Performance Prediction Program for Wind-Assisted Cargo Ships Prestandaprognosprogram För Fraktfartyg Med Vindassisterad Framdrivning

DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020

Performance Prediction Program for Wind-Assisted Cargo Ships Prestandaprognosprogram för fraktfartyg med vindassisterad framdrivning

MARTINA RECHE VILANOVA

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Performance Prediction Program for Wind-Assisted Cargo Ships MARTINA RECHE VILANOVA TRITA-SCI-GRU 2020:288

Degree Project in Mechanical Engineering, Second Cycle, 30 Credits Course SD271X, Degree Project in Naval Architecture Stockholm, Sweden 2020

School of Engineering Sciences KTH Royal Institute of Technology SE-100 44, Stockholm Sweden Telephone: +46 8 790 60 00

Per tu, Papi. Et trobem a faltar. Acknowledgements

I wish to express my sincere appreciation to my supervisor from the Fluid Engineering Department of DNV GL, Heikki Hansen, for his wonderful support, guidance and honesty. I would also like to pay my special regards to Hasso Hoﬀmeister for his constant dedication and help and to everyone from DNV GL whose assistance was a milestone in the completion of this project: Uwe Hollenbach, Ole Hympendahl and Karsten Hochkirch. It was a pleasure to work with all of you.

Furthermore, I wish to express my deepest gratitude to my supervisor Prof. Harry B. Bingham from the section of Fluid Mechanics, Coastal and Maritime Engineering at DTU, who always sup- ported, guided and steered me in the right direction. My thanks also go to my other supervisor, Hans Liwång from the Centre for Naval Architecture at KTH, who have always had an open ear for me since the ﬁrst day we met.

The contribution of Ville Paakkari from Norsepower Oy Ltd, who provided the Maersk Pelican data for the validation of this Performance Prediction Program, is truly appreciated.

Finally, I would also like to acknowledge the love and the unconditional support of my family, my friends, my mother, Dolors; my father, Carlos; and my sister, Ariadna. Thank you! Abstract

Due to the accelerating need for decarbonization in the shipping sector, wind-assisted cargo ships are able to play a key role in achieving the IMO 2050 targets on reducing the total annual GHG emissions from international shipping by at least 50%. The aim of this Master’s Thesis project is to develop a Performance Prediction Program for wind-assisted cargo ships to contribute knowledge on the performance of this technology. The three key characteristics of this model are its generic structure, the small number of input data needed and its ability to predict the performance of three possible Wind-Assisted Propulsion Systems (WAPS): Rotor Sails, Rigid Wing Sails and DynaRigs. It is a fast and easy tool able to predict, to a good level of accuracy and really low computational time, the performance of any commercial ship with these three WAPS options installed with only the main particulars and general dimensions as input data.

The hull and WAPS models predict the forces and moments, which the program balances in 6 degrees of freedom to predict the theoretical sailing performance of the wind-assisted cargo ship with the specified characteristics for various wind conditions. The model is able to play with different optimization objectives. This includes maximizing sailing speed if a VPP is run or maximizing total power savings if it is a PPP. The program is based on semi-empirical methods and a WAPS aerodynamic database created from published data on lift and drag coefficients. All WAPS data can be interpolated with the aim to scale to different sizes and configurations such as number of units and different aspect ratios. A model validation is carried out to evaluate its reliability. The model results are compared with the real sailing data of the Long Range 2 (LR2) class tanker vessel, the Maersk Pelican, which was recently fitted with two 30 meter high Rotor Sails; and results from another performance prediction program. In general, the two performance prediction programs and some of the real sailing measurements show good agreement. However, for some downwind sailing conditions, the performance predictions are more conservative than the measured values. Results showing and comparing power savings, thrust and side force coefficients for the different WAPS are also presented and discussed. The results of this Master’s Thesis project show how Wind-Assisted Propulsion Systems have high potential in playing a key role in the decarbonization of the shipping sector. WAPS can prove substantial power, fuel, cost, and emissions savings. Tankers and bulk-carriers are specially suitable for wind propulsion thanks to their available deck space and relatively low design speeds.

The Performance Prediction Program for wind-assisted cargo ships developed in this Master’s Thesis shows promising results with a good level of accuracy despite its generic and small number of input data. It can be a useful tool in early project stages to quickly and accurately assess the potential and performance of WAPS systems. Abstrakt

På grund av det accelererande behovet av att minska utsläppen från sjöfartssektorn, kan vindassisterade lastfartyg spela en nyckelroll för att uppnå IMO 2050. Syftet med detta examensarbete är att utveckla ett prestandaprognosprogram för vindassisterade lastfartyg för att bidra med kunskap om denna teknik. De tre viktigaste egenskaperna för denna modell är dess generiska struktur, det lilla antalet inmatningsdata som behövs och dess förmåga att förutsäga prestandan för tre möjliga vindassisterade framdrivningssystem (WAPS): Rotorsegel, styva vingsegel och DynaRigs. Det är ett snabbt och enkelt verktyg som med en hög grad av noggrannhet och med kort beräkningstid kan bedöma prestanda för kommersiella fartyg med dessa tre WAPS-alternativ.

Skrov- och WAPS-modellerna beräknar krafter och moment som balanseras i sex frihetsgrader. Modellen kan utgå från olika optimeringsmål. Detta inkluderar maximering av segelfarten eller maximeras totala energibesparingar. Programmet är baserat på semi-empiriska metoder och en WAPS aerodynamisk databas skapad från publicerad data om lyft- och motståndskoefficienter. Alla WAPS-data kan interpoleras med syftet att skala till olika storlekar och konfigurationer, så- som antal enheter och olika aspektförhållanden. En modellvalidering utförs för att utvärdera dess tillförlitlighet. Modellresultaten jämförs med verkliga seglingsdata för tankfartyget Maersk Pelican (klass Long Range 2, LR2), som nyligen utrustades med två 30 meter höga rotorsegel; och resultat från en andra data. Resultaten visar i allmänhet bra överensstämmelse. För vissa seglingsförhållanden är emellertid bedömningarna mer konservativa än de uppmätta värdena. Resultat som visar och jämför energibesparingar, tryckkraft och sidokraftkoefficienter för de olika WAPS presenteras och diskuteras också. Resultaten av detta examensarbete visar hur vindassisterade framdrivningssystem har stor potential att spela en nyckelroll i utvecklingen för sjöfartssektorn. WAPS kan leda till betydande energi-, bränsle-, kostnads- och utsläppsbesparingar. Tankfartyg och bulkfartyg är speciellt lämpliga för vindframdrivning tack vare deras tillgängliga däckutrymme och relativt låga hastigheter.

Prestandaprognosprogrammet för vindassisterade lastfartyg utvecklat här visar därmed lovande resultat trots dess generiska upplägg och lilla antal inmatningsdata. Det kan vara ett användbart verktyg i tidiga projektsteg för att snabbt utvärdera potential och prestanda för WAPS-system. Contents

Acknowledgementsi

Abstract ii

Abstrakt iii

Nomenclature v

1 Introduction 1 1.1 Background...... 1 1.2 Mission...... 1 1.3 Goals...... 1

2 Physics of Sailing2 2.1 Wind Velocity Triangle...... 2 2.2 Basic Steady State Condition...... 3

3 Performance Prediction Program6 3.1 Solution Algorithm...... 6 3.2 Free Variables...... 9 3.3 Conventions...... 9 3.4 Force Modules...... 10 3.5 Parameters...... 11 3.6 Conﬁgurations...... 11 3.7 User-Friendly interface...... 12

4 Hull Model 13 4.1 Force Modules...... 13 4.1.1 Mass...... 13 4.1.2 Buoyant Force...... 13 4.1.3 Total Hull Resistance...... 14 4.1.4 Hull Roughness...... 15 4.1.5 Side Force...... 15 4.1.6 Windage of the Superstructure...... 16 4.1.7 Propeller Thrust Force...... 16 4.1.8 Non-Moving Propeller Drag...... 17 4.1.9 Rudder Hydrodynamic Loads...... 17 4.1.10 Added Resistance in Waves...... 17 4.2 Input Data...... 18

5 Wind-Assisted Propulsion Systems Model 20 5.1 Rotor Sails...... 21 5.1.1 Conﬁgurations...... 22 5.1.2 Aerodynamic Loads...... 23 5.1.3 Data Source and Data Fitting...... 26 5.1.4 Spinning Power Required...... 27 5.1.5 Windage...... 27 5.1.6 Interaction...... 27

iv CONTENTS CONTENTS

5.1.7 Input Data...... 28 5.2 Rigid Wing Sails...... 28 5.2.1 Conﬁguration...... 30 5.2.2 Aerodynamic Loads...... 31 5.2.3 Data Source and Data Fitting...... 32 5.2.4 Windage...... 36 5.2.5 Interaction...... 36 5.2.6 Input Data...... 37 5.3 Soft Sails: The DynaRig...... 37 5.3.1 Conﬁguration...... 38 5.3.2 Aerodynamic Loads...... 38 5.3.3 Data Source and Data Fitting...... 39 5.3.4 Windage...... 40 5.3.5 Interaction...... 40 5.3.6 Input Data...... 40

6 Validation 41 6.1 Rotor Sails - Maersk Pelican...... 41

7 Applications 46 7.1 Rigid Wing Sails and DynaRigs - Case Study...... 46 7.2 PPP Results...... 48 7.3 WAPS Driving and Side Force Coeﬃcients...... 55

8 Conclusion 59

9 References 63

A Macros 64 A.1 Import Data...... 64 A.2 Polar...... 65 A.3 Calm Waters...... 67 A.4 Waves...... 69

v Nomenclature

Theory of Sailing

TWS, VT True Wind Speed TWA True Wind Angle

AW S, VA Apparent Wind Speed AW A Apparent Wind Angle TWC True Wind Course

V s Ship Speed AOA Angle of Attack

LA Aerodynamic Lift Force

DA Aerodynamic Drag Force

RA Total Aerodynamic Force

FA Driving Force

SA Aerodynamic Side Force

LH Hydrodynamic Lift Force

DH Hydrodynamic Drag Force

RH Total Hydrodynamic Resistance Force U/V Rotor Sail Velocity Ratio RPM Revolutions Per Minute

De/D End-plate Size Factor AR Aspect Ratio

PRS Rotor Sail Spinning Power Required

HRS Rotor Sail Height

DRS Rotor Sail Diameter

URS Rotor Sail Circumferential Speed ω Rotor Sail Angular Speed

δf Flap Deﬂection Angle

Cflap/CRW Flap Chord Ratio

CRW Rigid Wing Sail Chord Length

HRW Rigid Wing Sail Height

vi NOMENCLATURE NOMENCLATURE

HDyna DynaRig Height

CL Lift Coeﬃcient

CD Drag Coeﬃcient Naval Architecture LOA Length Over All

LP P Length Between Perpendiculars LW L Length of the Waterline B Beam

T Design Draft D Depth h Accommodation Height above Deck GZ Righting Arm

GM Metacentric Height WPA Waterplane Area

CW Waterplane Area Coeﬃcient

CB Block Coeﬃcient

CM Midship Section Area Coeﬃcient S Wetted Area Other Symbols

VPP Velocity Prediction Program PPP Power Prediction Program W AP S Wind-Assisted Propulsion Systems ρ Density

Re Reynolds Number Γ Circulation V Flow Speed

R Radius D Diameter CoE Centre of Eﬀort

vii Chapter 1

Introduction

1.1 Background

Undoubtedly, humanity is facing challenging times. While we are coping with the COVID-19 pan- demic, we are also setting targets to reduce greenhouse gas emissions with the aim to respond to the actual climate emergency. There is a clear need for decarbonization worldwide. Countries have committed to reduce their emissions under the Paris Agreement, which aims to limit global warming to well below 2◦C compared to pre-industrial levels and to pursue efforts to limit the increase to 1.5◦C. All economic sectors must find efficient and effective ways to do so. Maritime transport emits around 940 million tonnes of CO2 annually and is responsible for about 2.5% of global greenhouse gas (GHG) emissions according to the 3rd IMO GHG study [28]. The Inter- national Maritime Organization (IMO) has set its own strategy: the total annual GHG emissions should be reduced by at least 50% by 2050 compared to 2008, while, at the same time, pursuing efforts towards phasing them out entirely. This has driven ship owners and operators to re-think their propulsion systems. Introducing environmentally friendly fuels and alternative propulsion technology in the shipping industry is a must - we must move towards sustainability.

One green technology which is attracting a lot of attention again is wind propulsion: an old concept with a modern edge. For centuries, wind moved cargo around the globe, until it was replaced by steam and diesel during the industrial age. In fact, wind propulsion is defined as the use of a device, such as rotor sails, wing sails or soft sails, to capture the energy of the wind and generate forward thrust. Now, it comes back with a modern spin. Aeronautical technology has been implemented in wind propulsion devices to make them more efficient than traditional sails. Wind is easily available at sea and can directly drive ships without transformation losses. Implementa- tion of weather routing can play a significant role in increasing performance and savings. Wind propulsion devices are easy to retrofit to existent ships as a mean of auxiliary power, the so-called wind-assisted propulsion. New research and designs are aiming to have wind propulsion as the main power source for vessels. However, this research project focuses mainly in wind propulsion in combination with another main power source.

After the industrial revolution and the combustion engine, the research on wind propulsion gains momentum again in times of high fuel prices or the prospect of a shortage of fossil fuel. During the 20th century, the most famous modern wind-assisted propulsion systems were invented. Anton Flettner, in the 1920s, invented the Rotor Sail whose performance was further studied by Thom in the 1930s. In the late 1960s, Wilhelm Prölss developed the famous DynaRig, a modern interpretation of the square rig, which had to wait 45 years to see the light on the mega yacht "Maltese Falcon". Kites, on the other hand, were designed and developed for the use on commercial vessels. In the 1980s, the famous french marine conservation pioneer, Jacques Cousteau, invented the Turbosail. Driven by the high performance sailing regattas such as America’s Cup, Rigid Wing Sails have been under constant development. Most of them have been recently picked up after a long "sleep" by the merchant shipping industry as a green alternative to reach environmental targets and save costs. There is a growing industry focusing on the development of these sort of technologies right now with leading companies such as Norsepower (Rotor Sails), Airseas (Kites) and Econowind (Turbosails). Start-ups are emerging as well like Bound4Blue (Rigid Wing Sails)

1 1.2. MISSION CHAPTER 1. INTRODUCTION while some famous yacht designers are developing some wind-assisted projects such as VPLP (Soft Wing Sails) and Dykstra Naval Architects (DynaRig).

1.2 Mission

Despite having used wind in the maritime transport during centuries, there is still a substantial lack of knowledge on the performance of wind-assisted cargo ships. We are still missing test results confirming the cost-benefit value of this sort of technology. Further investigations are needed to identify the actual picture of wind propulsion. One major area is the performance data. Increased confidence with regard to wind-assisted propulsion systems is a must. Validated information must be generated to accurately predict the potential fuel savings resulting in cost savings. Thus, the mission of this Master’s Thesis research project is to contribute knowledge on the performance of Wind-Assisted Propulsion Systems (WAPS) on-board commercial vessels. To achieve it, a Performance Prediction Program for wind-assisted cargo ships is developed. Its two key features, which makes it different from anything out in the market right now, are the small number of input data needed and its generic approach which can treat any cargo ship with three possible different WAPS installed: Rotor Sails, Rigid Wing Sails and DynaRigs. It is a fast and easy tool able to predict, to a reasonable level of accuracy and really low computational time, the performance of any commercial ship with these three possible WAPS on-board with generic input data such as vessel main particulars and WAPS dimensions. It should be noted that no WAPS aerodynamic data is needed as input data, a data base is already introduced in the model. It is designed to be used as an early stage design tool. Its characteristics make it the perfect tool to provide a fast answer to customers when interested in the potential of wind-assisted propulsion systems.

1.3 Goals

The goals which need to be accomplished to implement the mission are the following ones:

• Researching the published data on lift and drag coefficients of three different types of wind- assisted propulsion systems: Rotor Sails, Rigid Wing Sails and DynaRigs. • Implementing coefficients for performance predictions with the possibility of scaling to different sizes and configurations such as number of units and different aspect ratios.

• Building up a prediction program based on generic force approximations such as semi- empirical methods to minimize the required input data. Thus, achieving a really low computational time. • Creating a WAPS aerodynamic database. • Comparing the performance between the three diﬀerent WAPS and deﬁning pros and cons of each device. • Prediction of power savings for each WAPS achieving the maximum level of accuracy despite its generic structure. • Implementing interface to route optimization algorithms to maximize overall power savings.

1 Chapter 2

Physics of Sailing

People has been harnessing the power of the wind to sail for centuries. It has helped civiliza- tions to develop, survive, explore, trade and entertain. In fact, sailing can be dated as far back as prehistoric times. However, despite having sailed for such a long time and seeing ships as an ancient invention, the physics behind it is rather complex. The aim of this chapter is to explain the basics of the physics of sailing as well as some important concepts which will be a must for a good understanding of this Master’s Thesis project.

By definition, sailing is the art of traveling along the boundary surface between two flow fields under an equilibrium of forces in both fields. In a real sailing condition, a choice of courses relative to wind direction is a must. This is made possible by lift generation in both fields: sails and hulls provide this cross-force from the fluid passing around them following Bernoulli’s principle. Without foils of particular characteristics it is only possible to sail ("drift") downwind.

The force generated by the sails must overcome the resistance to motion for the ship to move forward. As Isaac Newton defined in his first law of motion, inertia is the resistance experienced by an object to change its motion. In sailing vessels, this resistance to motion depends on both flow fields (water and air). Thus, sailing is a complicated game of hull and rig resistance, driving power of sails and stability.

2.1 Wind Velocity Triangle

The driving power of the sails is generated by the apparent wind. By deﬁnition, the apparent wind is the air ﬂow experienced by an observer in motion and is the relative velocity of the wind in relation to the observer. Its magnitude is the vector sum of the velocity of the headwind plus the velocity of the true wind. Or, in other words, it is the vector sum of the true wind velocity minus the vessel sailing speed (assuming the craft as frame of reference).

