Hydrofoils design for a Europe dinghy

BACHELOR FINAL THESIS Hydrofoils design for a Europe dinghy Author: Santiago Mañé Ubalde Director: José-Antonio Ortiz Marzo Degree: Bachelor’s degree in Aerospace Vehicle Engineering Examination session: Spring, 2021 Document: Report Bachelor final thesis Hydrofoils design for a Europe dinghy 1 Santiago Mañé Ubalde DECLARATION OF HONOR I declare that, The work in this Bachelor Thesis is completely my work, No part of this Bachelor Thesis is taken from other people’s work without giving them credit, All the references have been cited, I am authorised to make use of the data sources from open sources I am providing in this document. I understand that an infringement of this declaration leaves me subject to the foreseen disciplinary actions by the Universitat Politècnica de Catalunya. Title of the Thesis: Hydrofoils design for a Europe dinghy Santiago Mañé Ubalde Student Name June 22, 2021 Date Signature Bachelor final thesis Hydrofoils design for a Europe dinghy 2 Santiago Mañé Ubalde ABSTRACT This bachelor final thesis contains the development of a hydrofoil kit to be installed in an International Europe Class dinghy. It includes an aerodynamics and hydrodynamics theoretical introduction, as well as a general overview of hydrofoil technology. The thesis follows with the sizing of foiling surfaces through a mathematical study based on the appropriate aerodynamics concepts. The results are validated using the XFLR5 software. Then, the modelling process of the system and control mechanism is shown. Finally, a prototype of the concept is manufactured to demonstrate the viability of the project. The author of this thesis intends to enhance the performance of the International Europe Class dinghy and raise it to the level of foiling dinghies available in the market. Esta tesis de fin de grado contiene el desarrollo de un “kit” hidroala para ser instalado en una embarcación de vela ligera de la clase Europa. El proyecto incluye una breve introducción de carácter teórico a los campos de la hidrodinámica y aerodinámica, así como al funcionamiento de las hidroalas. Seguidamente, se presenta el proceso de dimensionamiento de las superficies sustentadoras, basado en un estudio matemático que incorpora conceptos relacionados con la aerodinámica. Los resultados obtenidos son validados con el software XFLR5. A continuación, se muestra el proceso de modelado del sistema así como del mecanismo de control que incluye. Finalmente, un prototipo del concepto es fabricado para demostrar la viabilidad del proyecto. El autor de este trabajo quiere mejorar las prestaciones del Europa para que este pueda igualar en rendimiento a los barcos de vela ligera de nueva generación disponibles en el mercado. Aquesta tesi de fi de grau conté el desenvolupament d'un “kit” hidroala per a ser instal·lat en una embarcació de vela lleugera de la classe Europa. El projecte inclou una breu descripció de caràcter teòric als camps de la hidrodinàmica i aerodinàmica, així com al funcionament de les hidroales. Seguidament, es presenta el procés de dimensionament de les superfícies de sustentació, basat en un estudi matemàtic que incorpora conceptes basats en l'aerodinàmica. Els resultats obtinguts són validats amb el software XFLR5. A continuació es mostra el procés de modelatge del sistema així com del mecanisme de control que incorpora. Finalment, un prototip del concepte és fabricat per demostrar la viabilitat del projecte. L'autor d'aquest treball vol millorar les prestacions de l'Europa perquè aquest pugui igualar en rendiment a les embarcacions de vela lleugera de nova generació disponibles en el mercat. Bachelor final thesis Hydrofoils design for a Europe dinghy 3 Santiago Mañé Ubalde ACKNOWLEDGMENT Throughout the writing of this thesis, I have received a great deal of support and assistance. Firstly I would like to thank my supervisor and tutor, Jose-Antonio OrtizMarzo, for his interest in this project. Since the day I presented the idea he offered constant support and feedback was crucial for the development of the thesis. The expertise of Toni Riera from N1Foils was crucial for the manufacturing phase. I would like to thank him and his team for sharing their knowledge about composite manufacturing and contributing to the prototype build. As important was the involvement of my friend and computer science engineer, Andreu Pla, and his 3D printer. Andreu printed all of the moulds and innumerable failed test models. I thank him for his advice, enthusiasm and patience, which shaped many of my ideas for this project into reality. I also have to acknowledge the contribution of classmates and friends Xavier Soria and Marc Martí. Thank you both for your unconditional support through all the career and project. In addition, I would like to thank all my friends that got involved with this project and my parents and little brother Àlvar for giving advice and being there when I needed it. Bachelor final thesis Hydrofoils design for a Europe dinghy 4 Santiago Mañé Ubalde TABLE OF CONTENTS DECLARATION OF HONOR .................................................................................................... 1 ABSTRACT ................................................................................................................................. 2 ACKNOWLEDGMENT ............................................................................................................... 3 TABLE OF CONTENTS ............................................................................................................ 4 LIST OF TABLES ....................................................................................................................... 7 LIST OF FIGURES ..................................................................................................................... 8 LIST OF SYMBOLS ................................................................................................................. 11 2. INTRODUCTION .............................................................................................................. 14 2.1. Aim .............................................................................................................................. 14 2.2. Scope ......................................................................................................................... 14 2.3. Requirements ............................................................................................................ 15 2.4. Background ............................................................................................................... 15 3. STATE OF THE ART ....................................................................................................... 17 3.1. The Europe dinghy ................................................................................................... 17 3.1.1. Technical characteristics ................................................................................. 17 3.1.2. Performance ...................................................................................................... 19 3.2. Introduction to hydrofoils ......................................................................................... 21 3.2.1. History of hydrofoils .......................................................................................... 22 3.2.2. Hydrofoil configuration ..................................................................................... 23 3.2.3. Single-handed foiling dinghies ........................................................................ 24 3.3. Introduction to hydrodynamics ................................................................................ 25 3.3.1. The Free surface .............................................................................................. 25 3.4. Aerodynamics of a wing .......................................................................................... 26 3.4.1. Profile aerodynamics ........................................................................................ 26 3.4.2. Boundary layer .................................................................................................. 27 3.4.3. Boundary layer detachment ............................................................................ 28 3.4.4. Aerodynamic coefficients ................................................................................ 29 3.4.5. Lift coefficient .................................................................................................... 29 3.4.6. Drag coefficient ................................................................................................. 30 3.4.7. Moment coefficient ........................................................................................... 31 3.4.8. Three-dimensional wing .................................................................................. 31 3.4.9. Three-dimensional lift coefficient .................................................................... 32 3.4.10. Three-dimensional drag coefficient ............................................................ 33 Bachelor final thesis Hydrofoils design for a Europe dinghy 5 Santiago Mañé Ubalde 3.4.11. Three-dimensional moment coefficient ..................................................... 34 3.4.12. Wing platform ................................................................................................ 34 3.4.13. Wing architecture .......................................................................................... 36 3.5. Stability ....................................................................................................................... 36 3.5.1. Longitudinal equilibrium ................................................................................... 37 3.5.2. Static stability .................................................................................................... 37 3.5.3. Dynamic stability ............................................................................................... 39 4. INITIAL SIZING ................................................................................................................. 40 4.1. Hydrofoil configuration selection ............................................................................ 41 4.2. Initial configuration definition .................................................................................. 42 4.3. Foil profile selection.................................................................................................. 42 4.4. Wing geometry definition ......................................................................................... 