Kitesailing Improving system performance and safety

J. van den Heuvel B.Sc. August 2010

Kitesailing Improving system performance and safety

Master of Science Thesis

For obtaining the degree of Master of Science in Aerospace Engineering at Delft University of Technology

J. van den Heuvel B.Sc.

August 2010

Faculty of Aerospace Engineering Delft University of Technology

⋅ Delft University of Technology

Copyright J. van den Heuvel B.Sc. All rights reserved. Delft University Of Technology Department Of Aerospace for Sustainable Engineering and Technology

The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace Engineering for acceptance a thesis entitled “Kitesailing” by J. van den Heuvel B.Sc. in partial fulfillment of the requirements for the degree of Master of Science.

Dated: August 2010

Readers: Prof.dr. W.J. Ockels

Dr.-Ing R. Schmehl

Ir. J. Breukels

P.D.C. Smit

Summary

In the world of high performance sailing people are using state of the art technology to push the limits in speed and performance. The introduction of the sport kitesurfing has shown the power that kites can generate. It has meant a revolution in the world of surfing. Kitesurfing only exists since 15 years and began to expand around the world only since the year 2000. Already in 2008 the 50 knots speed sailing barrier has been broken by a kite surfer being the first sailing system to do so. This is less than ten years after the sport started to become public in the world. This illustrates the potential in performance for the use of kites. Kites also offer the possibility of a revolution in other fields like sailing where systems are currently developed to provide propulsion for commercial vessels to save fossil fuels. Kite systems are also developed for clean energy production where wind energy at high altitude is harvested. These High Altitude Wind Power systems can also be applied to ships offering the possibility of sailing at a course of 0 degrees into the wind on pure wind energy. In this research the kite system is evolved such that the performance and safety is increased for kitesailing and energy production. Kitesailing offers higher sailing speeds and more extreme maneuvers compared to conventional sailing. Using kites for sailing has four main advantages over conventional sailing:

A larger sail area for the same boat is possible

● Higher true wind speeds are present at a kite

● Higher apparent wind speeds are created by flying cross-wind patterns (sinussing) with the kite ● A kite has more degrees of freedom to perform extreme maneuvers

● This report shows the results of the research that is focused on two goals: Improving the performance of a kitesailing propulsion system and improving the safety. Three different aspects play a dominant role in the development of the system. Improving the L/D ratio of the kite allows for sailing higher upwind. Scaling up the kite increases the pulling force which results in faster sailing. Safety is the most important factor of all that will determine if kitesailing can be practiced by the general public. These three areas of research apply

Kitesailing vi Summary equally to the fields of electricity generation and the large systems for commercial sailing. The research of every one of these aspects starts with a theoretical investigation after which new theories are developed and new designs being produced. Actual tests on the beach and during sailing show the improvements that have been made. To increase the performance and safety the following set of requirements is determined:

1. The kite is not allowed to generate more than 450 N in the center of the wind window while it is fully depowered for an 18 ft catamaran 2. The kite must have the possibility of creating zero lift on every position in the wind window. 3. The kite should be able to handle pulling forces of at least 3000 N. 4. The scaled kite must be able to handle twice the aerodynamic load per square meter without buckling compared to the original kite. 5. The L/D ratio of the kite should be as high as possible for sailing upwind.

The goal of this thesis is to determine what parameters should be focused on to effectively increase the performance of kitesailing and to design, produce and test a new kitesailing system that meets these requirements. From the sailing system analysis it follows that the focus should be on increasing the lift of the kite by either increasing the lift coefficient CL,A or the surface area SA for effectively improving the overall performance of the sailing system. The surface area is the most promising way to effectively increase the sailing speed. Increasing the kite area from 13 m2 to 25/,m2 increases the sailing speed by 30% on an upwind course. A 50 m2 kite doubles the sailing speed upwind compaerd to a 13 m2 kite. A bridle analysis and design program has been written with two different methods to deter- mine the discrete force distribution on the bridle points of an existing kite. The calculated aerodynamic loads on the tips using an aerodynamic lift distribution proved to be too small. The bridles designed using the original geometric bridle layout gave good general shapes of the kite during flight. A bridle configuration is designed which completely fulfills the requirements of supporting the kite such that it has its design shape during flight and of offering the possibility of zero lift on every position in the wind window. With this capability to depower the size of the kite can be made much larger than the sail area used on a conventional 18 ft catamaran and still keep within the safety requirements. Even in wind speeds of 15 m s the kite area can still be increased to 45 m2. ~ Rules of thumb have been derived for scaling of a tube kite. A new 25 m2 kite is designed, produced and tested. Tests have shown that this kite can easily cope with the design loads of 3000 N without buckling of the leading edge.

The maximum lift coefficient of CL max 1.1 of tube kites is already comparable to those of other ”flying wing airfoils”. Therefore this area is difficult to improve. The L/D ratio offers greater possibilities. ( ) > For improving the L/D ratio, four concepts have been analyzed:

Kitesailing vii

Adding a lower skin

● Adding an elliptical leading edge

● Adding winglets

● Increase the aspect ratio

● Adding a lower skin and an elliptical leading edge both improve the L/D ratio with almost 50%. Increasing the aspect ratio by 80% increases the L D max with the accompanying lift coefficient by 33% and the maximum lift coefficient CL max. The canopy tension also increases by 250%. Adding winglets is not usefull as long as( the~ ) aspect ratio can be increased. ( ) Field tests with a lower skin on a Naish Aero 4 m2 tube kite have shown that this concept can be successfully applied. The leading edge can be made with a minimum amount of foam of only 18 mm of maximum thickness on a 5 m2 tube kite.

Kitesailing results In 2009 and 2010 the ”‘Round of Texel”’ was sailed with the Hobie Tiger kitesailing catamaran. The lap times of the kitesailing catamaran and the fastest competitor using conventional sails on that day are given by following table:

Table 1: Laptimes of the record runs of the kitesailing catamaran and the fastest competitor using conventional sails in 2009 and 2010

2009 2010 Kitesailing 4:45 4:00 Conventional 2:07 2:30

It shows that the difference in lap time between the kitesailing system and conventional system between 2009 and 2010 has been decreased by one hour and ten minutes.

Kitesailing viii Summary

Kitesailing Acknowledgements

This project could not have been successful without all the help from so many people. I want to thank my supervising professor Wubbo Ockels, the chair holder of ASSET who has set up a great working environment for research on kites. Roland Schmehl for his great effort in getting the final details worked out and pushing me to take that extra step. I also owe many thanks to Jeroen Breukels who has provided me with great feedback for many months and to Pepijn Smit who has taken the effort to take a seat in my graduation committee to give his insights with his great expertise on kite designing. I thank Edwin Terink who has helped me so much on moments when technology resisted me, by keeping a close eye on my graduation schedule and by supporting me with his engineering capabilities that go far beyond mine. I also thank all others at ASSET who have helped me so much on numerous occasions and for giving me great new insights and who have been involved in having great lunches with lots of laughing: Stefan de Groot, Roland Verheul, Lyssandre Rammos, Aart de Wachter, Rolf van der Vlugt and Barend Lubbers. Also Nana Saneeh for arranging so much paperwork during my stay at ASSET. Of course my family and friends are not forgotten for their great support and enthusiasm which has helped me greatly, with Gerben as my kitesailing budy with whom I experienced already so many adventures. Shashika has a special place among all for her love and great support and the many meals she cooked for me so that I could work through the evenings to get the best result. I thank you all. John August 2010

Kitesailing x Acknowledgements

Kitesailing Contents

Summary v

Acknowledgements ix

Nomenclature xv

1 Introduction 1

2 Existing kitesailing systems 5 2-1 Traction-based kitesailing ...... 5 2-1-1 Transportation applications ...... 5 2-1-2 Recreational applications ...... 7 2-2 Electricity-based kitesailing ...... 14 2-3 Objectives ...... 16

3 Sailing system analysis 17 3-1 Maximum sailing speed ...... 17 3-2 Maximum aerodynamic area ...... 19 3-3 Kitesailing system analysis ...... 20 3-4 Requirements for improved traction kitesailing system ...... 23 3-4-1 Increased safety ...... 23 3-4-2 Larger pulling force ...... 25 3-4-3 Impact of L/D ratio on sailing ...... 26 3-4-4 Summing up the requirements ...... 26 3-4-5 Thesis goal ...... 27

Kitesailing xii Contents

4 Depower system design 29 4-1 Functional analysis ...... 29 4-1-1 Pitch behavior ...... 30 4-1-2 Attachment of power lines ...... 31 4-1-3 Examples of bridles currently used for tube kites ...... 31 4-1-4 Leading edge geometry ...... 32 4-1-5 Bar travel ...... 33 4-1-6 Objective ...... 34 4-2 Model definition ...... 34 4-3 Design strategy ...... 36 4-4 Program details ...... 38 4-4-1 Bridle force analysis ...... 38 4-4-2 Bridle design ...... 41 4-5 Testresults...... 43 4-5-1 Kite shape ...... 44 4-5-2 Force measurements ...... 48 4-5-3 Best practices ...... 50 4-6 Conclusions ...... 50

5 Scaling of kites 55 5-1 Introduction of scaling factors ...... 55 5-1-1 Terminology and assumptions ...... 55 5-1-2 Scaling factor calculations ...... 57 5-2 Canopy tension changes ...... 57 5-3 Tube pressure determination ...... 58 5-4 Stability of straight tubes ...... 61 5-4-1 Theory for collapse moment and stress criteria ...... 61 5-4-2 Deriving bridle point pitch relation using the stress criterium ...... 62 5-4-3 Deriving bridle point pitch relation using the collapsing moment criterium 64 5-4-4 Increasing the buckling resistance by the bridle ...... 64 5-5 Stability of tapered tubes ...... 65 5-5-1 Deriving position and magnitude of maximum tension in a tapered tube . 65 5-5-2 Increasing the stiffness by the bridle in a tapered tube ...... 66 5-6 Weight changes ...... 69 5-7 New kite design ...... 70

Kitesailing Contents xiii

6 Aerodynamic analysis 73 6-1 Analysis of tube kite aerodynamics ...... 73 6-1-1 Qualitative analysis on the aerodynamics of a tube kite ...... 73 6-1-2 Quantitative analysis on the aerodynamics of a tube kite ...... 78 6-2 Literature study ...... 79 6-2-1 Airfoil section design ...... 79 6-2-2 Aspect Ratio ...... 81 6-2-3 Non-planar wings ...... 83 6-2-4 Examples of experimental tube kite designs ...... 87 6-3 Applying aerodynamic theory to kites ...... 90 6-3-1 Airfoil analysis ...... 90 6-3-2 Aspect ratio on the Flow 5m kite ...... 90 6-3-3 Non-planar wings ...... 94 6-3-4 Trade off for concept to be worked out in detail ...... 96 6-4 Airfoil design ...... 97 6-5 Testsonalowerskin ...... 101 6-5-1 Fabric double skin ...... 101 6-5-2 Foam semi-double skin ...... 105 6-6 Conclusions ...... 105

7 Kitesailing system review 107 7-1 Maximum surface area ...... 107 7-2 Sailing speed ...... 108 7-3 Maximum pulling force is 5800 N ...... 109

8 Conclusions and recommendations 111 8-1 Conclusions ...... 111 8-2 Recommendations ...... 113

A Kite terminology 119

B Sailing system coefficient determination 123 B-1 Hydrodynamic parameters ...... 123 B-1-1 Lift ...... 123 B-1-2 Drag ...... 124 B-2 Aerodynamic parameters ...... 125

C Comparison of airfoil calculation programs 127

D Derivation of ratio between pressure drag and friction drag at optimum L/D 129

E Performance diagrams with an increase in wingspan 131

Kitesailing xiv Contents

Kitesailing Nomenclature

Latin Symbols

A Aspect ratio A′ Projected aspect ratio

Aeff Effective aspect ratio b Wing span m b′ Projected wing span m c Wing chord m

CD Drag coefficient

CL Lift coefficient cr Root chord m ct Tip chord m

CD0 Zero-lift drag coefficient

CDi Induced drag coefficient D Drag N

Di Induced drag N e Oswald efficiency factor F Force N f Scaling factor in one dimension f 2 Scaling factor in two dimensions

Fa Axial force N

Fg Gravitational force N

Fr Radial force N

Kitesailing xvi Nomenclature g Gravitational constant ms−2 I Area moment of inertia m4 k Span efficiency factor L Lift N l Length of LE between two bridle points m M Bending moment Nm

MR Resulting moment Nm n Number of bridle points on LE p Pressure Pa

Pbridle Bridle point pitch, distance between bridle points m q Distributed aerodynamic load Nm−1 q∞ Dynamic pressure Pa r Radius m

RA Resultant of aerodynamic forces m

RH Resultant of hydrodynamic forces m S Kite surface area m2 S′ Projected kite surface area m2 2 SA Aerodynamic surface area m 2 SH Hydrodynamic surface area m T Tether force N t Wall thickness m

Tp Force in power lines N

Ts Force in steering lines N TR Taper Ratio −1 VA Apparent wind velocity ms −1 VS Ship velocity ms −1 VW Wind velocity ms −1 V∞ Free stream wind velocity ms

Greek Symbols

α Geometric angle of attack

αeff Effective angle of attack

αi Induced angle of attack

αle Angle of leading edge segment with horizontal axis β Camber factor

βS ǫA ǫH , total system glide angle

ǫA arctan(DA LA , aerodynamic glide angle +

Kitesailing ~ ) Nomenclature xvii

ǫH arctan(DH LH , hydrodynamic glide angle η Elevation angle between the kite tether and the horizontal plane ~ ) γf Angle of rotation of a radial force γ Sailing course µ Freestream viscosity coefficient kg m−1s−1

ψb Total efficiency of a sailing system ρ Air density kg m−3 σ Tension Nm−2 −2 σM Maximum tension in axial direction Nm −2 σcanopy Canopy tension Nm

Abbreviations

2D Two Dimensional 3D Three Dimensional a.c. Aerodynamic Center a.o.a. Angle Of Attack ASSET Aerospace for Sustainable Engineering and Technology FBD Free Body Diagram HAWP High Altitude Wind Power L/D Lift over Drag ratio PSI Pound per Square Inch

Kitesailing xviii Nomenclature

Kitesailing Chapter 1

Introduction

In the world of high performance sailing people are using state of the art technology to push the limits in speed and performance. The introduction of the sport kitesurfing has shown the power that kites can generate. It has meant a revolution in the world of surfing. Kitesurfing only exists since 15 years and began to expand around the world only since the year 2000. Already in 2008 the 50 knots speed sailing barrier has been broken by a kite surfer according to Sailspeed records [2010] being the first sailing system to do so. This is less than ten years after the sport started to become public in the world. This example shows that even with such a short period of innovation the fastest kite surfer was faster than the fastest wind surfer which illustrates the potential in performance for the use of kites. Kites also offer the possibility of a revolution in other fields like sailing where systems are currently developed to provide propulsion for commercial vessels to save fossil fuels. Kite systems are also developed for clean energy production where wind energy at high altitude is harvested which is called High Altitude Wind Power (HAWP). Such HAWP systems can also be applied to ships offering the possibility of sailing at a course of 0 degrees into the wind on pure wind energy. For sailing using the traction of the kite directly the possible gains are very clear. In general, for almost every technology the rate of performance increase over time can be shown with an S-curve shown in Fig.1-1. Kites

Sails Performance

Time Figure 1-1: Illustration of the S-curves to illustrate the expected performance increase of kites over conventional sails

Kitesailing 2 Introduction

When a technology has reached the end of the S-curve then a new technology is needed to radically improve performance. This figure gives a graphical representation of the expected overtake of kites in performance over conventional sails. When looking at a conventional sailing catamaran in Fig.1-2 it is clear that the sail exerts a large heeling moment on the boat. Next to the fact that this limits the sailing speed it is also a factor for fun. Sailing on one hull gives all catamaran sailors a great thrill and satisfaction.

Figure 1-2: Professional sailing team Heemskerk/Tentij on their conventional catamaran in action, source: Sailshoot.com

In their evolution the conventional mast-supported sails get higher L/D ratios and get larger. The spinnaker sail that is used for downwind courses does not have a high L/D ratio but it doubles the surface area which is more valuable than the L/D ratio. The heeling moment is the limiting factor for the size of the sails. When making a kite of the sails the heeling moment is decimated such that the kite-sail can be made much larger. Also the mast becomes obsolete which saves mass on the boat. Figure 1-3 shows this evolution schematically. Next to a larger surface area a higher true wind speed is present at a kite compared to a sail because a kite is higher up in the air such that it suffers less from the boundary layer that is formed over the water. This boundary layer lowers the true wind speed and therefore at altitude the wind is stronger. This creates more pressure per unit area at a kite compared to a conventional sail. Higher apparent wind speed is created by flying crosswind patterns called ”‘sinussing”’ in kitesurfing. By sinussing an extra vertical crosswind component is added to the crosswind component created by the sailing speed. This creates more pressure per unit area compared to a conventional sail. Measurements performed during sailing in 12 knots of wind with a 13m tube on a half wind course showed a sailing speed of 5 knots without sinussing and a sailing speed of 12.5 knots when aggressively sinussing the kite. This shows that the sailing speed increased by a factor of 2.5 when sinussing the kite compared to a static kite. A conventional sail is static by definition. An extra advantage for recreational sailing is the possibility of more extreme maneuvers. Because a kite is in principle a conventional sail but with more degrees of freedom it can

Kitesailing 3

Figure 1-3: Schematic view on the sailing evolution be steered such that it pulls the boat forward, backward and upward. Extreme maneuvers are possible with this freedom of force direction. Sharp cornering, braking and jumping are common practice in kitesailing. Summing up, using kites has four main advantages over conventional sailing being:

A larger sail area for the same boat is possible

● Higher true wind speeds are present at a kite

● Higher apparent wind speeds are created by flying cross-wind patterns (sinussing) with the kite ● A kite has more degrees of freedom to perform extreme maneuvers

● Or in general: ”‘Kitesailing offers higher sailing speeds and more extreme maneuvers”’. The kite systems for all the mentioned different fields of research are similar in concept to the system used in kitesurfing. For the automated systems mostly a control pod is used to control the kite which works basically the same as a kite surfer controlling the kite. The choice is made to focus the research on the kitesailing system for an 18 ft catamaran which serves as a promoter of the use of kites and as a testing platform to test new kite systems in a rough environment. This report shows the results of the research that is focused on two goals: Improving the performance of a kitesailing propulsion system and improving the safety. Three different aspects play a dominant role in the development of the system. Improving the L/D ratio of the kite allows for sailing higher upwind. Scaling up the kite increases the pulling force which results in faster sailing. Safety is the most important factor of all that will determine if kitesailing can be practiced by the general public. These three areas of research apply equally to the fields of electricity generation and the large systems for commercial sailing.

Kitesailing 4 Introduction

The research of every one of these aspects starts with a theoretical investigation after which new theories are developed and new designs being produced. Actual tests on the beach and during sailing show the improvements that have been made. First the traction based and electrical based systems for kitesailing are explained in Chapter 2 together with the requirements for an improved kitesailing system. Then the impact of the surface area, the drag and the lift of a sail on a sailing boat are discussed in Chapter 3. Chapter 4 shows the theoretical research performed on increasing the safety and the test results of produced designs. The implications of scaling of a kite are shown in Chapter 5 and the end result, being a produced kite, is shown. Chapter 6 shows the theoretical research performed on the possibilities to improve the L D ratio of the kite together with tests performed in practice for validation of the chosen concept. Measurements on sailing speeds and pulling force with the developed kite are shown~ in Chapter 7. Please note that in Appendix A the terminology on kites that is used in this report is ex- plained.

Kitesailing Chapter 2

Existing kitesailing systems

Like the dictionary will describe:

”Kitesailing is sailing on a boat with a kite as the primary means of propulsion”.

Therefore, when kitesailing, you sail with a kite instead of with a conventional sail. Although kitesailing is not a widely known sport, it has been around for a long time. In 1827 George Pocock published his book ”The Aeropleustic Art or Navigation in the Air by the use of Kites, or Buoyant Sails” Pocock [1827]. The book is primarily concerned with the use of kites in transport. Figure 2-1 shows an illustration from this book in which he describes a boat race between boats with masts and sails and boats using a kite. In the recent decades with the availability of new materials and techniques more advanced kitesailing gear is developed. Two basic forms of kitesailing have emerged. These are traction- based kitesailing and electricity-based kitesailing. Traction-based kitesailing is similar to conventional sailing only using a kite instead of the conventional mast with a sail. Electricity- based kitesailing uses the kite to generate electricity which is fed into the engines to propel the ship.

2-1 Traction-based kitesailing

The use of traction-based kitesailing systems can be divided into two major groups being transportation and recreation. The transportation systems are used on commercial vessels to reduce the consumption of fossil fuels. The recreational systems are currently applied on small boats like canoes and small catamarans.

2-1-1 Transportation applications

The most well known project on kitesailing in the world at this moment is the system of ”SkySails”. This company develops traction kites to pull commercial vessels. Figure 2-2

Kitesailing 6 Existing kitesailing systems

Figure 2-1: Drawing of a boat race with conventional and kitesailing boats, source: Pocock [1827] shows a container ship of ”Beluga Shipping” which is the first company to implement the kite system of Skysails.

Figure 2-2: The first SkySails system applied on a commercial vessel, source: SkySails [2010]

This system uses a 160 m2 kite and is steered by an autopilot and by a joy stick if necessary. The line between the boat and the kite consists of a Dyneema mantle which is wounded around a copper core. This copper core is used for communication and energy transport towards the control pod by which the kite is steered. The Dyneema mantle carries the pulling force of the kite. A crane is used for launching and retrieving the kite and is located at the front end of the boat where the attachment point of the kite is also located. The effective

Kitesailing 2-1 Traction-based kitesailing 7 load of the 160 m2 kite is 8 tons of pulling force in the direction of the ship’s course under SkySails standard conditions according to SkySails [2010]. These conditions are given by: ship speed: 10 kts wind speed: 25 kts true wind direction: 130 SkySails flight mode: dynamic This system is being scaled up at the time of writing to 320 m2 and 640 m2 with effective loads of 16 and 32 tons of pulling force. The energy savings that are achievable according to Skysails is between 10% and 35%. This system is also modified to be implemented on super yachts in the future which fits in the following recreational group. The same type of system is also investigated by Naaijen & Koster [n.d.] and P. Naaijen & Dallinga [2006]. An other application of traction based kitesailing is proposed by Kim & Park [2009]. It discusses the possibility of pulling a ship with a kite using hydraulic turbines to generate electricity from the generated water flow due to the movement of the boat.

2-1-2 Recreational applications

A conceptual design of a yacht using a kite is shown in Fig.2-3.

Figure 2-3: Conceptual design of the Kitano kitesailing yacht, source: Kitano [2010]

A somewhat different approach was made by Dave Culp with the ”Flying spinnaker”. This is shown in Figure 2-4. The kite is meant to be used together with the conventional sails which are not used for the shown pictures. This is an intermediate solution between conven- tional sailing and pure kitesailing. The kite was used only for sailing downwind and had its attachment point directly on the deck of the boat so it does not introduce a large heeling moment such as any other spinnaker. This allowed for a much larger surface area of 4500 square ft. Although the sailing performance was promising this was banned since the 1st of July in 2005 from racing because authorities claimed it was too dangerous for other sailing vessels according to KitePower [2010]. This is a clear example that kitesailing can only exist when it is considered safe. More examples exist of smaller boats that are used for kitesailing. Figure 2-5 shows two different projects being ”Jacob’s Ladder” on the left and the ”KiteCat” on the right Jacob’s Ladder is a project of Ian Day. He stacked two-line Flexifoil kites to his extended Tornado catamaran and set a C-class sailing speed record in the late 1970’s. These Flexifoil

Kitesailing 8 Existing kitesailing systems

Figure 2-4: The AAPT flying spinnaker, source: Kiteship [2010]

Figure 2-5: The Jacob’s Ladder and KiteCat kitesailing projects, source: Canadian Windrider [2010] kites are one of the first steerable kites that used two lines. Being able to steer the kite, a boat could be sailed in different directions. The use of two lines however did not provide any possibility to depower the kite which made this system potentially dangerous. The small picture just left from the middle shows the catamaran on its rudders and the man holding tight to the boat. It shows the potential of excitement of kitesailing but this system was not safe at all. Another drawback with the used kites was that once they had crashed into the water, they could not be relaunched again. With the introduction of kite surfing the two-line kites evolved into four line kites that allowed for pitch control next to the steering capability. This ability to depower improved the safety and these surf kites were able to relaunch from the water. One of the pioneers in modern kitesailing is Peter Lynn who has developed his KiteCat after 1987 which is shown on the top right in Fig.2-5. It uses a standard Peter Lynn arc-kite and bar system that was developed for kite surfing. The boat was evolved during fifteen years into a one-man catamaran with planing hulls. Although this boat is fast, it is not faster than a kite surfer because the kite is the same but the drag of the boat is larger than a surfing board. Also, this system can only be sailed by one person with possible adaptations to be able to take a passenger with you. An example of kitesailing that is possible with a team is shown in Fig.2-6. This is a canoe of 300 kg that is sailed by a crew of four people. One flies the kite and is called the ”flyer” and one is the steersman who steers the boat using a simple paddle. The third person is the ”Ama-man” who has to position himself such that the boat does not easily flip over. The fourth person is the ”Bailer” who has to bail out all the water that gets inside the boat. The kite that is used is a 50m C-shape kite and is a scaled version of the kite surfing tube kite.

