perpendiculars
Lc/Lpp bulker container ferry tankerMIN 0.06 0.00 0.00 0.00MAX 0.32 0.08 0.19 0.36
The block coefficient presented the highest values for the tankers and the bulk carriers, since those
ships need larger hold spaces. The ferry ships presented the lowest values since they do not need
much cargo space below the DWL.
Table 4.5: Block Coefficient
Cb bulker container ferry tankerMIN 0.74 0.59 0.56 0.76MAX 0.85 0.75 0.71 0.85
The range of values of the relation between the beginning of the parallel midbody and the Lpp, presented
the smallest values for the ferry ships and bulk carriers. That means that they have a relatively small
aftbody, while tankers have the biggest aftbody lengths (table 4.4).
Table 4.6: x-position of the beginning of the parallel midbody vs length between perpendiculars
xStartCylinder/Lpp bulker container ferry tankerMIN 0.39 0.44 0.39 0.44MAX 0.50 0.50 0.43 0.53
Both block coefficient and length of the parallel midbody are directly related to the submerged hull,
having a big influence on the hull resistance and consequently on the ship velocity. For this reason, the
ferries presented the lowest values for these two parameter, in contrast with the bulkcarriers and the
tanker ships that presented the highest values.
4.2 Geometric Curves
Considering an already existing hull, the geometric curves are the easiest curves to obtain. In lines
plans some geometric curves such as the FOS and the FOB are directly represented by the last buttock
and the lower water line. When studying 3D models such as those used from DelfShip, it is necessary to
carrying out some geometric processing to obtain the desired curves, as the intersection of some plans
with the hull form.
4.2.1 Main Frame
The main frame definition says that its longitudinal position is at the section with maximum beam, in
particular, when the ships have cylindrical body, it was considered to be located on the beginning of
the parallel midbody, and almost every time presented the same shape type: two linear segments that
coincide with the FOB and the FOS, and a curved segment commonly known as the bilge.
The bilge can have a circular or a elliptical shape. In order to cover all the possible bilge types, instead
of studying the radius, it was studied the bilge height, width and area coefficient (table 4.7).
25
Table 4.7: Main Frame - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxbH [m] 1.630 10.010 1.800 4.870 1.630 10.010 1.700 5.200 2.220 7.710bW [m] 1.600 11.730 1.600 6.380 2.600 8.800 2.000 8.280 2.270 11.730coeffbilge 0.700 0.982 0.700 0.943 0.790 0.941 0.780 0.903 0.856 0.982
It is worth noting that the area coefficient of the bilge varies between 0.7 and almost 1.0, having the
biggest range for tankers ships. The same behaviour was presented for the bilge width, while the bilge
height presented the biggest range for the containers.
It was also studied the relation between the bilge height and it’s width (table 4.8). The container ships
always presented a circular or ellipsoidal bilge with the width larger than the height, maximizing the
container cargo space (figure 4.1). The tankers considered on the database in use, always showed
a ellipsoidal bilge where the width is larger than the height, while the bulk carriers and the ferry ships
showed both types of ellipsoidal bilges, height larger than the width and vice versa.
Table 4.8: Bilge width vs bilge height
bw/bh bulker container ferry tankerMIN 0.89 1.00 0.89 1.02MAX 1.31 2.44 1.59 1.65
Figure 4.1: Bilge width vs bilge height
Other main parameters that directly influence the shape of the main frame are the beam, draft, deadrise
and flare of the ship.
All the ships considered have a deadrise of 0o, a common characteristic of merchant ships, in order to
maximize the cargo volume. Most of the studied ships also presented a 0o flare, except two of them,
one ferry and one tanker (table 4.9).
Table 4.9: Flare range of values
flare bulker container ferry tankerMIN 0.00 0.00 0.00 0.00MAX 0.00 0.00 11.00 0.52
26
4.2.2 Longitudinal Contour
The longitudinal contour is one of the most important curves of the hull. With this curve the designer
can know if the ship has a bulbous bow, a vertical or non vertical transom panel, a stern bulb, and the
value of the height and Lpp. This curve is directly related with the FOB since the extreme points of the
keel line are the same as the extreme points of the FOB (see subsection 4.2.3). Its forward contour is
directly related with the definition of the stem and the bulbous bow (see subsections 4.2.7 and 4.2.8). Its
aft contour is directly related with the definition of the stern bulb and the transom panel (see subsections
4.2.9 and 4.2.10). Finally, the extreme points of the deck contour are the same for the longitudinal
contour (see subsection 4.2.6).
4.2.3 Flat of Bottom
As said before, the FOB is one of the easiest curves to obtain in a ship, since it coincides with the lower
water line of the ship.
This curve has a direct connection with the ship’s longitudinal contour since its extreme points coincide
with the beginning and the end of the keel line. It also has a direct connection with the Main Frame and
the parallel midbody.
The maximum value of y on FOB is automatically defined, since it has to coincide with the lowest point
on the bilge.
Defining the beginning and the length of the parallel midbody, a linear segment has to be automatically
defined. Sometimes, this linear segment presents a length larger than Lc, and for that to be considered
on the modelling procedure, two parameters had to be created. These parameters relate the length of
each part of the linear segment that are aft and forward of the parallel midbody, and the length of the
aftbody and the forebody, respectively (CFOBstraightAft and CFOBstraightFwd).
To complete the FOB contour, two other curve segments, one on the aftbody and other on the forebody,
had to be analysed, and for these two segments to be characterized, four other parameters had to be
created:
• Entrance angle of FOB;
• Run angle of FOB;
• FOBfullnessAft - Area coefficient of the aft curved segment of the FOB;
• FOBfullnessFwd - Area coefficient of the fwd curved segment of the FOB.
Almost every FOB curve begins after 50% of the length of the aftbody, except the ferry ships that pre-
sented the value for CFOBaft & 0.60. The FOB curve ends in almost every case near the forward
perpendicular. In some cases this curve finishes on 80% of the length of the forebody, and a few others
end forward of the forward-perpendicular (CFOBaft & 1.00).
The FOB curve shows a trend to have an entrance angle of 90o, i.e., the curve begins tangent to the
central line, except for one bulk carrier, one tanker and one ferry ship. The run angle shows a larger
27
Table 4.10: FOB - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCFOBaft 0.046 0.613 0.046 0.562 0.096 0.234 0.102 0.613 0.085 0.137CFOBfwd 0.802 1.009 0.802 1.003 0.816 1.009 0.861 0.950 0.880 1.001FOBentrance [o] 0.000 90.000 0.000 90.000 80.970 90.000 0.000 90.000 0.000 82.210FOBrun [o] 2.180 90.000 16.840 90.000 73.806 90.000 16.500 90.000 2.180 87.140CFOBstraightAft 0.000 0.130 0.000 0.130 0.000 0.026 0.000 0.028 0.000 0.000CFOBstraightFwd 0.000 0.063 0.000 0.062 0.000 0.063 0.000 0.024 0.000 0.000FOBfullnessAft 0.264 0.717 0.336 0.588 0.388 0.624 0.264 0.717 0.514 0.616FOBfullnessFwd 0.234 0.745 0.336 0.745 0.362 0.624 0.264 0.718 0.391 0.616
range of values being difficult to discover a trend, but for the majority of the studied ships, the values
vary between 75o and 90o, with the exception of one bulk carrier, one ferry and one tanker.
It is interesting to see that almost every analysed ship, presents the linear segment of the FOB with the
same length as the Lc (CFOBstraightAft∼= 0 and CFOBstraightFwd
∼= 0). Extrapolating, its possible to say
that the length of the parallel midbody can be measured by the length of the linear segment of the FOB.
4.2.4 Flat of Side
The FOS is also an easy curve to obtain in an existing ship, since it coincides with the buttock at
maximum beam.
This curve presents a very similar behaviour to the FOB. Its extreme points are directly related to the
Deck Line (subsection4.2.6) and to the Transom Panel Contour (subsection 4.2.10). To define the ex-
treme points of the FOB three parameters had to be created, two related to the x position of the extreme
points and another to the z position of the aft point of the FOS since it is possible to have a FOS that
ends on the transom panel:
• CFOSaft - The relation between the aft x-position and the length of the aftbody (related with the
deck line);
• CFOSfwd - The relation between the forward x-position and the length of the forebody (related with
the deck line and the transom panel);
• CFOSaftHeight - The relation between the aft z-position and the height (related with the transom
panel).
Once again, the FOS presented two curved segments, but this time, each of these segments had to be
divided at the intersection points of the FOS with the DWL. To analyse these intersection points, two pa-
rameters had to be created, relating the intersection points position and the length of the corresponding
body(CFOSemergeAft and CFOSemergeFwd).
A linear segment appears almost every time in the contour of the FOS, and similar to the FOB, this seg-
ment can also have a length larger than the Lc, and because of that, two parameters had to be analysed,
relating the length of each part of the linear segment that are aft and forward of the parallel midbody,
and the length of the aftbody (CFOSstraightAft) and the forebody (CFOSstraightFwd), respectively.
28
Table 4.11: FOS - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCFOSaft -0.164 0.806 0.218 0.806 -0.081 0.275 -0.164 0.373 0.217 0.610CFOSfwd 0.121 0.817 0.121 0.687 0.389 0.817 0.524 0.817 0.217 0.393CFOSaftHeight 0.412 1.000 0.720 1.000 0.739 1.000 0.412 1.000 1.000 1.000CFOSemergeAft 0.000 0.721 0.116 0.392 0.191 0.521 0.000 0.632 0.296 0.721CFOSemergeFwd 0.000 1.325 0.000 0.852 0.181 0.880 0.210 0.552 0.227 1.325CFOSstraightAft 0.000 0.262 0.000 0.262 0.000 0.100 0.000 0.029 0.000 0.139CFOSstraightFwd 0.000 0.325 0.000 0.220 0.000 0.046 0.000 0.002 0.000 0.325FOSentrance [o] -90.000 90.000 0.000 90.000 3.150 90.000 0.000 90.000 -90.000 65.380FOSrun [o] 90.000 251.500 90.000 251.500 90.770 152.440 95.000 180.000 90.000 168.390
Some cases presented values for the CFOSaft negative, meaning that the FOS will probably end on
the transom panel. That was the case of some containers and ferry ships, since they need bigger aft
parallelepiped space for cargo operations and storage. These two types of ships presented the smallest
values for the CFOSaft in contrast with the bulk carriers and the tanker ships that usually do not need
any cargo space on the aft part of the ship. For the same reason, the opposite was presented for the
CFOSfwd, that has larger values for the container and the ferry ships, and smaller values for the other
two types.
Analysing the CFOSaftHeight values (see table 5.8 and figure 5.4), it seems that for any tanker ship that
value is always 1, meaning that the FOS contour ends always on the deck.
In some studied hulls, the FOS contour presented CFOSemergeFwd values bigger than 1 meaning that the
longitudinal position of the forward intersection of the FOS and the DWL is larger than the longitudinal
position of the forward point of the FOS on the deck contour. Theoretically, this couldn’t happen since
the forward point of the FOS should be located on the deck and not on the DWL, meaning that this could
be a case of a not so reliable hull modelling. This behaviour, has a direct influence on the entrance angle
of the FOS (FOSentrance < 0).
4.2.5 Design Water Line
The DWL is one of the most important curves of the hull form, since it directly influences the ship’s
hydrostatic and hydrodynamic behaviours. This curve always presents at least 3 segments: one linear
segment and two curved ones. The linear segment is directly related to the FOS definition since its
extreme points coincide with the intersection between the DWL and the FOS curves (CFOSemergeAft
and CFOSstraightFwd). There can also be another linear segment at the aft part of the DWL, in the cases
where the DWL intersects the transom panel or when the aft body in the end of the DWL presents a
rectangular shape.
To define the curved segments it was necessary to introduce four additional parameters related to the
area coefficient of each segment (DWLfullnessAft and DWLfullnessFwd), the entrance angle(DWLentrance)
and run angle (DWLrun).
Theoretically, all DWL curves should have CDWLfwdX = 1, since by definition the forward perpendicular
is located on the forward point of the DWL. But, analysing the values on table 4.12 we see that this is
not confirmed, most of the models presented values equal to 1.000 but there is one model of a bulk
29
Table 4.12: DWL - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCDWLaftX -0.164 0.033 -0.046 0.032 -0.069 0.021 -0.164 -0.014 -0.048 0.033CDWLaftY 0.000 1.000 0.000 0.429 0.000 0.612 0.000 1.000 0.000 0.081CDWLfwdX 0.812 1.049 0.812 1.002 1.000 1.017 0.996 0.996 1.000 1.049DWLfullnessAft 0.637 1.000 0.698 0.736 0.637 0.870 0.656 1.000 0.701 0.831DWLfullnessFwd 0.564 0.841 0.700 0.780 0.570 0.693 0.564 0.696 0.698 0.841DWLentrance [o] 4.000 90.000 71.530 90.000 9.670 90.000 4.000 76.000 47.360 90.000DWLrun [o] 0.000 90.000 51.450 67.260 0.000 75.340 0.000 90.000 3.000 59.070
carrier that presents a value for CDWLfwdX < 1 and three other models, one ferry, one tanker and one
container that have values CDWLfwdX > 1.