When sailing, as the ship speeds up, the apparent wind increases its magnitude and the direction of origin moves forward. This wind is the apparent wind - the wind someone feels on-board and what the sails experience as inﬂow. If the ship reduces its velocity, the apparent wind tends towards being the same as the true wind. On the other side, the true wind stays the same regard- less of ship speed. It is an environmental factor.

This relation between true wind, ship sailing speed and apparent wind creates the widely known sailing concept of the wind velocity triangle. See Figure 2.1.

2 2.2. BASIC STEADY STATE CONDITION CHAPTER 2. PHYSICS OF SAILING

Figure 2.1: Wind velocity triangle. Source: [11]

Thus, the apparent wind speed and its apparent wind angle can be computed following,

AW S = pV s2 + TWS2 + 2 · V s · TWS cos (TWA) (2.1)

TWS · cos (TWA) + V s AW A = arccos (2.2) AW S The wind velocity triangle shape and its corresponding apparent wind speed highly depend on ship’s heading. When sailing pure downwind (TWA=180o), the total apparent wind speed is the true wind speed minus the boat speed. On the other hand, when sailing in beam-reach (TWA=90o), it is the hypotenuse of both vectors.

Some high performance crafts such as America’s cup or ice boats can sail at several multiples of the true wind speed. This is possible thanks to their low resistance to forward motion. The high performance racing boats have hydrofoils which push them out of the water and for the ice boats, ice friction is nearly negligible. Their dominant forward resisting force is then only aerodynamic. Thanks to this low resistance, they can sail faster and generate higher apparent wind speed (the speed needed to power the sails).

For high level of accuracy, another factor which needs to be accounted for is the leeway. Hardly ever, when sailing, the craft points in the exact direction it is going. The angle of leeway is deﬁned as the diﬀerence between the heading of the craft and its actual track through the water. The true wind direction is then corrected for this leeway angle.

2.2 Basic Steady State Condition

Since now a good understanding of the wind responsible for the propulsion of a sailing boat has been given, a basic steady state sailing condition is explained.

During stationary sailing, there is a balance of hull and sail forces. Or, in other words, there is an equilibrium of hydrodynamic and aerodynamic forces. When experiencing an apparent wind speed the trimmed sail generates a total aerodynamic force thanks to pressure difference between its leeward and windward sides. This force is composed of lift and drag. Lift is the force perpendicular to the incoming flow and defined as, 1 L = ρ · V 2 · A · C (2.3) A 2 air L while drag is the force parallel to the incoming flow and also defined as,

3 2.2. BASIC STEADY STATE CONDITION CHAPTER 2. PHYSICS OF SAILING

1 D = ρ · V 2 · A · C (2.4) A 2 air D Thus, the total aerodynamic force a sail can create depends on the angle of attack (trim), the sail shape, the sail area, the air density and the apparent wind speed and it is deﬁned as, q 2 2 RA = LA + DA (2.5) Depending on the alignment of the sail with the apparent wind, lift or drag are predominant in the total resulting aerodynamic force. For apparent wind angles aligned with the entry point of the sail (smaller AOA), the sail acts as an airfoil where lift is the major component of the resulting total aerodynamic force. On the other hand, when sailing downwind, the drag is the major component. This explains why racing sails are changed depending on which heading is followed.

As previously mentioned, this total aerodynamic force is counteracted by the forces on the water, the hydrodynamic ones. The total aerodynamic force is then decomposed into a driving force and a side force. The driving force points into the boat motion course and its responsibility is to overcome the hydrodynamic resistance to forward motion generated by the hull. The side force is perpendicular to boat motion and produces a heeling moment which tilts the craft sideways. In order to keep the course and prevent drifting and/or capsizing, another "sail" in the water (the keel) is needed to produce the same side force to counteract it. This reaction is the righting moment. See Figure 2.2.

Figure 2.2: A boat sailing steadily on the wind. Source: [44]

Thus, both flow fields forces must be balanced to have a stationary sailing condition. This is numerically defined as,

R~A + R~H = 0 (2.6)

F~A + S~A + L~H + D~H = 0 (2.7) where driving, F~A, and side, S~A, forces are expressed following,

F~A = L~A · sin(AW A) − D~A · cos(AW A) (2.8)

S~A = L~A · cos(AW A) + D~A · sin(AW A) (2.9) Sail and hull eﬃciency are hot topics in ship design. The closer the course to the relative apparent wind ﬂow (either sailing fast and/or upwind), the more important will be the lift component

4 2.2. BASIC STEADY STATE CONDITION CHAPTER 2. PHYSICS OF SAILING in air and water. High lift-to-drag ratios and high lift coefficients are the main characteristics of high performance lifting foils. If foils are able to generate high lift for negligible drag, the total aero-hydrodynamic force points nearly in the same direction as lift. This efficiency is computed with the so-called drag angles (or gliding angles) ε defined as,

LA cot εA = (2.10) DA

LH cot εH = (2.11) DH which together are equal to the relative apparent wind angle (AWA or γ in Figure 2.2),

AW A = εA + εH (2.12) A sailing craft is thus only eﬃcient at reducing the AWA and sailing upwind if it has a high performance aerodynamic system combined with a high performance hydrodynamic system.

5 Chapter 3

Performance Prediction Program

As discussed in chapter2, numerous forces act on a sailing vessel, dependent on parameters such as the environmental conditions and the setting of the control systems. To evaluate the performance of a wind-assisted cargo ship a Performance Prediction Program is developed.

A Performance Prediction Program is a mathematical model which predicts the theoretical sailing performance of a ship with speciﬁed characteristics for various wind conditions by balancing hydrodynamic and aerodynamic forces. Or, in other words, by balancing hull and sail forces. The method requires as input hydrodynamic hull and aerodynamic sail characteristics. Results are normally presented in the form of polar diagrams.

Velocity Prediction Programs (VPPs) to assess a sailing ship’s behaviour were initially developed at the Massachusetts Institute of Technology (MIT) during the early 1970s [31]. Since then, they have been further developed to account for transient behaviours (Dynamic VPP). Ship designers, model testers, sailmakers and also high performance sailors use VPPs to predict the performance of sailboats in design stage, prior to major modiﬁcations and before regattas, for instance.

For the development of this Performance Prediction Program for wind-assisted cargo ships, FS- Equilibrium - a modular workbench from the Fluid Engineering Department of the classiﬁcation society and maritime advisor DNV GL; is used. All hydrodynamic and aerodynamic forces are integrated via force modules. The particular quality of this software is its open modular architecture, which allows for setting up any combination of force modules. A wide selection of force modules is readily available based on semi-empirical models, but models can also be deﬁned by the user to include expressions, imported data or user-programmed modules. FS-Equilibrium can analyse stationary and also instationary sailing states. However, this Performance Prediction Program for wind-assisted cargo ships only focuses on stationary sailing states. The model has a two-part structure comprised of the solution algorithm and the ship model.

This chapter introduces the Performance Prediction Program model developed to predict the performance of wind-assisted cargo ships. First, a general overview of the solution algorithm is presented together with its conventions. Then, the ship model will be described. Finally, a user- friendly interface for this program is introduced.

3.1 Solution Algorithm

The solution algorithm must ﬁnd an equilibrium condition which the sum of the external forces, F , and moments, M, add up to zero in up to six degrees of freedom for given environmental conditions. A state which fulﬁlls these conditions is called a valid steady state condition and follows, X −→ F = 0 (3.1)

X −→ M = 0 (3.2)

6 3.1. SOLUTION ALGORITHM CHAPTER 3. PREDICTION PROGRAM

−→ T −→ T The force vector F = (Fx,Fy,Fz) denotes the linear forces and M = (Mx,My,Mz) , the angular moments. Calculating the equilibrium condition, a state vector results, which gives information about the ship speed, thrust and position.

To solve the equations 3.1 and 3.2, a balancing algorithm is used. It is a general optimisation problem with constraints which can be expressed in the form,

min f(x), x ∈ R (3.3) xmin ≤ x ≤ xmax where f is the so-called objective function to be optimized and x is the vector of free variables with its own minimum and maximum bounds. The algorithm used to perform this optimization with the equilibrium constraints (force and momentum residuals) is the Newton Raphson Method, named after Isaac Newton and Joseph Raph- son. In Newton’s Method [61], an approximation to the objective function is minimised iteratively until the minima coincide. The iterations start at an initial point xk. At this point, an approximation to the objective function f(x) is formulated through a Taylor expansion, 1 fˆ(x) = f(x ) + f 0(x )(x − x ) + f 00(x )(x )2 (3.4) k k k 2 k xk The ﬁrst order optimality condition to this second order approximation is easily found by solving,

ˆ0 0 00 f (x) = f (xk) + f (xk)(x − xk) = 0 (3.5) this will give the so called Newton step,

0 f (xk) x − xk = − 00 (3.6) f (xk) and the next iterate is,

0 f (xk) xk+1 = xk − 00 (3.7) f (xk) then the procedure is repeated starting from the new point xk+1. This is successively repeated until the diﬀerence between two iterates is small, |xk+1 − xk| < , where is small enough. This method is a fast algorithm but requires good starting points to ﬁnd a solution due to the linearisation of the method.

Furthermore, there are some parameters which need to be optimized when finding the equilibrium condition such as ship speed or delivered power. To simulate this, a second algorithm is employed in an outer optimisation loop. Here, besides other algorithms, the method of Hookes and Jeeves (pattern search) [27] - a family of numerical optimization methods that does not require a gradient; is used. This second algorithm is called the trim algorithm and the parameters to be minimized/maximized by it, trim objectives. In the solution algorithm of this Performance Prediction Program for wind-assisted cargo ships the user can choose between two different trim objectives: maximum ship speed and/or minimum delivered power. When the ship speed is the trim objective, a Velocity Prediction Program (VPP) is being run. The program finds the equilibrium condition in up to six degrees of freedom which gives the maximum sailing speed for the given wind conditions. On the other hand, if the delivered power is the trim objective, PD, a Power Prediction Program (PPP) is calculated. In this condition, the equilibrium for the specified degrees of freedom which requires minimum delivered power for the given wind and service speed conditions is found. This trim objective is mainly used when predicted power savings are needed. Apart from different optimization objectives, VPP and PPP require different free variables. For the VPP, the force in x coordinate, Fx, is set to be the forward speed while for the PPP, it is the engine RPM.

A schematic general outline of FS-Equilibrium in VPP mode is presented in Figure 3.1

7 3.1. SOLUTION ALGORITHM CHAPTER 3. PREDICTION PROGRAM

Figure 3.1: General Outline of FS-Equilibrium in VPP mode. Source: [13]

8 3.2. FREE VARIABLES CHAPTER 3. PREDICTION PROGRAM

3.2 Free Variables

The free variables of equations 3.1 and 3.2, once solved, will give information of the sailing condition. These free variables are here deﬁned as,

Condition Parameter F x Vs(VPP) or RPM(PPP) F y Leeway Angle F z Sinkage Mx Heel Angle My Pitch Angle Mz Rudder Deﬂection Angle

Table 3.1: Free variables.

All degrees of freedom have been defined since the aim of this Performance Prediction Program for wind-assisted cargo ships is to find the maximum speed (VPP) or minimum delivered power (PPP) of the wind-assisted ship while enforcing up to six degrees of freedom (See Figure 3.2). However, if needed or wanted, the model can be run for fewer degrees of freedom. As seen in Table 3.1, the free variables to solve equilibrium for F x can be defined as ship speed if a VPP is run or as engine revolutions per minute, RPM, if, instead, it is a PPP.

Figure 3.2: Six rigid-body degrees of freedom of a ship. Source: [5]

3.3 Conventions

As the FS-Equilibrium User Manual [13] states, the program distinguishes between several reference systems: −→ • Body-ﬁxed coordinate system B: A body ﬁxed system with xB axis along the centerline −→ −→ to the forward direction, yB pointing to the portside, zB is directed roughly along the mast. This coordinate system heels and trims with the boat.

• Absolute coordinate system A: This second coordinate system, called absolute coordinate −→ −→ system, shares the same origin with B, however the xA and yA axes remain in a horizontal −→ plane and zA is vertical (also upwards). • Hydro coordinate system H: This coordinate system is obtained by rotating the absolute −→ system until xH corresponds to the direction of the water ﬂow, and is therefore pointing aft, −→ −→ the angle between xH and xA corresponding to the leeway angle.

9 3.4. FORCE MODULES CHAPTER 3. PREDICTION PROGRAM

• Apparent wind coordinate system AW: This coordinate system is obtained by rotating the −−→ absolute coordinate system until xAW corresponds to the direction of the apparent wind, −→ making an angle of AWA with xA. • Effective wind coordinate system EW: This coordinate system is defined in a similar way as AW, but uses the effective wind angle EWA. The effective wind angle corresponds to an apparent wind angle taking into account the significant heeling angle of a sailing yacht.

See Figure 3.3 for reference.

The location of the origin must be body fixed but can be arbitrarily selected. Here, it is located at the aft, mid-ship and keel plate. This program is setup to find the equilibrium in the coordinate system A. Therefore, for all forces, the coordinate system used must be specified so that the forces can be transformed into the absolute system.

Figure 3.3: Coordinate systems used in FS-Equilibrium. Source: [13]

All input and output from FS-Equilibrium are in standard SI units i.e., Kg, meters, seconds and Newtons. However, the angles are in degrees by default. The true wind speed in the input is assumed to be at 10m above water level.

3.4 Force Modules

The forces and moments for the equilibrium conditions 3.1 and 3.2 are calculated according to numerous force modules describing the vessel. Generally, according to [13], the common forces acting on a ship are of four diﬀerent types,

• Gravity forces: mass forces produced by the weight of the hull and/or cargo, for instance. • Hydrostatic forces: forces due to the hydrostatic pressure acting on the hull, i.e. buoyancy and hydrostatic stability.

10 3.5. PARAMETERS CHAPTER 3. PREDICTION PROGRAM

• Hydrodynamic forces: forces imposed on the hull by the surrounding water ﬂow.

• Aerodynamic forces: forces imposed on the sails by the surrounding air ﬂow.

The differentiation is useful since each force type is generally defined in different coordinate systems as described before. In the following sections, each specific force to compute the total equilibrium condition will be explained.

3.5 Parameters

Numerous parameters influence each force module. All these parameters are also defined in FS- Equilibrium as variables. They can be briefly presented as,

• State variables: parameters such as velocities, heel, pitch and leeway angles which define the ship position. • Control variables: parameters freely defined by the user which can be used as devices of controlling the degrees of freedom. • Trim variables: parameters freely defined by the user which can be used to optimise an objective function with trim algorithms.

3.6 Conﬁgurations

For the purpose of studying the performance of cargo ships with three different Wind-Assisted Propulsion Systems (WAPS) installed, three sailing so-called configurations are defined:

• Pure Sailing Mode: at pure sailing condition, sail rig propulsion is responsible of for 100% of the total propulsion. Here, wind-assisted cargo ships are behaving as conventional sailing ships. All gravity, hydrostatic, hydrodynamic and aerodynamic force modules are turned on. The engine does not produce any thrust. • Combined Mode: in combined mode, which includes motor-sailing ships and sail-assisted ships, 100% of total propulsion is reached from the combination between sails and mechanical propulsion. Here, all gravity, hydrostatic, hydrodynamic and aerodynamic force modules are kept active. The engine does produce some thrust. • Pure Motor Mode: at pure motor mode (conventional motor ship), the total propulsion is from 100% mechanical propulsion. Sails are powered oﬀ. Thus, aerodynamic force modules are inactive except the windages such as the one from the superstructure and the ones from the non-retractable WAPS.

See Figure 3.4 for reference.

FS-Equilibrium offers the possibility to save a series of commands and execute them. Those are called macros. The aim of these macros are to run any specific condition or sailing configuration in the VPP or PPP. The macros are designed to jump from one configuration to the other (starting with pure sailing mode and finishing with conventional motor ship) to find the steady state conditions for given wind situations. For further information on macros see AppendixA.

11 3.7. USER-FRIENDLY INTERFACE CHAPTER 3. PREDICTION PROGRAM

Figure 3.4: Wind propulsion spectrum. Source: [51].

3.7 User-Friendly interface

With the aim to make this Performance Prediction Program a fast and accessible tool, a user- friendly interface has been designed and implemented. The user is able to load and change data from one cargo ship to another in the desired wind-assisted VPP/PPP without deep knowledge and technical understanding of how the entire software works or is designed. The interface is ba- sically responsible of loading and placing all data in their right place inside each force module or parameter. The data is obtained from an excel sheet (like the one in Figure 3.5), which the user is asked to ﬁll in. (For further information in the code see Appendix A.1). Once all data is loaded, to run the VPP/PPP for given wind conditions, the user must call diﬀerent macros depending on their interest.

Figure 3.5: User-friendly interface. Excel sheet. The user just needs to ﬁll the column named "Value".

12 Chapter 4

Hull Model

In this chapter, the hull model, which includes all forces acting on the hull due to the water and air ﬂow around it, is explained in detail. The minimum input data needed to run each force module and, in consequence, the entire hull model are exposed in the last section 4.2.

4.1 Force Modules

4.1.1 Mass The gravity module allows to calculate the forces due to a point mass located at a point in the body ﬁxed coordinates, in this case, the centre of gravity of the cargo ship. This mass module is then here used to model the non-movable mass of the vessel. It is based on Newton’s Second Law of Motion which states that in an inertial frame of reference, the vector sum of the forces, F , on an object is equal to the mass of that object (assumed constant) multiplied by the acceleration, a, of the object. It is then deﬁned as,

F = mass · acceleration (4.1) Since the program just deals with stationary sailing conditions, the mass moment of inertia of the ship is assumed not to be relevant.

4.1.2 Buoyant Force The buoyant module is used to model the forces due to the hydrostatic pressure acting on the hull, i.e. buoyancy and hydrostatic stability. Normally, this force and their respective rolling and pitching moments caused by perpendicular distance between the lines of buoyancy and weight are calculated thanks to a set of oﬀset points of the geometry of the ship hull. In this hull model, since any cargo ship must be modelled with few input data and as an early stage design tool, the set of oﬀset points will be normally not available. Thus, the buoyant force is modelled from basic ship theory equations and approximations according to [45].