Kitesailing 2-1 Traction-based kitesailing 9

The right picture shows that the kite has the possibility to lift the boat (partly) out of the water which adds to the excitement of the sport.

Figure 2-6: Kite canoe with a 50 m2 kite in 2004, source: Kiteboat.com [2010]

This system has great performance and has a steerable kite that can be depowered. It also makes kitesailing a real team sport but it has not been the breakthrough to make kitesailing a popular sport. The main reason for this has to be the lack of safety. The C-shape kite can depower but not so much as modern bow kites can. An example of the usage for kitesailing of a modern tube kite that has a lot of depower is the ”Catakite” system. This system is developed during the last few years specifically to be able to sail with a team of people. Also physically disabled people now have the opportunity to enjoy the kite sport on the water. This system uses a standard tube kite that is mounted on a fixed position in the middle of the boat.

Figure 2-7: The Catakite kitesailing system, source: MerVent [2010]

The layout of this system, when seen from the back, is shown schematically in Fig.2-8 in two situations. The top situation shows the catamaran in a steady horizontal sailing position. The moment that is created around the right hull depends on the kite force and the arm a. The lower picture shows the situation in case one hull is lifted out of the water. The arm a is now larger due to the shift of the center of pressure of the boat towards the right hull and the rotation of the boat. This creates a larger heeling moment on the boat in a situation where the boat is already tilted. In other words, when the boat starts to heel, the heeling moment only gets bigger. Therefore the design of this system is an instable configuration. From Hobiecat [2010] it is known that the mass of this boat is 146 kg including the mast, sails and the rest of all the rigging. This means that the mass of the boat with two people on board and the added system is approximately 280 kg. As is discussed in Section 3-4 a

Kitesailing 10 Existing kitesailing systems

Wind speed Kite force

a Waterline

Center of pressure of the boat

Wind speed Kite force

a

Waterline

Center of pressure of the boat

Figure 2-8: Schematic overview of the Catakite boat with the working line of the kite creating a moment with arm a around the center of pressure.

standard tube kite can handle a maximum pulling force of 1500 N before it starts to buckle. Taking the center of gravity of the boat on the middle of the front beam then the maximum kite force a cannot generate a moment large enough to flip the entire boat upside down. The influence of waves however play a very important role in this because in the situation of being in the surf, a boat can always flip over because of the breaking waves. However this system is mainly used on lakes and flat water. Also the kite can be depowered such that the kite force gets much smaller than 1500 N. Chapter 4 discusses this further in depth. If the kite forces get larger and the boat is sailed in big waves then at some point this system is not safe anymore. The system of Airplay Kitesailing takes the safety a step further. The basic philosophy behind the Airplay kitesailing systems is: ”Safety comes first. Performance comes second.” The second philosophy is that kitesailing is believed to be a team sport that should be enjoyed with friends. A catamaran type of boat is chosen for a number of reasons of which the most important ones are given. The first reason is that these types of boats are launched from the beach just like kite surfers do. A catamaran is also more stable in the surf compared to a monohull which adds to the safety. Also a catamaran offers a lot of space for the crew which is very useful for enjoying kitesailing with friends. The boat is a Hobie Tiger of 18 ft which is stripped of all sailing equipment that is not necessary for kitesailing. This means that everything that is used for the sail is stripped of the boat. A kite has a smaller heeling moment on the boat compared to a conventional sail. But still, it would generate a heeling moment that could flip the boat over. This can be dangerous and therefore a track is mounted on the boat to minimize the chance of flipping over. Figure 2-9 shows a schematic front view of the boat with the forces of the kite leading into the traveler on the side of the boat. In this figure the working line of the kite forces go through the center of pressure of the boat. In this way the kite does not impose a heeling

Kitesailing 2-1 Traction-based kitesailing 11 moment on the boat at all.

Wind speed Kite force

Waterline

Center of pressure of the boat Figure 2-9: Schematic overview of the boat with the working line of the kite forces going through the center of pressure

Figure 2-10 shows the track mounted on the front beam of the boat.

Figure 2-10: The track mounted on the front beam

The lines are all connected at the traveler that can slide freely over the track. Because the attachment point of the lines is now located on the side of the boat, the flyer also has to sit on the side of the boat when controlling the kite with a conventional bar system. This is shown on the left picture of Fig.2-11. The picture shows that the flyer can easily fall of the boat in such a position. Therefore the steering lines are extended such that the flyer can sit more in the center of the boat as is shown on the right picture.

Figure 2-11: The seating position of the flyer is moved towards the center of the boat

A close up of the flyer and the control system is shown in Fig.2-12. This is the system that was used during the 2008 season.

Kitesailing 12 Existing kitesailing systems

Figure 2-12: Close up of the position of the flyer with the Airplay kitesailing system of 2008

In 2009 the standard kite surf bar system was removed to ”clean up” the control system next to a range of minor adjustments. An other improvement was the second trampoline that was added to create more space on the boat and to allow easy access to every corner of the boat by the crew. Also the lines were extended from 25 meters to 40 meters to allow for larger crosswind patterns with the kite which increases the speed of the boat. The ”Round of Texel” was sailed during the 2009 season being the first to do so. The lap time was 4 hours and 45 minutes compared to the record of 2 hours and 7 minutes set by a conventional rigged high performance catamaran at the same day. This is a large difference and therefore the kitesailing system has to be evolved a lot further to close this gap. The pictures in Fig.2-13 show the Airplay team just after launch from the beach sailing towards the start of the lap around the island of Texel. The pictures in Fig.2-14 are taken just after completing it.

Figure 2-13: Beach start of the kitesailing catamaran, source: Texel Images [2009]

Figure 2-14: Scoring a victory by finishing the lap around Texel, source: Boot in Beeld [2009]

Kitesailing 2-1 Traction-based kitesailing 13

With a 13 m2 tube kite the top speed that has been recorded of 19 kts by GPS measurements in wind conditions of 23 kts. The maneuvers that can be performed with this kite are sharp turning and lifting half of the boat out of the water as is shown in Fig.2-15. It is now the goal to improve the overall speed and to start jumping.

Figure 2-15: A standard tube kite can lift half of the boat out of the water, source: Sailshoot [2008]

Kitesailing 14 Existing kitesailing systems

2-2 Electricity-based kitesailing

Indirect propulsion means first generating electrical power with the kite and then using this power to feed electrical engines that propel the boat. Two systems that use this kind of technique for the propulsion of a ship are the ”Laddermill ship project” developed at the TU Delft and the ”KiteNav project”. The TU Delft kite power demonstration system is a system that generates energy using one kite or more kites that are stacked. It consists of a ground station, lines with a control pod to steer the kite and the kite itself. The basic elements of the ground station are an electric motor that can also serve as an electric generator and a drum around which the line is stored. The kite pulls the line from the drum, spins up the generator and creates electrical energy that is stored into batteries or directly fed into the boat’s engines. When the line is wound of at maximum length it is retracted again with the kite in a depowered mode. This costs less energy than is generated in the up cycle and therefore net wind power is generated. A picture of this kite power system is shown in Fig.2-16.

Figure 2-16: TU Delft kite power demonstration system with the kite very close to the ground station

This system is being evolved and will be mounted on the ”Ecolution” in the spring of the year 2011. Figure 2-17 shows a picture of the Ecolution with its conventional sails mounted. The rear mast will be taken off and the ground station will take that place on the boat. The front mast is used for launching the kite. The KiteNav project works with a ground station based on the same principles with one major difference. Two lines are now used to steer the kite and both are wounded on a drum at the ground station. Figure 2-18 shows the ground station at an exhibition with these two

Kitesailing 2-2 Electricity-based kitesailing 15

Figure 2-17: Ecolution boat on which the Laddermill system will be built, source: Ecolution [2010] drums.

Figure 2-18: The ground station of the KiteNav project at the ”Uniamo Le Energie 2009” exhibition, source: KiteNav [2010]

This system has been successfully applied to a 38 ft yacht provided by Azimut-Benetti s.p.a. and was tested off the coast of Varazze in Italy. The kite was a 16 m2 tube kite and the boat weight is 12 tons. According to KiteNav [2010] the average boat speed was 3.2 kts in 6.5 kts of wind.

Kitesailing 16 Existing kitesailing systems

2-3 Objectives

For all the different kitesailing systems, including the electricity based systems that also offer a high potential for generating cheap and clean energy for the future, the same parameters for the system are important. It is the objective of this thesis to evolve the kite system such that it meets the needs better for kitesailing and energy production. The catamaran offers a platform on which the performance can be tested in a rough environment and in this way the huge power potential of kites can be demonstrated. It is also a good way to test the changes in the field without the need of electrical equipment such that the focus is strict on the kite itself. The objectives are to determine and to implement improvements from the research performed during this thesis on a new kite and to demonstrate the improvements during the ”‘Round of Texel”’ which is the biggest catamaran race in the world.

Kitesailing Chapter 3

Sailing system analysis

In the development of kitesailing it is one of the goals to increase the sailing speeds. Research is performed on the total system to determine what parameters of the kite influence the sailing speed most. The effect of the kite on the sailing performance can be described by three parameters: The surface area and the aerodynamic lift and drag coefficients of the kite. It is the objective of the following analysis to determine the sensitivity of the sailing speed of the boat with respect to these parameters. The maximum theoretical sailing speed is analyzed in Section 3-1. Section 3-2 determines the required surface area to reach the theoretical sailing speed. The present Hobie Tiger kitesailing system is analyzed in Section 3-3.

3-1 Maximum sailing speed

When moving at constant linear speed the external forces and moments acting on a sailing system need to be in equilibrium. Three types of external forces act on every sailing system. These are the aerodynamic and hydrodynamic forces and the gravitational forces. The gravi- tational forces act act opposite to the buoyancy forces and the kite forces that act in vertical direction. These forces are in equilibrium when the boat is translated in the horizontal plane. The basic forces that work on a sailing system viewed from the top are shown in Fig.3-1. This figure shows the lift and drag forces acting on a sailing system and their resulting forces. The resulting forces of the aerodynamic and hydrodynamic parts are in opposite direction and equal in magnitude when the sailing system moves at constant translational speed and therefore:

RH = RA (3-1)

The values for the aerodynamic and hydrodynamic glide angles ǫA and ǫH and the resulting total system glide angle βS are given by Eqs. (3-2), (3-3) and (3-4).

Kitesailing 18 Sailing system analysis

RA y

LA x ǫA

DA ǫA βS VS π γ ǫ βS H γ VW− DH VW VA γ βS

− VS

ǫH

LH RH Figure 3-1: Forces and wind velocities acting on a sailing system in a top view

DA ǫA = arctan (3-2) LA DH ǫH = arctan (3-3) LH βS = ǫA ǫH (3-4) + The relationship between the true wind velocity VW , the sailing speed VS and the apparent wind velocity VA is defined by the sailing velocity triangle also shown in Fig.3-1. The law of sines can be applied to determine the relation between the velocities which is the second basic analytic formula for the system:

VW VS VA = = (3-5) sin βS sin γ βS sin π γ

From Eq.3-5 teh following ratio can be derived:( − ) ( − )

VS sin γ βS = (3-6) VW sin βS ( − ) Using this equation the ratio of the sailing speed and true wind speed is plotted in Fig.3-2 as a function of the sailing course γ and the total system glide angle βS.

This figure shows that when βS increases then the maximum theoretical sailing speed ratio

VSmax VW increases on all sailing courses with the exception of sailing straight downwind.

Kitesailing~ 3-2 Maximum aerodynamic area 19

Direction of true wind 0

30 VS 30 Sailing VW course 1.5 γ [deg]

60 1 60

0.5

90 90 βS = 48 βS = 44 βS = 35 120 120

150 150 180

Figure 3-2: Polar plot of the ratio of the maximum theoretical sailing speed and true wind speed as a function of the sailing course and βS

3-2 Maximum aerodynamic area

To be able to reach these maximum speeds for given efficiencies of the system, the sail has to be large enough. If the sail area is too small then the maximum theoretical sailing speed cannot be reached. If the sail is too big then there can be no balance in the two resultant forces RA and RH which leads to a sailing course more downwind. Therefore, a maximum surface area can be determined. It is the first objective to determine the required sail area that is needed to reach the maximum theoretical sailing speed on all different sailing courses. The ship speed is calculated using Eq.(3-6) with βS given by Eq.(3-4). The lift of the boat is given by the lift formula:

1 2 LH CL,H ρH VH SH (3-7) = 2

The relation between the aerodynamic and the hydrodynamic lift is derived from Fig.3-1 using the fact that RA and RH are equal and is given by Eq.(3-8).

LH LA = sin (3-8) β βDA cos LA + The lift formula for the aerodynamic part rewritten for the surface area gives:

2LA SA = 2 (3-9) ρACL,AVA

Kitesailing 20 Sailing system analysis

in which the apparent wind VA is calculated as a function of VW using Eq.(3-5). Equation (3-9) is used to plot the required surface area for a range of courses in Fig.3-3. The used parameter values for the Hobie Tiger kitesailing catamaran are derived in Appendix B.

200

180 ] 2 160 m [ A

S 140

120

100

80

60

40 Required aerodynamic area

20

0 45 50 55 60 Sailing course γ [deg]

Figure 3-3: The required aerodynamic area that is needed to reach the maximum theoretical sailing speed as a function of the sailing course for the Hobie Tiger catamaran

This figure shows the trend that the required surface area to obtain the theoretical maximum sailing speed increases rapidly. When sailing straight downwind the required surface area goes to infinity. For an 18 ft catamaran the sail area is 21 m2. This is only enough for a course of 51○deg upwind. When sailing at larger angles the surface area is therefore too small.

3-3 Kitesailing system analysis

The effect of different parameters on the system is analyzed by deriving a fundamental equa- tion that describes a sailing system in general. The values of the used parameters for the aerodynamic part and the hydrodynamic part are derived in Appendix B. The effect of creating crosswind is not taken into account in this section.

The basic analytic formulas given by Eqs. (3-1) and (3-5) are applied together with the lift and drag formulas like Eq.(3-7) for both the aerodynamic and hydrodynamic parts of the system.

The drag coefficient of the boat CDH is calculated with:

C2 C C L (3-10) D = D0 πAe + Using this equation the lift coefficient of the boat CLH is calculated as a function of L DH .

Taking Eqs. (3-2), (3-3) and (3-4) to calculate the value for βS the equations are combined~ in the relation RH = RA. This gives the following expression for the required aerodynamic

Kitesailing 3-3 Kitesailing system analysis 21 surface area after rewriting it:

2 2 2 2 2 CLA CDA CLH CDH SH VS ρH S (3-11) A = ¼ C2 C2 ρ V 2 ( + LA)( DA+ A A)

When the sail area is increased the L/D( ratio+ also) increases because the aerodynamic areas of the boat, the lines and the sailors remain constant. This is also described in Vlugt [2009]. In the following analysis however this increase in aerodynamic efficiency due to a larger sail area is not taken into account.

This function is plotted for a range of sailing speed ratios VS VW and sailing courses γ. Figure 3-4 shows the plot for three different aerodynamic surface areas SA. The aerodynamic areas that are used in the calculations are the total areas consisting~ of the kite surface area and the other aerodynamic areas described in Appendix B.

150

180 [deg]

γ 150

13 120 25 50 Sailing course 90

60

30 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 VS VW

~ Figure 3-4: The speed ratio on a range of courses and three different kite areas

The effect of the lift and drag parameters is now investigated for the 13 m2 kite. Figure 3-5 shows the trends for different values of the aerodynamic lift coefficient of the total system. 2 The value CLA = 0.5 corresponds to the original 13 m kite on the Hobie Tiger catamaran. When the aerodynamic drag coefficient values of the system are varied the differences are smaller as is shown in Fig.3-6. The course upwind is now analyzed for the three different parameters. From GPS measure- ments it is known that with the original 13 m2 kite this course is 60 deg upwind and therefore this course is analyzed. Table 3-1 shows that on the upwind course of 60 deg, the lift coefficient gives by far the greatest improvement in speed. When looking at Fig.3-5 it also shows big increases in sailing speed on all the sailing courses. Doubling the surface area increases the sailing speed by almost 30% which is also a great improvement. Figure 3-4 shows that also on the downwind courses the surface area increases the sailing speed a lot. Decreasing the drag coefficient of the kite with 50% does not do so much for the sailing speed, only 12% increase. To make matters worse, on downwind courses the drag of the kite actually increases the sailing speed.

Kitesailing 22 Sailing system analysis

150

180 [deg]

γ 150

120 0.3 0.5 0.7 0.9 Sailing course 90

60

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 VS VW

~ Figure 3-5: The speed ratio on a range of courses and four different aerodynamic lift coefficients for the system with a 13 m2 kite

150

180 [deg]

γ 150

120 Sailing course 90

60

0.25 0.2 0.15 0.1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 VS VW

~ Figure 3-6: The speed ratio on a range of courses and four different aerodynamic drag coefficients for the system with a 13 m2 kite

Table 3-1: Comparing the change in sailing speed at γ = 60 deg for a factor 2 in increase of sailing area and lift coefficient and a factor 0.5 in drag coefficient compared to the original situation using 2 a 13 m kite. The original speed ratio is given by VS~VW = 0.15

VS VW new Change in % S 0.19 27 A ~ CL,A 0.24 60 CD,A 0.164 12

Conclusion:

From this analysis it follows that the focus should be on increasing the lift of the kite by either increasing the lift coefficient or the surface area for effectively improving the overall performance of the sailing system. The sensitivity of the lift coefficient CL,A is twice as high

Kitesailing 3-4 Requirements for improved traction kitesailing system 23

as for the surface area SA. However the surface area can be increased considerably more than the lift coefficient which is further discussed in the following chapters. Therefore the increase in surface area is the most promising way to effectively increase the sailing speed.

3-4 Requirements for improved traction kitesailing system

The strong points of kitesailing are a higher possible sailing speed and the possibility of extreme maneuvers. Therefore these two areas are the ones that should be focused on during the development of the sport. Next to this, when the performance increases also the safety mechanisms should improve with it. With the use of a standard tube kite of 13 m2 the safety is already good when using the applied rail system. The global goal for this research is to develop a sailing system that provides faster sailing and the possibility to start jumping with the boat while increasing the safety. Areas that can be improved on a kite are:

Increased safety

● Larger pulling force

● Higher Lift/Drag ratio

● 3-4-1 Increased safety

Safety is the most important issue in the development of the sport. Being able to shift the attachment point of all the lines from one side of the boat to the other decreases the heeling moment and already adds a lot of safety. The bow kite is the type of tube kite that offers most depower and is therefore used for kitesailing. Using this type of tube kite makes sure that kitesailing is already safe when using a small kite. However, when such a kite crashes on the water and relaunches in the middle of the wind window it will still generate a lot of pulling force. The worst case scenario is worked out to determine what the kite force can be before the boat flips over. It is important to bear in mind that a boat with no kite or sail at all can easily flip over if a braking wave enters on the side of the boat. Adding a kite or sail only adds to the possibility of flipping over in general. The most dangerous situation experienced during kitesailing is shown in Fig.3-7. In this figure the boat is put in an ”ideal” position to flip over by being tilted by a wave. It is possible to fix the traveler on one position. Therefore in the worst case the traveler is fixed on the high side of the boat.

In this case the boat is already at an angle of 45 deg with respect to the horizontal. Fg is the gravitational force assumed to be in the middle of the boat. The values a and b are the arms of the forces that create the two moments. The boat width is 2.5 meters which makes c = 79 cm by using Pythagoras. The arm of the gravitational force is assumed to be at 2 3 of this distance which makes b = 0.5 m η η ○ η Two values for that are most critical~ in this situation are = 0 deg and the value for between 40 45○deg where the force of the kite has the largest arm for creating a heeling

− Kitesailing 24 Sailing system analysis

Wind speed Fkite η a

Waterline Fg Center of pressure of the boat b Figure 3-7: Schematic overview of a critical situation, of a tilted boat due to a wave, experienced during kitesailing

○ moment. In the case of η = 0 deg the kite is located in the middle of the wind window after it has crashed on the water. The worst case in this situation is that the kite launches through the middle of wind window creating lots of force due to its crosswind speed. With a boat width of 2.50 meters and taking into account the end stops at the rail the value of a = 2 m is ○ assumed. For the case that η = 0 deg a becomes 1.6 m. The correcting moment that is created by the gravitational force is given by 0.5m g. The 2 3 mass is taken to be 300 kg and g = 9.81 m s . This makes the moment equal to 1, 5 10 Nm. ⋅ The allowable kite forces that are now calculated~ are derived from the static situation.⋅ In reality the boat can be in a dynamic situation. For example, the boat is tilted by a wave and therefore has a rotational velocity around the center of pressure. To prevent the boat from flipping over, first this rotational velocity has to be counteracted. This can not be done by the kite and has to be performed by the crew by positioning their mass (jumping!) to the high side of the boat. Therefore, when looking at the kite, only the static situation is taken into account. The allowable kite force when η = 40 45 deg is now calculated by:

− 3 1, 5 10 3 0.75 10 N (3-12) 2 = ⋅ ○ ⋅ The allowable kite force when η = 0 deg is given by:

3 1, 5 10 3 0.94 10 N (3-13) 1.6 = ⋅ Like earlier noted, from Loyd [1980] it is known that⋅ a kite can generate a flight speed of the L/D ratio of the kite multiplied by the true wind speed in the center of the wind window. From Vlugt [2009] it is known that a tube kite has a L/D ratio of 5.5. Taking into account that that the Lift and Drag depend linearly on V 2 this means that due to the crosswind speed a kite can generate 30 times more pulling force compared to the steady position on the edge of the wind window. With respect to the two described situations above it is clear that the ○ situation of the kite being in the center of the wind window with η = 0 deg is far more critical for safety than the situation of a more steady kite high up in the air.

Kitesailing 3-4 Requirements for improved traction kitesailing system 25

A safety factor of 2 is added for the basic requirement because the calculated maximum force barely prevents the boat from flipping over. The basic requirement for safety becomes: ”‘The kite is not allowed to generate more than 450 N in the center of the wind window while it is fully depowered for an 18 ft catamaran”’. If a lower maximum force of the kite in the critical situation is achieved there is room to improve the performance of the kite in terms of scaling or a higher L/D ratio until the limit of 450 N is reached. If there is the possibility of zero lift on any position in the wind window then the kite cannot create crosswind speed which would basically eliminate the danger that comes with a higher L/D ratio. The best achievable depower for a given kite is creating zero lift which also minimizes the drag. In this case the zero-lift drag becomes the measure that determines if a kite is safe for kitesailing. The second requirement for increasing the safety is: Create the possibility of zero lift on every position in the wind window.

3-4-2 Larger pulling force

Section 3-3 shows that creating a larger pulling force is the best way of increasing the sailing speed. The most promising way of achieving this is by increasing the aerodynamic surface area SA. However there are limits to the surface area that can be applied to a given boat. Force measurements performed during kitesailing with load cells on the lines have shown that the pulling forces for a kite surfer are roughly the same as the weight of the surfer. The boat with two people on it weigh around 300 kg. Therefore, 3000 N is the amount of force that the kite should be able to generate without buckling. A problem when using normal tube kites for kitesailing is that the loads on the kite are much higher compared to kitesurfing such that the leading edge starts to buckle. Figure 3-8 shows a kite with a buckled leading edge. This causes a complete loss of steering control of the kite which can only by solved by depowering the kite completely until the shape is right again. This reduces the speed of the boat, it can create dangerous situations and it is annoying for the crew. Therefore this has to be solved.