The aft point of the DWL can sometimes be located aft of the aft perpendicular (CDWLaftX < 0), es-
pecially in the cases where the DWL intersects the transom panel. These cases also presented values
of CDWLaftY > 0, and in the case of the ferry ship, this value can be pushed to the limit being equal
to 1.000. This happens in this type of ship because it needs to have an aft platform to load and unload
the cargo. This is also shown by the values of the DWLfullnessAft since it is the only type of ship that
presented values equal to 1.000.
4.2.6 Deck Line
The deck line is not an easy curve to obtain since in some 3D models and lines plans the weather deck
is also represented. The best way to determine where this curve is located, is knowing the depth value
of the ship.
The extreme points of this curve are directly related to the longitudinal contour, since their extreme points
are the same (see subsection4.2.2). To define the forward point it was necessary to study the parameter
that relates its x position and the length of the forebody (Cpeak).
Despite each deck line presenting different characteristics and segments, all of them present at least
two segments: a linear and a curved segment in the forward part of the ship. This linear segment is
directly related to the definition of the FOS curve since their extremes are the same (subsection 4.2.4).
The aft part of the deck line can have very different behaviours. Its definition is directly influenced by
the transom panel contour and, once again, by the FOS curve. If the transom panel has a beam equal
to the ship design beam, the linear segment of the deck goes from the forward point of the FOS to the
transom panel, if not there is another curve segment between the aft point of the linear segment and the
top segment of the transom panel.
To define the curved segments two parameters were created, relating the area coefficient of each seg-
ment (deckfullnessAft and deckfullnessFwd).
As expected, the container and the ferry ships have the biggest values of CPeak since there is a need to
have more deck space for cargo transport.
Some studied ship models did not presented a curved segment on the aft part of the deck contour
(deckfullnessAft = 1), that was the case of the container ship and the ferry ship, since they need bigger
aft space for the accommodation, load and unload of cargo. In other hand, the bulk carriers and the
30
Table 4.13: Deck - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCPeak 1.006 1.204 1.015 1.110 1.042 1.122 1.023 1.204 1.006 1.164deckfullnessAft 0.627 1.000 0.644 0.806 0.686 1.000 0.627 1.000 0.709 0.779deckfullnessFwd 0.620 0.861 0.761 0.824 0.620 0.850 0.630 0.780 0.753 0.861
tanker ships presented the smallest values for the same parameters, since they don’t use the deck for
cargo transport.
4.2.7 Stem
The stem is the highest forward part of the longitudinal contour. This curve does not have any influence
on the ship’s hydrodynamic and hydrostatic behaviour since it’s not part of the submerged hull. Since
the goal of this thesis was the development of a full hull model, this curve was still fully studied and
characterized using three parameters:
• CStemStraight - Relation between the length of the linear segment of the stem and the depth of the
ship;
• TgBulb - Tangent angle of the stem contour at the top beginning of the bulb longitudinal contour;
• TgPeak - Tangent angle of the stem contour at the peak.
As done for the others parameters, a study was also made on the range of values for each parameter
(table 4.14).
Table 4.14: Deck - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCstemStraight 0.000 0.102 0.000 0.102 0.000 0.042 0.000 0.056 0.000 0.000TgBulb 78.000 178.220 90.000 173.500 78.000 161.810 80.000 90.000 174.560 178.220TgPeak 10.000 49.500 10.000 42.840 33.000 45.000 23.150 49.500 19.140 44.090
The average values for the tgPeak vary between 20o and the 45o, in general the container ships present
the biggest values, and the bulk carriers the smallest.
Most of the hull models present values for the CstemStraight very close to zero. This happens in the cases
where there are big differences between the loading conditions, in order to have the smallest variations
on the geometry of the DWL.
Is important to refer that the stem curve is only completely characterized with two other property curves,
as we will see on the subsection 4.3.5.
4.2.8 Bulbous Bow
One of the entities of the hull that mostly interferers with hydrodynamics, and consequently economics
of the ship, is the bulbous bow. Its geometry directly influences the wave resistance and the propulsive
efficiency, for that reason, it was a part of the model that was studied with special attention.
31
Along the years several studies have been made on the geometry of the bulb and its influence on the
ship’s behaviour, and some parameters have been presented (see chapter 3). Some of those parame-
ters were used in this study and some new ones were considered.
In this study the first concern was to try to understand the relations between the type of ship and the
type of bulb (figure 4.2). Since it was considered a small population of ships, it is important to mention
that this study only has an academic propose.
Figure 4.2: Ship Type vs Bulb Type
Analysing figure 4.2, it is possible to notice that for most of the studied ferry ships the ∇-type bulb is
the most common. This type of bulbous are being more and more commonly used, especially for faster
ships, as the case of ferry ships. In other hand, the ∆-type bulb is usually used for slow ships, as the
bulk carriers and the tanker ships.
To characterize the bulbous bow, a set of at least three geometric curves and one property curve, had
to be studied: the lower and upper contour of the longitudinal contour, the maximum beam elevation
distribution and the maximum halfbeam contour.
The upper and lower contour of the longitudinal contour can be defined with seven parameters: four
distance parameters, two area coefficients and one tangent angle.
It is very interesting to notice that the values of the TgupperContour coincide with the ones for the TgBulb on
the stem contour (subsection 4.2.7), since they represent exactly the same measure. So, this parameter
could be eliminated on the developed hull model.
In other words, to study the longitudinal contour, the position of three points has to be analysed: the
lower and the upper points of the contour on the beginning of the bulb and the tip point. To define them,
the following parameters were necessary:
• Cza - z-position of the lower point of the bulb longitudinal contour;
• Chb - z-position of the upper point of the upper contour;
• Czb - z-position of the bulb tip (Kracht parameter);
32
• Clpr - Length of the bulb (Kracht parameter).
The area coefficients of the upper (BulbupperFullness) and the lower (BulblowerFullness) segments of the
longitudinal contour and the tangent angle on the upper point of the longitudinal contour (TgupperContour),
also had to be analysed.
The beam elevation distribution contour (figure 5.8) was more difficult to analyse. In the simpler models
this contour is set as a linear horizontal curve that passes through the tip point. But, since the values
of the z coordinates can be different at the maximum beam on the beginning of the bulb and at the bulb
tip, the contour was considered as an inclined linear curve that passes through these two points. It is
important to refer that this curve can also have a curved behaviour but since it is very difficult to analyse
and to apply this type of bulbous, a simplification was done considering the distribution as a linear curve.
So, to characterize this curve only two parameters were needed, the z-coordinate of the tip of the bulb
and the z-coordinate of the maximum beam on the beginning of the bulb (Chbe - Kracht parameter).
Finally, with this curve, the halfbeam distribution curve was assumed as a planar curve that passes
through the beam elevation distribution and the bulb surface. To characterize it, the maximum beam on
the beginning of the bulb (Cbb), its z position, and the area coefficient of this curve (BulbhalfbeamFullness),
were analysed.
Two other parameters related to the bulb transversal contour were created: the BulblowerTransvFullness
and the BulbupperTransvFullness, that characterize the area of the lower transversal segment and the
upper transversal segment, respectively. Finally, the CmoveBulb that relates the longitudinal position of
the beginning of the bulb and the longitudinal position of the forward perpendicular, was also analysed.
Table 4.15: Bow Bulb - Kracht Parameters Study - Types of Bulb
GENERAL ∇ - Type ∆ -Type O-TypeMinimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
Czb 0.205 0.917 0.599 0.809 0.205 0.675 0.535 0.917Clpr 0.008 0.041 0.031 0.041 0.008 0.040 0.011 0.033Cbb 0.094 0.348 0.094 0.169 0.108 0.180 0.118 0.348
It was expected that the values of Czb would be larger for ∇-type bulb following the O-type and the
∆-type, but that was not the case. The biggest values were presented for the O-type, followed by the
∇-type and then the ∆-type.
In terms of maximum beam of the bulb, the O-type presented the biggest values, followed by the ∆-type
and finally the ∇-type.
There wasn’t any correlation between the bulb length and the bulb type (Clpr), but, on other hand, there
is a clear one when comparing the first with the ship type (table 4.16). So, the ferry ships presented the
longest bulbs and the bulk carriers the shortest.
Table 4.16: Bulb Length vs Length between perpendiculars
Clpr bulker container ferry tankerMIN 0.01 0.02 0.03 0.02MAX 0.03 0.04 0.04 0.03
33
Table 4.17: Bow Bulb - New Parameters Study
GENERAL ∇ - Type ∆ -Type O-TypeMinimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
Cza 0.000 0.222 0.029 0.073 0.000 0.067 0.088 0.222Chb 0.777 1.462 0.777 1.015 0.889 1.016 0.859 1.462Chbe 0.265 0.905 0.495 0.735 0.265 0.390 0.517 0.905BulblowerFullness 0.652 0.834 0.732 0.824 0.708 0.834 0.652 0.818BulbupperFullness 0.415 1.218 0.907 1.218 0.415 1.000 0.507 0.977BulbhalfbeamFullness 0.609 0.877 0.650 0.745 0.609 0.877 0.641 0.840BulblowerTransvFullness 0.546 0.872 0.546 0.760 0.720 0.859 0.648 0.872BulbupperTransvFullness 0.550 0.951 0.670 0.938 0.550 0.780 0.563 0.951CmoveBulb -0.011 0.008 -0.011 0.001 0.000 0.004 0.000 0.008TgupperContour [o] 77.000 178.220 77.000 90.000 80.000 178.220 82.000 174.560
As expected the ∆-type bulbs analysed presented the smallest values for the Cza since the bulb can
easily begin at lower z positions, with contrast to the ∇-type.
Theoretically, the values for the Chb shouldn’t be bigger than 1.000, since for an optimum influence of
the bulbous bow on the ship hydrodynamics, the bulb volume has to be completely underwater. This is
not what was presented, since some of the values for each bulb type are bigger than 1.000.
The values of the maximum beam elevation (Chbe) are larger for the ∇-type and smaller for the ∆-type,
since its values are directly related to the difference between the positions of the lower and the upper
points of the longitudinal contour, showing what type of bulb are we dealing with.
Analysing the table 4.17 is possible to notice that for any bulb type, the range of values for are nearly the
same for the BulblowerFullness and for the BulbhalfbeamFullness. But, for the BulbupperFullness there is a
trend, since the ∇-type bulbs presented the highest values and the ∆-type the lowest.
As expected, the ∆-type bulb presented the biggest values of BulblowerTransvFullness, and the ∇-type
the lowest ones, and the opposite behaviour for the BulbupperTransvFullness.
There isn’t any trend for the CmoveBulb among the different bulb types, as well as for the TgupperContour,
with exception for the ∇-type that presented the smallest average values for this last parameter.
4.2.9 Stern Bulb
The Stern Bulb is directly related with the longitudinal contour of the hull form. To create it was necessary
to know the x and z coordinates of the bulb tip and the clearance, and also to know the angle between
the transom panel and the longitudinal contour at the lower point of the first one (TgTransom).
Table 4.18: Stern Bulb - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCXBulbT ip 0.011 0.082 0.025 0.063 0.046 0.082 0.068 0.068 0.011 0.070CZBulbT ip 0.130 0.299 0.230 0.299 0.150 0.207 0.207 0.207 0.130 0.288CXClearance 0.039 0.115 0.049 0.095 0.059 0.115 0.089 0.089 0.039 0.081CZClearance 0.239 0.452 0.271 0.435 0.252 0.357 0.357 0.357 0.239 0.452TgTransom [o] 93.000 117.210 101.000 115.450 95.370 103.650 93.000 107.150 102.390 117.210
As it should be, every longitudinal position of the clearance is forward of the longitudinal position of the
bulb tip, and the vertical position of the clearance is always higher then the vertical position of the bulb
tip. Analysing the table 4.18, is possible to notice that the bulk carriers presented the highest positions
34
for the bulb tip, and the container ship the lowest. The opposite was verified for the longitudinal position
of the bulb tip.