The rolling moment, Mx, also called righting moment, is estimated to be,

MX = GZ · ∆ = GMT · sin θ · ∆ (4.2) where GZ is the righting arm, ∆ is the displacement, GMT is the transversal metacentric height and θ is the heeling angle in radians. Following the same assumptions as before, the pitching moment, My, is estimated to be,

MY = GML · P itch · ∆ (4.3) where, GML is the longitudinal metacentric height and P itch is the pitching angle in radians. Thus, the buoyant force, F z, is deﬁned as,

FZ = gravity · (∆ + WPA · Sink · ρwater) (4.4) where WPA, the waterplane area, is approximated as,

13 4.1. FORCE MODULES CHAPTER 4. HULL MODEL

WPA = CW · LPP · BMID (4.5) where, according to [33], for bulk-carriers and tankers, the water plane area coeﬃcient, CW , is deﬁned as,

CW = 0.81 · CB + 0.24 (4.6)

The centre of buoyancy can be approximated from the block coefficient, CB, and the midship coefficient, CM , assuming that it will have the form of (LCB,0,KB). The longitudinal centre of buoyancy forward to LW L/2, LCB, is defined, according to Schneekluth [52], as,

LCB = −0.135 + 0.194CP (4.7) The height above the keel of the centre of buoyant force, KB, according to Normand [52], is,

KB = T (0.9 − 0.36CM ) (4.8) where, according to HSVA Hamburgische Schiﬀbau-Versuchsanstalt GmbH [58],

CB CP = (4.9) CM 1 CM = 3.5 (4.10) 1 + (1 − CB)

4.1.3 Total Hull Resistance The FS-Equilibrium software has a force module called The Holtrop Module which is used to predict the resistance of single screw ships, especially tankers, bulk carriers, general cargo, ﬁshing vessels, container ships and frigates in the preliminary design stage. This method was developed by a regression analysis of a collection of model experiments and full-scale data, available at the Netherlands Ship Model Basin [23], [24], [25] and [26]. The target of the Holtrop and Mennen study was to develop a numerical description of the ship’s resistance, the propulsion properties and the scale eﬀects between the model and the full size.

The total resistance of the ship is divided into six separate components. These components are calculated separately by the module. The total resistance according to Holtrop and Mennen is deﬁned as,

RT OT AL = RF (1 + k) + RAP P + RW + RB + RTR + RA (4.11) where,

RF is the frictional resistance deﬁned according to the ITTC-1957 friction formula [29], 1 0.0075 UL R = C ρV 2 · S with C = where Re = (4.12) F F 2 F (log(Re) − 2)2 ν

(1+k) is the form factor describing the viscous resistance of the hull form in relation to RF

RAP P is the resistance of appendages

RW is the wave-making and wave-breaking resistance

RB is the additional pressure resistance of bulbous bow near the water surface

RTR is the additional pressure resistance of immersed transom stern

RA is the model-ship correlation resistance (hull roughness and the still-air resistance).

14 4.1. FORCE MODULES CHAPTER 4. HULL MODEL

4.1.4 Hull Roughness Since the Holtrop and Mennen semi-empirical method is based on towing tank tests, a roughness allowance needs to be computed and added up. This force is based on the wetted area, S, of the hull (also approximated following Holtrop and Mennen [25]) and modelled as a hydrodynamic force module.

p S = LPP (2T + B) CM (0.453 + 0.4425CB − 0.2862CM

ABT (4.13) −0.003467B/T + 0.3696CWP ) + 2.38 CB

The roughness coeﬃcient, Croughness, is deﬁned according to Bowden and recommended by the ITTC 1978.

1 −6 3 150 · 10 −3 Croughness = (105 · − 0.64) · 10 (4.14) LPP The centre of eﬀort of this force is assumed to be the centre of buoyancy.

4.1.5 Side Force Wind-assisted ships experience a significant lateral force compared to conventional motor ships in response to the aerodynamic loads from the sailing devices such as Rotor Sails, Rigid Wing Sails and Soft Sails, for instance. The side force is computed with the approach by Schenzle [49] for sailing ships without long fin keels since, nowadays, wind-assisted cargo ships do not have these sort of devices on their hulls. Thus, the side force Fside is defined as,

2 2 2 Fside = F1side + F2side = ρV AcβH = ρV (k1T βH + k2T Lpp|βH |βH ) (4.15) where βH is the leeway angle in radians and k1 and k2 are constant factors obtained from tests in [49]. F1side is the cross-force generated when certain stream lines of the flow of the capture area Ac, being proportional to the square of the wing span (here draft, T ); are captured and deflected in the forward part of the hull by the full small drift angle βH . On the other hand, F2side accounts for increasing drift angles where the capture area is increasing along the hull due to an end-plate effect of the tip-vortex separation from the bottom or keel at an angle proportional to βH . This area is defined as proportional to the drift angle and to the chord-length, here Lpp. Thus, the side force coefficient is defined as, F T C = side = 2k β + 2k |β |β = C β + C |β |β (4.16) Y 1 2 1 H 2 H H 1Y H 2Y H H 2 ρV LT L and, their corresponding drag due-to-lift force, FXside, is, β F = F tan (4.17) Xside side 2 Following the same Schenzle approximation, the longitudinal centre of effort of this side force is computed as, Mside X1sideF1side + X2sideF2side Xside = = (4.18) Fside F1side + F2side where X1side is assumed to be at the bow of the vessel and X2side, at mid-length, Lpp/2. Thus, for small drift angles, βH , the longitudinal centre of effort of this side force is assumed to be at the bow of the vessel. For the transversal centre of effort, it is assumed to be at Yside = 0 since the vessel is assumed as symmetric. And, for the z coordinate of this point, it is assumed to be same as Zside = KB.

15 4.1. FORCE MODULES CHAPTER 4. HULL MODEL

4.1.6 Windage of the Superstructure This force module calculates the parasitic aerodynamic drag from the drag coeﬃcients and the projected areas in the three planes of the ship’s superstructure. Since this windage of the superstructure is not considered in the Holtrop and Mennen approximation, it is calculated in this separated force module.

As all aero-hydrodynamic forces, the parasitic aerodynamic resistance of the superstructure, RAA, is calculated as, 1 R = ρ AW S2 · C · A (4.19) AA 2 air D Superstructure

The drag coeﬃcient, CD, varies depending on the superstructure geometry, from 0.5 < CD < 1.2 approximately. ITTC/Blendermann [32] recommends assuming CD = 0.85 for bulk-carriers and tankers and CD = 0.8 for container vessels and RoRo’s. On the other hand, also from [32], the front area ASuperstructure is,

ASuperstructure = B · h (4.20) where h is the accommodation height above deck. For tankers and bulk-carriers, it can be assumed that each ﬂoor height is 3m and an additional height of 2m is added counting for equipment at the top of the vessel.

The centre of area, centre of eﬀort, is also required so that the moments and the wind velocity at the height of the feature can be calculated. Assuming a generic rectangular superstructure, it can be assumed to be (XSuperstructure, 0, h/2).

This windage of the vessel superstructure is a minor part of the total resistance (2-5%) in calm water. In weather conditions, it can be up to 10%.

4.1.7 Propeller Thrust Force The propeller thrust, in combined and pure motor configuration, is modelled as a Wageningen B-Screw series propeller [34]. These series are open-water propeller charts which describe the propeller thrust, T , and torque, Q, as it rotates in an homogeneous flow with a forward speed, VS. The geometry is described by the pitch ratio, P/D, and blade area ratio. In the FS-Equilibrium software, a readily available force module called WageningenB is used. This force module provides the key values needed to model the propeller thrust force: advance number, J, thrust coefficient, KT , torque coefficient, KQ, propeller efficiency, η0 and, also, the revolutions per minute RPM and the delivered power, PD, for each sailing condition.

When the propeller is acting in open water, the incident flow velocity, thrust and torque are expressed dimensionless following, V J = P Advance number (4.21) D · n T K = T hurst coefficient (4.22) T ρD4n2 Q K = T orque coefficient (4.23) Q ρD5n2 Thus, the propeller efficiency is defined as,

KT · J η0 = (4.24) KQ2π Since the propeller is operating in the ship’s wake, the water speed seen at the propeller is deﬁned as,

VP = Vs(1 − w) (4.25)

16 4.1. FORCE MODULES CHAPTER 4. HULL MODEL where w is the wake fraction which describes how much the boundary layer surrounding the ship slows down the mean velocity approaching the propeller in relation to the ship speed. A lower VP is beneﬁcial for the propeller. Thus, w should be as bigger as possible. A typical wake fraction value is in the order of 0.1. On the other hand, the propeller increases the total hull resistance by creating low-pressure at the aft of the vessel. Thus, R R = towed−hull (4.26) self−propelled (1 − t) where t is the thrust deduction which describes the resistance increase when using a propeller to create the thrust force. A smaller t is beneﬁcial. A typical thrust deduction value is in the order of 0.2. Finally, the delivered power is computed as,

Rself−propelled · VA PD = 1−t (4.27) η0 · ηR · 1−w

4.1.8 Non-Moving Propeller Drag When the ship is sailing in a pure sailing condition, the propeller does not need to generate thrust. So, it does not rotate. Assuming a non-variable pitch propeller, the drag experienced by a rigid non-moving disk at the aft of the ship is modelled as, 1 Drag = ρ · V 2 · C · A (4.28) 2 water ship flatplate T

The coeﬃcient of drag is assumed to be a ﬂat plate one, Cflatplate = 1.28 according to [37]. The total frontal area, AT is computed from blade are ratio of propeller following,

2 DiskArea = AT = BladeAreaRatio · π · R (4.29)

4.1.9 Rudder Hydrodynamic Loads The rudder hydrodynamic force module calculates lift and the total drag of low aspect ratio foils arbitrarily positioned, according to the systematic analysis of Whicker and Fehlner (1958) [62].

The sectional lift curve slope, a0, corrected from experimental observations, is given by,

a0 = 0.9 · 2π (4.30)

If not speciﬁed as input data, the module uses the following default values,

• Aspect ratio factor (eﬀective/geometric AR)=1.8 • Minimum sectional drag coeﬃcient = 0.0065

• Lift curve slope, a0 = 5.65487 • Oswald eﬃciency = 0.9

• Attachment point of shaft from leading edge relative to root chord length = 0.25

4.1.10 Added Resistance in Waves Up to here, the entire hull model is developed. However, it only predicts forces on the hull for calm waters conditions. When sailing, rough sea conditions are also encountered. This force module is designed to model the added resistance experienced by the ship when sailing in waves. It is based on a FS-Equilibrium force module called AddRT. This force module is based on a conﬁdential semi-empirical method used at DNV GL for high level assessment of the added resistance in a seaway.

The sea spectrum is modelled according to the Joint North Sea Wave Observation Project, JONSWAP spectrum [12]. Signiﬁcant wave height and wave period must be deﬁned as input data.

17 4.2. INPUT DATA CHAPTER 4. HULL MODEL

4.2 Input Data

All the minimum input data needed to run the entire hull model is summarized in the following Table 4.1.

Force Module Name Module Type Parameter Definition Mass Gravity Mass Total ship mass in Kg Mass Gravity CoG Centre of gravity [x,y,z] Buoyancy Hydrostatic GMT Transversal metacentric height Buoyancy Hydrostatic GML Longitudinal metacentric height Buoyancy Hydrostatic ∆ Total ship displacement H-HullTotal Hydrodynamic Lpp Length between perpendiculars H-HullTotal Hydrodynamic Lwl Length of waterline H-HullTotal Hydrodynamic B Beam H-HullTotal Hydrodynamic T Draft H-HullTotal Hydrodynamic TF Draft at forward H-HullTotal Hydrodynamic CB Block coefficient H-HullTotal Hydrodynamic CP Prismatic coefficient H-HullTotal Hydrodynamic CWP Waterplane area coefficient H-HullTotal Hydrodynamic LCB Longitudinal position of the center of buoyancy forward 0.5LPP as percentage of LPP . H-HullTotal Hydrodynamic AT Immersed transverse area of the transom H-HullTotal Hydrodynamic ABT Transverse sectional area of the bulb H-HullTotal Hydrodynamic hB Center of ABT over keel plane H-HullSideForce Hydrodynamic TA Draught at aft WindageSuperstructure Hydrodynamic h Accommodation height WindageSuperstructure Hydrodynamic Xsuperstructure Longitudinal centre position of the superstructure P-Propeller Hydrodynamic RPM Revolutions per minute P-Propeller Hydrodynamic Axis Axis of thrust force [x,y,z] P-Propeller Hydrodynamic D Diameter of the propulsor P-Propeller Hydrodynamic P/D Pitch ratio of the propulsor P-Propeller Hydrodynamic BladeAreaRatio Expanded blade area ratio of the propulsor P-Propeller Hydrodynamic Z Number of blades P-Propeller Hydrodynamic ηR Relative rotative efficiency P-Propeller Hydrodynamic t Thrust deduction factor P-Propeller Hydrodynamic w Wake fraction P-Propeller Hydrodynamic Centre Propeller centre H-RudderLiftDrag Hydrodynamic Span Span of the rudder H-RudderLiftDrag Hydrodynamic ChordTip Chord length at tip H-RudderLiftDrag Hydrodynamic ChordRoot Choprd length at root H-RudderLiftDrag Hydrodynamic Attachment Attachment point of shaft of foil in boat coordinate system AddedResistanceWaves Hydrodynamic Hs Significant wave height AddedResistanceWaves Hydrodynamic WaveTp Wave period

Table 4.1: Input data hull model.

Of course, if needed or wanted, extra data can be added and their respective default or approximated value will be neglected. For instance, if the centre of buoyancy is known, this can be added as input data and the software will compute everything with the given value instead of the approximated values according to 4.7 and 4.8.

18 4.2. INPUT DATA CHAPTER 4. HULL MODEL

Note that not all force modules from the entire hull model are shown in Table 4.1. The explanation is simple: not all modules need extra data to be run. Since the data is loaded directly from the user-friendly interface, it is easily shared between modules. There is no need to ask the user several times for the same parameter.

19 Chapter 5

Wind-Assisted Propulsion Systems Model

The research presented in this chapter deals with the Wind-Assisted Propulsion Systems (WAPS) models. The aim of this project is to develop a program able to predict, evaluate and compare the performance of wind-assisted cargo ships for three different WAPS: Rotor Sails, Rigid Wing Sails and DynaRigs. See Figure 5.1 for reference. These systems are chosen among others for three main reasons. Firstly, all these wind-assisted devices proved to be feasible. For instance, Rotor Sails are installed in present operating commercial vessels, Rigid Wing Sails are nothing else than vertical fully-studied airplane wings and DynaRigs are successfully used in several large sailing yachts. Secondly, all of these devices are arguably the most likely ones to be adopted by the shipping industry since an increasing number of companies are offering them as a viable solution to reduce emissions. Also, most of the technical papers presented in the last yearshave focused on the development, implementation, analysis and validation of these three devices. Finally, the last reason to only choose these three WAPS is the limited time for this research project. For further future work, more WAPS such as kites or turbosails could be definitely added to this Performance Prediction Program.

This fifth chapter is divided into three main sections, one for each WAPS model. The state- of-the-art and a bit of history of each device is firstly presented in each section. Secondly, the available configurations for each device model are shown. Then, the aerodynamic loads prediction and their corresponding data sources are detailed. Interaction assumptions when having several operating WAPS is also mentioned. Finally, the minimum input data needed to run each model is presented in a table.

Figure 5.1: From left to right: Rotor Sail, Rigid Wing Sail and Dyna Rig. Source: [51].

20 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

5.1 Rotor Sails

The Rotor Sail is an active rotating cylinder that generates aerodynamic loads due to the Mag- nus eﬀect. It is also commonly called a Flettner Rotor, named after the German inventor Anton Flettner, [18][19]. Assisted by Albert Betz (German physicist and a pioneer of wind turbine technology), Jakob Ackeret (Swiss aeronautical engineer, widely viewed as one of the foremost aeronautics experts of 20th century) and Ludwig Prandtl (German engineer), Flettner designed and built an experimental rotor vessel named Buckau in 1924 (Figure 5.2), later renamed the Baden-Baden [63]. Two 15.6x2.8 m Rotor Sails were installed with a total rotor area of 87.4 m2, [53]. The Rotors were designed as an additional source for propulsion, to reduce fuel consumption.

Baden-Baden crossed the Atlantic in 1926. The system failed to be a success due to the long investment depreciation period caused by the low fuel price. In 1926, a commercial ship named Barbara was built for the shipping company Rob. M. Sloman, [53]. She sailed for over six years, mainly in the Mediterranean Sea. The Rotor sails were proven to be a reliable and functional wind propulsion systems.

Figure 5.2: Anton Flettner’s ﬁrst Rotor ship, the Buckau. Reproduced from the United States Library of Congress’s Prints and Photographs division under the digital ID ggbain.37764.

However, due to low oil price during mid 20th century, Rotor Sails could not compete economically against conventional motor ships. It was not until the beginning of the new millennium when interest in Rotor Sails revived due to the desire to increase sailing efficiency and to reduce costs and the growing environmental concern. In August 2008, the RoLo (roll-on/lift-off) cargo ship ENERCON-developed E-ship 1 was launched (Figure 5.4). Four 27x4 meters Rotor Sails were installed. Enercon, the third-largest wind turbine manufacturer, claimed operational fuel savings of up to 25% compared to same-sized conventional freight vessels, [16]. In 2018, Maersk Pelican was fitted with two 30x5 meters Norsepower Rotor sails (Figure 5.3). Tests have been carried since then to proof their viability and performance. Savings of 8.2% fuel and associated Co2 have been confirmed, [39].

21 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

Figure 5.3: E-Ship 1. Source: [16] Figure 5.4: Maersk Pelican. Source: [39].