Figure 3-8: The leading edge of a tube kite buckles under high loads

To be able to generate a larger pulling force of the kite can be made bigger. But this scaling cannot be to drastic because all the power has to be controlled by the flyer. If the control forces get too big the flyer can not control the kite anymore and dangerous situations can occur.

Kitesailing 26 Sailing system analysis

The sport must evolve in steps because all the separate parts in the system influence each other. For example, a bigger kite needs a larger steering excitation and turns slower which influences the way of sailing. With a 13 m2 tube kite half of the boat could be pulled out of the water as is shown in Chapter 2. Therefore the 13m kite can pull 1500 N before it starts to buckle. Doubling the maximum pulling force will lead to the possibility of lifting the boat completely out of the water. Therefore, as a first step in evolving a standard tube kite, an increase in maximum pulling force of 100% is desired. Because the kite should not buckle at this load such as the 13 m2 kite does at 1500 N it is desired to increase the buckling resistance by 100% to be sure. This means that the scaled kite must be able to handle twice the aerodynamic load per square meter without buckling compared to the original kite. It is clear that a larger kite that can generate a larger pulling force is also potentially more dangerous than a smaller one.

3-4-3 Impact of L/D ratio on sailing

The L/D ratio has a big impact on every sailing boat for sailing upwind. Conventional sailing boats are able to sail sharper into the wind which is a disadvantage for a kitesailing boat. It is desired that this is improved. Section 3-3 shows that this factor improves the sailing speed best if the lift is increased instead of a lowered drag.

3-4-4 Summing up the requirements

The basis of the kite will be an existing design for a minimum effort in designing and to decrease the chance of making design errors. It is also required that the same materials are used as in other tube kites such that the kite can be repaired easily and to prevent introducing unexpected problems that can arise with the use of new materials. Also in this way the costs can be kept as low as possible. The kite will be a tube kite with a bridled leading edge. The requirements are:

1. The kite is not allowed to generate more than 450 N in the center of the wind window while it is fully depowered for an 18 ft catamaran

2. The kite must have the possibility of creating zero lift on every position in the wind window.

3. The kite should be able to handle pulling forces of at least 3000 N.

4. The scaled kite must be able to handle twice the aerodynamic load per square meter without buckling compared to the original kite.

5. The L/D ratio of the kite should be as high as possible for sailing upwind.

Kitesailing 3-4 Requirements for improved traction kitesailing system 27

3-4-5 Thesis goal

The goal of this thesis is to determine what parameters should be focused on to effectively increase the performance of kitesailing and to design, produce and test a new kitesailing system that meets these requirements.

Kitesailing 28 Sailing system analysis

Kitesailing Chapter 4

Depower system design

The capability to depower is an important safety feature for towing kites. Especially for kites with a large surface area it is a mandatory requirement to be able to quickly adjust the lift force of the kite. The state of maximum depower is reached when the aerodynamic lift is zero. This state is also called flagging because the kite will start flapping in the wind. In this case the kite will fall down which is needed for example in an emergency when the kite is launched from the beach. To fulfill the safety requirements on the kitesailing system stated in Section 3-4, it must be ensured that (a) the kite can be depowered to zero lift in every position in the wind window and (b) that the maximum pulling force is 450 N when fully depowered. To be able to systematically design a kite system that meets these requirements the design factors influencing the depower characteristics of a kite are identified in Section 4-1. An analysis and design program is written for creating more depower on a tube kite. For this the kite model is explained first in Section 4-2 then the design strategy is shown in Section 4-3. The program itself is explained in Section 4-4. The designs and first tests on the general shape of the kites is discussed in Section 4-5 together with the force measurements performed on the different designs. Section 4-6 shows the conclusions on this chapter.

4-1 Functional analysis

The goal of this analysis is to define the design parameters that influence the depower capa- bility of a kite and to determine the objective. Four design parameters are key to the amount of depower. First, the pitch behavior of the airfoil is considered. Then, the position of the power line attachment point is discussed. The third subsection investigates two basic bridles that are used on tube kites. Subsection 4 discusses the influence of the shape of the leading edge on the bridle design is discussed. The bar travel is discussed in Section 4-1-5. Finally the objective of the further analysis is outlined.

Kitesailing 30 Depower system design

4-1-1 Pitch behavior

The basic aerodynamic properties of an airfoil can be described by the CL α curve which quantifies the dependency of the aerodynamic lift on the angle of attack. The general shape of such a plot is shown in Fig.4-1. −

CL CL

0 α 0 CD

Figure 4-1: Lift cefficient as fuction of angle of attack (left) and lift coefficient as function of drag coefficient (right), source: Eppler [1990]

These curves show that the lift coefficient decreases with the angle of attack which results in a lower drag and resulting cable tension. The maximum lift coefficient is reached at the point where the airfoil ”stalls”.

When the angle of attack is lowered, the L/D ratio also gets lower because CL CD gets lower. In the equilibrium position of an airfoil this results in a lower elevation angle between the horizontal plane and the tether which is shown in Fig.4-2. ~

L

D VW α

η

Figure 4-2: Schematic side view of a tethered airfoil

The elevation angle is zero in the case of zero lift when tether force and drag force are aligned. The kite is approximated as a 2D airfoil with the power lines and steering lines approximated as a straight line. Although a kite has a cambered airfoil which has a positive lift coefficient

Kitesailing 4-1 Functional analysis 31 known from John D. Anderson [2001] it starts flapping at very low angles of attack which results in zero lift. This is a structural aero-elastic behavior due to the flexibility of the kite. Conclusion: The tether force is minimum when the angle of attack is zero. Also the elevation angle gets lower if the the angle of attack decreases.

4-1-2 Attachment of power lines

The attachment point of the tether influences the magnitude and direction of the resulting moment acting on the airfoil. The left figure in Fig.4-3 shows a positive pitching moment resulting from the tether force which decreases the angle of attack. On the right the tether force increases the angle of attack. L L

D D VW MR MR

T T Figure 4-3: Effect of tether attachment: pitching down (left), pitching up (right)

This shows that as long as the attachment point of the tether is located in front of the aerodynamic center the angle of attack can be lowered.

4-1-3 Examples of bridles currently used for tube kites

C-shaped kites generally do not have a bridle because it is not necessary for the structural integrity of the structure. The tip is the position where the power lines are attached to the kite. Figure 4-4 shows a side view of a C-shape kite and a Bow kite indicating the positions of the power line and steering line. The black areas represent the leading edge of the kites. The dotted lines show the direction and position in which the tether forces of the power lines work with respect to the aerodynamic center. This is the working-line of the tether forces. When the C-shape kite is depowered (shown in red), the working-line of the power line already goes through the aerodynamic center after a small rotation in pitch of the kite. The small rotation is the reason that a C-shaped kite does not have much depower. The bow kite resulted from the development of the C-shape kite and had two main advantages. First it has a larger projected area and second it has more depower capability. The projected area is left for discussion in Chapter 6. The depower increased because the position of the attachment points of the power lines was moved to the front of the kite. As a result the working-line of the power lines moves further in front of the aerodynamic center. This allows larger rotations in pitch of the kite before the working line of the power lines goes through the aerodynamic center. The bow kite introduced a bridle system to the tube kites. The bridle is an integral component of a kite with the function to transmit the aerodynamic forces on the flexible (inflatable) membrane structure of the kite to the tether. The two tasks are:

Kitesailing 32 Depower system design

C-shape Bow kite

Wind direction a.c. a.c.

Figure 4-4: A C-shape kite and a Bow kite seen from the side with the working line in front of the aerodynamic center

1 Support the kite such that it has its design shape during flight, especially in high load conditions

2 Have the capability of rotational freedom while supporting all the bridle attachment points on the kite such that the kite can depower

The bridle of a bow-kite can have many different forms. The Ozone Sport II 5 m2 kite has only knots that fix the geometry of the bridle. Other types have a pulley at the location where the power line is attached to the bridle and others have a pulley on every intersection. Cabrinha was the first kite brand to introduce a bridle with a pulley on every intersection on the Crossbow kite in 2006. This kite is still evolved every year and is one of the tube kites with the most depower. Almost every brand has a kite of this type in its product range that all work with the same principles but are categorized due to minor variations. Next to the Bow kite there are the Hybrid kite, Delta C-Shape kite, Sigma kite, SLE kite. The amount of depower that these kites have is discussed in Subsection 4-5-2.

4-1-4 Leading edge geometry

When the view of the observer is now fixed to the kite during a change in angle of attack, the bridle and tether rotate around the kite. The maximum elevation angle for a tube kite is 80 deg which corresponds to a maximum L/D ratio of 5.5 obtained from Vlugt [2009]. To be able to have the possibility of zero lift on every position in the wind window the bridle has to be able to rotate 80 deg around the leading edge. This is needed at a position with a low elevation angle where the largest rotation in pitch is needed for zero lift. The curvature of the leading edge of the kite has a significant influence on the bridle design which is shown in the following two examples. When the kite leading edge is straight, the bridle can always rotate freely around its attachment points on the kite as is shown in Fig.4-5. In this case the red bridle segment a b in the original situation keep the same values for a

Kitesailing − 4-1 Functional analysis 33

Knot a′ b′

a b

y

z x Wind direction

Figure 4-5: Rotation of a bridle around a straight leading edge and b during the rotation of the bridle to position with lengths a′ b′. The connection with the blue power line can simply be fixed by using a knot. − For a curved leading edge, a change in angle of attack affects the bridle geometry. A bridle element consists of one line (red) that is attached to the leading edge at both ends. Along this line, a pulley can travel freely. The pulley axis is attached to a power line (blue) which is leading to the ground. When the kite is depowered part a is becoming longer and part b is becoming shorter. This is shown in Fig.4-6.

′ b b Pulley a′ a

y

z x Wind direction

Figure 4-6: The pulley travels over the red bridle line a − b when the angle of attack is changed

This shows that the curved leading edge makes it necessary to use a pulley on the connection point of a power line with a bridle line. A consequence of using pulleys is that the forces in line part a are the same as in part b. This is a constraint when designing the bridle layout.

4-1-5 Bar travel

The pitch rotation of a kite is regulated by the kite flyer. The bar by which the kite is steered is also used to control the angle of attack of the kite. When the kite is depowered, the bar is moved towards the kite. The distance that the bar can move (bar travel) should be such that the rotation in pitch of the kite is not limited by the amount of possible bar travel.

Kitesailing 34 Depower system design

4-1-6 Objective

It is the objective to design a new bridle that supports the kite such that it has its design shape during high load conditions and such that it has the capability of at least 80 deg rotational freedom at low elevation angles while supporting all the bridle attachment points on the kite.

4-2 Model definition

The kite is a segmented inflatable structure. To model the kite the leading edge tube is approximated as a set of rigid beam elements connected with rotational joints. The bridle lines are positioned on the edges of every segment. The layout of the kite is copied from an existing kite. For existing kites the curvature of the leading edge is designed using tapered sections sewn to each other under an angle of several degrees sometimes with multiple sections between bridle points. Because the angles are small it is assumed that this does not influence the transfer of forces through the tube sections. Figure 4-7 shows this assumption schematically.

Simplification of real situation: Assumed situation:

MA MA

FA FA

FA FA Figure 4-7: The bending moments due to axial forces are neglected in the model

The entire leading edge of every tube kite is designed such that it does not buckle under the aerodynamic load. However with certain bridle designs the bending moments on the structure can increase above the structural limit. For one specific bridle design discussed in Section 4-5 a compression element was added to increase the bending stiffness of a tube section. Figure 4-8 illustrates the internal and external forces on a representative leading edge tube element.

The external load qα represents the aerodynamic load integrated over the chord length. The internal forces are the forces applied by the interaction of the membrane tube sections and the forces exerted by the bridle lines. These force vectors can be combined and decomposed into axial forces Fa and lateral forces Fl. This is the starting point for designing a new bridle which is further explained in Section 4-4. The model uses a body fixed reference frame. The distance between bridle points is called the ”Bridle point pitch” or, Pbridle. Because the wing tips are free ends of the structure it is assumed that they are not influenced by the axial forces going through the segment next to it on the inner side of the kite. Therefore the axial forces on a segment only influence the segments next to it towards the center of the kite. During the analysis of the kite and designing the bridle a quasi-static situation is assumed. The shape of the kite and the resulting distribution of forces on the bridle points has to be determined and serves as input for the program. One way of obtaining this relation is using a multi body analysis described by Breukels & Ockels [2010]. Using measurements described by

Kitesailing 4-2 Model definition 35

qα

Fl1

Fb2 Fb1 Fl2

Leading edge sections

q M α Fa M Bridle lines Fa yb Fl Fl P xb bridle Figure 4-8: Internal and external forces that act on a leading edge segment

Wachter [2008] like laser scanning and photogrammetry coupled with load cell measurements is a second possibility. With these methods the 3D shape of the kite can be determined. These methods do require considerable preparation time and resources. A much simpler method that can be compared to photogrammetry is by using only one camera to make pictures of the front of the kite during flight. They are taken during crosswind sweeps of a 5 m2 kite where the kite is highly loaded with 800-1000 N on average which is obtained from Vlugt [2009]. This gives the layout in the x y plane. For the positions in z-direction a picture is taken from the kite on the ground shown in Fig.4-9. −

z

Figure 4-9: Picture used to determine the z-positions of the bridle points

From the research performed by Wachter [2008] it is known that for a Flysurfer foil kite the shortening of the chord length is 5% maximum. Tube kites have struts that resist this shortening of the chord length therefore it is expected that the difference in chord length is less than 5% for a tube kite. Because these deflections are so small it is assumed that the deflection due to the flexibility of the kite does not change the positions of the bridle points

Kitesailing 36 Depower system design in z-direction. The flexibility of the kite is taken into account by applying rotational joints between the tube sections. From own experience in flying the kite it is known that these points in general start bending before the segments between the bridle points do. Because the leading edge is flexible it is crucial that the aerodynamic forces are in balance with all the internal forces. One of the requirements is that all the connection points in the bridle have a pulley such that these points can move. It is assumed that the friction of the pulleys does not influence the total amount of depower of the kite but only the velocity at which the kite can depower. This is not considered during this research.

4-3 Design strategy

The bridle design software is implemented in Excel. This tool is chosen above other programs such as Matlab because it can graphically show results in drawings next to the code. In this way the results during the design process can steer the next steps in designing the bridle. Also the computing power of programs such as Matlab is not needed because all calculations use simple vector and goniometric equations. First, a design for a small Ozone Sport 5 m2 kite is produced and tested to validate the program. After the validation of the program it is used to design a new bridle for the 25 m2 kite. The kites that are used already have their bridle points fixed on their leading edge which are therefore constraints for the designs. The location of these points is not changed for the new designs which creates the possibility to design new bridles for all existing tube kites.

Objective Build a bridle design program as a tool to design a bridle for a given kite that gives the same shape of the kite during flight and at the same time increases the depower of the kite compared to the bridle originally present on the kite. The general layout of the program is shown in Fig.4-10.

Geometric input The input for the program is the geometry of the leading edge of the kite in 3D with the location of the bridle points and the complete original bridle layout. The input data is determined from pictures of the kite in flight in high load conditions. Using the surface modeling software Rhino 3D, all the line lengths and angles with respect to the x- and y-axes of the kite are determined. The bridle point positions on the z-axis are input for the design program. The definitions for the leading edge sections bridle points and knots are given in Fig.4-11. This layout applies to an Ozone Sport 5 m2 kite.

Bridle analysis In this part the original bridle is analyzed and the forces that are needed on the bridle points to keep the leading edge in shape during flight are determined. These forces are the input for the bridle design part of the program. This program is further explained in subsection 4-4-1.

Kitesailing 4-3 Design strategy 37

Input: Output:

Geometry Bridle force Axial forces in x-y plane analysis leading edge

Bridle point forces Bridle forces decomposed

Geometry Bridle design y-z plane 3D bridle layout

Production lengths

Figure 4-10: Schematic diagram of the general layout of the analysis and design program

L1 L2 Bridle point 0

L3 Knot 4

Knot 3 L4

Knot 2 Bridle point 4

Knot 1

Figure 4-11: Definitions for leading edge sections, bridle points and bridle knots

Bridle design This is the part where the designer first determines the general desired shape of the bridle. The output of the program is the bridle layout including the forces as a percentage of the total forces in the leading edge and bridle elements. Also the length of the bridle lines that have to be produced are given. Subsection 4-4-2 explains this program in further detail.

Output The output of the bridle design consists of the axial forces in all the leading edge tube elements together with the forces in all the bridle lines. The geometric output consists of the schematic bridle layout in 3D together with the lengths of all bridle lines that have to be produced. Lengths of pigtails, losses in lines length due to knots and lengths of pulleys are all included to determine the line lengths as accurate as possible.

Kitesailing 38 Depower system design

4-4 Program details

The analysis and design program are now separately discussed in more detail.

4-4-1 Bridle force analysis

The objective of this program is to determine the discrete forces on the bridle points that counteract the aerodynamic force distribution and for which no axial forces are present in the tube elements of the leading edge. Two different methods have been used to determine the discrete forces on the bridle points. The first method is an aerodynamic method using an assumption of the aerodynamic force distribution on the kite. The second is a reverse engineering method that uses the bridle layout of the original bridle.

Aerodynamic force based method Breukels [2010] determined an aerodynamic load distri- bution on a Slingshot 16 m2 C-shaped tube kite. This load distribution is approximated by an ellipse with semi-mayor axis b and semi-minor axis a. Although this is a different shape compared to the used kites in this research it is the only aerodynamic distribution known at this point and therefore this is applied. The values for these numbers are a = 2.5 and b = 0.6. Figure 4-12 shows this schematically.

y q x ( ) a

x b Leading edge laid out on horizontal plane L1 L2 L3 L4

Figure 4-12: Assumed lift distribution on the kite laid out on the horizontal plane, source: Breukels [2010]

One segment is shown in Fig.4-13.

R

q x

( )

x

F1 F2 y x Figure 4-13: Aerodynamic and reaction forces acting on an arbitrary tube element

Kitesailing 4-4 Program details 39

The resultant force R that acts on a tube segment is calculated by integrating the distributed load over the length of the tube element:

R = S q dx (4-1)

As is described by meriam & Kraige [1998], this resultant R is located at the centroid of the area under consideration. The x-coordinate of this centroid is found by the principle of moments R x = ∫ x qdx, or:

⋅ ⋅ x q dx x ∫ (4-2) = R The forces that support the tube on either side are calculated by:

x F1 = R 1 (4-3) li (x − ) F2 = R (4-4) li

Geometric based method With this method the program performs the following operations:

Calculate forces on bridle points

● Decompose forces on bridle points in axial and lateral components

● Take influence of axial forces on previous tube element into account

● The input for this program is the set of angles α, β and γ shown in Fig.4-14 together with the positions of all the bridle knots and bridle points on the leading edge. Calculate forces on bridle points: First the bridle forces are determined using the original bridle layout. Figure 4-14 shows the forces on Knot 1 with the definitions that are used.

On the first knot, force FA is the tether force which is taken to be 100%. Forces on all other knots are calculated as a fraction of this force using basic goniometric relations. Equilibrium in the x- and y-direction gives the following set of equations which is solved for FB and FC :

cos α FA = sin β FB sin γ FC (4-5) sin α FA cos β FB cos γ FC (4-6) ( ) = ( ) + ( ) ( ) − ( ) + ( ) The forces FB are equal to the forces on the bridle points. Decompose forces on bridle points in axial and lateral components: The second step is decomposing the bridle point forces into an axial and a lateral component. This step is also visualized on the bottom right in Fig.4-8.

Kitesailing 40 Depower system design

y FB

FG

β γ x

Bridle knot

FA

α

Figure 4-14: Difinitions of forces and angles on a bridle knot

Take influence of axial forces on previous tube element into account:

The axial forces in the tube elements are shown in Fig.4-8 by FL1 and FL2 . The axial force present in leading edge segment 4 L4, which is also working on leading edge segment 3 L3, is decomposed into an axial and lateral component acting on bridle point 3. This gives the total axial and lateral force in leading edge segment 3 L3. The same procedure is applied for leading edge sections L2 and L1. The set of discrete forces in lateral direction are the forces that counteract the aerodynamic load. This set is the output of the program.

The two methods compared The outcome of these two methods shows quite different results. Fig.4-15 shows the forces as a percentage of the sum of the shown forces. The results from the aerodynamic method are shown on the left, from the geometric method on the right. For clarity only the forces on one side and the center of the kite are shown. The discrete forces on the right side are symmetrical with the left side.

27 28

26 22

25 22

16 13

6 15

Figure 4-15: Comparison of calculated force distribution of the two methods, left: Aerodynamic force based method, right: Geometric based method

This figure shows that the calculated forces at the tip region indicated by the black dotted line, are lower using the aerodynamic method compared to the geometric method. The region indicated by the green shows the opposite.

Kitesailing 4-4 Program details 41

To validate these two methods designs have been produced and tested using both distributions on the Ozone Sport II 5 m2 kite. As is shown in Section 4-5, it turned out that the forces on the tips were greater than the calculated forces using the aerodynamic method. This was shown by the tips moving outwards during flight. The designs using the geometric method all showed a very good shape of the kite during flight. One reason for the high force on the bridle point at the outer tip is the curvature of the leading edge in z-direction. Because of this, the bridle points are not located on one line in the y-z plane. Figure 4-16 shows the stresses in the x-y direction σxy on the left figure in red and the stresses in y-z direction σyz in blue. A general possible distribution of the resulting stresses is shown in the right figure.

y σxy σcanopy σyz x z

Bridle point 3

Bridle point 4

Pig tail steering line

Figure 4-16: Schematic representation of distributions of canopy stresses, in x-y and y-z direction on the left and resulting stresses on the right

The right figure shows that the stresses of a large area of the canopy are directed towards bridle point 4. This area is also shown by the dotted green line on the left figure. Only the stresses in small areas go to the other bridle points. Due to the large area with possibly lower stresses compared to the smaller areas to the front of the kite, the total force that is generated at bridle point 4 is larger than one would expect from the aerodynamic load distribution alone. The exact stress distribution is unknown but this is a possible explanation for the high force at the tip. Because of the better agreement with test data, the reverse engineering method is used for the bridle design of the 25 m2 kite.

4-4-2 Bridle design

The design program consists of the following parts:

Force rotation

● User interface

● Line length determination

● Kitesailing 42 Depower system design

Force rotation The input for this program is the set of discrete forces determined by the analysis program. The first part of the program also gets input from the last part of it, the ”Design interface” where the discrete forces are rotated to get to a final design. Figure 4-17 shows the definitions that are used here.

Tip area of the kite Center area of the kite

αle

Fa y

γf x Fr Ftot Figure 4-17: Rotation of a force creates an axial force in a tube element

When the lateral force Fl is rotated with an angle γf an axial force is introduced in the tube element together with a total force Ftot. This axial force influences the forces on the tube elements towards the center of the kite. Figure 4-18 shows how a rotation of the lateral force in bridle point 4 Fl4 creates an accompanying axial force Fa4 working on bridle point 3. This force is decomposed into the components δFa3 and δFl3 .

Tip area of the kite Center area of the kite

Bridle point 3

δFa3

δFl3 Fa4

Bridle point 4 y

Fa4 γ4 Fl4 x

Ftot4

Figure 4-18: An axial force in tube element 4 creates a lateral and an axial force in element 3

The new lateral force on bridle point 3 Fl3 that is needed as a bridle line force equals the original lateral force according to the input from the analysis program minus δFl3 . These calculations are done for every bridle point by the program and for all axial forces in the tube elements.

Kitesailing 4-5 Test results 43

User interface The general layout that is desired by the designer is implemented at this point and pairs of forces are coupled based on their position on the kite and on their magnitude. The forces are rotated by the user to get the basic design layout. When two forces are equal in magnitude they can be coupled and produced as one single bridle line. Figure 4-19 shows how the lateral forces in bridle points 3 and 4 are rotated with γ3 and γ4. The bridle lines resulting from these forces intersect in point P . This is the location of a pulley on this bridle line.

Tip area of the kite Center area of the kite

Bridle point 3

Fa3

Fl3

Ftot3 γ3 Bridle point 4 y

Fa4 Fl4

F γ4 tot4 x

P

Figure 4-19: Rotation of two forces with γ3 and γ4 creates equal magnitudes and an intersection for the pulley position P

This routine is performed for all forces acting on the bridle points and throughout the rest of the bridle. The program is made such that the force on bridle point 4 is rotated by the user with γ4 then γ3 is determined by an iteration loop such that force Ftot3 equals Ftot4 in magnitude. First this is performed for the 2D situation. The same routine is performed in the y-z plane such that a final design in 3D is obtained. Some remarks on basic design choices are discussed in Subsection 4-5-3.

