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## Ecological interests

The seaway is one of the most efficient way of transport in terms of CO2 emmissions. Figure 1.4 shows that a ship emits regarding the payload less than 10% of CO2 emitted by a truck and 2% of CO2 emitted by an airplane. According to (Smith et al., 2014), the overall maritime emission of CO2 per year over the period 2007-2012 is 810 million tonnes, which represents 2.6% of the global emission. For a ship, Ronen (2011) shows that the fuel consumption may represent more than 75% of the operating costs. In addition, the CO2 emissions could be considered as proportional to the fuel consumption. An estimation of the ratio of the fuel consumption and CO2 emissions can be found in Corbett et al. (2009). Consequently, the ecological and economical interests are joint. According to the International Maritime Organisation (Smith et al., 2014), CO2 emissions could increase drastically due to an important raise of gross domestic products. Indeed, depending on the socioeconomic scenario considered in Smith et al. (2014), the gross domestic production should be multiplied between three and seven. An important effort should be performed by the shipping industry to improve the fuel-efficiency of the world fleet. The effect of improving the fuel efficiency is investigated in (Smith et al., 2014). 16 scenarios for the period 2012-2050 were considered. These scenarios assume different input parameters such as the Representative Concentration Pathways (RCP, see (Moss et al., 2008)), the Shared Socioeconomic Pathway (SSP, see (Ebi et al., 2014)), a Fuel-Efficiency Improvement (FEI) compared to fleet average in 2012, the roll out of Emission Control Area (ECA) and the use of Liquefied Natural Gas (LNG) engine. RCP is a resultant radiative forcing in W.m-2 due to greenhouse gas. For instance, an RCP of 2.6 W.m-2 corresponds to a raise of the mean temperature on earth of 1.5° and is the most optimistic scenario. The most pessimistic RCP considered is 8.5 W.m-2. According to a RCP level, Smith et al. extrapolated the oil and coal demand. Five SSP were considered from 1 to 5, respectively named sustainability, middle of the road, fragmentation, inequality and conventional development. A SSP is a qualitative parameter. A narrative description of different SSP can be found in (Kriegler et al., 2012; Smith et al., 2014). For instance, the SSP middle of the road corresponds to “A world that sees the trends typical of recent decades continuing, with some progress towards achieving development goals. Dependency on fossil fuels is slowly decreasing. Development of low-income countries proceeds unevenly.” The full method of combining RCP and SSP is detailed in (Smith et al., 2014) according to the method proposed by Kriegler et al. (2012).

### Beyond the sea® project

The beyond the sea® project began in 2007 under the initiative of the french navigator Yves Parlier. In 2014, a consortium of industrial partners and research center joined the beyond the sea® project with the sponsorship of the French Environment and Energy Management Agency (ADEME). ADEME ranked the beyond the sea® project as the more convincing project to succeed in the call for project “ship of the future”. This consortium is composed of french industrial and academic partners able to offer expertise and technology to develop the system. The industrial and academic partners of the beyond the sea company are:

• Cousin Trestec, manufacturer of innovative ropes and braids.

• Porcher Industries, manufacturer of innovative fabrics.

• Bopp, designer and manufacturer of hydraulic and electrical winches and deck equipment for marine applications.

• CMA-CGM, worlwide shipping group.

• ENSTA Bretagne, a french national graduate engineering institute and the Dupuy de Lôme Research Institute.

• DAAM, a company handling a fleet of competition sailing boats. DAAM is in charge of trials carried out at sea.

The Beyond the sea® company is in charge of the practical knowledge for the kite design, control, launching and recovery procedures. To solve the associated technological challenges, the company works in close cooperation with research laboratories. The launching and recovery procedures have been investigated by Du Pontavice (2016) at the Ladhyx the research laboratory of the Ecole Polytechnique. The control of the kite is investigated by the IMS laboratory by Cadalen et al. (2017).

#### Scientific issue and objectives of the thesis

As shown by the literature review, the existing knowledge about ships towed by kites had been motivated by the demonstration of the economical interest of the kite by solving the equilibrium of the ship according to a mean kite towing force. To consider a mean towing force is a strong assumption. A kite performing a dynamic a flight imposes to the ship an oscillatory excitation. The coupling between a ship and a kite may modify the mean equilibrium of the system. The dynamic motions of the system, may have an impact on the fuel saving estimation. Moreover, the kite oscillatory excitation may represent a risk for the ship safety in terms of seakeeping and maneuverability, and crews must be trained about how the kite system works and interacts.