45 4.4.1. Platform .............................................................................................................. 45 4.4.2. Sizing .................................................................................................................. 45 4.5. Centreboard hydrofoil .............................................................................................. 53 4.5.1. Centreboard strut .............................................................................................. 53 4.6. Rudder hydrofoil ....................................................................................................... 54 4.6.1. Rudder strut ....................................................................................................... 55 4.7. Hydrodynamic and stability analysis ...................................................................... 55 5. FINAL DESIGN ................................................................................................................. 59 5.1. Control mechanism .................................................................................................. 59 5.1.1. Wand position.................................................................................................... 60 5.1.2. Mechanism concept ......................................................................................... 60 5.1.3. Flap trim ............................................................................................................. 61 5.2. Centreboard assembly ............................................................................................. 63 5.2.1. Centreboard foil and flap ................................................................................. 63 5.2.2. Centreboard strut .............................................................................................. 64 5.3. Rudder assembly ...................................................................................................... 66 5.3.1. Rudder foil.......................................................................................................... 66 5.3.2. Rudder strut ....................................................................................................... 66 5.4. Material selection ...................................................................................................... 68 5.4.1. Main bodies ....................................................................................................... 68 5.4.2. Secondary parts ................................................................................................ 68 6. PROTOTYPE MANUFACTURING ................................................................................ 70 6.1. Flap ............................................................................................................................. 70 6.2. Centreboard foil ........................................................................................................ 72 Bachelor final thesis Hydrofoils design for a Europe dinghy 6 Santiago Mañé Ubalde 6.2.1. Material choice .................................................................................................. 72 6.2.2. Mould manufacturing ........................................................................................ 74 6.2.3. Composite manufacturing ............................................................................... 75 6.2.4. Results and improvements .............................................................................. 79 6.3. Centreboard foil structural study ............................................................................ 79 7. BUDGET ............................................................................................................................ 82 7.1. Additive manufacturing ............................................................................................ 82 7.2. Composite manufacturing ....................................................................................... 82 7.3. Total cost ................................................................................................................... 83 8. ENVIRONMENTAL IMPACT .......................................................................................... 84 8.1. Direct impact ............................................................................................................. 84 8.2. Indirect impact ........................................................................................................... 85 8.2.1. Entropy resins & R*Concept ........................................................................... 86 9. NEXT STEPS .................................................................................................................... 87 10. CONCLUSIONS............................................................................................................ 88 11. BIBLIOGRAPHY ........................................................................................................... 89 Bachelor final thesis Hydrofoils design for a Europe dinghy 7 Santiago Mañé Ubalde LIST OF TABLES Table 1: mass distribution of the Europe dinghy. ......................................................... 18 Table 2: performance under an average wind speed of 42,6 km/h. ............................. 20 Table 3: performance under an average wind speed of 27,78 km/h. ........................... 20 Table 4: performance under an average wind speed of 14,82 km/h. ........................... 20 Table 5: average speed of the sailors in the different headings and wind conditions. .. 20 Table 6: platform comparison ...................................................................................... 41 Table 7: decision making. ........................................................................................... 41 Table 8: MOTH hydrofoils from different manufacturers. ............................................. 42 Table 9: Values from ................................................................................................... 47 Table 10: control mechanism components. ................................................................. 61 Table 11: flap deflection for different ride heights. ....................................................... 62 Table 12: filament comparison. ................................................................................... 69 Table 13: mechanical properties of the composite to be manufactured. ...................... 73 Table 14: mechanical properties of the foam of choice. .............................................. 73 Table 15: additive manufacturing cost. ........................................................................ 82 Table 16: composite manufacturing cost. .................................................................... 82 Table 17: displacements cost. ..................................................................................... 83 Table 18: total costs of the manufactured prototype. ................................................... 83 Table 19: energy consumption. ................................................................................... 84 Bachelor final thesis Hydrofoils design for a Europe dinghy 8 Santiago Mañé Ubalde LIST OF FIGURES Figure 1: US Navy's XCH-4 hydrofoil craft. [17] .................................................................. 15 Figure 2: lateral view of a Europe dinghy. [1] ....................................................................... 17 Figure 3: Europe dinghy hull blueprints used as a reference for the CAD model. [2] .... 18 Figure 4: headings of a sailboat. [3] ...................................................................................... 19 Figure 5: polar chart of the Europe dinghy. .......................................................................... 21 Figure 6: foiling AC75. [7] ........................................................................................................ 23 Figure 7: front view of a vessel equipped with submerged hydrofoils. ............................. 23 Figure 8: front view of a vessel equipped with surface piercing hydrofoils. .................... 23 Figure 9: MOTH. [8] ................................................................................................................. 24 Figure 10: WASZP. [9] ............................................................................................................. 25 Figure 11: submerge factor per unit of depth in chords...................................................... 26 Figure 12: basic geometry of an aerofoil, wing profile or aerodynamic profile. .............. 27 Figure 13: forces acting on the aerodynamic centre of an aerofoil................................... 27 Figure 14: boundary layer development. [11] ...................................................................... 28 Figure 15: Cl plot of a wing profile. ......................................................................................... 30 Figure 16: Cd polar. ................................................................................................................. 31 Figure 17: depiction of the trailing vortices and the generated downwash. [13] ............. 32 Figure 18: illustration showing the variations produced by the induced downwash. [14] ..................................................................................................................................................... 32 Figure 19: wing platforms. ....................................................................................................... 35 Figure 20: geometry of a wing. ............................................................................................... 36 Figure 21: static stability plots. ............................................................................................... 38 Figure 22: types of dynamic stability. .................................................................................... 39 Figure 23: initial sizing process overview. ............................................................................ 40 Figure 24: drag polar chart. ..................................................................................................... 43 Figure 25: lift representation. .................................................................................................. 44 Figure 26: comparison between the 3 wing profiles............................................................ 44 Figure 27: front view of the sailor position and sail centre of pressure. ........................... 