Line length determination When all the forces are connected and equal in magnitude the line lengths of all bridle sections are given by the program.

4-5 Test results

The primary function of a bridle is to support the kite such that it assumes the design shape under aerodynamic load. Depower capability is a secondary requirement for a kite. These two aspects are considered separately.

Kitesailing 44 Depower system design

4-5-1 Kite shape

Three different designs have been made using the bridle analysis and design program for the 5 m2 kite to validate the program. Then a design for the 25 m2 kite has been made, produced and tested. Table 4-1 shows the analysis methods that have been used for the different designs.

Table 4-1: The used analysis methods used for the different bridle designs on the 5 m2 kite

Analysis method: 5 m2 Design 1 Aerodynamic 5 m2 Design 2A Aerodynamic 5 m2 Design 2B Aerodynamic 5 m2 Design 3 Geometric

The general shape of the kite with the different bridles has to be compared with the original bridled kite. To be able to do this, pictures have been taken from the front of the kite in a powered setting in high load conditions during crosswind sweeps. The pictures that show the kite best in the x-y plane have been used to compare the shapes.

5 m2 kite, design 1 The design schematically shown in Fig.4-20 shows great ability to depower. During a test the kite could be instantly depowered on any position in the wind window. The disadvantage of this design is that during flight the tips move far outwards which creates a large amount of drag.

Figure 4-20: The first bridle design using a pulley on every intersection

The shape of the kite with its original bridle is shown on the left in Fig.4-21. This is the target shape to be realized with the new bridle. The shape during flight using this adapted bridle design is shown on the right picture in Fig.4-21. The difference in shape using the new and the original bridle is clearly visible. The tips are pulling the center of the kite downwards due to the difference in pulling force between the bridle lines on the tip and the center. Because of this the tips have a very large angle of attack of approximately 45○deg and the center has an angle of attack of approximately 0○deg. These numbers were not measured but simply determined by looking at the kite and are therefore not accurate.

5 m2 kite, design 2a In an effort to counteract the tips going outward the bridle was designed with a 20% larger pulling force on the center compared to the tip region. This 20% is

Kitesailing 4-5 Test results 45

Figure 4-21: The shape of the 5 m2 kite with its original bridle left and the first new bridle on the right determined from the kite and bridle layout of the right picture in Fig.4-21. According to the program this shape was possible if the forces of the center part of the kite were assumed to be 20% higher than the forces from the tip area. Figure 4-22 shows the design of the bridle.

Figure 4-22: Schematic outline of the second bridle design, version A on the left and B on the right

The shape of the kite during flight using this bridle is shown in Fig.4-23. It shows that the kite was still out of shape with the tips moving outwards and the center of the kite downwards.

Figure 4-23: The shape of the kite during flight with the second bridle design applied

A detail of the bridle is shown in Fig.4-24 and shows a pulley that is used to equal the forces on both sides. This type of construction is also used later on for other bridle designs.

5 m2 kite, design 2b To prevent the tips from being able to move outwards a horizontal line was added between the lowest bridle points on the tips. This modification is shown by the

Kitesailing 46 Depower system design

Figure 4-24: A pulley is used to enable the coupling of two forces that differ a factor two in force

dotted line on the right in Fig.4-22. Subsequent tests revealed significantly reduced flexibility in the tips as a result of this horizontal line. The kite has a very stable shape also during high load conditions. The steering is not noticeably influenced by this horizontal line.

Figure 4-25: A horizontal between the tips gives a good shape during flight

5 m2 kite, design 3 For this design the method of reverse engineering of the original bridle was used to determine the discrete forces on the bridle points. Figure 4-26 shows the third bridle design. The bridle point on the tip is now also supported and the bridle line coming from this point is rotated such that on average 20% of the pulling force of one power line is axial force going through the leading edge. This axial tensional force adds structural stability to the leading edge by making it more resistant to buckling. This is the same type of layout that the Cabrinha Crossbow kite has which is shown in Fig.4-27. The second advantage of a large pulling force at the tip is that all other forces on the bridle points are getting smaller. Small discrepancies between the theoretical bridle forces and real bridle forces are also getting smaller in magnitude because of this. Now the bending and torsional stiffness of the leading edge can take larger portions of the discrepancies between the forces making it more stable during flight. Figure 4-28 shows the shape of the kite using the third bridle design. These pictures show that the shape resulting from the new bridle comes much closer to the shape of the kite using the original bridle. Therefore the reverse engineering method is used to determine the forces on the bridle points for the 25 m2 kite.

Kitesailing 4-5 Test results 47

Figure 4-26: Schematic outline of the third bridle design

Figure 4-27: Schematic outline of the Cabrinha Crossbow bridle layout, source: Cabrinha kites [2010]

25 m2 kite, design 1 The design for the 25 m2 kite is shown in Fig.4-29. It also shows the magnitude of the forces in the bridle lines attached to the kite to show the large force introduced in the lowest bridle point. The red arrows show the relative magnitudes of the forces on the bridle points on the leading edge. Due to the large rotation of the force on the tip the other forces get smaller because the introduced axial tension supports the other leading edge sections towards the center of the kite.

The shape of the kite using this new bridle is shown in Fig.4-30 on the left, the right picture shows the kite with the original bridle.

This picture shows that the shape in the x-y plane is very similar for both bridle designs. The amount of depower however was not noticeably more than with the conventional bridle.

Kitesailing 48 Depower system design

Figure 4-28: The shape of the 5 m2 kite with the third bridle design applied left and the original bridle on the right

Figure 4-29: Left: schematic outline of the bridle design for the 25 m2 kite, Right: discrete force distribution

4-5-2 Force measurements

Three different bridles have been tested for depower on the Ozone Sport II 5 m2 kite. These are:

The standard bridle

● Design 3

● Design 2b

Kitesailing● 4-5 Test results 49

Figure 4-30: The shape of the 25 m2 kite with the original bridle applied left and the new bridle design on the right

The way of testing for depower is by setting the kite straight downwind on the beach on its trailing edge with an angle of attack of 90○deg. It is set in a maximum depower setting and launched straight up. The less depower it has the higher it will climb into the air and the higher the generated forces are. This situation is considered to be the most dangerous situation as is discussed in Section 3-4. Therefore this is the situation where the amount of depower matters most. The forces are measured using a spring scale set up between a big sand bag of 1 m3 on the beach and the steering system developed for kitesailing. The line length that is used for this test is 50m. The wind conditions were 8 knots of wind. The measured forces for the three designs are given in Fig.4-31. The blue bars show the initial forces of the kite while standing on its trailing edge with an angle of attack of 90○deg. The measured maximum forces during the launch using the original bridle were 18 times as high as using bridle design 2B. It should be mentioned that the value of 10 N is inaccurate in the way that the force seemed to be zero on the scale but that this cannot be true while the kite is still in the air due to the drag. Figure 4-32 shows a composition of the flight path of the original bridled kite. It shows that the kite launches itself to an elevation angle between the power lines and the beach of 45 degrees. The second bridle that was tested (Design 3) showed a much lower achieved elevation angle. The pictures that were taken are shown in Fig.4-33. The third bridle that was tested showed the best depower of all. Figure 4-34 shows the pictures taken in close-up. The kite immediately pitches to zero angle of attack when it is launched. When the kite is launched it immediately pitches to zero angle of attack. The kite cannot launch anywhere in the wind window if the steering lines are slack using this type of bridle. Conclusions: Design 2B fulfills the requirement of giving the kite the possibility of zero lift on any place in the wind window. During crosswind sweeps creating high loads on the kite the general shape also remained good as is shown in Fig.4-25.

Kitesailing 50 Depower system design

180

60 60 60 Maximum pulling force [N]

30

10

Original Design 3 Design 2B Figure 4-31: Bar diagram showing the measured forces before the launch (blue) and the peak forces during the launch for the different bridle designs (green)

4-5-3 Best practices

The reason for the large amount of depower of bridle 2B could be given by the fact that the lowest pulley on the bridle in the x-y plane is located close to the kite. Design 3 has this pulley located much more below the kite. Also the stability can be affected by the position of the lowest pulley. It can also be investigated if the pitch stability gets lower when the lowest pulley is close to the kite. This seems to be the case when flying the kite. An other design aspect is by the choice on the amount of axial tension that is introduced in the leading edge at the tip. Design 3 has 20% of the tether force introduced as axial tension in the leading edge. This pre-tensioning of the tube elements increases the buckling resistance.

4-6 Conclusions

A bridle analysis and design program has been written with two different methods to deter- mine the discrete force distribution on the bridle points of an existing kite. The calculated aerodynamic loads on the tips with the aerodynamic method proved to be too small. The bridles designed with the geometric method showed good general shapes during flight. Bridle design 2B completely fulfills the requirements of supporting the kite such that it has its design shape during flight and of offering the possibility of zero lift on every position in the wind window.

Kitesailing 4-6 Conclusions 51

Figure 4-32: Composition of the kite launch with the standard bridle attached, on the lower right corner the sand bag is visible to which the lines are attached

The original bridle on a 5 m2 kite created a peak force of 180 N in wind speeds of 8 knots. The requirement that a kite is not allowed to generate more than 450 N when it is depowered shows that the kite is allowed to be 2.5 times the surface area. This equals 12.5 m2 in these low wind conditions on a boat with a mass of 3000 N. With the desire to sail with bigger kites this shows that the tested original bridle should not be applied on a kite used for kitesailing if the requirement for a maximum force of 450 N is to be met. The kite using bridle design 2B gives such low forces when depowered that the size of the kite for kitesailing could be made much larger and still stay within the limits of the safety requirements. Because the shape of the 5 m2 kite with design 3 and of the 25 m2 kite for which the geometric method is used to determine the discrete forces on the bridle points, the assumption that the bridle points keep the same values in z-direction seems to be valid.

Kitesailing 52 Depower system design

Figure 4-33: Composition of the kite launch with bridle design 3 attached

Kitesailing 4-6 Conclusions 53

Figure 4-34: Composition of the kite launch with bridle design 2B attached

Kitesailing 54 Depower system design

Kitesailing Chapter 5

Scaling of kites

The pulling force of the kite can be adjusted by scaling of an existing kite design. This chapter starts with an introduction on scaling factors and on some general assumptions made for this chapter in Section 5-1. In this section also the scaling factors are determined for the new kite design. Section 5-2 discusses the changes in canopy tension when a kite is scaled up. The allowable tube pressure for a tube kite is determined in Section 5-3. Section 5-4 discusses the experienced problems on leading edge stability and the changes that occur when scaling a tube kite when the leading edge is assumed to be straight. The effect of taper which is present on every leading edge on these results is determined to validate the assumption of a straight leading edge in Section 5-5. Section 5-6 shows the changes in weight when a tube kite is scaled and Section 5-7 shows the design of the new kite that is produced.

5-1 Introduction of scaling factors

A tube kite basically consists of 3 main parts that make the airfoil and handle all the loads: The canopy, the leading edge and the struts. The leading edge and the struts are pressurized tubes and the canopy is a single membrane under tension. When scaling a kite these different elements are affected in different ways.

5-1-1 Terminology and assumptions

When a kite is scaled up it is common to scale in terms of surface area. In kitesurfing the size of the kite that is used by the surfer is chosen such that the pulling force of the kite matches with the wind velocity and the weight of the rider. When parts are considered like the length of a tube only one dimension is being scaled. This scaling factor in one dimension such as a length is called f. The factor by which the surface area is scaled is now f 2. Figure 5-1 schematically shows a tube element with a canopy attached to it as the original version with subscript 1 and the scaled version with subscript 2.

Kitesailing 56 Scaling of kites

S2 l2 S1 l1

r2 r1

Figure 5-1: Scaling of tube and canopy sections

The relation for the different parts is given by the set of Eqs. (5-1), (5-2) and (5-3).

l2 = l1 f (5-1) r2 = r1 f (5-2) 2 S2 = S1 f (5-3)

The type of material that is used for kites is rip-stop Polyester for the canopy the weight is in the order of 50 gr m−2. Dacron is a trade name for a heavier Polyester cloth weighing around 170 gr m−2 which is used for the tubular structure of the kite. These materials are available in only a few different⋅ thicknesses but all tube kites are basically made with a standard thickness for both⋅ materials. It is desired that the same materials are used as for all other tube kites. However when the theory is applied to the kite design in Section 5-6 the influence of the thickness is taken into account. For now the thickness of the material is considered constant and therefore:

t1 = t2 (5-4)

The leading edge is a pressurized membrane structure which is supported on different points where the bridle is attached. These points are called bridle points. The distance between these points is called the bridle point pitch (Pbridle). The model of the kite is further explained in Section 4-2. At the positions of the bridle points there are stress concentrations present. It is not the goal of this research to determine the magnitude and distribution of these stress concentrations. For this research it is assumed that the distribution of all the stresses remains the same and only the magnitude changes because the shape of the kite is not changed when scaling a kite. It is the goal to determine general relations that can act as rules of thumb to quickly predict certain consequences when scaling a kite. Therefore also only static effects of scaling are taken into account. The dynamic effects are left out to obtain simple relations. It is also assumed that the flight conditions of the original kite and the scaled kite are con- sidered equal. Another assumption is that the aerodynamic coefficients do not change when scaling a kite. If these would change because of increasing Reynolds numbers for example, the design of the profile can be adapted to obtain the same coefficients again. These changes in the profile should be such that the general stress distribution does not change and the derived relations still apply for scaling of the kite.

Kitesailing 5-2 Canopy tension changes 57

5-1-2 Scaling factor calculations

The largest forces occur when the boat is lifted out of the water. Therefore in these conditions the scaling factor for the desired increase in maximum pulling force Fkite must be calculated. If this is achieved then the propulsive force during regular sailing will likely increase by a factor larger than 2. This is because the sailing speeds are higher with a bigger kite which results in a higher VA for the boat and for the kite. This higher VA results in an increase of Fkite and in an extra increase in sailing speed. However, at the moment when Fkite is maximum the sailing speed is almost zero and therefore the increase Fkite due to the higher sailing speed is not taken into account for the calculation of the increase in surface area that is needed to increase the maximum pulling force Fkite. Sizing of a kite results in a larger total lift and drag due to the larger surface area of the kite. This lift and drag depends linearly on the surface area according to the lift and drag equations:

1 2 L Cl ρ V S (5-5) = 2 1 2 D Cd ρ V S (5-6) = 2

The total tension of the kite is simply given by adding these two vectors or using Pythagoras:

2 2 T = L D (5-7) √ Because the linear dependence of the forces on the+ surface area the following set of relations hold when scaling a kite.

2 L2 = L1 f (5-8) 2 D2 = D1 f (5-9) 2 T2 = T1 f (5-10)

5-2 Canopy tension changes

When the surface area of a kite is scaled up with a factor f 2 the chord is scaled by a factor f. When the lift and drag forces for a 2D airfoil are considered, Eqs. (5-5) and (5-6) still apply with the difference that the surface area S is replaced by the chord length. Therefore the distributed areodynamic loads are multiplied by a factor f when the surface area is increased by a factor f 2. In this calculation it is assumed that the distribution of the internal forces are exactly the same for the scaled version of a kite as for the original kite.

Figure 5-2 shows a straight panel that handles a force F1 in the original situation. This force is distributed over a length l1 which results in a distributed load σ1. When the surface area S is now increased by f 2, the distributed aerodynamic load is increased by a factor f. The

Kitesailing 58 Scaling of kites

S1 S2

F1

F2

l1 l2 Figure 5-2: Canopy tension after scaling width of the panel that handles the load is also increased by a factor f. The thickness t is constant as is explained in Section 5-1. The following relations hold:

l2 = l1 f (5-11) 2 S2 = S1 f (5-12) 2 F2 = F1 f (5-13)

The general equation for tension is given by:

F σ (5-14) = t l

If Eqs. (5-11) and (5-11) are combined with (5-14) then it shows that the tension in the fabric increases by a factor f with a constant thickness of the fabric which is shown in Eq.(5-15).

F f 2 σ2 σ1 f (5-15) = t l f =

5-3 Tube pressure determination

The increase in tension in the leading edge due to scaling is exactly the same as with the canopy panels with two differences. The leading edge is an inflated structure so the inner pressure has great influence on the stresses in the structure. Also the leading edge is supported by a bridle that supports the leading edge and can divert internal stresses from the leading edge into the bridle. The leading edge and struts of a kite are cylindrical beams that are loaded under an internal pressure. For such structures the circumferential stress σC and the longitudinal stress σL are given by the Boiler formula’s.

Kitesailing 5-3 Tube pressure determination 59

p r σ (5-16) C = t p r σL (5-17) = 2t

Additional internal stresses occur when an additional external load is applied to these struc- tures. An external load perpendicular to the beam results in a bending moment around the neutral line of the beam which results in compressive stresses on one side and tensile stresses on the other side. Extra tension forces going through the leading edge can be present as a result of the bridle layout. Summing up the stresses results in a new stress distribution on the beam. Figure 5-3 shows this schematically. Pressure tension: Bending: Sum:

σ1 σ2 σ1 σ2 + + + =

+ σ2 σ1 σ2

Figure 5-3: Tensions due to internal− pressure and an external bending− force are summed up

When σ1-σ2 becomes zero then wrinkling starts to occur as is described by Comer & Levy [1963]. Figure 5-4 shows an inflated circular-cylindrical cantilever beam that is wrinkled in the darker region. It shows that no longitudinal stresses are present in the wrinkled area. The structure however does not collapse until there is wrinkling present across the entire root cross section.

σM σM

A-A B-B

Wrinkled region Figure 5-4: Wrinkling and accompanying stress distributions of an inflated beam, source: Comer & Levy [1963]

When looking at the bending moment that is exerted on a structure and the accompanying deflection then it becomes clear that when an inflated structure starts to wrinkle it can still bear a considerable amount of externally applied loads as is stated by Breukels & Ockels

Kitesailing 60 Scaling of kites

[2008]. Figure 5-5 shows schematically how the bending moment relates to the deflection of an inflatable beam.

Unwrinkled Wrinkled Collapsed Bending moment

Deflection Figure 5-5: Three states of an inflated beam, source: Breukels & Ockels [2008]

For a kite it is desired that during normal flight conditions the leading edge does not wrinkle because it can disturb the aerodynamic flow. Also as is described by Breukels & Ockels [2008] when an inflatable beam is wrinkled it is more flexible. When surfing or sailing with a kite this is unwanted because the kite will respond slower to steering inputs and it does not give confidence if the kite surfer or kite sailor sees the kite wrinkling. Therefore when looking at Fig.5-3 the value σ1-σ2 should not become lower than zero. All tube kites have a leading edge made from Dacron material with a standard thickness. Therefore the σ t is the required material property for the Dacron material in the leading edge. For the situation in Fig.5-6 it is known from Verheul et al. [2009] that the maximum allowable stress for⋅ Dacron σ t equals 6 103 N/m in radial direction. The material itself can hold up to 26 103 N/m if no seam is applied. Some kites like the Ozone kites also have a seam in axial direction halfway of every⋅ leading⋅ edge segment. In this case the longitudinal internal stresses cannot⋅ exceed the axial stresses because the seam is again the limiting factor. The Mutiny kite however does not have such a seam halfway, only at the bridle point positions at the end of each section. From this is follows that the limiting factor for the tube material is the allowed tension at the seams needed for construction.

l

σ t

Figure 5-6: Tensile stresses in a tube with length l

Putting σ t in Eq.(5-16) results in the following equality:

⋅ F σ t p r (5-18) l = =

Kitesailing 5-4 Stability of straight tubes 61

This equation shows that the allowable pressure is inversely proportional with the radius. So for a given material the following relation holds:

p r = constant (5-19)

The safety factor used for kites is equal to 1.5. This follows from measuring the leading edge radius of the Ozone Instinct Edge II 13 m kite at the location of the center strut. The radius is 72 mm and the allowable pressure according to Ozone is 8 PSI which equals 55 103 N/m2. Putting these numbers in Eq.(5-18) results in a force per unit length of 4 103 N/m. Because the maximum allowable stress in Dacron is 6 103 N/m. The resulting safety factor⋅ is 1.5 for the leading edge of this kite. ⋅ ⋅ For the design of the leading edge with respect to stiffness this safety factor is kept the same, so the boundary condition for the allowable maximum stress per meter Dacron is given by:

3 σ t = p r = 4 10 N/m (5-20) ⋅ 5-4 Stability of straight tubes

The leading edge gives a tube kite it’s stiffness which keeps the kite in shape. During kite- sailing, when loading the kite very heavily during certain maneuvers, the leading edge of the conventional tube kite collapses under the stresses which results in violent flapping behavior of the kite. This causes a complete loss of lift and control over the kite. To prevent this in the new kite design, the leading edge must be made more resistant against collapsing. This can be done in three ways: by increasing the leading edge diameter, by increasing the pressure in the leading edge and by increasing the amount of bridle points that support the leading edge, effectively lowering the section length that is subject to a bending moment. As already mentioned in Section 5-1, the leading edge is scaled in such a way that the lift and drag coefficients are kept constant. In this way the total lift and drag scale linearly with the surface area. The number of bridle points and the positions of them are the variables that are changed to achieve a higher resistance against collapsing of the leading edge.

5-4-1 Theory for collapse moment and stress criteria

The leading edge sections and struts of a tube kite are pressurized membrane structures. Different theories are present to calculate the bending moments that deform these kind of structures such that they collapse under the applied loads. This moment is called ’the collapse moment’. According to Stein & Hedgepeth [1961] the collapse moment for a true pressurized membrane is given by the following equation:

3 Mcollapse = π p r (5-21)

Kitesailing 62 Scaling of kites

According to Wielgosz & Thomas [2002] this ’classical’ collapse moment is too large and in order to correlate to their experiments it should be reduced to:

π 3 Mcollapse π p r (5-22) = 4

In the PhD thesis report of Veldman [2005] it is stated that for low pressures (<0.25 bar overpressure) membrane structures should be regarded as shell structures. In this case the flexure formula can be used to determine the stresses in the fabric. Figure 5-7 shows a beam subject to a bending moment.

σ1

c1 M x (neutral line) c2 σ2

Figure 5-7: Stresses in a beam under a moment loading

The equation to calculate the tension σ is given by Eq.(5-23) from Gere & Timoshenko [1999]:

M y σ (5-23) x = I In which y is the vertical distance from the neutral line. A relation between the bridle point pitch (Pbridle) in an original situation and the scaled situation is derived and validated by deriving it using both the collapsing criterium and the stress criterium separately. The derived relation gives the change in bridle point pitch for which the kite will wrinkle or collapse under an equal aerodynamic load per square meter surface area of the kite.

5-4-2 Deriving bridle point pitch relation using the stress criterium

The variable I in the Flexure formula is given by:

3 Ix = Iy = π r t (5-24)

For a kite the leading edge has a circular cross section everywhere so:

y = r (5-25)

To determine the maximum moment working on the leading edge section the shear force and bending moment diagrams are drawn to show the position of maximum bending moment in the following figure:

The point where the maximum moment occurs is at x = 1 2 Pbridle. The static analysis is performed using Fig.5-9 to determine the value of the moment working on this position: ~ From this it follows that:

Kitesailing 5-4 Stability of straight tubes 63

Load distribution: V-line: M-line: q

F F + − − Pbridle Figure 5-8: FBD, shear force and bending moment diagrams of a leading edge section

q

A MA

F

1 2 l Figure 5-9: FBD~ of⋅ a leading edge section

+ Q Fx → 0 = 0 (5-26) + 1 Fy ↑ ∶ 0 q Pbridle F (5-27) Q = 2 + 1 1 1 MA Á M∶ A q Pbridle− Pbridle F Pbridle (5-28) Q = 2 4 2 ∶ − + Combining these equations gives for MA:

1 2 MA q P (5-29) = 8 bridle

Combining Eqs. (5-23), (5-24), (5-25) and (5-29) gives the maximum tension in a straight tube:

2 q Pbridle σstraight (5-30) = 8r π 2 t

In the previous section the boundary condition for σt was given in Eq.(5-20). Setting this equal with Eq.(5-30) and solving for Pbridle gives:

8 p πr3 P (5-31) bridle = ¾ q

This equation now gives the maximum allowable length between two bridle points such that the maximum loads for stiffness and strength are equal. Now taking subscript 1 as the original situation and subscript 2 as the scaled situation the variables in Eq.(5-31) are given by:

Kitesailing 64 Scaling of kites

r2 = r1 f (5-32) 1 p2 p1 (5-33) = f q2 = q1 f (5-34)

Combining Eqs. (5-31), (5-32), (5-33) and (5-34) gives the relation between the original distance and the new distance after scaling for which the maximum loads for stiffness and strength are equal:

Pbridle2 = Pbridle1 f (5-35) » 5-4-3 Deriving bridle point pitch relation using the collapsing moment criterium

Now the same relation is derived using the theory of Wielgosz & Thomas [2002]. Using Stein & Hedgepeth [1961] gives the same result because the term pi 4 cancels out in the equations. Wielgosz & Thomas [2002] state that the collapse moment is given by: ~ π 3 Mcollapse π p r (5-36) = 4 Taking subscript 1 as the original situation and subscript 2 as the scaled situation, the vari- ables in Eq.(5-36) are given by Eqs. (5-32), (5-33) and (5-34). Taking these equations together gives the following relation between the original collapsing moment and the collapsing moment for a scaled structure:

2 M2 = M1 f (5-37)

Filling in the moment Eq.(5-29) into (5-37) and solving gives:

Pbridle2 = Pbridle1 f (5-38) » Equations (5-35) and (5-38) give the same relation between the original and the scaled bridle point pitch which gives confidence in the derived relation.