The highest values for the vertical position of the clearance was presented for the tanker ships, and the
lowest for the container ships. Once again, the opposite was presented for the longitudinal position of
this point.
Is also very interesting to see that every studied hull, has 90 . TgTransom . 120.
There are also some property parameters needed to build the stern bulb, that will be mentioned in
chapter 5, that were not studied since they are very difficult to measure on existing hulls and even only
one sample form FRIENDSHIP-Framework presented values for these parameters. They are related
with the characterization of the radius of the shaft, the boundary between the bare hull and the stern
bulb and the distribution of the stern bulb volume.
In the present study some ships without stern bulb were considered, but they did not entered this partic-
ular study of the stern bulb.
4.2.10 Transom Panel
The transom is directly obtain from the deck contour, the longitudinal contour and the flat of side curve.
This curve is obtained by intersecting a vertical plan with the aft hull surfaces or analysing the highest
waterline.
The transom curve usually presents a linear segment on the bottom (ClinearBottom), followed by a curved
segment (transomfullness) and another linear segment on the other side of the curve depending on the
behaviour of the FOS (ClinearSide). Finally, it presents the top linear segment that is directly related to
the deck, since it coincides with its aft linear segment (CTransomTopY ).
Table 4.19: Stern Bulb - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCXTransom -0.164 -0.027 -0.089 -0.027 -0.089 -0.040 -0.164 -0.042 -0.076 -0.042CZTransom 0.697 1.344 0.828 1.344 0.797 1.127 0.697 1.316 0.955 1.316ClinearBottom 0.000 0.674 0.000 0.000 0.000 0.209 0.000 0.674 0.000 0.127ClinearSide 0.000 0.591 0.000 0.278 0.050 0.273 0.214 0.591 0.000 0.187CTransomTopY 0.344 1.000 0.344 0.846 0.829 1.000 0.718 1.000 0.448 0.632transomfullness 0.541 0.937 0.627 0.732 0.619 0.869 0.619 0.937 0.541 0.731tgbottom [o] 0.000 57.470 0.000 57.470 0.000 8.160 0.000 20.010 3.550 38.430tgside [o] 0.000 60.300 0.000 32.700 0.000 26.000 0.000 26.000 0.000 60.300panel inclination [o] 68.520 94.070 68.520 90.000 80.630 90.000 82.000 94.070 88.680 90.000
The container and the ferry ships presented the smallest values of CXTransom, since in these type of
ships, there is a need to have a large cargo volume aft. The same behaviour is presented for the
CZTransom values for the same reason and because in the case of the ferry ships there is also the need
to have a stern door to roll in and roll off the cargo. Some of the models studied, present transom
panels beginning on a z bigger than the draft (CZTransom > 1), not having any influence on the ship
hydrodynamic behaviour.
Since the container and the ferry ships need parallelepiped cargo space, especially in the aftbody,
they present larger values for the transomfullness as well as for the length of the linear side segment
35
(ClinearSide), for the length of the linear bottom segment (ClinearBottom) and for the length of the top
linear segment of the transom panel (CTransomTopY ).
This study includes the range of values for the panel inclination, but unfortunately, it was not possible to
include this parameter on the hull model as we will see on the next chapter. Its values vary between the
80o and 90o, showing that almost all of the considered ships have a vertical panel, with exception of one
ferry that has a panel inclined towards the centre of the ship and some other ships models that have a
panel inclined towards the aft of the ship.
4.3 Property Distribution Curves
The property curves represent the variation of some geometric properties of the hull form along one
direction and therefore they are not directly obtained from the hull but result from some geometric pro-
cessing. An attempt was made to have the highest number of values of this parameters but some of
them are not accurate enough.
In the following subsections, it will be presented a study of the SAC and the distribution curves of the
flare at bottom, flare at design water line, flare at deck, and the property distribution curves of the stem
radius and angle.
In the figure 4.3 there is a representation of the position of each flare distribution and how they should
be measured. It is important to notice that on the main frame the flare at bottom is the same as the
deadrise and the flare at design water line as the flare.
Figure 4.3: Position of the Flares
36
4.3.1 Sectional Area Curve
The Section Area Curve is one of the most important curves to develop the hull model form. To define
it, it is necessary to measure the area of some strategical chosen sections. These sections should be
the ones where the main changes on the hull form are located, as the end of the FOS or FOB. In the
present study the following sections were considered :
• Aft point of the DWL - Beginning of the submerged body (CareaDWLaft);
• Aft point of the FOB - Beginning of the presence of the FOB segment (CareaAftBase);
• Aft intersection point of the FOS and the DWL - Beginning of the presence of the FOS submerged
segment (CareaFOSemergeAft);
• Fwd intersection point of the FOS and the DWL - End of the presence of the FOS submerged
segment (CareaFOSemergeFwd);
• Fwd point of the FOB - End of the presence of the FOB segment (CareaFwdBase).
For each of the previous sections, the submerged area was measured and then divided by the sub-
merged area of the main frame in order to have coefficients and not absolute values, that are more
difficult to analyse (table 4.20).
Table 4.20: Sectional Area Curve - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCareaDWLaft 0.000 0.309 0.010 0.028 0.000 0.067 0.000 0.309 0.000 0.001CareaAftBase 0.084 0.913 0.085 0.820 0.182 0.505 0.119 0.913 0.084 0.278CareaFOSemergeAft 0.309 0.998 0.793 0.997 0.477 0.870 0.309 0.957 0.903 0.998CareaFOSemergeFwd 0.763 1.000 0.966 0.999 0.830 0.996 0.763 0.982 0.986 1.000CareaFwdBase 0.060 0.445 0.098 0.104 0.060 0.315 0.096 0.163 0.076 0.445
Analysing table 4.20 is possible to notice that in some cases, the CareaDWLaft is different from 0.000,
where part of the transom panel is submerged. Is also evident that the ferries and the container ships
presented the biggest values for this parameter and the bulker and the tanker the smallest, since the
first ones need more aft cargo space. The same behaviour appears on the CareaAftBase.
The biggest values of CareaFOSemergeAft were measured in the tanker ships and in the bulk carries, that
in these sections have almost the same area then the main frame section. Once again, this behaviour
is similar for the CareaFOSemergeFwd.
As it should be expected, the values of these parameters increase up to the x position of the parallel mid-
body, and then decrease along the x axis. The values for the CareaFOSemergeAft were always considered
to be larger then the values for the CareaAftBase, but, in the cases where the DWL intersects the transom
panel that does not happen. So, the developed model presented on chapter 5, should not be used for
this type of ship.
37
4.3.2 Flare at Bottom
As said before, this curve is very difficult to measure on existing hulls, since it is not a real geometric
curve. To create it, is necessary to define two parameters. The first one, the flareBulbT ip, represents
the flare at the bulb tip. The other, the tgBulbT ip, represents the tangent of the curve distribution,
and because of that it is not so easy do work with, especially in the beginning of a new design or in
existing hulls. The values presented on table 4.21 are only the ones related to the samples available on
FRIENDSHIP-Framework since the parameters mentioned before are input parameters of the samples
itself.
Table 4.21: FAB - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxflareBulbT ip [o] 0.000 45.000 - - 0.000 12.000 45.000 45.000 - -tgBulbT ip [o] 60.000 90.000 - - 85.000 90.000 60.000 60.000 - -
For all the ferries analysed, the flareBulbT ip presented values equal to 45o, while for the container
ships presented values between 0o and 12o. The tgBulbT ip always presented 60o for the ferries and
values between 85o and 90o for the container ships.
4.3.3 Flare at Design Water Line
Once again, the FADWL is a very difficult curve to analyse, for the same reasons presented before. In
this curve there is only one parameter that can be easily measured on existing hull shapes or in lines
plans, the flareOnFp that represents the flare at the forward perpendicular on z = draft.
There are two parameters, tgAtFOSemergefwd and tgAtFP , that are almost impossible to measure
on existing hulls since they do not represent real physical parameters, but ones that characterize the
curve distribution itself. The values presented on table 4.22 are only the ones related to the samples
available on FRIENDSHIP-Framework and that where analysed in the present work, with exception for
the flareOnFp that includes all the analysed models.
Table 4.22: FADWL - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxCmaxflare 0.590 0.750 0.000 0.000 0.590 0.750 0.750 0.750 0.000 0.000maxFlare [o] 30.000 45.000 0.000 0.000 30.000 45.000 45.000 45.000 0.000 0.000flareOnFp [o] -45.950 111.000 0.000 32.460 -45.950 111.000 0.000 0.000 -9.430 37.530tgAtFOSemerge [o] 19.000 45.000 0.000 0.000 20.000 45.000 19.000 45.000 0.000 0.000tgAtFP [o] 90.000 150.000 0.000 0.000 0.000 150.000 0.000 90.000 0.000 0.000
From table 4.22 it is possible to notice that the flareOnFp values have a wide variation range. The
models where the bulb has a volume that is not completely underwater this parameter has negative
values. In the cases where the forward longitudinal position of the DWL is aft of or on the forward
perpendicular, the flareOnFp is zero.
It is also possible to notice that on the FRIENDSHIP-Framework samples the maxFlare has values
between 30o and 45o and that its longitudinal position is usually on 75% of the forebody length.
38
4.3.4 Flare at Deck
The flare at deck is the last curve related to the flare of the hull surfaces and once again a very difficult
curve to obtain. It only needs one parameter, the flareAtFP , that represents the flare of the hull surface
at x = Lpp and z = height. Since it represents a real physical parameter it is very easy to measure in
existing hulls.
Table 4.23: FAD - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxflareAtFP [o] 17.000 54.380 28.740 40.000 32.360 52.810 17.000 40.000 34.380 54.380
Analysing table 4.23 is possible to notice that the average value for the flareAtFP is nearly 40o. The
smallest value was presented for one ferry ship, since for this ship type there is a need for a more vertical
surface at this longitudinal position. The biggest value was presented for a tanker, since there is no need
for big vertical spaces at this longitudinal positions.
4.3.5 Stem Property curves
To characterize the stem surface is necessary to analyse two property distribution curves: one related
with the radius of the surface and another related with the tangent angle between the radial part of
the curve and the curved segment. Thus, three horizontal intersection with the stem surface were
considered and the radius of an imaginary circle on the forward part of the intersection and the angle
that the curve makes in the point of the intersection with the imaginary circle, were analysed (figure 4.4).
Figure 4.4: Stem Properties
To analyse the radius curve distribution three parameters were necessary. The first one represents the
radius of the imaginary circle on z = draft, the second represents the radius on z = draft+ height−draft4
and the last one the radius on z = height (see table 4.24).
To analyse the tangent curve distribution it was only necessary one parameter that represents the tan-
gent of the intersection curve on z = height in the point of the intersection with the imaginary circle
(figure 4.4).
The radiusAtDwl is usually very small and in some cases it can have values of zero. From table 4.24
it is interesting to note that only some tankers and some bulk carriers presented values bigger than 1.0.
39
Table 4.24: Stem Property Distribution - Parameters Study
GENERAL Bulker Container Ferry TankerParameter Min Max Min Max Min Max Min Max Min MaxradiusAtDwl [m] 0.000 5.220 0.050 4.211 0.000 0.690 0.000 0.330 0.050 5.220radiusAtDeck [m] 0.530 50.000 0.530 50.000 1.985 32.000 2.000 50.000 1.400 17.900angleAtDeck 30.900 85.000 32.010 59.690 32.000 85.000 30.900 52.000 31.310 46.580Cradius25 [-] 0.000 14.850 0.833 1.547 0.000 14.850 2.030 10.000 0.000 2.733
The radiusAtDeck is usually much bigger than the radiusAtDwl, but in some analysed hulls this did
not happened.
Analysing table 4.24 it is also possible to notice that the biggest values of the angleAtDeck were found
in the hulls with the biggest values of radiusAtDeck.
40
Chapter 5
Development of the hull model
The hull model was built considering a set of parameters that relate the main dimensions of the hull
with other dimensions of its geometry, and some dependencies between different parameters. The pa-
rameters were applied on the geometric and property distribution curves of the hull. Using this kind of
approach, changes on the hull shape are easier to reach, because when the designer changes one pa-
rameter of the geometry, all the other parameters, that are dependent on the first one, are automatically
actualized.
The input of the parameter’s values can be done manually or by importing an ASCII file, then, the user
can modify any hull parameter. Despite that, it is advised to begin the changes with the main dimensions
and then the values of the coefficients that define each geometric curve of the hull form, and finally the
property curves that can be used to refine the hull shape. While some parameters are mandatory for
the generation process, many are optional. If a parameter is not specified, it is set to a default value.