47 Figure 28: top view of the sailor position and sail centre of pressure. ............................. 47 Figure 29: forces involved during stable flight. ................................................................... 48 Figure 30: comparison between the flapped foil and the normal foil. ............................... 49 Figure 31: intersection between the bidimensional and tridimensional Cl plots. ............ 50 Bachelor final thesis Hydrofoils design for a Europe dinghy 15 Santiago Mañé Ubalde 2.3. Requirements Certain requirements must be achieved to consider the project successful. These requisites will be listed below and ensure the viability of the project.  The converted Europe dinghy must be able to sustain stable hydrofoil sailing under certain wing conditions. This means that the hull must be completely above the water line and maintain a constant altitude without oscillating thanks to the control mechanism.  The prototype’s structure must sustain the loads under the previously described sailing conditions.  The installation of the foiling device under no circumstances should compromise the structural integrity of the hull and other essential components of the Europe dinghy. Furthermore, the device must be removable and require little to no modifications of the hull and other components. 2.4. Background A hydrofoil is a wing designed to operate in water. The higher viscosity and density of the medium allows an increased lift generation with a much smaller surface area than conventional wings. In boats, hydrofoils are used to raise the hull above the water, drastically reducing the drag, increasing at the same time efficiency and overall speed. Figure 1: US Navy's XCH-4 hydrofoil craft. [17] Bachelor final thesis Hydrofoils design for a Europe dinghy 16 Santiago Mañé Ubalde This technology has seen multiple commercial and military applications since the beginning of the 20th century. Despite its evident advantages, not until the 21st century it started to become popular in the world of sailing and specifically, dinghy sailing thanks to the contributions of the MOTH class. Dinghy sailing is a sport that consists of using the power of the wind to manoeuvre and command a usually small lightweight sailboat with a rigid hull where the crew or single patron seat on top. Many different dinghy classes exist around the world, the International Europe Class being one of them. As mentioned above, recently foiling dinghy sailboats are starting to gain some popularity among the sailing community. The technology is completely transforming the sport making it more intense as the sailboats become faster and more complex to handle. New sets of regulations to enable closer one-design racing appeared giving birth to new foiling classes such as the WASZP class. However, purposely foiling dinghies came at a cost and therefore are not available to everybody. Another solution is to design foiling kits for existing classes, and that is what this project is aiming for: creating a kit for the International Europe Class dinghy that once installed can provide the foiling experience to the user without the need of buying a completely new vessel. Bachelor final thesis Hydrofoils design for a Europe dinghy 17 Santiago Mañé Ubalde 3. STATE OF THE ART 3.1. The Europe dinghy The Europe is a single-handed racing dinghy designed in Belgium in 1960 by Alois Roland as a class legal Moth dinghy. The design later in 1976 evolved into its own onedesign class when the ISAF (International Sailing Federation) granted the Europe dinghy international status. Figure 2: lateral view of a Europe dinghy. [1] In 1992 it was introduced to the Olympic Games as the Women’s single-handed dinghy Class, a position which it maintained until 2008. Despite no longer being an Olympic class, the Europe dinghy remains very popular especially on the old continent where international events are organised annually. The Europe dinghy can absorb a wide range of body types thanks to its developmental rig, which allows a high level of trimming. This characteristic allows sailors to compete at the same level regardless of their physique. 3.1.1. Technical characteristics The hull of the modern Europe is made of fibreglass and weighs 45 kg. If we consider the other components needed to sail, the value increases to 60 kg. Since the foils will be installed to the hull, the original blueprints of 1960 have been considered as well as measurements from the current rulebook to make a 3D model. All the dimensions for this project will be taken from the same. Bachelor final thesis Hydrofoils design for a Europe dinghy 18 Santiago Mañé Ubalde Figure 3: Europe dinghy hull blueprints used as a reference for the CAD model. [2] It is important to know the weight of all the elements and the position of the centre of mass. Therefore, a list of all the components indicating its mass and position relative to the bow will be elaborated. Official documents from an existent Europe dinghy have been used to obtain the numerical values. Element Mass [kg] Centre of mass position [mm] Hull 45 1.744 Mast 5,55 647 Boom 3,25 647 Rudder blade 0,98 3.350 Rudder stock 1,27 3.350 Centreboard 2,80 1.606 Table 1: mass distribution of the Europe dinghy. From here, we can obtain the position relative to the bow of the gravity centre. Xcm=wh·xh+wm·xm+wbo·xbo+wbl·xbl+wst·xst+wc·xc wh+wm+wbo+wbl+wst+wc=1.634,50 mm If we consider the weight of the sailor to be ms=80 kg, and a normal position under normal sailing conditions (which will be discussed in more detail in further chapters) xs= 2900 mm, we obtain the following centre of mass: 𝐗𝐜𝐦𝐭=𝟐.𝟎𝟔𝟗,𝟖𝟎 𝐦𝐦 Bachelor final thesis Hydrofoils design for a Europe dinghy 19 Santiago Mañé Ubalde 3.1.2. Performance Since a Europe dinghy solely uses the wind to create a forward force to move, it is important to know the effects that the wind direction and speed will have on the dinghy’s behaviour. The main parameter which will affect the lift generation of the hydrofoils is the speed. Therefore, we have to study the effects that wind conditions have on the speed of the boat. The sail of a sailboat operates as a vertical wing, generating a lift force that decomposes in the forward force and a lateral force which in the case of the Europe dinghy must be compensated by the weight of the sailor. Depending on the sailing direction, the angle of attack varies and the value of these forces is modified, as well as the position of the sail. We can assume that an experienced sailor achieves at all times an optimal weight distribution and sail trim. On the following diagram, we can observe all the possible courses of a dinghy sail. Figure 4: headings of a sailboat. [3] A polar diagram indicating the boat speed function of the wind direction and intensity will be developed to study the behaviour of the dinghy under different wind conditions and headings. We will use the GPS speed parameters of 4 different participants of the 2015 Europe Class YOUTH European Championship, publicly available at the TracTrac app [4]. We will measure the speed at four stages of the race corresponding to four different headings. Furthermore, three races developed under different wind intensities will be analysed. The App does not provide the value of the medium speed of the sailor during a determinate heading, so the following numbers correspond to a visual approximation Bachelor final thesis Hydrofoils design for a Europe dinghy 20 Santiago Mañé Ubalde of the application’s data. Also, we are neglecting the effect of the chop conditions, wind gusts and wind turbulence from other dinghies Wind speed [km/h] Sailor Upwind [km/h] Broad reach [km/h] Beam reach [km/h] Downwind [km/h] 42,6 ESP-805 7,9 18 16,8 16 ESP-668 7,8 19 16 15,5 ESP-631 8 19,4 16,8 16,6 ESP-630 8,1 17,8 15,9 15,3 Table 2: performance under an average wind speed of 42,6 km/h. Wind speed [km/h] Sailor Upwind [km/h] Broad reach [km/h] Beam reach [km/h] Downwind [km/h] 27,78 ESP-805 8,6 15 15 14,3 ESP-668 8,4 16,4 14,6 12,6 ESP-631 8,8 16,8 14 11,1 ESP-630 8,5 15,8 14,8 10,8 Table 3: performance under an average wind speed of 27,78 km/h. Wind speed [km/h] Sailor Upwind [km/h] Broad reach [km/h] Beam reach [km/h] Downwind [km/h] 14,82 ESP-805 7,4 10,6 11,3 8 ESP-668 7,3 9,8 11,9 8,3 ESP-631 7,1 10 10,9 7,8 ESP-630 7,2 9,7 11 7,8 Table 4: performance under an average wind speed of 14,82 km/h. With these values in mind, we can calculate the average speed of the Europe dinghy for the defined headings and elaborate the polar chart. Wind Speed [km/h] Upwind [km/h] Beam reach [km/h] Broad reach [km/h] Downwind [km/h] 42,6 7,95 16,38 18,55 15,85 27,78 8,58 14,60 16 12,20 14,82 7,25 11,28 10,03 7,98 Table 5: average speed of the sailors in the different headings and wind conditions. Bachelor final thesis Hydrofoils design for a Europe dinghy 21 Santiago Mañé Ubalde Figure 5: polar chart of the Europe dinghy. Now, we will define the take-off at which the hydrofoils will generate sufficient lift to push the Europe’s hull out of the water (take-off speed). The fastest headings are beam reach and broad reach. Therefore the take-off is considered as the average beam reach speed of the Europe dinghy at wind intensities of 10 knots, which is classified as a medium wind intensity. If we interpolate for this value, we obtain a dinghy speed of 5,44 knots, which is 10 km/h or 2,8 m/s. 3.2. Introduction to hydrofoils A hydrofoil is a wing designed to operate in water. In the boating industry, hydrofoils are used to provide lift for the vessel at a certain speed, usually near the maximum hullborne drag, reducing the drag itself. Consequently, the boat can accelerate to a superior cruising speed, usually twice the take-off speed. Under these foiling conditions, the boat must be stable and controllable. This is achieved by introducing mechanical or electrical control mechanisms in a variety of configurations (Costa [5]). Bachelor final thesis Hydrofoils design for a Europe dinghy 22 Santiago Mañé Ubalde 3.2.1. History of hydrofoils The hydrofoil technology appeared at the end of the 19th century, coinciding with the development of aircraft. The Mecham brothers were the first to try the concept by creating a flying boat on American soil. Similar prototypes saw the light in Europe, remarkably Enrico Foralini’s concept from 1906. These machines aroused such an interest that even Alexander Graham Bell became involved in the technology. His associate Casey Baldwin and himself began designing and testing numerous prototypes. Inspired by Enrico Forlanini’s ideas they built the HD-4 which in 1919 broke the water speed record (Vellinga [6]). Despite this rapid development, hydrofoils did not see commercial applications until the end of WW2, when the technology was