5-4-4 Increasing the buckling resistance by the bridle

The resistance against collapsing can be increased by increasing the amount of bridle points that support the leading edge. By definition, when bridle points are added the distance between all the points decrease and the section lengths decrease. From Eq.(5-29) it is known that the bending moment applied on each section varies with l2 so decreasing l decreases the moment. This decreased moment decreases the tension σL in the leading edge while the aerodynamic loads on the kite remain the same or, when the allowed tension is kept constant, the areodynamic loads are allowed to increase.

Kitesailing 5-5 Stability of tapered tubes 65

The factor a is now introduced as the factor by which the maximum aerodynamic loads are allowed to increase. Again, subscript 1 is the original situation for a given kite and subscript 2 applies for the same kite with a different number of bridle points. Equation (5-39) gives this relation mathematically:

q2 = q1 a (5-39)

As is shown in Eq.(5-29), the bending moment varies linearly with the external distributed load q. Combining Eqs. (5-29) and (5-39) gives the following relation between the bending moments:

1 M2 M1 (5-40) = a

If the collapsing resistance has to be increased by a factor a for a given aerodynamic load q and combining Eqs. (5-29) and (5-40) the following relation is obtained:

1 l2 l1 (5-41) = ¾a

This is the relation that is to be used when for a given kite the allowable aerodynamic load is increased by a factor a.

5-5 Stability of tapered tubes

In the calculations in the previous sections it was assumed that the leading edge sections were straight beams. To validate this assumption the stresses in tapered beams are compared to those in straight beams. In the following subsections the position and value of the maximum stress is determined and compared to the straight beam outcomes. The calculations in this section have been performed using the computer programs Maple and Matlab.

5-5-1 Deriving position and magnitude of maximum tension in a tapered tube

First the position of maximum stress is determined. The Flexure formula (5-23) is again applied with the difference that ra is a function of x. Figure 5-10 shows a tapered tube from which this relation is derived.

x r = ra rb ra (5-42) Pbridle + ( − ) Now the flexure formula becomes:

1 1 2 4 2 q Pbridle x 2 q x σtapered = x 2 (5-43) π t 2 rA 2 rB rA ( − Pbridle)

( + ( − ) ) Kitesailing 66 Scaling of kites

rB

rA

x

Pbridle

Figure 5-10: Tapered tube with radius rA and rB

The Taper Ratio TR is the ratio between the biggest and the smallest radius in the structure and is given by:

rB TR = (5-44) rA

Differentiating Eq.(5-43) and substituting the Taper Ratio gives:

1 3 ′ 2 q Pbridle Pbridle x T R x σ = 2 3 (5-45) tr π Pbridle x T R x A ( − − ) The position x where the stresses are( maximal( follows+ from− ) setting) σ′ to zero. Solving for x gives:

P x bridle (5-46) = TR 1

The accompanying maximum stress σmax is determined+ by filling in Eq.(5-46) into (5-43):

2 Pbridle q σmax = 2 (5-47) 8 π tTRrA

Figure 5-11 shows the position on the leading edge section with length Pbridle where the largest internal stresses are present. The maximum taper ratio of the leading edge sections of a typical tube kite like the Ozone Instinct Edge II is 1.15. From Fig.5-11 it can be seen that the position where σmax occurs is at 43% of the section length compared to 50% for a section without taper.

5-5-2 Increasing the stiffness by the bridle in a tapered tube

When the goal is to increase the stiffness by adding bridle points in a tapered beam the relation from Eq.(5-41) is not as straightforward. This is because the taper ratio changes when the distance between two bridle points is changed due to the fixed leading edge layout. Figure 5-12 shows the situation when a leading edge section is cut horizontally in the longi- tudinal direction. From this figure the relation between the original rA1 and the new rA2 can

Kitesailing 5-5 Stability of tapered tubes 67

1 ) 0.9 bridle P 0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1 Position of maximum stress (fraction of

0 1 1.5 2 2.5 3 Taper Ratio

Figure 5-11: Position of maximum stress as function of the taper ratio

y

rB

rA1

rA2

x 0 Pbridle1 Pbridle2 Figure 5-12: Taper in a leading edge section for different situations

be derived. With this relation, the relation between Pbridle1 and Pbridle2 can be derived for a tapered tube. The relation between y and x that follows from this figure is given by:

x rB rA2 y = rB (5-48) Pbridle2 ( − ) − The relation between rA1 and rA2 that follows from Eqs. (5-48) and (5-44) is given by:

Pbridle2 rA2 = rA1 TR1 TR1 1 (5-49) Pbridle1 ( − ( − ) ) Equation (5-47) stated:

2 Pbridle q σmax = 2 (5-50) 8 π tTRrA

This σmax only depends on the material properties and is therefore constant. Taking subscript 1 as the original situation and subscript 2 as the new situation where the leading edge is made

Kitesailing 68 Scaling of kites more resistant against collapsing by a factor a, the two situations can be set equal to each other:

σmax1 = σmax2 (5-51)

1 2 1 2 8 Pbridle1 q1 8 Pbridle2 q2 2 = 2 (5-52) π t T R2 rA1 π t T R2 rA2

By definition the following relations hold:

q2 = q1 a (5-53) rB TR2 = (5-54) rA2

Combining and solving Eqs. (5-52), (5-53) and (5-54) gives:

2 2 Pbridle1 Pbridle2 a = (5-55) rA1 rA2

Substituting rA2 from Eq.(5-49) into Eq.(5-55) gives:

2 2 Pbridle2 a Pbridle1 (5-56) = Pbridle2 TR1 TR1 1 Pbridle1

Rewriting Eq.5-56 gives the following equation( − that− has) to be solved:

Pbridle2 2 Pbridle2 a TR2 1 TR2 = 0 (5-57) Pbridle1 Pbridle1 ( ) + ( − ) − Two solutions follow from this equation of which one gives a negative value for the length relation. The right solution is given by:

2 Pbridle2 TR2 1 TRR 2 2 T 2 1 4 a T R2 = (5-58) Pbridle1 » 2 a − + + − + + The relation of the ratio between l2 and l1 for different taper ratios and different desired values of a is shown in Fig. 5-13. As mentioned in the previous subsection the maximum taper ratio for a typical tube kite like the Ozone Instinct Edge II is 1.15. For this TR the outcome for a simplified, straight leading edge, the length ratio is given by the following equation with a = 2:

Pbridle2 = Pbridle1 0.707 (5-59)

Kitesailing ⋅ 5-6 Weight changes 69

2 a = 0.5 1.8 a = 1 a = 2 1.6 a = 3 a = 4 1.4 1 1.2 bridle P

~ 1 2

bridle 0.8 P

0.6

0.4

0.2

0 1 1.5 2 2.5 3 3.5 4 4.5 5 Taper ratio

Figure 5-13: Length ratio for different taper ratios and increases in stiffness a

In the case that TR = 1.15 is included in the leading edge with a = 2, the length ratio is given by:

Pbridle2 = Pbridle1 0.722 (5-60) ⋅ The difference for the length relations of a straight tube and a tapered tube with a TR typical for a tube kite leading edge is only 2% of the original distance between two bridle points. This difference is neglectible when designing a kite so the assumption that the leading edge is a structure with no taper is valid when scaling factors are considered and when bridle points are added to increase the buckling resistance.

5-6 Weight changes

The weight increases with the amount of fabric that is being used for the construction. When the surface area of the canopy is increased by f 2 the amount of material is also increased by f 2. This also holds for the leading edge and the struts because both the length and the radius of the tube sections are increased by f which results in the factor f 2 for the amount of fabric that is used. Comparing the weight of the original kite and the scaled kite shows that indeed the weight has has increased by a factor f 2. Considering that the kite is scaled with f 2 in both size and in weight while at the same time the tension in the fabric is increased by f, it shows that when a kite is scaled the canopy is becoming relatively weaker. This is because the thickness of the canopy is not scaled. If the thickness would be scaled by a factor f to reduce the internal stresses in the canopy to the original values, the weight of the canopy would also increase by a factor f. This shows

Kitesailing 70 Scaling of kites that when scaling a kite, it becomes relatively more heavy per unit surface area according to Eq.(5-61).

Wcanopy2 = Wcanopy1 f (5-61) Figure 5-14 shows this relation for the canopy without the consideration of dynamic effects.

3.5

3

2.5

2 Weight increase per unit area 1.5

1 1 2 3 4 5 6 7 8 9 10 Scaling factor for surface area

Figure 5-14: Weight increase per unit area in canopy panels while scaling while keeping a constant canopy tension σcanopy

The total weight of the leading edge scales linearly with the surface area keeping σL and σC constant by adding more bridle points.

5-7 New kite design

For the design of the scaled kite the sequence in this chapter is followed. The original kite is the Mutiny 12.5 m 2010 surfing kite. The requirements state that the new kite must be able to generate twice as much pulling force T as the original kite. Equation (5-10) shows that T varies linearly with the surface area. Therefore the size of the kite is doubled and the scaling factors are given by:

f = 2 (5-62) 2 f = √2 (5-63)

Therefore the surface area is doubled:

2 S2 = 25 m (5-64) The increase of tension in the canopy panels is given by Eq.(5-15). Combining this with the value for f gives:

σcanopy2 = σcanopy1 2 (5-65) √ Kitesailing ⋅ 5-7 New kite design 71

The thickness of the canopy fabric is not changed for this kite. According to Mutiny Kites it will degrade faster but it is strong enough for the kite to generate a pulling force T of 3000 N according to the requirement. This is also verified during tests as is discussed in Chapter 7. The weight scales proportionally with the surface area when the canopy thickness is not scaled as is shown in previous section. This is confimed by the actual weights of the original kite and the scaled version. The original kite weighs slightly more than 4 kg and the new kite weighs 8.5 kg. Therefore:

W2 = W1 2 (5-66) ⋅ The number of bridle points is calculated from Eqs. (5-35) and (5-41) and repeated here:

Pbridle2 = Pbridle1 f (5-67) » 1 P P (5-68) bridle2 = bridle1 ¾a

Taking these equations and considering the requirement that the leading edge should be twice as resistant against collapsing compared to the original one together with the value for the scaling factor f, the new section lengths are calculated using the following equation:

4 1 Pbridle2 Pbridle1 2 (5-69) = ¾2 √ With an original amount of 9 bridle points for the entire kite this equation leads to a total number of 15 bridle points for the scaled kite. The kite properties for the original and the scaled version are now given in the following table:

Table 5-1: Comparing the properties of the original kite and the scaled version

Original kite Scaled kite Surface area [m2] 12.5 25 Design load [N] 1000 3000 Weight [kg] 4.25 8.5 Number of bridle points 9 15

Figure 5-15 shows the CAD drawing in 3D that is produced in Rhino and Fig.5-16 shows the new 25m kite just after production on the factory floor.

Kitesailing 72 Scaling of kites

Figure 5-15: CAD model of the 25m kite

Figure 5-16: 25m kite on the factory floor

Kitesailing Chapter 6

Aerodynamic analysis

The L/D ratio is a very important factor for sailing as is explained in Chapter 3. Sailing courses sharper upwind are reached when the lift is increased or the drag reduced. A higher lift of the kite increases the sailing speed considerable. This chapter shows the results of the research that is performed on the possibilities to increase the total lift and the L/D ratio of surf kites. Section 6-1 shows an analysis on general aerodynamic properties of tube kites. Section 6-2 shows the literature study for the possible concepts to improve the L/D ratio. Section 6-3 shows the analysis performed on applying aerodynamic theory to tube kites together with a trade off for the most promising concept. The airfoil section that has been designed for a new kite is discussed in Section 6-4. Section 6-5 shows the tests that have been performed on a double skin on a tube kite. The final section shows the conclusions.

6-1 Analysis of tube kite aerodynamics

As a starting point the general aerodynamics of tube kites are investigated. First by qualita- tive then by quantitative analysis.

6-1-1 Qualitative analysis on the aerodynamics of a tube kite

A tube kite has three major areas that play a role in the aerodynamic performance. From Speer [n.d.] it is known that the pressure distribution on a rigid mast and sail has a peak on the leading edge. Also a separation bubble occurs behind the leading edge which is shown in Fig.6-1. This has also been analyzed by using Xfoil which is a program that uses a panel code by which aerodynamic properties of airfoils in a steady flow can be analyzed. Other similar programs exist and an overview of the most common analysis programs together with their main calculation methods is given in Appendix C.

Kitesailing 74 Aerodynamic analysis

Figure 6-1: Pressure distribution on an airfoil created by a teardrop shape mast and attached sail, source: Speer [n.d.]

Figure 6-2 shows the pressure distribution of the E423 high lift airfoil at the top and then the E335 flying wing airfoil. It is clearly visible that the high lift airfoil creates much more lift in the middle of the airfoil compared to the flying wing airfoil. The nose-down moment however is also much greater than that of the flying wing which even has a slight nose-up behavior. In general, tube kites have a neutral behavior and therefore a pressure distribution that is located primarily at the leading edge is expected. The pressure distribution on the airfoil at the center strut of the Ozone Sport 5m kite is analyzed and indeed shows a big pressure peak at the leading edge. This can be seen on th third airfoil in Fig.6-2. However it is known that a wake exists behind the leading edge with which Xfoil cannot cope. A different airflow on the bottom surface also changes the airflow on the top surface. To approximate the pressure distribution on the top surface better, a lower skin is added to eliminate the wake. The fourth airfoil is the same tube kite airfoil with an added lower skin and shows a different pressure distribution. However the global distribution has not changed. The lift distribution of the Eppler 335 airfoil which is used on tailless aircraft shows great similarity with the kite airfoil which means that for both airfoil designs the moment coefficient is an important parameter. In fact, a tube kite is a flying wing. A positive moment coefficient means a nose-up behavior of the airfoil and tube kite designers strive for this positive moment coefficient. This makes sure that the kite stays up in the air due to its positive angle of attack when the lines become slack for a moment. Because Xfoil cannot cope with the wake behind the leading edge an other ways have to be used to investigate the size of this wake. For this Tell Tails have been placed on the kite. Then the kite was flown on the beach and pictures have been taken to make the wake visible. Figure 6-3 shows the Ozone Sport 5 m2 kite with Tell Tails on the bottom surface on the left

Kitesailing 6-1 Analysis of tube kite aerodynamics 75

Figure 6-2: The E423 and E335 airfoils together with the Ozone Sport 5 m2 center profile (with and without a lower skin) analyzed in Xfoil

(in the circle) and Tell Tails on the top surface on the right side of the picture. Dozens of pictures have been taken and this is the best one to give an average behavior of the Tell Tails during flight.

It shows that there exists a wake up to 40% of the chord behind the leading edge which creates drag. This is further discussed in section 6-2. Also the tip vortices are clearly visible on all the pictures taken. The three Tell Tails on the left side of the kite in Figure 6-3 always

Kitesailing 76 Aerodynamic analysis

Figure 6-3: The Tell Tails in the circles show the wake behind the leading edge and the airflow around the tips

point outwards. A CFD analysis performed by Breukels [2010] also shows a big wake behind the leading edge as is shown in Fig. 6-4. The pictures clearly show the wake behind the leading edge that is getting smaller with increasing angle of attack. When the flight speed increases the aerodynamic loads also increase. Due to the higher loads the trailing edge moves towards the leading edge. This increases the camber of the profile. This is mostly the case in the middle of the trailing edge between two struts. The struts themselves have bending stiffness and therefore resist this deformation. The elasticity of the sail also influence this behavior. This is described by Boer [1980] and Boer [1982]. Tube kites have the struts to minimize the shortening of the chord lengths and the design of the canopy is such that this also reduces this behavior. Therefore the shortening of the chord lengths is very small but it is present. The change in aerodynamic characteristics however due to the shortening of the chord lengths is left outside the scope of this thesis.

Kitesailing 6-1 Analysis of tube kite aerodynamics 77

0 degrees angle of attack

8 degrees angle of attack

20 degrees angle of attack

Figure 6-4: CFD analysis showing turbulence intensity of a tube kite airfoil under various angles of attack, source: Breukels [2010]

Kitesailing 78 Aerodynamic analysis

6-1-2 Quantitative analysis on the aerodynamics of a tube kite

The report Wachter [2008] shows the work of windtunnel experiments on the Flysurfer Pulse II 6 m2 kite and Vlugt [2009] tested the same Pulse and the 2008 Airush Flow 5 m2 kite during crosswind tests on the beach. For more information on these types of testing the reader is referred to the respective reports. The results for the Pulse kite are considerably different in the two reports. For this analysis only the results of the beach tests are considered because in this way one type of testing is applied on two different kites. This is considered to give a better comparison between the two kites than comparing two different kites in two different testing situations. The maximum L/D ratio and the accompanying lift coefficient are given in Table 6-1 for the two kites.

Table 6-1: (L~D)max with accompanying CL and the maximum lift coefficient (CL)max for the 2008 Airush flow 5m and the Flysurfer Pulse II 6m

L D max CL CL max Flow 5.5 0.75 1.1 ( ~ ) ( ≥ ) Pulse 6 0.63 1.3

It shows that the Pulse kite has a higher maximum L/D ratio L D max than the Flow but that the accompanying lift coefficient is somewhat lower. The maximum lift coefficient ( ~ ) CL max for the pulse is 1.3. For the Flow this has not been determined, only that CL = 1.1 is possible at least. This shows a great difference CL at L D max and CL max. From Chapter 3 (it is) known that the total lift of a sail is more important than the L/D ratio for a sailing system therefore increasing the maximum lift coefficient C(L ~max) would be( advantageous.) However from Eppler [1990] it is known that this maximum lift coefficient CL max is comparable for ”flying wing” airfoils. ( ) ( ) The drag of a wing consists of two components, the zero-lift drag CD0 and induced drag CDi for which the following relation holds according to John D. Anderson [2001]:

C2 C C L (6-1) D = D0 π A e + For the Flow and Pulse the following drag relations are calculated in Vlugt [2009]:

2 CDF low = 0.0668 0.117 CL (6-2) 2 CDP ulse 0.0508 0.131 C (6-3) = + L + Combining CL = 0.75 at L D max with the drag relation for the Flow the drag coefficients become: ( ~ )

CD = CD0 CDi (6-4)

With the values for the coefficients given by: +

Kitesailing 6-2 Literature study 79

CD = 0.133 (6-5)

CD0 = 0.067 (6-6)

CDi = 0.066 (6-7)

This equality shows that the friction drag is equal to the pressure drag at L D max.

It is very interesting to see that this is exactly what Ruijgrok [1990] derives( mathematically~ ) for an airplane when flying at the velocity for minimum airplane drag. This derivation is shown in Appendix D. It shows that the zero-lift and induced drags are equal at the velocity for minimum airplane drag. This is also the situation in which L D max occurs.

A kite that flies steadily in the air can be regarded as an airplane( ~ that) flies in a stationary flight because both do not accelerate in any direction. In this case the lift of the kite is equal to the weight of the kite plus the tension of the line that works in vertical direction. Therefore CD0 = CDi is valid when a kite flies at the angle of attack with L D max. C For an airplane D0 increases with flight velocity according to Eq.(D-5)( ~ ) and the induced drag decreases with velocity. For a kite the ratio between CD0 and CDi does not change with flight velocity and stays 50 50 if the kite keeps flying at L D max.

− ( ~ ) 6-2 Literature study

The goal of this part of the research is to determine the area where the biggest improvement in L/D can be achieved. This area is then further investigated to reach a final conceptual design.

6-2-1 Airfoil section design

The airfoil shape of a tube kite is very different from almost all other airfoil shapes that are generally used and at the same time it is less efficient than an airplane airfoil in general. For example the Beechcraft Super King, which is a typical small two propeller aircraft, has a L/D ratio of 12 according to John D. Anderson [1985]. An airliner such as the Boeing 707 has a L/D ratio of 19 known from S. Hoerner [1985] and it is known from S. F. Hoerner [1965] that the wing of a glider with a moderate aspect ratio of 19 has a L/D ratio of approximately 31. Compared to the L/D ratio of 5.5 for the Flow 5m kite there is a big difference between these performances. Windtunnel research has been performed by Maughmer [2002] on 3D Sailwings to investigate the performances for small aircraft that would use wings made from fabric. Figure 6-5 shows the results of this wind tunnel analysis on eight different airfoil sections made out of a solid leading edge with a fabric canopy. The trailing edge was put under tension by a cable. The values for CL and CD are valid for the L D max situation.

This figure shows three basic types of airfoils( ~ ) that have been tested being the Sailvanes, the Semi-Sailwings and the Sailwings. The three different leading edge shapes that are tested are sharp, blunt and circular. Sailvane 3 and Semi-Sailwing 3 are a bit different compared to

Kitesailing 80 Aerodynamic analysis

Models L D Max CL CD

Sailvane 1 ( ~11).7 1.20 0.10

Sailvane 2 13.0 1.10 09.0

Sailvane 3 7.2 0.53 0.07

Semi-Sailwing 1 13.2 0.92 70.0

Semi-Sailwing 2 14.0 1.37 0.10

Semi-Sailwing 3 9.4 0.75 0.08

Sailwing 1 18.6 1.03 0.06

Sailwing 2 17.6 1.07 06.0

Figure 6-5: Compared airfoil sections with the maximum efficiencies and accompanying lift and drag coefficients, these are results from measurements in 3D, source: Maughmer [2002] the other shapes but are interesting to compare with the others. When comparing model 1 and 2 for the three airfoil types it is clear that the difference between the two leading edge shapes does not change much for the performance. For the Sailvane and the Semi-Sailwing the sharp leading edge is 6 and 11% more efficient compared to the blunt leading edge but for the Sailwing the blunt leading edge is 7% more efficient than the sharp one. No clear trend is visible on what will perform best on a tube kite from these test results yet. Adding a lower skin shows improvements in the L/D ratio, with a small improvement when creating a Semi-Sailwing which improves the L/D ratio by 10%. A much bigger improvement of 46% is made by adding a complete lower skin to create a Sailwing. The performance of the round leading edge of the Semi-Sailwings is rather poor compared to the other two leading edge shapes that perform 45% better in terms of L/D ratio than the round leading edge model.

The lift coefficient for the Semi-Sailwings show great variation. No explanation has been given for this by Maughmer [2002] and therefore no conclusions should be drawn from these numbers. The numbers that show little variation are the Sailvanes and the Sailwings. Com- paring the lift and drag coefficients shows that both are lower for the Sailwings compared to the Sailvanes. On average the Sailwings show a reduction of 9% in lift coefficient and 26% in drag coefficient. This reduction in lift coefficient could be explained by the fact that the wake behind the leading edge of a standard tube kite airfoil causes a high pressure under the canopy. This results in a high lift coefficient. It could also be the result of a changed CL-α curve such that the lift coefficient is lower at the position for L D Max. The greater reduction in value for the drag coefficient results in an increased value for L D max. The ( ~ ) Kitesailing ( ~ ) 6-2 Literature study 81 lower lift coefficient for a double skin kite is also supported from measurements in the field when comparing the Airush Flow and the Flysurfer Pulse II kites. Table 6-1 already showed a lift coefficient of 0.75 for the Flow kite and 0.63 for the Pulse at L D max. This reduction in lift coefficient is an interesting part of the outcome of this analysis and should be taken into consideration when designing a kite for a certain application. ( ~ )

Conclusions:

Comparing the values of L D max for Sailvanes 1 and 2 with Sailwings 1 and 2 shows that the increase in L D max by adding a lower skin is 46%. Comparing the Semi-Sailwings and averaging the results of types( ~ 1) and 2 results in an increase in L D max of 45% by adding an elliptical leading( ~ edge) on the kite. ( ~ )

6-2-2 Aspect Ratio

Increasing the aspect ratio A is a proven way of reducing the induced drag. This induced drag is drag caused by any real 3D wing. John D. Anderson [2001] describes the cause of induced drag as follows. A finite wing has low pressure on the top surface and a high pressure on the bottom surface. This causes an airflow at the wingtips from the bottom surface to the top surface which is shown in Fig.6-6.