All Rotor ship developers claim satisfactory performance of this first large scale Magnus effect application for commercial purposes. The advantages of Rotor Sail systems for cargo ships are numerous. The most obvious is fuel savings which will, of course, result in cost reduction. Having rotor sails operating on-board does not increase crew size. In fact, no significant crew training is needed to operate these devices. Their performance is mainly monitored. Furthermore, Rotor Sails require less cost for installation and maintenance per Newton of thrust force than other wind- assisted propulsion systems, [9]. From a maneuverability point of view, Rotor Sails are outstanding. The ship can be steered ahead or stern, depending on which direction they are spinning. Also, the vessel could be translated sideways without changing course thanks to their lateral force. Another brilliant characteristic of Rotor Sails are their inherent load limit. Since all rotating cylinders have a maximum operating spinning velocity, if they encounter high wind speeds, their velocity ratio drops and, consequently, their aerodynamic loads follow the same trend. Thus, Rotor Sails depower themselves which makes them a hurricane proof device, an advantage not inherent in other type of WAPS. On the other hand, the vibration they generate should be analysed and verified to comply with its acceptable limits. Otherwise, it could cause crew discomfort or even structural damage. Also, unlike other WAPS, since Rotor Sails are active rotating devices, they consume some power to spin. This power will be also computed and evaluated in this model to generate a fair performance comparison between WAPS.

5.1.1 Conﬁgurations The model is able to predict any Rotor Sail conﬁguration within the valid range exposed in the following Table 5.4.

Symbol Conﬁguration Parameter Valid Range AR Aspect ratio (Height/Diameter) [ 1.68:12 ] De/D Endplate size factor [ 1:3 ] RPM Revolutions per minute [ 0:∞ ]

Table 5.1: Rotor Sails conﬁgurations and their respective valid ranges.

Note that the aspect ratio of a Rotor Sails is deﬁned as the fraction of its height and its diameter. Also, there is no maximum spinning RPM for the devices in this model. However, ∞ RPM is not physically realistic. Normally, commercial Flettner Rotors spin at maximum RPM of 280 (small ones) or 180 (big ones).

22 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

5.1.2 Aerodynamic Loads 5.1.2.1 Magnus Effect The Magnus effect is the phenomenon responsible of the lifting force generated by rotor sails. Named after Gustav Magnus, Professor of Physics at the University of Berlin from 1834 to 1869; it is well-known for its influence on the trajectory of a spinning object moving through a fluid. The Magnus effect is present in many ball games like tennis or baseball. On a rotating cylinder, it can be described as superposition of two simple flows: the parallel flow and the circulatory flow. The resulting flow pattern is based on the resultant velocity vectors, sum of both the free-stream parallel flow velocity, Vfree, and the circulatory flow, Vrotating. The streamlines moving in the direction of the flow created by the Rotor, Vfavour, have a total velocity of,

Vfavour = Vrotating + Vfree (5.1) while, the streamlines moving against have a total velocity, Vagainst,

Vagainst = V free − Vrotating (5.2) Due to this velocity diﬀerence between rotating cylinder sides, a pressure distribution over the device appears as Bernoulli states in his theorem [38]: “Where the velocity increases, the pressure diminishes”. Since there is no symmetry between upper and underside of the cylinder, a lifting force is manifested – which tends to push the cylinder in the direction of lower pressure.

Figure 5.5: Magnus eﬀect seen in a rotating cylinder. The vertical arrow represents the resulting lift force. Source: [46].

The total aerodynamic force acting on the Rotor Sail due to the Magnus effect can be calculated from lift and drag. The total aerodynamic moment acting on it is the torque. As previously mentioned in Chapter2, the lift is the force perpendicular to the incoming flow. It is defined as, 1 Lift = ρ · AW S2 · Area · C (5.3) 2 air L The drag is the force parallel to the incoming flow. It is defined as, 1 Drag = ρ · AW S2 · Area · C (5.4) 2 air D In an ideal fluid used in inviscid theory, no energy is dissipated into friction or heat. The energy conversion only involves velocity and pressure changes. Assuming this condition, a theoretical lift coefficient value can be derived by substituting the expression of lift for the dimensionless lift coefficient into the Kutta-Joukowski theorem of lift equation defined as,

FL = ρ · Γ · AW S · Radius (5.5)

Thus, the lift coefficient of a rotating cylinder in an ideal fluid is, U C = 2π · (5.6) L V Where U/V is the velocity ratio of the Rotor Sail defined as, U ω · R = (5.7) V AW S

23 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

This, of course, is a theoretical value which does not considers viscosity. Viscosity is responsible for the wake created by a solid body moving through a fluid and therefore for induced pressure drag. Thus, this ideal lift coefficient is the maximum one can ever reach. All the other coefficients practically obtained by experiments in real fluids are much lower. On the other hand, the drag coefficient can not be derived from ideal fluid theory. It can only be established empirically by tests. However, what it is clear is the relation between lift and drag coefficients with the Rotor Sail velocity ratio. In fact, this is responsible for its inherent load limit. According to equations 5.6 and 5.7, at increasing apparent wind speed, the velocity ratio diminishes due to its maximum spinning RPM and the lift coefficient follows the same trend. Thus, the total force tends to a maximum total cylinder load limit (See Figure 5.6). As said before, Rotor Sails are storm-proof systems thanks to this characteristic.

Figure 5.6: Total cylinder aerodynamic force for TWS range. Data from Anton Flettner study [4].

5.1.2.2 The Aerodynamic Coefficients In the history of study and development of Rotor Sails and Magnus effect applications, several engineers and physics carried out experiments such as wind tunnel tests with the aim to determine lift and drag coefficients. All the studies got different results because of their different rotor configurations. However, most of them were inside an envelope between 50% and 25% of the theoretical lift coefficient. In 1924, Ackeret [43] conducted several experiments to investigate the effect of endplates in rotor sails. He tested two different aspect ratio rotor sails and four different endplate sizes. His findings were used to design the first rotor ship Buckau. Reid [48], in 1924, carried out a systematic series on a rotating cylinder of aspect ratio 13 and without endplates. One of his findings was that less power was required to rotate the Rotor Sail in moving than in still air. During a nine year period from 1925 to 1935, Thom [56] carried out experimental work on rotating cylinders. His work is agreed to be the most complete experimental work done on Rotor Sails. He investigated the effects of Reynolds number, the surface roughness, the aspect ratio and the end conditions. In fact, nowadays, the endplates of Rotor Sails are commonly named Thom disks. Thom reported lift coefficients as high as 18 for cylinders with large aspect ratio and Thom disks three times the Rotor diameter. Several years after, in 1961, Swanson [55] summarized some of the experimental results to date and the mathematical approach that had been taken to tackle on the problem back to that time. He discussed the Magnus effect, its history, and the work of its principal investigators providing a very useful set of curves of lift coefficients versus velocity ratio from previous works. More recent studies are from Badalamenti and Prince [3] and Bordogna et al. [7][8]. The first one carried out a series of tests on Rotor Sails with an aspect ratio of 5.1 with no endplates. Bordogna, studied the interaction effects on the performance of two Flettner rotors and their aerodynamic behavior at critical and supercritical Reynolds number. Nowadays, most companies developing Rotor Sails have their own curves based on their own experiments, but this data is mostly (if not entirely) confidential.

24 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

5.1.2.3 Effects on the Aerodynamic Coefficients The aerodynamic coefficients of a rotating cylinder can vary greatly depending on its configuration. In fact, there are several physical factors which impact the aerodynamics of a Magnus rotor [53]. These are: • Effect of velocity ratio: The flow around a rotating cylinder is rather complex. It con- sists of tip vortices and an alternate vortex shedding. In order to get a good aerodynamic performance, it is of significant interest to control them. There is always a critical velocity ratio where these phenomena start to cease. In fact, vortex shedding is created for Reynolds numbers all way up to approximately Re = 8 · 106. Thus, higher velocity ratio produces a quasi-steady flow where the flow topology is comparable to the potential theory solution. In other words, higher velocity ratio, higher lift coefficient. • Effects of aspect ratio: As in all aerodynamic elements, the ideal rotating cylinder is the infinitely long one since leakage flow and consequent pressure equalization around the ends does not occur. However, life is not perfect, and we have to face such phenomena when having 3D finite elements. Something is obvious though, the closer to an infinitely long rotating cylinder, the better the aerodynamic performance. Having higher aspect ratios gives higher maximum lift coefficients. There are, naturally, structural limitations to the slenderness - bending or deflection are not desired; and vessel stability such as a heeling moment limit. • Effect of endplates (Thom disks): The idea of implementing endplates to Rotors was firstly suggested by Prandtl in 1924. Ten years later, in 1934, Thom [56] did a deep study on the effect of them. His conclusions were that increasing the diameter relation between the endplate and the rotating cylinder, De/D, has a similar effect to increasing the aspect ratio. Or, in other words, higher diameter ratio De/D, higher lift coefficient. Thom stated that the lift coefficients were doubled when implementing endplates of De/D=3 and rotating at velocity ratios higher than 2. Also, since the maximum lift coefficient was higher, the peak of CL/CD was encountered at higher velocity ratios. On the other hand, the implementation of the endplates requires a higher delivered power due to higher friction. In his work, Thom also studied the aerodynamic behaviour of the rotating cylinder when adding Thom disks all along. This configuration leads to lower drag coefficient and much higher maximum lift coefficient (around 18 for a velocity ratio of 8) compared to the ones without spanwise disks. The trade-off, however, is that additional energy is needed to spin this configuration. To sum up, spanwise disks are good if the rotor-length is limited but more delivered power is required than normal Flettner rotors with endplates. • Effect of Reynolds Number: The Reynolds number does affect the aerodynamic performance. It affects the drag coefficient at all velocity ratios. Most of the available data sources considers this and they are an average between different Reynolds numbers. On the other hand, the Reynolds number only has a considerable impact on the lift coefficient at lower velocity ratios (lower than 2.5). • Effect of surface roughness: Thom [56] also studied the effect of surface roughness in the aerodynamic performance of rotating cylinders. He glued sand onto them and compared results. As widely known, gold ball roughness reduces drag coefficient and delays the boundary layer separation. So, Thom’s results concluded the same phenomenon: some roughness leads to higher maximum lift coefficient. The trade-off here was a higher torque coefficient which leads to higher delivered power required to spin the Rotor. Thus, the final overall performance, comparing lift and power, is the same as a normal Flettner Rotor. All in all, the only three effects which may affect the aerodynamic performance of Rotor Sails considered in this model are: the velocity ratio, the aspect ratio and the endplate size. The rest are neglected. For Thom spanwise disks, it is assumed that on-board of a ship there is no significant rotor-length limitations. So, compared with the increased required delivered power needed to spin them, it is not a viable option right now to consider for this model. Regarding the Reynolds number effect, since the normal operation velocity ratio is higher than 2.5, it is also neglected. Finally, surface roughness is not considered because it leads to similar overall performance as smooth Rotor Sails. The consideration of these three effects in this model will be seen in the following section 5.1.3.

25 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

5.1.3 Data Source and Data Fitting In this project, no wind tunnel tests will be carried out because of its aim to develop a general model which can work for all Rotor Sails configurations inside the valid range. Public sources will be used. It is decided to use the Ackeret [43] results for two main reasons: its wide acceptance as high- quality data inside the scientific community and its high velocity ratio range (up to 8 when most of the sources are up to 4). His work was based on the measurement of lift and drag coefficients as function of velocity ratio for two cylinders, one with a low aspect ratio of 1.68 and the other with a much higher one, 12. Also, he played with the endplates size. Normally, they are defined as function of its diameters De/D (diameter endplate/diameter rotor sail). Ackeret carried out wind tunnel tests for De/D of 1,1.5,2 and 3 for each different aspect ratio rotating cylinder. His findings are summarized in Figure 5.7.

15 14

AR 1.68 DeD 1 AR 1.68 DeD 1 AR 1.68 DeD 1.5 AR 1.68 DeD 1.5 AR 1.68 DeD 2 12 AR 1.68 DeD 2 AR 1.68 DeD 3 AR 1.68 DeD 3 AR 12 DeD 1 AR 12 DeD 1 AR 12 DeD 1.5 10 AR 12 DeD 1.5 10 AR 12 DeD 2 AR 12 DeD 2 AR 12 DeD 3 AR 12 DeD 3

Lift coefficient Lift Drag coefficient Drag 5 4

0 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Velocity Ratio, U/V Velocity Ratio, U/V

Figure 5.7: Ackeret lift and drag coeﬃcients. Source: [43]

With the aim to have more data available, wind tunnel tests results from the retrofitted cargo ship Fehn Pollux [57] are also included in this Rotor Sail model. The data is carefully selected to have similar trends for a better implementation of data fitting within the valid range. Thus, not all public sources presented before were useful for this model due to their significant difference in magnitude as result of various configurations and wind tunnel tests characteristics.

In order to be able to predict the aerodynamic loads of any Rotor Sail within the valid configuration range, the data is fitted following a cubic spline interpolation of consecutive data already integrated in FS-Equilibrium software. Cubic spline is a nonlinear function constructed of multiple third order polynomials. It interpolates grid wise defined data in a sequential manner with cspline fits [13]. See Figure 5.8 for reference. The three data variables of this model are shown in Table 5.2.

Symbol Variable Valid Range U/V Velocity ratio [ 0:8 ] De/D Endplate ratio [ 1:3 ] AR Aspect ratio [ 1.68:12 ]

Table 5.2: Data variables and their valida ranges.

These variables are based on the effects on the aerodynamic coefficients considered in this model (see previous section 5.1.2.3). No extrapolation is done. Assuming that the Rotor Sails configuration allowed by this model does not have a maximum bound for RPM, the system trims the Rotor Sails RPMs depending on wind conditions and trim objectives (VPP or PPP) to fit the velocity ratio within the valid range.

26 5.1. ROTOR SAILS CHAPTER 5. WAPS MODEL

Figure 5.8: Rotor Sails drag coeﬃcient data ﬁtted with CSpline function at the Performance Prediction Program for wind-assisted cargo ships as function of velocity ratio, aspect ratio and end-plate size. FS-Equilibrium Software.

The standard commercial dimensions for Rotor Sails are 18x3 meters with De/D of 6; and 35x5 meters with De/D of 8.3. Thus, the standard commercial aspect ratio is between 6-7 and the endplate ratio is around 1.5-2. All of them are within the valid range of this model.

5.1.4 Spinning Power Required The power needed to rotate the Flettner Rotor due to frictional drag is modelled based on ﬂat plate boundary layer [38], 1 P = F · U = ρ · U 2 · π · H · D · C · U (5.8) RS F RS 2 air RS RS RS F RS where CF is the frictional coeﬃcient. Approximated by Schlichting,

−2.3 9 CF = (2 log(Re) − 0.65) forRe < 10 (5.9) If the Rotor Sails have endplates, they are considered in the total spinning power required by adding their corresponding frictional force into equation 5.8.

5.1.5 Windage When the Rotor Sail is not rotating, in pure motor conﬁguration, and assuming non-retractable devices, their structure only creates air resistance, called windage. This total resistance is modelled here following, 1 R = ρ · AW S2 · H · D · C (5.10) windage 2 RS RS DRS This Rotor Sails windage is only considered in the x and y directions - z is neglected. The drag 6 coeﬃcient, CD, is assumed to be 0.5 (2D circular shape value for Reynolds number range of 10 according to [37]).

5.1.6 Interaction No interaction effects of the aerodynamic interaction on the performance of two or more Rotor Sails is considered in this model. It is assumed that the devices will be installed enough diameters apart to be able to operate independently. According to Bordogna et al. [7], when the Rotor Sails are set 15 diameters apart, their aerodynamic coefficients become closer to those of the non- interacting ones. However, when they are in an arrangement at a spacing of 3 diameters, their percentage of change reach average values of 20% with respect to the non-interacting Rotor Sails. Thus, for further model improvement in future work, this interaction effects could be definitely introduced assuming that aerodynamic coefficients of several rotating cylinders operating together are considerably influenced by the Rotor’s relative position, spacing and their velocity ratio.

27 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

5.1.7 Input Data The minimum input data needed to run this entire Rotor Sails model is exposed in the following Table 5.3.

Force Module Name Module Type Parameter Deﬁnition A-RotorSail Aerodynamic D Diameter A-RotorSail Aerodynamic De End-plate diameter A-RotorSail Aerodynamic H Rotor Sail height A-RotorSail Aerodynamic Max RPM Maximum rotating RPM A-RotorSail Aerodynamic CoE Position of each Rotor Sail on-board [x,y]

Table 5.3: Input data Rotor Sail model.

Note that the z coordinate of the CoE is automatically computed assuming the Rotor Sail is a HRS rectangle. Thus, z = 2 + D − T .

5.2 Rigid Wing Sails

Rigid Wing Sails are aerodynamic structures, airfoils, analogous to airplane wings. Their main differences are their vertical orientation and their ability to generate lift on either side. This last characteristic is vital for a vessel since, unlike airplanes, they must tack while following the wind. For this reason, Rigid Wing Sails are generally symmetric NACA profiles. Also, they can be cambered with flap implementation in their geometry. Flaps are high-lift systems which consist of leading and trailing-edge devices. Leading-edge flaps increase the maximum lift of an airfoil by delaying its stall angle. Trailing-edge flaps generate additional lift through an increase in the effective camber of the airfoil. Although, a higher maximum lift coefficient is achieved by implementing trailing-edge flaps but the stall angle is reduced. Among all trailing-edge devices employed today, plain flaps and slotted flaps are the most common in the maritime sector. Leading-edge flaps are rarely implemented in Rigid Wing Sails.

In the early years of the 20th Century, many experiments tried to fit aeroplane wings to ships. In fact, Anton Flettner suggested self-trimming wing sails to propel his wind ship the Buckau. However, as explained before, Fletter Rotors were successfully implemented in this ship finally. In Norway, a few years before the Second World War, Fin Utne designed a little self trimming vessel named Flaunder. It was unfortunately destroyed during the war as a potential weapon. It is not until the late 1960’s when John G. Walker [59] designed a 10 meter long Rigid Wing Sail propelled cruiser (Figure 5.9) . The system was an automated mechanics of rigid and rectangular sails with cylindrical masts. Their angle of attack adjustment was automatic. Popularly called Walker Wings, they are the first example of the successful implementation of Rigid Wing Sails on ships. In the 1980s, the U.S. government commissioned a study for which Walker was the engineer, that went into the economic feasibility of wind assisted propulsion in response to soaring fuel prices.