In total, the user can manipulate nearly one hundred parameters, depending on the desired detail and
specification.
This modelling procedure does not consider some types of shape characteristics, such as non vertical
transom panels and knuckles. The hull model has a stern bulb and a bulbous bow.
To develop the hull model, a CAE environment was used, FRIENDSHIP-Framework, that provides in-
tegrated simulation and automated geometry variation, allowing the hull shape definition as previously
described. This software facilitates the design process, and also allows the use of a set of optimization
strategies, leading to better performing hulls.
The software has a great number of advantages [40]
• Integration platform with tight interfacing of external codes and simulation programs;
• Improved design quality;
• Reduced development time;
• Lower costs and less time spent in model testing, less physical prototypes;
• Facilitated design and optimization, either from imported geometry or from scratch;
41
• Embedded optimization algorithms for systematic variation, single objective optimization and multi-
objective optimization.
To facilitate the introduction and variation of the parameters, it was created a control panel. The control
panel was built in a way that on each introduction or variation of one (or more) parameter(s) value(s), it
will check if the value is in an acceptable predefined range, displaying a message in the console if the
input is invalid, and, in some cases, also prints auxiliary messages in order to inform the user that with
that input the model will have a specific type of shape.
In resume, the model begins with the requirement of the main dimensions of the hull form, following the
parametric modelling, the hydrostatic or other type of performance analysis, and finally the application
of the Lackenby method, available as an integrated object in FRIENDSHIP-Framework.
Figure 5.1: Input Parameter Order and Curve Generation Order
42
5.1 Main Dimensions
The first step of the modelling procedure was the determination of the main dimensions. These values
will influence every component of the hull model, from the geometric curves, to the property curves and
the surfaces of the hull itself (table 5.1).
Table 5.1: Main Dimensions
Parameter Parameter name Default UnitsLpp Length Between Perpendiculars 180.00 [m]B Design Beam 32.20 [m]H Depth 23.00 [m]D Draft 10.50 [m]Cb Block Coefficient 0.65 [-]LCB = XCB
Lppx position of the centre of buoyancy 0.50 [-]
xMainFrame = X beginning parallelmidbodyLpp
x position of the beginning of the parallelmidbody 0.50 [-]
Lc = LengthoftheparallelmidbodyLpp
Length of the parallel midbody 0.00 [-]
With the x-position of the beginning of the parallel midbody and its length, two parameters were cal-
culated, relating the length of the aftbody and the forebody, that will be used to calculate many of the
parameters needed in the development of the geometric and the properties curves:
Length of AftBody = LAB =xMainFrame
Lpp(5.1)
Length of ForeBody = LFB =Lpp − xMainFrame − Lc
Lpp(5.2)
5.2 Geometric Curves
The development of the geometric curves begins with the definition of the extreme points. The x position
of these points are characterized with a parameter that relates the position itself and the length of the
aftbody or the forebody, depending if it is the aft point or the fore point of the curve.
The second phase of the geometric curves development was the construction of the beginning and the
end points of the parallel midbody.
Then, in some curves such as the FOS, some intermediate points were built, such as the intersection of
the FOS and the DWL. The x positions of these points were characterized with a parameter that relates
the x position of the point and the difference between one of the extreme points and the beginning or the
ending of the linear part of the curve that includes the parallel midbody. For example, on the construction
of FOS curve, the x position of the aft intersection of the FOS and the DWL was characterized with a
parameter that relates the x position of the point and the difference between the aft point of the FOS and
the beginning of the parallel midbody. In this way it is impossible to input values that will create a point
that is not between the aft point of the FOS and the beginning of the parallel midbody, thus making the
model stronger.
The next step was the construction of the curve itself. For almost every curve, the construction was
43
done using Poly-curves with F-Spline curves that allows the user to have the control of the entrance and
the run angle of each curve, and also the area and centroid of some segments of the curve. For that
to be possible, some parameters were created, for the entrance and run angles, and parameters that
represent a area coefficient for the segments where it is relevant to manipulate these values.
5.2.1 Main Frame
The main frame is one of the most important geometric curves on the development of the hull form. To
define it, four points (A, B, C and D) and one auxiliary point (I) were considered (see figure 5.2 and table
5.3).
Figure 5.2: Main Frame Curve
To create this curve, it was necessary to create the parameters mentioned in the previous chapter (table
5.2).
Table 5.2: Main Frame - Parameters
Parameter Parameter name Default Value Unitsdeadrise Deadrise 0.000 [o]flare Flare 0.000 [o]bH Bilge Height 2.000 [m]bW Bilge Width 2.000 [m]coeffbilge = BilgeArea
bh×bwFullness of the bilge 0.805 [-]
Some assumptions were also adopted:
• The main frame is located at the beginning of the parallel midbody;
• The flare is measured on the design water line;
• It wasn’t considered the possibility of the existence of keel.
44
Before the creation of the points of the Main Frame curve, it was necessary to set an auxiliary point (I),
where:
zI =(B/2)− (tan(flare)× height)
cos(deadrise)− (tan(flare)× sin(deadrise))× sin(deadrise) (5.3)
yI =(B/2)− (tan(flare)× height)
cos(deadrise)− (tan(flare)× sin(deadrise))× cos(deadrise) (5.4)
The next step was the creation of the points necessary for the construction of the Main Frame curve.
The points were all created in a yz plan located on the x = xBeginingParallelMidBody:
Table 5.3: Main Frame - Points
Point Point name Y [m] Z [m]A onKeel 0 0B onLowerBilge yI − bW tan(deadrise)× (yI − bWC onFOS (B/2)− tan(flare)× (H −D)− tan(flare)× (D − zI − bH ) zI + bHD onDWL (B/2)− tan(flare)× (H −D) D
Finally, with all the parameters and points defined, the segments of the Main Frame curve were devel-
oped (table 5.4 and figure
Table 5.4: Main Frame - Segments
Curve Name First Point Second Point Type of curveBottom A B LineBilge B C F-SplineWettSide C D Line
5.2.2 Flat of bottom
Figure 5.3: Flat of Bottom curve
To FOB curve (figure 5.3) , it was necessary to create the parameters mentioned on the previously
chapter (see table 5.5).
The FOB curve was developed with the creation of its points and segments on the xz plan in order to
ease the creation of the Meta-Surfaces and some calculations needed for the validation of the model
(table 5.6).
With all the parameters and points defined, the FOB curve it self was built by the development of three
different segments: one linear segment on the parallel midbody, and two curved ones on the aft and
forward part of the ship (see table 5.7 and figure 5.3).
45
Table 5.5: Flat of bottom - Parameters
Parameter Definition Explanation Default
CFOBaftXaftBase
LAB
x position of the aft point of theFOB 0.16
CFOBfwdXfwdBase−LAB−Lc
LFB
x position of the forward point ofthe FOB 0.94
CFOBstraightAftLSA
LAB
Length of the aft linear segmenton the aft of the parallelmidbody
0.00
CFOBstraightFwdLSF
LFB
Length of the fwd linearsegment on the fore of theparallel midbody
0.00
FOBrun - Run angle of the FOB [o] 90.00FOBentrance - Entrance angle of the FOB [o] 90.00
FOBfullnessAftAreaCurvedAftzB×(xB−xA)
Area coefficient of the aftcurved segment of the FOB 0.40
FOBfullnessFwdAreaCurvedFwdzC×(xD−xC)
Area coefficient of the forwardcurved segment of the FOB 0.50
Table 5.6: Flat of Bottom - Points
Point Point name X [m] Z [m]A onXaftBase CFOBaft × LAB 0B onFOBstraightAft LAB − (CFOBstraightAft × LAB tan(deadrise)× (yI − bW )
C onFOBstraightFwd LAB + LC + (CFOBstraightFwd × LFB) tan(deadrise)× (yI − bW )
D onXfwdBase LAB + LC + (CFOBfwd × LFB) 0
Table 5.7: Flat of Bottom - Segments
Curve Name First Point Second Point Type of curveFOBaft A B F-SplineFOBstraight B C LineFOBfwd C D F-Spline
5.2.3 Flat of side
Figure 5.4: Flat of Side curve
To create the FOS contour (figure 5.4), it was necessary to create the parameters mentioned in the
previous chapter (see table 5.8).
The FOS contour was created by the development of its segments on the xz plan in order to facilitate the
creation of the meta-surfaces and some calculations needed for the validation of the model (see table
46
Table 5.8: Flat of side - Parameters
Parameter Definition Explanation Default
CFOSaftxFOSaft
LAB
x Position of the aft point of theFOS -0.08
CFOSaftHeightzFOSaft
H
x Position of the aft point of theFOS 0.87
CFOSfwdxFOSaft−LAB−Lc
LFB
x Position of the forward point ofthe FOS 0.80
CFOSstraightAftLSALAB
Length of the aft straight linesegment on the aft of the parallelmidbody
0.00
CFOSstraightFwdLSFLFB
Length of the fwd straight linesegment on the fore of the parallelmidbody
0.00
CFOSemergeAftxFOSemergeAft−xFOSaft
LAB−xFOSaft−LSA
x Position of the aft point ofintersection of the FOS and theDWL
0.51
CFOSemergeFwdxFOSemergeFwd−LAB−LC−LSF
xFOSfwd−LAB−LC−LSF
x Position of the fwd point ofintersection of the FOS and theDWL
0.45
FOSrun - Run angle of the FOS [o] 90.00FOSentrance - Entrance angle of the FOS [o] 90.00
5.9).
Table 5.9: Flat of Side - Points
Point Point name X [m] Z [m]A onFOSaft CFOSaft × LAB CFOSaftheight ×H
B onFOSemergeAft CFOSemergeAft × (LAB − xFOSaft −LSA) + xFOSaft
D
C onFOSstraightAft LAB − LSA zI + bHD onStartCylinder LAB zI + bHE onEndCylinder LAB + LC zI + bHF onFOSstraightFwd LAB + LC + LSF zI + bH
G onFOSemergeFwd CFOSemergeFwd × (xFOSfwd − LAB −LC − LSF ) + (LAB + LC + LSF )
D
H onFOSfwd LAB + LC + (CFOSfwd × LFB) H
With all the parameters and points set, the FOS segments were created. There are two curved segments
on the aftbody and another two on the forebody, and a straight line segment that includes the parallel
midbody (see table 5.10 and figure 5.4).
Table 5.10: Flat of Side - Segments
Curve Name First Point Second Point Type of curveFOSaftDry A B F-SplineFOSaftWet B C F-SplineFOSstraight C F LineFOSfwdWet F G F-SplineFOSfwdDry G H F-Spline
5.2.4 Design Water Line
To create the DWL (figure 5.5), it was necessary to create the parameters mentioned on the previous
chapter (table 5.11).
47
Figure 5.5: Design Water Line curve
Table 5.11: Design Water Line - Parameters
Parameter Definition Explanation Default
CDWLaftXxDWLaft
LAB
x position of the aftpoint of the DWL 0.01
CDWLaftYyDWLaft
B/2
y position of the aftpoint of the DWL 0.00
CDWLfwdXXfDWLfwd−LAB−Lc
LFB
x position of theforward point of theDWL
1.00
DWLrun - Run angle of theDWL [o] 0.00
DWLentrance - Entrance angle of theDWL [o] 10.00
DWLfullnessAftAreaCurvedAft
(CDWLaftY ×B/2)×(xFOSemergeAft−xDWLaftX )
Area coefficient ofthe aft curvedsegment of the DWL
0.85
DWLfullnessFwdAreaCurvedFwd
(B/2)×(xDWLfwdX−xFOSemergeFwd)
Area coefficient ofthe forward curvedsegment of the DWL
0.63
The DWL curve was developed on the xz plan in order to facilitate the development of the surfaces of
the hull and some validation parameters (table 5.12).
Table 5.12: Design Water Line - Points
Point Point name X [m] Z [m]A onCPC CDWLaftX × LAB 0B onDWLaft CDWLaftX × LAB CDWLaftY × (B/2)
C onFOSemergeAft CFOSemergeAft × LAB (B/2)− tan(flare)× (H −D)
D onFOSemergeFwd (CFOSemergeFwd × LFB) + LAB+LC (B/2)− tan(flare)× (H −D)
E onDWLfwd CDWLfwdX × LFB 0
With the previous points, a set of 3 curves was developed in order to obtain the desired DWL curve
(table 5.13).
Table 5.13: Design Water Line - Segments
Curve Name First Point Second Point Type of curveDWLaft1 A B LineDWLaft2 B C F-SplineDWLstraight C D LineDWLfwd D E F-Spline
48
5.2.5 Deck Line
To develop the deck line (figure 5.6), it was necessary to create the parameters presented on table 5.14.