Streamline over top surface V∞

Streamline over bottom surface

Wing area = S Top view cr ct (Planform) Wing tip Wing root

Wing span b

Low pressure Front view High pressure

Figure 6-6: Effect of a finite wing on an airflow, the curvature of the streamlines over the top and bottom of the wing is exaggerated for clarity, source: John D. Anderson [2001]

This flow that is leaking around the wing tips establishes a circulatory flow that trails down- stream of the wing which creates a trailing vortex at each wing tip. These wing-tip vortices downstream of the wing induce a small downward component of air velocity in the neigh- borhood of the wing itself. This secondary movement induces a small velocity component in the downward direction at the wing which is called downwash denoted by the symbol ”w”.

Kitesailing 82 Aerodynamic analysis

The downwash combined with the free stream velocity produces a local relative wind which is canted downward in the vicinity of each airfoil section of the wing as is shown in Fig.6-7.

Di L αi

Local airfoil section of a finite wing αeff α V αi w αi Local relative wind

Figure 6-7: Effect of downwash on the local flow over a local airfoil section of a finite wing, source: John D. Anderson [2001]

The angle between the chord line and the direction of V∞ is the geometric angle of attack. The local relative wind is inclined below the direction of V∞ by the angle αi called the induced angle of attack. The presence of downwash has two important effects on the local airfoil section. First the effective angle of attack αeff is lower than the geometrical angle of attack. Second the local lift vector is aligned perpendicular to the local relative wind and hence is inclined behind the vertical by the angle αi. Consequently there is a component of the local lift vector in the direction of V∞, that is, there is a drag created by the presence of downwash. This drag is defined as induced drag denoted by Di. The standard relation used in aviation for the total drag is given by Eq.6-1 and found form John D. Anderson [2001] and is given by the following equation:

C2 C C L (6-8) D = D0 π A e + The induced part of the drag is given by:

C2 C L (6-9) Di = π A e

This relation shows that the induced drag varies linearly with the aspect ratio. The aspect ratio is given by the wingspan squared b2 divided by the wing surface area S.

Kroo [2005] states that a 10% increase( in) wingspan, keeping the same surface area, reduces the induced drag by 17% which is simply the outcome of filling in the equation of the aspect ratio into Eq.(6-9). When applying this theory to kites a very interesting effect on the performance of a kite emerges. In Section 6-1 it is already proven that at the flight condition for L D max the induced drag is equal to the zero-lift drag CDi = CD0 . This relation is valid as long as the drag relation shown above is valid. ( ~ ) ( ) Kitesailing 6-2 Literature study 83

For the now following derivation it is assumed that the zero-lift drag coefficient CD0 does not change with a changing aspect ratio. During personal communications with Ir. W.A. Timmer have confirmed this assumption to be valid. He states that for a change in aspect ratio from 3.8 to 6.8 and high Reynolds numbers that are between 3 106 and 6 106 this is a valid assumption for a turbulent airfoil that a tube kite has. For Reynolds numbers that are between 1 106 and 2 106 the difference is much bigger. As is discussed⋅ later on⋅ in Section 6-4 the Reynolds numbers for a 5m tube kite during a crosswind sweep in 10 knots of true ⋅ ⋅ 6 6 wind speed are given by Remin = 2.5 10 for a standard tube kite and Remax = 5 10 for a tube kite with a doubled L/D ratio. When bigger kites are considered, like a 25m kite for ⋅ ⋅ kitesailing then also the Reynolds number increases. Therefore CD0 is considered constant.

When the induced drag is now lowered by increasing the aspect ratio the relation CDi = CD0 is not equal anymore for the given flight conditions. But it should be valid to get L D max, so one of the parameters must be changed to make the two types of drag equal again.( ) ( ~ ) The only parameter that can be changed is the lift coefficient because the aspect ratio and Oswald efficiency factor are fixed numbers in a certain flight condition for a given kite. There- fore, when for a given kite the aspect ratio is increased and keeping a constant surface area, the lift coefficient should be increased to reach the maximum value for the L/D ratio. This means that the angle of attack where L D max is reached is increased by increasing the aspect ratio. ( ~ ) It also means that by increasing the aspect ratio the total lift of the kite is increased at L D max. The dependence of the relation between the lift coefficient C and the angle of attack α is ( ~ ) L also investigated in Laurea [2007]. Figure 6-8 shows The CL α curve for a wing with two different aspect ratios and a surf kite shape using the same airfoil. − It shows that a lower aspect ratio reduces the lift coefficient for every positive angle of attack. The non-planar configuration of a surf kite also lowers the lift coefficients which is further discussed in the following subsection.

6-2-3 Non-planar wings

A tube kite is a wing that is called a non-planar wing in aviation. These are wings that are cambered in the spanwise direction. Cone [1962] performed very basic research on all kinds of non-planar shapes and their performance compared to planar wings. It shows that non- planar configurations influence the induced drag and create induced lift. First the influence of non-planar wings on induced drag is considered then the effect on induced lift. The optimally loaded planar wing with given aspect ratio serves as the baseline for all other considered wing shapes in this section. The work of Cone [1962] serves as the basis of this analysis. In his research an optimum elliptical lift distributions for all the wing shapes is assumed for simplicity. This elliptical lift distribution creates a downwash behind the wing which is constant in spanwise direction which gives the lowest induced drag possible for a planar wing. The ratio of the wing span of the baseline wing over the projected wing span of the non-planar wing is called ψ:

b ψ (6-10) = b′

Kitesailing 84 Aerodynamic analysis

Figure 6-8: CL − α curve for different wings, Spalart-Allmaras turbulence model, STAR-CCM+ 6 simulations at Re = 3 10 , source: Laurea [2007] ⋅ For all wings in this section, the wing span and the total lift generated are assumed to be the same to be able to make good comparisons and therefore, ψ = 1.0. The center chord is also taken to be constant which means that the projected aspect ratio is constant. The camber factor β is introduced to describe the amount of camber of a non-planar wing. It describes the ratio of the height over the semi-span of the wing according to:

d β (6-11) = b′ 2

Figure 6-9 shows this relation graphically. ~ b′ d

Figure 6-9: Distances used to define the camber factor of a non-planar wing

The different shapes are semi-circular shapes, semi-elliptical shapes, endplates and winglets.

Kitesailing 6-2 Literature study 85

A family of circular and elliptical shapes is shown in Fig.6-10.

β β

1.0 ∶ 1.0 ∶ 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 Figure 6-10: Families of circular and elliptical shapes as described by Cone [1962]

The last two basic shapes are the end plates and winglets. Both are vertical surfaces added to the wing tip to reduce the drag induced by the tip vortices. Adding these vertical surfaces also adds friction drag which decreases the gained drag reductions. High aspect ratio end- plates reduce the increase in this so called wetted area and were termed winglets by Richard Whitcomb, who provided some of the early experimental data and practical design guidelines for such devices in Whitcomb [1976]. Cone [1962] introduced the ”‘span efficiency factor”’ k which influences the effective aspect ratio according to the following equation:

Aeff = k A (6-12)

If k > 1 then the non-planar system is more efficient than the optimum flat wing. Which means that the non-planar system has less induced drag than the flat elliptical wing for equal total lift forces. If k < 1 then the non-planar system is less efficient compared to the planar system. The induced drag is now given by:

2 CL CDi = (6-13) π Aeff

Cone [1962] proved that for the circular arc segments the value for k is given by the following relation:

1.00 0.50 β2 k (6-14) = ψ2 + Figure 6-11 shows the span efficiency factors that are achieved for semi-ellipse arcs and circular-arc segments compared to the camber factor β. Now some other wing shapes are considered. Figure 6-12 shows a set of different layouts of non-planar wings and their corresponding span efficiency factors. This span efficiency factor is equal to the ratio of the induced drag of a planar wing over that of the non-planar system of the same span and lift. Each of the geometries is permitted a vertical extent of 20% of the wing span which means β = 0.4. Also each design has the same projected span, center chord and total lift. Similar results for a variety of shapes have been described by Munk [1921], Letcher [1972], Jones [1950] and of course Cone [1962].

Kitesailing 86 Aerodynamic analysis

Figure 6-11: The variation of the span efficiency factor of semi-ellipse arcs with the camber factor. ψ = 1.0, source: Cone [1962]

13.0 1.36

1.38 1.05

1.41

1.32 1.45

1.33 1.46

Figure 6-12: Span efficiency for various optimally loaded non-planar systems (h/b=0.2), source: Kroo [2005]

The results of the span efficiency factors for all the different shapes show that spanwise camber is most effective near the tip. This is also proved by Lowson [1990] who performed lots of research on winglets. What he basically proves is that the sharper the corner is between the horizontal wing and the winglet the greater the L/D improvement is. A straight angle of 90 degrees is therefore optimal if no other effects are taken into account such as compressibility effects. Because of the low flying speeds for kites these compressibility effects are not taken into account.

For aircraft the span is very often limited by regulations or by the space available at airports. In these cases the use of winglets can increase the L/D ratio considerably as is shown in

Kitesailing 6-2 Literature study 87

6-12. The reason that winglets are not since long used on every aircraft is that extra bending moments are introduced compared to a non-planar wing. Also increasing the span at fixed area reduces the chord length and the structural box height when the airfoil thickness/chord ratio is constrained. When fixing the structural weight. These bending moments have to be counteracted by additional structural material which adds weight which is also described in Kroo [2005]. For kites there are no span constraints for kitesurfing or kitesailing. The downside of a high aspect ratio kite though is that it turns slower due to the larger moment of inertia and it is more difficult to have the same amount of depower compared to low aspect ratio kites which is governed further in Chapter 4. It is interesting to compare the increase in performance when applying winglets and when increasing the aspect ratio. The decrease in induced drag is now taken equal for both concepts. The possible increase in lift at L D max is left outside the equations because this increase in lift can be achieved after the induced drag is lowered in the first place. ( ~ ) In Fig.6-12 it is shown that adding a winglet on every tip with a height of 20% of the wingspan gives a span efficiency factor of 1.41 which reduces the induced drag by 30%. This leads to a total drag reduction of 15% because half of the total drag is induced drag at L D Max. This results in an increase of the L/D ratio by 17%. Putting this improvement in Eq.(6-13) this results in an increase of the wingspan of 18.7%. This means that one winglet( ~ of) 20% span has the same effect of increasing the wingspan with 9.35% which is exactly the relation that Kroo [2001] uses when he states that a vertical surface located at the wing tip is worth approximately 45% of its height as additional span, if optimally loaded. The result from this is that as long as the maximum span is not reached yet there is no clear advantage of using winglets to decrease the induced drag. The effect of spanwise camber on induced lift is a fairly underdeveloped area of research. Figure 6-8 shown in previous subsection shows that the spanwise camber of a tube kite lowers the lift coefficient at positive angles of attack. Cone [1962] describes it only briefly and only a qualitative analysis is found in this report. An explanation for the lower lift coefficient when a wing is bent downwards to the tips (anhedral) is that the lower pressure on the top surface of the wing is more vulnerable to the surrounding air that can flow easier towards this region from all sides than is the case with dihedral. This causes faster pressure recovery and results in a lower lift on the top surface. There is a wing in ground effect on the lower surface because air is trapped between the tips. However this positive effect has less significance than the negative effect on the top surface because the absolute pressure coefficients are higher than on the lower surface. Applying a Vortex Lattice method in the aerodynamic simulation described by Breukels [2010] this has also been supported.

6-2-4 Examples of experimental tube kite designs

Three kite brands are known that have tried two different technical concepts in the search for higher aerodynamic efficiencies. The first one is a double skin kite to minimize the wake behind the leading edge. The second concept is a leading edge with two tubes with different diameters instead of one to approach the elliptical shape of airplane wings. The Wipika double skin tube kite is shown in Fig.6-13.

Kitesailing 88 Aerodynamic analysis

Figure 6-13: Double skin Wipika kite tested in 2006

Also Don Montague who used to design the Naish kites has experimented with a partially double skinned tube kite as can be seen in Fig.6-14.

Figure 6-14: Semi-double skin Naish kite

Gaastra is the only brand that actually sold a type of kite with an unconventional design in the search for higher L/D ratio. This kite had a dual leading edge and was offered to the public in 2003 but only for one year. It was the Gaastra Phoenix 25 m kite which is shown in Fig.6-15. This kite was specifically designed for low wind conditions and had to compete with the 20 m kites that were common in those days. A short test report can be read on Phoenix 25m test report [2003].

Figure 6-15: Gaastra Phoenix 25m with dual leading edge

There is one kite already present that applies both a double skin and a dual leading edge. This is the Kiteplane developed at ASSET of the Delft University of Technology. Figure 6-16

Kitesailing 6-2 Literature study 89 shows this kite that is designed as an airplane for stability reasons.

Figure 6-16: Kiteplane with double skin airfoil and dual leading edge

The L/D ratio of this kite is not high yet because of some production errors and the problems that arise with a flat wingspan. The tension on the trailing edge is not high enough to keep the airfoil nicely in shape and the trailing edge of the vertical tail planes are never straight. A new design that is being produced at the time of writing should give better results.

The examples in this section show that efforts are made to increase the efficiencies of tube kites by changing the airfoil. However they are not used in kitesurfing at all. The interesting question becomes: Why are they not used in kitesurfing? A number of possible reasons for this can be given.

First of all the concepts have not been developed to such an extend that they provide a proven increase in L/D ratio. All these experimental surfing kites either use a modified leading edge or a double skin to some extend. Section 6-2 shows the theoretical improvements that have been proved in windtunnel testing. These possible gains are considerable but also have their drawbacks. When applying a double skin and a non-circular leading edge a number of difficulties arise that are not easily solved. These difficulties are experienced in flight tests and are discussed in Section 6-5. It shows that it is difficult to get the airfoil shape right and stable under various flying conditions.

Other drawbacks for the use in kitesurfing are practical disadvantages. Extra weight is added by the added material which is bad for kitesurfers in general because they need stronger wind speeds before they can go out on the water. A dual leading edge also means more pumping to get the kite inflated. More elements on the kite also means that more parts can break which likely reduces durability. Also a crashed kite with double skin can get water inside the kite which makes it impossible to relaunch it again. An other reason is that the extra elements will definitely make the kite more expensive for the end users. These reasons all work against the technological advances that could be achieved in kite designs.

The final remark is that for kitesurfing the L/D ratio is an important parameter but not the most important one. The focus is on fast turning, a good L/D ratio and lots of depower. For kitesailing however the L/D ratio is of much more importance and definitely worth the effort of performing research on. The following section shows the preliminary research to define concepts for improving the L/D ratio of a tube kite.

Kitesailing 90 Aerodynamic analysis

6-3 Applying aerodynamic theory to kites

The theory found in literature is applied on existing tube kites. First the airfoil is redesigned for the Ozone Sport 5 m2 kite. Then the influence of the aspect ratio on the Airush Flow 5 m2 kite is considered. Also research has been performed on a rectangular wing with different non-planar configurations. A trade-off is made to determine the concept that is worked out in more detail.

6-3-1 Airfoil analysis

From the analysis performed in Subsection 6-2-1 it is known that the performance of the round leading edge of the Semi-Sailwings is rather poor compared to the other two leading edge shapes which perform 45% better in terms of L/D ratio than the round leading edge model. This analysis is also performed using Xfoil for which the two tested airfoils are shown in Fig.6-17. The airfoil is that of the Ozone Sport 5m kite with an added lower skin. The added elliptical leading edge shows no change in total lift but does show an improvement of the L/D ratio of 40% which is comparable to the result of Maughmer. The way that the leading edge and the added lower skin are designed is discussed in Section 6-4. Extensive research is required to investigate what the difference is in performance between an optimal elliptical shape and the current leading edge shapes. This is outside the scope of this thesis.

Figure 6-17: Compared airfoil sections with and without an elliptical leading edge

In this figure the purple line shows the profile of the original Ozone Sport 5m kite. The green line shows the shape of the lower skin and the dark solid area is the added volume to achieve an elliptical leading edge. According to Maughmer [2002] such an airfoil shape will perform so good that he says: ”It has been found that the L/D ratio of the Sailwing can approach that of a hard wing.”

6-3-2 Aspect ratio on the Flow 5m kite

The theory on the aspect ratio is now applied to the Airush Flow 5 m tube kite. 2 The value CD0 is assumed constant again as long as the term CL varies linearly with CD. This is the case for the straight part of the CL-α curve that any airfoil has. The test results for 2 the CD-CL curve and the L/D-CL curve of the 2008 Airush Flow 5m taken from Vlugt [2009] are shown in Figs. 6-18 and 6-19. Both figures have the same correlation coefficient of 0.872. When this correlation coefficient equals 1 then the data is perfect so this data has reasonable accuracy. The data points are measured during the crosswind sweep tests performed on the beach and described by Vlugt [2009].

Kitesailing 6-3 Applying aerodynamic theory to kites 91

Figure 6-18: Experimentally obtained relation between the kite drag coefficient and the lift coefficient squared of the Flow 5m kite, source: Vlugt [2009]

Figure 6-19: Experimentally obtained relation between the lift coefficient and the lift to drag ratio of the Flow 5m kite, source: Vlugt [2009]

From Fig.6-18 it is concluded that for lift coefficient values up to CL = 1 the drag varies 2 linearly with CL and therefore Eq.(6-1) is valid up to this point. Figure 6-19 shows that the value for the lift coefficient is 0.75 at maximum L/D for this kite which is also used in Section 6-1. Using Matlab the relation is derived for the aspect ratio and the optimum lift coefficient for the kite. In this program the lift coefficient is changed by a step function and each time the according aspect ratio is calculated according to Eq.(6-15).

2 CL A = (6-15) π CD0 e

The maximum lift coefficient is taken to be 1.0 because this is within the limit for which the zero-lift drag coefficient remains constant for this tube kite. Table 6-2 shows the results of some aerodynamic properties that are of particular interest. In these calculations it is assumed that the zero-lift drag coefficient is not affected by increasing the aspect ratio because the total surface area and the profile shape is assumed to be constant. The results from this table are plotted and shown in the following figures. Figure 6-21 shows the accompanying lift coefficient for varying aspect ratios of the Flow tube kite. The original aspect ratio is 3.8. If this is increased to 6.8 the lift coefficient at L D max will increase from 0.75 to 1.0 which is an increase of 33% and therefore considerable. The increase in lift to drag ratio is shown in Fig.6-21. Both the trends are shown for an( increase~ ) in aspect ratio when including an increased lift coefficient and keeping the lift coefficient constant at a value of 0.75 as one would do when applying standard aircraft theory.

Kitesailing 92 Aerodynamic analysis

Table 6-2: Comparing the lift coefficient and L/D ratio with a change in aspect ratio using newly derived relations for the Flow 5m kite with CDi = CD = 0.0668

CL Aspect ratio L D max 0.60 2.45 4.49 ( ~ ) 0.65 2.87 4.87 and 0.70 3.34 5.24 0.75 3.83 5.61 0.80 4.36 5.99 0.85 4.92 6.36 0.90 5.51 6.74 0.95 6.14 7.11 1.00 6.81 7.49

1

0.90

0.80

0.7

0.6

0.5

0.4

0.3 Cl accompanying (L/D)max 0.2

0.1

0 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Aspect ratio

Figure 6-20: Increase in lift resulting from an increase in aspect ratio for the Flow 5m kite

Figure 6-21 shows that this increase of lift coefficient together with the aspect ratio increases the lift to drag ratio more than is predicted by conventional airfoil theory. For the optimum aspect ratio of 6.8 that accompanies a lift coefficient of 1.0 shows a difference in L D max of more than 4% together with the already achieved improvement of 28% comparing to the old situation and the increased total lift of the kite of 33%. When comparing these( ~ accom-) panying angles of attack settings belonging to the different lift coefficients and applying it to a crosswind sweep, as described in Chapter 2, the improvement is even of some more value. During a crosswind motion the flight velocity depends linearly on the L/D ratio. The total 2 lift of the kite therefore varies linearly with CL L D . The relation for the total lift as a function of the aspect ratio for both angle of attack settings is shown in Fig.6-22. ⋅ ( ~ ) This figure shows that during a crosswind motion the difference in total lift for the kite with aspect ratio of 6.8 is more than 8%.

Kitesailing 6-3 Applying aerodynamic theory to kites 93

8

7

6

5

4 L/D max 3

2

1.00 Including an increased CL With constant CL of 0.75 0 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Aspect ratio

Figure 6-21: Increase in L/D resulting from an increase in aspect ratio for the Flow 5m kite

60

50

40

30

20

10

Product of lift coefficient and (L/D) squared Including an increased CL With constant CL of 0.75 0 2.5 3 3.5 4 4.5 5 5.5 6 6.5 Aspect ratio

Figure 6-22: Difference in total lift for the Flow 5m tube kite in pure crosswind sweep using the original optimum angle of attack and the new optimum angle of attack using derived theory

When designing a kite the value for the aspect ratio determines the wingspan and the chord lengths. These are the values that can be used in the actual design of the kite so it is interesting to plot the relations shown above again with the increase in actual wingspan instead of the required aspect ratio. Appendix E shows the same performance diagrams but then with the increase in wingspan instead of the aspect ratio for the Flow 5m kite.

Kitesailing 94 Aerodynamic analysis

Conclusions:

The aspect ratio has a big impact on kite performance. The most interesting effect of in- creasing the aspect ratio is that the total lift at L D max increases considerably. The 2008 Airush Flow 5m tube kite is analyzed. Increasing the aspect ratio from 3.8 to 6.8, which is equal to an increase in the wingspan of 30%, and( keeping~ ) the surface area constant results in a total increase in lift of 33% at an increase of 33% of L D max.

( ~ ) 6-3-3 Non-planar wings

Because tube kites are designed with different amounts of spanwise camber it is interesting to compare some basic shapes to determine if there are big differences in performance. Four types of kites are considered: A planar wing with wingspan b. An Elliptical shaped kite with ′ ′ β = 0.5 and a projected span b = b. A C-shaped kite also with projected span b = b and a planar wing again, created by taking the C-shape kite and folding it out on a flat plane. These wings are shown in Fig.6-23.

Planar wing 2

C-shape (β = 1.0)

Elliptical (β = 0.5)

Planar wing 1

Figure 6-23: The four kite shapes that are compared

The assumptions in this analysis are that all the wings have an optimal lift distribution. Just as in sub section 6-2-2 also the profile of the wings change with the change in Reynolds numbers such that the zero-lift drag coefficient remains constant for all wings. The wings are all assumed to be rectangular shapes for simplicity. The dimensions of the projected wingspan ′ and the chord length of the initial planar wing are given by b = 1.7 and c = 1 both in meters. An extra note is that the effect of induced lift is not taken into account. Therefore it is expected that the real values are different than the outcomes shown here. Because no numbers on this induced lift are at hand the effect of this cannot be quantified. The geometric dimensions of the wings are given by Table 6-3 where c is the root chord length, b is the wingspan, A is the aspect ratio and S is the surface area. The accents indicate it is the projected value of these dimensions.

The values for the span efficiency factor k are taken from Fig.6-5. The values for the zero-drag lift coefficient is taken to be the same as it is for the Flow 5m kite and therefore CD0 = 0.07. This means that CDi = 0.07 because CDi = CD0 is valid at L D max. The lift coefficients are

Kitesailing ( ~ ) 6-3 Applying aerodynamic theory to kites 95

Table 6-3: Geometric values for the compared wings

c b’ b A’ A S’ S Planar wing 1 1 1.7 1.7 1.7 1.7 1.7 1.7 Elliptical (β = 0.5) 1 1.7 2.06 1.7 2.06 1.7 2.06 C-shape (β = 1.0) 1 1.7 2.67 1.7 2.67 1.7 2.67 Planar wing 2 1 2.7 2.67 2.67 2.67 2.67 2.67 now calculated using Eq.6-16 which is Eq.(6-15) rewrited.

′ CL = C D0 k πA (6-16) » The aerodynamic coefficients are given by Table 6-4.