28 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

Figure 5.9: Planesail. John G. Walker’s invention. Source: [59]

Trials of the Rigid Wing Sails fitted aboard commercial vessels demonstrated significant fuel savings, between 15% and 25%. However, as for Flettner Rotors in this time period, Rigid Wing Sails failed to be widely implemented due to the oil price drop. It was not until the beginning of the 21st Century when Rigid Wing Sails were widely seen again. High performance sailing yachts implemented them and they showed unprecedented speeds in famous regattas such as America’s Cup. Also, an increasing interest in Rigid Wing Sails is seen in the design of autonomous research drones. In fact, most of them have a self-trimming Rigid Wing Sail as their main propulsion system. Maribot VANE, from KTH Maritime Robotics Laboratory, is a good example [47]. Nowadays, Rigid Wing Sails are attracting attention again in the maritime sector as a mean to reduce fuel and emissions in order to fulfill IMO requirements. Among other promising projects involving these devices, there are two important ongoing projects, such as the British Windship Technology Project [40] (Figure 5.10) and the Swedish Wind-Powered Car Carrier, wPCC, [60] (Figure 5.11). However, most of the projects involving Rigid Wing Sails for commercial vessels are still in their design stage.

Rigid Wing Sails have numerous characteristics which make them a perfect choice as wind- assisted propulsion system. The geometry of Rigid Wing Sails provides higher lift-to-drag ratio than traditional soft sails which leads to unprecedented sailing speeds for high performance sailing yachts. Its internal structure gives a constant shape to the airfoil which is not dependent on the tension in the lines as for traditional sails. This makes it much easier and precise to ﬁnd the optimal trim (the angle of attack can be changed easily and quickly) for given wind conditions. No crew increase is required after ﬁtting these devices and crew safety is maintained at all times. They are really easy to operate, everything is monitored. They require minimum maintenance. These WAPS are also easy to install. Most of them are retractable which reduces risk in storms and possible cargo handling. On the other hand, they are much more complex and expensive than traditional soft sails. Depending on how many Rigid Wing Sails are needed to propel the vessel or reach minimum target savings, they could interfer with cargo handling and other functions on deck.

29 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

Figure 5.10: The Windship Technology Project. Figure 5.11: Wind-Powered Car Carrier (wPCC) Source: [14]. Project. Source: [60].

5.2.1 Configuration The model allows the user to choose between three different Rigid Wing Sails configurations: a plain symmetric profile, a symmetric profile with a trailing edge plain flap and a symmetric profile with a trailing edge slotted flap (see Figure 5.12). Thus, the performance of these three different Rigid Wing Sails can be predicted with this model. The user can also choose how big the flap is (for both of them) compared to the chord length of the symmetric profile. This is computed in percentage. If a 50% plain flap chord is chosen, then the flap is half of the chord of the symmetric profile plain wing. Regarding flap deflection, the user can also states maximum degrees of rotation with respect to the axis of symmetry.

Figure 5.12: Rigid Wing Sails conﬁgurations included in this Performance Prediction Program. Source: [4].

As in the Rotor Sails model, the Rigid Wing Sails model also has some bounds in the conﬁguration of these three possible devices. They are shown in Table 5.4.

Symbol Conﬁguration Parameter Valid Range AR Aspect ratio [ 0:∞ ] o o δf Flap deﬂection angle [ 0 :45 ] CF lap/CRW Flap chord ratio [ 0%:30% ]

Table 5.4: Rigid Wing Sails conﬁgurations and their respective valid ranges.

Note that the aspect ratio of Rigid Wing Sails is deﬁned as the fraction of its height and its plain wing chord length.

30 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

5.2.2 Aerodynamic Loads Rigid wing sails can deliver a thrust force by means of a lift force generated by the motion through the air. The lift is defined as the component force acting in the plane of symmetry in a direction perpendicular to the inflow direction. In addition to the lift, a force along the flow direction of the sail, drag, is always present. From the linearized 2D form of Bernoulli’s equation and the Kutta- Joukowski theorem [38][1], both aerodynamic forces can be expressed in the non-dimensional forms, Lift 2 = CL(Re, α) (5.11) 0.5 · ρair · AW S · Area Drag 2 = CD(Re, α) (5.12) 0.5 · ρair · AW S · Area Aerodynamic forces vary directly with air density, the square of the apparent wind speed and the total airfoil area. Both aerodynamic coefficients depend on Reynolds number, Re, and the angle of attack, α. Viscous effects depend primarily on the chord length of the airfoil (length of the body parallel to the free-stream direction). Thus, the Reynolds number is computed with this length. Values of lift and drag coefficients can be obtained by wind tunnel tests. There is a practical difficulty in preserving the full-scale Re number though. Thus, the drag is assumed to be the total sum of the frictional drag of a flat plate at zero angle of attack accounted for the Re number dependence and the rest is assumed as pressure drag which only depends on the angle of attack so that,

CD(Re, α) = CF (Re) + CP (α) (5.13)

On the other hand, the lift coeﬃcient is assumed to be independent of the Re number at low angles of attack. Thus, it depends only on the angle of attack,

CL(Re, α) = CL(α) (5.14)

Note that lift does depend on Reynolds number after stalling. At low angle of attack, where lift is low, drag is insensitive to Re (it has a comparable value to the flat plate frictional drag). When stall is approached, the drag increases appreciably and in a manner sensitive to Re. But, drag is really small compared to lift - the effects are of less significance. For the simplest airfoil case, a flat plate, with an angle of attack α, it follows from 5.11 that,

CL = 2πα (5.15)

Thus, the lift coefficient of a flat plate is 2π times the angle of attack. It is clear that plots of the coefficients against the angle of attack is a convenient way of describing the aerodynamic characteristics of a rigid wing sail. The lift increases almost linearly with angle of attack until a maximum value is reached, whereupon the wing is said to “stall”. The drag coefficients have a minimum value at a low lift coefficient, and the shape of the curve is approximately parabolic at angles of attack below the stall (see Figure 5.13). The ideal wing gives high lift for minimum drag. This configuration is improved by use of some retractable devices such as trailing-edge flaps. When deflected, these high-lift systems are responsible for an effective camber generation in the airfoil. Unlike thickness, camber does play a role in the magnitude of the lift coefficient. The cambered parabolic arc represents a substantial improvement over a flat plate plane from the standpoint of uniform loading and pressure distribution. This effect on the total lift coefficient is expressed in the form, CL(α) = CL(0) + 2πα (5.16) where the term CL(0) represents the effects of camber at 0 angle of attack and 2πα, the effects of the angle of attack. Generally, the centre of pressure of a symmetric airfoil is assumed to be at its 25% of chord length [38].

In 3D, the flow at each section along the span of the Rigid Wing Sail can be approximatly as 2D. However, at the tips, due to pressure leakage, vortices appear. The effects are twofold: the lift is reduced, and the drag increased. The aspect ratio of airfoils (the ratio of span to mean chord) plays a significant role in the total aerodynamic loads magnitude. A large aspect ratio wing means

31 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL that the flow is nearly independent of the transverse coordinate z and a 2D approximation is valid. On the other hand, for lower aspect ratios, 3D flow effects are important and must be included.

1.5 0.1

0.09

0.08

0.07 1

0.06

0.05

0.04

Lift coefficient Lift Drag coefficient Drag 0.5 0.03

0.02

0.01

0 0 0 2 4 6 8 10 12 14 16 18 20 Angle of Attack, AOA

Figure 5.13: NACA 0012 simple airfoil 2D lift and drag coeﬃcients.

With the aim to discover the exact values of lift and drag coefficients for different airfoils, a lot of wind tunnel test have been and are carried out. However, most of the literature available for this sort of technology is focused on aerospace and aircraft science. Little literature is available for this specific WAPS. Thus, a first principle approve is used to predict the aerodynamic performance of this sort of technology instead of experimental data.

5.2.3 Data Source and Data Fitting The lift and drag prediction model for Rigid Wing Sails is divided into two main parts: 2D prediction and 3D prediction. The 2D approximation accounts for the profile shape and the camber effect while the 3D approximation modifies the 2D results to account for the effects of aspect ratio and tip vortices. The assumptions of this model are,

• No wing-ship interference is considered. • No profile thickness effects are considered due to their negligible effects on lift coefficient.

The 2D profile data (lift and draq coefficients as function of angle of attack) is obtained from the NACA 0012 symmetric profile [2]. The NACA tested many families of wing sections. Their investigations were outstanding. They were further systematized by separation of the effects of camber and thickness distribution, and the experimental work was performed at higher Reynolds numbers than were generally obtained elsewhere. NACA created the NACA four-digit wing sections which NACA 0012 profile is part of. The first integer means the maximum value of the mean-line ordinate (camber) in percentage of the chord. The second one, the distance from the leading edge to the location of the maximum camber in tenth of the chords.The third and fourth integers are the section thickness in per cent of the chord. Thus, NACA 0012 is a symmetric profile with 12% thickness. In order to model the effect of camber on lift and drag coefficients when having flaps, the DAT- COM 1978 [17] and Young [64] methods are implemented. DATCOM 1978, as stated in [17], is a collection, correlation, codification and recording of best knowledge, opinion and judgment in the area of aerodynamic stability and control prediction methods from the United States Air Force. It presents substantiated techniques to predict and model several aerodynamic effects such as flap implementation (section 6.1 in [17]). With this method, lift increase due to trailing-edge plain and slotted flap implementation is modelled. These sorts of high-lift devices increase lift for 0 degrees of angle of attack while reaching a higher maximum lift coefficient but a lower stalling angle (see Figures 5.14 and 5.19 for reference).

32 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

Figure 5.14: Flap deflection effect for a symmetric NACA profile with a plain flap. Source: [1].

Two equations are used to model the effects: one that computes the increase of lift coefficient at 0 angle of attack, ∆CL, (different for plain and slotted flaps) and the other that calculates the increase of the maximum lift coefficient magnitude (same for both flaps). The equations are dependent on flap chord length, flap deflection and lift coefficient of symmetric profile (here, NACA 0012). The increase of lift coefficient for plain flaps at 0 degrees angle of attack, ∆CL, is defined as, CLδ 0 ∆CL = δf (CLδ)theory · K (5.17) (CLδ)theory

CLδ where δf is the flap deflection in degrees, the factor depends on airfoil profile charac- (CLδ)theory teristics and flap chord length and K0 is the flap span factor. The same lift increase for slotted flaps is expressed as, ∆CL = CLααδ · δf (5.18) where the factor CLα depends on airfoil profile characteristics and αδ is a function of flap deflection and chord length. Note that all factors can be got from semi-empirical DATCOM graphs. The increase of the maximum lift coefficient magnitude for plain and slotted flaps is defined by DATCOM as, ∆CLmax = k1k2k3(∆CLmax)base (5.19) k1, k2 and k3 are factors which consider the relative flap chord, the flap deflection and the flap kinematics respectively. The last factor provides the maximum increase in the lift coefficient for a flap with a 25% flap chord at a reference flap angle. These factors are obtained from the following graphs in Figures 5.15, 5.16 and 5.17, respectively.

Figure 5.15: k1. Source: [17].

33 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

Figure 5.16: k2. Source: [17] Figure 5.17: k3. Source: [17].

The increase of lift coefficient is added to 2D symmetrical profile following equation 5.16. All lift increases due to flap deflections result in also drag increments due to its cambered shape. These variances in drag magnitude, ∆CDflap are modelled in here according to Young [64].

∆CDflap = ∆1∆2 (5.20) where ∆1 and ∆2 are functions (see Figure 5.18) representing the contribution of the flap chord and deflection angle to the total flap drag, respectively. The equation is only valid for flaps all along the wingspan.

Figure 5.18: ∆1 and ∆2 functions from Young. Source: [64]

Until here, the 2D aerodynamic loads prediction of a rigid wing sail is modelled. In Figure 5.19, the lift coefficient data as a function of angle of attack is plotted for a 30% chord length plain flap with different flap deflections. The data is obtained from this model prediction. NACA 0012 symmetric profile is assumed.

34 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

2.5

1.5

1 Lift coefficient Lift

Plain Airfoil Flap deflected 5 ° 0.5 Flap deflected 15 ° Flap deflected 25 ° Flap deflected 35 ° Flap deflected 45 ° 0 0 2 4 6 8 10 12 14 16 18 20 Angle of Attack, AOA

Figure 5.19: 2D lift coefficients of a NACA 0012 with 30% chord length trailing edge plain flap with variable flap deflection.

It can be seen that the single Wing Sail with the plain flap has approximately 20-60 % higher maximum lift potential in comparison to the one plain airfoil without the trailing edge flap. If we employ the trailing edge flap, the effective camber of the airfoil is increased, and the pressure gradient from the stagnation point to the suction peak point is increased. This results in increased velocity at the suction peak (low-pressure region on the upper surface), which causes a larger pressure difference between the upper and the lower surfaces of the wing-sail. For these reasons, the single Wing Sail with a flap can have better aerodynamic performance than the one without a flap. Furthermore, an early stall angle can be observed as a function of flap deflection - higher deflection leads to higher maximum lift coefficient but earlier stalling angle.

The 3D model accounts for downwash reducing lift and induced drag due to spillage around wing tips. It also accounts for different aspect ratios. These effects are modelled according to Prandtl’s lifting line theory [1][38]. It is the simplest 3D wing theory based on the concept of the lifting line. The wing is replaced by a straight line. The circulation is replaced by a vortex filament which lies along the straight line; and, at each spanwise station, the strength of the vortex is proportional to the local intensity of the lift. 3D lift and drag coefficients are derived as,

CL2D CL = (5.21) CL2D 1 + ARπ C2 C = C + C = C + L (5.22) D D2D Di D2D ARπe where, CL2D and CD2D are the 2D lift and drag coefficients which account for angle of attack and camber. As seen, CL is reduced from CL2D value as function of aspect ratio AR. If aspect ratio tends to infinity, CL ≈ CL2D. CD2D is the 2D drag coefficient at zero lift due to skin friction and form. CDi is the induced drag coefficient produced at the wing tips due to lift. CD adds induced drag to ideal 2D drag coefficient. If the aspect ratio tends to infinity, CD ≈ CD2D. e is the Oswald efficiency which depends on the lift distribution. For an elliptic lift distribution, it gets its maximum value, 1.

All data is loaded into the developed model in the software. It is fitted to find the right values for each given input conditions such as flap dimensions following a cubic spline interpolation of consecutive data in FS-Equilibrium software. The three data variables of this model are shown in Table 5.5.

35 5.2. RIGID WING SAILS CHAPTER 5. WAPS MODEL

Symbol Variable Valid Range α Angle of Attack [ 0:90 ] o o δf Flap deﬂection [ 0 :45 ] CF lap/CRW Flap chord ratio [ 0%:30% ]

Table 5.5: Data variables and their valid ranges.

The Performance Prediction Program constantly trims the angle of attack and the ﬂap deﬂection (if applied) of the Rigid Wing Sails to optimise the trim objective (minimum total power or maximum speed). Note that the angle of attack valid range is up to 90 degrees - downwind condition is also modelled according to plain airfoil wind tunnel tests of [50].

5.2.4 Windage Rigid Wing Sails are assumed retractable since most of the commercial ones are fold-able. Thus, no air resistance is modelled for this devices. If needed, it can be modelled similar to section 5.1.5.

5.2.5 Interaction Interaction effects on the aerodynamic performance of a Rigid Wing Sail cascade is a topic that concerns naval architects. Several studies have been carried to find out on the interaction effects between several sails for many years. It is not surprising than most of the studies have been focused on jib-main sail interaction for sailing yachts. Little literature is available for Rigid Wing Sails cascade for cargo ships. The aim of this section is to summarize the findings and studies carried out in this topic while explaining how this effect is considered in this program.

Generally, the key parameter in the determination of the effects on the aerodynamic performance of multiple Rigid Wing Sails are the number of sails employed, the spacing between them, the apparent wind angle, the angle of attack (trim) of each sail and their camber. For most of the studies [20][30][21], the overall interaction effects on the aerodynamic performance of several Rigid Wing Sails are not beneficial. According to [30], when having interaction, each Wing Sail produces thrust coefficients smaller by about 21-43% (with flap) and 24-37% (without flap) than those of the single Wing Sail. The mechanism of the flow interaction that causes the overall average altered aerodynamic performance in a jib-main sail configuration is based on an circulation differential following The Venturi effect and the so-called "slot effect". The front sail (jib), which is located further upstream in the wind direction, gets a beneficial lift increase from having the main sail behaving as a flap. However, the stagnation point on the rear wing-sail shifts toward its leading edge (the head effect) and this leads to the strength of the suction peak point of the rear Wing Sails to be considerably reduced.

However, some wind tunnel tests have proven that a favorable performance can be achieved for a wide range of AWA for a two Rigid Wing Sails configuration if the AOA of each sail is independently trimmed [6][10][36]. This favorable performance means that the average thrust force generated per sail in a cascade is higher than the single sail alone. Another interesting finding from Chapin [10] is the camber effect on the overall aerodynamic performance. Chapin focuses on the interaction between multiple sails (mainsail-jib) as function of camber and trim and what can be done to optimize design and maximize performance. His findings are that for maximum driving force and driving-heeling ratio, camber optimums are higher than for single sails. Thus, with the positive interaction between mainsail and jib it is possible to design higher camber sails to increase the resultant propulsive force for a give sail surface. All these findings open a new world of research. Finding a beneficial overall aerodynamic performance of multiple Rigid Wing Sails would be a valuable discovery which would greatly help the development of wind propulsion in the shipping sector. Maybe, the key remains in trimming each sail and adjusting its camber independently while accounting for the surrounding aerodynamic interactions. However, right now, in general WAPS applications, the more sails you use, the less efficient becomes the whole sail plan.

In this model, a performance increase for a large range of AWAs, from 30o

36 5.3. SOFT SAILS: THE DYNARIG CHAPTER 5. WAPS MODEL if multiple Rigid Wing Sails could interact with a beneficial overall performance. The users are able to turn this property on and off depending on their needs. This interaction is modelled as a percentage of change as function of AWA. The rigid DynaRigs used in the wind tunnel tests of Bordogna [6], despite of the fairly different shape with a NACA 0012 profile, are assumed to behave in a similar way as rigid wing sails regarding interaction effects on the aerodynamic performance. If the interaction effects should be precisely modelled, this should be changed. However, with the target of this implementation to this model, it is a fair assumption.