In order to facilitate the development of the Meta-Surfaces and the calculation of the validation parame-
ters, the Deck points and segments were created on the xz plan.
With all the points and parameters defined, the segments needed to build the deck line were developed
(see table 5.16 and figure 5.6).
Figure 5.6: Deck Line
Table 5.14: Deck Line - Parameters
Parameter Definition Explanation Default
CPeakxPeak−Lc−LAB
LFB
x position of theforward point of thedeck line
1.12
deckfullnessAftAreaCurvedAft
(xFOSaft−xTransom)×(B−LTransomPanelTop)
Area coefficient ofthe aft curvedsegment of the deckline
0.85
deckfullnessFwdAreaCurvedFwd
(xpeak−xFOSfwd)×B
Area coefficient ofthe forward curvedsegment of the DeckLine
0.73
Table 5.15: Deck Line - Points
Point Point name X [m] Z [m]A onSLP CXTransom × LAB 0B onTransom CXTransom × LAB CTransomTopY × (B/2)C onDeckStraightAft CFOSaft × LAB B/2D onDeckStraightFwd LAB + LC + (CFOSfwd × LFB) B/2E onPeak LAB + LC + (CPeak × LFB) 0
Table 5.16: Deck Line- Segments
Curve Name First Point Second Point Type of curveDeckTransom A B LineDeckaft B C F-SplineDeckstraight C D LineDeckfwd D E F-Spline
49
Figure 5.7: Stem contour
5.2.6 Stem
To develop the stem longitudinal contour (figure 5.7), the parameters presented on table 5.17 were
created.
Table 5.17: Stem - Parameters
Parameter Definition Explanation Default
CStemStriaghtlength of the linar segment
D
Length of the straight line segmentof the stem 0
Tgbulb - Tangent angle at the top beginningof the bulb longitudinal contour 80
TgPeak - Tangent angle at the peak 45
With all the parameters values defined, the points of the stem contour were created (table 5.18).
Table 5.18: Stem - Points
Point Point name X [m] Z [m]A onBulb Lpp × (1 + CmoveBulb) Chb ×DB onLinear Lpp × (1 + CmoveBulb) (Chb + CStemStriaght)×DC onPeak LAB + LC + (CPeak × LFB) D
Finally, with all the points created, the curve itself was developed in two different segments (table 5.19)
Table 5.19: Stem- Segments
Curve Name First Point Second Point Type of curveStemLinear A B LineStemCurved B C F-Spline
5.2.7 Bulbous Bow
To create the bulbous bow curves, some of the Kracht linear and non-linear bulb parameters were used,
as mentioned in the previous chapter (table 5.20).
Some other parameters mentioned in the previous chapter were also created in order to completely
characterize the bulbous bow (table 5.21). It is important to mention that all the curves created for the
50
Table 5.20: Bow Bulb - Kracht Parameters
Parameter Definition Explanation DefaultClpr
Length of theBulbLpp
Length Coefficient 0.04Czb
Z bulb tipD
z bulb Tip Coefficient 0.63Cbb
Max beamon the beginning of theBulbB
Beam Coefficient 0.18
development of the bulb surfaces, where created on the origin of the referential and then a translation
was made to all of them by the CmoveBulb parameter.
The first step was the creation of the longitudinal contour of the bulb (5.8). This curve was divided into
two curves (upper contour and lower contour) as mentioned on the previous chapter. For that to be
possible three points were created on the xz plan (table 5.22).
Figure 5.8: Bulb Longitudinal Contour
With all the points and parameters that are necessary to create the longitudinal contour of the bulb, its
segments were finally created (see table 5.23 and figure 5.8).
The following step was the development of the distribution curve of the maximum beam of the bulb
sections. For that, two points were created on the xz plan (table 5.24) as well as a F-Spline between
these two points.
The final step was the development of the contour of the plan that intersects the bulb surface and that
passes through the halfbeam elevation distribution. For that, two points were again created on the xz
plan (table 5.25) with a F-Spline between them.
5.2.8 Stern Bulb
The Stern Bulb is one of the hardest parts of the hull form to build. For that reason it was necessary to
create a set of property distribution and geometric curves.
The first step was the definition of some parameters in order to define the longitudinal contour of the
stern bulb (table 5.26 and figure 5.9).
51
Table 5.21: Bow Bulb - New Parameters
Parameter Formula Explanation Default
CzaZLowerPoint
D
z position of the lowerpoint of the lowerlongitudinal contour ofthe bulb
0.066
ChbZUpperPoint
D
z position of the upperpoint of the upperlongitudinal contour ofthe bulb
0.890
ChbeZLowerPoint
D
z position of themaximum beam on thebeginning of the bulb
0.370
CmoveBulboffsetToFp
Lpp
x distance between theLpp and the beginning ofthe bulb surface
0.004
BulblowerFullnessAreaLowerLongitudinal
BulbLength×(ZTip−ZLowerPoint)
Area coefficient of thelower longitudinalcontour of the bulb
0.730
BulbupperFullnessAreaUpperLongitudinal
BulbLength×(ZUpperPoint−ZTip)
Area coefficient of theupper longitudinalcontour of the bulb
1.000
BulbhalfbeamFullnessAreaHalfbeamContour
MaxHalfbeam×BulbLenght
Area coefficient of thehalfbeam distributioncontour of the bulb
0.850
BulblowerSectionFullnessAreaLowerTransversal
MaxHalfbeam×(ZMaxBeam−ZLowerP.)
Area coefficient of thelower transversalcontour of the bulb
0.780
BulbupperSectionFullnessAreaLowerTransversal
MaxHalfbeam×(ZUpperP.−ZMaxBeam)
Area coefficient of theupper transversalcontour of the bulb
0.780
TgupperContour -
Tangent of the uppercontour at the upperpoint of the upperlongitudinal contour [o]
80.000
Table 5.22: Bulb Longitudinal Contour - Points
Point Point name X [m] Z [m]A LowerPoint 0 Cza ×DB BulbTip CLPR × Lpp Czb ×DC UpperPoint 0 Chb ×D
Table 5.23: Bulb Longitudinal Contour - Segments
Curve Name First Point Second Point Type of curve Star Angle End AngleLow A B F-Spline - 0.00Upp C B F-Spline TgupperContour 180.00
Table 5.24: Bulb Halfbeam Elevation Distribution - Points
Point Point name X [m] Z [m]D onFP 0 Chbe ×DB onTip CLPR × Lpp Czb ×D
Table 5.25: Bulb Halfbeam Distribution - Points
Point Point name X [m] Z [m]E onFP 0 Cbb ×B/2F onTip CLPR × Lpp 0
52
Figure 5.9: Stern Bulb - Longitudinal Contour
Table 5.26: Stern Bulb - Longitudinal Contour - Parameters
Parameter Definition Explanation Default
CXBulbTipX Bulb Tip
LAB
x position of the stern bulbtip 0.076
CZBulbTipZ Bulb Tip
H
z position of the stern bulbtip 0.183
CXClearanceX Clearance
LAB
x position of the sternclearance 0.124
CZClearanceZClearance
H
z position of the sternclearance 0.326
TgTransom - Tangent at Transom [o] 103.000
Figure 5.10: Stern Bulb - Boundary
After this step, the geometric boundary between the bare hull and the bulb surface was created (figure
5.10). For that to be possible, a set of parameters was created (table 5.27).
After all the parameters being defined, three points were created on the xz plan(table 5.28).
With all the parameters and the points defined, the segments of the boundary between the bare hull and
the stern bulb, were created (table 5.29 and figure 5.10).
Finally, it was created a set of parameters to define the shaft hole on the stern bulb (table 5.30). If the
values for the outerHorizontalAxis and the outerV erticalAxis are the same, the stern bulb will have a
53
Table 5.27: Stern Bulb - Boundary - Parameters
Parameter Definition Explanation Default
CxBilgeAft x bare hull aftLAB
x position of the beginningof the stern bulb 0.40
CxMaxBeamxMaxBeam
Lpp
x position of the max beamof the stern bulb 0.26
CyMaxBeam MaxBeamB/2 max beam of the stern bulb 0.50
fullnessaftAreaaftContour
(xmaxBeam−xsternBulbAft)×MaxBeam
Area coefficient of the aftsegment 0.57
fullnessfwdAreafwdContour
(xbareHullAft−xmaxBeam)×MaxBeam
Area coefficient of the fwdsegment 0.80
tgAft - Tangent angle of the aftsegment 18.00
Table 5.28: Stern Bulb - Boundary - Points
Point Point name X [m] Y [m]A SternBulbAft xbulbT ip + (xclearance − xbulbT ip)× 0.4 0B SternBulbMaxBeam CxMaxBeam× Lpp CyMaxBeam×B/2C BareHullAftBase CxBilgeAft× LAB 0
Table 5.29: Stern Bulb - Boundary - Segments
Curve Name First Point Second Point Type of curve Star Angle [o] End Angle [o]aft A B F-Spline tgAft 0
fore B C F-Spline 0 -90
circular distribution of volume near the shaft hole, and if the values are different the stern bulb will have
an elliptical distribution of volume.
Table 5.30: Stern Bulb - Shaft - Parameters
Parameter Explanation DefaultHubRadius Shaft radius [m] 0.3
outerHorizontalAxisHorizontal distance from the center of the shaft line and the endof the stern bulb surface at x = xBulbTip [m] 0.4
outerV erticalAxisHorizontal distance from the center of the shaft line and the endof the stern bulb surface at x = xBulbTip [m] 0.4
5.2.9 Transom Panel
As in the other curves, the development of the transom panel contour begun with the definition of the
parameters that are needed for its creation (table 5.31).
The next step was the creation of the points needed for the development of the segments of the transom
panel. All the points were created on a plan parallel to the yz plan on x = xtransom (table 5.32).
Finally, the segments of the transom panel were created (see table 5.33 and figure 5.11).
5.3 Property Distribution Curves
The property curves represent the variation of some geometric properties of the hull form along one
direction and therefore they are not directly obtained from the hull but result from some geometric pro-
cessing. These curves are very difficult to measure on existing models or lines plans, since they are not
54
Figure 5.11: Transom
Table 5.31: Transom Panel - Parameters
Parameter Definition Explanation Default
CXTransomX Transom bottom
LAB
x position of the lower pointof the transom -0.080
CZTransomZ Transom bottom
D
z position of the lower pointof the transom 1.117
ClinearBottomLength of the linear bottom segment
B/2
Length of the straight linebottom segment of thetransom panel
0.000
ClinearSideLength of the linear side segment
H
Length of the straight sidesegment of the transompanel
0.200
CTransomTopYLength of the linear top segment
B/2
Length of the straight topside segment of the transompanel
1.000
transomfullnessArea of the curved segment
(yonFlatSide−zonBilge)×(zonFlatSide−zonBilge)
Area coefficient of thecurved segment of thetransom panel
0.780
tgbottom -Tangent at the straight linebottom segment of thetransom panel [o]
0.000
tgside -Tangent at the straight sidesegment of the transompanel [o]
0.000
Table 5.32: Transom Panel - Points
Point Pointname Y [m] Z [m]
A onTransom 0 CZTransom ×DB onBilge cos(tgbottom)× ClinearBottom × (B/2) sin(tgbottom)× ClinearBottom × (B/2) + CZTransom ×DC onFlatSide (B/2)− sin(tgside)× (ClinearSide ×H) H − cos(tgside)× (ClinearSide ×H)D onDeck CTransomTopY × (B/2) HE onSLP 0 H
55
Table 5.33: Transom Panel - Segments
Curve Name First Point Second Point Type of curvetransomFlatBottom A B LinetransomBilge B C F-SplinetransomFlatSide C D LinetransomTop D E Line
curves that exist in reality.
Most of the parameters that it will be presented were considered the same for every tested model. After
the first generation of the hull form, the architect can change them in order to obtain the desired hull
shape.
5.3.1 Sectional Area Curve
Figure 5.12: Sectional Area Curve
As said before, this is one of the most important curves for the naval architects. With this curve, they can
change the distribution of the submerged hull volume (by calculating and changing the LCB position)
and the prismatic coefficient. So, to define the SAC (figure 5.12) some parameters where created (see
table 5.34).