mature enough thanks to the developments in the aerospace industry and the understanding of foil behaviour. The public began to perceive hydrofoils as a much faster alternative to conventional boats. The German engineer Hanns von Schertel established in Switzerland the Supramar Company which in 1952 launched the first commercial hydrofoil, the PT10. Soon, the company was selling its product all around the world. During the same period, the Soviet Union rushed the development of hydrofoils both for civilian and military applications. It was believed that thanks to their superior mobility, speed and supposed immunity to torpedoes, hydrofoils would end up replacing conventional boats. However, the serious drawbacks of the hydrofoil configuration became evident and soon its popularity declined. Most of the militaries abandoned their programs and nowadays, only a handful of hydrofoil vessels are operating in commercial routes, mostly in rivers or lakes. The technology is sensitive to surface objects impacts. Also, the cost of manufacturing is superior to its conventional counterparts, as well as its maintenance, which is also more complex. Moreover, their speed is no match to that of a modern airliner, rendering the technology useless for intercontinental travel. Recently hydrofoil popularity has risen again in the sailing world, where speed and efficiency matter the most. Vessels with hydrofoils have substituted the conventional boats in America’s cup vastly improving the spectacle of the race. To put into perspective, the AC75 hydrofoil boat class introduced for the 2021 cup can achieve speeds of over 50 knots or 92,6 km/h while the conventional vessels used in the 2017 edition achieve speeds of 12 knots or 22 km/h. In the same manner, foiling single-handed dinghies have recently appeared as new classes, such as the WASZP class, a derivative from the also foiling MOTH, which are replacing the conventional, much slower, singlehanded dinghies like the Europe. Bachelor final thesis Hydrofoils design for a Europe dinghy 23 Santiago Mañé Ubalde Figure 6: foiling AC75. [7] 3.2.2. Hydrofoil configuration Hydrofoils exist in a large variety of shapes and sizes, but generally, a hydrofoil vessel must incorporate a forward lifting surface and an aft lifting surface for longitudinal stability. The loads do not have to be equally distributed. Alternatively, in a canard configuration, the forward foil acts as the stabilizer. To provide stability and maintain a constant lift the principle of variable-area stabilization is used through surface piercing hydrofoils. This early configuration can be incorporated using V or W shape hydrofoils and does not require any mechanical or electrical control system. However, this configuration is sensitive to waves and thus it can only operate under certain conditions. An alternative is to submerge both lifting surfaces. With this distribution, the effects of wave height are mitigated but it must incorporate a variable incidence foil or flap control to provide the necessary stability. Figure 8: front view of a vessel equipped with surface piercing hydrofoils. Figure 7: front view of a vessel equipped with submerged hydrofoils. Bachelor final thesis Hydrofoils design for a Europe dinghy 24 Santiago Mañé Ubalde 3.2.3. Single-handed foiling dinghies  MOTH The same development class that gave birth to the Europe has become a highperformance foiling class, the International MOTH. The design restrictions of this class are lax, allowing the manufacturers to introduce innovations and test new concepts. It is considered the most extended foiling class of today as well as the fastest single-handed dinghy in the world. Figure 9: MOTH. [8] The MOTH uses a double submerged foil configuration. The main central foil, situated at the middle of the hull, forward to the sitting position of the sailor, provides a large portion of the lift. The rear hydrofoil, which also acts as a rudder, also provides positive lift, stabilizing the configuration. The front foil incorporates a mechanical flap linked to a wand that hangs from the bow of the dinghy. The wand measures the proximity of the waterline and automatically adapts the lift of the main foil, thus maintaining a constant ride height.  WAZP The WASZP is the cheaper alternative to the MOTH and therefore the design is very similar. Given its competitive price, this class is rapidly expanding and currently, international events are held all over the globe. Bachelor final thesis Hydrofoils design for a Europe dinghy 31 Santiago Mañé Ubalde and represents the friction drag forces. k and j are given values which can be obtained from the appropriate reference, but the methodology is out of the scope of this project. Figure 16: Cd polar. 3.4.7. Moment coefficient Normally, we study the variation of the wing profile moment at ¼ of the profile’s chord to the angle of attack. All aerodynamic profiles present negative aerodynamic coefficients, which indicates that an anti-clockwise moment is generated. A wing profile generates a constant moment independent of the angle of attack and a moment inversely proportional to the angle of attack, denominated m0 and mα respectively. 3.4.8. Three-dimensional wing The previously discussed points refer to the aerodynamics of bi-dimensional wing profiles. When studying three-dimensional wings of finite spans, the fluid behaves differently. It has been explained that the pressure difference between the upper and lower surface of a wing generates lift. However, in a finite wing, this pressure imbalance makes the flow at the lower surface curve onto the low-pressure zone at the upper surface, generating a circulatory motion or a trailing vortex. These vortices induce a small velocity component in the downward direction of the wing, called downwash. Bachelor final thesis Hydrofoils design for a Europe dinghy 32 Santiago Mañé Ubalde Figure 17: depiction of the trailing vortices and the generated downwash. [13] This downwash is combined with the freestream velocity, creating a local relative wind and an induced angle of attack. Therefore, the angle of attack seen by the local aerofoil section is the angle between the chord line and the local relative wind, the effective angle of attack. In addition to that, drag is generated due to the presence of the downwash. This drag is defined as induced drag. Figure 18: illustration showing the variations produced by the induced downwash. [14] 3.4.9. Three-dimensional lift coefficient The lift coefficient of a three-dimensional wing is denominated CL and expressed as: CL=L 12ρu∞ 2S (8) As well as the lift coefficient for a wing profile, there is an angle of attack range for which it presents a linear behaviour. Therefore, CL=CLα(α−α0), being CLα the slope of the Bachelor final thesis Hydrofoils design for a Europe dinghy 33 Santiago Mañé Ubalde equation, α the wing’s angle of attack and α0 the angle of attack for which the lift is null. The fact that the lift generated by a wing is inferior to the one generated by the equivalent profile is represented by a smaller slope. The Prandtl theory approximates the threedimensional lift slope based on the bi-dimensional value and different parameters of the wing. For an elliptical platform, which is considered the most efficient three-dimensional wing shape, the slope of the lift curve: CLα=Clα (1+Clα πɅ) (9) Ʌ is known as the aspect ratio or AR of the wing, and is defined as Ʌ=b2/S, where S is the wing’s surface and b its span. For greater aspect ratios, the value CLα will be closer to Clα. For wings without an elliptical shape, we have to incorporate to the expression the Oswald efficiency number e. This is a correction factor that depends on the aspect ratio and shape of the wing. Typically its range is between 0,7 and 0,85. Therefore, the generic expression of the lift curve slope for a three-dimensional wing is: CLα=Clα (1+Clα πɅ)e (10) 3.4.10. Three-dimensional drag coefficient The three-dimensional drag coefficient is defined as: CD=D/(1/2·ρ·u∞ 2· S) (11) As mentioned before, the induced downwash generates an induced drag, as shown in Figure 18. This can be expressed in terms of lift, Di=Lαi. The induced angle of attack can be expressed as αi=CL/πɅ, and the lift can take the form of L=CL·1/2·ρ·u_∞2· S. Then: Bachelor final thesis Hydrofoils design for a Europe dinghy 34 Santiago Mañé Ubalde Di=12ρu∞ 2SCL2 πɅ→CDi=CL2 πɅ (12) If we want to achieve smaller induced drags we have to build a wing with a high aspect ratio. The previous expression is valid again for elliptical platforms since they have a constant induced angle of attack for all its span. For generic wing shapes, we have to one more time introduce the Oswald efficiency number to the expression and, therefore, they present higher induced drags. If we also add to the expression the friction drag we obtain the total drag coefficient formula. CD=CL2 πɅe+Cd0 (13) 3.4.11. Three-dimensional moment coefficient The last of the aerodynamic coefficients it’s not of particular interest when studying threedimensional wings. The only thing that can be said about it is the addition of the wing’s surface instead of the chord on the non-dimensionalization of the parameter, CM1/4=M/(1/2·ρ·u∞ 2· c · S) (14) What is more relevant in three-dimensional wings is the study of moments of an overall wing-tail configuration with respect to its centre of masses, which is crucial to study its stability. This will be commented further below in chapter 3.5. 3.4.12. Wing platform We have mentioned the existence of the elliptical wing platform, which is defined as the most efficient wing shape. It presents a constant downwash throughout the wing as well as the induced angle of attack. Hence, it has the smaller induced drag of all wing platforms. Its lift distribution is known as elliptical lift distribution, where the root profiles generate a greater lifting force than the ones situated at the tip, diminishing the generation of bending moments that could compromise the structural integrity of the Bachelor final thesis Hydrofoils design for a Europe dinghy 35 Santiago Mañé Ubalde wing. Despite this favourable lift distribution, when the aeroplane stalls, the first section that stops generating lift are the tips, where the control surfaces are normally located. In addition, this geometry is difficult to manufacture. The alternative is producing a tapper wing platform, easier to manufacture and its lift distribution is close to the elliptical one, although not as good. The higher the tapper ratio, the more will the wing performance resemble an elliptical. Finally, rectangular wing platforms have the worst aerodynamic performance of all the platforms. However, it has the advantage that the tips do not stall, making them more forgiving in emergencies. Also, some commercially available submerged hydrofoils dinghies such as the WASZP use this platform since the profile can be extruded using aluminium, making it easier and cheaper to manufacture than the other alternatives. Figure 19: wing platforms. Bachelor final thesis Hydrofoils design for a Europe dinghy 36 Santiago Mañé Ubalde 3.4.13. Wing architecture Multiple parameters interfere with the definition of a wing geometry. Previously we have defined the 𝐴𝑅 of a wing, as well as the chord and span. The last two concepts are represented in the following figure. Figure 20: geometry of a wing. Other important parameters that we must contemplate when sizing a foil are the following:  The swept angle or φ is defined as the angle between the line that goes through the 25% of the chords along the span and the line perpendicular to the root chord.  