5.2.6 Input Data The minimum input data needed to run this entire Rigid Wing Sails model is shown in the following Table 5.6. Force Module Name Module Type Parameter Deﬁnition A-RW Aerodynamic CRW Rigid Wing Sail chord length A-RW Aerodynamic HRW Rigid Wing Sail height A-RW Aerodynamic α Falp deﬂection range A-RW Aerodynamic CF lap/CRW Flap chord ratio A-RW Aerodynamic CoE Position of each Rigid Wing Sail on-board [x,y]

Table 5.6: Input data Rigid Wing Sail model.

Note that the z coordinate of the CoE, as in the previous model, is automatically computed HRW assuming the Rigid Wing Sail is a rectangle. Thus, z = 2 + D − T .

5.3 Soft Sails: The DynaRig

The DynaRig is a square rig developed in the late 1960’s by Wilhelm Prölss, a German engineer. The main characteristic of this WAPS is its free-standing mast with the yards connected rigidly to it. The sails are trimmed to the wind by rotating the mast. Prölss designed this sort of sails for cargo ships initially. He carried out wind tunnel tests for a 6-masted bulk carrier of 16000 DWT at the Hamburg University between the 1960’s and the 1970’s (Figure 5.20). He named this ship the DynaSchiﬀ (the DynaShip). The DynaRig proved to be about twice as eﬃcient as traditional square rig sails. Thus, a much higher average sailing speed could be maintained over selected ocean routes.

Figure 5.20: Wilhelm Prölss with a model of the DynaRig. Source: [22].

Prölss took patents of his design in all shipbuilding countries worldwide. Sadly, he died before any ship installed DynaRigs. Some people showed interest but none of the projects involving DynaRigs

37 5.3. SOFT SAILS: THE DYNARIG CHAPTER 5. WAPS MODEL ended up becoming a reality. Partly because of the end of the first oil crisis, little research on the new device, nonexistence of full size test rigs and the difficulty to build a mast with sufficient stiffness to withstand the loads of such a rig. It was not until the beginning of the new millennium when wind propulsion for cargo ships attracted attention again and so did the DynaRig. The DynaRig saw the light on the mega yacht "Maltese Falcon" in 2006 [42]. Ten years later, in 2016, the DynaRig sailing yacht "Black Pearl" was released (Figure 5.21). However, DynaRig has not been limited to mega yachts and some concepts for commercial vessels involve this technology like the WASP EcoLiner Project, a sail-assisted cargo ship under design at Dykstra naval architects (Figure 5.22).

Figure 5.21: Black Pearl sailing yacht Figure 5.22: Dykstra Naval Architects WASP Source: Tom van Oossanen. (EcoLiner) Project. Source: [15].

The DynaRig is claimed to have numerous brilliant features. Because of its full automatization, no crew increase is needed - they can be managed by the same limited number of crew on-board a conventional motor ship. Its nice design makes it suitable also for the yachting sector. Their aerodynamic eﬃciency doubles the conventional squared soft sails, and as Rigid Wing Sails, Dy- naRigs are more precisely controllable while ﬁnding the optimal trim (the angle of attack can be changed easily and quickly). On the other hand, their cost measured over the expected lifetime of a commercial vessel is higher that of its competitor, the Rigid Wing Sails.

5.3.1 Conﬁguration The model is able to predict any DynaRig conﬁguration within the valid range exposed in the following Table 5.7.

Symbol Conﬁguration Parameter Valid Range AR Aspect ratio 2 approx.

Table 5.7: DynaRig conﬁguration and their respective valid range.

Note that the aspect ratio of a DynaRig is deﬁned as the fraction of its height and its chord length. All DynaRigs have similar aspect ratio, between 1.5-2. This is the reason behind the conﬁguration valid range.

5.3.2 Aerodynamic Loads The DynaRig generates aerodynamic loads following the same principles explained in previous section 5.2.2. DynaRigs are cambered sails. The potential of the DynaRig is evident as soon as the AWA becomes large. As this angle becomes larger, a higher camber becomes more optimum [42]. However, when having several DynaRigs interacting, it is not always the same mast which needs the deepest camber. For this reason, an average camber of 10% - 12% is the most common

38 5.3. SOFT SAILS: THE DYNARIG CHAPTER 5. WAPS MODEL for this technology. The centre of pressure of these sails sits just forward of and near the centre-line of the mast for an optimum performance trimming.

As its competitor, the Rigid Wing Sails, the DynaRig does not required any active power to generate aerodynamic forces such as the Rotor Sail. Little power (assumed negligible in this model) is required for trimming them though.

Several wind tunnel tests have been carried out with the aim to get the aerodynamic coeﬃcients for this device since Prölss invented the DynaRig. Among others, some of the most recent ones are the studies for the "Maltese Falcon" rig design [42], the wind tunnel tests of a 3000 DWT DynaRig assisted merchant ship from Smith [54] and the wind tunnel tests of two DynaRig arrangements from Bordogna [6].

5.3.3 Data Source and Data Fitting The data of this DynaRig model is based on the ﬁndings of the Bordogna’s wind tunnel tests [6]. This data source is chosen since no sail-hull interaction is accounted for unlike Smith [54], for instance. The DynaRig was virtually trimmed via a computer program which omptimizes the maximum thrust for each AWA. The DynaRig model of these wind tunnel tests is a 1.85 aspect ratio sail with a camber of 10%. Also, as stated before in section 5.2.5, in his research, Bordogna studies the aerodynamic performance of a single DynaRig, a two-DynaRig conﬁguration with GD = 2.5 (horizontal distance between the two sails masts relative to sail chord) and another two-DynaRig with GD = 4. The data is shown in Figure ??.

Figure 5.23: Driving and side force coeﬃcients from Bordogna [6].

Lift and drag coeﬃcients are extracted from driving and side coeﬃcients as function of AWA from 5.23 following,

CX = CL sin(AW A) − CD cos(AW A) (5.23)

CY = CL cos(AW A) + CD sin(AW A) (5.24) The Reynolds number effect is assumed negligible. The aspect ratio effect is also negligible since the model just accepts DynaRig configurations of the average commercial aspect ratio of 2.

The data is ﬁtted following a sequential linear interpolation. This computes sequentially an interpolation for each parameter. It requires that the data points are given in a grid mode - same set of x’s and y’s. The only variable is the AWA. See Figure 5.24 for reference.

39 5.3. SOFT SAILS: THE DYNARIG CHAPTER 5. WAPS MODEL

Figure 5.24: Drag coefficient data of the DynaRig model fitted following a sequential linear interpolation at FS-Equilibrium software. The drag coefficient is plotted against the AWA.

5.3.4 Windage When the DynaRig sails are not producing forward thrust, they are completely reefed. In pure motor configuration, and assuming non-retractable masts, their structure only creates air resistance, windage. This total resistance is modelled here following, 1 R = ρ · V 2 · H · D · C (5.25) windage 2 Dyna DynaMast DDyna This DynaRig windage is only considered in the x and y directions - z is neglected. The drag 6 coefficient, CD, is assumed to be 0.5 (2D circular shape value for Reynolds number range of 10 according to [37]). The yards are not considered in this air resistance with the aim to simplify the model. It is assumed that the masts will be also be trimmed while sailing in pure motor configuration so that the yards produce minimum air resistance. However, the mast, assuming a generic circular shape, will be responsible of most of the total real air resistance of the non- retractable DynaRig structure.

5.3.5 Interaction Interaction eﬀect is modelled in the same way as previous section 5.2.5 and with the same aim: to show to the users what could be achieved if multiple rigid wing sails could interact with a beneﬁcial overall performance.

According to the Maltese Falcon design team [42], when having a multi-DynaRig conﬁguration, a diﬀerent camber for each mast as function of the AWA improves aerodynamic performance.

5.3.6 Input Data The minimum input data needed to run this DynaRig model is exposed in Table 5.8,

Force Module Name Module Type Parameter Deﬁnition 2 A-DynaRig Aerodynamic SailAreaDyna DynaRig Sail Area [m ] A-DynaRig Aerodynamic HDyna DynaRig height A-DynaRig Aerodynamic DDynaMast Diameter of the DynaRig mast A-DynaRig Aerodynamic CoE Position of each DynaRig on-board [x,y]

Table 5.8: Input data DynaRig model.

Note that the z coordinate of the CoE, as in all the previous models, is automatically computed HDyna assuming the DynaRig is a rectangle. Thus, z = 2 + D − T .

40 Chapter 6

Validation

In this chapter a validation of the Performance Prediction Program for wind-assisted cargo ships model is carried out. The content focuses on the validation of the Rotor Sails and hull models. The Long Range 2 (LR2) class tanker vessel Maersk Pelican, ﬁtted with two 30 meters high Norsepower Rotor Sails, is used thanks to its real sailing data provided by Norsepower.

Unfortunately, the Rigid Wing Sail and the DynaRig models could not be validated as the Rotor Sail due to a lack of data available. Similar data as the Maersk Pelican one for these two WAPS could not be obtained since most of the projects involving these technologies for commercial vessels are still in their design stage and, generally, they are under a conﬁdentiality agreement. However, in the following Chapter7, a rough comparison with a 4 degrees of freedom ship performance prediction model developed at Chalmers University of Technology is presented for both devices.

6.1 Rotor Sails - Maersk Pelican

Maersk Pelican, a Long Range 2 (LR2) class tanker vessel, was ﬁtted with two 30 meter high Norsepower Rotor Sails on the 27th of August of 2018. Its main particulars are shown in the following Table 6.1. Performance data was continuously acquired until 1st of September of 2019 by independent ship performance specialists in order to prove the feasibility and performance of the technology. During this period, the vessel sailed in waters of Europe, the Middle East, Africa and Asia. The data, processed according to BS ISO 19030-2:2016, was given to the author of this Master’s Thesis project thanks to Norsepower as a validation tool for this model. Norsepower is currently the world’s leading sail technology provider for commercial shipping.

LOA Length over all 244.6 m LPP Length between perpendiculars 233 m B Beam 42.03 m T Design Draft 15.45 m D Depth 22.2 m DWT Deadweight Tonnage 109647 T MCR Engine Power 15260 KW Vs Design Speed 15.3 Kn

Table 6.1: Maersk Pelican main dimensions according to IHS Fairplay World Register of Ships.

To present better the data used to perform this validation, the data treatment carried out by engineers involved in the Maersk Pelican evaluation project is here explained. Note that the author of this thesis was not involved at all in this process. Most of the trial data set was collected between 11.5-13.5 Knots ship speed, excluding overall speed proﬁle under 4Kn by the Therefore, 12.5Kn speed is chosen to investigate the polar diagrams. See Figure 6.1 for reference. The measured data was corrected for wind resistance and the contribution of speed loss due to fouling was determined using CFD full scale modelling. The net eﬀect of the Rotor Sails was assessed by considering comparisons of shaft power including the additional power needed for the Rotor Sails.

41 6.1. ROTOR SAILS - MAERSK PELICAN CHAPTER 6. VALIDATION

Curves for performance at various conditions were ﬁtted through data plots of LOG speed and shaft power for similar load conditions and wind conditions. The curves were used to compare performance with and without rotors for the same load and wind conditions. Polar diagrams of the net propulsion saved as a function of true wind speed and true wind angle relative to the bow were built. The real sailing data presented in the diagrams is representative of average corrected trial data points for a ship speed through water of 12.5 Kn and all load conditions. Approximately 70% of the data points used to construct these polar diagrams have an average recorded true wind speed between 2.5 m/s to 7.5 m/s.

Figure 6.1: LOG Speed histogram above 4 knots in percentage from validated data set of the Maersk Pelican. Reproduced from source: [41], with permission of Norsepower.

As a first step of this validation process, the main particulars of the Maersk Pelican and other input data required by this Performance Prediction Program are loaded into the model thanks to the confidential reports provided by Norsepower. The Rotor Sails are not yet loaded into the model, the Maersk Pelican is still a conventional motor vessel. Then, the delivered power predicted from our model at design service speed, 15.3Kn, is compared with the prime mover specifications. While the ship vessel detail report states that the propeller at maximum 105 rpm requires a total power delivered of 15260KW while sailing at a service speed of 15.30 Kn, the model predicts a delivered power of 15030.28KW for same conditions. Thus, the model underestimates the delivered power of this ship in about 2% of error. Secondly, the rotor sails are introduced to the model with exact same dimensions and configurations of the real ones (30x5 m, 1.7 DeD and 160 maximum RPMs). They are also modelled in the exact place of installation on-board of the Maersk Pelican. The PPP is run for all TWS and TWA ranges of the given trial data. The sailing speed is set at 12.5Kn and added resistance due to waves is not considered. The net effect of the rotor sails is assessed by considering the additional spinning power required by the rotor sails. Windage of the rotor sails when they are not rotating is also accounted for. The model is able to check if it is more favorable to have them rotating slowly or completely turned off. Thus, the optimum condition is always set. RPMs are constantly trimmed for maximum power savings. Both rotors are assumed to rotate at same RPMs. Interaction on the aerodynamic performance of them is not accounted for. If interaction would be considered, RPMs should be trimmed independently for each rotor sail since setting of the RPMs of each rotor sail is key to reduce their detrimental aerodynamic interaction effects and increase the overall fuel savings according to [6]. This PPP results are plotted against Norsepower (NP) PPP model and real trial data in Figure 6.2.

42 6.1. ROTOR SAILS - MAERSK PELICAN CHAPTER 6. VALIDATION

0 0 3000 3000 330 30 330 30

2000 2000

300 60 300 60 1000 1000

0 0

270 -1000 90 270 -1000 90

240 120 240 120

Trial 0-2.5 m/s Trial 2.5-5.0 m/s 210 150 210 150 PPP 1.25 m/s PPP 3.75 m/s NP 1.25 m/s 180 NP 3.75 m/s 180

0 0 3000 3000 330 30 330 30

2000 2000

300 60 300 60 1000 1000

0 0

270 -1000 90 270 -1000 90

240 120 240 120

Trial 5.0-7.5 m/s Trial 7.5-10 m/s PPP210 6.25 m/s 150 PPP210 8.75 m/s 150 NP 6.25 m/s 180 NP 8.75 m/s 180

0 3000 330 30

2000

300 60 1000

270 -1000 90

240 120

Trial 10.0-12.5 m/s 210 PPP 15011.25 m/s 180 NP 11.25 m/s

Figure 6.2: Trial data vs own PPP vs Norsepower (NP) estimated total propulsion saving polar diagrams, relative to the bow and true wind speed of Maersk Pelican Rotor Sails Vessel. Savings in KW. Reproduced with permission of the copyright owner, Norsepower.

43 6.1. ROTOR SAILS - MAERSK PELICAN CHAPTER 6. VALIDATION

The Performance Prediction Program developed in this Master’s Thesis project is proven to match the Norsepower PPP very well for all conditions and the trial data for some ranges. The windage in upwind condition is clearly seen in the PPP data as negative power savings are obtained - higher delivered power is required than without Rotor Sails installed. The model does not show the large forces coming from the measurement campaign in downwind condition. These high downwind values given by the Maersk Pelican data could possibly be affected by inaccurate TWS measurements or currents. When measured on-board, TWS is calculated from AWS and ship speed. AWS gets small downwind (gets nearly 0 at 6.25 m/s of TWS since Vs is 12.5Kn). These possible inaccuracies could lead to these large differences. Also, the PPP results show a perfect symmetry since a symmetric hull is assumed. The divergence in symmetry for trial data could come from wave patterns of different sailing routes.

For a better understanding, the power savings according to minimum and maximum TWS of one of the ranges, 7.5-10 m/s, are plotted in Figure 6.3. It is seen how power savings increase with TWS while matching in great measure the trial data for a signiﬁcant TWA range.

0 3000 330 30

2000

300 60 1000

270 -1000 90

240 120

Trial 7.5-10 m/s PPP 7.5 m/s 210 150 NP 8.75 m/s PPP 10 m/s 180

Figure 6.3: Trial data vs own PPP vs Norsepower (NP) estimated total propulsion saving polar diagrams, relative to the bow and true wind speed of Maersk Pelican Rotor Sails Vessel for TWS range 7.5-10 m/s. Savings in KW. Reproduced with permission of the copyright owner, Norsepower.

Finally, the PPP power savings results are plotted together in absolute values. See Figure 6.4 for reference. It is seen how power savings increase with TWS and how negative savings of the upwind conditions (TWA=0o) follow exactly the same trend - they increase with TWS. For much higher TWS, the overall power savings would show a trend to reach a limit as presented in previous section7.

44 6.1. ROTOR SAILS - MAERSK PELICAN CHAPTER 6. VALIDATION

0 3000 330 30

2000

300 60 1000

0 11.25m/s 8.75m/s 270 -1000 90 6.25m/s 3.75m/s 1.25m/s

240 120

210 150 180

Figure 6.4: Own PPP estimated total propulsion saving polar diagram, relative to the bow and true wind speed of Maersk Pelican Rotor Sails Vessel. Absolute power savings in KW.

45 Chapter 7

Applications

In this chapter results extracted from the Performance Prediction Program developed in this Mas- ter’s Thesis project are presented. The aim is to show to the reader the main differences in the performance between the several WAPS available in the model: Rotor Sails, Rigid Wing Sails and DynaRigs. The cargo ship used to perform these calculations is the Long Range 2 (LR2) class tanker vessel, Maersk Pelican. Its main particulars are displayed in the previous Table 6.1. Thanks to their available deck space, tankers and bulk-carriers are specially suitable for wind propulsion. Also, due to their low sailing speed, for tankers and bulk-carriers it will be more challenging to fulfill the requirements of the Energy Efficiency Design Index (EEDI).

This chapter is divided into three sections. The first one presents the rough comparison of the Rigid Wing Sails and the DynaRig models developed in this Master’s Thesis with the 4 degrees of freedom ship performance prediction model developed at Chalmers University of Technology. This is used as a reference to compare and check the validity of both models. The second section presents the PPP results of the three different WAPS (Rotor Sails, Rigid Wing Sails and DynaRigs) installed on-board of the Maersk Pelican. The third focuses on the thrust and side force coefficients for each WAPS studied with the aim to show non-dimensional values easy to scale for different wind conditions and WAPS configurations.