Table 5.34: Sectional Area Curve - Parameters
Parameter Definition Explanation Default
CareaDWLaftArea atDWLaft section
Area onMainFrame
Area coefficient of thesection at DWL aft 0.000
CareaAftBaseArea atAftBase sectionArea onMainFrame
Area coefficient of thesection at aft base 0.200
CareaFOSemergeAftArea at FOS emerge aft section
Area onMainFrame
Area coefficient of thesection at the aft intersectionof the DWL and the FOS
0.800
CareaFOSemergeFwdArea at FOS emerge fwd section
Area onMainFrame
Area coefficient of thesection at the fwdintersection of the DWL andthe FOS
0.900
CareaFwdBaseArea at FwdBase section
Area onMainFrame
Area coefficient of thesection at the fwd base 0.135
The SAC segments were developed between the aft longitudinal position of the DWL and the forward
perpendicular, on the xz plan and a scale was applied to every z coordinate in order to have a smaller
curve and easier to visualize. The applied scale was:
56
scale = 0.5× Lpp (5.5)
Table 5.35: Sectional Area Curve - Points
Point Point name X [m] Z [m]A onDWLaft CDWLaft × LAB CareaDWLaft × scale
B onAftBase CFOBaft × LAB CareaAftBase × scale
C onFOSemergeAft CFOSemergeAft × LAB CareaFOSemergeAft × scale
D onStarCylinder LAB scale
E onEndCylinder LAB + LC scale
F onFOSemergeFwd (CFOSemergeFwd × LFB) + LAB + LC CareaFOSemergeFwd × scale
G onFwdBase CFOBfwd × LFB + LAB + LC CareaFwdBase × scale
After having all the points defined, the segments of the SAC were created, mostly using the F-Spline
curves (see table 5.36 and figure 5.12).
Table 5.36: Sectional Area Curve - Segments
Curve Name First Point Second Point Type of curve Start Angle End AngleSACaft1 A B F-Spline 90 -SACaft2 B C F-Spline - -SACaft3 C D F-Spline - 90SACcylinder D E Line - -SACfwd1 E F F-Spline 90 -SACfwd2 F G F-Spline - -
At the beginning of the model construction, one of the objectives was to develop a hull form that would
follow the SAC curve created by the introduction of the previous parameters, but, with the development
of the hull shape this idea had to be abandoned because it was practically impossible to do it on the
zones where the stern and bow bulbs were. An attempt was made to make a secondary SAC curve
considering only the stern and the bow bulbs areas, but this showed to be completely impossible to do
without having a hull already built. So, the SAC curve was applied only to the surfaces between the
beginning of the parallel midbody and the end of the FOS curve.
5.3.2 Flare At Bottom
Figure 5.13: Flare at Bottom curve
The FAB distribution curve were set between the forward base longitudinal position and the bulb tip
57
longitudinal position. To build this property distribution curve (figure 5.13) two additional parameters
were necessary:
• flareBulbT ip - Flare angle at the bulb tip;
• tgBulbT ip - Tangent of the curve distribution at the bulb bow tip.
After having the parameters values, the points needed for the development of the FAB curve distribution
were created (table 5.37). The points were created on the xz plan in order to facilitate the meta-surfaces
development. The z values of the curve distribution were all submitted to a scale in order to have a curve
easier to see.
Table 5.37: Flare at Bottom - Points
Point Point name X [m] Z [m]A on09FwdBase 0.9× (LAB + LC + (CFOBfwd × LFB)) flare/10B onFOSfwd LAB + LC + (CFOSfwd × LFB) flare/10C onBulbTip Lpp + (Clpr × Lpp) flareBulbT ip/10
With all the points defined, the segments of the curve distribution were created (see table 5.38 and figure
5.13).
Table 5.38: Flare at Bottom - Segments
Curve Name First Point Second Point Type of curve Start Angle End AngleFABaft A B line - -FABfwd B C F-Spline 90 tgBulbT ip
5.3.3 Flare At Design Water Line
The FADWL distribution curve (figure 5.14) is one of the most difficult curves to measure on an existing
hull form.
This curve was developed and analysed only between the forward longitudinal position of the intersection
of the FOS and the DWL, and the forward perpendicular, since it is between these two positions that
there are relevant variations. To develop the different segments of the curve it was necessary to create
some parameters (see table 5.39 and the following equation).
Cmaxflare =XMaxFlare− LAB − LC
LFB(5.6)
Table 5.39: Flare at Design Water Line - Parameters
Parameter Parameter name Default UnitsmaxFlare Maximum value of the flare 45.00 [o]flareOnFp Flare on the forward perpendicular 0.00 [o]tgAtFOSemerge Tangent of the flare at DWL distribution on at FOS emerge 45.00 [o]tgAtFp Tangent of the flare at DWL distribution on at forward perpendicular 90.00 [o]
The next step was the development of the three points needed for the creation of the segments of the
FADWL distribution curve (table 5.12).
58
Figure 5.14: Flare at Design Water Line
Table 5.40: Flare at Design Water Line - Points
Point Point name X [m] Z [m]A onFOSemerge (CFOSemergeFwd × LFB) + LAB + LC flareB onMax (Cmaxflare × LFB) + LAB + LC maxFlareC onFp Lpp flareOnFp
With all the parameters and points defined, the segments needed to build the FADWL distribution curve
were developed (see table 5.41).
Table 5.41: Flare at Design Water Line - Segments
Curve Name First Point Second Point Type of curve Start Angle [o] End Angle [o]FADWLaft A B F-Spline tgAtFOSemerge 90FADWLfwd B C F-Spline 90 tgAtFp
5.3.4 Flare At Deck
The FAD distribution curve was developed between the forward longitudinal position of the FOS and the
forward perpendicular, by using a third degree spline curve with four points (see table 5.42 and figure
5.15).
Table 5.42: Flare at Deck - Points
Point Point name X [m] Z [m]A p00 LAB + LC + (CFOSfwd × LFB) flareB p01 p00x + p03x−p00x
33/8× flareAtFP
C p02 p00x + 2(p03x−p00x)3
3/4× flareAtFPD p03 Lpp flareAtFP
The only additional parameter created was the flareAtFP , that represents the flare of the hull surface
59
Figure 5.15: Flare at Deck
at the forward perpendicular.
5.3.5 Stern Property curves
To develop the stem surface it is necessary to create two property curve distributions, one for the dis-
tribution of the radius and another for the distribution of the angles. To build these two curves, it was
necessary to create a secondary curve that relates the x position of each point and their z position. For
that to be possible, a Generic Curve, available on FRIENDSHIP-Framework was used, with the following
equation:
GenericCurve(t) =
X(t) = 0
Y (t) = 0
Z(t) = D + (H −D)× t
(5.7)
To develop the curve distribution of the stem radius (figure 5.16), three parameters were needed:
• radiusDWL - Radius of the forward curved segment of the DWL;
• Cradius25 - Relation between the radius at the DWL and at the curve that intersects the hull surface
at 25% of the difference between the draft and the depth;
• radiusDeck - Radius of the forward curved segment of the Deck curve.
Having the values for all the parameters, it was possible to define the points for the development of
the property distribution curve of the stem surface radius (table 5.43). To build it, a second degree
interpolation curve with the three points was used, as in figure 5.16 (see table 5.43).
60
Figure 5.16: Stem - Radius distribution
Table 5.43: Stem - Radius Distribution - Points
Point Point name X [m] Z [m]A p00 radiusDWL GenericCurve(0)ZB p01 Cradius25 × radiusDWL GenericCurve(0.25)ZC p03 radiusDeck GenericCurve(1)Z
Figure 5.17: Stem - Angle distribution
To develop the curve distribution of the angles (figure 5.17) of the stem surface, only one parameter was
needed: AngleDeck that represents the tangent angle of the deck curve after its forward radius.
A two degree interpolation curve with a set of four points was used, to develop the curve distribution of
the angles (see table 5.44 and figure 5.17)
The x values of the curve distribution were all submitted to a scale in order to have a curve easier to
61
Table 5.44: Stem - Angle Distribution - Points
Point Point name X [m] Z [m]A p00 DWLentrance × 0.1 GenericCurve(0)ZB p01 AngleDeck × 0.095 GenericCurve(0.05)ZC p02 AngleDeck × 0.14 GenericCurve(0.5)ZD p03 AngleDeck × 0.1 GenericCurve(1)Z
see.
5.4 Surfaces
The majority of the hull mode surfaces were created with Meta Surfaces, a surface concept available on
FRIENDSHIP-Framework that collects information available in two distinct directions and that is more
flexible than the well-known surface generation techniques such as extrusion, lofting, revolution, and so
on, available on every CAD system, since they do not assume any particular representation and char-
acteristics, being directly linked to Feature modelling. This type of surface ensures a smooth transition
from one surface to the next, by guaranteeing that both surfaces have equal tangent angles along the
boundary.
In order, to create this Meta Surfaces some Features were created. These Features are high-level
entities, available on FRIENDSHIP, that encapsulate any user-defined command sequence and that
makes it available for writing macros and subroutines. They represent specific work processes which
can be stored externally and reused [41].
To link the Features and the Meta Surfaces, some Curve Engines were also needed. These objects
store the distribution of every input of the Features along the third axis of the hull. So, with the Curve
Engine, several cross-section were generated at arbitrary x-positions.
To develop the hull model,the hull surface had to be divided into 23 different sub-surfaces, as seen in
figure 5.18.
Figure 5.18: Surfaces
The aftbody was built with six surfaces, where one is the transom panel and another the stern bulb
(figure 5.19 (a)). The forebody was built with seventeen surfaces (figure 5.19 (b)).
As it can be seen on the previous figure, in the forebody, the FOS and FOB were built seperatly from
the bilge, and were divided on the longitudinal position where the FOS intersects the DWL, where the
62
(a) Aftbody Surfaces (b) Forebody Surfaces
Figure 5.19: Hull Surfaces - Bodies
FOS and FOB end. The bulbous bow was created using three surfaces, one from the forward point of
the FOB to the beginning of the bulb, and two others for the bulb it self (figure 5.20 (a)). The stem was
built with three surfaces, as it can be seen in figure 5.20 (b).
(a) Bulbous Bow Surfaces (b) Stem Surfaces
Figure 5.20: Hull Surfaces - Components
5.5 Hydrostatic Calculations
The hydrostatic calculations were carried out using a Feature available on FRIENDSHIP-Framework,
that is based on discrete sectional data either from a section group or an offset group. The output of this
Feature is a set of hydrostatic characteristics of the hull: submerged volume (5), longitudinal positions
of the centre of buoyancy and floatation, waterplane area (AWP ), and traversal and longitudinal second
moment (IT and IL). With these results, it was possible to calculate the block coefficient (equation
5.8), the midship coefficient (equation 5.9), the prismatic coefficient (equation 5.10), the waterplane
coefficient (equation 5.11) and the transversal metacentric heigh (equation 5.12).
Cb =5
Lpp ×B ×D(5.8)
Cm =AmainFrame
B ×D(5.9)
Cp = Cm × Cb (5.10)
63
CWP =AWP
LWL ×B(5.11)
KMT = BM + KB =IT5
+ D (5.12)
The hydrostatic results from the Feature and the results from the previous equations, will be very useful
for the validation of the surface generation (see chapter 6), and to apply the Lackenby transformation
(see subsection 5.6).
5.6 Lackenby Transformation
In order to obtain the desired hull shape with a certain hydrostatic characteristics, the Lackenby Trans-
formation was applied. This method is available as a Feature in FRIENDSHIP-Framework, and its called
"Generalized Lackenby".
Figure 5.21: Lackenby Transformations [34]
64
The classical Lackenby method [42] considers a hull form, and changes it according to the prismatic
coefficient, the longitudinal centre of buoyancy and forward and aft position of the parallel midbody. To
do so, shift functions are created to determine how much each section needs to be moved longitudinally,
in order to have the desired hydrostatic characteristics. This method is illustrated in figure 5.21 in the
middle scheme.
The transformation method applied on the Feature "Generalized Lackenby", is based on the original
Lackenby approach but extends it by means of smooth delta curves [34]. Initial offset data of a ship
hull is slightly moved along the x axis according to user-defined constraints, such as the change of
the prismatic coefficient or the change of the centre of buoyancy. Based on the sectional area curve,
generated as mentioned on section 5.5, and the difference between the desired prismatic coefficient and
centre of buoyancy, and the ones obtained in the previous section, this Feature internally creates fair
delta curves for which the tangent angles can also be controlled. The sections that can be transformed
are set by the user as boundaries, being possible to set a fix parallel midbody. This method is illustrated
in figure 5.21 on the bottom scheme.
5.7 Control Panels
In order to facilitate the import and changes of the input values, a Feature was created to import the
input values from an ASCII file with the format described in Appendix A. This Feature also allows some
parameters to be not specified. In these cases the Feature considers the default value and then the
designer can change any parameter, until he has the desired hull shape.