From the kite design point of view, ship motions due to the kite and the sea state may modify the kite flight leading to an increase of the wind loading applied on the kite. The dynamic loading will probably leads to a heavier design. Consequently, the wind velocity required to launch the kite will increase. As discussed in Sec. 1.3, the kite cost increases with the wind loading and may have a significant impact on the kite profit.

The aim of this thesis is therefore to investigate the effect of the dynamic motions of a ship towed by kite on safety, profits and fuel savings. The dynamic motions of a ship towed by kite depends on parameters such as the kite area, tether length and tether attachment point. The scientific issue is to determine the influence of these parameters on the dynamic motions of the systems and on its operability. The chosen strategy is to investigate this problematic with quasi-analytical and numerical modeling approaches. As much as possible, employed methods should be transferable as in-house code to provide dedicated tools to design kite towing systems for ships. Therefore, modeling must be open for different types of ship. Moreover, in applied physics, numerical methods are generally developed to describe an identified phenomenon. On the contrary, for this scientific issue, the practical knowledge on the kite towing of large ship is almost nonexistent or confidential1 Consequently, methods developed in this study should be fast enough to run a large number of configurations and accurate enough to represent the important physics phenomena related to the system. The trade off between computational time and accuracy associated to this work is therefore arbitrary.

**Comparison with experimental data**

The zero-mass kite model is compared to the experimental data obtained by Behrel et al. (2017). As shown in this section, the zero mass kite model dependends on two parameters, the kite lift coefficient Clk and the lift to drag angle ǫk. These coefficients must be adapted in order to fit the data. The onshore full scale trials (Behrel et al., 2017) was performed with a classical kite Cabrinha® Switchblade of 5 m2 designed for kite-surfing. The tether length was 80 m long. During the run, the kite performed eight shape trajectories controlled by an autopilot based on the algorithm proposed in (Fagiano et al., 2013). The experimental kite position is determined with a 3D load cell assuming that the tethers are straight, which seems reasonable as a first approach. The evolution of the wind velocity with the altitude was identified thanks to a SOnic Detection And Ranging (SODAR). Experimental results presented here correspond to a phase averaging post-processing of a 5 minutes kite flight run.