The dihedral angle δ is the angle between the horizontal plane which contains the root chord and the medium plane between the top surface and the bottom surface of the wing.  The twist can be geometrical or aerodynamic. The geometrical twist θg is defined as the angle between the profile chord and a reference chord, normally the one of the root profile. On the other hand, the aerodynamic twist consists of variating the profile shape along the span of the wing. 3.5. Stability In this section, the longitudinal stability of plane configurations will be explained. This theory can be also used in hydrofoil configuration like in our case study. The stability of a plane is a property related to the equilibrium state, and it studies the behaviour of the aeroplane when one of the variables which define the equilibrium state is perturbed. When studying the equilibrium of a wing-tail configuration the effects of the control surfaces are neglected. With that being said, we first have to distinguish between two types of stability: static and dynamic. The first one refers to the initial reaction of the aeroplane in front of perturbations under stable flight. The second one refers to the evolution of the equilibrium variables after the initial perturbation. Bachelor final thesis Hydrofoils design for a Europe dinghy 37 Santiago Mañé Ubalde 3.5.1. Longitudinal equilibrium The longitudinal equilibrium is the study of the equilibrium state neglecting the lateral and directional variables. The equations that define such equilibrium are moments and forces characterized on the lateral plane of the aeroplane or hydrofoil. These equations are the following: ∑F=0 (15) ∑Mcm=0 (16) If the sum of all the forces acting on the configuration is equal to 0 and the sum of all the moments on the centre of mass is also null then at that moment the configuration is under longitudinal equilibrium. However, it does not mean that it will be statically stable nor dynamically stable. 3.5.2. Static stability As mentioned above, when talking about static stability, we are referring to the study of the moments and forces that appear on the aeroplane immediately after the incidence of a perturbation such as a wind gust. If the resultant forces amplify the perturbation, we say that the configuration is statically unstable whereas if they mitigate the effects of the perturbation the configuration is statically stable. Finally, if the perturbation effects are not amplified nor mitigated we have neutral static stability. For the study of the static stability of a configuration we often make use of the nondimensional global moment coefficient, which is expressed as: CM,cm=∑ Mcm,y 12ρu∞ 2Sc (17) Note that we are taking as reference all the moments acting over the configuration with respect to the centre of mass. If we further develop the expression we obtain: Bachelor final thesis Hydrofoils design for a Europe dinghy 38 Santiago Mañé Ubalde CM,cm=CM0+CMα·α+CMδe·δe (18) Where CM0 is the moment coefficient independent to the angle of attack, CMα is the derivative of the moment coefficient of the configuration with respect to the angle of attack, CMδe is the derivative of again CM,mc to δe, which is defined the deflexion angle of the elevator. If we plot this expression in terms of α, we obtain a graph that characterises the stability of the configuration. The intersection point with the x axis indicates the angle of attack for which we have longitudinal equilibrium. Moreover, the sign of CM,cm can give us an idea of the type of static stability. A positive value of CM,mc indicates that if a perturbation increases the angle of attack, the resulting moment will do the same, further increasing the effect of the perturbation. Therefore, these circumstances, the configuration will be instable. On the other hand, if CM,cm<0 the opposite happens, indicating a stable configuration. Finally, if CM,cm=0, the configuration is neutral. Figure 21: static stability plots. 3.5.2.1. Influence of the centre of mass position We know that for a configuration to be statically stable, CM,cm must be negative. Among other parameters, this coefficient is related to the position of the centre of mass. In a foiling dinghy, the position of the sailor is constantly adapted to achieve the longitudinal equilibrium. There exists a sitting position for which CM,cm=0 and it receives the name of neutral point. If the sailor positions itself in front of this point, the configuration becomes stable but the angle of attack that guarantees equilibrium decreases. On the other hand, Bachelor final thesis Hydrofoils design for a Europe dinghy 39 Santiago Mañé Ubalde if the sailor delays its position behind the neutral point the configuration becomes unstable and the equilibrium angle of attack increases. 3.5.3. Dynamic stability As previously announced, dynamic stability studies the time evolution of the flight variables, such as the angle of attack, when the equilibrium condition has been modified by a perturbation. A configuration is dynamically unstable when the variations produced by the perturbation are amplified through time. When the opposite situation occurs, we say that the configuration is dynamically stable. Finally, when the variables are not increased nor mitigated, the configuration is dynamically neutral. Figure 22: types of dynamic stability. Bachelor final thesis Hydrofoils design for a Europe dinghy 40 Santiago Mañé Ubalde 4. INITIAL SIZING In this section, the initial concept will be defined through a mathematical study based on the explained theory. To begin, the selection of the initial configuration will be discussed. Afterwards, an aerodynamic and stability study will be presented in which the platform geometry, dimensions and overall characteristics are determined. Finally, the results will be validated using the XFLR5 software. Figure 23: initial sizing process overview. Bachelor final thesis Hydrofoils design for a Europe dinghy 47 Santiago Mañé Ubalde The values from Figure 26 and Figure 28 are: X Value W 10 knots1 αw 30° ws 80 kg hs 1,848 m hw 0,900 m Table 9: values from the previous figures. From here, we can obtain the lateral wind force using equilibrium of moments: Fy·hw=9,81·Ws·hs→Fy=382,208 N Simple trigonometry will give us the value of the longitudinal force: Fx=tan∝w·Fy→Fx=220,668 N And finally we obtain the moment generated by the wind: Mw=hw·Fx→Mw=407,794 Nm 1 As mentioned in chapter 3.1.2, 10 knots correspond to a moderate wind intensity. In addition, the value of α indicates that the dinghy is sailing beam reach. Figure 27: front view of the sailor position and sail centre of pressure. Figure 28: top view of the sailor position and sail centre of pressure. Bachelor final thesis Hydrofoils design for a Europe dinghy 48 Santiago Mañé Ubalde Now we have all the forces involved under foiling conditions but for the moments generated by the hydrofoils themselves, M1 and M2. It has been decided to neglect them since their magnitude will be significantly inferior to Mw. Figure 29: forces involved during stable flight. Using Equations (15) and (16) we finally obtain the lifts to be generated by both hydrofoils: L2+L1+(wt2)·9,81=0 (19) Mw+L2·(X2−Xcmt)−L1·(Xcmt−X1)=0 (20) Combining the previous equations we are left with an equation system which has the following solutions: 𝐋𝟏=𝟏.𝟏𝟏𝟔,𝟐𝟎 𝐍 𝐋𝟐=𝟐𝟔𝟓,𝟒𝟕 𝐍 Therefore, with these values in mind, it can be said that the front foil needs to generate 80% of the total lift, while the rear foil accounts for the other 20%. 2 Wt corresponds to the sum of the weight of all the components plus the sailor’s body mass. It has been considered that the centreboard foil and rudder foil will weigh the same as the centreboard and rudder, respectively. Bachelor final thesis Hydrofoils design for a Europe dinghy 49 Santiago Mañé Ubalde 4.4.2.2. Surface calculation Now that we know the forces that the foiling surfaces have to generate and the speed and medium in which they have to operate, using the explained wing theory we will determine the surface dimensions. We have previously analysed the bi-dimensional profile NACA 63-412 on XFLR5 under the stable flight conditions, obtaining its Cl curve, (Figure 15) the linear section of which has a slope Clα=0,1145. However, the centreboard foil when taking off will have a fully deflected flap, and therefore we must also determine the Cl of the flapped foil. The addition of the flap does not modify the slope of the linear segment but changes the intersection point with the x-axis since it displaces the curve to the left, improving the stall behaviour. Figure 30: comparison between the flapped foil and the normal foil. We have previously decided on an intrinsic angle for both hydrofoils of 1° since at this angle they less drag is generated. From Figure 30 we can see that at 1° the foil with a 30° flap more than triples the lift generated by the foil without flap (1,456>0,350). The linear section of the represented Cl can be expressed as eq.(6) indicates: 30° flap→Cl=0,097α+1,387 (21) no flap→Cl=0,1145α+0,337 (22) -1.5 -1 -0.5 0 0.5 1 1.5 2 -20 -10 010 20 α Cl flap 30º no flap Bachelor final thesis Hydrofoils design for a Europe dinghy 50 Santiago Mañé Ubalde We can observe that as explained, the slopes are nearly equal and the flap curve is displaced to the left (0,0970≅0,1145). The three-dimensional 𝐶𝐿 curve is expressed also as CL=CLα·α+CLα0. Combining it with eq.(8) & eq.