Another Feature was created to export the parameters values of the final hull shape, allowing the de-
signer to know the values that where used to create the hull shape, even after all the possible changes.
A Feature was also developed to allow the designer to export the values of all validation parameters
created, into an ASCII file. This Feature can also export the hydrostatic results, before and after the
application of the Lackenby Transformation, and the desired number of hull sections defined only by the
number of points set by the user.
65
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Chapter 6
Validation of the parametric modelling
of the hull form
After the development of the hull model, a validation process was carried out by trying to reproduce
some of the existing hull forms analysed in chapter 4 and then a measure of the resulting differences
was made. The geometric curves were the first to be analysed, followed by the validation of the surfaces
and finally the hydrostatics properties
To analyse the result values of the validation, the error between the values of the existing hulls and the
ones obtained by the application of the parametric hull model developed was calculated:
error [%] =Real −Model
Real× 100 (6.1)
With the error results, the normal distribution was calculated in order to understand if the values were
acceptable or not. The tools of Microsoft Excel were used to calculate the average and the standard
deviation of each distribution, and to create the graphics for each distribution.
The graphics of each normal distribution, applied to each set of error values for each measure parameter,
are presented in the following subsections.
6.1 Geometric Curves Validation
The validation of the geometric curves was made focusing mainly on the area, perimeter and centroid of
each curve. The geometric curves analysed were only the Main Frame, FOB, FOS, DWL, Deck contour,
Bulbous Bow and Transom Panel, since those curves are the ones where is possible to measure all the
parameters needed for its development.
6.1.1 Main Frame
The parameters of the main frame that were studied were the area, the midship coefficient and its x
position.
67
Analysing figure 6.1 (a), is possible to see that the average value of the three chosen parameters are
nearly zero, validating the characterization of this curve, using the parameters set presented on chapters
4 and 5.
6.1.2 Flat of Bottom
To validate the Flat of Bottom curve, it was analysed a set of four parameters: the FOB curve area,
longitudinal position of the centroid, perimeter and length of the straight segment.
Analysing figure 6.1 (b), is possible to consider that the set of parameters used to develop the FOB
curve are suitable for the ship types in study, since the differences between the real hulls and the hull
model are considerably small.
In some cases, there is a small difference between the ship’s real values and the ones obtained by the
developed model, especially for the FOB area. This happens in the case of one ferry ship that has
different longitudinal positions for the maximum y value of the FOB and for the minimum z value of the
FOS, being very difficult to know what is the longitudinal position of the main frame (beginning of the
parallel midbody). Cases as the one described before, are not considered on the developed model,
since the minimum z value of the FOS and the maximum values of the y of the FOB are considered the
same.
(a) Main Frame Validation (b) FOB Validation
Figure 6.1: Main Frame and FOB Validation
6.1.3 Flat of Side
To validate the flat of side curve, some parameters were considered, similarly to what was done to the
flat of bottom curve 6.1.2: FOS curve area, longitudinal position of the centre mass, perimeter and length
of the straight segment.
Once again, the parameter set used for the FOS development can be considered suitable for the FOS
characterization of the ship types in study, since the average error values are considerably small.
In some cases, the perimeter of the FOS presented considerable differences between the real hull form
and the hull model values (figure 6.2 (a)). This happened in the cases where the run angle of the FOS
is too big or in the cases that the FOS have more than one inflection point in the aft and fwd curved
segment. In this cases, the developed model shouldn’t be used.
68
6.1.4 Design Water Line
As previously done for the FOB and to the FOS, the same coefficients were considered and one was
added relating the length of the DWL itself, i.e., the difference between the longitudinal position of the
forward and the aft point of the DWL.
Once again, analysing figure 6.2 (b) it is possible to consider that the set of parameters used to develop
this curve is valid, since the errors between the real hull and the hull model are nearly zero.
This analysis is very important since the geometric characteristics of the waterplane have a big influence
in both the hydrodynamic and hydrostatic behaviour of the ship.
(a) FOS Validation (b) DWL Validation
Figure 6.2: FOS and DWL Validation
6.1.5 Deck Contour
To validate the characteristics of the Deck Line the equivalent parameters of the ones used for FOB and
FOS curves were used.
The parameter set used to develop the deck contour can be considered suitable for the ship types in
study, since the average value for the error between the geometric characteristics of the real hull and
the hull model, are considerably small.
6.1.6 Bulbous Bow
To validate the bulbous bow three parameters were considered: the longitudinal and transversal area
contour, and the volume of the bulb.
The first two validation parameters on figure 6.3 (b) are directly influenced by the area coefficient pa-
rameters presented on chapters 4 and 5, therefore, the average error between the real hull and the
hull model for this parameters are nearly 1%. This validates the parameter set chosen for the bulb
longitudinal and transversal contour characterization on the previous chapters.
The volume of the bulb presented an average error value close to 2%. Since the bulb volume does not
have any parameter that directly characterizes it, the average error value obtained can be considered a
very positive one.
69
(a) Deck Validation (b) Bulb Validation
Figure 6.3: Deck and Bulb Validation
6.1.7 Transom Panel
To study the validation of the transom panel the area and the perimeter of the curve were considered,
as done before, and the y and z coordinates of the centroid.
Analysing figure 6.4 is possible to conclude that the parameter set used to develop the transom panel
are acceptable, since the average error values are very small, with exception for the YCG that presented
a considerable error between the real hull and the hull model. This happened in the cases where there
is not a smooth transition from the linear bottom and the linear side to the curve segment, so in this type
of cases, this model should not be used. This measure parameter does not have any meaning for real
hulls because every hull has the transom panel YCG always equal to zero since there is a symmetry on
the hull geometry, but, in the present study, this was done using half of the transom panel in order to
better understand the differences between the geometries.
Figure 6.4: Transom Panel Validation
6.2 Property Curves Validation
Since the measure and determination of the property curves is very difficult to achieve for hulls that
already exist, its validation was not executed.
70
6.3 Submerged Hull Validation
To measure the quality of the generated hull surfaces, some hydrostatic parameters were considered.
The parameters chosen for this study were: the block and the prismatic coefficients, the waterplane
coefficient, the transverse metacentric height, the longitudinal position of the centre of buoyancy and the
submerged volume of the ship.
This analysis was done for the resulting hull, before and after the application of the Generalized Lackenby
Method (see previous subsection 5.6).
(a) Before Lackenby (b) After Lackenby
Figure 6.5: Submerged Hull Validation
From the analysis of the results on figure 6.5, it is possible to notice that, in some cases, after the
application of the Generalized Lackenby Method, the resulting hull presented fewer similarities with the
existing hull, then before the application.
Despite the discrepancies shown before, it could be concluded that for some cases, the method pre-
viously presented for the characterization of the hull curves are a very good starting point to the hull
modelling and reproduction.
6.4 Reproduction of existing hulls
In this subsection, three hulls of the ones that were reproduced with the developed model are presented.
Their main dimensions are presented on table 6.1 and the differences on the hydrostatic characteristics
on table 6.2.
It is important to notice that for the RoPax, there are several important differences on the geometry.
On of them is the not existence of a stern bulb, and the fact that the transom panel has a completely
different geometry from the considered on the developed model. Despite of these geometric differences,
it is possible to notice many important similarities on the hull shape.
Table 6.1: Main Dimensions of reproduced hulls
Lpp [m] B [m] H [m] D [m] CbContainership 180.00 32.20 23.00 10.50 0.661RoPax 180.00 28.00 20.00 7.70 0.698Tanekr 319.00 42.80 7.50 13.00 0.591
71
Table 6.2: Differences of the hydrostatic calculations
dCb [%] dCp [%] dCwp [%] dKMt [%] dLCB [%] dVolume [%]Containership -2.22 -9.57 +1.65 +2.94 -2.34 -2.21RoPax +4.38 +4.41 +7.30 +2.27 -4.54 -0.41Tanker -11.03 -18.47 +2.36 +10.48 -3.40 -10.40
Figure 6.6: Containership - Original
Figure 6.7: Containership - Model
Figure 6.8: RoPax - Original
Figure 6.9: RoPax - Model
Figure 6.10: Tanker - Original
Figure 6.11: Tanker - Modelo
72
Chapter 7
Conclusions
A parametric hull model that could be used in various stages of the ship design, such as hull optimization,
CFD studies, was developed and presented on this thesis
A study of the geometric and property distribution curves was done focusing on merchant ships. The
main objective of this study was the analysis and characterization of the possible different curve shapes.
Nine geometric curves and seven property distribution curves, were considered. The study of the prop-
erty distribution curves presented a bigger challenge then the study of the geometric curves, since they
represent functions of hull surfaces properties along one direction, and not real contours of the hull.
Some parameters representing distances, integral measures and angles, were defined in order to char-
acterize and distinguish the different curve shapes. Sometimes these parameters can be very difficult
to define at an early stage of the hull development, especially the ones related with the property curves,
which are even more difficult do measure from existing hulls since they do not represent physical real
curves.
After the definition of each considered parameter, a study of the range of values was done, in order to
understand the trends, limits and correlations between the parameters values.
Some correlations were found between the characteristics of the curves and the ship type, contrary to
the case of the bulbous bow whose parameters depend only on the bulbous type. For example, the
parameters that characterize the aftbody of the container ships and the ferries presented very similar
values, since both need parallelepiped space in the aft part of the hull, in order to increase the cargo
volume and to facilitated cargo operations.
A parametric hull form model was developed and implemented using the software tool FRIENDSHIP-
Framework. The model development started with the definition of nearly one hundred parameters, then
the points, curves and finally the hull surfaces. This approach facilitates the beginning of the develop-
ment of a hull from scratch, and faster and easier changes on the hull form, allowing the automation,
quantification and reproduction of the exactly same hull shape with a certain set of input parameters.
To develop the hull model, some assumptions had to be taken, limiting the geometry types. For example,
when defining the SAC curve, the values for the CareaFOSemergeAft were considered bigger than the
values for the CareaAftBase, and, as studied in some existing hulls, when the DWL intersects the transom
73
panel this does not happen.
The developed hull model is composed by twenty three surfaces. The aftbody has six surfaces and the
forebody seventeen. The stern bulb was developed with only one surface, while the bulbous bow with
three surfaces. In the foreboy the FOS surface was divided into two surfaces, one from the beginning of
the parallel midbody to the forward intersection of the FOS with the DWL, and another until the forward
point of the FOS. The same was done to the FOB but this time with one more surface from the forward
longitudinal position of the FOS to the forward position of the FOB.
At the final stage of the hull development, some hydrostatic calculations were done, and the Lackenby
Transformation was applied, in order to do small adjustments on the prismatic coefficient and of the
longitudinal position of the centre of buoyancy values.
Some of the considered curves were more important for the modelling of the hull shape then others.
That is the case of the Main Frame, Longitudinal Contour, FOS, FOB, DWL, Deck contour and SAC.
These curves require special attention, and were the ones used for the validation of the hull.
In order to validate the developed hull parametric model, an implementation of parameters values of
existing hulls was done, as well as a comparison between some characteristics of some curves. Al-
though for some curves the discrepancies found were very small, it was possible to validate the set
of parameters that were used to characterize them. With the developed model, the recreation of some
studied hulls was very difficult. Despite the discrepancies, it was possible to conclude that the developed
procedure can be used to obtain the initial hull model and be applied in some other studies, such as the
cargo volume estimation, CFD calculations, and so on, but does not has enough accuracy to be used
for construction.
During the development of this thesis some barriers appeared due to the difficulty in acquiring sufficiently
good ship models/line plans for analysis and determination of the parameters needed for the hull shape
study.
7.1 Future Work
The developed hull form model presented some limitations. One of the most relevant was the inability to
set the block coefficient as an input. To solve this problem, instead of using the Generalized Lackenby
Transformation, that has several limitation, it would be very useful to use the developed hull in an opti-
mization procedure, allowing the modification of the SAC, and even for some other parameters chosen
by the designer, especially the parameters that were set with the default values, in order to obtain the
desired block coefficient.
Another important limitation of the model is the assumption of the halfbeam elevation contour of the
bulbous bow as a planar curve and not a 3D curve. In future works, it would be very interesting to define
new parameters to characterize this curve as a 3D curve, in order to have an increased accuracy on the
bulb generation.
The developed parametric hull model was also built considering only merchant ships with bulbous bow,
stern bulb and vertical transom panels, limiting the types of ships possible to reproduce. In the future,
74
it would be very interesting to have the possibility to develop a hull form with the optional addition of
bulbous bow and stern bulb, and even the possibility to have an inclined transom panel, as it happens in
many merchant ships, and even to extend the study and the model to other ship types.