Table 6-4: Coefficients for the compared wings with CD0 = CDi = 0.07

k CL Planar wing 1 1.0 0.61 Elliptical (β = 0.5) 1.3 0.70 C-shape (β = 1.0) 1.5 0.75 Planar wing 2 1.0 0.77

From the geometric values and the calculated coefficients the performance values are calcu- lated and shown in Table 6-5. All the values should be multiplied with the dynamic pressure q∞ given by:

1 2 q∞ ρ V (6-17) = 2

Table 6-5: Performance of the four different wing types

2 ′ 2 LD L D max L m L m Planar wing 1 1.04 0.24 4.37 0.61 0.61 ( ~ ) ( ~ ) ~ Elliptical (β = 0.5) 1.19 0.29 4.11 0.70 0.58 C-shape (β = 1.0) 1.27 0.37 3.41 0.75 0.48 Planar wing 2 2.05 0.37 5.47 0.77 0.77

These values are the real values experienced when using the kite and therefore determine the real performance of the kite. The percentages that give the differences are now given in Table 6-6 to get a good overview of the performance differences.

Conclusions:

1. A vertical surface located at the wing tip is worth approximately 45% of its height as additional span, if optimally loaded.

Kitesailing 96 Aerodynamic analysis

Table 6-6: Differences with respect to planar wing 1

L L D max Planar wing 1 0% 0% ( ~ ) Elliptical (β = 0.5) 14% -6% C-shape (β = 1.0) 22% -22% Planar wing 2 97% 25% Planar wing 2 61% 61% (Compared to C-shape)

2. Increasing the spanwise camber of a kite results in more lift and a lower L/D ratio, both at L D max.

3. At( L~ D) max, an elliptical wing with a camber factor β = 0.5 has 14% more lift and a 6% lower L/D ratio compared to the planar wing with the same projected area. ( ~ ) 4. A C-shape wing with β = 1.0 has 22% more lift and a 22% lower L/D ratio, both at L D max, compared to the planar wing with the same projected area.

5.( When~ ) a C-shape kite is a laid out as a flat wing it has 60% more lift and a 60% higher L/D ratio, both at L D max, compared to the original C-shape kite.

6. Planar wing 2 has 97%( ~ more) lift than Planar wing 1 and a 25% higher L D max.

( ~ ) 6-3-4 Trade off for concept to be worked out in detail

To make the decision on what to investigate in more depth, a number of different parameters are considered. The first one is the theoretical improvement in maximum L/D ratio. The first possible concept is the airfoil shape. This can decrease the profile drag and as such create higher L/D ratio. The second way to improve the L/D ratio is to decrease the induced drag. This can be achieved either by adding winglets or by increasing the aspect ratio. The analysis shows that as long as the aspect ratio can be increased this is an easier and more efficient way to increase the L/D ratio because adding winglets gives the same result as adding 45% of this winglet height as extra span. Also, adding winglets requires a special design for the construction whereas increasing the aspect ratio a bit keeps the basic construction of a tube kite exactly the same. An extra reason to prefer looking at increasing the aspect ratio is that the gains that can be achieved compared to winglets are much higher. Next to the aerodynamic improvements the added weight could be an interesting parameter together with the extra tension in the canopy that is introduced which could lead to the need for more material which increases the weight again. It is decided that only the increase in tension is shown because the added weight which is needed for a certain improvement is highly dependent on the design itself. The following section will clarify this. The change in canopy tension when increasing the aspect ratio results from the changes in total lift determined in the previous subsections and multiplying it with the change in chord length. This gives a basic idea on the change of internal forces through the canopy.

Kitesailing 6-4 Airfoil design 97

Table 6-7: Aerodynamic improvements that can be achieved per concept together with changes in canopy tension

L D max CL at L D max Canopy tension Lower skin 46% -9% -50% ( ~ ) ( ~ ) Elliptical leading edge 45% - - Winglets (20%) 9% 9% 9% Aspect ratio 80% 33% 33% 240%

+ Table 6-7 shows the aerodynamic improvements that can be achieved per concept. It is clearly visible that the adjustments on the profile promise the biggest improvements in L/D ratio. Adding winglets creates the least amount of improvement. Increasing the aspect ratio has the clear advantage that the total lift of the kite is also improved. From these numbers the choice has been made to investigate the airfoil shape in more depth. The gains in L/D ratio are much bigger and the two concepts for this can be combined because they are part of one airfoil design. Also Maughmer [2002] says about airfoils with an elliptical leading edge and double skin in relation to simplified versions: ”It is inconceivable of a situa- tion in which the potential benefit in weight saving, cost, or more-simplified construction for any of the modified versions could be justified in relation to the performance penalties.” The theoretical gains are in increase in L/D ratio of almost 100% which is extremely interesting. The advantage of more lift per unit area when applying an increased aspect ratio is of less importance at this moment because already the kite is scaled up to a size of 25m as a first step from tube kites which will already give a great improvement in total lift generated. This is shown in Chapter 5.

6-4 Airfoil design

The choice is made to design an airfoil that has an added lower skin and an elliptical leading edge. The design of these parts are now treated separately. The basic shape of the kite that is considered to improve is the Ozone Sport II 5 m tube kite. The profile is determined by taking pictures at an angle of 90 degrees to the struts of which a picture is shown in Fig.6-24.

Figure 6-24: Picture from which the profile of the center chord is determined

Such a picture is then loaded in the CAD program Rhinoceros to draw the outline of the profile. It has become obvious from this kite and others that for these tube kites a large part

Kitesailing 98 Aerodynamic analysis of the profile all the way to the trailing edge is designed to be completely straight. Figure 6-25 shows the profile as it comes out of Rhino.

Figure 6-25: Center chord profile of the Ozone Sport II 5m tube kite

Adding a lower skin creates a relatively large volume inside the kite. For construction three different types are worth considering. These are by using pressurized membranes next to each other as is shown in Fig.6-26, by using foam or by applying only sheets of fabric. Using a lightweight foam is the most heavy solution but gives the best defined shape because it can be assumed to deform very little under the aerodynamic loads. Multiple pressurized membranes are lighter than foam but make the surface area very bumpy because every tube is by definition round and it is still heavier than only using sheets of fabric. Using only fabric is the lightest solution but is also the only one without structural rigidity and is therefore also the most difficult one to apply at first glance.

Figure 6-26: Airfoil created out of tubes with a top layer on it

The bumps that occur on the surfaces when using tubes do not necessarily mean that it influences the airflow in a negative way. LeBeau & Reasor [2007] shows that in cases of very low Reynolds numbers it can even have a positive effect on the performance of the airfoil by delaying separation. To keep the weight minimal it is decided to make this lower skin only out of fabric. The profile design that comes out is shown in Fig. 6-27

Figure 6-27: Center chord profile of the Ozone Sport II 5m tube kite including a lower skin

The shape of the lower skin is determined by the pressure below the kite and by the pressure inside the kite. During initial tests in the field it was found that these pressures were the key for a good design. If the pressure inside is higher than the pressure at the bottom then the fabric will start ”ballooning”. This ballooning of a lower skin is shown in the next section in which the field tests are discussed. From Boer [1982] it is known that the pressure coefficient on the lower skin for such a configuration is constant. This means that the fabric will maintain a semi-circular shape during flight given that the pressure inside the kite is lower than underneath it. An example of how such a pressure distribution can look like is shown in Fig.6-28. This distribution is dependent on the airflow and on the shape of the profile. The shape of this figure based on measurements performed by Boer [1982]. The dashed line gives a possible pressurecoefficient inside the kite which is higher than the one on the top surface and lower compared to the bottom surface. As long as this is the case, there will be no ballooning effect.

Kitesailing 6-4 Airfoil design 99

CP

0.00

0.00 0.25 0.50 0.75 1.00

x c

~ Figure 6-28: Global pressure distribution on a Sailwing, based on windtunnel measurements, source: Boer [1982]

The curvature of the lower skin is also of great importance. Simulations in Xfoil showed that if the curvature is bigger then the moment coefficient becomes bigger which increases the tendency of the kite to go nose-down which is avoided as much as possible by kite designers as is discussed in Section 6-1. The problem however with a more straight lower surface is that the tension in the skin becomes larger. If the lower skin is only attached to the trailing edge and the leading edge then this tension pulls them together. The more straight the panel is, the more it will pull the trailing edge and leading edge together which deforms the kite from its original shape. This is also experienced in flight tests. It is not visible by eye but when the kite starts to stall faster or even does not fly at all then you know that the lower surface is folding the kite together which is terrible for performance. Supporting the lower skin by adding a rib at every strut made from fabric is one way to deal with these stresses which is already common practice for paragliders or other foil kites. Another way is by increasing the stiffness of the struts such that they are able to handle these forces without bending too much. The leading edge is designed using an ellipse as the basic shape. This shape is also used by Boer [1982] and worked very well although it is stated that optimizing that shape would lead to better performances. The shape of the ellipse is given by Eq.(6-18) with a = 2 and b = 1.

x 2 y 2 1 (6-18) a b = In the report of Boer [1982] it is concluded that+ such an ellipse gives the highest L/D values if it is rotated by more than 20○. This is the initial leading edge shape that is put into Xfoil to determine the performance of the airfoil. A great number of ellipse shapes have been created to match the kite’s profile. The best match turned out to be an ellipse with a = 120mm and b = 60mm (profile 6.2). The profile with this ellipse is tested together with some 15 other leading edge shapes but none proved to perform significantly better. This shape also matched very nicely with the existing leading edge shape of the kite. Which may, or may not be a coincidence. After this elliptical shape is determined Xfoil is used to optimize the shape to the flow conditions. The Reynolds number is calculated according to Eq.(6-19).

ρV c Re (6-19) = µ

Kitesailing 100 Aerodynamic analysis

The values that apply in the flight conditions during the crosswind sweep tests in which the kite will be tested are given by:

3 ρ = 1.225 kg/m (6-20) −5 µ = 1.79 10 kg/ms (6-21) c 1.3 m (6-22) = ⋅

The flight speed is calculated by assuming a true wind speed of 10 knots and a maximum L/D ratio of 11 2 5.5 . The flight speed in a crosswind sweep then becomes 110 knots which equals 202 km h which is equal to 34 m/s. For a kite this is extremely fast and this is only achieved when( ⋅ the) maximum theoretical increase in L/D is achieved. This speed is unheard of for kites at~ this moment and tests in the future have to show if this is possible. 6 The Reynolds number follows from this speed and therefore Remax = 5 10 . The minimum Reynolds number is calculated with a L/D ratio of the standard kite which is assumed to be the same as the Flow 5m kite and equals 5.5. The accompanying flight⋅ speed then becomes 6 17 m/s which results in Remin = 2.5 10 . Figure 6-29 shows the profile with the⋅ dark area as the part that is made from foam to create the elliptical leading edge. The purple part is the shape of the original kite and the yellow line show the outline of the lower skin made from fabric.

Figure 6-29: Final design of improved center chord profile of the Ozone Sport II 5m tube kite

The leading edge is now zoomed in on in Fig.6-30 to show the tiny amount of foam that is needed to construct it. The widest part is only 2 cm thick which keeps the added weight to a minimum and also takes away the need to construct it from tubes or fabric. Also because of the structural rigidity of the foam and the extension over the canopy of the kite it could introduce a much larger region of laminar flow if the surface is created smooth enough. As is shown in Section 6-1 this part of the kite is where almost all the lift is created and therefore it is a very critical part too. The possible gains from this effect are not treated here any further however.

10 mm 2 mm 18 mm

Figure 6-30: Thicknesses of the foam on the leading edge at the center strut

Kitesailing 6-5 Tests on a lower skin 101

The elliptical part of the leading edge can be made of Polypropyleen closed cell foam which is very light and non-water absorbing which makes it suitable to use on the water. It is easy to cut into the desired shape by using a hot-wire. Also it is very flexible so it can not easily break or get damaged in any expected circumstance. Future work on this is putting the entire 3D design of the kite in Rhino and create a 3D design for the foam part of the entire leading edge as well for the lower skin. Also the ribs for the lower skin have to be carefully designed. The way that the foam parts should be attached to the kite is by encapsulating them in rip-stop nylon with extended flaps that can be sewn onto the kite. Another area that should be investigated is possible problems that occur during folding up of the kite. Also the shape of the leading edge can be optimized further. When this is done it is wise to keep in mind that is seems best to design the leading edge with a large radius. According to the test results of Maughmer [2002] the difference in performance between a sharp and a blunt leading edge is negligible. However a sharp leading edge has more abrupt stalling characteristics and the weight of the added foam can be minimized because the standard leading edge shape of tube kites is also fairly blunt already. A complete round leading edge is very bad in performance according to Maughmer [2002].

6-5 Tests on a lower skin

Tests have been performed to investigate the problems that occur when applying a double skin and solve them to validate the design shown in the previous subsection. Also a foam section of the kite is tested which constructed a Semi-Sailwing to see if this would be easier in construction and getting test results.

6-5-1 Fabric double skin

The double skin made out of rip-stop nylon fabric has been tested in phases to experience all the effects that play a role in successfully designing a double skin tube kite. All the tests have been performed on a Naish Aero 4 m tube kite which was the smallest tube kite available. Figure 6-31 shows this kite with only a part of the lower skin constructed on it. It clearly shows the large volume that is created within the profile.

Figure 6-31: A part of a double skin constructed on a Naish Aero 4m tube kite

Then the complete lower skin was produced and tested. Fig.6-32 shows what happens if the inner pressure is to low.

Kitesailing 102 Aerodynamic analysis

Figure 6-32: The top surface is under zero tension due to the absence of a pressure difference above and below the surface

The lower skin has holes in it near the trailing edge to allow the struts to pass through them in this design. These holes cannot transfer internal stresses which results in stress concentrations at the edges of the holes as is shown Fig.6-33.

Figure 6-33: stress concentrations are created by the cuts in the fabric and air can move freely between the volume inside the kite and the airflow underneath the kite

The fact that air can move freely between the volume within the kite and the airflow under- neath the kite creates a loss of control over the pressure within the kite. Figure 6-32 showed that the pressure within the kite was too low which is created by air leaking away at the back of the kite through the trailing edge, which was not sealed, and through these holes. To create a higher pressure within the kite the trailing edge was sealed by Velcro to allow access to the valves within the kite and to allow fine tuning of the lower skin.

Figure 6-34: Two airinlets increase the pressure inside the kite

Kitesailing 6-5 Tests on a lower skin 103

Sealing of the trailing edge and having the two air inlets proved to create an over pressure with respect to the surrounding airflow. The pictures in Fig.6-35 show ballooning of the lower skin which results in a shortening of the chord lengths between the struts.

Figure 6-35: Bollooning of the airfoil creates shorter chord lengths

The shape of the trailing edge is closely fotographed on the ground and shown in Fig.6-36.

Figure 6-36: Ballooning near the trailing edge in close up

When one air inlet is closed the general shape of the kite starts to look a lot better showing no ballooning and a sharper leading edge. Figure 6-37 shows it in flight.

Figure 6-37: The general shape with only one air inlet open during flight

The next problem that has to be tackled is the stress concentrations around the cuts in the lower skin. Figure 6-33 already showed these stress concentrations and Fig.6-38 shows them for the entire kite when flying just above the ground. Closing the cuts for the struts resulted in a nice shape of the lower skin. Also closing both of the air intakes results in a completely sealed of volume inside the kite which gives the best

Kitesailing 104 Aerodynamic analysis

Figure 6-38: Stress concentrations are present everywhere on the lower surface where cuts are made

control over the pressure because then it is always constant and equal to the static pressure with the value for Cp shown in Fig.6-28 equal to zero. Sealing off the volume creates the best shape of the kite and is shown in Fig.6-39. It gives a very nice sharp leading edge and the lower skin does not show all kinds of tension lines. What is also surprising is that the lower skin is made out of a single panel up to this point with no apparent problems at all except that it seems to create a lot of compression forces on the struts that cause them to bend which is visible on some pictures.

Figure 6-39: Closing the volume inside the kite leads to the best general shape of the kite

The problem at this point is that the length of the trailing edge of the kite is lowered because the two skins have to fold around the struts. The resulting shape of the top surface is shown in Fig.6-40. This caused the kite to fly awful due to the continuous stalling of the wing.

Figure 6-40: The shortening of the trailing edge results in continuous stall of the kite

Kitesailing replacemen 6-6 Conclusions 105

At this point this particular lower skin has to be modified extensively to make the next steps in improvement. For future work it is advised to create the lower skin out of more panels to create a double curved surface that matches the top surface such that the stress distribution becomes more or less the same as for the top surface. It is also advised to redesign the struts for attachment of the lower skin over the entire length of the struts. To improve the shape of the trailing edge and make it nicely sharp it is probably best to add a series of small ribs that extend to the point where ballooning occurs occasionally.

6-5-2 Foam semi-double skin

Only one test on the foam double skin has been performed and is therefore quickly addressed here. The two pictures in Fig.6-41 show the modified kite. The idea was to quickly produce and test a Semi-Sailwing as was tested by Maughmer [2002] and discussed in Section 6-2. It is constructed using Polypropylene closed cell foam which is cut using a hot-wire. Production is easy but mounting it on the kite firmly proves to be more of a challenge. The tests resulted in failure of the foam construction because the leading edge was not sealed off properly and wind got under the foam panels. No further research was performed because the expectations of the double skin were much higher in terms of performance and weight.

Figure 6-41: A semi-double skin constructed from foam on the Ozone Sport II 5m tube kite

6-6 Conclusions

The lift coefficient of tube kites is already comparable to those of other ”flying wing airfoils”. Adding a lower skin and an elliptical leading edge both improve the L/D ratio with almost 50%. Increasing the aspect ratio increases the L D max with the accompanying lift coefficient and the maximum lift coefficient CL max. The canopy tension also increases considerably. Adding winglets is not usefull as long as the aspect( ~ ) ratio can be increased. ( ) The field tests have shown that the secret to a good design of a twin skin tube kite is getting the static pressure inside the kite to be higher than the value at the top surface and lower than the value on the bottom surface over the entire chord length. Preferably everywhere on the kite. Sealing off the volume as much as possible gives the best general shape of the kite due to a constant pressure that is between those at the top and at the bottom of the kite.

Kitesailing 106 Aerodynamic analysis

New strut designs are needed to attach the lower skin to and to increase the bending stiffness of the struts such that the kite will keep its design shape also under high loads. The shape of the lower skin should also be designed as a double curved surface.

Kitesailing Chapter 7

Kitesailing system review

The kite that is developed has been implemented in kitesailing and in the TU Delft kite power demonstration system. The increase in sailing speed is tested at the ”Round of Texel”. Six hundred catamarans compete in this race making it the biggest catamaran race in the world. The maximum surface area that is primarily limited by the safety requirements is discussed in Section 7-1. The improvement in sailing speed is discussed in Section 7-2. Section 7-3 shows the maximum pulling force of the kite and the buckling behavior.

7-1 Maximum surface area

The sailing speed of the boat is increased when using a larger sail area which is shown in Chapter 3. The size of the kite however is limited by the safety requirements. Chapter 4 shows that the bridle of a kite can be made such that the possibility of zero lift on every position in the wind window is present. The safety requirement that limits the surface area is that the kite is not allowed to generate more than 450 N when it is in a zero lift mode. The drag is calculated using the drag relation from John D. Anderson [2001]:

1 2 D CD ρA VA SA (7-1) = 2 Because the lift is zero, the drag coefficient, calculated by Eq.6-8, is given by CD = CD0. Taking D = 450 N the relation for the surface area SA and the apparent wind speed VA can be given using Eq.7-1. Figure 7-1 shows the plot of the surface areas against the apparent wind speed VA.

The values for the zero lift drag coefficient CD0 (source: Vlugt [2009]) and the air density ρA are given by:

CD0 = 0.07 (7-2) 3 ρA = 1.225 kg m (7-3)

[ ~ ] Kitesailing 108 Kitesailing system review

15

14.5

14 ] s m ~

[ 13.5 A V 13

12.5

12

11.5

Apparent wind speed 11

10.5

10 40 50 60 70 80 90 100 110 Kite area S [m2]

Figure 7-1: Allowable surface area for a range of apparent wind speeds for a limited total drag of 450 N at zero lift

Figure 7-1 shows that for an apparent wind speed of 15 m s the surface area of the kite can be 46 m2 for which it still meets the safety requirements. At this point other criteria will limit the sail area like handling forces that get too large. ~

7-2 Sailing speed

In 2009 and 2010 the ”‘Round of Texel”’ was sailed with the Hobie Tiger kitesailing catamaran. The recorded GPS plots are shown in Fig.7-2. The wind direction in 2009 was west-northwest and in 2010 it was north-northwest.

17 17

Figure 7-2: Track of the kitesailing record runs around Texel in 2009 (left) and 2010 (right)

Table 7-1 shows the lap times of the kitesailing catamaran and the fastest competitor using conventional sails on that day.

Table 7-1: Laptimes of the record runs of the kitesailing catamaran and the fastest competitor using conventional sails in 2009 and 2010

2009 2010 Kitesailing 4:45 4:00 Conventional 2:07 2:30

Kitesailing 7-3 Maximum pulling force is 5800 N 109

It is clear that the performance of the kitesailing system has increased considerably. The difference in lap time between the kitesailing system and conventional system between 2009 and 2010 has been decreased by one hour and ten minutes. The average sailing speeds measured by the GPS in 2009 and in 2010 are shown in Table 7-2 together with the speeds sailed by the top class F18 catamaran team Heemskerk/Tentij obtained from personal conversations with them.

Table 7-2: Average sailing speeds (in knots) on three different courses in 2009 and 2010 for the kitesailing catamaran and the maximum sailing speeds of the top class F18 catamaran team Heemskerk/Tentij

2009 2010 F18 Heemskerk/Tentij Upwind (60 deg) 6 9 12 Half wind (90 deg) 10 16 22 Downwind (135 deg) 11 15 30

The wind conditions and currents were similar for both years but certainly not the same. The results in table 7-2 give a nice indication together with the results from Table 7-1. The measured average sailing speeds have increased in 2010 by 50% on average. compared to 2009. When comparing these numbers with the analysis in Chapter 3 this increase in speed is larger than expected. Table 3-1 shows that the increase in sailing speed in an upwind course of 60 deg between the original 13 m2 and the new 25 m2 kite is 27%. The difference can be explained by stronger winds in 2010, possibly more favourable currents on the measured intervals or improved skills of the sailors.

7-3 Maximum pulling force is 5800 N

The strength and buckling resistance is determined on the TU Delft kite power demonstration system which is discussed in Section 2-2. A picture of the ground station is shown in Fig.7-3.

Figure 7-3: Laddermill ground station on which the line forces are measured

During flight tests on the Laddermill system the forces at which the kite starts to buckle is measured to be between 4000 and 4500 N. The force at which multiple bridle points and lines failed was measured to be at 5800/,N. A picture, 1 second before failure, is shown in Fig.7-4.

Kitesailing V∞

110 Kitesailing system review

Figure 7-4: Buckling at the tips of the 25m kite with a tether force of 5800 N

This picture shows that the kite buckles at the lowest bridle point that is moved from its design position to the next bridle attachment point on the leading edge. This is shown in Fig.7-5.

Figure 7-5: CAD drawing of the 25m kite with the change of the lowest bridle attachment point

The change of the position of the lowest bridle point on both sides was made because the tip area between the original point and the steering line attachment points bended outwards during flight. Moving the point to the shown location solved this problem. This point moves inwards during high load conditions. The center of the kite with the bridle points more closely together stays in good shape as is visible in Fig.7-4.

Kitesailing Chapter 8

Conclusions and recommendations

Kites are increasingly applied to areas like sailing and energy production. Kitesailing offers higher sailing speeds and more extreme maneuvers compared to conventional sailing. To increase the performance and safety the following set of requirements is determined:

1. The kite is not allowed to generate more than 450 N in the center of the wind window while it is fully depowered for an 18 ft catamaran

2. The kite must have the possibility of creating zero lift on every position in the wind window.

3. The kite should be able to handle pulling forces of at least 3000 N.

4. The scaled kite must be able to handle twice the aerodynamic load per square meter without buckling compared to the original kite.

5. The L/D ratio of the kite should be as high as possible for sailing upwind.

The goal of this thesis is to determine what parameters should be focused on to effectively increase the performance of kitesailing and to design, produce and test a new kitesailing system that meets these requirements.

8-1 Conclusions

The designed systems for kitesailing fully meet the requirements. Also the parameters that should be focused on in the future are determined.