(10), the expression expands to: L 12ρu2S=Clα (1+Clα πɅ)e·α+CLα0 (23) From which we know all the variables but for the surface (Ʌ=b2/S), CLα0, and b. A low Oswald factor e of 0,7 has been chosen to ensure that the obtained surface meets the requirements, and the angle of attack will be the hydrofoils intrinsic angle of 1°. A span of 1,2 m will be considered for the centreboard foil, and 0,82 m for the rudder foil. Thus, a second equation must be defined if an exact solution must be extracted. It is known that both the bi-dimensional plot and the three-dimensional approximation intersect the y-axis at the same point, denominated p (pf when studying the flap configuration). Figure 31: intersection between the bidimensional and tridimensional Cl plots. Therefore, we obtain the following expression: Clα·p+Clα0=Clα (1+Clα πɅ)e·p+CLα0 (24) Bachelor final thesis Hydrofoils design for a Europe dinghy 51 Santiago Mañé Ubalde a) Centreboard hydrofoil surface To obtain the surface of the centreboard flap, we will consider taking off conditions, which as mentioned above involve a speed of 2,8 m/s and a 30° deflected flap. In addition, we will use seawater density of 1.024 kg/m3 and consider the lift obtained on previous calculations of 1.116,2 N. Combining equations (21), (23) & (24) we obtain: 0,097·(pf+0,7 (1+0,097·Sc π))+CLα0+1,387=0 (25) 0,097 (1+0,097·Sc π·1,2 )0,7+CLα0−1.116,2 121.024·2,82·Sc=0 (26) From here, we can determine the surface of the centreboard hydrofoil 𝐒𝐜=𝟎,𝟐𝟒 𝐦𝟐, knowing that pf=−14,2. b) Rudder hydrofoil surface The dimensions of the rudder hydrofoil are related to the cruise conditions and not the take-off conditions. Therefore, when taking off it will be producing less lift than necessary to ensure flight if the angle of attack is not modified. Luckily, due to the foil double foil distribution, when taking off the centreboard foil will tilt the hull backwards, increasing the angle of attack of the rudder foil. Firstly, we must know the cruise speed. At this speed, the centreboard hydrofoil must be able to maintain flight with the flap deflected 0°. We can compute the speed for different surfaces at which the centreboard produces the 1.116,2 N. This can be represented on a graph where we can determine the speed at which the necessary lift is achieved with the previously obtained surface. Bachelor final thesis Hydrofoils design for a Europe dinghy 52 Santiago Mañé Ubalde Figure 32: surface-speed plot for the centreboard hydrofoil. We obtain a cruise speed of 5,4 m/s. For this speed, we repeat the procedure followed for the centreboard hydrofoil but using eq.(22), a lift of 265,47 N and considering the span of 0,82 m to obtain the rudder hydrofoil results. 0,1145·(p+ 0,7 (1+0,1145·Sr π))+CLα0+0,337=0 (27) 0,1145 (1+0,1145·Sr π·0,82 )0,7+CLα0−265,47 121.024·2,82·Sr=0 (28) Knowing that p=−2,9, we obtain the rudder foil surface, 𝐒𝐫=𝟎,𝟎𝟗 𝐦𝟐 Bachelor final thesis Hydrofoils design for a Europe dinghy 53 Santiago Mañé Ubalde 4.5. Centreboard hydrofoil Once the foil's surface has been determined and knowing that it must incorporate a 30% of the chord flap and present a tapered platform, now we can define its dimensions. Figure 33: centreboard foil hydrodynamic dimensions. We can see the centre of the foil, denominated section s, has been made of a constant chord to serve as a surface to connect the vertical strut. The dimensions of the root chord and the tip chord are 230 mm and 170 mm respectively. The tip has an offset of 42 mm so the trailing edge of the contact point between the flap and foil is completely horizontal. The architecture will not present a dihedral angle nor twist to simplify the construction process. Furthermore, dihedral angles on hydrofoil configurations might have an undesirable behaviour since the tips of the foil will be closer to the surface and thus lose performance. 4.5.1. Centreboard strut The centreboard foil will be attached to a vertical strut with a symmetrical NACA 0012 profile. At the same time, the strut will be fixed to the centreboard hole of the Europe’s hull. Bachelor final thesis Hydrofoils design for a Europe dinghy 54 Santiago Mañé Ubalde Figure 34: centreboard strut hydrodynamic dimensions. The dimensions of the strut have been chosen considering a flight height of 0,4 m and the submergence factor influence. At the chosen flight height the proximity to the surface of the foil should be sufficient so that the submergence factor does not have an impact on the generated lift. The geometry of the strut will be discussed further below in chapter 5.2.2. The NACA 0012 is a symmetrical profile. This means that it will not be generating any lateral forces. From all the other symmetrical NACA series we have elected this profile mainly for its thickness; a thicker profile is less likely to suffer from structural fatigue. In addition, thicker profiles are easier to manufacture. 4.6. Rudder hydrofoil The dimensions of the rudder hydrofoil are the following: Figure 35: rudder foil hydrodynamic dimensions. Again, section s has been added to provide additional surface to attach the vertical strut. Also, the foil will not present dihedral angle nor twist due to mentioned reasons. Bachelor final thesis Hydrofoils design for a Europe dinghy 55 Santiago Mañé Ubalde 4.6.1. Rudder strut The rudder foil will be attached to a vertical strut of also a symmetrical NACA 0012 profile. This strut will also act as a rudder and its dimensions have been defined considering the flight height and trying to minimise the submerge factor as much as possible when stable flight is achieved at 0,4 m. Figure 36: rudder strut hydrodynamic dimensions. 4.7. Hydrodynamic and stability analysis Once all the foil geometries have been defined, we can introduce them to the XLFR5 software to analyse its hydrodynamic performance and stability. We will test the configuration during cruise speed or 5,4 m/s. Therefore, the flap of the centreboard foil must be deflected 0°. Since the struts have not been completely defined and the drag of the Europe’s hull is not known we cannot obtain valid results of the total drag force of the configuration. In other words, we can only validate if the configuration achieves sufficient lift and stability at cruise speed. Bachelor final thesis Hydrofoils design for a Europe dinghy 56 Santiago Mañé Ubalde Figure 37: representation of the hydrofoils on XFLR5. Firstly, the forces and moments acting over the dinghy as well as the foil distribution have to be computed on the software. Then, an analysis is defined with the cruise conditions. The following plots were obtained: Figure 38: CL of the configuration. -0.2 0 0.2 0.4 0.6 0.8 1 -6 -4 -2 0 2 4 6 CL α Bachelor final thesis Hydrofoils design for a Europe dinghy 63 Santiago Mañé Ubalde 5.2. Centreboard assembly 5.2.1. Centreboard foil and flap The geometry of the foiling surface was previously defined in a rigorous mathematical sizing and tested using XFLR5. A hole at the centre of the foil has been added to permanently fix the centreboard strut. On the other hand, the flap has been sectioned from the foil model and will be designed as a completely different piece. The geometry of both foil’s trailing edge and flap have been adapted to allow the needed deflections. Moreover, the flap includes a support for a slat mechanism to connect it with the defined control system. Figure 47: centreboard foil and flap CAD model. The will be attached to the foil by means of four nylon hinges. Bachelor final thesis Hydrofoils design for a Europe dinghy 64 Santiago Mañé Ubalde 5.2.2. Centreboard strut The strut geometry was designed considering the dimensions of the hull’s centreboard hole and the defined ride height. At the bottom surface, an extrusion has been included to fit into the mentioned foil hole. This fixation is meant to be permanent and would require the addition of an adhesive such as epoxy resin. Figure 48: centreboard strut and foil attachment. On the other hand, to fix the strut to the Europe’s hull two stoppers have been modelled. These pieces will prevent the strut from slipping upwards when the lifting force is applied and will also be glued with epoxy resin directly to the strut. The centreboard strutfoil assembly will be introduced to the hull’s centreboard hole from the bottom surface. To prevent it from falling, two M10 threaded rods of 230 mm will be inserted and fixed with adhesive into the strut. Then, using M10 nuts and washers the strut will be secured to the centreboard plate, preventing the movement of the assembly. This fixation is removable and fulfils the project technical requirements. Since this fixation is not permanent the foil can be installed and removed without damaging the hull. Further details of all the fixing elements can be seen in ANNEX A. The geometry has suffered slight modifications to accommodate the control mechanism. Most noticeably, a capillary tube of 1.120 mm, with an internal diameter of 4 mm and an external diameter of 5 mm, runs across the strut. The flap rod is supposed to fit inside it. Bachelor final thesis Hydrofoils design for a Europe dinghy 65 Santiago Mañé Ubalde Element Number Strut 1 Centreboard plate 2 M10 threaded rods 3 M10 nuts and washers 4 Stoppers 5 Hull’s centreboard hole 6 Capillary tube 7 Flap 8 Centreboard foil 9 Figure 51: centreboard strut and its fixing elements. Figure 49: centreboard strut and its fixing elements. Figure 50: capillary tube inside the centreboard strut. Bachelor final thesis Hydrofoils design for a Europe dinghy 66 Santiago Mañé Ubalde 5.3. Rudder assembly 5.3.1. Rudder foil The geometry of the rudder foiling surface has been modelled in the same manner as the centreboard counterpart. Also, hole has been added to serve as a fixing point for the rudder strut. Figure 52: rudder foil CAD model. 5.3.2. Rudder strut The rudder strut has been designed with a fixed angle of attack. It must fit the regulatory Europe’s rudder stock and be completely removable. At the bottom surface, like in the centreboard strut, an extrusion has been added to fit into the rudder foil hole. The union between the rudder strut and foil is also meant to be non-removable and needs the application of an adhesive such as epoxy resin. Since instead of the rudder we are attaching the rudder strut, this last element must also pivot to allow the steering of the dinghy. Bachelor final thesis Hydrofoils design for a Europe dinghy 67 Santiago Mañé Ubalde Figure 53: rudder strut and foil assembly installed to the rudder stock (red). Figure 54: global assembly. Bachelor final thesis Hydrofoils design for a Europe dinghy 68 Santiago Mañé Ubalde 5.4. Material selection Once the concept has been defined, the materials in which the elements have to be listed. The said components can be divided into four categories: fixing elements, secondary parts, main bodies and rods. The only components that have to be manufactured are the secondary parts and the main bodies. The rest can be directly purchased. Its price is specified in the BUDGET document. 