In some curves, the possibility of having more inflection points, would be very helpful, especially in the
case of the FOS contour. The stern bulb should also have a more in depth study since it is very difficult
to know the values of all its parameters, from existing hulls.
In order to obtain a hull form with improved fairness as required for production, it would be very useful to
introduce a set of parameters for the characterization of the surfaces itself and not only for the curves,
thus having a bigger control on the hull shape and fairness, especially for the surfaces where the property
distribution curves are difficult to analyse and characterize.
75
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Bibliography
[1] S. Harries, C. Abt, and K. Hochkirch. Modeling meets Simulation-Process Integration to improve
Design. In Honorary colloquium for Prof. Hagen, Prof. Schlüter and Prof. Thiel, pages 1–12, 2004.
[2] C. Abt, S. D Bade, L. Birk, and S. Harries. Parametric Hullform Design – A Step Towards One
Week Ship Design. 8th International Symposium on Practical Design of Ships and Other Floating
Structures (PRADS), Shanghai, I(September):67–74, 2001.
[3] J. H. Evans. Basic Design Concepts. Journal of the American Society for Naval Engineers,
71(4):671–678, 1959.
[4] I. L Buxton. Engineering Economics Applied to Ship Design. Computer Aided Design - Transactions
of the Royal Institution of Naval Architects (RINA), October 19(4):409–428, 1973.
[5] D. Andrews. Creative Ship Design. Transactions of the Royal Institution of Naval Architects (RINA),
1981.
[6] F. Mistree, W. F. Smith, B. A. Bras, J. K. Allen, and D. Muster. Decision-Based Design: A contem-
porary Paradigm In Ship Design. Transactions, Society of Naval Architects and Marine Engineers,
98:565–597, 1990.
[7] S. Harries, F. Tillig, M. Wilken, and G. Zaraphonitis. An Integrated Approach for Simulation in
the Early Ship Design of a Tanker. In 10th Int’ernational Conference on Computer Applications
and Information Technology in the Maritime Industries (COMPIT), Hamburg, number May, pages
411–425, 2011.
[8] H. Nowacki and S. Harries. Form parameter approach to the design of fair hull shapes. In 10th
International Conference on Computer Appliactions (ICCAS), Cambridge, 1999.
[9] J. J. Maisonneuve, S. Harries, J. Marzi, H. C. Raven, U. Viviani, and H. Piippo. Towards Optimal
Design of Ship Hull Shapes. In 8th International Marine Design Conference, pages 31–42, 2003.
[10] C. Abt and S. Harries. A New Approach to Integration of CAD and CFD for Naval Architects. In 6th
COMPIT, Contona, pages 467–479, 2007.
[11] S. Harries and C. Abt. Parametric Curve Design Applying Fairness Criteria. In International Work-
shop on creating fair and shape-preserving curves and surfaces. Berlin (Potsdam, Teubner): Net-
work Fairshape, 1998.
77
[12] K. G. Pigounakis, N. S. Sapidis, and P. D. Kaklis. Fairing Spatial B-spline Curves. Journal of Ship
Research, 40(4), 1996.
[13] T. D. Lyon and F. Mistree. A Computer-based Method for the Preliminary Design of Ships. Jornal
of Ship Research, 29(4):251–269, 1985.
[14] C. Smith and R. G. Woodhead. A Design Scheme for Ship Structures. Transactions of the Royal
Institution of Naval Architects (RINA), 116:47–57, 1974.
[15] G. L. Koutroukis. Parametric design and multiobjective optimization - Study of an ellipsoidal con-
tainership. PhD thesis, National Technical University of Athens, 2012.
[16] A. Papanikolaou. Holistic ship design optimization. Computer-Aided Design, 42(11):1028–1044,
2010.
[17] A. Papanikolaou, G. Zaraphonitis, E. Boulougouris, U. Langbecker, S. Matho, and P. Sames. Multi-
objective optimization of oil tanker design. Journal of Marine Science and Technology, 15(4):359–
373, 2010.
[18] D. Andre and J. Koza. A parallel implementation of genetic programming that achieves super-linear
performance. Information Sciences, 106(3):201–218, 1998.
[19] C. M. Fonseca and P. J. Fleming. Genetic Algorithms for Multiobjective Optimization: Formulation,
Discussion and Generalization. ICGA, 93:416–423, 1993.
[20] N. Srinivas and K. Deb. Multiobjective Optimization Using Nondominated Sorting in Genetic Algo-
rithms. Evolutionary Computation, 2(3):221–248, 1994.
[21] M. Erickson, A. Mayer, and J. Horn. Multi-objective optimal design of groundwater remediation sys-
tems: application of the niched Pareto genetic algorithm (NPGA). Advances in Water Resources,
25(1):51–65, 2002.
[22] K. Deb, A. Pratap, S. Agarwal, and T. Meyarivan. A fast and elitist multiobjective genetic algorithm:
NSGA-II. IEEE Transactions, 6(2):182–197, 2002.
[23] S. Harries. Serious Play in Ship Design. In Tradition and Future of Ship Design in Berlin, Collo-
quium, 2007.
[24] H. Nowacki, G. Creutz, and F. C. Munchmeyer. Ship Lines Creation by Computer - Objectives,
Methods and Results, 1977.
[25] H. Nowacki, D. Liu, and X. Lu. Faking Bézier curves with constraints. Computer Aided Geometric
Design, 7:43–55, 1990.
[26] H. Nowacki and X. Lu. Fairing composite polynomial curves with constraints Horst. Computer Aided
Geometric Design, 11(1):1–15, 1994.
[27] A. M. Kracht. Design of Bulbous Bows. SNAME Transactions, 86:197–217, 1978.
78
[28] F. Pérez, J. A. Suárez, J. A. Clemente, and A. Souto. Geometric modelling of bulbous bows with
the use of non-uniform rational B-spline surfaces. Journal of Marine Science and Technology,
12(2):83–94, 2007.
[29] A. M. Kracht and A. Jacobsen. D-series systematic experiments with models of fast twin-screw
displacement ships. SNAME Transactions, 100:199–222, 1992.
[30] C. Abt, S. Harries, J. Heimann, and H. Winter. From Redesign to Optimal Hull Lines by means of
Parametric Modeling. In 2nd Intl. Conf. Computer Applications and Information Technology in the
Maritime Industries, pages 444–458, 2003.
[31] M. Bole. Early Stage Integrated Parametric Ship Design. In 2th International Conference on Com-
puter Applications in Shipbuilding (ICCAS), pages 447–460, 2005.
[32] A. Mancuso. Parametric design of sailing hull shapes. Ocean Engineering, 33(2):234–246, 2006.
[33] M. Bole and B-S. Lee. Integrating Parametric Hull Generation into Early Stage Design. Ship
Technology Research, 53(3):115–137, 2006.
[34] C. Abt and S. Harries. Hull Variation and Improvement using the Generalized Lackenby Method of
the FRIENDSHIP-Framewotk, 2007.
[35] F. Pérez, J. A. Clemente, J. A. Suárez, and J. M. González. Parametric Generation , Modeling, and
Fairing of Simple Hull Lines With the Use of Nonuniform Rational B-Spline Surfaces. Journal of
Ship Research, 52(1):1–15, 2008.
[36] S. Harries, H. Hinrichsen, and K. Hochkirch. Development and Application of a new Form Feature
to enhance the Transport Efficiency of Ships. In Hauptversammlung der Schiffbautechnischen
Gesellschaft, Berlin, number November, 2007.
[37] K. Cudby. K-spline: a new curve for advanced hull modelling. 3rd High Performance Yacht Design
Conference, (May):74–81, 2008.
[38] K. Hochkirch and V. Bertram. Slow Steaming Bulbous Bow Optimization for a Large Container-
ship. In 8th International Conperance on Computer and IT Applications in the Marine Industries
(COMPIT), Budapest, pages 390–398, 2009.
[39] http://www.delftship.net/.
[40] FRIENDSHIP SYSTEMS. FRIENDSHIP-Framework The competitive edge in hull form optimization,
2012.
[41] FRIENDSHIP SYSTEMS. FRIENDSHIP-Framework User Guide, 2012.
[42] H Lackenby. On the systematic geometric variation of ship forms. Transactions of The Institute of
Naval Architects (INA), 92:289–315, 1950.
79
THIS PAGE WAS INTENTIONALLY LEFT IN BLANK.
Appendix A
List of the Model Parameters - ASCII
input file
Name of the ship
"Main Dimensions"
Lpp
beam
height
draft
block coefficient
XCB [%Lpp]
"Parallel Midbody"
Aft Body Lenght [%Lpp]
Parallel Mid body Length [%Lpp]
"Midship Section"
Bilge Height
Bilge Width
Bilge Fullness
Deadrise
Flare
"Longitudinal Contour - Keel Line"
X Aft Base [% AftBody Length]
X Fwd Base [% ForeBody Length]
"Longitudinal Contour - Transom Bottom Point"
X Transom [% AftBody Length]
Z Transom [% Draft]
"Longitudinal Contour - Deck Extreme Points"
X Peak [% ForeBody Length]
81
"Longitudinal Contour - Bulb Stern Contour"
X Bilge Aft [% AftBody Length]
X Bulb Tip [% AftBody Length]
Z Bulb Tip [% Height]
X Clearance [% AftBody Length]
Z Clearance [% Height]
Tangent at Transom [o]
"Stem"
Tangent Angle on the beginning of the Bulb [o]
Tangent Angle on Peak [o]
Length of the straight segment [% Height]
"Stem - Angles"
Angle on Deck [o]
"Stem - Radius"
Radius on DWL [m]
Radius on Deck [m]
Radius on 25% of the height of the stem [% Radius on DWL]
"Flat of Bottom"
Entrance angle [o]
Run Angle [o]
Fullness Aft
Fullness Fwd
Straight Length aft Cylinder [% AftBody Length]
Straight Length fwd Cylinder [% ForeBody Length]
"Flat of Side"
X Aft [% AftBody Length]
X FOS emerge aft [%(AftBody Length- XAft)]
X Fwd [% ForeBody Length]
X FOS emerge fwd [%(ForeBody Length-X Fwd)]
Z Aft [% Heigth]
Straigth Length aft Cylinder [% AftBody Length]
Straight Length fwd Cylinder [% ForeBody Length]
Entrance Angle
Run Angle
"Design Water Line"
X Aft [% AftBody Length]
Y Aft [% Halfbeam]
Fullness Aft
X Fwd [% ForeBody Length]
82
Fullness Fwd
Entrance Angle
Run Angle
"Deck Contour"
Fullness Fwd
Fullness Aft
"Bulb (Bow)"
Bulb Length [% Lpp]
Z Tip [% Draft]
Z Bottom Point [% Draft]
Z Top Point [% Draft]
X Offset to FP [% Lpp]
Bulb Halfbeam at FP [% Halfbeam]
Bulb Z Max Halfbeam at FP [% Draft]
Lower contour Fullness
Upper contour Fullness
Halfbeam contour Fullness
Bulb Upper Section Fullness
Bulb Lower Section Fullness
Tangent on Top Point at FP [o]
"Bulb Stern - Bossing"
Hub Radius [m]
External Horizontal Half Diameter [m]
External Vertical Half Diameter [m]
"Bulb Stern - Fairing Boundary"
X top point aft [% (XBulbClearance - XBulbTip]
X at max beam [%Lpp]
Max beam [% Halfbeam]
Tangent aft [o]
Fullness aft contour
Fullness fwd contour
"Bulb Stern - Fairing Intermediate"
weight at bottom
weight at top
weight factor
"Transom Panel"
Length of the straight bottom segment [% Halfbeam]
Length of the straight side segment [% Height]
Tangent at bottom segment [o]
83
Tangent at side segment [o]
Fullness of the curved segment
Length of the top segment [% Halfbeam]
"Sectional Area Curve"
Section area at aft point of DWL [% MidShip Section Area]
Section area at aft base [% MidShip Section Area]
Section area at FOS emerge aft [% MidShip Section Area]
Section area at FOS emerge fwd [% MidShip Section Area]
Section area at fwd base [% MidShip Section Area]
"Flare at DWL"
Max Flare Angle [o]
X of Max flare Angle [% ForeBody Length]
Flare on FP [o]
Tangent of Flare at DWL curve distribution on FOS emerge fwd [o]
Tangent of Flare at DWL curve distribution on FP [o]
"Falre at Deck"
Flare on Peak [o]
"Flare at Bottom"
Flare on Bulb Tip [o]
Tangent of Flare at Bottom curve distribution on Bulb Tip [o]
84