Kitesailing 112 Conclusions and recommendations

Sailing system analysis From the sailing system analysis it follows that the focus should be on increasing the lift of the kite by either increasing the lift coefficient CL,A or the surface area SA for effectively improving the overall performance of the sailing system. The surface area is the most promising way to effectively increase the sailing speed. Increasing the kite area from 13 m2 to 25 m2 increases the sailing speed by 30% on an upwind course. A 50 m2 kite doubles the sailing speed upwind compaerd to a 13 m2 kite.

Depower system design A bridle analysis and design program has been written with two different methods to determine the discrete force distribution on the bridle points of an exist- ing kite. The calculated aerodynamic loads on the tips using an aerodynamic lift distribution proved to be too small. The bridles designed using the original geometric bridle layout gave good general shapes of the kite during flight. A bridle configuration is designed which completely fulfills the requirements of supporting the kite such that it has its design shape during flight and of offering the possibility of zero lift on every position in the wind window. With this capability to depower the size of the kite can be made much larger than the sail area used on a conventional 18 ft catamaran and still keep within the safety requirements. Even in wind speeds of 15 m s the kite area can still be increased to 45 m2. ~

Scaling of kites Rules of thumb have been derived for scaling of a tube kite. A new 25 m2 kite is designed, produced and tested. Tests have shown that this kite can easily cope with the design loads of 3000 N without buckling of the leading edge.

Aerodynamic analysis The maximum lift coefficient of CL max > 1.1 for tube kites is al- ready comparable to those of other ”flying wing airfoils”. Therefore this area is difficult to improve. The L/D ratio offers greater possibilities. ( ) For improving the L/D ratio, four concepts have been analyzed:

Adding a lower skin

● Adding an elliptical leading edge

● Add winglets

● Increase the aspect ratio

Adding● a lower skin and an elliptical leading edge both improve the L/D ratio with almost 50%. Increasing the aspect ratio by 80% increases the L D max with the accompanying lift coefficient by 33% and the maximum lift coefficient CL max. The canopy tension also increases by 250%. Adding winglets is not usefull as long as( the~ ) aspect ratio can be increased. ( ) Field tests with a lower skin on a Naish Aero 4 m2 tube kite have shown that this concept can be successfully applied. The leading edge can be made with a minimum amount of foam of only 18 mm of maximum thickness on a 5 m2 tube kite.

Kitesailing 8-2 Recommendations 113

Kitesailing results In 2009 and 2010 the ”‘Round of Texel”’ was sailed with the Hobie Tiger kitesailing catamaran. The lap times of the kitesailing catamaran and the fastest competitor using conventional sails on that day are given by following table:

Table 8-1: Laptimes of the record runs of the kitesailing catamaran and the fastest competitor using conventional sails in 2009 and 2010

2009 2010 Kitesailing 4:45 4:00 Conventional 2:07 2:30

It shows that the difference in lap time between the kitesailing system and conventional system between 2009 and 2010 has been decreased by one hour and ten minutes.

8-2 Recommendations

For the depower it is recommended that the best performing bridle design on the 5 m2 kite is applied to the 25 m2 kite and that the stability of this bridle is tested and improved if necessary. The forces needed to control the kite by the kite flyer should be investigated and ways have to be found to decrease these forces such that larger kites can be used for kitesailing. For increasing the L/D ratio of the kite it is recommended that a new kite is developed with struts that also support the lower skin over the entire chord length. The foam parts of the leading edge should be further developed and tested.

Kitesailing 114 Conclusions and recommendations

Kitesailing Bibliography

Boer, R. den. (1980). Low speed aerodynamic characteristics of a two-dimensional sailwing with adjustable slack of the sail (No. Report LR-907). Kluyverweg 1 - Delft: Delft University of Technology, Department of Aerospace Engineering.

Boer, R. den. (1982). Numerical and experimental investigation of the aerodynamics of double membrane sailwing airfoil sections (No. Report LR-345). Delft University of Technology, Department of Aerospace Engineering.

Boot in beeld. (2009, June 12). http://www.bootinbeeld.nl.

Breukels, J. (2010, April 21). An engineering methodology for kite design. In . Delft University of Technology.

Breukels, J., & Ockels, W. J. (2008). Analysis of complex inflatable structures using a multi- body dynamics approach.

Breukels, J., & Ockels, W. J. (2010). Simulation of a flexible arc-shaped surf kite. Submitted to AIAA journal of aircraft.

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Canadian windrider. (2010, July 7). http://www.canadianwindrider.com/products/ watercraft/kitecat.html#Kite Cat.

Comer, R., & Levy, S. (1963). Deflections of an inflated circular-cylindrical cantilever beam.

Cone, C. (1962). The Theory of Induced Lift and Minimum Induced Drag on Non-Planar Lifting Systems. NASA TR-R-139.

Ecolution. (2010, July 15). http://www.ecolutions.nl/.

Eppler, R. (1990). Airfoil design and data. Springer-Verlag Berlin.

Eppler airfoil design and analysis code [Computer software manual]. (n.d.).

Kitesailing 116 BIBLIOGRAPHY

Gere, J. M., & Timoshenko, S. P. (1999). Mechanics of Materials. Stanly Thornes (Publishers) Ltd.

Hobiecat. (2010, July 15). http://www.hobiecat.nl.

Hoerner, S. (1965). Fluid-dynamic drag. Hoerner.

Hoerner, S. (1985). Fluid-Dynamic Lift. Vancouver: Hoerner Fluid Dynamics.

Hoerner, S. F. (1965). Fluid-Dynamic Drag. Vancouver: Hoerner Fluid Dynamics.

J.A.Keunig, B. V. (2009). A new Method for the Prediction of the Side Force on Keel and Rudder of a Sailing Yacht based on the Results of the Delft Systematic Yacht Hull Series. The 19th Chesapeake sailing yacht symposium, p.19-29.

Javafoil [Computer software manual]. (n.d.).

John D. Anderson, J. (1985). Pilot’s operating handbook and Airplane Flight Manual for the Super King Air B200T & B200CT. Wichita, Kansas, U.S.A.: Beech Aircraft Corporation.

John D. Anderson, J. (2001). Fundamentals of Aerodynamics. New York: McGraw-Hill.

Jones, R. (1950). The spanwise distribution of lift for minimum induced drag of wings having a given lift and a given bending moment. NACA TN 2249.

Kim, J., & Park, C. (2009). Wind power generation with a parawing on ships, a proposal. Journal of energy, 35 , 1425-1432.

Kitano. (2010, July 15). http://www.yankodesign.com/2007/11/08/kite-sailing-yacht.

Kiteboat.com. (2010, July 7). http://www.kiteboat.com.

Kitenav. (2010, July 15). http://www.kitenav.com.

Kitepower. (2010, July 16). http://www.kitepower.com.au/news/index.php?id=1,61,0, 0,1,0.

Kiteship. (2010, July 15). http://www.kiteship.com.

Kroo, I. (2001). Drag Due to Lift: Concept for Prediction and Reduction. Annu. Rev. Fluid Mech..

Kroo, I. (2005). Nonplanar Wing Concepts for Increased Aircraft Efficiency. VKI lecture series on Innovative Configurations and Advanced Concepts for Future Civil Aircraft.

Laurea, T. di. (2007). Aerodynamic study of airfoils and wings for power kites applications [MSc Thesis]. Torino, Italy.

LeBeau, R., & Reasor, D. (2007). Numerical investigation of the effects of bumps on inflatable wing profiles.

Letcher, J. (1972). V-Wings and Diamond-Ring Wings of Minimum Induced Drag. Journal of Aircraft, No.8 , 9 .

Kitesailing BIBLIOGRAPHY 117

Lowson, M. (1990). Minimum induced drag for wings with spanwise camber. Journal of aircraft, 27 , p.627-631.

Loyd, M. L. (1980). Crosswind kite power. Journal of energy, 4 , p.106-111.

Maughmer, M. D. (2002). A comparison of the characteristics of eight sailwing airfoil sections. , Vol. 40 , pp. 523 – 536. meriam, J., & Kraige, L. (1998). Engineering Mechanics. John Wiley & Sons Inc.

Mervent. (2010, July 15). http://www.mer-vent.com/galerie/show picture.php? album=salon%20nautique%202008&picture=20&pass=.

Munk, M. (1921). The minimum induced drag of aerofoils. NACA Rept. 121.

Naaijen, P., & Koster, V. (n.d.). Performance of auxiliary wind propulsion for merchant ships using a kite.

Phoenix 25m test report. (2003, April 2). http://www.kite-surf.com/userreviews/show review.php?Ratings Index=839.

P. Naaijen, V. K., & Dallinga, R. (2006). On the power savings by an auxiliary kite propulsion system. International shipbuilding progress, 53 , 255-279.

Pocock, G. (1827). Sail performance: theory and practice. London: W. Wilson.

Ruijgrok, G. J. J. (1990). Elements of Airplane Performance. Delft, the Netherlands: Delft University Press.

Sailshoot. (2008, September 25). http://www.Sailshoot.nl.

Sailspeed records. (2010, April 22). http://www.sailspeedrecords.com/ 500-metre-records.html.

Skysails. (2010, July 15). http://www.skysails.com.

Speer, T. E. (n.d.). Aerodynamics of teardrop wingmasts. Des Moines Washington U.S.A.

Stein, M., & Hedgepeth, J. M. (1961). Analysis of partly wrinkled membranes (No. D-813). Washington: NASA, Langly Research Center.

Texel images. (2009, June 12). http://www.texelimages.nl.

Veldman, S. J. (2005). Design and Analysis Methodologies for Inflated Beams. PhD Thesis, Delft University of Technology, Delft, the Netherlands.

Verheul, R. F., Breukels, J., & Ockels, W. J. (2009, May 4 – 7). Meterial selection and joining methods for the purpose of a high-altitude inflatable kite. In The 50th Structures, Structural Dynamics , and Materials Conference. Palm Springs, California.

Vlugt, R. van der. (2009). Aero- and Hydrodynamic Performance Analysis of a Speed Kite- boarder [MSc Thesis]. Delft, the Netherlands.

Kitesailing 118 BIBLIOGRAPHY

Wachter, A. de. (2008). Deformation and Aerodynamic Performance of a Ram-Air Wing [MSc Thesis]. Delft, the Netherlands.

Whitcomb, R. (1976). A design approach and selected wind tunnel results at high subsonic speeds for wing-tip mounted winglets. NASA TN D-8260.

Wielgosz, C., & Thomas, J. C. (2002). Deflections of inflatable fabric panels at high pressure. Thin-Walled Structures, Vol. 40 , pp. 523 – 536.

Xfoil: An analysis and design system for low reynolds number airfoils [Computer software manual]. (n.d.).

Kitesailing Appendix A

Kite terminology

Some important terms are addressed to assist the reader who is not familiar with them.

Kite: A kite is a tethered, unpowered, heavier-than-air device which is able to achieve flight by generating an aerodynamic force.

Wind window: This is the area in which the kite can fly. The shape of it is a part of a sphere. At the edges the kite has little pulling force and can be at rest. When the kite flies through the middle of the wind window it flies very fast. In theory, according to Loyd [1980], the ground speed of a kite straight downwind is equal to the true wind velocity times the L D ratio of the kite. This high speed gives a kite lots of power. Figure A-1 shows the wind window of a kite. ~ Minimum power

True wind

Maximum power Minimum power

Figure A-1: The wind window of a kite

Crosswind: A kite that moves through the wind window has a velocity component that has an angle with respect to the true wind. This component of extra wind velocity is called crosswind and is described by Loyd [1980]. Figure A-2 shows this schematically.

Kitesailing 120 Kite terminology

Crosswind speed

(Kite)

True wind Figure A-2: Top view of wind window with a kite flying crosswind

Apparent wind: Adding the vector of the true wind and the crosswind is called the apparent wind. this is schematically shown in Fig.A-3.

True wind speed Apparent wind speed

Crosswind speed of the kite

Figure A-3: Apparent wind is the combination of the true wind and crosswind

Crosswind sweep: When flying from one side of the wind window to the other you ”sweep” the kite generating crosswind. When measuring the generated forces, the ground speed of the kite and the true wind speed and applying the theory of Loyd [1980], the aerodynamic coefficients of a kite can be calculated. This kind of testing is performed by Vlugt [2009] from which a number of results have been used in the research on aerodynamics in Chapter 6. Now the names of some basic elements of a tube kite are discussed and shown in Fig.A-4.

Power lines: Lines at the front of the kite through which the greater part of the generated pulling force of the kite is transferred to the surfer or the boat.

Steering lines: The lines by which the kite is steered and by which the angle of attack of the kite is controlled.

Leading edge: The inflated tube at the front of the kite.

Trailing edge: The entire edge at the back of the kite through which a thin wire goes to increase the stiffness of the trailing edge.

Kitesailing 121

Strut Power line

Steering line Canopy

Leading edge

Trailing edge

Bridle

Bridle point

Figure A-4: The basic elements on a tube kite

Bridle: The construction of lines that support the leading edge and to which the power lines are connected. In engineering terms: ”The bridle is an integral component of a kite with the function to transmit the aerodynamic forces on the flexible (inflatable) membrane structure of the kite to the tether”.

Bridle point: A point at which a line of the bridle is connected to (the leading edge of) the kite

Canopy: The fabric that creates the surface area of the kite.

Strut: An inflated tube positioned parallel to the air flow that keeps the canopy in its desired shape The steering lines are attached to a bar usually made from carbon fiber material. This bar is used to control the kite. In kitesailing the person who is controlling the kite is called the ”flyer”. By lowering the angle of attack of the kite the aerodynamic forces, lift and drag, become smaller which causes a decrease in total pulling force of the kite. This is called depowering the kite. Powering the kite means that the angle of attack is increased which creates more pulling force of the kite. Other terms:

Kitesailing 122 Kite terminology

Flagging: Flagging of a kite means that it has zero angle of attack such that there is no tension on the trailing edge and it starts flapping in the wind like a flag does. The kite does not generate any lift and produces only drag.

Kitesailing Appendix B

Sailing system coefficient determination

The coefficients for the kitesailing system on the Hobie Tiger are here determined.

B-1 Hydrodynamic parameters

These parameters are divided in lift and drag parameters.

B-1-1 Lift

To determine the hydrodynamic lift coefficient of the boat the Extended keel Method from J.A.Keunig [2009] is applied. This theory applies to regular sailing yachts. For catamarans the two hulls do influence each other but it is unclear in what way because no research was found that describes this effect. Therefore this effect is not taken into account. Also the resistance due to waves is not taken into account. Figure B-1 shows the definitions used in this method for the boat.

Figure B-1: Definitions of the Extended keel method, source: J.A.Keunig [2009]

Kitesailing 124 Sailing system coefficient determination

From J.A.Keunig [2009] the ratio of the lift coefficient and the angle of attack of a sailing boat is calculated according to:

dCL 5.7ARe = (B-1) dα ARe2 1 .8 cosλ cosλ4 4 ¼ The effective aspect ratio ARe of the keel is+ determined by:+

4 bk T c ARe = (B-2) cre ct ( + ) in which: + bk = Span of keel T c = Draft of canoe body cre = Root chord of extended keel ct = Tip chord of keel The hydrodynamic surface area of a Hobie Tiger hull with dagger board and rudder is deter- 2 mined using an average wetted surface area of 0.3 5 = 1.5 m for one hull. The dagger boards 2 2 are 0.7 0.3 = 0.42 m each. The rudders are 0.50 0.3 = 0.15 m each. The parameters are given in Table B-1. ∗ ∗ ∗ Table B-1: Geometry parameters of a Hobie Tiger hull with dagger board

bk [m] 0.7 T c [m] 0.1 cre [m] 0.3 ct [m] 0.25 λ [deg] 0 2 SHull [m ] 1.50 2 SDaggerB. [m ] 0.42 2 SRudder [m ] 0.15 2 SH [m ] 4.4

From J.A.Keunig [2009] it is known that the angle of attack of the hull (Leeway angle) can be 9 deg for which above relations still apply. This gives the maximum angle of attack that is assumed for this analysis.

B-1-2 Drag

The drag is calculated by assuming the following well known relation:

C2 C C L (B-3) D = D0 π A e + This relation is valid as long as the lift - angle of attack⋅ ⋅ curve is a straight line which is the case up to 9 degrees.

Kitesailing B-2 Aerodynamic parameters 125

From S. Hoerner [1965] it is known that for a round bottom shape as is the case with the catamaran the value of the zero lift drag is given by: CD0 = 0.05. The value for the Oswald efficiency factor can vary between 1 and 0. Meaning 1 for the perfect elliptical lift distribution and lower values for poorer lift distributions. Due to the fact that the dagger boards have a very smooth surface due to the gel coat on it and the careful design it is assumed that this factor is 0.8. Table B-2 shows the parameter values for the hydrodynamic part.

Table B-2: Performance parameters of a Hobie Tiger hull with dagger board

CLH ,max 0.7

CD0 0.05 A 5.8 e 0.8

B-2 Aerodynamic parameters

The aerodynamic area is the combination of the kite, the lines, the two sailors and the boat. The projected area of the Ozone 13 m2 kite is determined from the picture shown in Fig.2-14. Using the CAD program Rhino and the length of the center strut that is measured, the projected area of this kite is calculated to be 9.2 m2. This means that 70% of the total surface area is effectively creating lift. This projected area is the surface area on which the lift and drag coefficients apply that are obtained from Vlugt [2009]. The aerodynamic surface area of the boat is assumed to be the width of the boat (2.5 m) multiplied by the height of the boat (0.60 m). The line area is determined by four lines of 50 m with a diameter of 2 mm. The aerodynamic area of each sailor is assumed to be 0.5 m2 taken from S. Hoerner [1965] which is also applied in the sailing analysis program of Vlugt [2009]. This program, in which the wind gradient (the increase in wind velocity with increasing height) is taken into account, is used to determine the parameters. From GPS measurements it is known that the sailing course upwind is 60 deg with a ratio between the sailing speed and the true wind speed of 1 3. The wind speed was 17 kts and the sailing speed 6 kts. ~ The values that are obtained are given in Table B-3.

Kitesailing 126 Sailing system coefficient determination

Table B-3: Values of kitesailing system parameters

3 ρgA [k m ] 1.225 3 ρH [kg m ] 1000 2 SKite 13m~ [m ] 9.2 2 SKite 25m~ [m ] 17.5 2 SKite(50m) [m ] 35 2 SLines( [m) ] 0.4 2 SSailors( [)m ] 1.0 2 SBoat [m ] 1.4

CLKite 1.1

CLA 0.5

CDA 0.2 L DA 2.5

~

Kitesailing Appendix C

Comparison of airfoil calculation programs

For the aerodynamic analysis of airfoils different programs can be used. This appendix shows the main characteristics of how these programs work. It serves only to give a basic under- standing of the differences between the programs and to to give a detailed comparison to determine which program could give the most accurate results. The described programs here are all free to download from the internet. The most widely used programs are Xfoil, Javafoil and the Eppler code. They all use a potential flow analysis as a basis. The manuals from “XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils” [n.d.], “Javafoil” [n.d.], and “Eppler airfoil design and analysis code” [n.d.] of the programs state the following about the inviscid formulation: Xfoil: Simple linear-vorticity stream function panel method, equations are closed with an explicit Kutta condition. Javafoil: Higher order panel method with a linearly varying vorticity distribution. Eppler: The potential-flow airfoil analysis method employs panels with parabolic vorticity distributions. This shows that the difference is in the way that the vorticity distribution is calculated. Xfoil and Javafoil use a linear vorticity distribution and Eppler is the only one to use a parabolic vorticity distribution. For the viscous formulation the following structures are present within the programs: Xfoil: Xfoil uses a two-equation lagged dissipation integral BL formulation and an envelope en transition criterion. The total velocity at each point on the airfoil surface and wake, with contributions from the freestream, the airfoil surface vorticity, and the equivalent viscous source distribution, is obtained from the panel solution with the Karman-Tsien correction added. This is incorporated into the viscous equations, yielding a nonlinear elliptic system which is readily solved by a full-Newton method.

Kitesailing 128 Comparison of airfoil calculation programs

Javafoil: It solves a set of differential equations to find the various boundary layer parameters. It is a so called integral method. The equations and criteria for transition and separation are based on the procedures described by Eppler. A standard compressibility correction according to Karman and Tsien has been implemented to take mild Mach number effects into account. Eppler: The laminar and turbulent boundary-layer development is computed using integral momentum and energy equations. The turbulent boundary-layer method is based on the best available empirical skin-friction, dissipation, and shape-factor laws. The prediction of separa- tion is determined by the shape factor based on energy and momentum thicknesses. Recently, a new empirical transition criterion has been implemented that considers the instability his- tory of the boundary layer. The results predicted using the new criterion are comparable to those using the en method. The boundary-layer characteristics at the trailing edge are used for the calculation of the profile-drag coefficient by a Squire-Young type formula. This shows that Javafoil and the Eppler code are pretty similar because Javafoil is based on the Eppler code for the equations and criteria for transition and separation. For a more in depth analysis the reader is encouraged to read on in the manuals and their references. Other aerodynamic analysis programs are: Aerofoil, Profoil, Winfoil and Pablo.

Kitesailing Appendix D

Derivation of ratio between pressure drag and friction drag at optimum L/D

This derivation originates from Ruijgrok [1990] (p.220-224) and is applied to the situation of a kite in flight. For an airplane an analytical representation of drag and power required curves can be obtained by using the parabolic approximation for the lift-drag polar:

C2 C C L (D-1) D = D0 πAe + Where CD0 is the zero-lift drag coefficient, A is the wing aspect ratio and e is the Oswald’s efficiency factor. The equation that calculates the drag in general is given by:

1 2 D CD ρV S (D-2) = 2

Combining the parabolic drag equation Eq.D-1 with Eq.(D-2) gives:

2 1 2 CL 1 2 D CD0 ρV S ρV S (D-3) = 2 πR A e 2 + From the basic equation L = W which is valid⋅ for⋅ an airplane in flight with no vertical acceleration, we have:

W C (D-4) L = 1 ρV 2S 2

Kitesailing 130Derivation of ratio between pressure drag and friction drag at optimum L/D

Substituting Eq.(D-4) into (D-3) yields:

2 1 2 W D C ρV S D0 D (D-5) = D0 1 = i 2 πAe ρV 2S + 2 +

In Eq.(D-5), D0 is the zero-lift drag and Di is the induced drag of the airplane. Examination of this expression indicated that at a given altitude the zero-lift drag increases with V, while the induced drag decreases with increasing flight velocity.

The speed for minimum drag corresponds to the condition dD dV = 0. Differentiating Eq.(D-5) with respect to V and setting the derivative to zero, we readily obtain: ~

W 2 1 VDmin = (D-6) ¿ S ρ C πAe Á D0 ÀÁ » Insertion of this expression into Eq.(D-5) produces the following equations:

CD0 D0 D 2W (D-7) = i = ¾πAe C D 2W D0 (D-8) min = ¾πAe

Equation (D-7) shows that at the velocity for minimum airplane drag corresponding to CD = 2CD0 and CL = CD0 πAe, the zero-lift drag and induced drag are equal. Now taking: »

L CL = (D-9) D CD and combining this equation with L = W gives:

CD D = W (D-10) CL

This means that if the drag is the minimum drag then CL CD is maximal.

Therefore: ~

L C C at (D-11) D0 = Di D max ( )

Kitesailing Appendix E

Performance diagrams with an increase in wingspan

The following figures show the increase in performance as a result of an increase in the wingspan as is discussed in Section 6-2.

1.00

0.90

0.80

0.7

0.6

0.5

0.4

0.3 Cl accompanying (L/D)max 0.2

0.1

0 0.80 0.90 1.00 1.10 1.20 1.30 Incerase in wingspan

Figure E-1: Increase in lift of the Flow 5m kite as a result of an increase in wingspan while keeping a constant surface area

Kitesailing 132 Performance diagrams with an increase in wingspan

8

7

6

5

4 L/D max 3

2

1.00 Including an increased CL With constant CL of 0.75 0 0.80 0.90 1.00 1.10 1.20 1.30 Increase in wingspan

Figure E-2: Increase in L/D ratio of the Flow 5m kite as a result of an increase in wingspan while keeping a constant surface area

60

50

40

30

20

10

Product of lift coefficient and (L/D) squared Including an increased CL With constant CL of 0.75 0 0.80 0.90 1.00 1.10 1.20 1.30 Increase in wingspan

Figure E-3: Total lift force of the Flow 5m kite divided by the dynamic pressure as a result of an increase in wingspan while keeping a constant surface area

Kitesailing