7.1 Rigid Wing Sails and DynaRigs - Case Study

The case study from the 4 degrees of freedom ship performance prediction model developed at Chalmers University of Technology [35] is used as reference to carry out a rough comparison with the Rigid Wing Sail and DynaRig models presented in this Master’s Thesis project.

In the case study of [35], an Aframax Oil Tanker on a route between Cape Lopez, Gabon, and Point Tupper, Canada, is used. The tanker is 250 m length, 40 m in beam and 14m in design draft. To predict comparable results, the Maersk Pelican, with similar main particulars (see Table 6.1), is used as case study vessel in our PPP model. The DynaRig and the Rigid Wing Sail with 30% chord trailing edge plain ﬂap are both set to the same dimensions as the Aframax Oil Tanker case study: 1000 m2 of sail area. Both are positioned midships of the vessel. Since the case study route is an Atlantic Ocean route, a range of 8 m/s to 10 m/s is assumed as average TWS according to [51] and the average annual real data base. The Maersk Pelican is set to sail at the same service speed as the Aframax Oil Tanker, at 15.7 Kn. Since the wind angle weighting is not given for the case study and according to Schenzle [51] the relative directions of true wind to the ship’s heading has constant probability from 0o to 360o, 360o polar plots are presented as results. Overall predicted power savings for each WAPS independently are obtained by subtracting the total power delivered in wind-assisted mode from the pure motor mode. Windage is assumed for the DynaRig. Rigid Wing Sails are assumed retractable. The results presented in the Oil Tanker case study are in percentage of fuel savings. To get the fuel savings, they could be calculated following equation 7.1. T (P − P ) · SFOC) s = M (7.1) BASE W AP S 1 · 106 R

46 7.1. RIGID WING SAILS AND DYNARIGS - CASE STUDY CHAPTER 7. APPLICATIONS

where, PBASE is the power supplied by the main engine at baseline thrust without the WAPS installed in KW, PW AP S is the same power but when the WAPS are onboard, SFOC is the speciﬁc fuel oil consumption at the given power in g/kW h, Ts is the ship operating time in hours and MR is the mass of fuel saved in Tonnes. However, assuming a SFOC constant, percentage power savings give the same results than percentage fuel savings. Thus, the results got from the PPP are presented in Figures 7.1 and 7.2.

0 10 330 30

5 300 60

DynaRig TWS 8m/s 270 -5 90 DynaRig TWS 9m/s DynaRig TWS 10m/s

240 120

210 150 180

Figure 7.1: PPP fuel savings results in percentage for the 1000 m2 DynaRig.

47 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS

0 330 10 30

5 300 60

Rigid Wing Sail TWS 8m/s 270 -5 90 Rigid Wing Sail TWS 9m/s Rigid Wing Sail TWS 10m/s

240 120

210 150 180

Figure 7.2: PPP fuel savings results in percentage for the 1000 m2 Rigid Wing Sail with 30% chord trailing edge plain ﬂap.

Both models results are in line with the results presented in the Aframax Oil Tanker case study with all of the uncertainties involved. It should be noted that this rough comparison is based on several assumptions: an average TWS over the given route, a TWA uniformly distributed over all angles and a similar vessel. However, the aim is to check if similar values are reached with our PPP model. For the single DynaRig, the 4 degrees of freedom performance prediction program of Lu and Rings- berg [35] predicts 5.6% of average fuel savings compared to no WAPS installed. For the single Rigid Wing Sail, they estimate 8.8% of overall average fuel savings. The PPP developed in this Master’s Thesis predicts 5.87% of maximum fuel savings for the Dy- naRig, at 9 m/s of TWS. On the other hand, the Rigid Wing Sails model predicts maximum fuel savings of 7.95% at 10 m/s of TWS.

With all the uncertainties involved and despite Lu and Ringsberg [35] results being overall average fuel savings for a speciﬁc route, the PPP predicts similar values for maximum savings at the average TWS of the given route.

7.2 PPP Results

A Power Prediction Program (PPP) is decided to be the focus of this study since most of the actual wind propulsion applications are in fact in wind-assisted vessel where WAPS are installed to save power, reduce fuel consumption and related emissions. Thus, power savings seems the most reasonable and, probably, useful results achieved from these performance prediction simulations.

Each Wind-Assisted Propulsion Systems must be installed independently on-board of the Maersk Pelican cargo ship and the results should be presented in polar plots to be able to compare their performances. Moreover, wind and sailing conditions must be set equally for all simulations. According to Schenzle [51], the values of annual average true wind speed are exposed in Table 7.1.

48 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS

The relative directions of true wind to the ship’s heading has uniform probability from 0o to 360o. Then, the polar plots will also cover this range of TWA.

The Caribbean Sea 6-7 m/s The North Sea 7-8 m/s The North Atlantic Ocean 8-10 m/s

Table 7.1: Annual average true wind speed according to [51]

The proposed average true wind speed to run the PPP is 10 m/s, an average TWS in the North Atlantic Ocean. The service speed of 12.5Kn is set according to the mean real sailing speed of the Maersk Pelican.

The first challenge when comparing the performance of each WAPS is setting their total sail areas. An area for each WAPS that gives a total similar forward thrust for given wind and sailing conditions is needed. Otherwise, the results would be difficult to be interpreted. The required difference in size will also gives us the efficiency of each WAPS in terms of forward thrust per square meter of projected sail area. To do so, a first performance prediction calculation is done for one 30x5m and De/D of 2 Rotor Sail installed in the mid-ship of the Maersk Pelican in the wind and sailing conditions previously defined as default (10m/s of TWS and 12.5Kn of Vs). Its maximum forward thrust, which is experienced at 110o of TWA, is used to get the Rotor Sail lift coefficient at this wind condition. Assuming that all Rigid Wing Sails have the same aspect ratio as the DynaRig, which is 2, their maximum lift coefficient is obtained from the model data source (low aspect ratio effects due to tip vortices and pressure leakage are accounted for for Rigid Wing Sails maximum lift and drag coefficients). Then, the area needed to equalize the Rotor Sail lift at maximum forward thrust for each WAPS is computed following the Lift Equation 5.3. The performance efficiency of each wind-assisted device is given as a factor of Newton of lift force generated per square meter of projected sail area. The results, normalized to the least efficient device, are shown in Table 7.2.

2 2 WAPS 3D CL Area m N/m Normalized Rotor Sail (AR=6 & DeD=2) 9.15 150 650.37 7.76 Rigid Wing Sail No Flap (AR=2) 1.18 1163.47 83.45 1 Rigid Wing Sail 30% Plain Flap (AR=2) 1.70 807.59 120.8 1.44 Rigid Wing Sail 30% Slotted Flap (AR=2) 1.73 793.58 122.93 1.47 DynaRig (AR=2) 1.48 927.63 105.17 1.25

Table 7.2: WAPS eﬃciency comparison.

These findings show the relation in area between WAPS to generate the same maximum lift. Thus, their efficiency in creating a lift force per square meter of projected sail area. The Rotor Sails are the most efficient ones. They are nearly 8 times more efficient than a Rigid Wing Sail plain airfoil without flaps followed by Rigid Wing Sails with slotted flaps, plain flaps, the DynaRig and finally the Rigid Wing Sail without flaps. Thus, a Rigid Wing Sail with aspect ratio of 2 has to be nearly 8 times bigger in size than a Rotor Sail to produce same forces. However, the Rotor Sail’s trade-off is its required power to spin which does not allow it to always rotate as fast as they could to maximize lift. To make this efficiency relation more visual, the required difference in size is shown in Figure 7.3.

49 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS

Figure 7.3: WAPS area proportions according to Table 7.2

The efficiency of Rigid Wing Sails could be significantly improved if higher aspect ratios could be achieved by manufacturers. With this aim, the same previous process is done for the ideal infinitely long sails. These Rigid Wing Sails’ 2D lift coefficients are also compared with the maximum lift coefficient of high aspect ratio Rotor Sail for same wind conditions (note that the Rotor lift coefficient presented before was the one obtained for maximum savings when trimming its RPM, not the overall maximum in the data source). The DynaRig is not considered in this comparison since its aerodynamic coefficients cannot be easily scaled for aspect ratio effects in the model. The results are presented in Table 7.3.

2 WAPS CL Area N/m Normalized Rotor Sail (AR=12 & DeD=2) 14.95 150 1062.18 10.30 Rigid Wing Sail No Flap 1.45 1310.23 103.11 1 Rigid Wing Sail 30% Plain Flap 2.34 813.43 166.08 1.61 Rigid Wing Sail 30% Slotted Flap 2.40 793.47 170.26 1.65

Table 7.3: Inﬁnitely long WAPS eﬃciency comparison.

The results show how all WAPS become more efficient with higher aspect ratios than lower ones - they are able to create more lift per square meter of projected sail area. Most importantly, it is seen how Rotor Sails are about 10 times more efficient per area than Rigid Wing Sails. On the same trend, both flapped Rigid Wing Sails stand out from their plain airfoil twin being about 1.6 times more efficient in maximum lift generation per area.

Secondly, the WAPS efficiency results are used to design the Rigid Wing Sails and the DynaRigs aiming at similar savings as the single 30x5m rotor sail installed at mid-ship of Maersk Pelican. Aiming to have more visual plots, it is decided to use the WAPS configurations presented in previous Table 7.2 but setting a total projected sail area of 800 m2 for all Rigid Wing Sails and DynaRig. It was considered to use each WAPS specific required area to achieve exactly the same maximum savings as the Rotor Sail but the result trends were tricky to interpret due to total area scale effects. All WAPS are placed in the same location, at mid-ship, but the vertical component of the centre of effort of each one is changed depending on their mast height (Rigid Wing Sails and DynaRig have same vertical component because of their equal aspect ratio). To compute power savings, the delivered power of the traditional pure motor Maersk Pelican (without any WAPS installed) is firstly predicted for the same wind conditions and sailing speed. Then, all WAPS performance are run independently. Finally, to get the total power savings for each WAPS, the total delivered power when having one system installed is subtracted from the pure motor Maersk Pelican values for each simulation point. Rotor Sails’ RPMs and AOA as well as flap deflections are trimmed constantly to maximize total power savings. Windages for DynaRig and Rotors (Rigid Wing Sails are assumed retractable) are also included. These air resistance forces are active when the WAPS produces a higher negative forward thrust than its own windage component. In those conditions, WAPS’s aerodynamic forces are assumed non-active. Total Rotor Sail spinning power required as function of its RPMs is also accounted in the calculation of total

50 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS power savings - it is added to the delivered power of the wind-assisted cargo ship before subtracting the conventional pure motor values (without WAPS installed). Thus, the total savings of the Rotor Sails already accounts for its own power required to spin. The power savings for all ﬁve diﬀerent WAPS for the reference condition at 10 m/s of TWS and 12.5Kn of sailing speed are presented in Figure 7.4.

0 0 1500 15 330 30 330 30

1000 10

300 60 300 60 500 5

0 0

270 -500 90 270 -5 90

240 120 240 120 Rotor Sails Rotor Sails Rigid Wing Sail Plain Airfoil Rigid Wing Sail Plain Airfoil DynaRig DynaRig 210 150 210 150 Rigid Wing Sail Plain Flap Rigid Wing Sail Plain Flap Rigid Wing Sail Slotted Flap 180 Rigid Wing Sail Slotted Flap 180

Figure 7.4: Power savings polar diagrams for all WAPS in service conditions for Maersk Pelican (12.5Kn and 10m/s TWS) for TWA relative to the bow. Left, absolute power savings in KW. Right, power savings in percentage.

Note that maximum savings for all WAPS are very similar as intended by selecting the sail area of 800 m2. The results show that Rotor Sails perform undoubtedly better than the other WAPS in downwind and broad reach sailing courses. Trailing edge slotted and plain flaps are able to generate much higher forward thrust than the plain airfoil which leads to overall higher power savings for all TWAs. In pure downwind (TWA=180o), all Rigid Wing Sails perform equally since the AOA is set at 90o and the major component of the total aerodynamic force is drag. The DynaRig stands out in upwind sailing courses where it beats all its competitors. Note that for the non-retractable devices such the DynaRig and the Rotor Sail, windage is accounted for the overall power savings calculations. This is clearly seen at pure upwind condition (TWA=0o) where savings are negative - the vessel has to deliver higher power to overcome these air resistance force components than without WAPS installed. For the Rotor Sails, it is concluded that for pure upwind course it is worth it to have the Rotor Sail rotating at a velocity ratio, U/V , around 1 than turning it off and having only its windage component. At this low velocity ratio, the drag force is lower than its non-rotating windage thanks to flow circulation. Thus, higher power savings are achieved if the Rotor Sail is rotating at this low velocity ratio, even though it consumes some spinning power, than turning it off and having to overcome the air resistance of the non-rotating device. The percentage of savings are for one WAPS of each type installed at mid-ship of the Maersk Pel- ican. The results could be scaled to predict the savings when more devices are installed. However, interaction effects in the overall aerodynamic performance and the non-linear hydrodynamic effects such as propeller efficiency, drag due to side force and rudder hydrodynamic side force would play a key role and should be considered for a more accurate calculation.

To compare the WAPS performance for diﬀerent wind conditions and same sailing speed of 12.5Kn, the TWS is increased from 10m/s to 14m/s. The results are shown in Figure 7.5.

51 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS

0 0 3000 30 330 30 330 30

2000 20 300 60 300 60 1000 10

0 0 270 90 270 90

Figure 7.5: Power savings polar diagrams for all WAPS at 14m/s of TWS and 12.5Kn of sailing speed for TWA relative to the bow. Left, absolute power savings in KW. Right, power savings in percentage.

It is clearly seen how the Rotor Sail does not perform as well as the other sails for higher TWS. Due to its maximum RPMs limit (160 in this case) and the increasing TWS, the Rotor cannot reach the same high velocity ratios - which gave it the high lift coeﬃcients. Thus, Rotor Sails tend to have a maximum power savings as function of TWS. On the contrary, Rigid Wing Sails and the DynaRig increase exponentially as function of TWS. See Figure 7.6 for reference. Rigid Wing Sails and DynaRig will also have a real power limit due to ship stability and their own structural limit loads. In general terms, for increasing TWS with same sailing speed, higher savings in absolute values and in percentage are achieved.

11000

10000

9000

8000

7000

6000

5000

4000 Power Savings, KW Savings, Power

3000

2000

1000

0 0 5 10 15 20 25 30 TWS, m/s

Figure 7.6: Power savings as function of TWS for TWA=90o. In blue, Rotor Sail power savings in KW. In red, Rigid Wing Sail with trailing edge slotted ﬂaps power savings in KW.

Now, the TWS is decreased to 6 m/s but the sailing speed is kept as before. The results are shown in Figure 7.5.

52 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS

0 0 600 4 330 30 330 30

400 2 300 60 300 60 200

0 0

270 -200 90 270 -2 90

Figure 7.7: Power savings polar diagrams for all WAPS at 6m/s of TWS and 12.5Kn of sailing speed for TWA relative to the bow. Left, absolute power savings in KW. Right, power savings in percentage.

For decreased TWS, both power savings in absolute values and in percentage are reduced compared to the ones with higher TWS. However, same trends as 10m/s of TWS are achieved while comparing the performance of the WAPS. The Rotor Sail beats all of them in downwind and broad reach while the Rigid Wing with trailing edge slotted flap is the outstanding one for a wide range of reaching TWA. The DynaRig keeps performing greatly in up-dwind. Note that the Rotor Sail does not show a depowering because it can reach the high lift coefficients while rotating at lower RPMs. The results show that for an optimal performance the Rotor Sails should be constantly trimmed as function of the TWS. In the following Figure 7.8, the Rotor Sail’s RPMs trimming of this model for maximum power savings is shown. The results are for TWA 90o and are plotted as function of TWS. In ideal conditions, where there would not be any RPMs limit, Rotor Sails will not power-off because the high velocity ratios could also be achieved for increasing TWS but the power required to spin would also increase dramatically. In fact, this characteristic makes Rotor Sails the perfect storm-proof wind-assisted propulsion system. For increasing TWS, they tend to reduce their total aerodynamic loads to negligible values even while still rotating at maximum RPMs.

53 7.2. PPP RESULTS CHAPTER 7. APPLICATIONS

180

160

140

120

100

80 RPM Rotor Sails Rotor RPM 60

0 0 5 10 15 20 25 30 TWS, m/s

Figure 7.8: Rotor sail’s RPMs trimming as function of TWS for TWA 90o.

In another set of simulations, the TWS is kept at 10m/s and the sailing speed is modiﬁed. Firstly, the service speed is increased up to the maximum designed sailing speed of the Maersk Pelican, 15Kn. Then, it is reduced to 8Kn. Results are presented in following Figures 7.9 and 7.10.

0 0 2000 10 330 30 330 30

300 1000 60 300 60 0

-5 0

270 90 270 -10 90

Figure 7.9: Power savings polar diagrams for all WAPS at 15Kn of sailing speed and 10 m/s of TWS for TWA relative to the bow. Left, absolute power savings in KW. Right, power savings in percentage.

54 7.3. WAPS DRIVING AND SIDE FORCE COEFFICIENTS CHAPTER 7. APPLICATIONS

0 0 1000 330 30 330 30 20

500 300 60 300 10 60

0 0

270 -500 90 270 -10 90

Figure 7.10: Power savings polar diagrams for all WAPS at 8Kn of sailing speed and 10 m/s of TWS for TWA relative to the bow. Left, absolute power savings in KW. Right, power savings in percentage.

While playing with sailing speed, WAPS performance show nearly exact patterns. The only thing changing are the magnitudes of the overall power savings. For higher sailing speeed, higher absolute power savings are achieved but the values in percentage are signiﬁcantly reduced. On the other hand, for lower service speed, lower overall power savings in absolute values are obtained but the percentage is signiﬁcantly increased. To sum up, reducing sailing speed leads to higher power savings, higher fuel savings and lower emissions when having WAPS installed on-board compared to conventional motor ship at same speed.

All results presented in this chapter have average heeling and leeway angles values of 0.2o and 1o, respectively. The reason behind these really low values are the wide beam of the Maersk Pelican and the single WAPS used in each run.