5.4.1. Main bodies The main bodies category includes the lifting surfaces and struts. Their function is to generate the lifting forces and transmit them to the hull. Therefore, they must withstand major loads. In addition to that, they must be lightweight and waterproof, since they have to be easily lifted and operate underwater. In the dinghy industry, similar components such as the rudder or centreboard are manufactured using composites. Therefore, it is interesting to use composite materials for the main bodies due to their exceptional mechanical properties, relative lightness and ease of moulding. To speed up the manufacturing process a monocoque construction has been chosen for the main bodies. This means that there will not be any internal structure and the composite skin will distribute and support the structural loads by itself. The election of the composite and further details of the manufacturing process can be seen in chapter 6. 5.4.2. Secondary parts The secondary parts category includes multiple customised mechanical and structural components which must be prototyped. The majority of these components do not withstand critical loads and therefore faster and cheaper prototyping methodologies can be used. It has been decided that all of these components will be 3D printed. The most popular 3D printing materials for basic 3D printers are PLA, ABS and nylon. All of them can be bought for a reasonable price but present different properties.  PLA PLA or Polylactic Acid is the default filament of choice for most extrusion-based 3D printers. The main advantages of this material are its low melting temperature which allows the printer to operate at lower temperatures, increasing the lifespan of certain components. PLA is also known for its stiffness and good overall strength and it can be considered biodegradable since is derived mainly from corn corps or sugar. However, it is the less durable of the three materials and also the densest, and it presents the lowest service temperature. Bachelor final thesis Hydrofoils design for a Europe dinghy 69 Santiago Mañé Ubalde  ABS ABS or Acrylonitrile Butadiene Styrene was one of the first plastics to be used in additive manufacturing. ABS is known for its toughness and impact resistance and therefore the resulting pieces are less susceptible to wear than if they were made of other materials. It also presents a higher melting point, making it more difficult to work with than PLA, but the resulting elements can withstand harsher conditions. One of the main downsides of this material is its heavy contraction process when cooling, making it difficult to work with.  Nylon Nylon, also known as Polyamide, is the only material of the three with partial flexibility. It presents a high impact resistance. However, Nylon is hygroscopic, which means that it absorbs moisture and water. Hence, it is not the ideal material for marine applications. PLA ABS Nylon Ultimate strength 65 40 85 Stiffness 7,5/10 5/10 5/10 Durability 4/10 8/10 8/10 Maximum service temperature 52°C 98°C 95°C Density 1,24 g/cm3 1,04 g/cm3 1,06 g/cm3 Printability 9/10 8/10 8/10 Extruder temperature 190-220 °C 220-250 °C 220-270 °C Bed temperature 45-60 °C 95-110 °C 70-90 °C Biodegradable Yes No No Price/kg 20 30 40 Table 12: filament comparison. Since the PLA is the only biodegradable alternative, it is less demanding to the 3D printer and presents more than adequate mechanical properties, it has been decided that PLA will be the base material for all the secondary parts and other 3D printing processes to be carried out. Bachelor final thesis Hydrofoils design for a Europe dinghy 70 Santiago Mañé Ubalde 6. PROTOTYPE MANUFACTURING The objective of this project was initially to build a fully functional prototype. However, due to budget and schedule restrictions, the prototype has been scaled down to the centreboard foil and the flap, demonstrating that the manufacturing of such components is possible. Therefore, in the near future a fully functional prototype could be assembled, but for now, this is out of the scope of the project. 6.1. Flap The flap, being a secondary part and a non-structural element, was 3D printed using PLA filaments as mentioned in section 5.4.2. Due to its complex geometry and being a nonstructural element, it was decided to manufacture the flap with a 3D printer using PLA filaments. The used 3D printer, a Creality CR-10, can print within a space of 300x300x400 mm. It was not possible to print the whole flap section from one piece, and therefore it was divided into 5 sections which then would be assembled using adhesive and notches incorporated into the design. In addition, the edges have been rounded to increase the aesthetic appearance. Figure 55: flap CAD model. Bachelor final thesis Hydrofoils design for a Europe dinghy 71 Santiago Mañé Ubalde After conducting numerous tests, one of which involved the printing of a scale Europe dinghy hull, it was determined that the best parameters for printing the flap are a 10% infill and 3 exterior layers. It is also very important to determine the tolerances for the notches. After conducting other several tests, it was determined that for the used nozzle of 0,4 mm, material (PLA) and finish quality, and the tolerance is 0,3 mm. After the sections were printed, they were assembled and glued together using cyanoacrylate. The printer worked non-stop for 2 days and 3h, consuming a total of 360 g of PLA. Figure 58: assembled flap. Figure 56: printing of the flap sections. Figure 57: printed flap sections. Bachelor final thesis Hydrofoils design for a Europe dinghy 72 Santiago Mañé Ubalde 6.2. Centreboard foil The centreboard foil had to be manufactured using composite materials. Manufacturing composite processes usually involve some sort of moulding, to shape the matrix and reinforcement. Then, the material is cured, a process in which the reinforcement is fixed within the matrix. The curing process usually requires specialised machinery and the manipulation of composite fibres and after processes have to be done in an adequate environment with proper ventilation. For these reasons, it was decided to approach a specialised company in the sector. Figure 59: N1Foils logo. N1Foils is a company that specialised in the manufacturing of dinghy equipment, mainly centreboards and rudders, based in Cabrera de Mar. After an initial approach, the company manager Toni Riera offered its installations and expertise to develop the prototype. 6.2.1. Material choice 6.2.1.1. Reinforcement N1Foils works with carbon fibre fabric and E-glass fibre fabric-based composites. Fibreglass and Carbon fibre have similar strength characteristics. Although fibreglass presents a slightly inferior tensile strength and stiffness, it is significantly cheaper, a key factor for the viability of the project. Therefore, it was decided to use fibreglass fabric as reinforcement. The used fabric is an E-glass woven twill, which is produced by the interlacing of warp (0°) and weft (90°) fibres. The fabric’s integrity is maintained by the mechanical interlocking of the fibres. Bachelor final thesis Hydrofoils design for a Europe dinghy 79 Santiago Mañé Ubalde Further irregularities were produced by wrinkles on the plastic backs, which left marks over the surface of the foil. After some trimming and polishing, the final result came to light. Figure 71: finished centreboard foil prototype. Some of the imperfections had been scaled down, but still, the leading edge is far from the shape defined by the mould. However, with a more aggressive polishing process, the discrepancies could be rectified to obtain a more exact result. 6.2.4. Results and improvements The final result of the centreboard foil manufacturing is a solid composite piece with a foam core and E-glass fibre reinforcement with some major irregularities mainly on the leading edge. As mentioned above, such irregularities were produced by the deformation of the moulds. If the moulds are printed with more infill or filled with epoxy resin, for example, they could increase their structural integrity and handle the pressures of the curing process. On the other hand, to prevent the epoxy from sticking to the mould’s surface, plastic sheets were used. Such plastic sheets produced irregularities over the foil’s surface. Therefore, a more refined alternative has to be studied and implemented. Overall, it can be said that the manufacturing of foiling surfaces through the described method is feasible although it needs some improvements. 6.3. Centreboard foil structural study The main objective of this subsection is to prove if the final result can withstand the calculated loads. SOLIDWORKS software was used for this purpose. The parameters of the materials had to be introduced and the composite sandwich was defined. Then, to simplify calculations, it was decided to use a constant lift distribution. This is not a realistic approach, since on a three-dimensional wing less lift is generated near the tips. A constant lift distribution means that more loads are generated. Therefore, if the material withstands the loads of the defined case, it means that it would also resist the real lift distribution. Bachelor final thesis Hydrofoils design for a Europe dinghy 80 Santiago Mañé Ubalde A pressure was applied to the lower face of the foil, corresponding to the centreboard lift divided by the value of the same surface. 𝑃=1.116,20 𝑁/0,17 𝑚2 =𝟔.𝟕𝟔𝟒,𝟖𝟒 𝑵/𝒎𝟐. The surface which is supposed to be connected to the strut was defined as a fix. Then, a mesh was defined and the simulation was run. Figure 72: factor of safety at the lower surface of the foil & minimum value. Figure 73: deformations under the defined loads. Bachelor final thesis Hydrofoils design for a Europe dinghy 81 Santiago Mañé Ubalde The results show a minimum factor of safety at the centre of the lower surface of 1,353. The factor of safety is defined as: FoS= yeld stress working stress (29) Therefore, having a factor of safety superior to 1 means that the material is working below its limit. In our case, the foil can withstand 1,353 times the defined load before failure occurs. The deformation diagram also shows successful results, since the tips only flex a maximum of 10,39 mm. With these results on hand, it can clearly be said that the manufactured prototype can withstand the design loads. Bachelor final thesis Hydrofoils design for a Europe dinghy 82 Santiago Mañé Ubalde 7. BUDGET The costs of manufacturing the fully functional prototype as well as of the whole project are specified in the BUDGET document. In this section, only the manufacturing costs of the flap and centreboard foil prototypes will be determined. 