**Table of contents :**

Contents

List of Figures

List of Tables

Notations

Reference frames and parameterizations

**I. Introduction **

**1. Context **

1.1. Preliminaries

1.2. Ecological interests

1.3. Economical interest

1.4. Beyond the sea® project

**2. Position of the problem and strategy **

2.1. State of the art

2.2. Scientific issue and objectives of the thesis

2.3. Organization of the thesis

**II. Kite modeling **

**3. Zero-mass kite model **

Résumé: Modélisation du kite sans masse

3.1. Introduction

3.2. Kite velocity and force

3.3. Wind gradient

3.4. Kite trajectory and control

3.4.1. Control

3.4.2. Trajectory

3.5. An upper bound of the kite force

3.6. Comparison with experimental data

3.6.1. Comparison with the zero-mass model

3.6.2. Modification of the kite aerodynamic specs

3.7. Conclusion

**4. Static analysis of tethers **

4.1. Introduction

4.2. Mathematical model

4.2.1. Reformulation of the catenary

4.2.2. Tether Load Model

4.2.3. Aerodynamic Kite Model

4.2.4. Kite static equilibrium

4.2.5. Verification of the implementation

4.3. Case of Study

4.4. Comparison with a finite element tether modeling

4.5. Tether effect on static kite flight configurations

4.5.1. Results

4.5.2. Analysis

4.5.3. Discussion

4.6. Conclusion

**5. Low wind limit of kite operability **

5.1. Introduction

5.2. An analytical criterion

5.3. Analysis

5.4. Conclusion

**III. Ship modeling **

**6. Time domain seakeeping modeling **

6.1. Introduction

6.2. Frequency domain solution

6.3. Time domain solution

6.3.1. Transformation into the s and c frames: unified coordinates systems

6.3.2. Impulse response function

6.4. Identification of the state-space systems

6.4.1. Structure of the state-space systems

6.5. Incoming waves and diffraction

6.6. Time domain equation of motion

6.7. Time domain validation case

6.7.1. Results

6.7.2. Analysis and Discussion

6.8. Conclusion

**7. Extension of the time domain seakeeping for the maneuvering motions **

7.1. Introduction

7.2. Maneuvering apparatus and other external forces modelings

7.2.1. Propeller model

7.2.2. Rudder model

7.2.3. Hull advance resistance

7.2.4. Windage model

7.2.5. Modeling of a varying forward speed

7.3. A mixed seakeeping and maneuvering model

7.3.1. Maneuvering equations of motion

7.3.2. 6 dof mixed equations of motion

7.4. Case of study

7.4.1. Kriso Container Ship modeling

7.4.2. Benchmark results

7.5. Validation of the mixed seakeeping and maneuvering model

7.5.1. Results

7.5.2. Analysis and discussion

7.6. Conclusion

**IV. Towards kite towing of ships **

**8. Mean equilibrium of a ship towed by kite **

8.1. Introduction

8.2. Equations of the mean equilibrium of a ship towed by kite

8.2.1. Equilibrium equation

8.2.2. Kite efficiency

8.3. Case of study

8.4. Influence of the windage force

8.5. Influence of the true wind speed

8.6. Remarks on the kite efficiency and the mean aerodynamic pressure

8.7. Conclusion

**9. Interactions between a kite and a ship **

9.1. Introduction

9.2. Coupling methods

9.2.1. A monolithic approach

9.2.2. A segregated approach

9.3. Case of study

9.4. Calm water case

9.4.1. Kite excitation spectrum

9.4.2. Comparison of the segregated approach with the monolithic approach

9.5. Regular beam wave case

9.5.1. Comparison between the trajectory definitions in r˜wra and rwra .

9.5.2. Interactions with regular beam waves

9.5.3. kite lock-in phenomenon

9.6. Discussion

9.7. Discussion

9.8. Conclusion

**10. Course keeping stability **

10.1. Introduction

10.2. Self course keeping stability

10.2.1. Analytical requirements

10.2.2. Results

10.2.3. Analysis and discussion

10.3. Ship active control

10.3.1. Controller

10.3.1.1. Rudder autopilot

10.3.1.2. Propeller autopilot

10.3.2. Calm water case

10.3.3. Regular beam wave case

10.4. Conclusion

11. 6 dof free sailing simulations of ships towed by kite

11.1. Introduction

11.2. Calm water case

11.2.1. Consistence of the dynamic modeling with the static modeling .

11.2.2. Influence of the kite and ship interaction on the performance

11.3. Regular wave case

11.4. Influence of the kite lock-in phenomenon on the performance

11.5. Conclusion

**V. General conclusion and perspectives **

**12. Conclusion **

**13. Perspectives **

**Appendix **

A. Onshore and offshore measurement set-up

A.1. Main sensors

A.1.1. Forces Measurements

A.1.2. Onshore Wind Measurements

A.2. Kite control system

A.2.1. Control And Data Acquisition System

A.2.2. Dynamic Flight Automatic Pilot

A.3. Kiteboat specific sensors

A.3.1. Inertial Measurement Unit (IMU)

A.3.2. Rudder Angle

A.3.3. Onboard Wind Measurements

**B. Kite modelling **

B.1. Zero-mass kite model: time step convergence

B.2. Static analysis

B.2.1. Finite element method: Young modulus convergence

B.2.2. Finite element method mesh convergence

B.2.3. Diameter and mass per unit of length of Dyneema® SK78

B.3. Low wind limit of kite operability

B.3.1. Ratio between the kite mass and the kite area

**C. Ship motions **

C.1. Transformation of the h to the s frame

C.2. Laplace transform of the retardation function

C.3. Infinite frequency added mass

C.4. Illustrating example of the identification of the Laplace transform of the retardation matrix

C.4.1. First step: time domain identification

C.4.2. Second step: frequency domain identification

C.5. DTMB 5512 transfer functions

C.5.1. Analytical expressions

C.5.2. Heave

C.5.3. Roll

C.5.4. Pitch

C.6. A direct extension of the time domain seakeeping model to maneuvering motions

C.6.1. Viscous effect modeling on the horizontal ship motions

C.6.2. Results

C.6.3. Analyse and discussion

C.6.4. Conclusion

C.7. Kriso Container Ship

C.7.1. Open water propeller data

C.7.2. Kriso Container Ship hull adavance resistance

C.7.3. Kriso Container Ship maneuvering coefficients

C.7.4. Kriso Container Ship interaction coefficients

C.7.5. Kriso Container Ship windage coefficients

C.7.6. Kriso Container Ship transfer functions

C.7.6.1. Analytical expressions

C.7.6.2. Sway

C.7.6.3. Heave

C.7.6.4. Roll

C.7.6.5. Pitch

C.7.6.6. Yaw

**Bibliography**