7.3 WAPS Driving and Side Force Coeﬃcients

Finally, side and driving/thrust force coeﬃcients for each WAPS are presented in this chapter. The aim is to show non-dimensional results. Thus, the reader can have a better idea of the performance of these WAPS in general terms. Side, CS, and driving, CT , coeﬃcients are obtained from this performance prediction program for 10m/s of TWS and 12.5Kn of sailing speed according to,

DrivingF orce C = (7.2) T 1 2 2 ρair · Area · AW S SideF orce C = (7.3) S 1 2 2 ρair · Area · AW S The results are shown in Figures 7.11, 7.12, 7.13, 7.14 and 7.15. These results can be really useful to give an idea of how much forward thrust and its respective side force each WAPS is able to generate. Since they are in non-dimensional form, by multiplying each coeﬃcient by the WAPS area and the AWS at power of 2 (following equations 7.2 and 7.3), the driving and side force for 360o of TWA can be computed easily.

55 7.3. WAPS DRIVING AND SIDE FORCE COEFFICIENTS CHAPTER 7. APPLICATIONS

8 0 15 330 30 6

300 60 4 s

5 2

270 0 90 0 Side Coefficient, C Coefficient, Side

-2

240 120 -4

-6 0 20 40 60 80 100 120 140 160 180 210 150 AWA 180 Figure 7.11: Rotor sail (AR=6 and DeD=2) force coefficients for maximum power savings for Maersk Pelican at 10m/s of TWS and 12.5Kn of sailing speed as function of AWA. Left, driving force coefficient. Right, side force coefficient.

0 1.4

330 30 1.2 1.5

300 1 60

0.8 s

0.5 0.6

0.4 270 0 90

0.2 Side Coefficient, C Coefficient, Side 0

-0.2 240 120 -0.4

-0.6 210 150 0 20 40 60 80 100 120 140 160 180 AWA 180

Figure 7.12: DynaRig (AR=2) force coefficients for maximum power savings for Maersk Pelican at 10m/s of TWS and 12.5Kn of sailing speed as function of AWA. Left, driving force coefficient. Right, side force coefficient.

56 7.3. WAPS DRIVING AND SIDE FORCE COEFFICIENTS CHAPTER 7. APPLICATIONS

0 1.2 1.5 330 30 1

1 0.8

300 60 s 0.6 0.5

0.4 270 0 90

0.2 Side Coefficient, C Coefficient, Side

240 120 -0.2

-0.4 210 150 0 20 40 60 80 100 120 140 160 180 AWA 180

Figure 7.13: Rigid Wing Sail (AR=2) force coefficients for maximum power savings for Maersk Pelican at 10m/s of TWS and 12.5Kn of sailing speed as function of AWA. Left, driving force coefficient. Right, side force coefficient.

0 2 2 330 30 1.5 1.5 1 300 60

1 s 0.5 0.5 0 270 0 90

-0.5 Side Coefficient, C Coefficient, Side

-1

240 120 -1.5

-2 210 150 0 20 40 60 80 100 120 140 160 180 AWA 180

Figure 7.14: Rigid Wing Sail with trailing edge plain flap (AR=2) force coefficients for maximum power savings for Maersk Pelican at 10m/s of TWS and 12.5Kn of sailing speed as function of AWA. Left, driving force coefficient. Right, side force coefficient. Blue, 30% flap chord. Red, 10% flap chord.

57 7.3. WAPS DRIVING AND SIDE FORCE COEFFICIENTS CHAPTER 7. APPLICATIONS

0 2 2 330 30 1.5 1.5 1 300 60

1 s 0.5 0.5 0 270 0 90

-0.5 Side Coefficient, C Coefficient, Side

-1

240 120 -1.5

-2 210 150 0 20 40 60 80 100 120 140 160 180 AWA 180

Figure 7.15: Rigid Wing Sail with trailing edge slotted flap (AR=2) force coefficients for maximum power savings for Maersk Pelican at 10m/s of TWS and 12.5Kn of sailing speed as function of AWA. Left, driving force coefficient. Right, side force coefficient. Blue, 30% flap chord. Red, 10% flap chord.

It is seen that Rotor Sails are the most efficient WAPS studied in this project. Its maximum thrust coefficient is approximately 14 while the other WAPS reach an average maximum of 1.5. On the other hand, Rotor Sails do produce higher heeling coefficient than other WAPS. For all Rigid Wing Sails and the DynaRig, at pure downwind (AWA=180o), the side force coefficient tends to be 0 because drag is the major total aerodynamic force component and the perpendicular component, lift, is nearly 0. Rotor Sails do not show the same trend due to their condition of active rotating devices. At pure downwind, high Rotor Sail side force coefficient is still achieved - generating maximum drag force implies generating high lift force in perpendicular direction. For both trailing edge plain and slotted flapped airfoils, driving and side force coefficients are plotted for two different configurations: when the flap chord is 10% and 30% of the total airfoil chord. With higher flap chord, the profile can have higher camber and, thus, produce higher driving force which also leads to higher side force, generally.

58 Chapter 8

Conclusion

The Performance Prediction Program for wind-assisted cargo ships fulfills its mission and accom- plishes its goals. The performance of three different Wind-Assisted Propulsion Systems (WAPS): Rotor Sails, Rigid Wing Sails and DynaRigs; for any cargo ship is predicted with only the ship main particulars and general configuration dimensions as required input data. Thanks to its user- friendly interface, it can be a useful tool in early project stages to quickly and accurately assess the potential and performance of WAPS. The program is based on semi-empirical methods and a WAPS aerodynamic database created from published data on lift and drag coefficients. All WAPS data is interpolated with the aim to scale to different sizes and configurations such as number of units and different aspect ratios.

The Performance Prediction Program has been tested and evaluated. It proved to work following its design criteria: Rotor Sails’ RPMs and the angle of attack as well as flap deflections are trimmed for each operating condition to maximize performance. This includes maximizing sailing speed if a VPP is run or maximizing total power savings if it is a PPP. Windage for the DynaRig and the Rotors (Rigid Wing Sails are assumed retractable) and the Rotor Sail spinning power required are also accounted for in the calculation. The Performance Prediction Program for Rotor Sails has been validated with the Norsepower performance prediction model and the real sailing data from the Long Range 2 (LR2) class tanker vessel, the Maersk Pelican which was fitted with two 30 meter high Norsepower Rotor Sails on the 27th of August of 2018. Rigid Wing Sails and DynaRigs models have been compared with a 4 degrees of freedom ship performance prediction model developed at Chalmers University of Tech- nology with all of the uncertainties and assumptions involved. Despite its generic structure and the small number of input data needed, the model developed in this Master’s Thesis is able to predict the performance of any cargo ship with three different WAPS installed with a good level of accuracy.

After comparing the aerodynamic performance of the three different WAPS presented in this project, Rotor Sails are seen as the most efficient WAPS studied with a much higher potential of driving force generation per square meter of projected sail area than the other devices. They are followed by the Rigid Wing Sails with trailing edge slotted flaps, plain flaps, the DynaRigs and finally, by the un-flapped Rigid Wing Sails. Rotor Sails perform better than the other WAPS in downwind and broad reach headings for the selected sail areas. On the other hand, the DynaRig proved high performance in upwind conditions. For the Rigid Wing Sails, implementing trailing edge high lifting devices improves greatly the performance compared to the symmetric plain airfoil. In fact, the Rigid Wing Sail with trailing edge slotted flap performs outstandingly for the widest range of TWA. In general terms, when installing WAPS on-board, for increasing TWS, higher savings are achieved. On the other hand, for decreasing service speed, higher percentage savings are achieved but lower absolute savings. This means that when sailing slower the WAPS do not generate higher forward thrust but its contribution results in a much higher percentage of the total engine power required. The results also show that for an optimal performance all WAPS should be constantly trimmed as function of the TWS and TWA to reach optimal coefficients. Rotor Sails are seen as a very good storm-proof wind-assisted propulsion system thanks to their inherent ability to limit their own total aerodynamic load due to their maximum design spinning velocity.

59 CHAPTER 8. CONCLUSION

The output data of this Performance Prediction Program for wind-assisted cargo ships is designed to be used as input data of the route optimisation algorithm to maximise savings.

The results of this Master’s Thesis project show how Wind-Assisted Propulsion Systems (WAPS) have high potential in playing a key role in the decarbonization of the shipping sector. WAPS can prove substantial power, fuel, cost, and emissions savings. Tankers and bulk-carriers are specially suitable for wind propulsion thanks to their available deck space and relatively low design speeds.

Further possible work on the development of this Performance Prediction Program is to implement more WAPS such as Kites and Turbosails. Moreover, research on how each WAPS can be designed and optimized for the interaction eﬀects on the aerodynamic performance when they are placed close together for maximum overall sail power is needed. Thus, accurate sail-sail and sail-hull interaction eﬀects on their aerodynamic performance could also be included.

60 References

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63 Appendix A

Macros

Several macros have been designed in this Performance Prediction Program. They are presented in this chapter.

A.1 Import Data

This macro is responsible for loading all input data in its right place inside the force modules. It is part of the user-friendly interface.

#! py import csv import f s

#import input file fname="data . csv" print ("File␣name:␣"+fname) input = csv.DictReader(open(fname), delimiter=’; ’)

#set ForceModules values i =0 for row in input :

i f i <= 1 : print ( row ) ModuleName = row["ModuleName"] Parameter = row["Parameter"] Value = row["Value"] print ("ModuleName : ␣"+ModuleName) print ("Parameter :␣␣"+Parameter) print ("Value:␣␣␣␣␣␣"+Value) i=i +1 fs .cmd("set␣%s␣%s" % (Parameter , Value))

e l i f i > 1 and i <= 5 : print ( row ) ModuleName = row["ModuleName"] Parameter = row["Parameter"] Value = row["Value"] print ("ModuleName : ␣"+ModuleName)

64 A.2. POLAR APPENDIX A. MACROS

print ("Parameter :␣␣"+Parameter) print ("Value:␣␣␣␣␣␣"+Value) i=i +1 fs .cmd("set␣%s.%s␣%s" % (ModuleName, Parameter , Value))

e l i f i > 5 and i <= 7 6 : i=i +1 print ( row ) ModuleName = row["ModuleName"] Parameter = row["Parameter"] Value = row["Value"] print ("ModuleName : ␣"+ModuleName) print ("Parameter :␣␣"+Parameter) print ("Value:␣␣␣␣␣␣"+Value)

fs .cmd("module␣%s␣%s␣%s" % (ModuleName, Parameter , Value))

e l i f i >= 7 7 : i=i +1 print ( row ) ParameterName = row["ModuleName"] ValueCharacteristics = row["Parameter"] value = row["Value"] print ("ParameterName : ␣"+ParameterName) print ("ValueCharacteristics :␣␣"+ValueCharacteristics) print ("Value:␣␣␣␣␣␣"+value)

fs .cmd("set␣Parameter.%s.%s␣%s" % (ParameterName, ValueCharacteristics , value))

A.2 Polar

This macros jumps from pure sailing, combined and pure motor modes. Setting a minimum target speed, the model predicts the performance of wind-assisted cargo ships. #! py import os , f s

# d e f a u l t s −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− hs=0 VsMinKn = 4 VsTargetKn = 4

TWA_range=range (180 ,20 , −5) #Headings.extend(range(275,361,5)) #upwind

TWS_range_kn=range ( 5 , 4 0 , 5 ) outPath="./ test" fname="Test" append=False

# initialize −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− fnameOut=os .path. join(outPath ,fname+". csv") fnameCnd=os .path. join (outPath ,fname+".con") fnameTab=os .path. join (outPath ,fname+".tab")

65 A.2. POLAR APPENDIX A. MACROS

#Create ouput directory if it does not exist i f not os.path. exists(outPath): os.makedirs(outPath)

#Delete old output file i f not append : print "Overwriting␣output␣files ." i f os.path. isfile (fnameOut): os.remove(fnameOut) i f os.path. isfile (fnameCnd): os.remove(fnameCnd) i f os.path. isfile (fnameTab): os.remove(fnameTab)

#Variables definition kn = 0.514444 VsMin=VsMinKn∗kn VsTarget=VsTargetKn∗kn

#Find sailing trim fs .cmd("defaults") fs .condition("pitch" ,0.0) fs .cmd("adjust␣sink")

#Set parameters fs .condition("Hs",hs)

# run p o l a r −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− for tws in TWS_range_kn :

for twa in TWA_range :

tws_ms = tws∗kn

fs . condition("TWS", str ( tws)+"∗kn" ) #fs . condition("TWS", tws_ms) fs . condition("TWA", twa)

#Balance Vs in sailing configuration fs .cmd("defaults") fs .cmd("balanceVs") fs.condition("config","Sail")

#fs . find_trim("TWC") fs . balance("TWA")

#Check if sailing above VsMin is possible Vs=f s . eval ( "Vs" )

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx")

#fs .write_conline(fnameOut,0 ,";")

#print(FxResid)

# Find RPM (Power) at Target Speed if not sailing above VsMin i f Vs

66 A.3. CALM WATERS APPENDIX A. MACROS

fs . condition("config","Combined") fs .cmd("balanceRPM") fs . condition("Vs",VsTarget) fs . condition("RPM" ,100) fs . balance("TWA") #fs . find_trim("TWC")

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx") FxSails=fs . eval ("FxFlettner")

#fs .write_conline(fnameOut,0 ,";")

# Find RPM (power) for motoring without sails if sail drive force i s negative i f FxSails <0 or Status==0 or StatusFx==0: fs .cmd("defaults") fs .cmd("condition␣config␣Motor") fs .cmd("balanceRPM") fs . condition("Vs",VsTarget) fs . condition("RPM" ,100)

fs . balance("TWA")

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx")

#fs .write_conline(fnameOut,0 ,";")

# Find Speed at maximum power if Target speed is not achieved when motoring i f Status==0 or StatusFx==0: fs .cmd("defaults") fs .cmd("condition␣config␣Motor") fs .cmd("balanceVs") fs . condition("RPM" ,130)

fs . balance("TWA")

#fs .write_conline(fnameOut,0 ,";")

#Write output to files fs . write_condition(fnameTab,1) #Write output defined in Settings fs .write_conline(fnameOut,0 ,";") #Write condition table row to file fs . save_condition(fnameCnd,1) #Write condition to file

A.3 Calm Waters

This macros runs a PPP in calm waters. #! py import os , f s

# d e f a u l t s −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

67 A.3. CALM WATERS APPENDIX A. MACROS hs = 0 Vs_range_kn = [12.5] #IN kNOTS PLEASE kn = 0.514444 #Vs_range=kn∗Vs_range_kn

TWA_range = range(180 , −10 , −10)

TWS_range_kn = [ 2 1 . 8 7 ] #range(1,26,1) outPath = "./Maerskresults" fname = "Maerskresults" append = False

#Create ouput directory if it does not exist i f not os.path. exists(outPath): os.makedirs(outPath)

#Find sailing trim fs .cmd("defaults") fs .condition("pitch" ,0.0) fs .cmd("adjust␣sink")

#Set parameters

fs .condition("Hs",hs)

# run p o l a r −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− for Vs in Vs_range_kn :

for tws in TWS_range_kn :

for TWA in TWA_range :

tws_ms = tws∗kn Vs_ms = Vs∗kn

fs . condition("TWS", str ( tws)+"∗kn" ) fs . condition ("TWA" , TWA) fs .condition("Vs", str (Vs)+"∗kn" )

#Balance RPM (Power) at target speed in combined configuration

fs .cmd("defaults")

68 A.4. WAVES APPENDIX A. MACROS

fs .cmd("balanceRPM") fs .condition("config","combined") fs . condition("RPM" ,105) fs . condition("Vs",Vs_ms) fs . condition("RPMflettnerTRM")

fs . find_trim("TWA")

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx") FxWAPS=f s . eval ( "FxWAPS" )

# Find RPM (power) for motoring without sails if sail drive force i s negative i f FxWAPS<=0 or Status==0 or StatusFx==0: fs .cmd("defaults") fs .cmd("condition␣config␣Motor") fs .cmd("balanceRPM") fs . condition("Vs",Vs_ms) fs . condition("RPM" ,105)

fs . find_trim("TWA")

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx")

A.4 Waves

This macros runs a PPP in rough sea. #! py import os , f s

# d e f a u l t s −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− hs_range = [0,1,2,3,4,5,6,7,8,9,10,11,11.5] Ts_range = [4.5,5.5,6.5,7.5,8.5,9.5,10.5,11.5] Vs_range_kn = range ( 5 , 1 3 , 1 ) #[ 1 2 . 5 , 1 3 . 5 ] #IN kNOTS PLEASE kn = 0.514444 #Vs_range=kn∗Vs_range_kn

TWA_range = range(180 , −10 , −10)

TWS_range_kn = range ( 1 0 , 1 5 , 1 ) outPath = "./resultsWaves" fname = "resultsWaves" append = False\\

69 A.4. WAVES APPENDIX A. MACROS

#Create ouput directory if it does not exist i f not os.path. exists(outPath): os.makedirs(outPath)

#Find sailing trim fs .cmd("defaults") fs .condition("pitch" ,0.0) fs .cmd("adjust␣sink")

# run p o l a r −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− for Vs in Vs_range_kn :

for tws in TWS_range_kn :

for TWA in TWA_range :

for hs in hs_range :

for Ts in Ts_range :

tws_ms = tws∗kn Vs_ms = Vs∗kn

#Set parameters fs . condition("TWS", str ( tws)+"∗kn" ) fs . condition ("TWA" , TWA) fs .condition("Vs", str (Vs)+"∗kn" ) fs.condition("Hs", hs) fs.condition("Ts", Ts)

#Balance RPM (Power) at target speed in combined configuration

fs .cmd("defaults") fs .cmd("balanceRPM") fs .condition("config","combined") fs . condition("RPM" ,105) fs . condition("Vs",Vs_ms) fs . condition("RPMflettnerTRM")

fs . find_trim("TWA")

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx") FxWAPS=f s . eval ( "FxWAPS" )

70 A.4. WAVES APPENDIX A. MACROS

fs . find_trim("TWA")

Status=f s . eval ( " Status " ) StatusFx=fs . eval ("StatusFx")

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