7.1. Additive manufacturing As explained in chapter 6, the flap and mould of the centreboard foil were 3D printed. This process consumes PLA filament as well as energy in the form of electricity. Since we know the energy consumption of the used printer and the weight of the mentioned elements, we can approximate the total cost of the additive manufacturing process. One roll of PLA printing filament costs 20 € and weighs 1 kg, which gives us a relation of 0,02 €/g. On the other hand, the electricity cost is estimated to 0,276 €/kWh and the 3D printer consumes 0,7 kW. The cost of the machinery will not be considered since the used 3D printer was lent by a friend. Additive manufacturing PLA [g] Printing time [h] Filament price [€/g] Energy consumption [€/kWh] Cost Flap 360 51 0,02 0,276 17,05 € Moulds 1.235 154 54,45 € Total: 1.595 205 71,5 € Table 15: additive manufacturing cost. 7.2. Composite manufacturing The manufacturing costs of the centreboard foil were assumed by N1Foils. However, they will be determined to give the reader a broader picture of the project’s cost. Moreover, the commute costs to the N1Foils workshop will also be considered. Composite manufacturing Cost 3 h labour + machinery 100 € 0,7 m2 of E-glass fibre fabric 10 € 0,4 m3 of 2 cm thick PVC foam sheet 20 € 0,4 ml of epoxy + 0,2 ml of hardener 7 € 3 m plank of pine wood 27 € Total: 165 € Table 16: composite manufacturing cost. Bachelor final thesis Hydrofoils design for a Europe dinghy 83 Santiago Mañé Ubalde A total of three car trips were done to the N1Foils workshop. The distance of the commute is 64 km and the used car consumes an average of 6,9 l/100 km of diesel, the cost of which is 1,24 €/l. All trips required paying a 1,28 € toll. Displacements Trips Distance/trip [km/trip] Fuel consumption [l/km] Fuel price [€/l] Toll [€/trip] Cost 3 64 6,9/100 1,24 1,28 20,27 € Table 17: displacements cost. 7.3. Total cost The total cost of the manufactured prototype ascends to 256,77 €. Total Additive manufacturing 71,5 € Composite manufacturing 165 € Displacements 20,27 € Total cost 256,77 € Table 18: total costs of the manufactured prototype. Bachelor final thesis Hydrofoils design for a Europe dinghy 84 Santiago Mañé Ubalde 8. ENVIRONMENTAL IMPACT Although this is a project of relative minor dimensions in which no major manufacturing processes have been carried out, it is important to record and present the environmental impact of all the activities. The objective of this section is to give a general idea of how much of an impact can have little human activities such as this thesis and present possible solutions that could have made the project greener. 8.1. Direct impact The main direct environmental impact of this project comes in the form of electricity consumption. The production of this thesis required the use of a desktop computer and the manufacturing of the prototype makes extensive use of a 3D printer. The total energy of the previous appliances has been estimated in the budget section. Appliance Working hours [h] Energy consumption [kW] Total energy consumption [kWh] 3D printing 100 0,7 70 Desktop computer 600 0,3 180 Table lamp 600 0,06 36 Total: 286 Table 19: energy consumption. It is estimated that the Spanish peninsular electrical network emission factor is 0,27 kg CO2/kWh. Therefore, this project has led to the generation of 77,22 kg of CO2. Moreover, it is also interesting to determine the number of nuclear residues that this project generated. The values referring to the nuclear waste generation of the Spanish peninsular electrical network indicate that for every consumed kWh, 0,55 mg of nuclear waste are generated. Therefore this project generated 157,3 mg of nuclear waste. To manufacture the centreboard prototype, a total of three car trips were done to the N1Foils workshop. The distance of the commute is 64 km. The used car consumes an average of 6,9 l/100 km of diesel and has CO2 emissions of 146 g/km. Therefore, those commutes supposed the emission of 28 kg of CO2, which add up to a total of 105,22 kg. Bachelor final thesis Hydrofoils design for a Europe dinghy 85 Santiago Mañé Ubalde 8.2. Indirect impact All the materials involved in the manufacturing of the prototype have an impact on the environment. The raw materials for their products generally come from large industrial complexes and mining plants. Furthermore, their production requires a significate energy input which generally does not come from renewable energies. There is no way determining the impact that the production of the project’s materials had on the environment, and thus it will not be quantified. Luckily, the majority of the materials used, such as the PLA plastic and steel from the fixing elements and rods, can be easily recycled or processed once their lifespan is over. The same cannot be said about composite materials. Composite materials are known for their exceptional mechanical properties and relative lightness. That is why they are used in the manufacturing of wind turbines and aircraft. However, the recycling of this material is a challenge of its own due to its heterogenic nature. There exist various technologies which can be used to recycle composites but generally it is an expensive process whose result presents an inferior quality to brand new composites. Figure 74: wind turbine landfill. [16] Proposing solutions for those problems are out of the scope of this project. However, the use of biodegradable composites such as wood could be studied and incorporated in future iterations of the project. Bachelor final thesis Hydrofoils design for a Europe dinghy 86 Santiago Mañé Ubalde 8.2.1. Entropy resins & R*Concept The resin used to manufacture the prototype presents a formulation, denominated Super Sap and produced by Entropy resins. As opposed to combinational epoxies, which are mainly petroleum-based, Super Sap epoxy contains bio-renewable materials sourced as co-products or from waste streams of other industrial processes, such as wood pulp and bio-fuels production. These natural components have excellent elongation and exceptionally high adhesion properties. As opposed to 100% petroleum derivated epoxies, the production of Super Sap epoxy supposes a reduction in CO and greenhouse gas emissions of approximately 50%. In addition, it demands less power and water consumption. Furthermore, less harmful by-products are generated. R*Concept is a company based in Barcelona that specialized in selling bio-resins under its brand. The company is fully compromised with the sustainability of our environment and since 2019 they accomplished the goal of being carbon neutral. This means that all the energy consumed in their facility comes from green sources. If more prototypes had to be made, R*Concept would be the brand of choice. Bachelor final thesis Hydrofoils design for a Europe dinghy 87 Santiago Mañé Ubalde 9. NEXT STEPS As previously announced, budget and time limitations prevented the manufacturing of a full manufacturing prototype. Therefore, it is a priority to produce a prototype, install it on an Europe dinghy and test the results. Moreover, the studied manufacturing process presents some flaws that need to be rectified. Therefore, it is also fundamental to find solutions to this process or studying new alternatives. Following this step, the hydrodynamic design could be enhanced by conducting CFD analysis with the appropriate software. In addition, it is primordial to study the drag of the configuration and try to reduce it, a task that could also be done with the CFD software. With the results of the conducted CFD analysis, a structural study of the design could also be performed, followed by a more exhaustive material selection process. The objective is to reduce manufacturing costs and increase the structural safety of the prototype. On the other hand, the control mechanism needs some refinement and its behaviour has to be mathematically defined to further understand its effects on the ride height. If we remember, it was decided to use a mechanical control mechanism instead of a PID controller. Further analysis of the electrical alternative could be performed since it presents numerous advantages and also it would be a revolutionary concept if successfully installed. Finally, a marketing study could be done to determine the commercial feasibility of the project. If the results were positive, the prototype would have to be adapted for serial manufacturing through further refinement of the components. Bachelor final thesis Hydrofoils design for a Europe dinghy 88 Santiago Mañé Ubalde 10. CONCLUSIONS The results of this project demonstrate that old conventional dinghy designs can be adapted to equal the performance of their foiling counterparts. In the case of the Europe dinghy, this is possible by installing two hydrofoils, one in place of the centreboard and the other one instead of the rudder, in a tandem configuration. The result is a compact removable kit that respects the structural integrity of the hull. The design incorporates a control mechanism that adapts the deflection of a flap depending on the ride height, allowing stable flight at speeds nearly twice the one achieved without hydrofoils. The initial sizing of the foils was done through aerodynamic theory. After intensive research and study of the forces involved during sailing, an algorithm was developed. The outcomes of the approach were then tested using XFLR5 software. The results presented some discrepancies, but by modifying the position of the sailor 10 cm the initial objectives of lift generation and stability were achieved. After that, a modelling process captured the obtained aerodynamic configuration in a three-dimensional design and the control mechanism was incorporated. All this process was done considering the initial objective of respecting the structural integrity of the dinghy’s hull. The design of the control mechanism although successful, its final result was not exhaustively tested and would need some refinement if future work is to be carried out. The prototype manufacturing process, as well as material selection, was overall the most challenging part of this thesis. Several limitations downgraded the initial objective of manufacturing a fully functional prototype to a sample of the centreboard and flap assembly, to prove that the full manufacturing was possible if more resources were available. The manufacturing of the flap proved feasible through additive manufacturing and the final results are considered successful. On the other hand, the obtained centreboard prototype which was manufactured using composite materials presented some irregularities which would prevent it from generating the necessary lift. However, the imperfections of the followed process can be easily resolved.